diff --git a/CHANGELOG.md b/CHANGELOG.md index f9dc73862e..60e91ac0f2 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -47,6 +47,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0 - New settings parameter MGAAnnualGeneration to switch between different MGA formulations (#681) - Add validation for `Can_Retire` column in multi-stage GenX since the current implementation does not allow a resource to switch from can_retire = 0 to can_retire = 1 between stages. (#683) +- Add tutorials for running GenX (#637 and #685) ### Fixed - Set MUST_RUN=1 for RealSystemExample/small_hydro plants (#517). diff --git a/docs/make.jl b/docs/make.jl index 70479f3adb..5fd26c6e0f 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -4,15 +4,16 @@ import DataStructures: OrderedDict DocMeta.setdocmeta!(GenX, :DocTestSetup, :(using GenX); recursive = true) -pages = OrderedDict("Welcome Page" => [ +pages = OrderedDict( + "Welcome Page" => [ "GenX: Introduction" => "index.md", "Installation Guide" => "installation.md", "Limitation of GenX" => "limitations_genx.md", - "Third Party Extensions" => "third_party_genx.md", + "Third Party Extensions" => "third_party_genx.md" ], "Getting Started" => [ "Running GenX" => "Getting_Started/examples_casestudies.md", - "Commertial solvers" => "Getting_Started/commercial_solvers.md", + "Commertial solvers" => "Getting_Started/commercial_solvers.md" ], "Tutorials" => [ "Tutorials Overview" => "Tutorials/Tutorials_intro.md", @@ -21,7 +22,9 @@ pages = OrderedDict("Welcome Page" => [ "Tutorial 3: K-Means and Time Domain Reduction" => "Tutorials/Tutorial_3_K-means_time_domain_reduction.md", "Tutorial 4: Model Generation" => "Tutorials/Tutorial_4_model_generation.md", "Tutorial 5: Solving the Model" => "Tutorials/Tutorial_5_solve_model.md", - "Tutorial 6: Post Processing" => "Tutorials/Tutorial_6_solver_settings.md", + "Tutorial 6: Solver Settings" => "Tutorials/Tutorial_6_solver_settings.md", + "Tutorial 7: Policy Constraints" => "Tutorials/Tutorial_7_setup.md", + "Tutorial 8: Outputs" => "Tutorials/Tutorial_8_outputs.md" ], "User Guide" => [ "Overall workflow" => "User_Guide/workflow.md", @@ -35,13 +38,13 @@ pages = OrderedDict("Welcome Page" => [ "Slack Variables for Policies" => "User_Guide/slack_variables_overview.md", "Method of Morris Inputs" => "User_Guide/methodofmorris_input.md", "Running the Model" => "User_Guide/running_model.md", - "Model Outputs" => "User_Guide/model_output.md", + "Model Outputs" => "User_Guide/model_output.md" ], "Model Concept and Overview" => [ "Model Introduction" => "Model_Concept_Overview/model_introduction.md", "Notation" => "Model_Concept_Overview/model_notation.md", "Objective Function" => "Model_Concept_Overview/objective_function.md", - "Power Balance" => "Model_Concept_Overview/power_balance.md", + "Power Balance" => "Model_Concept_Overview/power_balance.md" ], "Model Reference" => [ "Core" => "Model_Reference/core.md", @@ -50,7 +53,7 @@ pages = OrderedDict("Welcome Page" => [ "Flexible Demand" => "Model_Reference/Resources/flexible_demand.md", "Hydro" => [ "Hydro Reservoir" => "Model_Reference/Resources/hydro_res.md", - "Long Duration Hydro" => "Model_Reference/Resources/hydro_inter_period_linkage.md", + "Long Duration Hydro" => "Model_Reference/Resources/hydro_inter_period_linkage.md" ], "Must Run" => "Model_Reference/Resources/must_run.md", "Retrofit" => "Model_Reference/Resources/retrofit.md", @@ -61,17 +64,17 @@ pages = OrderedDict("Welcome Page" => [ "Long Duration Storage" => "Model_Reference/Resources/long_duration_storage.md", "Storage All" => "Model_Reference/Resources/storage_all.md", "Storage Asymmetric" => "Model_Reference/Resources/storage_asymmetric.md", - "Storage Symmetric" => "Model_Reference/Resources/storage_symmetric.md", + "Storage Symmetric" => "Model_Reference/Resources/storage_symmetric.md" ], "Co-located VRE and Storage" => "Model_Reference/Resources/vre_stor.md", "Thermal" => [ "Thermal" => "Model_Reference/Resources/thermal.md", "Thermal Commit" => "Model_Reference/Resources/thermal_commit.md", - "Thermal No Commit" => "Model_Reference/Resources/thermal_no_commit.md", + "Thermal No Commit" => "Model_Reference/Resources/thermal_no_commit.md" ], "Hydrogen Electrolyzers" => "Model_Reference/Resources/electrolyzers.md", "Scheduled maintenance for various resources" => "Model_Reference/Resources/maintenance.md", - "Resource types" => "Model_Reference/Resources/resource.md", + "Resource types" => "Model_Reference/Resources/resource.md" ], "Maintenance" => "Model_Reference/maintenance_overview.md", "Policies" => "Model_Reference/policies.md", @@ -86,15 +89,16 @@ pages = OrderedDict("Welcome Page" => [ "Multi-Stage Modeling Introduction" => "Model_Reference/Multi_Stage/multi_stage_overview.md", "Configure multi-stage inputs" => "Model_Reference/Multi_Stage/configure_multi_stage_inputs.md", "Model multi stage: Dual Dynamic Programming Algorithm" => "Model_Reference/Multi_Stage/dual_dynamic_programming.md", - "Endogenous Retirement" => "Model_Reference/Multi_Stage/endogenous_retirement.md", + "Endogenous Retirement" => "Model_Reference/Multi_Stage/endogenous_retirement.md" ], "Method of Morris" => "Model_Reference/methodofmorris.md", - "Utility Functions" => "Model_Reference/utility_functions.md", + "Utility Functions" => "Model_Reference/utility_functions.md" ], "Public API Reference" => [ "Public API" => "Public_API/public_api.md"], "Third Party Extensions" => "additional_third_party_extensions.md", - "Developer Docs" => "developer_guide.md") + "Developer Docs" => "developer_guide.md" +) # Build documentation. # ==================== @@ -108,8 +112,10 @@ makedocs(; canonical = "https://genxproject.github.io/GenX.jl/stable", assets = ["assets/genx_style.css"], sidebar_sitename = false, - collapselevel = 1), - pages = [p for p in pages]) + collapselevel = 1 + ), + pages = [p for p in pages] +) # Deploy built documentation. # =========================== @@ -122,4 +128,5 @@ deploydocs(; devurl = "dev", push_preview = true, versions = ["stable" => "v^", "v#.#.#", "dev" => "dev"], - forcepush = false) + forcepush = false +) diff --git a/docs/src/Tutorials/Tutorial_1_configuring_settings.md b/docs/src/Tutorials/Tutorial_1_configuring_settings.md index 8ba1968665..a25b85a41d 100644 --- a/docs/src/Tutorials/Tutorial_1_configuring_settings.md +++ b/docs/src/Tutorials/Tutorial_1_configuring_settings.md @@ -17,15 +17,11 @@ To see how changing the settings affects the outputs, see Tutorials 3 and 7. Below is the settings file for `example_systems/1_three_zones`: -```@raw html - -``` +![png](./files/genxsettings.png) -All `genx_settings.yml` files in `Example_Systems` specify most parameters. When configuring your own settings, however, it is not necessary to input all parameters as defaults are specified for each one in `configure_settings.jl`. +All `genx_settings.yml` files in `example_systems` specify most parameters. When configuring your own settings, however, it is not necessary to input all parameters as defaults are specified for each one in `configure_settings.jl`. -```@raw html - -``` +![png](./files/default_settings.png) To open `genx_settings.yml` in Jupyter, use the function `YAML.load(open(...))` and navigate to file in the desired directory: @@ -69,11 +65,9 @@ YAML.write_file("example_systems/1_three_zones/settings/genx_settings.yml", new_ The empty file will look like this: -```@raw html - -``` +![png](./files/genx_settings_none.png) -Now, we run GenX and output the file `capacity.csv` from the `Results` folder. To do this, we use the function `include`, which takes a .jl file and runs it in jupyter notebook: +Now, we run GenX and output the file `capacity.csv` from the `results` folder. To do this, we use the function `include`, which takes a .jl file and runs it in jupyter notebook: ```julia diff --git a/docs/src/Tutorials/Tutorial_2_network_visualization.md b/docs/src/Tutorials/Tutorial_2_network_visualization.md index 67624d285f..9c598962d7 100644 --- a/docs/src/Tutorials/Tutorial_2_network_visualization.md +++ b/docs/src/Tutorials/Tutorial_2_network_visualization.md @@ -24,10 +24,9 @@ network = CSV.read("example_systems/1_three_zones/system/Network.csv",DataFrame, MA, CT, and ME are the abbreviations for states Massachusetts, Connecticut, and Maine. However, since the US region of New England contains other states as well, MA in this case is also used to refer to those states. -Columns `Start_Zone` and `End_Zone` specify the network of the three regions. In this case, there are only two network lines, specified in the `Network_Lines` columns. The `Start_Zone` column indicates that the first node, MA, is the source of both lines as both rows have value 1. Rows `z1` and `z2` have values of 2 and 3 in `End_Zone`, which means both nodes CT and ME recieve energy from node MA. This is also indicated in the column `transmission_path_name'. +Columns `Start_Zone` and `End_Zone` specify the network of the three regions. In this case, there are only two network lines, specified in the `Network_Lines` columns. The `Start_Zone` column indicates that the first node, MA, is the source of both lines as both rows have value 1. Rows `z1` and `z2` have values of 2 and 3 in `End_Zone`, which means both nodes CT and ME recieve energy from node MA. This is also indicated in the column `transmission path name'. Below is a visualization of the network: -```@raw html - -``` +![png](./files/new_england.png) + diff --git a/docs/src/Tutorials/Tutorial_3_K-means_time_domain_reduction.md b/docs/src/Tutorials/Tutorial_3_K-means_time_domain_reduction.md index 4e9a49a6e6..5648c1eadc 100644 --- a/docs/src/Tutorials/Tutorial_3_K-means_time_domain_reduction.md +++ b/docs/src/Tutorials/Tutorial_3_K-means_time_domain_reduction.md @@ -3,19 +3,19 @@ [Interactive Notebook of the tutorial](https://github.com/GenXProject/GenX-Tutorials/blob/main/Tutorials/Tutorial_3_K-means_Time_Domain_Reduction.ipynb) -A good tool to reduce computation time of GenX is to use [Time-domain reduction](@ref). Time Domain Reduction is a method that selects a smaller set of time steps from the data in a way that reduces computation time while still capturing the main information of the model. In this tutorial, we go over how TDR works in GenX and how it uses K-means clustering to choose the optimal time steps. For more information on TDR in capacity expansion models, see [Mallapragada et al](https://www.sciencedirect.com/science/article/pii/S0360544218315238). +A good tool to reduce computation time of GenX is to use [Time-domain reduction](@ref). Time-domain Reduction is a method that selects a smaller set of time steps from the data in a way that reduces computation time while still capturing the main information of the model. In this tutorial, we go over how TDR works in GenX and how it uses K-means clustering to choose the optimal time steps. For more information on TDR in capacity expansion models, see [Mallapragada et al](https://www.sciencedirect.com/science/article/pii/S0360544218315238). ### Table of Contents * [Time Domain Reduction](#TDR) * [K-Means Clustering](#Kmeans) * [Results of Time Domain Reduction](#TDRResults) - * [Reconstruction](#Reconstruction) +* [Reconstruction](#Reconstruction) * [Extreme Periods](#ExtPeriods) * [Objective Values and Representative Periods](#ObjVals) ### Time Domain Reduction -To see how Time Domain Reduction works, let's look at the `Doad_data` in `example_systems/1_three_zones`: +To see how Time Domain Reduction works, let's look at the `Demand_data` in `example_systems/1_three_zones`: ```julia @@ -29,9 +29,6 @@ using Plots using Clustering using ScikitLearn @sk_import datasets: (make_blobs) -``` - WARNING: redefinition of constant make_blobs. This may fail, cause incorrect answers, or produce other errors. - PyObject ```julia case = joinpath("example_systems/1_three_zones"); @@ -88,7 +85,7 @@ loads |> width=600,height=400,linewidth=.01) ``` -![svg](./files/output_14_0.svg) +![svg](./files/t3_demand.svg) As in [Tutorial 1: Configuring Settings](@ref), we can open the `genx_settings.yml` file for `1_three_zones` to see how `TimeDomainReduction` is set. If it's set to 1, this means TDR is being used. @@ -118,7 +115,7 @@ genx_settings_TZ = YAML.load(open((joinpath(case,"settings/genx_settings.yml"))) "WriteShadowPrices" => 1 ``` -To visualize how TDR decreases computation time, let's start by running `SmallNewEngland/OneZone` without TDR. In the third section of this tutorial, we'll run the example again using TDR. +To visualize how TDR decreases computation time, let's start by running `example_systems/1_three_zones` without TDR. In the third section of this tutorial, we'll run the example again using TDR. To run GenX without TDR, we start by editing the settings to set `TimeDomainReduction` to 0: @@ -158,14 +155,16 @@ And run it using `include`. (Note: this process will take a few minutes): ```julia @time include("example_systems/1_three_zones/Run.jl") ``` +Time elapsed for writing is + 142.404724 seconds This took a little while to run, and would take even longer for larger systems. Let's see how we can get the run time down using Time Domain Reduction. The next sections go over how K-means clustering is used to perform TDR, and how to interpret the resulting files in GenX. ### K-means clustering -Let's go over how TDR works. To perform TDR, GenX uses __K-means clustering__. K-means is an optimization method that clusters data into several groups based on their proximity to "centers" determined by the algorithm. +Let's go over how TDR works. To perform TDR, GenX uses __K-means clustering__. _K_-means is an optimization method that clusters data into several groups based on their proximity to "centers" determined by the algorithm. -K-means finds a set number of groups such that the variance between the distance of each point in the group to the mean of the group is minimized. +_K_-means finds a set number of groups such that the variance between the distance of each point in the group to the mean of the group is minimized. ```math \begin{align*} @@ -173,7 +172,7 @@ K-means finds a set number of groups such that the variance between the distance \end{align*} ``` -Where $\mathbf{S} = \{S_1, ... , S_k\}$ are the clusters, with $x$ denoting the elements of the clusters, and $\mu_i$ the mean of each cluster, i.e. the mean of the distances from each point to the center of the cluster. By taking the argmin over $\mathbf{S}$, the points $x$ are clustered into groups where their distance to the center is the smallest. For more information on how k-means works, see the [Wikipedia](https://en.wikipedia.org/wiki/K-means_clustering). +Where $\mathbf{S} = \{S_1, ... , S_k\}$ are the clusters, with $x$ denoting the elements of the clusters, and $\mu_i$ the mean of each cluster, i.e. the mean of the distances from each point to the center of the cluster. By taking the argmin over $\mathbf{S}$, the points $x$ are clustered into groups where their distance to the center is the smallest. For more information on how _k_-means works, see the [Wikipedia](https://en.wikipedia.org/wiki/K-means_clustering). GenX uses the package `Clustering.jl`, with documentation [here](https://juliastats.org/Clustering.jl/dev/kmeans.html#K-means). As an example, using the package `ScikitLearn.jl`, let's generate data that can cluster easily. @@ -184,7 +183,7 @@ X, y = make_blobs(n_samples=50,centers=centers); # From scikit-learn b = DataFrame(X,:auto) ``` -Note that clustering works for data without obvious groupings, but using blobs as an example makes k-means easier to visualize. +Note that clustering works for data without obvious groupings, but using blobs as an example makes _k_-means easier to visualize. ```julia @@ -192,6 +191,8 @@ plotly() Plots.scatter(b[!,"x1"],b[!,"x2"],legend=false,title="Before K-means Clustering") ``` +![png](./files/t3_nokmeans.png) + Now we use the function `kmeans`, which is also used in `src/time_domain_reduction` in GenX. @@ -217,11 +218,13 @@ plotly() Plots.scatter(b[!,"x1"],b[!,"x2"],legend=false,marker_z=R.assignments,c=:lightrainbow,title="After K-means Clustering") ``` +![png](./files/t3_kmeans.png) + In GenX, the representative periods are the centers of the clusters, each representing one week of the year. In the above example that would mean there are 52 data points gathered into 11 clusters (to see this for yourself, change `make_blobs` to have 52 data points and 11 clusters.) ### Results of Time Domain Reduction -To visualize the results of TDR, we'll set TDR = 1 back in the `genx_settings.yml` file in `Example_Systems_Tutorials/SmallNewEngland/OneZone/`: +To visualize the results of TDR, we'll set TDR = 1 back in the `genx_settings.yml` file in `example_systems/1_three_zones`: ```julia @@ -245,7 +248,7 @@ And run GenX again with TDR: @time include("example_systems/1_three_zones/Run.jl") ``` -Csv files with the results of TDR are generated automatically in a folder called `TDR_results` found within the same folder containing the input csv files, in this case `Example_Systems_Tutorials/SmallNewEngland/OneZone`. The csv files in this folder show the files used in `Run.jl` that have been pared down from the initial input files. +Csv files with the results of TDR are generated automatically in a folder called `TDR_results` found within the same folder containing the input csv files, in this case `example_systems/1_three_zones`. The csv files in this folder show the files used in `Run.jl` that have been pared down from the initial input files. As an example, consider the input file `Fuels_data.csv`: @@ -268,7 +271,7 @@ As you can see, the original has all 8,760 hours, while the TDR version only has loads_TDR = CSV.read(joinpath(case,"TDR_Results/Demand_data.csv"),DataFrame,missingstring="NA") ``` -The 1,848 hours are divided into 11 sections of 168 hours, with each section representing one week of the original data. The number of hours per representative period is set in `time_domain_reduction_settings.yml`. Also specified in the file are the minimum and maximum number of clusters we would like to have (in this case 8 and 11). The k-means algorithm will then select the number of clusters that should be sufficient to capture the GenX model in fewer time steps (in this case 11). +The 1,848 hours are divided into 11 sections of 168 hours, with each section representing one week of the original data. The number of hours per representative period is set in `time_domain_reduction_settings.yml`. Also specified in the file are the minimum and maximum number of clusters we would like to have (in this case 8 and 11). The _k_-means algorithm will then select the number of clusters that should be sufficient to capture the GenX model in fewer time steps (in this case 11). ```julia @@ -286,7 +289,9 @@ Below, we create arrays out of the representative weeks and plot them on the sam ```julia Period_map = CSV.read(joinpath(case,"TDR_Results/Period_map.csv"),DataFrame,missingstring="NA") ``` - +``` @raw html +
52×3 DataFrame
27 rows omitted
RowPeriod_IndexRep_PeriodRep_Period_Index
Int64Int64Int64
1141
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+``` ```julia # Find array of unique representative periods @@ -317,7 +322,7 @@ loads_with_TDR |> color={"Week:n", scale={scheme="paired"},sort="decsending"}, title="MW Load per hour with TDR Representative Weeks", width=845,height=400) ``` -![svg](./files/output_58_0.svg) +![svg](./files/t3_TDR_demand.svg) TDR is performed for four total data sets: demand (found in Demand.csv), wind and solar (found in Generators_variability.csv), and fuel prices (found in Fuels.csv). Above is just the demand load for one of the three total nodes in the example system, which is why the data may not appear to "represent" all 52 weeks (notice there are fewer representative periods in the fall). Instead, the periods more accurately represent all the data time series combined, including some other parts of the data not seen in this particular plot. @@ -384,7 +389,7 @@ myscheme = ["#a6cee3","#a6cee3","#1f78b4","#b2df8a","#33a02c","#fb9a99","#e31a1c width=845,height=300) ``` -![svg](./files/output_65_0.svg) +![svg](./files/t3_ext_periods.svg) The first plot (with Extreme Periods off) may not have the week with the highest peak highlighted. If the week with the highest demand is highlighted, try re-running the cell with Extreme Periods Off plotting the results. @@ -396,7 +401,7 @@ YAML.write_file(joinpath(case,"settings/time_domain_reduction_settings.yml"), ti rm(joinpath(case,"TDR_results"), recursive=true) ``` -#### Reconstruction +### Reconstruction Below is a plot of a reconstruction of the data using only the weeks isolated as representative periods. This is what GenX reads when it runs the solver with TDR on. @@ -443,6 +448,8 @@ G2 = Plots.plot(recon[!,:hour], recon[!,:MW], linewidth=1.7, Plots.plot(G1,G2,layout=(2,1)) ``` +![svg](./files/t3_recon.svg) + Each color represents one of the representative weeks. The range of 8-11 representative periods was chosen by the developers because it was deemed to be the smallest set that still matches the optimal value of the data well. The next section of this Tutorial goes over how the optimal values of the data change as the number of representative periods changes. @@ -617,6 +624,8 @@ scatter!(twinx(),obj_val_plot[:,1],times,color=:red,markeralpha=.5,label=:"Time" ygrid!(:on, :dashdot, 0.1) ``` +![svg](./files/t3_obj_val.svg) + Here, we can see that while having very few representative periods produces an objective value that differs greatly from the orignal, once we reach around 12 representative periods the difference begins to taper out. Therefore, the original choice of 11 maximum periods in `1_three_zones` decreases the run time of GenX significantly while while maintaining an objective value close to the original. diff --git a/docs/src/Tutorials/Tutorial_4_model_generation.md b/docs/src/Tutorials/Tutorial_4_model_generation.md index 116b76fe2d..39031fb630 100644 --- a/docs/src/Tutorials/Tutorial_4_model_generation.md +++ b/docs/src/Tutorials/Tutorial_4_model_generation.md @@ -13,9 +13,7 @@ We'll start by explaining JuMP, the optimization package that GenX uses to gener * [Run generate_model](#Run) -```@raw html - -``` +![png](./files/jump_logo.png) JuMP is a modeling language for Julia. It allows users to create models for optimization problems, define variables and constraints, and apply a variety of solvers for the model. @@ -122,16 +120,30 @@ When `Run.jl` is called, the model for GenX is constructed in a similar way, but The basic structure of the way `Run.jl` generates and solves the model is as follows: -```@raw html - -``` +![png](./files/LatexHierarchy.png) The function `run_genx_case(case)` takes the "case" as its input. The case is all of the input files and settings found in the same folder as `Run.jl`. For example, in `example_systems/1_three_zones`, the case is: -```@raw html - +```julia +cd(readdir,"example_systems/1_three_zones") ``` + + + + 9-element Vector{String}: + ".DS_Store" + "README.md" + "Run.jl" + "TDR_results" + "policies" + "resources" + "results" + "settings" + "system" + + + `Run_genx_case` defines the __setup__, which are the settings in `genx_settings.yml`. From there, either `run_genx_case_simple(case, mysetup)` or`run_genx_case_multistage(case, mysetup)` is called. Both of these define the __inputs__ and __optimizer__. The optimizer is the solver as specified in `genx_settings.yml`, and the inputs are a variety of parameters specified by the settings and csv files found in the folder. Both of these functions then call `generate_model(mysetup, myinputs, OPTIMIZER)`, which is the main subject of this tutorial. As in the above example, `generate_model` utilizes the JuMP functions `Model()`, `@expression`, `@variable`, and `@constraints` to form a model. This section goes through `generate_model` and explains how the expressions are formed to create the model. @@ -260,7 +272,7 @@ typeof(OPTIMIZER) MathOptInterface.OptimizerWithAttributes ``` -The "inputs" argument is generated by the function `load_inputs` from the case in `run_genx_case_simple` (or multistage). If TDR is set to 1 in the settings file, then `load_inputs` will draw some of the files from the `TDR_Results` folder. `TDR_Results` is produced when the case is run. +The "inputs" argument is generated by the function `load_inputs` from the case in `run_genx_case_simple` (or multistage). If TDR is set to 1 in the settings file, then `load_inputs` will draw some of the files from the `TDR_results` folder. `TDR_results` is produced when the case is run. ```julia diff --git a/docs/src/Tutorials/Tutorial_7_setup.md b/docs/src/Tutorials/Tutorial_7_setup.md new file mode 100644 index 0000000000..0d93604c83 --- /dev/null +++ b/docs/src/Tutorials/Tutorial_7_setup.md @@ -0,0 +1,2872 @@ +# Tutorial 7: Policy Constraints + +[Interactive Notebook of the tutorial](https://github.com/GenXProject/GenX-Tutorials/blob/main/Tutorials/Tutorial_7_Setup.ipynb) + +As show in previous tutorials, the settings file can be changed to adapt to a number of different systems. In Tutorial 3, we discussed how the setting Time Domain Reduction can reduce the computation time of the solver. Other settings, however, directly impact the values of the solution itself. This tutorial goes over the policy attributes in the settings and shows how implementing certain policies affects the optimal solution in GenX. To demonstrate these effects, we will be using `example_systems/1_three_zones`. + +## Table of Contents +* [No Policy Constraints](#NoPolicies) +* [CO2 Cap](#CO2Cap) + * [Mass Cap](#MassCap) + * [Tolerance](#Tolerance) + * [CO2 Slack](#CO2Slack) + * [Load-based Cap](#LoadCap) + * [Generator-based Cap](#GenerateCap) +* [Energy Share Requirement](#ESR) +* [Capacity Reserve Margin](#CRM) +* [Minimum Capacity Requirement](#MCR) +* [All Together](#All) + + +## No Policy Constraints + + +```julia +using JuMP +using HiGHS +using GenX +using CSV +using DataFrames +using Plots +using StatsPlots +``` + + +```julia +case = joinpath("example_systems/1_three_zones") + +genx_settings = GenX.get_settings_path(case, "genx_settings.yml"); +writeoutput_settings = GenX.get_settings_path(case, "output_settings.yml") +setup = GenX.configure_settings(genx_settings,writeoutput_settings) +``` + + Configuring Settings + + + + + + Dict{Any, Any} with 33 entries: + "HydrogenHourlyMatching" => 0 + "NetworkExpansion" => 1 + "TimeDomainReductionFolder" => "TDR_results" + "WriteOutputs" => "full" + "SystemFolder" => "system" + "EnableJuMPStringNames" => 1 + "Trans_Loss_Segments" => 1 + "ModelingtoGenerateAlternativeSlack" => 0.1 + "PoliciesFolder" => "policies" + "MultiStage" => 0 + "ComputeConflicts" => 1 + "OverwriteResults" => 0 + "ModelingToGenerateAlternatives" => 0 + "MaxCapReq" => 0 + "MinCapReq" => 1 + "CO2Cap" => 2 + "WriteShadowPrices" => 1 + "OperationalReserves" => 0 + "ParameterScale" => 1 + "EnergyShareRequirement" => 0 + "PrintModel" => 0 + "TimeDomainReduction" => 1 + "DC_OPF" => 0 + "CapacityReserveMargin" => 0 + "MethodofMorris" => 0 + ⋮ => ⋮ + + + +The settings we'll focus on here are , `CO2Cap`, `EnergyShareRequirement`, `CapacityReserveMargin`, and `MinCapReq`. Each of these ensures that the environmental impact of the model is taken into account, and are therefore referred to as __policy settings__ . For more information on what each one does, see the documentation on [Emission mitigation policies]. + + +```julia +println("MaxCapReq: ", setup["MaxCapReq"]) +println("MinCapReq: ", setup["MinCapReq"]) +println("CO2Cap: ", setup["CO2Cap"]) +println("EnergyShareRequirement: ", setup["EnergyShareRequirement"]) +println("CapacityReserveMargin: ", setup["CapacityReserveMargin"]) +``` + + MaxCapReq: 0 + MinCapReq: 1 + CO2Cap: 2 + EnergyShareRequirement: 0 + CapacityReserveMargin: 0 + + +`1_three_zones` uses `MinCapReq` and `CO2Cap`. For the purpose of this tutorial, we're going to set these back to zero to start. + + +```julia +setup["MinCapReq"] = 0 +setup["CO2Cap"] = 0; +``` + +Now, we'll generate and solve the model using these results: + + +```julia +## Delte Previous TDR Results +if "TDR_results" in cd(readdir,case) + rm(joinpath(case,"TDR_results"), recursive=true) +end + +### Create TDR_Results +TDRpath = joinpath(case, setup["TimeDomainReductionFolder"]) +system_path = joinpath(case, setup["SystemFolder"]) +settings_path = GenX.get_settings_path(case) + +if setup["TimeDomainReduction"] == 1 + GenX.prevent_doubled_timedomainreduction(system_path) + if !GenX.time_domain_reduced_files_exist(TDRpath) + println("Clustering Time Series Data (Grouped)...") + GenX.cluster_inputs(case, settings_path, setup) + else + println("Time Series Data Already Clustered.") + end +end + +``` + + Clustering Time Series Data (Grouped)... + Reading Input CSV Files + Network.csv Successfully Read! + Demand (load) data Successfully Read! + Fuels_data.csv Successfully Read! + + + Thermal.csv Successfully Read. + Vre.csv Successfully Read. + Storage.csv Successfully Read. + Resource_energy_share_requirement.csv Successfully Read. + Resource_capacity_reserve_margin.csv Successfully Read. + Resource_minimum_capacity_requirement.csv Successfully Read. + + + Summary of resources loaded into the model: + ------------------------------------------------------- + Resource type Number of resources + ======================================================= + Thermal 3 + VRE 4 + Storage 3 + ======================================================= + Total number of resources: 10 + ------------------------------------------------------- + Generators_variability.csv Successfully Read! + Validating time basis + CSV Files Successfully Read In From example_systems/1_three_zones + Error: Geography Key 1 is invalid. Select `System' or `Zone'. + + + + + + Dict{String, Any} with 9 entries: + "RMSE" => Dict("ME_NG"=>0.210014, "ME_onshore_wind_z3"=>0.310986, "D… + "OutputDF" => 1848×19 DataFrame + "ColToZoneMap" => Dict("Demand_MW_z3"=>3, "CT_battery_z2"=>2, "MA_natural_ga… + "ClusterObject" => KmeansResult{Matrix{Float64}, Float64, Int64}([-0.734116 2… + "TDRsetup" => Dict{Any, Any}("IterativelyAddPeriods"=>1, "ExtremePeriods… + "Assignments" => [1, 1, 1, 1, 2, 2, 2, 2, 2, 3 … 6, 9, 3, 10, 10, 10, 11,… + "InputDF" => 1680×52 DataFrame + "Weights" => [673.846, 1179.23, 842.308, 673.846, 1010.77, 1347.69, 134… + "Centers" => Any[4, 8, 12, 15, 20, 23, 27, 30, 44, 48, 49] + + + + +```julia +OPTIMIZER = GenX.configure_solver(settings_path,HiGHS.Optimizer); +inputs = GenX.load_inputs(setup, case) +``` + + Reading Input CSV Files + Network.csv Successfully Read! + Demand (load) data Successfully Read! + Fuels_data.csv Successfully Read! + + Summary of resources loaded into the model: + ------------------------------------------------------- + Resource type Number of resources + ======================================================= + Thermal 3 + VRE 4 + Storage 3 + ======================================================= + Total number of resources: 10 + ------------------------------------------------------- + Generators_variability.csv Successfully Read! + Validating time basis + CSV Files Successfully Read In From example_systems/1_three_zones + + + Thermal.csv Successfully Read. + Vre.csv Successfully Read. + Storage.csv Successfully Read. + Resource_energy_share_requirement.csv Successfully Read. + Resource_capacity_reserve_margin.csv Successfully Read. + Resource_minimum_capacity_requirement.csv Successfully Read. + + + + + Dict{Any, Any} with 67 entries: + "Z" => 3 + "LOSS_LINES" => [1, 2] + "STOR_HYDRO_SHORT_DURATION" => Int64[] + "RET_CAP_CHARGE" => Set{Int64}() + "pC_D_Curtail" => [50.0, 45.0, 27.5, 10.0] + "pTrans_Max_Possible" => [5.9, 4.0] + "pNet_Map" => [1.0 -1.0 0.0; 1.0 0.0 -1.0] + "omega" => 4.01099, 4.01099, 4.01099, 4.01099, 4.01099, … + "pMax_Line_Reinforcement" => [2.95, 2.0] + "RET_CAP_ENERGY" => Int64[] + "RESOURCES" => AbstractResource + "COMMIT" => [1, 2, 3] + "pMax_D_Curtail" => [1.0, 0.04, 0.024, 0.003] + "STOR_ALL" => [8, 9, 10] + "THERM_ALL" => [1, 2, 3] + "REP_PERIOD" => 11 + "PWFU_Num_Segments" => 0 + "STOR_LONG_DURATION" => Int64[] + "THERM_COMMIT_PWFU" => Int64[] + "STOR_SYMMETRIC" => [8, 9, 10] + "VRE" => [4, 5, 6, 7] + "RETRO" => Int64[] + "THERM_COMMIT" => [1, 2, 3] + "TRANS_LOSS_SEGS" => 1 + "H" => 168 + ⋮ => ⋮ + + + + +```julia +EP = GenX.generate_model(setup,inputs,OPTIMIZER) +``` + + Discharge Module + Non-served Energy Module + Investment Discharge Module + Unit Commitment Module + Fuel Module + CO2 Module + Investment Transmission Module + Transmission Module + Dispatchable Resources Module + Storage Resources Module + Storage Investment Module + Storage Core Resources Module + Storage Resources with Symmetric Charge/Discharge Capacity Module + Thermal (Unit Commitment) Resources Module + + + + + + A JuMP Model + Minimization problem with: + Variables: 120136 + Objective function type: AffExpr + `AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 35112 constraints + `AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 20331 constraints + `AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 97949 constraints + `VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 1 constraint + `VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 116439 constraints + Model mode: AUTOMATIC + CachingOptimizer state: EMPTY_OPTIMIZER + Solver name: HiGHS + Names registered in the model: FuelCalculationCommit_single, cFuelCalculation_single, cMaxCap, cMaxCapEnergy, cMaxCapEnergyDuration, cMaxFlow_in, cMaxFlow_out, cMaxLineReinforcement, cMaxNSE, cMaxRetCommit, cMaxRetEnergy, cMaxRetNoCommit, cMinCap, cMinCapEnergy, cMinCapEnergyDuration, cNSEPerSeg, cPowerBalance, cSoCBalInterior, cSoCBalStart, cStartFuel_single, cTAuxLimit, cTAuxSum, cTLoss, eAvail_Trans_Cap, eCFix, eCFixEnergy, eCFuelOut, eCFuelStart, eCNSE, eCStart, eCVar_in, eCVar_out, eELOSS, eELOSSByZone, eEmissionsByPlant, eEmissionsByZone, eExistingCap, eExistingCapEnergy, eFuelConsumption, eFuelConsumptionYear, eFuelConsumption_single, eGenerationByThermAll, eGenerationByVRE, eGenerationByZone, eLosses_By_Zone, eNet_Export_Flows, eObj, ePlantCFuelOut, ePlantCFuelStart, ePlantFuel_generation, ePlantFuel_start, ePowerBalance, ePowerBalanceDisp, ePowerBalanceLossesByZone, ePowerBalanceNetExportFlows, ePowerBalanceNse, ePowerBalanceStor, ePowerBalanceThermCommit, eStartFuel, eTotalCFix, eTotalCFixEnergy, eTotalCFuelOut, eTotalCFuelStart, eTotalCNSE, eTotalCNSET, eTotalCNSETS, eTotalCNetworkExp, eTotalCStart, eTotalCStartT, eTotalCVarIn, eTotalCVarInT, eTotalCVarOut, eTotalCVarOutT, eTotalCap, eTotalCapEnergy, eTransMax, eZonalCFuelOut, eZonalCFuelStart, vCAP, vCAPENERGY, vCHARGE, vCOMMIT, vFLOW, vFuel, vNEW_TRANS_CAP, vNSE, vP, vRETCAP, vRETCAPENERGY, vS, vSHUT, vSTART, vStartFuel, vTAUX_NEG, vTAUX_POS, vTLOSS, vZERO + + + + +```julia +GenX.solve_model(EP,setup) +``` + + Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms + Presolving model + 118155 rows, 81204 cols, 422835 nonzeros + 110998 rows, 74047 cols, 423349 nonzeros + Presolve : Reductions: rows 110998(-42394); columns 74047(-46089); elements 423349(-47782) + Solving the presolved LP + IPX model has 110998 rows, 74047 columns and 423349 nonzeros + Input + Number of variables: 74047 + Number of free variables: 3696 + Number of constraints: 110998 + Number of equality constraints: 16867 + Number of matrix entries: 423349 + Matrix range: [4e-07, 1e+01] + RHS range: [7e-01, 2e+01] + Objective range: [1e-04, 4e+02] + Bounds range: [2e-03, 2e+01] + Preprocessing + Dualized model: no + Number of dense columns: 15 + Range of scaling factors: [5.00e-01, 1.00e+00] + IPX version 1.0 + Interior Point Solve + Iter P.res D.res P.obj D.obj mu Time + 0 8.62e+00 3.81e+02 3.30336414e+06 -5.31617580e+06 3.30e+03 0s + 1 4.09e+00 1.06e+02 2.34353411e+05 -5.13796175e+06 1.43e+03 0s + 2 3.78e+00 7.03e+01 1.87013341e+05 -1.15199236e+07 1.34e+03 0s + 3 1.33e+00 4.12e+01 -3.76464137e+05 -1.37088411e+07 7.85e+02 1s + Constructing starting basis... + 4 4.13e-01 1.08e+01 2.66640168e+05 -8.48314805e+06 2.43e+02 3s + 5 1.12e-01 5.62e+00 3.71879810e+05 -5.58576107e+06 1.28e+02 4s + 6 7.53e-03 1.62e+00 2.30531116e+05 -1.92720962e+06 3.67e+01 5s + 7 9.27e-04 1.77e-01 1.30486918e+05 -3.83901614e+05 5.66e+00 6s + 8 1.14e-04 4.38e-02 5.27259057e+04 -1.00386376e+05 1.48e+00 7s + 9 1.52e-05 6.88e-03 2.76584248e+04 -2.19746140e+04 3.52e-01 8s + 10 5.20e-06 2.59e-03 1.39025442e+04 -7.44814138e+03 1.35e-01 8s + 11 2.36e-06 1.09e-03 1.02345396e+04 -1.80403130e+03 7.13e-02 10s + 12 1.03e-06 3.59e-04 7.72508848e+03 1.35005473e+03 3.59e-02 12s + 13 6.67e-07 1.53e-04 6.83171406e+03 2.57204744e+03 2.35e-02 15s + 14 5.06e-07 7.64e-05 6.41494456e+03 3.13597410e+03 1.79e-02 18s + 15 3.52e-07 4.64e-05 5.95636098e+03 3.44861286e+03 1.36e-02 21s + 16 1.69e-07 2.49e-05 5.33436713e+03 3.75261594e+03 8.58e-03 24s + 17 1.38e-07 2.05e-05 5.23488752e+03 3.81660239e+03 7.68e-03 26s + 18 1.21e-07 1.95e-05 5.23765885e+03 3.83998603e+03 7.57e-03 28s + 19 7.35e-08 1.60e-05 5.05272742e+03 3.91685812e+03 6.15e-03 30s + 20 6.04e-08 1.49e-05 5.02221768e+03 3.93278446e+03 5.90e-03 33s + 21 2.85e-08 1.13e-05 4.88298181e+03 4.01774654e+03 4.68e-03 35s + 22 2.29e-08 6.29e-06 4.83470832e+03 4.00260600e+03 4.48e-03 37s + 23 1.31e-08 3.63e-06 4.72358228e+03 4.16712858e+03 3.00e-03 38s + 24 9.10e-09 2.96e-06 4.70648899e+03 4.19085995e+03 2.77e-03 40s + 25 4.45e-09 1.89e-06 4.63836996e+03 4.26416898e+03 2.01e-03 41s + 26 3.49e-09 1.84e-06 4.63722238e+03 4.26628187e+03 1.99e-03 42s + 27 2.15e-09 1.23e-06 4.59679916e+03 4.32342389e+03 1.47e-03 43s + 28 1.87e-09 1.07e-06 4.59259771e+03 4.33476451e+03 1.39e-03 46s + 29 1.58e-09 1.05e-06 4.59058841e+03 4.33567604e+03 1.37e-03 48s + 30 1.18e-09 8.27e-07 4.58014487e+03 4.35414040e+03 1.21e-03 49s + 31 7.95e-10 4.22e-07 4.56632970e+03 4.39355672e+03 9.27e-04 51s + 32 4.34e-10 3.79e-07 4.55792749e+03 4.39835388e+03 8.56e-04 51s + 33 2.37e-10 2.16e-07 4.54724964e+03 4.42097386e+03 6.77e-04 52s + 34 2.10e-10 2.06e-07 4.54686537e+03 4.42339252e+03 6.62e-04 53s + 35 7.73e-11 1.26e-07 4.53250796e+03 4.44139125e+03 4.89e-04 54s + 36 1.55e-11 1.06e-07 4.52064756e+03 4.44667475e+03 3.97e-04 55s + 37 1.50e-11 1.03e-07 4.52062467e+03 4.44749533e+03 3.92e-04 55s + 38 9.79e-12 1.00e-07 4.52199331e+03 4.44806728e+03 3.96e-04 56s + 39 8.92e-12 6.93e-08 4.52041735e+03 4.46101031e+03 3.19e-04 56s + 40 7.30e-12 5.17e-08 4.52001352e+03 4.46367984e+03 3.02e-04 57s + 41 4.70e-12 3.05e-08 4.51328477e+03 4.47536516e+03 2.03e-04 57s + 42 3.83e-12 2.70e-08 4.51240381e+03 4.47626904e+03 1.94e-04 58s + 43 2.85e-12 2.63e-08 4.51136761e+03 4.47647929e+03 1.87e-04 59s + 44 2.10e-12 1.31e-08 4.50946086e+03 4.48203628e+03 1.47e-04 59s + 45 1.31e-12 4.15e-09 4.50665353e+03 4.48821996e+03 9.88e-05 60s + 46 9.09e-13 3.31e-09 4.50579733e+03 4.48871202e+03 9.15e-05 61s + 47 9.09e-13 3.26e-09 4.50576718e+03 4.48852664e+03 9.24e-05 61s + 48 7.53e-13 2.25e-09 4.50502226e+03 4.49018328e+03 7.95e-05 62s + 49 7.53e-13 2.21e-09 4.50492035e+03 4.48999997e+03 7.99e-05 62s + 50 5.83e-13 1.52e-09 4.50350728e+03 4.49199895e+03 6.17e-05 63s + 51 1.99e-13 1.32e-09 4.50092854e+03 4.49240806e+03 4.57e-05 63s + 52 1.78e-13 1.23e-09 4.50080001e+03 4.49253227e+03 4.43e-05 64s + 53 9.24e-14 7.11e-10 4.49993325e+03 4.49367022e+03 3.36e-05 64s + 54 7.11e-14 5.59e-10 4.49966942e+03 4.49408670e+03 2.99e-05 65s + 55 7.11e-14 5.54e-10 4.49963721e+03 4.49407202e+03 2.98e-05 65s + 56 7.11e-14 5.25e-10 4.49964358e+03 4.49413082e+03 2.95e-05 66s + 57 4.97e-14 3.86e-10 4.49901737e+03 4.49483758e+03 2.24e-05 66s + 58 4.97e-14 3.77e-10 4.49900976e+03 4.49485417e+03 2.23e-05 66s + 59 4.97e-14 3.61e-10 4.49894867e+03 4.49494477e+03 2.15e-05 67s + 60 2.84e-14 2.16e-10 4.49842279e+03 4.49567956e+03 1.47e-05 67s + 61 2.84e-14 1.25e-10 4.49813093e+03 4.49622420e+03 1.02e-05 67s + 62 2.13e-14 9.05e-11 4.49785493e+03 4.49641576e+03 7.71e-06 68s + 63 2.13e-14 2.46e-11 4.49758346e+03 4.49698685e+03 3.20e-06 68s + 64 2.13e-14 1.77e-11 4.49754878e+03 4.49704995e+03 2.67e-06 68s + 65 2.13e-14 3.18e-12 4.49747123e+03 4.49722789e+03 1.30e-06 69s + 66 2.13e-14 1.36e-12 4.49740334e+03 4.49723907e+03 8.80e-07 69s + 67 2.13e-14 1.36e-12 4.49734663e+03 4.49727135e+03 4.03e-07 70s + 68 2.13e-14 9.66e-13 4.49734376e+03 4.49727731e+03 3.56e-07 70s + 69 2.13e-14 5.68e-13 4.49732633e+03 4.49728530e+03 2.20e-07 70s + 70 2.13e-14 4.55e-13 4.49731802e+03 4.49730841e+03 5.15e-08 71s + 71 2.13e-14 4.83e-13 4.49731683e+03 4.49730985e+03 3.74e-08 71s + 72 2.13e-14 1.92e-12 4.49731281e+03 4.49731141e+03 7.53e-09 72s + 73 2.13e-14 5.35e-12 4.49731227e+03 4.49731210e+03 9.13e-10 72s + 74* 2.13e-14 2.73e-12 4.49731219e+03 4.49731218e+03 7.21e-11 72s + 75* 2.84e-14 7.65e-12 4.49731219e+03 4.49731218e+03 4.94e-12 73s + 76* 3.55e-14 4.81e-12 4.49731219e+03 4.49731219e+03 4.09e-13 73s + 77* 3.55e-14 7.19e-12 4.49731219e+03 4.49731219e+03 2.31e-15 73s + Running crossover as requested + Primal residual before push phase: 1.40e-09 + Dual residual before push phase: 5.05e-10 + Number of dual pushes required: 41031 + Number of primal pushes required: 722 + Summary + Runtime: 73.32s + Status interior point solve: optimal + Status crossover: optimal + objective value: 4.49731219e+03 + interior solution primal residual (abs/rel): 5.48e-11 / 3.35e-12 + interior solution dual residual (abs/rel): 7.19e-12 / 1.79e-14 + interior solution objective gap (abs/rel): -5.22e-10 / -1.16e-13 + basic solution primal infeasibility: 2.78e-17 + basic solution dual infeasibility: 5.41e-16 + Ipx: IPM optimal + Ipx: Crossover optimal + Solving the original LP from the solution after postsolve + Model status : Optimal + IPM iterations: 77 + Crossover iterations: 4712 + Objective value : 4.4973121850e+03 + HiGHS run time : 73.55 + LP solved for primal + + + + + + (A JuMP Model + Minimization problem with: + Variables: 120136 + Objective function type: AffExpr + `AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 35112 constraints + `AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 20331 constraints + `AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 97949 constraints + `VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 1 constraint + `VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 116439 constraints + Model mode: AUTOMATIC + CachingOptimizer state: ATTACHED_OPTIMIZER + Solver name: HiGHS + Names registered in the model: FuelCalculationCommit_single, cFuelCalculation_single, cMaxCap, cMaxCapEnergy, cMaxCapEnergyDuration, cMaxFlow_in, cMaxFlow_out, cMaxLineReinforcement, cMaxNSE, cMaxRetCommit, cMaxRetEnergy, cMaxRetNoCommit, cMinCap, cMinCapEnergy, cMinCapEnergyDuration, cNSEPerSeg, cPowerBalance, cSoCBalInterior, cSoCBalStart, cStartFuel_single, cTAuxLimit, cTAuxSum, cTLoss, eAvail_Trans_Cap, eCFix, eCFixEnergy, eCFuelOut, eCFuelStart, eCNSE, eCStart, eCVar_in, eCVar_out, eELOSS, eELOSSByZone, eEmissionsByPlant, eEmissionsByZone, eExistingCap, eExistingCapEnergy, eFuelConsumption, eFuelConsumptionYear, eFuelConsumption_single, eGenerationByThermAll, eGenerationByVRE, eGenerationByZone, eLosses_By_Zone, eNet_Export_Flows, eObj, ePlantCFuelOut, ePlantCFuelStart, ePlantFuel_generation, ePlantFuel_start, ePowerBalance, ePowerBalanceDisp, ePowerBalanceLossesByZone, ePowerBalanceNetExportFlows, ePowerBalanceNse, ePowerBalanceStor, ePowerBalanceThermCommit, eStartFuel, eTotalCFix, eTotalCFixEnergy, eTotalCFuelOut, eTotalCFuelStart, eTotalCNSE, eTotalCNSET, eTotalCNSETS, eTotalCNetworkExp, eTotalCStart, eTotalCStartT, eTotalCVarIn, eTotalCVarInT, eTotalCVarOut, eTotalCVarOutT, eTotalCap, eTotalCapEnergy, eTransMax, eZonalCFuelOut, eZonalCFuelStart, vCAP, vCAPENERGY, vCHARGE, vCOMMIT, vFLOW, vFuel, vNEW_TRANS_CAP, vNSE, vP, vRETCAP, vRETCAPENERGY, vS, vSHUT, vSTART, vStartFuel, vTAUX_NEG, vTAUX_POS, vTLOSS, vZERO, 73.97517013549805) + + + +Using `value.()`, we can see what the total capacity is of the optimized model: + + +```julia +totCap_base = value.(EP[:eTotalCap]) +``` + + + + + 10-element Vector{Float64}: + 10.41532872265646 + 10.085613331810192 + 0.0 + 0.0 + 0.0 + 0.0 + 2.026239619715743 + 0.0 + 0.0 + 0.16552558225070782 + + + +Each element corresponds to the MW value of the node in the grid. In `1_three_zones`, there are ten nodes, each of which are either natural gas, wind, solar, or battery plants. We can see which is which using `RESOURCE_NAMES` in the inputs dictionary: + + +```julia +RT = inputs["RESOURCE_NAMES"]; +DataFrame([RT totCap_base],["Resource","Total Capacity"]) +``` + + + +```@raw html +
10×2 DataFrame
RowResourceTotal Capacity
AnyAny
1MA_natural_gas_combined_cycle10.4153
2CT_natural_gas_combined_cycle10.0856
3ME_natural_gas_combined_cycle0.0
4MA_solar_pv0.0
5CT_onshore_wind0.0
6CT_solar_pv0.0
7ME_onshore_wind2.02624
8MA_battery0.0
9CT_battery0.0
10ME_battery0.165526
+``` + + +To visualize the impact of the emmissions policies, let's group the nodes together by type and plot the data. + + +```julia +# Group by plant type +totCapB = [totCap_base[1] + totCap_base[2] + totCap_base[3], totCap_base[4] + totCap_base[6], + totCap_base[5] + totCap_base[7], totCap_base[8] + totCap_base[9] + totCap_base[10]] +totCapB = reshape(totCapB,(:,1)) # Convert to matrix +``` + + + + + 4×1 Matrix{Float64}: + 20.500942054466652 + 0.0 + 2.026239619715743 + 0.16552558225070782 + + + + +```julia +colors=[:silver :yellow :deepskyblue :violetred3] + +G1 = groupedbar(transpose(totCapB), bar_position = :stack, bar_width=0.1,size=(400,450), + labels=["Natural Gas" "Solar" "Wind" "Battery"], + title="No Emissions Policies \n Obj Val: $(round(objective_value(EP),digits=6))",xticks=[ ],ylabel="GW",color=colors) +``` + +![svg](./files/t7_1p_none.svg) + +As you can see, with no limit on emissions, GenX goes straight to using natural gas. Let's try changing the settings to enforce emissions constraints. + +## CO2 Cap + +The setting `CO2Cap` specifies if the model should have a constraint on CO$_2$ emmissions, and, if so, what that constraint should look like. There are three types, mass, load-based, and generator-based. + +### Mass Cap + +The first type of constraint, done by setting `CO2Cap` to "1", is a mass based constraint, which simply puts a limit on the total tons of CO$_2$ able to be produced per megawatt of electricty. + + +```julia +setup["CO2Cap"] = 1; +``` + + +```julia +inputs = GenX.load_inputs(setup, case) +EP2 = GenX.generate_model(setup,inputs,OPTIMIZER) +GenX.solve_model(EP2,setup) +``` + + Reading Input CSV Files + Network.csv Successfully Read! + Demand (load) data Successfully Read! + Fuels_data.csv Successfully Read! + + Summary of resources loaded into the model: + ------------------------------------------------------- + Resource type Number of resources + ======================================================= + Thermal 3 + VRE 4 + Storage 3 + ======================================================= + Total number of resources: 10 + ------------------------------------------------------- + Generators_variability.csv Successfully Read! + Validating time basis + CO2_cap.csv Successfully Read! + CSV Files Successfully Read In From example_systems/1_three_zones + Discharge Module + + + Thermal.csv Successfully Read. + Vre.csv Successfully Read. + Storage.csv Successfully Read. + Resource_energy_share_requirement.csv Successfully Read. + Resource_capacity_reserve_margin.csv Successfully Read. + Resource_minimum_capacity_requirement.csv Successfully Read. + + Non-served Energy Module + Investment Discharge Module + Unit Commitment Module + Fuel Module + CO2 Module + Investment Transmission Module + Transmission Module + Dispatchable Resources Module + Storage Resources Module + Storage Investment Module + Storage Core Resources Module + Storage Resources with Symmetric Charge/Discharge Capacity Module + Thermal (Unit Commitment) Resources Module + CO2 Policies Module + Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms + Presolving model + 118158 rows, 81204 cols, 433923 nonzeros + 110739 rows, 73785 cols, 435465 nonzeros + Presolve : Reductions: rows 110739(-42656); columns 73785(-46354); elements 435465(-46757) + Solving the presolved LP + IPX model has 110739 rows, 73785 columns and 435465 nonzeros + Input + Number of variables: 73785 + Number of free variables: 3696 + Number of constraints: 110739 + Number of equality constraints: 16605 + Number of matrix entries: 435465 + Matrix range: [4e-07, 1e+01] + RHS range: [7e-01, 2e+01] + Objective range: [1e-04, 4e+02] + Bounds range: [2e-03, 2e+01] + Preprocessing + Dualized model: no + Number of dense columns: 15 + Range of scaling factors: [5.00e-01, 4.00e+00] + IPX version 1.0 + Interior Point Solve + Iter P.res D.res P.obj D.obj mu Time + 0 1.16e+01 3.76e+02 3.33411424e+06 -5.16532632e+06 4.37e+03 0s + 1 6.12e+00 1.19e+02 2.67580772e+05 -5.49991870e+06 2.15e+03 0s + 2 5.78e+00 8.43e+01 2.63971420e+05 -1.26660532e+07 2.19e+03 1s + 3 2.60e+00 5.19e+01 -6.33191198e+04 -1.58670064e+07 1.38e+03 1s + Constructing starting basis... + 4 7.34e-01 1.69e+01 8.22606550e+05 -1.15977191e+07 4.66e+02 3s + 5 3.33e-01 5.93e+00 6.52520930e+05 -5.60493380e+06 1.92e+02 5s + 6 1.40e-01 1.86e+00 4.30003244e+05 -2.61740021e+06 7.56e+01 6s + 7 7.48e-02 6.92e-01 3.17908008e+05 -1.47858711e+06 3.76e+01 7s + 8 1.34e-02 2.13e-01 1.58499195e+05 -7.36966970e+05 1.06e+01 8s + 9 8.58e-03 1.84e-01 1.38726156e+05 -6.77517443e+05 8.88e+00 9s + 10 1.85e-03 1.25e-01 1.06997055e+05 -5.46895734e+05 6.03e+00 10s + 11 9.24e-04 6.46e-02 8.86553337e+04 -3.44818602e+05 3.62e+00 11s + 12 4.63e-04 4.30e-02 7.38073046e+04 -2.58650422e+05 2.62e+00 12s + 13 2.59e-04 1.76e-02 5.82580398e+04 -1.15494132e+05 1.25e+00 13s + 14 1.82e-04 1.25e-02 5.26785356e+04 -8.56355514e+04 9.61e-01 14s + 15 8.88e-05 9.97e-03 4.58204676e+04 -6.94861851e+04 7.82e-01 15s + 16 4.53e-05 6.30e-03 3.78921045e+04 -3.64421549e+04 4.86e-01 16s + 17 2.06e-05 3.52e-03 3.37528536e+04 -1.59069943e+04 3.10e-01 17s + 18 1.03e-05 1.99e-03 3.04164644e+04 -2.07682393e+03 1.95e-01 18s + 19 8.47e-06 1.65e-03 3.00013657e+04 4.67701651e+02 1.75e-01 19s + 20 7.43e-06 1.51e-03 2.96873596e+04 1.69164986e+03 1.65e-01 20s + 21 4.34e-06 1.21e-03 2.86080014e+04 4.49654207e+03 1.41e-01 21s + 22 3.15e-06 9.70e-04 2.84959673e+04 6.35826288e+03 1.28e-01 21s + 23 8.47e-07 3.92e-04 2.73823203e+04 1.23933845e+04 8.37e-02 22s + 24 2.40e-07 1.04e-04 2.61231516e+04 1.76443726e+04 4.63e-02 23s + 25 2.22e-07 9.36e-05 2.60148183e+04 1.78437138e+04 4.45e-02 24s + 26 1.62e-07 7.29e-05 2.55552259e+04 1.84206144e+04 3.88e-02 24s + 27 1.22e-07 5.52e-05 2.50949238e+04 1.91000865e+04 3.25e-02 25s + 28 1.09e-07 4.85e-05 2.50021728e+04 1.92517935e+04 3.12e-02 26s + 29 8.94e-08 4.45e-05 2.47907107e+04 1.93334302e+04 2.96e-02 27s + 30 8.24e-08 4.34e-05 2.47681701e+04 1.93720252e+04 2.92e-02 28s + 31 7.16e-08 2.50e-05 2.46362518e+04 1.99291856e+04 2.54e-02 29s + 32 4.66e-08 2.01e-05 2.42437587e+04 2.01152325e+04 2.23e-02 29s + 33 4.19e-08 1.97e-05 2.42647574e+04 2.01301840e+04 2.23e-02 30s + 34 2.79e-08 1.90e-05 2.40142742e+04 2.01663344e+04 2.08e-02 31s + 35 2.32e-08 6.69e-06 2.39399116e+04 2.06855599e+04 1.75e-02 31s + 36 1.07e-08 5.30e-06 2.34566702e+04 2.08955297e+04 1.38e-02 32s + 37 9.51e-09 4.35e-06 2.33786345e+04 2.11021969e+04 1.22e-02 33s + 38 8.47e-09 3.86e-06 2.33591312e+04 2.11486293e+04 1.19e-02 34s + 39 4.72e-09 2.75e-06 2.31415700e+04 2.13759124e+04 9.49e-03 35s + 40 4.12e-09 2.60e-06 2.31287674e+04 2.13971288e+04 9.30e-03 35s + 41 4.08e-09 2.30e-06 2.31279677e+04 2.14560762e+04 8.98e-03 36s + 42 2.31e-09 1.19e-06 2.29798114e+04 2.17571173e+04 6.57e-03 37s + 43 2.12e-09 1.08e-06 2.29572577e+04 2.17902511e+04 6.27e-03 37s + 44 1.50e-09 6.92e-07 2.28682893e+04 2.19491402e+04 4.93e-03 38s + 45 1.44e-09 5.32e-07 2.28678426e+04 2.19786865e+04 4.77e-03 39s + 46 7.50e-10 1.52e-07 2.27876378e+04 2.21512825e+04 3.41e-03 39s + 47 6.72e-10 1.34e-07 2.27673512e+04 2.21739594e+04 3.18e-03 40s + 48 4.76e-10 2.75e-08 2.27150227e+04 2.23098580e+04 2.17e-03 41s + 49 3.86e-10 2.55e-08 2.26819898e+04 2.23156051e+04 1.97e-03 41s + 50 3.42e-10 2.05e-08 2.26687731e+04 2.23252871e+04 1.84e-03 42s + 51 3.03e-10 1.42e-08 2.26566767e+04 2.23383080e+04 1.71e-03 42s + 52 1.93e-10 1.06e-08 2.26117685e+04 2.23551537e+04 1.38e-03 43s + 53 1.66e-10 3.63e-09 2.25954131e+04 2.24149312e+04 9.68e-04 44s + 54 8.18e-11 9.07e-10 2.25454653e+04 2.24370312e+04 5.82e-04 44s + 55 5.43e-11 4.51e-10 2.25280247e+04 2.24432375e+04 4.55e-04 46s + 56 5.00e-11 4.05e-10 2.25264013e+04 2.24433424e+04 4.46e-04 46s + 57 4.69e-11 3.79e-10 2.25244405e+04 2.24432461e+04 4.36e-04 47s + 58 4.68e-11 3.45e-10 2.25244112e+04 2.24428231e+04 4.38e-04 47s + 59 4.43e-11 3.07e-10 2.25225216e+04 2.24434057e+04 4.24e-04 48s + 60 4.09e-11 2.55e-11 2.25200762e+04 2.24519301e+04 3.66e-04 48s + 61 3.36e-11 2.18e-11 2.25158099e+04 2.24513558e+04 3.46e-04 49s + 62 2.89e-11 1.00e-11 2.25119474e+04 2.24545183e+04 3.08e-04 49s + 63 1.40e-11 1.82e-12 2.24943596e+04 2.24673979e+04 1.45e-04 50s + 64 7.30e-12 9.09e-13 2.24854412e+04 2.24712286e+04 7.62e-05 50s + 65 6.03e-12 9.09e-13 2.24836491e+04 2.24717155e+04 6.40e-05 51s + 66 3.78e-12 2.27e-13 2.24803516e+04 2.24733198e+04 3.77e-05 51s + 67 1.71e-12 2.27e-13 2.24769782e+04 2.24737620e+04 1.73e-05 52s + 68 3.41e-13 2.27e-13 2.24749307e+04 2.24737943e+04 6.10e-06 52s + 69 2.64e-13 9.09e-13 2.24743978e+04 2.24739891e+04 2.19e-06 53s + 70 1.82e-13 5.65e-13 2.24742311e+04 2.24740852e+04 7.83e-07 53s + 71 2.84e-13 9.09e-13 2.24741715e+04 2.24741245e+04 2.52e-07 54s + 72 8.02e-14 2.21e-12 2.24741476e+04 2.24741372e+04 5.59e-08 54s + 73 1.97e-13 3.76e-12 2.24741425e+04 2.24741405e+04 1.08e-08 55s + 74 2.16e-13 4.30e-12 2.24741412e+04 2.24741409e+04 1.56e-09 55s + 75* 3.92e-13 4.87e-12 2.24741410e+04 2.24741410e+04 1.34e-10 56s + 76* 5.84e-12 3.78e-12 2.24741410e+04 2.24741410e+04 1.00e-11 56s + 77* 3.24e-12 3.33e-12 2.24741410e+04 2.24741410e+04 1.95e-12 56s + Running crossover as requested + Primal residual before push phase: 1.33e-07 + Dual residual before push phase: 8.94e-07 + Number of dual pushes required: 34869 + Number of primal pushes required: 3818 + Summary + Runtime: 56.21s + Status interior point solve: optimal + Status crossover: optimal + objective value: 2.24741410e+04 + interior solution primal residual (abs/rel): 2.42e-10 / 9.32e-12 + interior solution dual residual (abs/rel): 3.61e-09 / 8.97e-12 + interior solution objective gap (abs/rel): 3.00e-07 / 1.33e-11 + basic solution primal infeasibility: 3.53e-13 + basic solution dual infeasibility: 2.56e-14 + Ipx: IPM optimal + Ipx: Crossover optimal + Solving the original LP from the solution after postsolve + Model status : Optimal + IPM iterations: 77 + Crossover iterations: 4765 + Objective value : 2.2474141017e+04 + HiGHS run time : 56.47 + LP solved for primal + + + + + + (A JuMP Model + Minimization problem with: + Variables: 120139 + Objective function type: AffExpr + `AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 35112 constraints + `AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 20331 constraints + `AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 97952 constraints + `VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 4 constraints + `VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 116439 constraints + Model mode: AUTOMATIC + CachingOptimizer state: ATTACHED_OPTIMIZER + Solver name: HiGHS + Names registered in the model: FuelCalculationCommit_single, cCO2Emissions_systemwide, cFuelCalculation_single, cMaxCap, cMaxCapEnergy, cMaxCapEnergyDuration, cMaxFlow_in, cMaxFlow_out, cMaxLineReinforcement, cMaxNSE, cMaxRetCommit, cMaxRetEnergy, cMaxRetNoCommit, cMinCap, cMinCapEnergy, cMinCapEnergyDuration, cNSEPerSeg, cPowerBalance, cSoCBalInterior, cSoCBalStart, cStartFuel_single, cTAuxLimit, cTAuxSum, cTLoss, eAvail_Trans_Cap, eCFix, eCFixEnergy, eCFuelOut, eCFuelStart, eCNSE, eCStart, eCVar_in, eCVar_out, eELOSS, eELOSSByZone, eEmissionsByPlant, eEmissionsByZone, eExistingCap, eExistingCapEnergy, eFuelConsumption, eFuelConsumptionYear, eFuelConsumption_single, eGenerationByThermAll, eGenerationByVRE, eGenerationByZone, eLosses_By_Zone, eNet_Export_Flows, eObj, ePlantCFuelOut, ePlantCFuelStart, ePlantFuel_generation, ePlantFuel_start, ePowerBalance, ePowerBalanceDisp, ePowerBalanceLossesByZone, ePowerBalanceNetExportFlows, ePowerBalanceNse, ePowerBalanceStor, ePowerBalanceThermCommit, eStartFuel, eTotalCFix, eTotalCFixEnergy, eTotalCFuelOut, eTotalCFuelStart, eTotalCNSE, eTotalCNSET, eTotalCNSETS, eTotalCNetworkExp, eTotalCStart, eTotalCStartT, eTotalCVarIn, eTotalCVarInT, eTotalCVarOut, eTotalCVarOutT, eTotalCap, eTotalCapEnergy, eTransMax, eZonalCFuelOut, eZonalCFuelStart, vCAP, vCAPENERGY, vCHARGE, vCO2Cap_slack, vCOMMIT, vFLOW, vFuel, vNEW_TRANS_CAP, vNSE, vP, vRETCAP, vRETCAPENERGY, vS, vSHUT, vSTART, vStartFuel, vTAUX_NEG, vTAUX_POS, vTLOSS, vZERO, 56.83114790916443) + + + + +```julia +totCap2 = value.(EP2[:eTotalCap]) +totCapB2 = [totCap2[1] + totCap2[2] + totCap2[3], totCap2[4] + totCap2[6], + totCap2[5] + totCap2[7], totCap2[8] + totCap2[9] + totCap2[10]] + +DataFrame([RT totCap2],["Resource Type","Total Capacity"]) +``` + + + +```@raw html +
10×2 DataFrame
RowResource TypeTotal Capacity
AnyAny
1MA_natural_gas_combined_cycle0.423658
2CT_natural_gas_combined_cycle0.629033
3ME_natural_gas_combined_cycle0.35463
4MA_solar_pv42.9756
5CT_onshore_wind0.0
6CT_solar_pv67.9858
7ME_onshore_wind7.80683
8MA_battery13.262
9CT_battery29.851
10ME_battery2.62375
+``` + + + +```julia +G2 = groupedbar(transpose(totCapB2), bar_position = :stack, bar_width=0.1,size=(100,450), + labels=["Natural Gas" "Solar" "Wind" "Battery"],legend = false,title="CO2 Mass Cap \n Obj Val: $(round(objective_value(EP2),digits=6))", +xticks=[ ],ylabel="GW",color=colors) +plot(G2,G1,size=(900,450),titlefontsize=8) + +``` +![svg](./files/t7_2p_mass_none.svg) + + + +The model favors solar power now, but natural gas and wind are also used. One thing to note is that the objective value of this system is much higher than it was without emissions constraints. The amount of CO$_2$ allowed is determined by the input file CO2_cap.csv: + + +```julia +CO2Cap = CSV.read(joinpath(case,"policies/CO2_cap.csv"),DataFrame,missingstring="NA") +``` + + + +```@raw html +
3×11 DataFrame
RowColumn1Network_zonesCO_2_Cap_Zone_1CO_2_Cap_Zone_2CO_2_Cap_Zone_3CO_2_Max_tons_MWh_1CO_2_Max_tons_MWh_2CO_2_Max_tons_MWh_3CO_2_Max_Mtons_1CO_2_Max_Mtons_2CO_2_Max_Mtons_3
String3String3Int64Int64Int64Float64Float64Float64Float64Float64Float64
1MAz11000.050.00.00.0180.00.0
2CTz20100.00.050.00.00.0250.0
3MEz30010.00.00.050.00.00.025
+``` + + +#### Tolerance + +Let's try setting the CO$_2$ emissions tolerance to 0 for all nodes: + + +```julia +CO2Cap2 = copy(CO2Cap); # Save old tolerances +``` + + +```julia +CO2Cap2[!,"CO_2_Max_tons_MWh_1"] = [0.0;0.0;0.0]; +CO2Cap2[!,"CO_2_Max_tons_MWh_2"] = [0.0;0.0;0.0]; +CO2Cap2[!,"CO_2_Max_tons_MWh_3"] = [0.0;0.0;0.0]; +CO2Cap2[!,"CO_2_Max_Mtons_1"] = [0.0;0.0;0.0]; +CO2Cap2[!,"CO_2_Max_Mtons_2"] = [0.0;0.0;0.0]; +CO2Cap2[!,"CO_2_Max_Mtons_3"] = [0.0;0.0;0.0]; +``` + + +```julia +CSV.write(joinpath(case,"policies/CO2_cap.csv"),CO2Cap2) +``` + + + + + "example_systems/1_three_zones/policies/CO2_cap.csv" + + + + +```julia +inputs = GenX.load_inputs(setup, case) +EP3 = GenX.generate_model(setup,inputs,OPTIMIZER) +GenX.solve_model(EP3,setup) +``` + + Reading Input CSV Files + Network.csv Successfully Read! + Demand (load) data Successfully Read! + Fuels_data.csv Successfully Read! + + Summary of resources loaded into the model: + ------------------------------------------------------- + Resource type Number of resources + ======================================================= + Thermal 3 + VRE 4 + Storage 3 + ======================================================= + Total number of resources: 10 + ------------------------------------------------------- + Generators_variability.csv Successfully Read! + Validating time basis + CO2_cap.csv Successfully Read! + CSV Files Successfully Read In From example_systems/1_three_zones + Discharge Module + + + Thermal.csv Successfully Read. + Vre.csv Successfully Read. + Storage.csv Successfully Read. + Resource_energy_share_requirement.csv Successfully Read. + Resource_capacity_reserve_margin.csv Successfully Read. + Resource_minimum_capacity_requirement.csv Successfully Read. + + Non-served Energy Module + Investment Discharge Module + Unit Commitment Module + Fuel Module + CO2 Module + Investment Transmission Module + Transmission Module + Dispatchable Resources Module + Storage Resources Module + Storage Investment Module + Storage Core Resources Module + Storage Resources with Symmetric Charge/Discharge Capacity Module + Thermal (Unit Commitment) Resources Module + CO2 Policies Module + Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms + Presolving model + 62715 rows, 59025 cols, 206619 nonzeros + 55750 rows, 52060 cols, 206345 nonzeros + Presolve : Reductions: rows 55750(-97645); columns 52060(-68079); elements 206345(-275877) + Solving the presolved LP + IPX model has 55750 rows, 52060 columns and 206345 nonzeros + Input + Number of variables: 52060 + Number of free variables: 3696 + Number of constraints: 55750 + Number of equality constraints: 11515 + Number of matrix entries: 206345 + Matrix range: [4e-07, 1e+01] + RHS range: [7e-01, 2e+01] + Objective range: [1e-04, 4e+02] + Bounds range: [2e-03, 2e+01] + Preprocessing + Dualized model: no + Number of dense columns: 12 + Range of scaling factors: [5.00e-01, 1.00e+00] + IPX version 1.0 + Interior Point Solve + Iter P.res D.res P.obj D.obj mu Time + 0 8.66e+00 3.74e+02 3.32626622e+06 -5.13181178e+06 3.28e+03 0s + 1 4.14e+00 1.16e+02 8.23203603e+05 -4.36728593e+06 1.47e+03 0s + 2 3.82e+00 7.84e+01 7.99936610e+05 -9.74711636e+06 1.47e+03 0s + 3 2.29e+00 4.73e+01 6.28103564e+05 -1.28672691e+07 1.11e+03 0s + Constructing starting basis... + 4 3.38e-01 1.80e+01 1.09797314e+06 -8.08041855e+06 2.88e+02 1s + 5 1.83e-01 6.66e+00 7.53792907e+05 -4.07570830e+06 1.33e+02 2s + 6 8.56e-02 2.91e+00 4.53047274e+05 -2.12656299e+06 6.27e+01 2s + 7 4.32e-02 1.06e+00 2.95761273e+05 -9.82158558e+05 2.74e+01 3s + 8 2.45e-02 4.65e-01 2.07805891e+05 -5.33311956e+05 1.42e+01 3s + 9 1.41e-02 2.62e-01 1.50001050e+05 -3.47096559e+05 8.53e+00 3s + 10 1.09e-02 2.01e-01 1.34054733e+05 -3.01418233e+05 7.08e+00 3s + 11 3.02e-03 1.70e-01 9.84009565e+04 -2.78142992e+05 5.84e+00 4s + 12 6.80e-04 1.29e-01 8.22624601e+04 -2.40603504e+05 4.88e+00 4s + 13 5.19e-04 8.27e-02 7.53145221e+04 -1.68983726e+05 3.45e+00 4s + 14 2.11e-04 5.30e-02 6.28457097e+04 -1.25280563e+05 2.49e+00 4s + 15 8.42e-05 2.34e-02 5.29276919e+04 -7.04624346e+04 1.44e+00 5s + 16 4.88e-05 1.67e-02 4.48734610e+04 -4.78632217e+04 1.05e+00 5s + 17 3.17e-05 1.36e-02 4.18106416e+04 -3.79473404e+04 8.85e-01 5s + 18 1.54e-05 7.88e-03 3.47578913e+04 -1.29683476e+04 5.12e-01 6s + 19 5.88e-06 3.32e-03 3.06596888e+04 3.42643300e+03 2.74e-01 6s + 20 3.16e-06 1.13e-03 2.91816414e+04 1.11818829e+04 1.69e-01 6s + 21 2.01e-06 7.37e-04 2.80927086e+04 1.35130431e+04 1.35e-01 7s + 22 1.72e-06 6.41e-04 2.77751797e+04 1.42624417e+04 1.24e-01 7s + 23 1.64e-06 5.49e-04 2.77386064e+04 1.47199954e+04 1.19e-01 7s + 24 7.12e-07 4.66e-04 2.64331519e+04 1.56194992e+04 9.88e-02 8s + 25 2.77e-07 2.78e-04 2.60769883e+04 1.74334827e+04 7.80e-02 8s + 26 2.04e-07 1.45e-04 2.59822889e+04 1.87097084e+04 6.48e-02 8s + 27 7.83e-08 8.86e-05 2.50321932e+04 2.02590181e+04 4.24e-02 9s + 28 6.65e-08 7.45e-05 2.50172059e+04 2.04898905e+04 4.01e-02 9s + 29 5.27e-08 5.73e-05 2.49264089e+04 2.09172601e+04 3.55e-02 9s + 30 3.63e-08 4.90e-05 2.48125703e+04 2.11310315e+04 3.25e-02 10s + 31 2.24e-08 2.37e-05 2.46270269e+04 2.20176436e+04 2.29e-02 10s + 32 1.61e-08 1.80e-05 2.44783423e+04 2.23689799e+04 1.85e-02 10s + 33 1.48e-08 1.67e-05 2.44673758e+04 2.24042775e+04 1.81e-02 11s + 34 1.34e-08 1.10e-05 2.44514558e+04 2.26133491e+04 1.61e-02 11s + 35 5.16e-09 8.66e-06 2.42796001e+04 2.27599671e+04 1.33e-02 11s + 36 3.11e-09 3.47e-06 2.42120824e+04 2.31931323e+04 8.91e-03 11s + 37 5.68e-14 2.68e-06 2.40481768e+04 2.32862443e+04 6.66e-03 12s + 38 5.68e-14 1.15e-06 2.39818085e+04 2.36142391e+04 3.21e-03 12s + 39 5.68e-14 1.13e-06 2.39814115e+04 2.36145091e+04 3.21e-03 12s + 40 5.68e-14 9.70e-07 2.39782559e+04 2.36292988e+04 3.05e-03 13s + 41 6.39e-14 9.03e-07 2.39740539e+04 2.36364177e+04 2.95e-03 13s + 42 8.53e-14 8.87e-07 2.39736934e+04 2.36389906e+04 2.92e-03 13s + 43 8.53e-14 4.51e-07 2.39668070e+04 2.37015134e+04 2.32e-03 14s + 44 5.68e-14 3.63e-07 2.39530038e+04 2.37286287e+04 1.96e-03 14s + 45 6.39e-14 2.62e-07 2.39399533e+04 2.37645087e+04 1.53e-03 15s + 46 7.11e-14 2.35e-07 2.39403195e+04 2.37681261e+04 1.50e-03 15s + 47 5.68e-14 1.07e-07 2.39354909e+04 2.38220443e+04 9.89e-04 15s + 48 5.83e-14 8.32e-08 2.39319570e+04 2.38298216e+04 8.91e-04 16s + 49 6.34e-14 8.23e-08 2.39320866e+04 2.38307615e+04 8.84e-04 16s + 50 5.68e-14 2.73e-08 2.39222759e+04 2.38676200e+04 4.76e-04 16s + 51 5.68e-14 1.81e-08 2.39090601e+04 2.38790981e+04 2.61e-04 17s + 52 5.68e-14 2.13e-09 2.39087205e+04 2.38918872e+04 1.47e-04 17s + 53 5.68e-14 6.69e-10 2.39073686e+04 2.38988570e+04 7.42e-05 17s + 54 5.68e-14 1.71e-10 2.39057985e+04 2.39011287e+04 4.07e-05 17s + 55 5.68e-14 4.37e-11 2.39047907e+04 2.39026178e+04 1.89e-05 18s + 56 5.68e-14 2.50e-11 2.39045148e+04 2.39028929e+04 1.41e-05 18s + 57 5.68e-14 1.27e-11 2.39040896e+04 2.39032417e+04 7.39e-06 18s + 58 5.68e-14 2.27e-12 2.39039185e+04 2.39036010e+04 2.77e-06 18s + 59 5.68e-14 4.55e-13 2.39038268e+04 2.39036756e+04 1.32e-06 18s + 60 5.68e-14 9.09e-13 2.39037810e+04 2.39037207e+04 5.26e-07 18s + 61 5.68e-14 2.27e-13 2.39037547e+04 2.39037335e+04 1.85e-07 19s + 62 5.68e-14 2.27e-13 2.39037481e+04 2.39037351e+04 1.13e-07 19s + 63 5.68e-14 4.55e-13 2.39037407e+04 2.39037385e+04 1.93e-08 19s + 64 5.68e-14 1.14e-13 2.39037395e+04 2.39037392e+04 2.44e-09 19s + 65* 5.68e-14 2.27e-13 2.39037393e+04 2.39037393e+04 1.93e-10 19s + 66* 8.53e-14 2.27e-13 2.39037393e+04 2.39037393e+04 1.22e-11 19s + 67* 5.68e-14 9.09e-13 2.39037393e+04 2.39037393e+04 1.62e-12 19s + Running crossover as requested + Primal residual before push phase: 7.05e-08 + Dual residual before push phase: 9.91e-07 + Number of dual pushes required: 2532 + Number of primal pushes required: 3866 + Summary + Runtime: 19.36s + Status interior point solve: optimal + Status crossover: optimal + objective value: 2.39037393e+04 + interior solution primal residual (abs/rel): 2.26e-10 / 1.38e-11 + interior solution dual residual (abs/rel): 2.64e-09 / 6.57e-12 + interior solution objective gap (abs/rel): 2.04e-07 / 8.51e-12 + basic solution primal infeasibility: 4.44e-15 + basic solution dual infeasibility: 2.08e-15 + Ipx: IPM optimal + Ipx: Crossover optimal + Solving the original LP from the solution after postsolve + Model status : Optimal + IPM iterations: 67 + Crossover iterations: 1428 + Objective value : 2.3903739324e+04 + HiGHS run time : 19.55 + LP solved for primal + + + + + + (A JuMP Model + Minimization problem with: + Variables: 120139 + Objective function type: AffExpr + `AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 35112 constraints + `AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 20331 constraints + `AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 97952 constraints + `VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 4 constraints + `VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 116439 constraints + Model mode: AUTOMATIC + CachingOptimizer state: ATTACHED_OPTIMIZER + Solver name: HiGHS + Names registered in the model: FuelCalculationCommit_single, cCO2Emissions_systemwide, cFuelCalculation_single, cMaxCap, cMaxCapEnergy, cMaxCapEnergyDuration, cMaxFlow_in, cMaxFlow_out, cMaxLineReinforcement, cMaxNSE, cMaxRetCommit, cMaxRetEnergy, cMaxRetNoCommit, cMinCap, cMinCapEnergy, cMinCapEnergyDuration, cNSEPerSeg, cPowerBalance, cSoCBalInterior, cSoCBalStart, cStartFuel_single, cTAuxLimit, cTAuxSum, cTLoss, eAvail_Trans_Cap, eCFix, eCFixEnergy, eCFuelOut, eCFuelStart, eCNSE, eCStart, eCVar_in, eCVar_out, eELOSS, eELOSSByZone, eEmissionsByPlant, eEmissionsByZone, eExistingCap, eExistingCapEnergy, eFuelConsumption, eFuelConsumptionYear, eFuelConsumption_single, eGenerationByThermAll, eGenerationByVRE, eGenerationByZone, eLosses_By_Zone, eNet_Export_Flows, eObj, ePlantCFuelOut, ePlantCFuelStart, ePlantFuel_generation, ePlantFuel_start, ePowerBalance, ePowerBalanceDisp, ePowerBalanceLossesByZone, ePowerBalanceNetExportFlows, ePowerBalanceNse, ePowerBalanceStor, ePowerBalanceThermCommit, eStartFuel, eTotalCFix, eTotalCFixEnergy, eTotalCFuelOut, eTotalCFuelStart, eTotalCNSE, eTotalCNSET, eTotalCNSETS, eTotalCNetworkExp, eTotalCStart, eTotalCStartT, eTotalCVarIn, eTotalCVarInT, eTotalCVarOut, eTotalCVarOutT, eTotalCap, eTotalCapEnergy, eTransMax, eZonalCFuelOut, eZonalCFuelStart, vCAP, vCAPENERGY, vCHARGE, vCO2Cap_slack, vCOMMIT, vFLOW, vFuel, vNEW_TRANS_CAP, vNSE, vP, vRETCAP, vRETCAPENERGY, vS, vSHUT, vSTART, vStartFuel, vTAUX_NEG, vTAUX_POS, vTLOSS, vZERO, 19.870718002319336) + + + + +```julia +totCap3 = value.(EP3[:eTotalCap]) + +totCapB3 = [totCap3[1] + totCap3[2] + totCap3[3], totCap3[4] + totCap3[6], + totCap3[5] + totCap3[7], totCap3[8] + totCap3[9] + totCap3[10]] + +println(DataFrame([RT totCap3],["Resource Type","Total Capacity"])) +println(" ") + +println("Objective Value: ", objective_value(EP3)) + +G3 = groupedbar(transpose(totCapB3), bar_position = :stack, bar_width=0.1,size=(400,450), xticks=[ ],ylabel="GW", + labels=["Natural Gas" "Solar" "Wind" "Battery"],color=colors, + title="CO2 Mass Cap, Zero Tolerance \n Obj Val: $(round(objective_value(EP3),digits=6))") + +plot(G3,G2,size=(800,450),titlefontsize=8) +``` + + 10×2 DataFrame + Row│Resource Type Total Capacity + │Any Any + ─────┼─────────────────────────────────────────────── + 1 │ MA_natural_gas_combined_cycle 0.0 + 2 │ CT_natural_gas_combined_cycle 0.0 + 3 │ ME_natural_gas_combined_cycle 0.0 + 4 │ MA_solar_pv 44.2331 + 5 │ CT_onshore_wind 0.0 + 6 │ CT_solar_pv 71.8741 + 7 │ ME_onshore_wind 5.55301 + 8 │ MA_battery 15.1583 + 9 │ CT_battery 30.3461 + 10 │ ME_battery 2.16509 + + Objective Value: 23903.739324217397 + + +![svg](./files/t7_2p_mass_zero.svg) + + +As you can see, the use of natural gas has been eliminated compeltely. Note that the objective value increases here as well as renewable energy tends to cost more than natural gas. + +#### CO2 Slack + +Another thing we can do is, instead of demanding that the model 100% meet the CO$_2$ cap, we can add a penalty for if it violates the cap. This lets the system allow some CO$_2$ emmissions if it's determined the cost of the grid with some emmissions is low enough that it will offset the cost from the penalty variable. GenX will automatically incorporate this feature if a file by the name "CO2_cap_slack.csv" is in the policies folder of the directory. For more information on other types of policy slack variables in GenX, see the documentation on [Policy Slack Variables]. + +Here, the CO$_2$ slack cap models a [carbon tax](https://en.wikipedia.org/wiki/Carbon_tax#:~:text=A%20carbon%20tax%20is%20a,like%20more%20severe%20weather%20events.of) of \$250 per ton of emissions. + + +```julia +CO2Cap_slack = DataFrame(["CO_2_Cap_Zone_1" 250; "CO_2_Cap_Zone_2" 250; "CO_2_Cap_Zone_2" 250],["CO2_Cap_Constraint","PriceCap"]) +``` + + + +```@raw html +
3×2 DataFrame
RowCO2_Cap_ConstraintPriceCap
AnyAny
1CO_2_Cap_Zone_1250
2CO_2_Cap_Zone_2250
3CO_2_Cap_Zone_2250
+``` + + + +```julia +CSV.write(joinpath(case,"policies/CO2_cap_slack.csv"),CO2Cap_slack) +``` + + + + + "example_systems/1_three_zones/policies/CO2_cap_slack.csv" + + + +And run it again, + + +```julia +inputs = GenX.load_inputs(setup, case) +EP4 = GenX.generate_model(setup,inputs,OPTIMIZER) +GenX.solve_model(EP4,setup) +``` + + Reading Input CSV Files + Network.csv Successfully Read! + Demand (load) data Successfully Read! + Fuels_data.csv Successfully Read! + + Summary of resources loaded into the model: + ------------------------------------------------------- + Resource type Number of resources + ======================================================= + Thermal 3 + VRE 4 + Storage 3 + ======================================================= + Total number of resources: 10 + ------------------------------------------------------- + Generators_variability.csv Successfully Read! + Validating time basis + CO2_cap.csv Successfully Read! + CSV Files Successfully Read In From example_systems/1_three_zones + Discharge Module + Non-served Energy Module + + + Thermal.csv Successfully Read. + Vre.csv Successfully Read. + Storage.csv Successfully Read. + Resource_energy_share_requirement.csv Successfully Read. + Resource_capacity_reserve_margin.csv Successfully Read. + Resource_minimum_capacity_requirement.csv Successfully Read. + + Investment Discharge Module + Unit Commitment Module + Fuel Module + CO2 Module + Investment Transmission Module + Transmission Module + Dispatchable Resources Module + Storage Resources Module + Storage Investment Module + Storage Core Resources Module + Storage Resources with Symmetric Charge/Discharge Capacity Module + Thermal (Unit Commitment) Resources Module + CO2 Policies Module + Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms + Presolving model + 118155 rows, 81204 cols, 422835 nonzeros + 110998 rows, 74047 cols, 423349 nonzeros + Presolve : Reductions: rows 110998(-42397); columns 74047(-46092); elements 423349(-58873) + Solving the presolved LP + IPX model has 110998 rows, 74047 columns and 423349 nonzeros + Input + Number of variables: 74047 + Number of free variables: 3696 + Number of constraints: 110998 + Number of equality constraints: 16867 + Number of matrix entries: 423349 + Matrix range: [4e-07, 1e+01] + RHS range: [7e-01, 2e+01] + Objective range: [1e-04, 4e+02] + Bounds range: [2e-03, 2e+01] + Preprocessing + Dualized model: no + Number of dense columns: 15 + Range of scaling factors: [5.00e-01, 4.00e+00] + IPX version 1.0 + Interior Point Solve + Iter P.res D.res P.obj D.obj mu Time + 0 8.63e+00 3.73e+02 3.32376039e+06 -5.09189122e+06 3.23e+03 0s + 1 4.16e+00 1.08e+02 3.13266750e+05 -4.82993364e+06 1.41e+03 0s + 2 3.81e+00 7.25e+01 2.97980565e+05 -1.07780002e+07 1.30e+03 0s + 3 1.46e+00 3.93e+01 -1.26079071e+05 -1.28105929e+07 7.47e+02 1s + Constructing starting basis... + 4 3.74e-01 1.45e+01 3.73463343e+05 -8.41202259e+06 2.69e+02 3s + 5 2.49e-01 2.56e+00 3.78613518e+05 -3.12923412e+06 7.93e+01 5s + 6 1.75e-02 1.04e+00 2.12473288e+05 -1.52758882e+06 2.44e+01 6s + 7 9.80e-04 2.35e-01 1.33331872e+05 -4.99760720e+05 6.87e+00 7s + 8 2.77e-04 7.80e-02 7.82710921e+04 -1.61510326e+05 2.34e+00 9s + 9 1.09e-04 2.70e-02 5.47955571e+04 -6.12119167e+04 9.57e-01 10s + 10 3.77e-05 7.08e-03 4.55523212e+04 -2.90274240e+04 4.91e-01 11s + 11 1.64e-05 2.18e-03 3.11621436e+04 -7.43748662e+03 2.29e-01 12s + 12 7.39e-06 8.70e-04 2.26704941e+04 3.11900828e+02 1.27e-01 14s + 13 3.59e-06 2.72e-04 1.86489763e+04 4.05425979e+03 8.00e-02 16s + 14 1.90e-06 1.28e-04 1.56168633e+04 6.05326027e+03 5.19e-02 17s + 15 1.47e-06 6.25e-05 1.47851456e+04 7.20102502e+03 4.10e-02 20s + 16 1.02e-06 4.01e-05 1.38005552e+04 7.70711780e+03 3.28e-02 23s + 17 5.81e-07 1.81e-05 1.24913828e+04 8.58555743e+03 2.10e-02 26s + 18 3.56e-07 1.37e-05 1.18351621e+04 8.78570877e+03 1.64e-02 31s + 19 2.30e-07 1.13e-05 1.14288935e+04 8.93097599e+03 1.34e-02 33s + 20 1.42e-07 9.21e-06 1.12192893e+04 9.03497649e+03 1.17e-02 36s + 21 1.04e-07 5.91e-06 1.11251312e+04 9.20617340e+03 1.03e-02 37s + 22 6.54e-08 5.00e-06 1.09266006e+04 9.30098656e+03 8.73e-03 38s + 23 3.83e-08 3.59e-06 1.07816598e+04 9.45321722e+03 7.13e-03 40s + 24 3.66e-08 2.80e-06 1.07744564e+04 9.52604230e+03 6.70e-03 41s + 25 1.07e-08 2.21e-06 1.06144079e+04 9.59738956e+03 5.46e-03 43s + 26 5.77e-09 1.68e-06 1.05031968e+04 9.71311617e+03 4.24e-03 44s + 27 4.09e-09 1.48e-06 1.04791745e+04 9.74918379e+03 3.92e-03 45s + 28 2.28e-09 1.14e-06 1.04271389e+04 9.82526444e+03 3.23e-03 45s + 29 1.81e-09 9.51e-07 1.04093731e+04 9.87287016e+03 2.88e-03 46s + 30 1.59e-09 7.09e-07 1.04047419e+04 9.92089105e+03 2.59e-03 47s + 31 1.03e-09 3.29e-07 1.03752597e+04 1.00341461e+04 1.83e-03 47s + 32 6.21e-10 3.01e-07 1.03644649e+04 1.00391050e+04 1.74e-03 48s + 33 3.74e-10 2.57e-07 1.03380266e+04 1.00569556e+04 1.51e-03 49s + 34 1.20e-10 1.65e-07 1.03095303e+04 1.00951029e+04 1.15e-03 49s + 35 8.55e-11 1.39e-07 1.03018149e+04 1.01086583e+04 1.04e-03 50s + 36 5.07e-11 9.62e-08 1.02845256e+04 1.01405678e+04 7.72e-04 50s + 37 4.04e-11 8.97e-08 1.02823253e+04 1.01443584e+04 7.39e-04 51s + 38 2.54e-11 5.51e-08 1.02817374e+04 1.01594329e+04 6.55e-04 51s + 39 1.73e-11 3.65e-08 1.02723681e+04 1.01802747e+04 4.93e-04 52s + 40 1.50e-11 3.37e-08 1.02704612e+04 1.01830824e+04 4.68e-04 52s + 41 2.61e-12 2.79e-08 1.02584016e+04 1.01890289e+04 3.72e-04 52s + 42 2.42e-12 2.59e-08 1.02587461e+04 1.01906586e+04 3.65e-04 53s + 43 2.04e-12 2.16e-08 1.02588163e+04 1.01942759e+04 3.46e-04 53s + 44 1.69e-12 2.05e-08 1.02582342e+04 1.01954859e+04 3.36e-04 54s + 45 1.04e-12 1.61e-08 1.02537386e+04 1.02028401e+04 2.73e-04 54s + 46 9.38e-13 1.33e-08 1.02531945e+04 1.02071474e+04 2.47e-04 55s + 47 3.94e-13 7.40e-09 1.02494139e+04 1.02173046e+04 1.72e-04 55s + 48 2.31e-13 4.66e-09 1.02462035e+04 1.02243167e+04 1.17e-04 55s + 49 1.24e-13 1.54e-09 1.02449049e+04 1.02308377e+04 7.54e-05 56s + 50 9.59e-14 1.22e-09 1.02441557e+04 1.02318785e+04 6.58e-05 56s + 51 8.53e-14 7.46e-10 1.02438516e+04 1.02335717e+04 5.51e-05 57s + 52 1.42e-14 3.41e-10 1.02409154e+04 1.02358650e+04 2.71e-05 57s + 53 1.07e-14 1.08e-10 1.02400964e+04 1.02379817e+04 1.13e-05 57s + 54 1.07e-14 3.88e-11 1.02398951e+04 1.02384972e+04 7.49e-06 58s + 55 1.07e-14 2.85e-11 1.02397667e+04 1.02386509e+04 5.98e-06 58s + 56 1.07e-14 5.40e-12 1.02395468e+04 1.02389275e+04 3.32e-06 58s + 57 1.07e-14 1.24e-12 1.02394822e+04 1.02391409e+04 1.83e-06 59s + 58 1.07e-14 5.68e-13 1.02394092e+04 1.02392128e+04 1.05e-06 59s + 59 1.42e-14 2.56e-13 1.02393456e+04 1.02392605e+04 4.56e-07 59s + 60 1.07e-14 1.99e-13 1.02393207e+04 1.02392697e+04 2.73e-07 60s + 61 1.07e-14 5.19e-13 1.02393026e+04 1.02392801e+04 1.21e-07 60s + 62 1.42e-14 4.83e-13 1.02392989e+04 1.02392826e+04 8.73e-08 60s + 63 1.42e-14 7.18e-13 1.02392933e+04 1.02392837e+04 5.18e-08 61s + 64 1.42e-14 2.95e-13 1.02392903e+04 1.02392845e+04 3.08e-08 61s + 65 1.42e-14 1.46e-12 1.02392900e+04 1.02392874e+04 1.37e-08 61s + 66 1.07e-14 5.17e-12 1.02392895e+04 1.02392888e+04 3.76e-09 62s + 67* 1.42e-14 3.08e-12 1.02392891e+04 1.02392890e+04 3.57e-10 62s + 68* 1.42e-14 4.08e-12 1.02392891e+04 1.02392891e+04 4.85e-11 62s + 69* 1.42e-14 3.69e-12 1.02392891e+04 1.02392891e+04 9.52e-12 62s + 70* 1.42e-14 1.83e-12 1.02392891e+04 1.02392891e+04 1.83e-12 62s + 71* 1.78e-14 7.22e-12 1.02392891e+04 1.02392891e+04 4.13e-14 63s + 72* 1.42e-14 6.20e-12 1.02392891e+04 1.02392891e+04 4.51e-18 63s + Running crossover as requested + Primal residual before push phase: 4.73e-09 + Dual residual before push phase: 6.20e-12 + Number of dual pushes required: 31290 + Number of primal pushes required: 2494 + Summary + Runtime: 62.84s + Status interior point solve: optimal + Status crossover: optimal + objective value: 1.02392891e+04 + interior solution primal residual (abs/rel): 2.10e-13 / 1.28e-14 + interior solution dual residual (abs/rel): 6.20e-12 / 1.54e-14 + interior solution objective gap (abs/rel): -2.04e-10 / -1.99e-14 + basic solution primal infeasibility: 7.64e-14 + basic solution dual infeasibility: 2.10e-15 + Ipx: IPM optimal + Ipx: Crossover optimal + Solving the original LP from the solution after postsolve + Model status : Optimal + IPM iterations: 72 + Crossover iterations: 1881 + Objective value : 1.0239289084e+04 + HiGHS run time : 63.07 + LP solved for primal + + + + + + (A JuMP Model + Minimization problem with: + Variables: 120139 + Objective function type: AffExpr + `AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 35112 constraints + `AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 20331 constraints + `AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 97952 constraints + `VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 1 constraint + `VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 116442 constraints + Model mode: AUTOMATIC + CachingOptimizer state: ATTACHED_OPTIMIZER + Solver name: HiGHS + Names registered in the model: FuelCalculationCommit_single, cCO2Emissions_systemwide, cFuelCalculation_single, cMaxCap, cMaxCapEnergy, cMaxCapEnergyDuration, cMaxFlow_in, cMaxFlow_out, cMaxLineReinforcement, cMaxNSE, cMaxRetCommit, cMaxRetEnergy, cMaxRetNoCommit, cMinCap, cMinCapEnergy, cMinCapEnergyDuration, cNSEPerSeg, cPowerBalance, cSoCBalInterior, cSoCBalStart, cStartFuel_single, cTAuxLimit, cTAuxSum, cTLoss, eAvail_Trans_Cap, eCCO2Cap_slack, eCFix, eCFixEnergy, eCFuelOut, eCFuelStart, eCNSE, eCStart, eCTotalCO2CapSlack, eCVar_in, eCVar_out, eELOSS, eELOSSByZone, eEmissionsByPlant, eEmissionsByZone, eExistingCap, eExistingCapEnergy, eFuelConsumption, eFuelConsumptionYear, eFuelConsumption_single, eGenerationByThermAll, eGenerationByVRE, eGenerationByZone, eLosses_By_Zone, eNet_Export_Flows, eObj, ePlantCFuelOut, ePlantCFuelStart, ePlantFuel_generation, ePlantFuel_start, ePowerBalance, ePowerBalanceDisp, ePowerBalanceLossesByZone, ePowerBalanceNetExportFlows, ePowerBalanceNse, ePowerBalanceStor, ePowerBalanceThermCommit, eStartFuel, eTotalCFix, eTotalCFixEnergy, eTotalCFuelOut, eTotalCFuelStart, eTotalCNSE, eTotalCNSET, eTotalCNSETS, eTotalCNetworkExp, eTotalCStart, eTotalCStartT, eTotalCVarIn, eTotalCVarInT, eTotalCVarOut, eTotalCVarOutT, eTotalCap, eTotalCapEnergy, eTransMax, eZonalCFuelOut, eZonalCFuelStart, vCAP, vCAPENERGY, vCHARGE, vCO2Cap_slack, vCOMMIT, vFLOW, vFuel, vNEW_TRANS_CAP, vNSE, vP, vRETCAP, vRETCAPENERGY, vS, vSHUT, vSTART, vStartFuel, vTAUX_NEG, vTAUX_POS, vTLOSS, vZERO, 63.40430498123169) + + + + +```julia +value.(EP4[:eCTotalCO2CapSlack]) +``` + + + + + 2816.8936379034667 + + + + +```julia +totCap4 = value.(EP4[:eTotalCap]) + +totCapB4 = [totCap4[1] + totCap4[2] + totCap4[3], totCap4[4] + totCap4[6], + totCap4[5] + totCap4[7], totCap4[8] + totCap4[9] + totCap4[10]] + +println(DataFrame([RT totCap4],["Resource Type","Total Capacity"])) +println(" ") + +println("Objective Value: ", objective_value(EP4)) + +G4 = groupedbar(transpose(totCapB4), bar_position = :stack, bar_width=0.1,size=(400,450), xticks=[ ],ylabel="GW", + labels=["Natural Gas" "Solar" "Wind" "Battery"],legend=false,color=colors, + title="CO2 Mass Cap, Zero + Slack Tolerance \n Obj Val: $(round(objective_value(EP4),digits=6))") + +plot(G4,G3,G2,size=(900,450),layout=(1,3),titlefontsize=8) +``` + + DataFrame + Row │Resource Type Total Capacity + │Any Any + ─────┼─────────────────────────────────────────────── + 1 │ MA_natural_gas_combined_cycle 6.20579 + 2 │ CT_natural_gas_combined_cycle 7.42028 + 3 │ ME_natural_gas_combined_cycle 0.0 + 4 │ MA_solar_pv 14.2444 + 5 │ CT_onshore_wind 12.0451 + 6 │ CT_solar_pv 5.26796 + 7 │ ME_onshore_wind 8.48774 + 8 │ MA_battery 2.29813 + 9 │ CT_battery 2.86763 + 10 │ ME_battery 0.390909 + + Objective Value: 10239.289084181632 + + +![svg](./files/t7_3p_slack.svg) + + + +Adding in the slack variables allowed for some natural gas to be used once again and decreased the overall cost (objective function). + +### Load-based Cap + +Another way to set the CO$_2$ emissions cap is to limit emissions as a function of the total demand in that region. This can be done by setting `CO2Cap` to "2" in the setup: + + +```julia +setup["CO2Cap"] = 2; +``` + +Let's set the CO2_cap.csv back to it's original data, and remove the slack cap: + + +```julia +rm(joinpath(case,"policies/CO2_cap_slack.csv")) +CSV.write(joinpath(case,"policies/CO2_cap.csv"),CO2Cap) +``` + + + + + "example_systems/1_three_zones/policies/CO2_cap.csv" + + + + +```julia +inputs = GenX.load_inputs(setup, case) +EP5 = GenX.generate_model(setup,inputs,OPTIMIZER) +GenX.solve_model(EP5,setup) +``` + + Reading Input CSV Files + Network.csv Successfully Read! + Demand (load) data Successfully Read! + Fuels_data.csv Successfully Read! + + Summary of resources loaded into the model: + ------------------------------------------------------- + Resource type Number of resources + ======================================================= + Thermal 3 + VRE 4 + Storage 3 + ======================================================= + Total number of resources: 10 + ------------------------------------------------------- + Generators_variability.csv Successfully Read! + Validating time basis + CO2_cap.csv Successfully Read! + CSV Files Successfully Read In From example_systems/1_three_zones + Discharge Module + Non-served Energy Module + + + Thermal.csv Successfully Read. + Vre.csv Successfully Read. + Storage.csv Successfully Read. + Resource_energy_share_requirement.csv Successfully Read. + Resource_capacity_reserve_margin.csv Successfully Read. + Resource_minimum_capacity_requirement.csv Successfully Read. + + + Investment Discharge Module + Unit Commitment Module + Fuel Module + CO2 Module + Investment Transmission Module + Transmission Module + Dispatchable Resources Module + Storage Resources Module + Storage Investment Module + Storage Core Resources Module + Storage Resources with Symmetric Charge/Discharge Capacity Module + Thermal (Unit Commitment) Resources Module + CO2 Policies Module + Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms + Presolving model + 118158 rows, 81204 cols, 467187 nonzeros + 110739 rows, 73785 cols, 468729 nonzeros + Presolve : Reductions: rows 110739(-42656); columns 73785(-46354); elements 468729(-46757) + Solving the presolved LP + IPX model has 110739 rows, 73785 columns and 468729 nonzeros + Input + Number of variables: 73785 + Number of free variables: 3696 + Number of constraints: 110739 + Number of equality constraints: 16605 + Number of matrix entries: 468729 + Matrix range: [4e-07, 1e+01] + RHS range: [7e-01, 4e+03] + Objective range: [1e-04, 4e+02] + Bounds range: [2e-03, 2e+01] + Preprocessing + Dualized model: no + Number of dense columns: 15 + Range of scaling factors: [5.00e-01, 4.00e+00] + IPX version 1.0 + Interior Point Solve + Iter P.res D.res P.obj D.obj mu Time + 0 1.71e+03 3.41e+02 2.96378701e+06 -4.23587199e+06 5.75e+05 0s + 1 1.13e+03 1.31e+02 -4.89641638e+08 -8.84226731e+06 3.61e+05 0s + 2 1.09e+03 1.07e+02 -4.90812561e+08 -3.51675964e+07 4.11e+05 1s + 3 3.74e+02 5.23e+01 -3.72143959e+08 -3.93800995e+07 1.67e+05 1s + Constructing starting basis... + 4 1.74e+02 2.59e+01 -1.89656388e+08 -4.38688644e+07 8.52e+04 3s + 5 1.55e+02 2.32e+01 -1.66927356e+08 -4.54471496e+07 8.00e+04 5s + 6 2.66e+01 8.62e+00 9.40431644e+06 -4.92415912e+07 2.67e+04 6s + 7 2.77e+00 7.85e-01 1.11318915e+07 -4.76427177e+07 3.01e+03 8s + 8 6.28e-01 3.10e-01 1.16295577e+07 -3.03610025e+07 1.13e+03 10s + 9 2.91e-01 1.04e-01 1.07968497e+07 -1.69468432e+07 4.87e+02 11s + 10 1.59e-01 8.85e-02 1.01816820e+07 -1.56044371e+07 4.27e+02 12s + 11 8.12e-02 5.53e-02 8.96818818e+06 -1.14192748e+07 2.85e+02 13s + 12 3.88e-02 3.75e-02 7.95015583e+06 -9.07252228e+06 2.05e+02 14s + 13 1.86e-02 2.40e-02 6.21487140e+06 -6.41755461e+06 1.30e+02 15s + 14 6.01e-03 1.42e-02 4.80373854e+06 -4.66630024e+06 8.23e+01 18s + 15 2.80e-03 8.10e-03 3.07276238e+06 -2.78932663e+06 4.44e+01 19s + 16 1.05e-08 1.61e-03 1.54522332e+06 -1.15219019e+06 1.60e+01 20s + 17 3.81e-09 1.40e-04 4.33083581e+05 -9.75643163e+04 2.89e+00 21s + 18 2.40e-09 3.64e-05 1.17725979e+05 -2.92212886e+04 7.91e-01 22s + 19 9.04e-10 1.11e-05 6.41480326e+04 -1.64155777e+04 4.33e-01 23s + 20 7.36e-10 6.49e-06 4.91641901e+04 -1.03802768e+04 3.20e-01 24s + 21 6.56e-10 4.00e-06 4.47995622e+04 -6.50448658e+03 2.75e-01 25s + 22 3.74e-10 2.11e-06 3.33171246e+04 -2.19844201e+03 1.91e-01 25s + 23 4.11e-10 1.17e-06 3.13473710e+04 -2.25128297e+02 1.69e-01 27s + 24 5.32e-10 9.05e-07 3.07180077e+04 6.59187318e+02 1.61e-01 30s + 25 2.07e-10 5.74e-07 2.40909020e+04 2.36880496e+03 1.17e-01 31s + 26 1.46e-10 3.48e-07 1.95591688e+04 3.82235596e+03 8.44e-02 33s + 27 9.56e-11 2.77e-07 1.91099002e+04 4.16735208e+03 8.02e-02 35s + 28 1.16e-10 1.72e-07 1.68130157e+04 5.05922686e+03 6.31e-02 37s + 29 1.10e-10 1.14e-07 1.58420855e+04 5.68901990e+03 5.45e-02 39s + 30 1.00e-10 9.13e-08 1.50304186e+04 6.09927663e+03 4.79e-02 41s + 31 4.79e-11 4.62e-08 1.44849049e+04 6.49417572e+03 4.29e-02 43s + 32 5.38e-11 3.14e-08 1.33010538e+04 7.09832458e+03 3.33e-02 44s + 33 1.97e-11 2.65e-08 1.31349015e+04 7.15881992e+03 3.21e-02 48s + 34 4.25e-11 2.05e-08 1.26742180e+04 7.39203286e+03 2.83e-02 49s + 35 3.24e-11 1.56e-08 1.23110122e+04 7.63239675e+03 2.51e-02 51s + 36 4.28e-11 1.03e-08 1.20230845e+04 7.85317825e+03 2.24e-02 53s + 37 1.56e-11 7.64e-09 1.12986653e+04 8.11596241e+03 1.71e-02 54s + 38 2.81e-11 5.87e-09 1.11528506e+04 8.19787914e+03 1.59e-02 56s + 39 2.28e-11 3.67e-09 1.06041200e+04 8.51424102e+03 1.12e-02 59s + 40 1.25e-11 3.02e-09 1.05115674e+04 8.58142162e+03 1.04e-02 62s + 41 7.03e-12 2.68e-09 1.03942162e+04 8.63482986e+03 9.44e-03 63s + 42 1.77e-11 2.01e-09 1.03904932e+04 8.70538318e+03 9.04e-03 65s + 43 4.66e-11 1.63e-09 1.03579306e+04 8.76566015e+03 8.54e-03 66s + 44 1.96e-11 1.36e-09 1.01427363e+04 8.86378332e+03 6.86e-03 67s + 45 3.52e-11 9.40e-10 1.00522553e+04 9.00927911e+03 5.60e-03 69s + 46 4.02e-11 6.12e-10 9.95594984e+03 9.12097703e+03 4.48e-03 70s + 47 4.90e-12 4.94e-10 9.90731026e+03 9.18680967e+03 3.87e-03 72s + 48 1.55e-11 4.61e-10 9.90647522e+03 9.19643998e+03 3.81e-03 73s + 49 1.17e-11 4.18e-10 9.90023591e+03 9.20935084e+03 3.71e-03 74s + 50 3.61e-11 3.73e-10 9.89683026e+03 9.21663764e+03 3.65e-03 75s + 51 1.84e-11 3.46e-10 9.85096096e+03 9.23460950e+03 3.31e-03 76s + 52 7.42e-12 2.95e-10 9.78480033e+03 9.27774527e+03 2.72e-03 77s + 53 3.37e-11 2.51e-10 9.78057662e+03 9.30246448e+03 2.56e-03 78s + 54 1.43e-11 1.70e-10 9.77649230e+03 9.34200543e+03 2.33e-03 79s + 55 9.01e-12 1.18e-10 9.73939839e+03 9.39121374e+03 1.87e-03 80s + 56 4.50e-11 9.00e-11 9.72960001e+03 9.41702931e+03 1.68e-03 81s + 57 3.25e-11 6.25e-11 9.70849173e+03 9.44892074e+03 1.39e-03 82s + 58 9.01e-11 5.72e-11 9.69018439e+03 9.45729846e+03 1.25e-03 83s + 59 6.80e-11 4.15e-11 9.68317655e+03 9.47569218e+03 1.11e-03 84s + 60 1.68e-11 2.38e-11 9.67429417e+03 9.51041472e+03 8.79e-04 85s + 61 4.47e-11 1.79e-11 9.65746593e+03 9.53257688e+03 6.70e-04 86s + 62 3.95e-11 1.43e-11 9.65470621e+03 9.54043028e+03 6.13e-04 87s + 63 7.96e-11 8.76e-12 9.64849756e+03 9.56065424e+03 4.71e-04 87s + 64 6.17e-12 5.12e-12 9.64469171e+03 9.57460001e+03 3.76e-04 88s + 65 7.14e-11 4.06e-12 9.63840771e+03 9.58058736e+03 3.10e-04 89s + 66 1.43e-11 2.70e-12 9.63355725e+03 9.58844693e+03 2.42e-04 90s + 67 8.82e-12 2.42e-12 9.62962513e+03 9.59238503e+03 2.00e-04 90s + 68 5.56e-11 1.68e-12 9.62718274e+03 9.59579105e+03 1.68e-04 91s + 69 6.50e-12 1.05e-12 9.62258889e+03 9.60351437e+03 1.02e-04 92s + 70 2.18e-11 9.95e-13 9.62203860e+03 9.60540964e+03 8.92e-05 92s + 71 1.79e-10 3.84e-13 9.62055756e+03 9.61022195e+03 5.54e-05 93s + 72 5.57e-11 6.82e-13 9.61970045e+03 9.61377588e+03 3.18e-05 94s + 73 6.29e-11 5.40e-13 9.61958853e+03 9.61443607e+03 2.76e-05 94s + 74 1.14e-10 3.13e-13 9.61921628e+03 9.61498366e+03 2.27e-05 95s + 75 6.88e-11 1.85e-13 9.61887340e+03 9.61542318e+03 1.85e-05 96s + 76 5.60e-10 3.69e-13 9.61870185e+03 9.61564680e+03 1.64e-05 96s + 77 5.59e-10 4.83e-13 9.61842859e+03 9.61678126e+03 8.84e-06 97s + 78 6.89e-10 5.12e-13 9.61807911e+03 9.61688976e+03 6.38e-06 97s + 79 3.62e-10 3.98e-13 9.61785021e+03 9.61733220e+03 2.78e-06 98s + 80 1.09e-10 3.98e-13 9.61769612e+03 9.61747059e+03 1.21e-06 99s + 81 2.20e-10 3.02e-13 9.61761335e+03 9.61750430e+03 5.85e-07 99s + 82 1.17e-09 8.24e-13 9.61757268e+03 9.61751083e+03 3.32e-07 100s + 83 4.79e-10 8.53e-13 9.61755931e+03 9.61753499e+03 1.30e-07 101s + 84 5.65e-10 1.72e-12 9.61755460e+03 9.61753993e+03 7.87e-08 101s + 85 6.45e-10 3.25e-12 9.61754798e+03 9.61754458e+03 1.83e-08 102s + 86 5.31e-10 5.47e-12 9.61754612e+03 9.61754560e+03 2.83e-09 103s + 87 2.06e-10 2.54e-12 9.61754586e+03 9.61754575e+03 5.86e-10 103s + 88* 1.53e-09 8.29e-12 9.61754581e+03 9.61754579e+03 7.40e-11 105s + 89* 8.48e-10 4.73e-12 9.61754580e+03 9.61754580e+03 1.14e-11 107s + Running crossover as requested + Primal residual before push phase: 1.05e-05 + Dual residual before push phase: 3.29e-06 + Number of dual pushes required: 25720 + Number of primal pushes required: 3952 + Summary + Runtime: 110.60s + Status interior point solve: optimal + Status crossover: optimal + objective value: 9.61754580e+03 + interior solution primal residual (abs/rel): 2.90e-08 / 7.03e-12 + interior solution dual residual (abs/rel): 9.59e-09 / 2.38e-11 + interior solution objective gap (abs/rel): 2.01e-06 / 2.09e-10 + basic solution primal infeasibility: 7.86e-13 + basic solution dual infeasibility: 1.59e-15 + Ipx: IPM optimal + Ipx: Crossover optimal + Solving the original LP from the solution after postsolve + Model status : Optimal + IPM iterations: 89 + Crossover iterations: 2840 + Objective value : 9.6175458026e+03 + HiGHS run time : 110.86 + LP solved for primal + + + + + + (A JuMP Model + Minimization problem with: + Variables: 120139 + Objective function type: AffExpr + `AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 35112 constraints + `AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 20331 constraints + `AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 97952 constraints + `VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 4 constraints + `VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 116439 constraints + Model mode: AUTOMATIC + CachingOptimizer state: ATTACHED_OPTIMIZER + Solver name: HiGHS + Names registered in the model: FuelCalculationCommit_single, cCO2Emissions_systemwide, cFuelCalculation_single, cMaxCap, cMaxCapEnergy, cMaxCapEnergyDuration, cMaxFlow_in, cMaxFlow_out, cMaxLineReinforcement, cMaxNSE, cMaxRetCommit, cMaxRetEnergy, cMaxRetNoCommit, cMinCap, cMinCapEnergy, cMinCapEnergyDuration, cNSEPerSeg, cPowerBalance, cSoCBalInterior, cSoCBalStart, cStartFuel_single, cTAuxLimit, cTAuxSum, cTLoss, eAvail_Trans_Cap, eCFix, eCFixEnergy, eCFuelOut, eCFuelStart, eCNSE, eCStart, eCVar_in, eCVar_out, eELOSS, eELOSSByZone, eEmissionsByPlant, eEmissionsByZone, eExistingCap, eExistingCapEnergy, eFuelConsumption, eFuelConsumptionYear, eFuelConsumption_single, eGenerationByThermAll, eGenerationByVRE, eGenerationByZone, eLosses_By_Zone, eNet_Export_Flows, eObj, ePlantCFuelOut, ePlantCFuelStart, ePlantFuel_generation, ePlantFuel_start, ePowerBalance, ePowerBalanceDisp, ePowerBalanceLossesByZone, ePowerBalanceNetExportFlows, ePowerBalanceNse, ePowerBalanceStor, ePowerBalanceThermCommit, eStartFuel, eTotalCFix, eTotalCFixEnergy, eTotalCFuelOut, eTotalCFuelStart, eTotalCNSE, eTotalCNSET, eTotalCNSETS, eTotalCNetworkExp, eTotalCStart, eTotalCStartT, eTotalCVarIn, eTotalCVarInT, eTotalCVarOut, eTotalCVarOutT, eTotalCap, eTotalCapEnergy, eTransMax, eZonalCFuelOut, eZonalCFuelStart, vCAP, vCAPENERGY, vCHARGE, vCO2Cap_slack, vCOMMIT, vFLOW, vFuel, vNEW_TRANS_CAP, vNSE, vP, vRETCAP, vRETCAPENERGY, vS, vSHUT, vSTART, vStartFuel, vTAUX_NEG, vTAUX_POS, vTLOSS, vZERO, 111.20706605911255) + + + + +```julia +totCap5 = value.(EP5[:eTotalCap]) + +totCapB5 = [totCap5[1] + totCap5[2] + totCap5[3], totCap5[4] + totCap5[6], + totCap5[5] + totCap5[7], totCap5[8] + totCap5[9] + totCap5[10]] + +toPlot = [transpose(totCapB2);transpose(totCapB5)] + +println(DataFrame([RT totCap5],["Resource Type","Total Capacity"])) +println(" ") + +G5 = groupedbar(transpose(totCapB5), bar_position = :stack, bar_width=.8,size=(500,450), xticks=[ ],ylabel="GW", + labels=["Natural Gas" "Solar" "Wind" "Battery"],color=colors, + title="CO2 Load Rate Cap \n Obj Val: $(round(objective_value(EP5),digits=6))") +plot(G5,G2,size=(800,450), titlefontsize=9) +``` + + 10x2 DataFrame + Row | Resource Type Total Capacity + │ Any Any + ─────┼─────────────────────────────────────────────── + 1 │ MA_natural_gas_combined_cycle 8.3383 + 2 │ CT_natural_gas_combined_cycle 2.0596 + 3 │ ME_natural_gas_combined_cycle 0.527558 + 4 │ MA_solar_pv 18.4836 + 5 │ CT_onshore_wind 13.1932 + 6 │ CT_solar_pv 13.4186 + 7 │ ME_onshore_wind 11.3012 + 8 │ MA_battery 4.24838 + 9 │ CT_battery 4.50189 + 10 │ ME_battery 1.02331 + + +![svg](./files/t7_2p_load_mass.svg) + + + +### Generator-based Cap + +Finally, the third type of emissions cap in GenX is where the constraint is based on the ratio between the CO$_2$ cap and the generation of each node. + + +```julia +setup["CO2Cap"] = 3; +``` + + +```julia +inputs = GenX.load_inputs(setup, case) +EP6 = GenX.generate_model(setup,inputs,OPTIMIZER) +GenX.solve_model(EP6,setup) +``` + + Reading Input CSV Files + Network.csv Successfully Read! + Demand (load) data Successfully Read! + Fuels_data.csv Successfully Read! + + Summary of resources loaded into the model: + ------------------------------------------------------- + Resource type Number of resources + ======================================================= + Thermal 3 + VRE 4 + Storage 3 + ======================================================= + Total number of resources: 10 + ------------------------------------------------------- + Generators_variability.csv Successfully Read! + Validating time basis + CO2_cap.csv Successfully Read! + CSV Files Successfully Read In From example_systems/1_three_zones + Discharge Module + + + Thermal.csv Successfully Read. + Vre.csv Successfully Read. + Storage.csv Successfully Read. + Resource_energy_share_requirement.csv Successfully Read. + Resource_capacity_reserve_margin.csv Successfully Read. + Resource_minimum_capacity_requirement.csv Successfully Read. + + + Non-served Energy Module + Investment Discharge Module + Unit Commitment Module + Fuel Module + CO2 Module + Investment Transmission Module + Transmission Module + Dispatchable Resources Module + Storage Resources Module + Storage Investment Module + Storage Core Resources Module + Storage Resources with Symmetric Charge/Discharge Capacity Module + Thermal (Unit Commitment) Resources Module + CO2 Policies Module + Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms + Presolving model + 118158 rows, 81204 cols, 439344 nonzeros + 110739 rows, 73785 cols, 440886 nonzeros + Presolve : Reductions: rows 110739(-42656); columns 73785(-46354); elements 440886(-54272) + Solving the presolved LP + IPX model has 110739 rows, 73785 columns and 440886 nonzeros + Input + Number of variables: 73785 + Number of free variables: 3696 + Number of constraints: 110739 + Number of equality constraints: 16605 + Number of matrix entries: 440886 + Matrix range: [4e-07, 1e+01] + RHS range: [7e-01, 2e+01] + Objective range: [1e-04, 4e+02] + Bounds range: [2e-03, 2e+01] + Preprocessing + Dualized model: no + Number of dense columns: 15 + Range of scaling factors: [5.00e-01, 4.00e+00] + IPX version 1.0 + Interior Point Solve + Iter P.res D.res P.obj D.obj mu Time + 0 8.76e+00 3.68e+02 3.33955953e+06 -4.97437905e+06 3.24e+03 0s + 1 4.28e+00 1.43e+02 -2.33497546e+05 -5.06214948e+06 1.60e+03 0s + 2 3.87e+00 8.66e+01 -3.47321172e+05 -1.15250215e+07 1.45e+03 1s + 3 2.40e+00 4.93e+01 -6.12062937e+05 -1.60606245e+07 1.08e+03 1s + Constructing starting basis... + 4 1.00e+00 2.05e+01 1.18453276e+05 -1.28403154e+07 4.55e+02 3s + 5 7.57e-01 1.68e+01 1.98998600e+05 -1.20496551e+07 3.90e+02 7s + 6 4.01e-01 1.11e+01 3.68752096e+05 -9.85292291e+06 2.70e+02 9s + 7 1.69e-01 2.89e+00 4.01592303e+05 -3.46185082e+06 8.23e+01 10s + 8 1.94e-02 8.41e-01 2.49236130e+05 -1.42423792e+06 2.40e+01 12s + 9 3.13e-03 3.34e-01 1.41607109e+05 -6.32482360e+05 9.69e+00 13s + 10 1.53e-03 2.07e-01 1.23187989e+05 -4.48100415e+05 6.79e+00 14s + 11 4.26e-04 1.34e-01 1.20904571e+05 -3.54933673e+05 5.58e+00 15s + 12 1.92e-04 8.44e-02 1.04908501e+05 -2.54959177e+05 3.93e+00 16s + 13 8.09e-05 4.83e-02 8.49988300e+04 -1.63933485e+05 2.44e+00 18s + 14 4.62e-05 2.72e-02 7.06545133e+04 -1.02323699e+05 1.51e+00 19s + 15 1.94e-05 1.68e-02 5.24639561e+04 -6.95227074e+04 9.61e-01 20s + 16 1.02e-05 9.84e-03 3.77185714e+04 -4.17894192e+04 5.70e-01 22s + 17 6.81e-06 6.93e-03 3.08242939e+04 -2.91084107e+04 4.08e-01 23s + 18 3.58e-06 3.36e-03 2.57406414e+04 -1.44027309e+04 2.52e-01 24s + 19 1.77e-06 2.13e-03 2.24464783e+04 -8.64942680e+03 1.87e-01 26s + 20 8.10e-07 1.60e-03 2.00886717e+04 -5.98699450e+03 1.53e-01 27s + 21 4.67e-07 9.13e-04 1.76885055e+04 -1.32644122e+03 1.08e-01 29s + 22 2.19e-07 5.64e-04 1.53684619e+04 1.46187383e+03 7.78e-02 31s + 23 1.74e-07 4.77e-04 1.49485301e+04 2.12578093e+03 7.14e-02 34s + 24 1.03e-07 2.97e-04 1.37756560e+04 3.92211046e+03 5.43e-02 35s + 25 8.23e-08 2.03e-04 1.33224182e+04 4.96097392e+03 4.58e-02 37s + 26 6.69e-08 1.35e-04 1.28827892e+04 5.89161111e+03 3.81e-02 39s + 27 5.54e-08 5.85e-05 1.24932478e+04 7.23288405e+03 2.85e-02 41s + 28 3.67e-08 4.30e-05 1.17469879e+04 7.63959217e+03 2.22e-02 43s + 29 3.44e-08 3.56e-05 1.16936961e+04 7.73126184e+03 2.14e-02 46s + 30 1.64e-08 2.46e-05 1.09468658e+04 8.09132155e+03 1.54e-02 48s + 31 1.28e-08 1.98e-05 1.08111979e+04 8.22677378e+03 1.39e-02 50s + 32 8.98e-09 1.32e-05 1.06618652e+04 8.43574381e+03 1.20e-02 54s + 33 6.40e-09 1.23e-05 1.05084042e+04 8.48572171e+03 1.09e-02 55s + 34 6.03e-09 8.69e-06 1.04928796e+04 8.61992062e+03 1.01e-02 56s + 35 3.31e-09 6.98e-06 1.02642253e+04 8.74639498e+03 8.17e-03 58s + 36 3.12e-09 6.41e-06 1.02570400e+04 8.76891800e+03 8.00e-03 59s + 37 2.68e-09 4.60e-06 1.02120829e+04 8.91995727e+03 6.95e-03 60s + 38 1.41e-09 3.18e-06 1.01085720e+04 9.01554382e+03 5.87e-03 62s + 39 1.37e-09 2.31e-06 1.01047794e+04 9.08685475e+03 5.47e-03 63s + 40 1.06e-09 1.98e-06 1.00606064e+04 9.12387842e+03 5.03e-03 64s + 41 5.24e-10 1.13e-06 9.91648667e+03 9.28792782e+03 3.38e-03 65s + 42 4.98e-10 1.10e-06 9.91527075e+03 9.29016011e+03 3.36e-03 67s + 43 3.69e-10 1.02e-06 9.88770629e+03 9.30443644e+03 3.13e-03 69s + 44 3.55e-10 7.63e-07 9.88504084e+03 9.33991073e+03 2.93e-03 70s + 45 2.06e-10 4.05e-07 9.82906056e+03 9.43570351e+03 2.11e-03 71s + 46 2.02e-10 3.62e-07 9.82827522e+03 9.44146127e+03 2.08e-03 74s + 47 1.90e-10 3.22e-07 9.82379653e+03 9.45113014e+03 2.00e-03 75s + 48 9.94e-11 2.15e-07 9.78341274e+03 9.48706810e+03 1.59e-03 76s + 49 8.38e-11 2.01e-07 9.77551388e+03 9.49181672e+03 1.52e-03 77s + 50 4.59e-11 1.75e-07 9.74064260e+03 9.50762968e+03 1.25e-03 78s + 51 3.34e-11 1.19e-07 9.72951560e+03 9.54230950e+03 1.00e-03 79s + 52 2.62e-11 9.58e-08 9.72573311e+03 9.55294569e+03 9.27e-04 79s + 53 2.08e-11 4.63e-08 9.70432411e+03 9.59417118e+03 5.91e-04 80s + 54 9.60e-12 4.06e-08 9.69614280e+03 9.59920478e+03 5.20e-04 82s + 55 6.07e-12 2.67e-08 9.69178503e+03 9.61073037e+03 4.35e-04 82s + 56 1.02e-11 1.94e-08 9.68738193e+03 9.62154935e+03 3.53e-04 83s + 57 2.69e-11 8.60e-09 9.67895715e+03 9.63526917e+03 2.34e-04 84s + 58 1.57e-11 4.55e-09 9.67420309e+03 9.64278621e+03 1.69e-04 85s + 59 2.28e-11 2.55e-09 9.67122848e+03 9.64774778e+03 1.26e-04 85s + 60 3.88e-11 1.82e-09 9.66945757e+03 9.65096502e+03 9.92e-05 86s + 61 2.83e-11 1.00e-09 9.66699692e+03 9.65455335e+03 6.68e-05 86s + 62 2.73e-11 8.69e-10 9.66606426e+03 9.65556481e+03 5.63e-05 87s + 63 1.83e-11 7.05e-10 9.66498918e+03 9.65678888e+03 4.40e-05 88s + 64 1.56e-11 6.47e-10 9.66447640e+03 9.65724431e+03 3.88e-05 88s + 65 2.19e-11 2.62e-10 9.66409009e+03 9.66025109e+03 2.06e-05 89s + 66 7.78e-12 9.83e-11 9.66368883e+03 9.66207263e+03 8.67e-06 89s + 67 1.84e-11 7.20e-11 9.66349991e+03 9.66236162e+03 6.11e-06 90s + 68 2.47e-11 1.74e-11 9.66350655e+03 9.66290499e+03 3.23e-06 90s + 69 1.18e-11 5.33e-12 9.66339437e+03 9.66318656e+03 1.11e-06 91s + 70 1.13e-11 1.59e-12 9.66335658e+03 9.66328211e+03 3.99e-07 91s + 71 4.69e-11 4.26e-13 9.66334140e+03 9.66331249e+03 1.55e-07 92s + 72 1.37e-11 1.99e-13 9.66333277e+03 9.66332230e+03 5.62e-08 93s + 73 9.00e-12 4.83e-13 9.66332930e+03 9.66332548e+03 2.05e-08 93s + 74 1.55e-11 1.62e-12 9.66332820e+03 9.66332729e+03 4.84e-09 94s + 75 5.26e-11 1.23e-12 9.66332779e+03 9.66332745e+03 1.79e-09 94s + 76* 5.68e-11 2.59e-12 9.66332773e+03 9.66332767e+03 3.36e-10 95s + 77* 2.07e-11 5.92e-12 9.66332772e+03 9.66332771e+03 4.70e-11 96s + 78* 1.07e-10 7.45e-12 9.66332771e+03 9.66332771e+03 5.07e-12 98s + 79* 2.20e-10 9.85e-12 9.66332771e+03 9.66332771e+03 3.44e-13 98s + 80* 1.15e-10 6.51e-12 9.66332771e+03 9.66332771e+03 6.25e-14 99s + Running crossover as requested + Primal residual before push phase: 3.25e-07 + Dual residual before push phase: 2.20e-08 + Number of dual pushes required: 26184 + Number of primal pushes required: 3501 + Summary + Runtime: 101.61s + Status interior point solve: optimal + Status crossover: optimal + objective value: 9.66332771e+03 + interior solution primal residual (abs/rel): 1.27e-09 / 7.78e-11 + interior solution dual residual (abs/rel): 1.40e-10 / 3.48e-13 + interior solution objective gap (abs/rel): 6.66e-09 / 6.89e-13 + basic solution primal infeasibility: 5.33e-14 + basic solution dual infeasibility: 4.34e-14 + Ipx: IPM optimal + Ipx: Crossover optimal + Solving the original LP from the solution after postsolve + Model status : Optimal + IPM iterations: 80 + Crossover iterations: 2929 + Objective value : 9.6633277143e+03 + HiGHS run time : 101.86 + LP solved for primal + + + + + + (A JuMP Model + Minimization problem with: + Variables: 120139 + Objective function type: AffExpr + `AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 35112 constraints + `AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 20331 constraints + `AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 97952 constraints + `VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 4 constraints + `VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 116439 constraints + Model mode: AUTOMATIC + CachingOptimizer state: ATTACHED_OPTIMIZER + Solver name: HiGHS + Names registered in the model: FuelCalculationCommit_single, cCO2Emissions_systemwide, cFuelCalculation_single, cMaxCap, cMaxCapEnergy, cMaxCapEnergyDuration, cMaxFlow_in, cMaxFlow_out, cMaxLineReinforcement, cMaxNSE, cMaxRetCommit, cMaxRetEnergy, cMaxRetNoCommit, cMinCap, cMinCapEnergy, cMinCapEnergyDuration, cNSEPerSeg, cPowerBalance, cSoCBalInterior, cSoCBalStart, cStartFuel_single, cTAuxLimit, cTAuxSum, cTLoss, eAvail_Trans_Cap, eCFix, eCFixEnergy, eCFuelOut, eCFuelStart, eCNSE, eCStart, eCVar_in, eCVar_out, eELOSS, eELOSSByZone, eEmissionsByPlant, eEmissionsByZone, eExistingCap, eExistingCapEnergy, eFuelConsumption, eFuelConsumptionYear, eFuelConsumption_single, eGenerationByThermAll, eGenerationByVRE, eGenerationByZone, eLosses_By_Zone, eNet_Export_Flows, eObj, ePlantCFuelOut, ePlantCFuelStart, ePlantFuel_generation, ePlantFuel_start, ePowerBalance, ePowerBalanceDisp, ePowerBalanceLossesByZone, ePowerBalanceNetExportFlows, ePowerBalanceNse, ePowerBalanceStor, ePowerBalanceThermCommit, eStartFuel, eTotalCFix, eTotalCFixEnergy, eTotalCFuelOut, eTotalCFuelStart, eTotalCNSE, eTotalCNSET, eTotalCNSETS, eTotalCNetworkExp, eTotalCStart, eTotalCStartT, eTotalCVarIn, eTotalCVarInT, eTotalCVarOut, eTotalCVarOutT, eTotalCap, eTotalCapEnergy, eTransMax, eZonalCFuelOut, eZonalCFuelStart, vCAP, vCAPENERGY, vCHARGE, vCO2Cap_slack, vCOMMIT, vFLOW, vFuel, vNEW_TRANS_CAP, vNSE, vP, vRETCAP, vRETCAPENERGY, vS, vSHUT, vSTART, vStartFuel, vTAUX_NEG, vTAUX_POS, vTLOSS, vZERO, 102.19283390045166) + + + + +```julia +totCap6 = value.(EP6[:eTotalCap]) + +totCapB6 = [totCap6[1] + totCap6[2] + totCap6[3], totCap6[4] + totCap6[6], + totCap6[5] + totCap6[7], totCap6[8] + totCap6[9] + totCap6[10]] + +println(DataFrame([RT totCap6],["Resource Type","Total Capacity"])) +println(" ") + +G6 = groupedbar(transpose(totCapB6), bar_position = :stack, bar_width=.7,size=(500,450), xticks=[ ],ylabel="GW", + labels=["Natural Gas" "Solar" "Wind" "Battery"],legend=false,color=colors, + title="CO2 Generation Rate Cap \n Obj Val: $(round(objective_value(EP6),digits=6))",ylabelfontsize=8) +plot(G2,G5,G6,size=(900,450), titlefontsize=8,layout=(1,3),) +``` + + 10×2 DataFrame + Row │ Resource Type Total Capacity + │ Any Any + ─────┼─────────────────────────────────────────────── + 1 │ MA_natural_gas_combined_cycle 4.08764 + 2 │ CT_natural_gas_combined_cycle 5.84863 + 3 │ ME_natural_gas_combined_cycle 0.887681 + 4 │ MA_solar_pv 20.0639 + 5 │ CT_onshore_wind 13.6798 + 6 │ CT_solar_pv 13.3512 + 7 │ ME_onshore_wind 9.61782 + 8 │ MA_battery 3.73538 + 9 │ CT_battery 4.85316 + 10 │ ME_battery 1.21815 + + + +![svg](./files/t7_3p_mass_load_gen.svg) + + + +## Energy Share Requirement + +Many countries have policies that demand a certain percentage of energy provided to consumers comes from renewable energy (in the US, these are called [renewable portfolio standards](https://www.eia.gov/energyexplained/renewable-sources/portfolio-standards.php#:~:text=Renewable%20portfolio%20standards%20(RPS)%2C,energy%20sources%20for%20electricity%20generation). In GenX, this policy can be implemented by setting `Energy_share_requirement` to 1 in the setup, and adding a file called `Energy_share_requirement.csv` to the policies folder. + + +```julia +ESR = CSV.read(joinpath(case,"policies/Energy_share_requirement.csv"),DataFrame,missingstring="NA") +``` + + + +```@raw html +
3×4 DataFrame
RowColumn1Network_zonesESR_1ESR_2
String3String3Float64Float64
1MAz10.2590.348
2CTz20.440.44
3MEz30.7760.776
+``` + + + +```julia +setup["CO2Cap"] = 0 # set back to 0 to compare +setup["EnergyShareRequirement"] = 1; +``` + + +```julia +inputs = GenX.load_inputs(setup, case) +EP7 = GenX.generate_model(setup,inputs,OPTIMIZER) +GenX.solve_model(EP7,setup) +``` + + Reading Input CSV Files + Network.csv Successfully Read! + Demand (load) data Successfully Read! + Fuels_data.csv Successfully Read! + + Summary of resources loaded into the model: + ------------------------------------------------------- + Resource type Number of resources + ======================================================= + Thermal 3 + VRE 4 + Storage 3 + ======================================================= + Total number of resources: 10 + ------------------------------------------------------- + Generators_variability.csv Successfully Read! + Validating time basis + Energy_share_requirement.csv Successfully Read! + CSV Files Successfully Read In From example_systems/1_three_zones + Discharge Module + + + Thermal.csv Successfully Read. + Vre.csv Successfully Read. + Storage.csv Successfully Read. + Resource_energy_share_requirement.csv Successfully Read. + Resource_capacity_reserve_margin.csv Successfully Read. + Resource_minimum_capacity_requirement.csv Successfully Read. + + + Non-served Energy Module + Investment Discharge Module + Unit Commitment Module + Fuel Module + CO2 Module + Investment Transmission Module + Transmission Module + Dispatchable Resources Module + Storage Resources Module + Storage Investment Module + Storage Core Resources Module + Storage Resources with Symmetric Charge/Discharge Capacity Module + Thermal (Unit Commitment) Resources Module + Energy Share Requirement Policies Module + Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms + Presolving model + 118157 rows, 81204 cols, 433677 nonzeros + 110999 rows, 74047 cols, 428770 nonzeros + Presolve : Reductions: rows 110999(-42395); columns 74047(-46089); elements 428770(-57145) + Solving the presolved LP + IPX model has 110999 rows, 74047 columns and 428770 nonzeros + Input + Number of variables: 74047 + Number of free variables: 3696 + Number of constraints: 110999 + Number of equality constraints: 16867 + Number of matrix entries: 428770 + Matrix range: [4e-07, 1e+01] + RHS range: [7e-01, 5e+04] + Objective range: [1e-04, 4e+02] + Bounds range: [2e-03, 2e+01] + Preprocessing + Dualized model: no + Number of dense columns: 15 + Range of scaling factors: [5.00e-01, 1.00e+00] + IPX version 1.0 + Interior Point Solve + Iter P.res D.res P.obj D.obj mu Time + 0 3.25e+03 3.28e+02 2.96057527e+06 -4.42499145e+06 1.05e+06 0s + 1 2.15e+03 1.54e+02 -3.67625092e+08 -9.92129159e+06 7.04e+05 0s + 2 2.00e+03 1.45e+02 -4.48234657e+08 -1.62120314e+07 6.90e+05 0s + Constructing starting basis... + 3 1.80e+03 1.38e+02 -1.57967721e+09 -1.32554204e+07 6.35e+05 3s + 4 4.26e+02 4.25e+01 -8.07136821e+08 -1.80687324e+07 1.79e+05 4s + 5 2.74e+02 1.46e+01 -4.80957944e+08 -2.11824340e+07 8.47e+04 5s + 6 2.31e+02 1.06e+01 -3.88916132e+08 -2.25389566e+07 7.06e+04 7s + 7 3.97e+01 2.56e+00 -8.90467652e+06 -2.42140640e+07 1.74e+04 8s + 8 1.49e+00 1.05e+00 1.55238132e+07 -2.27145059e+07 4.78e+03 9s + 9 4.23e-01 9.61e-02 1.52981739e+07 -2.07731077e+07 7.27e+02 9s + 10 2.43e-02 1.03e-02 8.29803125e+06 -3.74951138e+06 1.06e+02 10s + 11 2.19e-03 2.07e-03 2.70601909e+06 -1.07157895e+06 2.38e+01 14s + 12 3.20e-04 3.41e-05 7.22109443e+05 -1.33114881e+05 4.62e+00 15s + 13 2.18e-05 5.81e-06 4.97580885e+04 -2.36873031e+04 3.94e-01 16s + 14 8.07e-06 1.45e-06 3.01069381e+04 -8.59032120e+03 2.08e-01 18s + 15 4.16e-06 6.72e-07 1.93254730e+04 -3.46407201e+03 1.22e-01 19s + 16 2.30e-06 3.55e-07 1.43100849e+04 -8.01714933e+02 8.10e-02 22s + 17 1.34e-06 1.67e-07 1.16397836e+04 8.01991381e+02 5.81e-02 25s + 18 7.61e-07 9.17e-08 9.47348310e+03 1.85600560e+03 4.08e-02 27s + 19 4.47e-07 5.75e-08 8.09797935e+03 2.54641687e+03 2.98e-02 30s + 20 3.33e-07 3.47e-08 7.62653275e+03 3.04869441e+03 2.45e-02 35s + 21 1.98e-07 1.57e-08 6.79376066e+03 3.83391059e+03 1.59e-02 40s + 22 1.00e-07 1.07e-08 6.23436569e+03 4.07366075e+03 1.16e-02 43s + 23 5.72e-08 8.56e-09 5.90537240e+03 4.22893896e+03 8.98e-03 52s + 24 3.15e-08 7.40e-09 5.69783264e+03 4.32217640e+03 7.37e-03 56s + 25 1.96e-08 6.71e-09 5.60290779e+03 4.37626021e+03 6.57e-03 60s + 26 1.62e-08 6.58e-09 5.58260471e+03 4.38624817e+03 6.41e-03 61s + 27 9.83e-09 4.68e-09 5.47138439e+03 4.58570163e+03 4.75e-03 63s + 28 7.08e-09 4.32e-09 5.43675159e+03 4.61957103e+03 4.38e-03 66s + 29 5.90e-09 3.78e-09 5.44745537e+03 4.64477569e+03 4.30e-03 68s + 30 2.60e-09 3.39e-09 5.38567861e+03 4.68523417e+03 3.75e-03 69s + 31 1.86e-09 3.13e-09 5.40360769e+03 4.70093259e+03 3.76e-03 71s + 32 5.79e-10 1.84e-09 5.32616721e+03 4.86253824e+03 2.48e-03 72s + 33 5.26e-10 1.66e-09 5.32704123e+03 4.87901733e+03 2.40e-03 74s + 34 3.48e-10 1.52e-09 5.32856456e+03 4.89218629e+03 2.34e-03 75s + 35 1.82e-10 1.07e-09 5.29562500e+03 4.96409486e+03 1.78e-03 76s + 36 1.42e-10 8.01e-10 5.28983765e+03 5.00359981e+03 1.53e-03 78s + 37 8.66e-11 7.18e-10 5.28033482e+03 5.01649890e+03 1.41e-03 79s + 38 4.00e-11 5.38e-10 5.27675684e+03 5.03862584e+03 1.28e-03 81s + 39 2.74e-11 4.02e-10 5.26154650e+03 5.07181296e+03 1.02e-03 82s + 40 1.33e-11 3.51e-10 5.26154482e+03 5.07895810e+03 9.78e-04 83s + 41 9.37e-12 1.52e-10 5.25770976e+03 5.11634640e+03 7.57e-04 84s + 42 6.61e-11 6.56e-11 5.24263265e+03 5.14509162e+03 5.23e-04 85s + 43 2.70e-11 5.14e-11 5.23939943e+03 5.15308245e+03 4.62e-04 86s + 44 1.07e-11 4.52e-11 5.23760193e+03 5.15544594e+03 4.40e-04 87s + 45 2.14e-11 3.78e-11 5.23695511e+03 5.15880466e+03 4.19e-04 88s + 46 4.52e-11 2.37e-11 5.22793680e+03 5.16829652e+03 3.20e-04 89s + 47 3.88e-11 1.68e-11 5.22613710e+03 5.17238445e+03 2.88e-04 90s + 48 3.04e-11 9.86e-12 5.22130177e+03 5.18278901e+03 2.06e-04 91s + 49 1.60e-11 8.28e-12 5.21769964e+03 5.18522708e+03 1.74e-04 91s + 50 2.50e-11 5.20e-12 5.21732077e+03 5.18949974e+03 1.49e-04 92s + 51 1.46e-11 2.94e-12 5.21565661e+03 5.19332457e+03 1.20e-04 93s + 52 6.28e-12 1.96e-12 5.21252321e+03 5.19649375e+03 8.59e-05 93s + 53 1.10e-11 1.34e-12 5.21137346e+03 5.19788591e+03 7.23e-05 94s + 54 4.52e-11 1.05e-12 5.20952040e+03 5.19902667e+03 5.62e-05 95s + 55 1.97e-13 9.66e-13 5.20946552e+03 5.19915263e+03 5.52e-05 95s + 56 1.03e-10 6.57e-13 5.20878855e+03 5.20069905e+03 4.33e-05 96s + 57 1.00e-10 7.67e-13 5.20790740e+03 5.20157745e+03 3.39e-05 97s + 58 1.08e-11 3.41e-13 5.20718489e+03 5.20231634e+03 2.61e-05 97s + 59 5.84e-11 5.04e-13 5.20697661e+03 5.20275991e+03 2.26e-05 98s + 60 6.10e-11 4.83e-13 5.20642800e+03 5.20316879e+03 1.75e-05 98s + 61 1.21e-11 2.34e-13 5.20626891e+03 5.20342248e+03 1.52e-05 99s + 62 4.88e-11 5.97e-13 5.20609848e+03 5.20403285e+03 1.11e-05 99s + 63 4.11e-11 2.27e-13 5.20583889e+03 5.20443275e+03 7.53e-06 100s + 64 4.08e-11 2.84e-13 5.20572643e+03 5.20464048e+03 5.82e-06 100s + 65 1.77e-12 2.84e-13 5.20565183e+03 5.20500872e+03 3.45e-06 101s + 66 3.26e-12 5.12e-13 5.20546080e+03 5.20514462e+03 1.69e-06 101s + 67 8.10e-11 2.27e-13 5.20539707e+03 5.20527700e+03 6.43e-07 102s + 68 1.14e-10 2.84e-13 5.20537158e+03 5.20530783e+03 3.42e-07 102s + 69 7.20e-11 5.19e-13 5.20535889e+03 5.20534226e+03 8.91e-08 102s + 70 8.66e-11 2.51e-12 5.20535373e+03 5.20534725e+03 3.47e-08 103s + 71 1.74e-11 3.55e-12 5.20534982e+03 5.20534876e+03 5.66e-09 103s + 72 7.05e-12 3.38e-12 5.20534916e+03 5.20534900e+03 8.61e-10 104s + 73* 3.63e-13 3.95e-12 5.20534910e+03 5.20534906e+03 1.93e-10 104s + 74* 2.57e-11 7.55e-12 5.20534908e+03 5.20534907e+03 3.92e-11 105s + 75* 9.13e-11 2.43e-12 5.20534908e+03 5.20534908e+03 5.53e-12 105s + Running crossover as requested + Primal residual before push phase: 4.25e-06 + Dual residual before push phase: 1.04e-06 + Number of dual pushes required: 31721 + Number of primal pushes required: 2358 + Summary + Runtime: 105.88s + Status interior point solve: optimal + Status crossover: optimal + objective value: 5.20534908e+03 + interior solution primal residual (abs/rel): 1.25e-10 / 2.61e-15 + interior solution dual residual (abs/rel): 4.75e-09 / 1.18e-11 + interior solution objective gap (abs/rel): 1.03e-06 / 1.98e-10 + basic solution primal infeasibility: 2.45e-14 + basic solution dual infeasibility: 2.50e-16 + Ipx: IPM optimal + Ipx: Crossover optimal + Solving the original LP from the solution after postsolve + Model status : Optimal + IPM iterations: 75 + Crossover iterations: 2950 + Objective value : 5.2053490785e+03 + HiGHS run time : 106.12 + LP solved for primal + + + + + + (A JuMP Model + Minimization problem with: + Variables: 120136 + Objective function type: AffExpr + `AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 35112 constraints + `AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 20333 constraints + `AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 97949 constraints + `VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 1 constraint + `VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 116439 constraints + Model mode: AUTOMATIC + CachingOptimizer state: ATTACHED_OPTIMIZER + Solver name: HiGHS + Names registered in the model: FuelCalculationCommit_single, cESRShare, cFuelCalculation_single, cMaxCap, cMaxCapEnergy, cMaxCapEnergyDuration, cMaxFlow_in, cMaxFlow_out, cMaxLineReinforcement, cMaxNSE, cMaxRetCommit, cMaxRetEnergy, cMaxRetNoCommit, cMinCap, cMinCapEnergy, cMinCapEnergyDuration, cNSEPerSeg, cPowerBalance, cSoCBalInterior, cSoCBalStart, cStartFuel_single, cTAuxLimit, cTAuxSum, cTLoss, eAvail_Trans_Cap, eCFix, eCFixEnergy, eCFuelOut, eCFuelStart, eCNSE, eCStart, eCVar_in, eCVar_out, eELOSS, eELOSSByZone, eESR, eESRDischarge, eEmissionsByPlant, eEmissionsByZone, eExistingCap, eExistingCapEnergy, eFuelConsumption, eFuelConsumptionYear, eFuelConsumption_single, eGenerationByThermAll, eGenerationByVRE, eGenerationByZone, eLosses_By_Zone, eNet_Export_Flows, eObj, ePlantCFuelOut, ePlantCFuelStart, ePlantFuel_generation, ePlantFuel_start, ePowerBalance, ePowerBalanceDisp, ePowerBalanceLossesByZone, ePowerBalanceNetExportFlows, ePowerBalanceNse, ePowerBalanceStor, ePowerBalanceThermCommit, eStartFuel, eTotalCFix, eTotalCFixEnergy, eTotalCFuelOut, eTotalCFuelStart, eTotalCNSE, eTotalCNSET, eTotalCNSETS, eTotalCNetworkExp, eTotalCStart, eTotalCStartT, eTotalCVarIn, eTotalCVarInT, eTotalCVarOut, eTotalCVarOutT, eTotalCap, eTotalCapEnergy, eTransMax, eZonalCFuelOut, eZonalCFuelStart, vCAP, vCAPENERGY, vCHARGE, vCOMMIT, vFLOW, vFuel, vNEW_TRANS_CAP, vNSE, vP, vRETCAP, vRETCAPENERGY, vS, vSHUT, vSTART, vStartFuel, vTAUX_NEG, vTAUX_POS, vTLOSS, vZERO, 106.45424795150757) + + + + +```julia +totCap7 = value.(EP7[:eTotalCap]) + +totCapB7 = [totCap7[1] + totCap7[2] + totCap7[3], totCap7[4] + totCap7[6], + totCap7[5] + totCap7[7], totCap7[8] + totCap7[9] + totCap7[10]] + +println(DataFrame([RT totCap7],["Resource Type","Total Capacity"])) +println(" ") + +G7 = groupedbar(transpose(totCapB7), bar_position = :stack, bar_width=.7,size=(500,450), xticks=[ ],ylabel="GW", + labels=["Natural Gas" "Solar" "Wind" "Battery"],legend=false,color=colors, + title="Energy Share Requirement \n Obj Val: $(round(objective_value(EP7),digits=6))",ylabelfontsize=8) +plot(G7,G2,G5,G6,size=(900,900), titlefontsize=8,layout=(2,2)) +``` + + 10×2 DataFrame + Row │ Resource Type Total Capacity + │ Any Any + ─────┼─────────────────────────────────────────────── + 1 │ MA_natural_gas_combined_cycle 8.58778 + 2 │ CT_natural_gas_combined_cycle 9.43521 + 3 │ ME_natural_gas_combined_cycle 0.0 + 4 │ MA_solar_pv 2.99333 + 5 │ CT_onshore_wind 5.61694 + 6 │ CT_solar_pv 0.242229 + 7 │ ME_onshore_wind 6.28897 + 8 │ MA_battery 0.253804 + 9 │ CT_battery 0.0 + 10 │ ME_battery 0.723348 + + + +![svg](./files/t7_4p_esr_mass_load_gen.svg) + + +The Energy Share Requriement policy also has the possibiliy to be run with slack variables + +## Capacity Reserve Margin + +The Capacity Reserve Margin constraint demands that a certain amount of energy always be available in each zone, expressed as a fraction of the demand. Once again, we can enforce a Capacity Reserve Margin by setting its option to "1" in the setup and adding the relevant file, `Capacity_reserve_margin.csv`. + + +```julia +CapacityReserve = CSV.read(joinpath(case,"policies/Capacity_reserve_margin.csv"),DataFrame,missingstring="NA") +``` + + + +``` @raw html +
3×3 DataFrame
RowColumn1Network_zonesCapRes_1
String3String3Float64
1MAz10.156
2CTz20.156
3MEz30.156
+``` + + + +```julia +setup["CapacityReserveMargin"] = 1; +``` + + +```julia +inputs = GenX.load_inputs(setup, case) +EP8 = GenX.generate_model(setup,inputs,OPTIMIZER) +GenX.solve_model(EP8,setup) +``` + + Reading Input CSV Files + Network.csv Successfully Read! + Demand (load) data Successfully Read! + Fuels_data.csv Successfully Read! + + Summary of resources loaded into the model: + ------------------------------------------------------- + Resource type Number of resources + ======================================================= + Thermal 3 + VRE 4 + Storage 3 + ======================================================= + Total number of resources: 10 + ------------------------------------------------------- + Generators_variability.csv Successfully Read! + Validating time basis + Capacity_reserve_margin.csv Successfully Read! + + + Thermal.csv Successfully Read. + Vre.csv Successfully Read. + Storage.csv Successfully Read. + Resource_energy_share_requirement.csv Successfully Read. + Resource_capacity_reserve_margin.csv Successfully Read. + Resource_minimum_capacity_requirement.csv Successfully Read. + + + Energy_share_requirement.csv Successfully Read! + CSV Files Successfully Read In From example_systems/1_three_zones + Discharge Module + Non-served Energy Module + Investment Discharge Module + Unit Commitment Module + Fuel Module + CO2 Module + Investment Transmission Module + Transmission Module + Dispatchable Resources Module + Storage Resources Module + Storage Investment Module + Storage Core Resources Module + Storage Resources with Symmetric Charge/Discharge Capacity Module + Thermal (Unit Commitment) Resources Module + Energy Share Requirement Policies Module + Capacity Reserve Margin Policies Module + Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms + Presolving model + 131093 rows, 97836 cols, 538890 nonzeros + 123634 rows, 90378 cols, 543137 nonzeros + Presolve : Reductions: rows 123634(-42696); columns 90378(-46390); elements 543137(-47991) + Solving the presolved LP + IPX model has 123634 rows, 90378 columns and 543137 nonzeros + Input + Number of variables: 90378 + Number of free variables: 3696 + Number of constraints: 123634 + Number of equality constraints: 22110 + Number of matrix entries: 543137 + Matrix range: [4e-07, 1e+01] + RHS range: [7e-01, 5e+04] + Objective range: [1e-04, 4e+02] + Bounds range: [2e-03, 2e+01] + Preprocessing + Dualized model: no + Number of dense columns: 15 + Range of scaling factors: [5.00e-01, 1.00e+00] + IPX version 1.0 + Interior Point Solve + Iter P.res D.res P.obj D.obj mu Time + 0 4.21e+03 3.50e+02 3.04628199e+06 -5.21772232e+06 1.46e+06 0s + 1 2.81e+03 1.90e+02 -5.15281627e+08 -1.06058690e+07 1.02e+06 0s + 2 2.45e+03 1.56e+02 -6.44386109e+08 -2.55847744e+07 9.81e+05 1s + 3 1.18e+03 1.41e+02 -8.43467846e+08 -2.60789874e+07 6.78e+05 1s + Constructing starting basis... + 4 7.54e+02 4.73e+01 -7.60379207e+08 -3.49951229e+07 3.40e+05 3s + 5 6.33e+01 1.39e+01 -5.44467100e+05 -3.65314462e+07 6.81e+04 4s + 6 2.27e+01 2.74e+00 -1.77683713e+06 -4.81835016e+07 1.90e+04 10s + 7 9.77e-01 6.10e-01 1.48697352e+07 -4.12620606e+07 3.32e+03 13s + 8 1.52e-01 4.78e-02 1.42095518e+07 -1.48990864e+07 4.03e+02 14s + 9 1.65e-02 1.88e-02 7.71351293e+06 -6.37275792e+06 1.39e+02 15s + 10 3.46e-03 2.65e-03 4.64755286e+06 -1.55341587e+06 3.68e+01 18s + 11 4.76e-04 1.28e-03 9.51929576e+05 -7.48785467e+05 8.94e+00 20s + 12 8.26e-05 6.15e-05 2.94145739e+05 -7.77919316e+04 1.78e+00 21s + 13 3.54e-05 6.20e-06 1.35212127e+05 -1.45337724e+04 7.13e-01 22s + 14 2.53e-05 7.28e-12 1.14387567e+05 -2.21312822e+04 6.50e-01 23s + 15 2.33e-05 7.28e-12 1.13339554e+05 -2.13641483e+04 6.41e-01 24s + 16 7.71e-06 4.55e-12 4.42306187e+04 -1.29028659e+04 2.72e-01 25s + 17 7.64e-07 1.82e-12 1.81970294e+04 -4.92740686e+03 1.10e-01 26s + 18 3.72e-07 3.64e-12 1.39021979e+04 -1.32749886e+03 7.24e-02 30s + 19 2.03e-07 9.09e-13 1.13821414e+04 7.45236578e+02 5.06e-02 32s + 20 1.05e-07 9.09e-13 9.13639056e+03 2.30432056e+03 3.25e-02 35s + 21 7.73e-08 4.55e-13 8.59719038e+03 3.17398498e+03 2.58e-02 38s + 22 3.33e-08 3.69e-13 7.37618406e+03 3.92635014e+03 1.64e-02 43s + 23 1.53e-08 9.09e-13 6.71318380e+03 4.46082497e+03 1.07e-02 52s + 24 7.16e-09 2.98e-13 6.28228488e+03 4.71698031e+03 7.44e-03 56s + 25 5.19e-09 9.09e-13 6.18110316e+03 4.82937601e+03 6.43e-03 62s + 26 2.24e-09 4.55e-13 5.92131571e+03 5.04272325e+03 4.18e-03 66s + 27 1.26e-09 4.55e-13 5.85499040e+03 5.13102116e+03 3.44e-03 73s + 28 5.94e-10 4.55e-13 5.79725408e+03 5.18715779e+03 2.90e-03 76s + 29 3.86e-10 4.83e-13 5.76431193e+03 5.26258597e+03 2.38e-03 79s + 30 2.36e-10 3.69e-13 5.74367493e+03 5.28432035e+03 2.18e-03 81s + 31 1.68e-10 2.56e-13 5.72937706e+03 5.32860855e+03 1.90e-03 83s + 32 6.05e-11 2.27e-13 5.70998585e+03 5.35418213e+03 1.69e-03 85s + 33 5.53e-11 2.42e-13 5.70850651e+03 5.40373271e+03 1.45e-03 86s + 34 2.90e-11 2.42e-13 5.68596077e+03 5.43998304e+03 1.17e-03 88s + 35 2.67e-11 4.26e-13 5.67637386e+03 5.45111176e+03 1.07e-03 91s + 36 2.99e-11 2.27e-13 5.67168974e+03 5.46214213e+03 9.96e-04 92s + 37 1.99e-11 1.42e-13 5.65940618e+03 5.48204771e+03 8.43e-04 93s + 38 6.70e-11 4.55e-13 5.65532213e+03 5.49686649e+03 7.53e-04 94s + 39 6.23e-11 3.13e-13 5.64168791e+03 5.51202371e+03 6.16e-04 95s + 40 3.89e-11 3.27e-13 5.63853210e+03 5.52780109e+03 5.26e-04 97s + 41 1.20e-11 1.99e-13 5.63441684e+03 5.54194604e+03 4.40e-04 98s + 42 1.79e-11 4.55e-13 5.63069684e+03 5.54896357e+03 3.88e-04 100s + 43 2.83e-11 2.42e-13 5.62970471e+03 5.55078636e+03 3.75e-04 101s + 44 7.99e-11 5.40e-13 5.61992128e+03 5.55549414e+03 3.06e-04 103s + 45 3.20e-11 2.56e-13 5.61211218e+03 5.56079764e+03 2.44e-04 104s + 46 1.21e-11 3.41e-13 5.61177375e+03 5.56505674e+03 2.22e-04 106s + 47 4.72e-11 2.56e-13 5.60993414e+03 5.56837792e+03 1.98e-04 107s + 48 4.70e-12 3.41e-13 5.60465748e+03 5.57191765e+03 1.56e-04 108s + 49 2.44e-11 3.69e-13 5.60465096e+03 5.57377173e+03 1.47e-04 109s + 50 2.47e-11 3.41e-13 5.60235807e+03 5.58002161e+03 1.06e-04 109s + 51 3.24e-11 2.56e-13 5.60149552e+03 5.58255142e+03 9.00e-05 110s + 52 3.31e-11 1.71e-13 5.60101493e+03 5.58433865e+03 7.93e-05 111s + 53 2.00e-11 3.13e-13 5.59892601e+03 5.58668138e+03 5.82e-05 112s + 54 7.84e-11 1.60e-13 5.59885342e+03 5.58685974e+03 5.70e-05 112s + 55 4.61e-11 2.27e-13 5.59865140e+03 5.58847015e+03 4.84e-05 113s + 56 7.16e-11 2.56e-13 5.59762653e+03 5.58975937e+03 3.74e-05 114s + 57 1.03e-11 2.56e-13 5.59747335e+03 5.59024473e+03 3.44e-05 115s + 58 7.64e-12 3.13e-13 5.59715338e+03 5.59061047e+03 3.11e-05 115s + 59 2.17e-11 3.13e-13 5.59711186e+03 5.59070395e+03 3.05e-05 116s + 60 1.40e-11 2.27e-13 5.59696797e+03 5.59107740e+03 2.80e-05 117s + 61 7.00e-11 4.26e-13 5.59606722e+03 5.59162281e+03 2.11e-05 117s + 62 4.94e-11 6.25e-13 5.59525601e+03 5.59289962e+03 1.12e-05 118s + 63 1.92e-11 2.27e-13 5.59505259e+03 5.59297104e+03 9.89e-06 119s + 64 1.11e-11 3.69e-13 5.59462252e+03 5.59327739e+03 6.39e-06 120s + 65 8.66e-13 3.13e-13 5.59453155e+03 5.59338209e+03 5.46e-06 120s + 66 2.17e-11 3.13e-13 5.59446120e+03 5.59350884e+03 4.53e-06 121s + 67 1.12e-11 3.13e-13 5.59440854e+03 5.59367478e+03 3.49e-06 122s + 68 4.11e-11 3.98e-13 5.59427052e+03 5.59378913e+03 2.29e-06 122s + 69 1.04e-11 2.27e-13 5.59416188e+03 5.59391997e+03 1.15e-06 123s + 70 4.31e-12 2.56e-13 5.59412273e+03 5.59393435e+03 8.95e-07 124s + 71 8.96e-11 3.98e-13 5.59408396e+03 5.59399407e+03 4.27e-07 124s + 72 1.26e-10 4.26e-13 5.59405507e+03 5.59402936e+03 1.22e-07 125s + 73 3.69e-11 3.98e-13 5.59405082e+03 5.59403909e+03 5.58e-08 126s + 74 1.24e-12 2.36e-12 5.59404612e+03 5.59404129e+03 2.30e-08 126s + 75 1.33e-11 5.07e-12 5.59404352e+03 5.59404265e+03 4.10e-09 127s + 76 1.91e-11 4.70e-12 5.59404309e+03 5.59404298e+03 5.09e-10 127s + 77* 6.85e-11 7.82e-12 5.59404305e+03 5.59404303e+03 1.27e-10 128s + 78* 6.30e-11 2.17e-12 5.59404305e+03 5.59404304e+03 2.84e-11 128s + 79* 1.53e-11 1.32e-12 5.59404305e+03 5.59404304e+03 6.24e-12 129s + Running crossover as requested + Primal residual before push phase: 1.85e-05 + Dual residual before push phase: 1.60e-06 + Number of dual pushes required: 40477 + Number of primal pushes required: 2267 + Summary + Runtime: 129.76s + Status interior point solve: optimal + Status crossover: optimal + objective value: 5.59404305e+03 + interior solution primal residual (abs/rel): 4.70e-09 / 9.83e-14 + interior solution dual residual (abs/rel): 6.10e-09 / 1.52e-11 + interior solution objective gap (abs/rel): 1.29e-06 / 2.30e-10 + basic solution primal infeasibility: 3.88e-14 + basic solution dual infeasibility: 1.21e-15 + Ipx: IPM optimal + Ipx: Crossover optimal + Solving the original LP from the solution after postsolve + Model status : Optimal + IPM iterations: 79 + Crossover iterations: 5019 + Objective value : 5.5940430448e+03 + HiGHS run time : 130.05 + LP solved for primal + + + + + + (A JuMP Model + Minimization problem with: + Variables: 136768 + Objective function type: AffExpr + `AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 40656 constraints + `AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 27725 constraints + `AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 97949 constraints + `VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 1 constraint + `VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 133071 constraints + Model mode: AUTOMATIC + CachingOptimizer state: ATTACHED_OPTIMIZER + Solver name: HiGHS + Names registered in the model: FuelCalculationCommit_single, cCapacityResMargin, cESRShare, cFuelCalculation_single, cMaxCap, cMaxCapEnergy, cMaxCapEnergyDuration, cMaxFlow_in, cMaxFlow_out, cMaxLineReinforcement, cMaxNSE, cMaxRetCommit, cMaxRetEnergy, cMaxRetNoCommit, cMinCap, cMinCapEnergy, cMinCapEnergyDuration, cNSEPerSeg, cPowerBalance, cSOCMinCapRes, cSoCBalInterior, cSoCBalStart, cStartFuel_single, cTAuxLimit, cTAuxSum, cTLoss, cVSoCBalInterior, cVSoCBalStart, eAvail_Trans_Cap, eCFix, eCFixEnergy, eCFuelOut, eCFuelStart, eCNSE, eCStart, eCVar_in, eCVar_in_virtual, eCVar_out, eCVar_out_virtual, eCapResMarBalance, eCapResMarBalanceNSE, eCapResMarBalanceStor, eCapResMarBalanceStorVirtual, eCapResMarBalanceThermal, eCapResMarBalanceTrans, eCapResMarBalanceVRE, eELOSS, eELOSSByZone, eESR, eESRDischarge, eEmissionsByPlant, eEmissionsByZone, eExistingCap, eExistingCapEnergy, eFuelConsumption, eFuelConsumptionYear, eFuelConsumption_single, eGenerationByThermAll, eGenerationByVRE, eGenerationByZone, eLosses_By_Zone, eNet_Export_Flows, eObj, ePlantCFuelOut, ePlantCFuelStart, ePlantFuel_generation, ePlantFuel_start, ePowerBalance, ePowerBalanceDisp, ePowerBalanceLossesByZone, ePowerBalanceNetExportFlows, ePowerBalanceNse, ePowerBalanceStor, ePowerBalanceThermCommit, eStartFuel, eTotalCFix, eTotalCFixEnergy, eTotalCFuelOut, eTotalCFuelStart, eTotalCNSE, eTotalCNSET, eTotalCNSETS, eTotalCNetworkExp, eTotalCStart, eTotalCStartT, eTotalCVarIn, eTotalCVarInT, eTotalCVarInT_virtual, eTotalCVarIn_virtual, eTotalCVarOut, eTotalCVarOutT, eTotalCVarOutT_virtual, eTotalCVarOut_virtual, eTotalCap, eTotalCapEnergy, eTransMax, eZonalCFuelOut, eZonalCFuelStart, vCAP, vCAPENERGY, vCAPRES_charge, vCAPRES_discharge, vCAPRES_socinreserve, vCHARGE, vCOMMIT, vFLOW, vFuel, vNEW_TRANS_CAP, vNSE, vP, vRETCAP, vRETCAPENERGY, vS, vSHUT, vSTART, vStartFuel, vTAUX_NEG, vTAUX_POS, vTLOSS, vZERO, 130.46769380569458) + + + + +```julia +totCap8 = value.(EP8[:eTotalCap]) + +totCapB8 = [totCap8[1] + totCap8[2] + totCap8[3], totCap8[4] + totCap8[6], + totCap8[5] + totCap8[7], totCap8[8] + totCap8[9] + totCap8[10]] + +println(DataFrame([RT totCap8],["Resource Type","Total Capacity"])) +println(" ") + +G8 = groupedbar(transpose(totCapB8), bar_position = :stack, bar_width=.7,size=(500,450), xticks=[ ],ylabel="GW", + labels=["Natural Gas" "Solar" "Wind" "Battery"],color=colors, + title="Capacity Reserve Margin + ESR \n Obj Val: $(round(objective_value(EP8),digits=6))",ylabelfontsize=8) + +plot(G8,G7,G2,size=(900,450), titlefontsize=8,layout=(1,3)) +``` + + 10×2 DataFrame + Row │ Resource Type Total Capacity + │ Any Any + ─────┼─────────────────────────────────────────────── + 1 │ MA_natural_gas_combined_cycle 8.59939 + 2 │ CT_natural_gas_combined_cycle 14.7124 + 3 │ ME_natural_gas_combined_cycle 0.0 + 4 │ MA_solar_pv 2.89028 + 5 │ CT_onshore_wind 5.82195 + 6 │ CT_solar_pv 0.0 + 7 │ ME_onshore_wind 6.28764 + 8 │ MA_battery 0.346698 + 9 │ CT_battery 0.0 + 10 │ ME_battery 0.586507 + + + + +![svg](./files/t7_3p_csm_esr_mass.svg) + + + +Capacity Reserve Margin also has the possibiliy to be run with slack variables. + +## Minimum Capacity Requirement + +The last policy we'll talk about is [Minimum Capacity Requirement], which requires the grid to produce at least a certain amount of energy from renewables, as specified in the input file: + + +```julia +MinCapacity = CSV.read(joinpath(case,"policies/Minimum_capacity_requirement.csv"),DataFrame,missingstring="NA") +``` + + + +```@raw html +
3×3 DataFrame
RowMinCapReqConstraintConstraintDescriptionMin_MW
Int64String15Int64
11MA_PV5000
22CT_Wind10000
33All_Batteries6000
+``` + + +This policy ensures some renewable energy is used in the grid regardless of emissions constraints. If a fourth column containing price cap requirements exists (not shown above), that column is treated as a slack variable. + + +```julia +setup["CapacityReserveMargin"] = 0 +setup["EnergyShareRequirement"] = 0 +setup["MinCapReq"] = 1; +``` + + +```julia +inputs = GenX.load_inputs(setup, case) +EP9 = GenX.generate_model(setup,inputs,OPTIMIZER) +GenX.solve_model(EP9,setup) +``` + + Reading Input CSV Files + Network.csv Successfully Read! + Demand (load) data Successfully Read! + Fuels_data.csv Successfully Read! + + Summary of resources loaded into the model: + ------------------------------------------------------- + Resource type Number of resources + ======================================================= + Thermal 3 + VRE 4 + Storage 3 + ======================================================= + Total number of resources: 10 + ------------------------------------------------------- + Generators_variability.csv Successfully Read! + Validating time basis + Minimum_capacity_requirement.csv Successfully Read! + CSV Files Successfully Read In From example_systems/1_three_zones + Discharge Module + Non-served Energy Module + + + Thermal.csv Successfully Read. + Vre.csv Successfully Read. + Storage.csv Successfully Read. + Resource_energy_share_requirement.csv Successfully Read. + Resource_capacity_reserve_margin.csv Successfully Read. + Resource_minimum_capacity_requirement.csv Successfully Read. + + + Investment Discharge Module + Unit Commitment Module + Fuel Module + CO2 Module + Investment Transmission Module + Transmission Module + Dispatchable Resources Module + Storage Resources Module + Storage Investment Module + Storage Core Resources Module + Storage Resources with Symmetric Charge/Discharge Capacity Module + Thermal (Unit Commitment) Resources Module + Minimum Capacity Requirement Module + Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms + Presolving model + 118156 rows, 81204 cols, 422838 nonzeros + 110999 rows, 74047 cols, 423352 nonzeros + Presolve : Reductions: rows 110999(-42396); columns 74047(-46089); elements 423352(-47784) + Solving the presolved LP + IPX model has 110999 rows, 74047 columns and 423352 nonzeros + Input + Number of variables: 74047 + Number of free variables: 3696 + Number of constraints: 110999 + Number of equality constraints: 16867 + Number of matrix entries: 423352 + Matrix range: [4e-07, 1e+01] + RHS range: [7e-01, 2e+01] + Objective range: [1e-04, 4e+02] + Bounds range: [2e-03, 2e+01] + Preprocessing + Dualized model: no + Number of dense columns: 15 + Range of scaling factors: [5.00e-01, 1.00e+00] + IPX version 1.0 + Interior Point Solve + Iter P.res D.res P.obj D.obj mu Time + 0 2.34e+01 3.82e+02 3.30488922e+06 -5.33223155e+06 8.91e+03 0s + 1 1.39e+01 1.13e+02 -3.26111454e+06 -8.08059083e+06 4.78e+03 0s + 2 1.34e+01 8.13e+01 -3.30809039e+06 -2.14818717e+07 5.04e+03 0s + 3 5.10e+00 4.43e+01 -3.63727490e+06 -2.49670027e+07 2.64e+03 1s + Constructing starting basis... + 4 2.75e+00 1.66e+01 -1.55659888e+06 -2.27832740e+07 1.26e+03 3s + 5 2.41e+00 1.37e+01 -1.18396821e+06 -2.13578247e+07 1.11e+03 4s + 6 1.39e+00 4.43e+00 -4.94217397e+04 -1.44985483e+07 5.28e+02 6s + 7 6.13e-02 7.91e-01 8.34862433e+05 -6.93418288e+06 9.35e+01 7s + 8 3.76e-03 7.97e-02 4.24408301e+05 -1.09263439e+06 1.31e+01 8s + 9 2.88e-04 1.00e-02 1.65630895e+05 -1.75207574e+05 2.37e+00 9s + 10 6.57e-05 2.60e-03 6.19697724e+04 -5.01450660e+04 6.76e-01 10s + 11 3.78e-05 3.11e-04 4.59001513e+04 -1.47138829e+04 3.33e-01 10s + 12 2.79e-05 3.01e-04 5.07134714e+04 -1.34380343e+04 3.51e-01 11s + 13 1.85e-05 3.28e-05 3.85580458e+04 -4.46651304e+03 2.31e-01 12s + 14 1.19e-05 1.47e-05 3.43652640e+04 -5.85635923e+03 2.16e-01 13s + 15 5.83e-06 5.94e-06 2.04363590e+04 -8.78181923e+02 1.14e-01 13s + 16 3.62e-06 3.07e-06 1.57058304e+04 7.47097166e+02 8.02e-02 15s + 17 1.73e-06 1.98e-06 1.14474070e+04 1.51572830e+03 5.33e-02 18s + 18 7.85e-07 1.23e-06 8.92169592e+03 2.32540240e+03 3.54e-02 19s + 19 4.32e-07 8.80e-07 7.80843740e+03 2.81479174e+03 2.68e-02 20s + 20 2.62e-07 4.48e-07 7.20548085e+03 3.52684341e+03 1.97e-02 22s + 21 1.47e-07 2.24e-07 6.67664231e+03 4.07755176e+03 1.39e-02 25s + 22 6.82e-08 1.82e-07 6.25539980e+03 4.21836942e+03 1.09e-02 28s + 23 5.27e-08 1.49e-07 6.14225406e+03 4.35222081e+03 9.59e-03 30s + 24 5.23e-08 1.48e-07 6.19401540e+03 4.41443087e+03 9.54e-03 32s + 25 4.08e-08 1.37e-07 6.11156615e+03 4.46928744e+03 8.80e-03 34s + 26 2.62e-08 1.04e-07 5.99485482e+03 4.65688588e+03 7.17e-03 35s + 27 1.01e-08 5.40e-08 5.91238184e+03 4.88375941e+03 5.51e-03 36s + 28 9.25e-09 4.67e-08 5.88906267e+03 4.95194014e+03 5.02e-03 39s + 29 8.47e-09 4.18e-08 5.87830260e+03 4.97446884e+03 4.84e-03 42s + 30 2.90e-09 3.49e-08 5.71712195e+03 5.04256956e+03 3.61e-03 45s + 31 1.58e-09 1.80e-08 5.66248175e+03 5.22792362e+03 2.33e-03 50s + 32 9.36e-10 1.16e-08 5.62108661e+03 5.31620530e+03 1.63e-03 53s + 33 7.54e-10 9.50e-09 5.61131446e+03 5.34069905e+03 1.45e-03 56s + 34 3.64e-10 6.78e-09 5.58350503e+03 5.37914296e+03 1.09e-03 57s + 35 1.61e-10 4.60e-09 5.57381755e+03 5.40507612e+03 9.04e-04 58s + 36 9.58e-11 3.34e-09 5.55921197e+03 5.43192782e+03 6.82e-04 60s + 37 5.96e-11 1.90e-09 5.55589825e+03 5.45455261e+03 5.43e-04 62s + 38 3.27e-11 6.28e-10 5.54709869e+03 5.48816147e+03 3.16e-04 63s + 39 2.12e-11 4.02e-10 5.54216424e+03 5.49586924e+03 2.48e-04 64s + 40 1.40e-11 2.87e-10 5.53737841e+03 5.50195705e+03 1.90e-04 64s + 41 8.74e-12 7.64e-11 5.53451883e+03 5.51121430e+03 1.25e-04 65s + 42 4.45e-12 5.82e-11 5.53082515e+03 5.51293739e+03 9.58e-05 65s + 43 2.69e-12 4.91e-11 5.52895320e+03 5.51381040e+03 8.11e-05 66s + 44 1.49e-12 3.09e-11 5.52752865e+03 5.51632502e+03 6.00e-05 66s + 45 1.12e-12 2.18e-11 5.52678261e+03 5.51817779e+03 4.61e-05 66s + 46 9.73e-13 1.64e-11 5.52653183e+03 5.51873543e+03 4.18e-05 67s + 47 6.75e-13 1.09e-11 5.52588469e+03 5.51976155e+03 3.28e-05 67s + 48 5.12e-13 7.28e-12 5.52538622e+03 5.52088538e+03 2.41e-05 68s + 49 3.62e-13 7.28e-12 5.52505789e+03 5.52116706e+03 2.08e-05 68s + 50 1.21e-13 1.46e-11 5.52401306e+03 5.52162795e+03 1.28e-05 68s + 51 7.82e-14 7.28e-12 5.52389039e+03 5.52195984e+03 1.03e-05 69s + 52 4.97e-14 7.28e-12 5.52369651e+03 5.52214739e+03 8.30e-06 69s + 53 2.13e-14 7.28e-12 5.52355424e+03 5.52243013e+03 6.02e-06 69s + 54 2.13e-14 7.28e-12 5.52339956e+03 5.52263709e+03 4.08e-06 70s + 55 2.13e-14 7.28e-12 5.52340007e+03 5.52266984e+03 3.91e-06 70s + 56 2.84e-14 7.28e-12 5.52339771e+03 5.52268533e+03 3.82e-06 70s + 57 2.13e-14 7.28e-12 5.52333480e+03 5.52273001e+03 3.24e-06 71s + 58 2.13e-14 7.28e-12 5.52333465e+03 5.52276044e+03 3.08e-06 71s + 59 2.13e-14 7.28e-12 5.52331312e+03 5.52282782e+03 2.60e-06 71s + 60 2.13e-14 7.28e-12 5.52329636e+03 5.52284551e+03 2.42e-06 72s + 61 2.13e-14 7.28e-12 5.52328626e+03 5.52292698e+03 1.92e-06 72s + 62 2.13e-14 7.28e-12 5.52328402e+03 5.52294138e+03 1.84e-06 72s + 63 2.13e-14 1.92e-13 5.52322974e+03 5.52307280e+03 8.41e-07 73s + 64 2.84e-14 7.28e-12 5.52320719e+03 5.52313866e+03 3.67e-07 73s + 65 2.84e-14 1.17e-13 5.52319028e+03 5.52316431e+03 1.39e-07 73s + 66 2.13e-14 1.82e-12 5.52318739e+03 5.52317535e+03 6.45e-08 73s + 67 2.13e-14 4.55e-13 5.52318545e+03 5.52317686e+03 4.60e-08 74s + 68 2.13e-14 7.28e-12 5.52318141e+03 5.52317952e+03 1.01e-08 74s + 69 2.84e-14 7.28e-12 5.52318051e+03 5.52318024e+03 1.41e-09 74s + 70* 2.13e-14 6.90e-12 5.52318041e+03 5.52318036e+03 2.41e-10 74s + 71* 2.84e-14 4.07e-12 5.52318040e+03 5.52318040e+03 3.09e-11 75s + 72* 3.55e-14 5.53e-12 5.52318040e+03 5.52318040e+03 5.06e-12 75s + 73* 4.26e-14 7.88e-12 5.52318040e+03 5.52318040e+03 6.38e-13 75s + 74* 3.55e-14 2.81e-12 5.52318040e+03 5.52318040e+03 1.07e-13 75s + Running crossover as requested + Primal residual before push phase: 2.03e-08 + Dual residual before push phase: 5.16e-09 + Number of dual pushes required: 26618 + Number of primal pushes required: 2605 + Summary + Runtime: 75.26s + Status interior point solve: optimal + Status crossover: optimal + objective value: 5.52318040e+03 + interior solution primal residual (abs/rel): 7.73e-11 / 4.73e-12 + interior solution dual residual (abs/rel): 4.28e-10 / 1.07e-12 + interior solution objective gap (abs/rel): 9.06e-09 / 1.64e-12 + basic solution primal infeasibility: 6.22e-15 + basic solution dual infeasibility: 3.25e-15 + Ipx: IPM optimal + Ipx: Crossover optimal + Solving the original LP from the solution after postsolve + Model status : Optimal + IPM iterations: 74 + Crossover iterations: 2077 + Objective value : 5.5231804025e+03 + HiGHS run time : 75.47 + LP solved for primal + + + + + + (A JuMP Model + Minimization problem with: + Variables: 120136 + Objective function type: AffExpr + `AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 35112 constraints + `AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 20334 constraints + `AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 97949 constraints + `VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 1 constraint + `VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 116439 constraints + Model mode: AUTOMATIC + CachingOptimizer state: ATTACHED_OPTIMIZER + Solver name: HiGHS + Names registered in the model: FuelCalculationCommit_single, cFuelCalculation_single, cMaxCap, cMaxCapEnergy, cMaxCapEnergyDuration, cMaxFlow_in, cMaxFlow_out, cMaxLineReinforcement, cMaxNSE, cMaxRetCommit, cMaxRetEnergy, cMaxRetNoCommit, cMinCap, cMinCapEnergy, cMinCapEnergyDuration, cNSEPerSeg, cPowerBalance, cSoCBalInterior, cSoCBalStart, cStartFuel_single, cTAuxLimit, cTAuxSum, cTLoss, cZoneMinCapReq, eAvail_Trans_Cap, eCFix, eCFixEnergy, eCFuelOut, eCFuelStart, eCNSE, eCStart, eCVar_in, eCVar_out, eELOSS, eELOSSByZone, eEmissionsByPlant, eEmissionsByZone, eExistingCap, eExistingCapEnergy, eFuelConsumption, eFuelConsumptionYear, eFuelConsumption_single, eGenerationByThermAll, eGenerationByVRE, eGenerationByZone, eLosses_By_Zone, eMinCapRes, eMinCapResInvest, eNet_Export_Flows, eObj, ePlantCFuelOut, ePlantCFuelStart, ePlantFuel_generation, ePlantFuel_start, ePowerBalance, ePowerBalanceDisp, ePowerBalanceLossesByZone, ePowerBalanceNetExportFlows, ePowerBalanceNse, ePowerBalanceStor, ePowerBalanceThermCommit, eStartFuel, eTotalCFix, eTotalCFixEnergy, eTotalCFuelOut, eTotalCFuelStart, eTotalCNSE, eTotalCNSET, eTotalCNSETS, eTotalCNetworkExp, eTotalCStart, eTotalCStartT, eTotalCVarIn, eTotalCVarInT, eTotalCVarOut, eTotalCVarOutT, eTotalCap, eTotalCapEnergy, eTransMax, eZonalCFuelOut, eZonalCFuelStart, vCAP, vCAPENERGY, vCHARGE, vCOMMIT, vFLOW, vFuel, vNEW_TRANS_CAP, vNSE, vP, vRETCAP, vRETCAPENERGY, vS, vSHUT, vSTART, vStartFuel, vTAUX_NEG, vTAUX_POS, vTLOSS, vZERO, 75.7959840297699) + + + + +```julia +totCap9 = value.(EP9[:eTotalCap]) + +totCapB9 = [totCap9[1] + totCap9[2] + totCap9[3], totCap9[4] + totCap9[6], + totCap9[5] + totCap9[7], totCap9[8] + totCap9[9] + totCap9[10]] + +println(DataFrame([RT totCap9],["Resource Type","Total Capacity"])) +println(" ") + +G9 = groupedbar(transpose(totCapB9), bar_position = :stack, bar_width=.7,size=(500,450), xticks=[ ],ylabel="GW", + labels=["Natural Gas" "Solar" "Wind" "Battery"],legend=false,color=colors, + title="Minimum Capacity Requirement \n Obj Val: $(round(objective_value(EP9),digits=6))",ylabelfontsize=8) + +plot(G9,G8,G7,G2,size=(900,900), titlefontsize=8,layout=(2,2)) +``` + + 10×2 DataFrame + Row │ Resource Type Total Capacity + │ Any Any + ─────┼─────────────────────────────────────────────── + 1 │ MA_natural_gas_combined_cycle 9.47511 + 2 │ CT_natural_gas_combined_cycle 8.40465 + 3 │ ME_natural_gas_combined_cycle 0.0 + 4 │ MA_solar_pv 5.0 + 5 │ CT_onshore_wind 10.0 + 6 │ CT_solar_pv 0.0 + 7 │ ME_onshore_wind 0.0 + 8 │ MA_battery 0.128507 + 9 │ CT_battery 4.28065 + 10 │ ME_battery 1.59085 + + +![svg](./files/t7_4p_mcr_csm_esr_mass.svg) + + +## All Together + +`1_three_zones` has defaults of `CO2Cap = 2` and `MinCapReq = 1`. To see how everything comes together, let's add ESR and CRM in as well: + + +```julia +setup["MinCapReq"] = 1 +setup["CO2Cap"] = 2 +setup["EnergyShareRequirement"] = 1 +setup["CapacityReserveMargin"] = 1; +``` + + +```julia +inputs = GenX.load_inputs(setup, case) +EP10 = GenX.generate_model(setup,inputs,OPTIMIZER) +GenX.solve_model(EP10,setup) +``` + + Reading Input CSV Files + Network.csv Successfully Read! + Demand (load) data Successfully Read! + Fuels_data.csv Successfully Read! + + Summary of resources loaded into the model: + ------------------------------------------------------- + Resource type Number of resources + ======================================================= + Thermal 3 + VRE 4 + Storage 3 + ======================================================= + Total number of resources: 10 + ------------------------------------------------------- + Generators_variability.csv Successfully Read! + Validating time basis + Capacity_reserve_margin.csv Successfully Read! + Minimum_capacity_requirement.csv Successfully Read! + Energy_share_requirement.csv Successfully Read! + CO2_cap.csv Successfully Read! + CSV Files Successfully Read In From example_systems/1_three_zones + Discharge Module + + + Thermal.csv Successfully Read. + Vre.csv Successfully Read. + Storage.csv Successfully Read. + Resource_energy_share_requirement.csv Successfully Read. + Resource_capacity_reserve_margin.csv Successfully Read. + Resource_minimum_capacity_requirement.csv Successfully Read. + + + Non-served Energy Module + Investment Discharge Module + Unit Commitment Module + Fuel Module + CO2 Module + Investment Transmission Module + Transmission Module + Dispatchable Resources Module + Storage Resources Module + Storage Investment Module + Storage Core Resources Module + Storage Resources with Symmetric Charge/Discharge Capacity Module + Thermal (Unit Commitment) Resources Module + CO2 Policies Module + Energy Share Requirement Policies Module + Capacity Reserve Margin Policies Module + Minimum Capacity Requirement Module + Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms + Presolving model + 131097 rows, 97836 cols, 583245 nonzeros + 123901 rows, 90641 cols, 586406 nonzeros + Presolve : Reductions: rows 123901(-42435); columns 90641(-46130); elements 586406(-49082) + Solving the presolved LP + IPX model has 123901 rows, 90641 columns and 586406 nonzeros + Input + Number of variables: 90641 + Number of free variables: 3696 + Number of constraints: 123901 + Number of equality constraints: 22373 + Number of matrix entries: 586406 + Matrix range: [4e-07, 1e+01] + RHS range: [7e-01, 5e+04] + Objective range: [1e-04, 4e+02] + Bounds range: [2e-03, 2e+01] + Preprocessing + Dualized model: no + Number of dense columns: 15 + Range of scaling factors: [5.00e-01, 4.00e+00] + IPX version 1.0 + Interior Point Solve + Iter P.res D.res P.obj D.obj mu Time + 0 5.30e+03 3.22e+02 3.13997460e+06 -4.50780216e+06 1.69e+06 0s + 1 3.53e+03 1.84e+02 -3.86867578e+08 -1.04799903e+07 1.20e+06 0s + 2 2.99e+03 1.79e+02 -4.64684777e+08 -1.23686026e+07 1.12e+06 1s + Constructing starting basis... + 3 2.03e+03 1.48e+02 -2.85325444e+09 -1.06915573e+07 9.68e+05 3s + 4 1.45e+03 5.36e+01 -2.20472171e+09 -2.15853094e+07 5.20e+05 6s + 5 5.72e+02 2.55e+01 -7.34160531e+08 -2.85605099e+07 2.70e+05 8s + 6 1.52e+02 9.55e+00 -6.47264055e+07 -2.78488489e+07 9.45e+04 10s + 7 2.02e+01 1.79e+00 2.31123203e+07 -2.71227296e+07 1.70e+04 14s + 8 1.25e+00 1.73e-01 2.78294575e+07 -2.15984056e+07 1.70e+03 17s + 9 6.87e-01 1.01e-01 2.46933049e+07 -1.61205280e+07 1.04e+03 20s + 10 3.29e-01 6.17e-02 2.40546197e+07 -1.56062552e+07 7.59e+02 22s + 11 1.55e-01 3.97e-02 2.03010629e+07 -1.19472220e+07 4.90e+02 24s + 12 6.17e-02 2.00e-02 1.58293799e+07 -7.68786756e+06 2.58e+02 26s + 13 3.21e-02 7.58e-03 1.16341185e+07 -3.68819752e+06 1.19e+02 28s + 14 5.73e-03 2.53e-03 4.99822439e+06 -1.84838835e+06 4.06e+01 31s + 15 2.04e-04 2.53e-09 9.67831330e+05 -2.16110538e+05 5.64e+00 33s + 16 6.41e-05 6.62e-10 3.11314108e+05 -5.67635644e+04 1.75e+00 37s + 17 1.87e-05 1.78e-10 1.02250933e+05 -1.96360216e+04 5.79e-01 39s + 18 9.31e-06 9.91e-11 7.06100466e+04 -1.48397467e+04 4.06e-01 40s + 19 3.70e-06 5.73e-11 3.96082759e+04 -8.05455770e+03 2.26e-01 41s + 20 3.28e-06 4.27e-11 3.82171130e+04 -6.25733365e+03 2.11e-01 43s + 21 1.59e-06 2.73e-11 2.68362068e+04 -2.39421912e+03 1.39e-01 44s + 22 1.15e-06 2.36e-11 2.56652324e+04 -1.92773607e+03 1.31e-01 48s + 23 6.03e-07 1.36e-11 2.08387443e+04 9.30026259e+02 9.45e-02 50s + 24 3.68e-07 8.19e-12 1.81640559e+04 2.92313732e+03 7.24e-02 52s + 25 3.10e-07 5.91e-12 1.72489969e+04 3.83317942e+03 6.37e-02 56s + 26 2.39e-07 4.09e-12 1.61203457e+04 4.88465026e+03 5.33e-02 59s + 27 1.73e-07 3.64e-12 1.48295799e+04 5.55407232e+03 4.40e-02 61s + 28 1.44e-07 2.73e-12 1.42754988e+04 6.29135803e+03 3.79e-02 64s + 29 8.49e-08 1.14e-12 1.28069756e+04 7.07462835e+03 2.72e-02 67s + 30 7.31e-08 9.09e-13 1.26298795e+04 7.31806811e+03 2.52e-02 71s + 31 5.30e-08 9.09e-13 1.20848925e+04 7.73537437e+03 2.06e-02 73s + 32 4.21e-08 1.82e-12 1.18122159e+04 8.13586949e+03 1.75e-02 75s + 33 2.39e-08 9.09e-13 1.14149641e+04 8.30558496e+03 1.48e-02 77s + 34 1.60e-08 4.55e-13 1.10801208e+04 8.63533586e+03 1.16e-02 79s + 35 1.30e-08 3.69e-13 1.09411593e+04 8.83346002e+03 1.00e-02 83s + 36 8.91e-09 4.83e-13 1.07431756e+04 8.89580519e+03 8.77e-03 85s + 37 5.99e-09 2.27e-13 1.05961030e+04 9.02764246e+03 7.45e-03 88s + 38 4.85e-09 3.13e-13 1.05383085e+04 9.05248333e+03 7.05e-03 89s + 39 4.45e-09 3.41e-13 1.05136942e+04 9.13561353e+03 6.54e-03 91s + 40 4.23e-09 1.99e-13 1.04966448e+04 9.18695690e+03 6.22e-03 93s + 41 2.40e-09 6.25e-13 1.03049603e+04 9.27134867e+03 4.91e-03 94s + 42 1.47e-09 4.55e-13 1.02280746e+04 9.41441297e+03 3.86e-03 96s + 43 1.03e-09 2.27e-13 1.01746657e+04 9.47565695e+03 3.32e-03 99s + 44 8.01e-10 3.41e-13 1.01513061e+04 9.48693587e+03 3.15e-03 101s + 45 5.03e-10 2.84e-13 1.00966206e+04 9.52771181e+03 2.70e-03 102s + 46 3.06e-10 2.84e-13 1.00688557e+04 9.57071855e+03 2.36e-03 103s + 47 2.44e-10 5.40e-13 1.00557587e+04 9.57656156e+03 2.27e-03 105s + 48 1.89e-10 1.81e-13 1.00328512e+04 9.61968546e+03 1.96e-03 106s + 49 1.64e-10 5.97e-13 1.00260933e+04 9.63360286e+03 1.86e-03 107s + 50 1.86e-10 2.27e-13 9.99901149e+03 9.65578822e+03 1.63e-03 108s + 51 8.00e-11 8.81e-13 9.99387541e+03 9.67539200e+03 1.51e-03 109s + 52 8.00e-11 2.56e-13 9.99333474e+03 9.68646833e+03 1.46e-03 110s + 53 6.18e-11 3.98e-13 9.98008312e+03 9.70915205e+03 1.29e-03 110s + 54 8.00e-11 2.27e-13 9.96536538e+03 9.73027009e+03 1.12e-03 111s + 55 5.46e-11 5.68e-13 9.94153050e+03 9.78635740e+03 7.37e-04 112s + 56 2.95e-11 3.13e-13 9.93239666e+03 9.79987086e+03 6.29e-04 113s + 57 4.37e-11 6.25e-13 9.92881475e+03 9.81037466e+03 5.62e-04 114s + 58 9.09e-11 2.56e-13 9.92687487e+03 9.81524886e+03 5.30e-04 115s + 59 8.37e-11 3.13e-13 9.91943642e+03 9.82987624e+03 4.25e-04 116s + 60 2.94e-11 7.39e-13 9.90937510e+03 9.84468538e+03 3.07e-04 117s + 61 1.09e-11 1.99e-13 9.90384575e+03 9.84900802e+03 2.60e-04 118s + 62 4.73e-11 1.99e-13 9.89878174e+03 9.86141678e+03 1.77e-04 119s + 63 1.43e-11 2.84e-13 9.89460308e+03 9.86618770e+03 1.35e-04 120s + 64 5.21e-11 1.99e-13 9.89193935e+03 9.86936430e+03 1.07e-04 120s + 65 4.37e-11 7.11e-13 9.89058874e+03 9.87123409e+03 9.19e-05 121s + 66 1.06e-10 1.42e-13 9.88773562e+03 9.87325788e+03 6.87e-05 122s + 67 2.18e-11 4.55e-13 9.88672573e+03 9.87498544e+03 5.57e-05 123s + 68 6.55e-11 5.68e-13 9.88612597e+03 9.87857947e+03 3.58e-05 124s + 69 1.75e-10 4.26e-13 9.88493177e+03 9.87912210e+03 2.76e-05 124s + 70 3.96e-10 2.27e-13 9.88436495e+03 9.88063726e+03 1.77e-05 125s + 71 2.09e-10 3.13e-13 9.88433519e+03 9.88080074e+03 1.68e-05 126s + 72 1.12e-10 6.82e-13 9.88391819e+03 9.88129195e+03 1.25e-05 126s + 73 4.78e-10 8.24e-13 9.88340973e+03 9.88203826e+03 6.51e-06 127s + 74 2.83e-10 3.13e-13 9.88340067e+03 9.88230236e+03 5.21e-06 128s + 75 3.21e-10 1.21e-13 9.88336541e+03 9.88238526e+03 4.65e-06 129s + 76 1.84e-10 2.56e-13 9.88330624e+03 9.88266293e+03 3.05e-06 129s + 77 3.08e-10 3.41e-13 9.88330730e+03 9.88300302e+03 1.44e-06 130s + 78 3.40e-10 1.34e-12 9.88324655e+03 9.88310691e+03 6.63e-07 131s + 79 5.61e-10 6.22e-13 9.88321826e+03 9.88313132e+03 4.13e-07 132s + 80 1.33e-10 1.04e-12 9.88320942e+03 9.88313520e+03 3.52e-07 132s + 81 6.55e-10 1.40e-12 9.88319429e+03 9.88314640e+03 2.27e-07 133s + 82 3.26e-10 7.11e-13 9.88318935e+03 9.88315310e+03 1.72e-07 134s + 83 3.31e-10 1.55e-12 9.88318186e+03 9.88315734e+03 1.16e-07 134s + 84 1.07e-09 3.55e-12 9.88317725e+03 9.88316598e+03 5.35e-08 135s + 85 4.30e-10 3.68e-12 9.88317303e+03 9.88316877e+03 2.03e-08 135s + 86 6.50e-10 4.82e-12 9.88317188e+03 9.88317115e+03 3.46e-09 136s + 87* 4.99e-10 5.93e-12 9.88317181e+03 9.88317173e+03 3.40e-10 137s + 88* 1.01e-09 8.27e-12 9.88317178e+03 9.88317177e+03 5.01e-11 138s + 89* 4.77e-10 1.42e-11 9.88317178e+03 9.88317178e+03 8.36e-12 140s + Running crossover as requested + Primal residual before push phase: 3.57e-05 + Dual residual before push phase: 2.51e-06 + Number of dual pushes required: 30806 + Number of primal pushes required: 4202 + Summary + Runtime: 144.53s + Status interior point solve: optimal + Status crossover: optimal + objective value: 9.88317178e+03 + interior solution primal residual (abs/rel): 3.06e-08 / 6.40e-13 + interior solution dual residual (abs/rel): 7.13e-09 / 1.77e-11 + interior solution objective gap (abs/rel): 1.66e-06 / 1.68e-10 + basic solution primal infeasibility: 3.19e-12 + basic solution dual infeasibility: 6.25e-08 + Ipx: IPM optimal + Ipx: Crossover optimal + Solving the original LP from the solution after postsolve + Model status : Optimal + IPM iterations: 89 + Crossover iterations: 3032 + Objective value : 9.8831717769e+03 + HiGHS run time : 144.82 + LP solved for primal + + + + + + (A JuMP Model + Minimization problem with: + Variables: 136771 + Objective function type: AffExpr + `AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 40656 constraints + `AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 27728 constraints + `AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 97952 constraints + `VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 4 constraints + `VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 133071 constraints + Model mode: AUTOMATIC + CachingOptimizer state: ATTACHED_OPTIMIZER + Solver name: HiGHS + Names registered in the model: FuelCalculationCommit_single, cCO2Emissions_systemwide, cCapacityResMargin, cESRShare, cFuelCalculation_single, cMaxCap, cMaxCapEnergy, cMaxCapEnergyDuration, cMaxFlow_in, cMaxFlow_out, cMaxLineReinforcement, cMaxNSE, cMaxRetCommit, cMaxRetEnergy, cMaxRetNoCommit, cMinCap, cMinCapEnergy, cMinCapEnergyDuration, cNSEPerSeg, cPowerBalance, cSOCMinCapRes, cSoCBalInterior, cSoCBalStart, cStartFuel_single, cTAuxLimit, cTAuxSum, cTLoss, cVSoCBalInterior, cVSoCBalStart, cZoneMinCapReq, eAvail_Trans_Cap, eCFix, eCFixEnergy, eCFuelOut, eCFuelStart, eCNSE, eCStart, eCVar_in, eCVar_in_virtual, eCVar_out, eCVar_out_virtual, eCapResMarBalance, eCapResMarBalanceNSE, eCapResMarBalanceStor, eCapResMarBalanceStorVirtual, eCapResMarBalanceThermal, eCapResMarBalanceTrans, eCapResMarBalanceVRE, eELOSS, eELOSSByZone, eESR, eESRDischarge, eEmissionsByPlant, eEmissionsByZone, eExistingCap, eExistingCapEnergy, eFuelConsumption, eFuelConsumptionYear, eFuelConsumption_single, eGenerationByThermAll, eGenerationByVRE, eGenerationByZone, eLosses_By_Zone, eMinCapRes, eMinCapResInvest, eNet_Export_Flows, eObj, ePlantCFuelOut, ePlantCFuelStart, ePlantFuel_generation, ePlantFuel_start, ePowerBalance, ePowerBalanceDisp, ePowerBalanceLossesByZone, ePowerBalanceNetExportFlows, ePowerBalanceNse, ePowerBalanceStor, ePowerBalanceThermCommit, eStartFuel, eTotalCFix, eTotalCFixEnergy, eTotalCFuelOut, eTotalCFuelStart, eTotalCNSE, eTotalCNSET, eTotalCNSETS, eTotalCNetworkExp, eTotalCStart, eTotalCStartT, eTotalCVarIn, eTotalCVarInT, eTotalCVarInT_virtual, eTotalCVarIn_virtual, eTotalCVarOut, eTotalCVarOutT, eTotalCVarOutT_virtual, eTotalCVarOut_virtual, eTotalCap, eTotalCapEnergy, eTransMax, eZonalCFuelOut, eZonalCFuelStart, vCAP, vCAPENERGY, vCAPRES_charge, vCAPRES_discharge, vCAPRES_socinreserve, vCHARGE, vCO2Cap_slack, vCOMMIT, vFLOW, vFuel, vNEW_TRANS_CAP, vNSE, vP, vRETCAP, vRETCAPENERGY, vS, vSHUT, vSTART, vStartFuel, vTAUX_NEG, vTAUX_POS, vTLOSS, vZERO, 145.17469787597656) + + + + +```julia +totCap10 = value.(EP10[:eTotalCap]) + +totCapB10 = [totCap10[1] + totCap10[2] + totCap10[3], totCap10[4] + totCap10[6], + totCap10[5] + totCap10[7], totCap10[8] + totCap10[9] + totCap10[10]] + +println(DataFrame([RT totCap10],["Resource Type","Total Capacity"])) +println(" ") + +G10 = groupedbar(transpose(totCapB10), bar_position = :stack, bar_width=.7,size=(500,450), xticks=[ ],ylabel="GW", + labels=["Natural Gas" "Solar" "Wind" "Battery"],color=colors, + title="MCR + ESR + CSM + CO2 Load Cap \n Obj Val: $(round(objective_value(EP10),digits=6))",ylabelfontsize=8) + +plot(G10, titlefontsize=8) +``` + + 10×2 DataFrame + Row │ Resource Type Total Capacity + │ Any Any + ─────┼─────────────────────────────────────────────── + 1 │ MA_natural_gas_combined_cycle 8.51325 + 2 │ CT_natural_gas_combined_cycle 5.43676 + 3 │ ME_natural_gas_combined_cycle 0.552834 + 4 │ MA_solar_pv 17.9707 + 5 │ CT_onshore_wind 12.5249 + 6 │ CT_solar_pv 14.9714 + 7 │ ME_onshore_wind 11.4099 + 8 │ MA_battery 4.55918 + 9 │ CT_battery 4.08421 + 10 │ ME_battery 0.764153 + + + +![svg](./files/t7_4p_mcr_csm_esr_mass.svg) + + +```julia + +``` diff --git a/docs/src/Tutorials/Tutorial_8_outputs.md b/docs/src/Tutorials/Tutorial_8_outputs.md new file mode 100644 index 0000000000..c1b6f8ee19 --- /dev/null +++ b/docs/src/Tutorials/Tutorial_8_outputs.md @@ -0,0 +1,875 @@ +# Tutorial 8: Outputs + +[Interactive Notebook of the tutorial](https://github.com/GenXProject/GenX-Tutorials/blob/main/Tutorials/Tutorial_8_Outputs.ipynb) + +Once an instance of GenX is run, a series of csv files describing the outputs are created and put in to a folder titled `results`. This folder will appear automatically in the case folder. For a detailed description of all files, see the [GenX Outputs](@ref) documentation. This tutorial goes over key files in `results` and visualizes some of the outputs. + +### Table of Contents +* [Power](#power) +* [Cost and Revenue](#cost) +* [Emmissions](#emms) + +Let's get things started by running an instance of GenX using `Run.jl`. You can skip this step if you already have a results folder you would like to analyze. + + +```julia +using DataFrames +using CSV +using YAML +using GraphRecipes +using Plots +using PlotlyJS +using VegaLite +using StatsPlots +``` + + +```julia +case = joinpath("example_systems/1_three_zones"); +``` + + +```julia +include("example_systems/1_three_zones/Run.jl") +``` + + Configuring Settings + Clustering Time Series Data (Grouped)... + Reading Input CSV Files + Network.csv Successfully Read! + Demand (load) data Successfully Read! + Fuels_data.csv Successfully Read! + + + Thermal.csv Successfully Read. + Vre.csv Successfully Read. + Storage.csv Successfully Read. + Resource_energy_share_requirement.csv Successfully Read. + Resource_capacity_reserve_margin.csv Successfully Read. + Resource_minimum_capacity_requirement.csv Successfully Read. + + + + Summary of resources loaded into the model: + ------------------------------------------------------- + Resource type Number of resources + ======================================================= + Thermal 3 + VRE 4 + Storage 3 + ======================================================= + Total number of resources: 10 + ------------------------------------------------------- + Generators_variability.csv Successfully Read! + Validating time basis + Minimum_capacity_requirement.csv Successfully Read! + CO2_cap.csv Successfully Read! + CSV Files Successfully Read In From /Users/mayamutic/Desktop/GenX-Tutorials/Tutorials/example_systems/1_three_zones + Configuring Solver + Loading Inputs + Reading Input CSV Files + Network.csv Successfully Read! + Demand (load) data Successfully Read! + Fuels_data.csv Successfully Read! + + Summary of resources loaded into the model: + ------------------------------------------------------- + Resource type Number of resources + ======================================================= + Thermal 3 + VRE 4 + Storage 3 + ======================================================= + Total number of resources: 10 + ------------------------------------------------------- + Generators_variability.csv Successfully Read! + Validating time basis + Minimum_capacity_requirement.csv Successfully Read! + CO2_cap.csv Successfully Read! + CSV Files Successfully Read In From /Users/mayamutic/Desktop/GenX-Tutorials/Tutorials/example_systems/1_three_zones + Generating the Optimization Model + + + Thermal.csv Successfully Read. + Vre.csv Successfully Read. + Storage.csv Successfully Read. + Resource_energy_share_requirement.csv Successfully Read. + Resource_capacity_reserve_margin.csv Successfully Read. + Resource_minimum_capacity_requirement.csv Successfully Read. + + Discharge Module + Non-served Energy Module + Investment Discharge Module + Unit Commitment Module + Fuel Module + CO2 Module + Investment Transmission Module + Transmission Module + Dispatchable Resources Module + Storage Resources Module + Storage Investment Module + Storage Core Resources Module + Storage Resources with Symmetric Charge/Discharge Capacity Module + Thermal (Unit Commitment) Resources Module + CO2 Policies Module + Minimum Capacity Requirement Module + Time elapsed for model building is + 5.887781667 + Solving Model + Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms + Presolving model + 118038 rows, 81083 cols, 466827 nonzeros + 110619 rows, 73664 cols, 468369 nonzeros + Presolve : Reductions: rows 110619(-42779); columns 73664(-46475); elements 468369(-47001) + Solving the presolved LP + IPX model has 110619 rows, 73664 columns and 468369 nonzeros + Input + Number of variables: 73664 + Number of free variables: 3696 + Number of constraints: 110619 + Number of equality constraints: 16605 + Number of matrix entries: 468369 + Matrix range: [4e-07, 1e+01] + RHS range: [8e-01, 4e+03] + Objective range: [1e-04, 7e+02] + Bounds range: [2e-03, 2e+01] + Preprocessing + Dualized model: no + Number of dense columns: 15 + Range of scaling factors: [5.00e-01, 8.00e+00] + IPX version 1.0 + Interior Point Solve + Iter P.res D.res P.obj D.obj mu Time + 0 1.82e+02 5.20e+02 2.74110935e+06 -9.20003322e+06 9.39e+04 0s + 1 1.19e+02 1.85e+02 -5.15491323e+07 -1.56990646e+07 5.70e+04 0s + 2 1.16e+02 1.50e+02 -5.24235846e+07 -4.43639951e+07 6.32e+04 1s + 3 3.82e+01 7.90e+01 -3.78240082e+07 -4.91067811e+07 2.48e+04 1s + Constructing starting basis... + 4 1.50e+01 4.69e+01 -1.55669921e+07 -5.24473820e+07 1.26e+04 4s + 5 1.08e+01 3.68e+01 -1.04270740e+07 -5.34777833e+07 1.03e+04 5s + 6 2.02e+00 1.32e+01 1.78253836e+06 -4.42778415e+07 3.28e+03 6s + 7 2.13e-01 1.56e+00 2.27050184e+06 -1.69980996e+07 4.42e+02 8s + 8 1.99e-02 3.66e-01 1.38286053e+06 -4.54007601e+06 1.02e+02 9s + 9 7.25e-03 1.59e-01 1.04876462e+06 -2.67941780e+06 5.28e+01 10s + 10 5.00e-03 1.18e-01 9.54695852e+05 -2.19740360e+06 4.20e+01 11s + 11 2.55e-03 8.92e-02 9.62825668e+05 -2.02235540e+06 3.86e+01 12s + 12 1.23e-03 5.57e-02 9.06154486e+05 -1.61397732e+06 2.88e+01 13s + 13 8.25e-04 4.55e-02 8.50982220e+05 -1.42601127e+06 2.47e+01 14s + 14 4.67e-04 2.99e-02 7.87488727e+05 -1.12886839e+06 1.86e+01 15s + 15 2.66e-04 2.09e-02 7.13648088e+05 -9.18336741e+05 1.44e+01 16s + 16 1.08e-04 1.25e-02 5.49221416e+05 -6.47879126e+05 9.37e+00 17s + 17 2.48e-05 7.94e-03 3.46061560e+05 -4.61304054e+05 5.71e+00 19s + 18 1.01e-05 3.42e-03 1.83821789e+05 -2.00914905e+05 2.43e+00 20s + 19 4.07e-06 3.05e-03 8.92521427e+04 -1.79940971e+05 1.62e+00 21s + 20 2.32e-06 6.40e-04 7.78040127e+04 -5.60566929e+04 7.50e-01 22s + 21 8.58e-07 2.28e-04 4.31894440e+04 -2.23356614e+04 3.58e-01 23s + 22 6.57e-07 1.54e-04 4.00530649e+04 -1.69523138e+04 3.10e-01 24s + 23 3.28e-07 9.35e-05 2.85728271e+04 -9.35216394e+03 2.05e-01 25s + 24 3.19e-07 8.61e-05 2.84621914e+04 -8.84896370e+03 2.02e-01 27s + 25 1.88e-07 7.27e-05 2.38512793e+04 -7.05855824e+03 1.67e-01 28s + 26 1.25e-07 4.25e-05 2.06483772e+04 -2.29444044e+03 1.24e-01 29s + 27 8.52e-08 2.94e-05 1.93840344e+04 -7.43312356e+02 1.08e-01 30s + 28 4.26e-08 1.57e-05 1.55476712e+04 2.51649304e+03 7.01e-02 32s + 29 3.28e-08 1.03e-05 1.48244443e+04 3.71569832e+03 5.97e-02 34s + 30 1.97e-08 5.79e-06 1.34432901e+04 5.04894425e+03 4.51e-02 36s + 31 1.60e-08 4.11e-06 1.29661877e+04 5.70523948e+03 3.90e-02 40s + 32 1.29e-08 2.50e-06 1.25046561e+04 6.46897465e+03 3.24e-02 43s + 33 1.10e-08 1.77e-06 1.21681482e+04 6.95806253e+03 2.80e-02 45s + 34 9.03e-09 1.20e-06 1.17942632e+04 7.37735035e+03 2.37e-02 47s + 35 8.36e-09 8.75e-07 1.16689507e+04 7.61101800e+03 2.18e-02 50s + 36 5.05e-09 7.46e-07 1.09362653e+04 7.76380519e+03 1.70e-02 51s + 37 2.31e-09 4.73e-07 1.04305053e+04 8.02182477e+03 1.29e-02 53s + 38 1.54e-09 3.37e-07 1.01805357e+04 8.29224222e+03 1.01e-02 54s + 39 1.40e-09 2.47e-07 1.01569154e+04 8.40516136e+03 9.41e-03 57s + 40 1.32e-09 2.29e-07 1.01417025e+04 8.43289860e+03 9.18e-03 61s + 41 1.30e-09 1.85e-07 1.01370889e+04 8.50324712e+03 8.78e-03 62s + 42 1.09e-09 1.37e-07 1.00815866e+04 8.60006398e+03 7.96e-03 63s + 43 8.94e-10 1.09e-07 1.00184156e+04 8.66341527e+03 7.28e-03 65s + 44 7.15e-10 7.94e-08 9.96247094e+03 8.73797483e+03 6.58e-03 66s + 45 3.38e-10 5.48e-08 9.81246478e+03 8.82514229e+03 5.30e-03 67s + 46 1.96e-10 3.88e-08 9.73048449e+03 8.91021222e+03 4.41e-03 68s + 47 1.58e-10 3.09e-08 9.70120639e+03 8.96100550e+03 3.98e-03 69s + 48 8.73e-11 1.87e-08 9.63351889e+03 9.05587884e+03 3.10e-03 70s + 49 4.53e-11 8.50e-09 9.58546144e+03 9.14690441e+03 2.36e-03 72s + 50 3.66e-11 4.10e-09 9.56746403e+03 9.21860822e+03 1.87e-03 73s + 51 2.08e-11 3.03e-09 9.52048699e+03 9.24367874e+03 1.49e-03 76s + 52 1.09e-11 2.43e-09 9.49319901e+03 9.26588343e+03 1.22e-03 77s + 53 5.73e-12 1.94e-09 9.47529880e+03 9.28196289e+03 1.04e-03 78s + 54 5.27e-12 1.59e-09 9.46285225e+03 9.29875030e+03 8.82e-04 79s + 55 3.67e-12 1.52e-09 9.45597250e+03 9.30095244e+03 8.33e-04 80s + 56 1.75e-12 1.22e-09 9.45179686e+03 9.31195889e+03 7.51e-04 81s + 57 3.04e-11 1.00e-09 9.44732720e+03 9.32669073e+03 6.48e-04 82s + 58 2.55e-11 5.84e-10 9.43948980e+03 9.34808459e+03 4.91e-04 83s + 59 2.06e-11 3.64e-10 9.43331328e+03 9.36391778e+03 3.73e-04 84s + 60 5.92e-12 2.32e-10 9.43127125e+03 9.37217204e+03 3.17e-04 85s + 61 5.80e-12 7.80e-11 9.42595625e+03 9.38759526e+03 2.06e-04 85s + 62 2.43e-11 4.87e-11 9.42485062e+03 9.39270257e+03 1.73e-04 86s + 63 6.10e-12 2.84e-11 9.42230551e+03 9.39721826e+03 1.35e-04 87s + 64 3.02e-11 2.06e-11 9.41851226e+03 9.39922232e+03 1.04e-04 88s + 65 7.68e-12 1.31e-11 9.41545711e+03 9.40267444e+03 6.87e-05 89s + 66 3.56e-11 5.95e-12 9.41476857e+03 9.40633324e+03 4.53e-05 89s + 67 2.52e-11 5.71e-12 9.41439309e+03 9.40677438e+03 4.09e-05 90s + 68 6.47e-11 4.77e-12 9.41368241e+03 9.40741592e+03 3.37e-05 91s + 69 1.02e-11 3.50e-12 9.41352178e+03 9.40807301e+03 2.93e-05 91s + 70 1.81e-11 2.61e-12 9.41317436e+03 9.40888102e+03 2.31e-05 92s + 71 4.19e-11 9.41e-13 9.41301486e+03 9.41024157e+03 1.49e-05 92s + 72 2.36e-10 7.39e-13 9.41247409e+03 9.41108729e+03 7.45e-06 93s + 73 3.36e-10 5.12e-13 9.41246723e+03 9.41147776e+03 5.32e-06 94s + 74 1.71e-10 1.99e-13 9.41229429e+03 9.41188577e+03 2.19e-06 94s + 75 3.35e-10 4.01e-13 9.41222697e+03 9.41203307e+03 1.04e-06 95s + 76 1.60e-10 6.82e-13 9.41217628e+03 9.41205260e+03 6.64e-07 96s + 77 5.99e-10 1.42e-12 9.41215300e+03 9.41209472e+03 3.13e-07 96s + 78 6.44e-11 7.21e-13 9.41214245e+03 9.41212653e+03 8.55e-08 97s + 79 6.69e-11 6.79e-13 9.41213955e+03 9.41213348e+03 3.26e-08 98s + 80 4.03e-10 1.36e-12 9.41213754e+03 9.41213419e+03 1.80e-08 98s + 81 3.37e-10 2.61e-12 9.41213656e+03 9.41213608e+03 2.60e-09 99s + 82* 2.65e-10 6.98e-12 9.41213642e+03 9.41213636e+03 3.52e-10 99s + 83* 2.52e-10 6.65e-12 9.41213641e+03 9.41213640e+03 6.97e-11 101s + 84* 2.01e-10 4.96e-12 9.41213641e+03 9.41213641e+03 1.32e-11 104s + 85* 1.31e-10 6.08e-12 9.41213641e+03 9.41213641e+03 1.20e-12 104s + Running crossover as requested + Primal residual before push phase: 3.02e-07 + Dual residual before push phase: 4.01e-07 + Number of dual pushes required: 24726 + Number of primal pushes required: 3458 + Summary + Runtime: 107.62s + Status interior point solve: optimal + Status crossover: optimal + objective value: 9.41213641e+03 + interior solution primal residual (abs/rel): 3.75e-09 / 9.14e-13 + interior solution dual residual (abs/rel): 2.40e-09 / 3.42e-12 + interior solution objective gap (abs/rel): 1.95e-07 / 2.08e-11 + basic solution primal infeasibility: 5.02e-14 + basic solution dual infeasibility: 1.09e-15 + Ipx: IPM optimal + Ipx: Crossover optimal + Solving the original LP from the solution after postsolve + Model status : Optimal + IPM iterations: 85 + Crossover iterations: 2764 + Objective value : 9.4121364078e+03 + HiGHS run time : 107.89 + LP solved for primal + Writing Output + Time elapsed for writing costs is + 0.8427745 + Time elapsed for writing capacity is + 0.277263333 + Time elapsed for writing power is + 0.6167225 + Time elapsed for writing charge is + 0.18541725 + Time elapsed for writing capacity factor is + 0.235379791 + Time elapsed for writing storage is + 0.132649083 + Time elapsed for writing curtailment is + 0.155876791 + Time elapsed for writing nse is + 0.438298833 + Time elapsed for writing power balance is + 0.297414291 + Time elapsed for writing transmission flows is + 0.103818667 + Time elapsed for writing transmission losses is + 0.097776166 + Time elapsed for writing network expansion is + 0.080605 + Time elapsed for writing emissions is + 0.280204166 + Time elapsed for writing reliability is + 0.093714833 + Time elapsed for writing storage duals is + 0.391718917 + Time elapsed for writing commitment is + 0.085516291 + Time elapsed for writing startup is + 0.045873 + Time elapsed for writing shutdown is + 0.027687542 + Time elapsed for writing fuel consumption is + 0.31172675 + Time elapsed for writing co2 is + 0.053309291 + Time elapsed for writing price is + 0.056254791 + Time elapsed for writing energy revenue is + 0.21793425 + Time elapsed for writing charging cost is + 0.155090166 + Time elapsed for writing subsidy is + 0.244266583 + Time elapsed for writing time weights is + 0.061457459 + Time elapsed for writing co2 cap is + 0.084762792 + Time elapsed for writing minimum capacity requirement is + 0.090502375 + Time elapsed for writing net revenue is + 0.8798285 + Wrote outputs to /Users/mayamutic/Desktop/GenX-Tutorials/Tutorials/example_systems/1_three_zones/results + Time elapsed for writing is + 6.909353542 + + +Below are all 33 files output by running GenX: + + +```julia +results = cd(readdir,joinpath(case,"results")) +``` + + + + + 33-element Vector{String}: + "CO2_prices_and_penalties.csv" + "ChargingCost.csv" + "EnergyRevenue.csv" + "FuelConsumption_plant_MMBTU.csv" + "FuelConsumption_total_MMBTU.csv" + "Fuel_cost_plant.csv" + "MinCapReq_prices_and_penalties.csv" + "NetRevenue.csv" + "RegSubsidyRevenue.csv" + "SubsidyRevenue.csv" + "capacity.csv" + "capacityfactor.csv" + "charge.csv" + ⋮ + "power.csv" + "power_balance.csv" + "prices.csv" + "reliability.csv" + "run_settings.yml" + "shutdown.csv" + "start.csv" + "status.csv" + "storage.csv" + "storagebal_duals.csv" + "time_weights.csv" + "tlosses.csv" + + + +### Power + +The file `power.csv`, shown below, outputs the power in MW discharged by each node at each time step. Note that if TimeDomainReduction is in use the file will be shorter. The first row states which zone each node is part of, and the total power per year is located in the second row. After that, each row represents one time step of the series. + + +```julia +power = CSV.read(joinpath(case,"results/power.csv"),DataFrame,missingstring="NA") +``` +``` @raw html +
1850×12 DataFrame
1825 rows omitted
RowResourceMA_natural_gas_combined_cycleCT_natural_gas_combined_cycleME_natural_gas_combined_cycleMA_solar_pvCT_onshore_windCT_solar_pvME_onshore_windMA_batteryCT_batteryME_batteryTotal
String15Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64
1Zone1.02.03.01.02.02.03.01.02.03.00.0
2AnnualSum1.04015e73.42459e68.94975e52.47213e72.90683e72.69884e72.625e75.06354e61.45833e74.90368e61.463e8
3t1-0.0-0.0-0.0-0.08510.78-0.05300.610.02537.45673.3417022.2
4t2-0.0-0.0-0.0-0.08420.78-0.06282.040.02537.450.017240.3
5t3-0.0-0.0-0.0-0.08367.78-0.02409.840.02537.451828.2415143.3
6t4-0.0-0.0-0.0-0.08353.78-0.02762.241591.462537.450.015244.9
7t5-0.0-0.0-0.0-0.07482.39-0.00.01617.462980.641384.6213465.1
8t6-0.0-0.0-0.0-0.02429.93-0.02797.241717.965535.370.012480.5
9t7-0.0-0.0-0.0-0.011868.8-0.01374.731320.78871.4431340.6716776.4
10t8-0.0-0.0-0.0-0.02656.93-0.00.02115.965535.371452.6211760.9
11t9-0.0-0.0-0.03061.280.03110.82982.24868.8175389.440.015412.6
12t10-0.0-0.0-0.06100.227597.995543.690.00.00.01521.1220763.0
13t11-0.0-0.0-0.08314.290.06341.983080.240.02458.820.020195.3
⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮⋮
1839t1837-0.0-0.0-0.06712.182541.66736.37305.6081410.33763.7261427.8219897.6
1840t1838-0.0-0.0-0.06514.150.06847.243153.240.03464.220.019978.9
1841t1839-0.0-0.0-0.05582.073848.886280.20.0195.4222048.31571.1219526.0
1842t1840-0.0-0.0-0.03688.139349.984892.73490.611006.020.00.022427.4
1843t1841-0.0-0.0-0.0509.228124.991351.083653.061218.52507.81828.2419192.9
1844t1842-0.0-0.0-0.0-0.02918.2-0.06896.822194.615535.37256.86317801.9
1845t1843-0.0-0.0-0.0-0.06800.37-0.07324.661838.113950.1541.947219955.2
1846t1844-0.0-0.0-0.0-0.09505.82-0.05683.661744.782567.93838.07720340.3
1847t1845-0.0-0.0-0.0-0.03491.93-0.05128.561597.615535.371107.4916861.0
1848t1846-0.0-0.0-0.0-0.012135.6-0.05021.751341.111140.561125.920764.9
1849t1847-0.0-0.0-0.0-0.08875.71-0.03605.98974.612665.481783.7917905.6
1850t1848-0.0-0.0-0.0-0.013549.1-0.04098.0541.61205.311478.2719872.3
+``` + + +Below is a visualization of the production over the first 168 hours, with the load demand curve from all three zones plotted on top: + + +```julia +# Pre-processing +tstart = 3 +tend = 170 +names_power = ["Solar","Natural_Gas","Battery","Wind"] + +power_tot = DataFrame([power[!,5]+power[!,7] power[!,2]+power[!,3]+power[!,4] power[!,9]+power[!,10]+power[!,11] power[!,6]+power[!,8]], + ["Solar","Natural_Gas","Battery","Wind"]) + +power_plot = DataFrame([collect(1:length(power_tot[tstart:tend,1])) power_tot[tstart:tend,1] repeat([names_power[1]],length(power_tot[tstart:tend,1]))], + ["Hour","MW", "Resource_Type"]); + +for i in range(2,4) + power_plot_temp = DataFrame([collect(1:length(power_tot[tstart:tend,i])) power_tot[tstart:tend,i] repeat([names_power[i]],length(power_tot[tstart:tend,i]))],["Hour","MW", "Resource_Type"]) + power_plot = [power_plot; power_plot_temp] +end + +loads = CSV.read(joinpath(case,"system/Demand_data.csv"),DataFrame,missingstring="NA") +loads_tot = loads[!,"Demand_MW_z1"]+loads[!,"Demand_MW_z2"]+loads[!,"Demand_MW_z3"] +power_plot[!,"Demand_Total"] = repeat(loads_tot[tstart:tend],4); +``` + + +```julia +power_plot |> +@vlplot()+ +@vlplot(mark={:area}, + x={:Hour,title="Time Step (hours)",labels="Resource_Type:n",axis={values=0:12:168}}, y={:MW,title="Load (MW)",type="quantitative"}, + color={"Resource_Type:n",scale={scheme="accent"},sort="descending"},order={field="Resource_Type:n"},width=845,height=400)+ +@vlplot(mark=:line,x=:Hour,y=:Demand_Total,lables="Demand",color={datum="Demand",legend={title=nothing}},title="Resource Capacity per Hour with Load Demand Curve, all Zones") +``` + +![svg](./files/t8_cap.svg) + + +We can separate it by zone in the following plot: + + +```julia +Zone1 = [power[2,2] power[2,5] 0 power[2,9]] +Zone2 = [power[2,3] power[2,7] power[2,6] power[2,10]] +Zone3 = [power[2,4] 0 power[2,8] power[2,11]] + +colors=[:silver :yellow :deepskyblue :violetred3] + +groupedbar(["Zone 1", "Zone 2", "Zone 3"],[Zone1; Zone2; Zone3], bar_position = :stack, bar_width=0.5,size=(400,450), + labels=["Natural Gas" "Solar" "Wind" "Battery"], + title="Resource Allocation in MW Per Zone",ylabel="MW",color=colors, titlefontsize=10) +``` + +![svg](./files/t8_resource_allocation.svg) + +Below is a heatmap for the natural gas plant in Massachusetts. It is normalized by the end capacity in `capcity.csv`. To change which plant the heat map plots, change the DataFrame column in `power` when defining `power_cap` below, and the corresponding capacity. + + +```julia +capacity = CSV.read(joinpath(case,"results/capacity.csv"),DataFrame,missingstring="NA") +Period_map = CSV.read(joinpath(case,"TDR_results/Period_map.csv"),DataFrame,missingstring="NA") + +# Take the EndCap and power of MA_natural_gas_combined_cycle +cap = capacity[1,"EndCap"] +power_cap = power[3:end,"MA_natural_gas_combined_cycle"]/cap; + +# Reconstruction of all hours of the year from TDR +recon = [] +for i in range(1,52) + index = Period_map[i,"Rep_Period_Index"] + recon_temp = power_cap[(168*index-167):(168*index)] + recon = [recon; recon_temp] +end + +# Convert to matrix format +heat = recon[1:24] +for i in range(1,364) + heat = [heat recon[(i*24-23):(i*24)]] +end + +``` + + +```julia +Plots.heatmap(heat,yticks=0:4:24,xticks=([15:30:364;], + ["Jan","Feb","Mar","Apr","May","Jun","Jul","Aug","Sept","Oct","Nov","Dec"]), + size=(900,200),c=:lajolla) +``` + +![svg](./files/t8_heatmap.svg) + + + +### Cost and Revenue + +The basic cost of each power plant and the revenue it generates can be found in files `costs.csv`, `NetRevenue.csv`,and `EnergyRevenue.csv`. `NetRevenue.csv` breaks down each specific cost per node in each zone, which is useful to visualize what the cost is coming from. + + +```julia +netrevenue = CSV.read(joinpath(case,"results/NetRevenue.csv"),DataFrame,missingstring="NA") +``` + + + +``` @raw html +
10×28 DataFrame
RowregionResourcezoneClusterR_IDInv_cost_MWInv_cost_MWhInv_cost_charge_MWFixed_OM_cost_MWFixed_OM_cost_MWhFixed_OM_cost_charge_MWVar_OM_cost_outFuel_costVar_OM_cost_inStartCostCharge_costCO2SequestrationCostEnergyRevenueSubsidyRevenueOperatingReserveRevenueOperatingRegulationRevenueReserveMarginRevenueESRRevenueEmissionsCostRegSubsidyRevenueRevenueCostProfit
String3String31Int64Int64Int64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64Float64
1MAMA_natural_gas_combined_cycle1115.54734e80.00.08.72561e70.00.03.69253e72.10416e80.03.84832e70.00.02.77103e90.00.00.00.00.01.84321e90.02.77103e92.77103e91.43051e-6
2CTCT_natural_gas_combined_cycle2121.42906e80.00.02.11911e70.00.01.22258e74.97792e70.07.75292e60.00.08.4423e80.00.00.00.00.06.10375e80.08.4423e88.4423e81.19209e-7
3MEME_natural_gas_combined_cycle3133.52336e70.00.08.77661e60.00.04.02739e62.26505e70.03.33663e60.00.02.19267e80.00.00.00.00.01.45243e80.02.19267e82.19267e80.0
4MAMA_solar_pv1141.27007e90.00.02.79327e80.00.00.00.00.00.00.00.01.5494e90.00.00.00.00.00.00.01.5494e91.5494e9-2.86102e-6
5CTCT_onshore_wind2151.40748e90.00.06.25617e80.00.02.90683e60.00.00.00.00.02.036e90.00.00.00.00.00.00.02.036e92.036e9-5.00679e-6
6CTCT_solar_pv2161.35108e90.00.02.97142e80.00.00.00.00.00.00.00.01.64822e90.00.00.00.00.00.00.01.64822e91.64822e99.53674e-7
7MEME_onshore_wind3171.03673e90.00.04.60821e80.00.02.625e60.00.00.00.00.01.50017e90.00.00.00.00.00.00.01.50017e91.50017e92.38419e-6
8MAMA_battery1084.29792e72.23673e80.01.07426e75.59033e70.07.59532e50.08.97367e50.01.3432e80.04.48833e80.00.00.00.00.00.00.04.48833e84.69275e8-2.0442e7
9CTCT_battery2091.08405e85.73615e80.02.70957e71.43365e80.02.1875e60.02.58447e60.05.24177e80.01.31941e90.00.00.00.00.00.00.01.31941e91.38143e9-6.20165e7
10MEME_battery30103.58043e71.03994e80.08.94925e62.59915e70.07.35552e50.08.69036e50.03.81057e70.02.03732e80.00.00.00.00.00.00.02.03732e82.14449e8-1.0717e7
+``` + + + +```julia +xnames = netrevenue[!,2] +names1 = ["Investment cost" "Fixed OM cost" "Variable OM cost" "Fuel cost" "Start Cost" "Battery charge cost" "CO2 Sequestration Cost" "Revenue"] + +netrev = [netrevenue[!,6]+netrevenue[!,7]+netrevenue[!,8] netrevenue[!,9]+netrevenue[!,11]+netrevenue[!,11] netrevenue[!,12]+netrevenue[!,14] netrevenue[!,13] netrevenue[!,15] netrevenue[!,16] netrevenue[!,17]] + +groupedbar(xnames,netrev, bar_position = :stack, bar_width=0.9,size=(850,800), + labels=names1,title="Cost Allocation per Node with Revenue",xlabel="Node",ylabel="Cost (Dollars)", + titlefontsize=10,legend=:outerright,ylims=[0,maximum(netrevenue[!,"Revenue"])+1e8],xrotation = 90) +StatsPlots.scatter!(xnames,netrevenue[!,"Revenue"],label="Revenue",color="black") + +``` + +![svg](./files/t8_cost.svg) + + + +### Emissions + +The file `emmissions.csv` gives the total CO2 emmissions per zone for each hour GenX runs. The first three rows give the marginal CO2 abatement cost in $/ton CO2. + + +```julia +emm1 = CSV.read(joinpath(case,"results/emissions.csv"),DataFrame) +``` + + + +``` @raw html +
1852×5 DataFrame
1827 rows omitted
RowZone123Total
String15Float64Float64Float64Float64
1CO2_Price_1444.9210.00.00.0
2CO2_Price_20.0468.6680.00.0
3CO2_Price_30.00.0240.860.0
4AnnualSum4.14279e61.30236e66.03017e56.04816e6
5t10.00.00.00.0
6t20.00.00.00.0
7t30.00.00.00.0
8t40.00.00.00.0
9t50.00.00.00.0
10t60.00.00.00.0
11t70.00.00.00.0
12t80.00.00.00.0
13t90.00.00.00.0
⋮⋮⋮⋮⋮⋮
1841t18370.00.00.00.0
1842t18380.00.00.00.0
1843t18390.00.00.00.0
1844t18400.00.00.00.0
1845t18410.00.00.00.0
1846t18420.00.00.00.0
1847t18430.00.00.00.0
1848t18440.00.00.00.0
1849t18450.00.00.00.0
1850t18460.00.00.00.0
1851t18470.00.00.00.0
1852t18480.00.00.00.0
+``` + + + +```julia +# Pre-processing +tstart = 470 +tend = 1500 +names_emm = ["Zone 1","Zone 2","Zone 3"] + +emm_tot = DataFrame([emm1[3:end,2] emm1[3:end,3] emm1[3:end,4]], + ["Zone 1","Zone 2","Zone 3"]) + + +emm_plot = DataFrame([collect((tstart-3):(tend-3)) emm_tot[tstart:tend,1] repeat([names_emm[1]],(tend-tstart+1))], + ["Hour","MW","Zone"]); + +for i in range(2,3) + emm_plot_temp = DataFrame([collect((tstart-3):(tend-3)) emm_tot[tstart:tend,i] repeat([names_emm[i]],(tend-tstart+1))],["Hour","MW","Zone"]) + emm_plot = [emm_plot; emm_plot_temp] +end + +``` + + +```julia +emm_plot |> +@vlplot(mark={:line}, + x={:Hour,title="Time Step (hours)",labels="Zone:n",axis={values=tstart:24:tend}}, y={:MW,title="Emmissions (Tons)",type="quantitative"}, + color={"Zone:n"},width=845,height=400,title="Emmissions per Time Step by Zone") +``` + +![svg](./files/t8_emm1.svg) + + + + +Let's try changing the CO2 cap, as in Tutorial 7, and plotting the resulting emmissions. + + +```julia +genx_settings_TZ = YAML.load(open((joinpath(case,"settings/genx_settings.yml")))) +genx_settings_TZ["CO2Cap"] = 0 +YAML.write_file((joinpath(case,"settings/genx_settings.yml")), genx_settings_TZ) + +include("example_systems/1_three_zones/Run.jl") + +# run outside of notebook +``` + + Configuring Settings + Time Series Data Already Clustered. + Configuring Solver + Loading Inputs + Reading Input CSV Files + Network.csv Successfully Read! + Demand (load) data Successfully Read! + Fuels_data.csv Successfully Read! + + Summary of resources loaded into the model: + ------------------------------------------------------- + Resource type Number of resources + ======================================================= + Thermal 3 + VRE 4 + Storage 3 + ======================================================= + Total number of resources: 10 + ------------------------------------------------------- + + + Thermal.csv Successfully Read. + Vre.csv Successfully Read. + Storage.csv Successfully Read. + Resource_energy_share_requirement.csv Successfully Read. + Resource_capacity_reserve_margin.csv Successfully Read. + Resource_minimum_capacity_requirement.csv Successfully Read. + + + Generators_variability.csv Successfully Read! + Validating time basis + Minimum_capacity_requirement.csv Successfully Read! + CSV Files Successfully Read In From /Users/mayamutic/Desktop/GenX-Tutorials/Tutorials/example_systems/1_three_zones + Generating the Optimization Model + Discharge Module + Non-served Energy Module + Investment Discharge Module + Unit Commitment Module + Fuel Module + CO2 Module + Investment Transmission Module + Transmission Module + Dispatchable Resources Module + Storage Resources Module + Storage Investment Module + Storage Core Resources Module + Storage Resources with Symmetric Charge/Discharge Capacity Module + Thermal (Unit Commitment) Resources Module + Minimum Capacity Requirement Module + Time elapsed for model building is + 0.531860834 + Solving Model + Running HiGHS 1.6.0: Copyright (c) 2023 HiGHS under MIT licence terms + Presolving model + 118035 rows, 81083 cols, 422475 nonzeros + 110878 rows, 73926 cols, 422989 nonzeros + Presolve : Reductions: rows 110878(-42517); columns 73926(-46210); elements 422989(-48026) + Solving the presolved LP + IPX model has 110878 rows, 73926 columns and 422989 nonzeros + Input + Number of variables: 73926 + Number of free variables: 3696 + Number of constraints: 110878 + Number of equality constraints: 16867 + Number of matrix entries: 422989 + Matrix range: [4e-07, 1e+01] + RHS range: [8e-01, 2e+01] + Objective range: [1e-04, 7e+02] + Bounds range: [2e-03, 2e+01] + Preprocessing + Dualized model: no + Number of dense columns: 15 + Range of scaling factors: [5.00e-01, 1.00e+00] + IPX version 1.0 + Interior Point Solve + Iter P.res D.res P.obj D.obj mu Time + 0 2.34e+01 6.62e+02 3.28242911e+06 -1.30284671e+07 1.55e+04 0s + 1 1.39e+01 1.95e+02 -2.79051574e+06 -1.70869614e+07 8.32e+03 0s + 2 1.34e+01 1.41e+02 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5.68e-13 5.58697892e+03 5.58214126e+03 2.60e-05 57s + 48 2.13e-14 5.36e-13 5.58691900e+03 5.58233212e+03 2.46e-05 58s + 49 2.13e-14 3.73e-13 5.58656054e+03 5.58365417e+03 1.56e-05 58s + 50 2.13e-14 3.55e-13 5.58656104e+03 5.58367145e+03 1.55e-05 58s + 51 2.13e-14 2.31e-13 5.58641950e+03 5.58394090e+03 1.33e-05 59s + 52 2.13e-14 2.56e-13 5.58608647e+03 5.58430397e+03 9.56e-06 59s + 53 2.13e-14 1.43e-13 5.58604712e+03 5.58455329e+03 8.01e-06 59s + 54 2.13e-14 3.13e-13 5.58604145e+03 5.58455679e+03 7.96e-06 59s + 55 2.13e-14 1.99e-13 5.58598248e+03 5.58506295e+03 4.93e-06 60s + 56 2.13e-14 2.56e-13 5.58593821e+03 5.58507236e+03 4.64e-06 60s + 57 2.13e-14 1.99e-13 5.58578478e+03 5.58540690e+03 2.03e-06 60s + 58 2.84e-14 2.91e-13 5.58578450e+03 5.58540754e+03 2.02e-06 61s + 59 2.13e-14 2.56e-13 5.58572083e+03 5.58541744e+03 1.63e-06 61s + 60 2.84e-14 2.56e-13 5.58571491e+03 5.58541894e+03 1.59e-06 61s + 61 2.13e-14 1.63e-13 5.58565078e+03 5.58546281e+03 1.01e-06 61s + 62 2.13e-14 3.41e-13 5.58557843e+03 5.58548803e+03 4.85e-07 62s + 63 2.13e-14 3.98e-13 5.58557613e+03 5.58548563e+03 4.85e-07 62s + 64 2.13e-14 3.69e-13 5.58556537e+03 5.58552541e+03 2.14e-07 62s + 65 2.13e-14 3.13e-13 5.58556537e+03 5.58552559e+03 2.13e-07 62s + 66 2.13e-14 1.42e-13 5.58555314e+03 5.58553125e+03 1.17e-07 63s + 67 2.13e-14 1.74e-13 5.58555081e+03 5.58553284e+03 9.64e-08 63s + 68 2.13e-14 2.13e-13 5.58554989e+03 5.58553484e+03 8.07e-08 63s + 69 2.13e-14 5.68e-13 5.58554752e+03 5.58553671e+03 5.80e-08 63s + 70 2.13e-14 4.83e-13 5.58554607e+03 5.58553831e+03 4.16e-08 64s + 71 2.13e-14 2.13e-13 5.58554582e+03 5.58554198e+03 2.06e-08 64s + 72 2.13e-14 8.92e-13 5.58554574e+03 5.58554196e+03 2.03e-08 64s + 73 2.13e-14 1.09e-12 5.58554539e+03 5.58554200e+03 1.82e-08 64s + 74 2.13e-14 3.23e-12 5.58554405e+03 5.58554312e+03 4.99e-09 65s + 75 2.13e-14 5.31e-12 5.58554382e+03 5.58554334e+03 2.58e-09 65s + 76 2.13e-14 7.04e-12 5.58554366e+03 5.58554353e+03 7.22e-10 65s + 77* 2.84e-14 1.57e-12 5.58554362e+03 5.58554357e+03 2.79e-10 65s + 78* 3.55e-14 4.18e-12 5.58554360e+03 5.58554358e+03 1.16e-10 65s + 79* 3.55e-14 5.29e-12 5.58554360e+03 5.58554360e+03 2.36e-11 66s + 80* 3.55e-14 5.19e-12 5.58554360e+03 5.58554360e+03 3.40e-12 66s + 81* 3.55e-14 1.16e-11 5.58554360e+03 5.58554360e+03 3.27e-13 66s + 82* 3.55e-14 9.05e-12 5.58554360e+03 5.58554360e+03 2.97e-14 66s + Running crossover as requested + Primal residual before push phase: 9.82e-08 + Dual residual before push phase: 1.24e-07 + Number of dual pushes required: 18968 + Number of primal pushes required: 2204 + Summary + Runtime: 66.29s + Status interior point solve: optimal + Status crossover: optimal + objective value: 5.58554360e+03 + interior solution primal residual (abs/rel): 1.51e-10 / 8.54e-12 + interior solution dual residual (abs/rel): 8.46e-10 / 1.20e-12 + interior solution objective gap (abs/rel): 2.29e-09 / 4.10e-13 + basic solution primal infeasibility: 1.43e-14 + basic solution dual infeasibility: 6.89e-16 + Ipx: IPM optimal + Ipx: Crossover optimal + Solving the original LP from the solution after postsolve + Model status : Optimal + IPM iterations: 82 + Crossover iterations: 1447 + Objective value : 5.5855435982e+03 + HiGHS run time : 66.51 + LP solved for primal + Writing Output + Time elapsed for writing costs is + 0.099885792 + Time elapsed for writing capacity is + 0.000646583 + Time elapsed for writing power is + 0.021790625 + Time elapsed for writing charge is + 0.0167645 + Time elapsed for writing capacity factor is + 0.021259458 + Time elapsed for writing storage is + 0.009532667 + Time elapsed for writing curtailment is + 0.019054083 + Time elapsed for writing nse is + 0.0452305 + Time elapsed for writing power balance is + 0.053504209 + Time elapsed for writing transmission flows is + 0.004709417 + Time elapsed for writing transmission losses is + 0.013975458 + Time elapsed for writing network expansion is + 0.000157 + Time elapsed for writing emissions is + 0.050411042 + Time elapsed for writing reliability is + 0.005842667 + Time elapsed for writing storage duals is + 0.024307708 + Time elapsed for writing commitment is + 0.006124458 + Time elapsed for writing startup is + 0.012590917 + Time elapsed for writing shutdown is + 0.012514292 + Time elapsed for writing fuel consumption is + 0.054159667 + Time elapsed for writing co2 is + 0.019371417 + Time elapsed for writing price is + 0.005712875 + Time elapsed for writing energy revenue is + 0.010585041 + Time elapsed for writing charging cost is + 0.005354792 + Time elapsed for writing subsidy is + 0.000396208 + Time elapsed for writing time weights is + 0.000497875 + Time elapsed for writing minimum capacity requirement is + 0.000146875 + Time elapsed for writing net revenue is + 0.011134208 + Wrote outputs to /Users/mayamutic/Desktop/GenX-Tutorials/Tutorials/example_systems/1_three_zones/results_1 + Time elapsed for writing is + 0.530491792 + + + +```julia +emm2 = CSV.read(joinpath(case,"results_1/emissions.csv"),DataFrame) +``` + + + +``` @raw html +
1849×5 DataFrame
1824 rows omitted
RowZone123Total
String15Float64Float64Float64Float64
1AnnualSum1.68155e71.41088e74310.213.09286e7
2t1997.1690.00.0997.169
3t2997.1690.00.0997.169
4t3997.1690.00.0997.169
5t4997.1690.00.0997.169
6t5997.1690.00.0997.169
7t6997.1690.00.0997.169
8t7997.1690.00.0997.169
9t8997.1690.00.0997.169
10t9997.1690.00.0997.169
11t101471.460.00.01471.46
12t11997.1690.00.0997.169
13t121115.810.00.01115.81
⋮⋮⋮⋮⋮⋮
1838t18372789.351012.990.03802.34
1839t18382835.211012.990.03848.2
1840t18392520.571012.990.03533.56
1841t18401496.47445.850.01942.32
1842t18412571.261012.990.03584.25
1843t18422835.211012.990.03848.2
1844t18432835.211012.990.03848.2
1845t18442625.42960.1840.03585.6
1846t18452506.32342.3910.02848.71
1847t18462277.59342.3910.02619.98
1848t18471960.08524.5260.02484.6
1849t18481566.77342.3910.01909.16
+``` + + + +```julia +# Pre-processing +tstart = 470 +tend = 1500 +names_emm = ["Zone 1","Zone 2","Zone 3"] + +emm_tot2 = DataFrame([emm2[3:end,2] emm2[3:end,3] emm2[3:end,4]], + ["Zone 1","Zone 2","Zone 3"]) + + +emm_plot2 = DataFrame([collect((tstart-3):(tend-3)) emm_tot2[tstart:tend,1] repeat([names_emm[1]],(tend-tstart+1))], + ["Hour","MW","Zone"]); + +for i in range(2,3) + emm_plot_temp = DataFrame([collect((tstart-3):(tend-3)) emm_tot2[tstart:tend,i] repeat([names_emm[i]],(tend-tstart+1))],["Hour","MW","Zone"]) + emm_plot2 = [emm_plot2; emm_plot_temp] +end +``` + + +```julia +emm_plot2 |> +@vlplot(mark={:line}, + x={:Hour,title="Time Step (hours)",labels="Zone:n",axis={values=tstart:24:tend}}, y={:MW,title="Emmissions (Tons)",type="quantitative"}, + color={"Zone:n"},width=845,height=400,title="Emmissions per Time Step by Zone") +``` + +![svg](./files/t8_emm2.svg) + + + + +We can see how the emmissions, summed over all zones, compare in the following plot: + + +```julia +emm1sum = sum(eachcol(emm_tot)); +emm2sum = sum(eachcol(emm_tot2)); + +Plots.plot(collect((tstart-3):(tend-3)),emm1sum[tstart:tend],size=(800,400),label="Load Based CO2 Cap", + xlabel="Time Step (Hours)",ylabel="Emmissions (Tons)",thickness_scaling = 1.1,linewidth = 1.5, + title="Emmisions per Time Step",xticks=tstart:72:tend) +Plots.plot!(collect((tstart-3):(tend-3)),emm2sum[tstart:tend],label="No CO2 Cap",linewidth = 1.5) +``` +![svg](./files/t8_emm_comp.svg) + + + +Finally, set the CO2 Cap back to 2: + + +```julia +genx_settings_TZ["CO2Cap"] = 2 +YAML.write_file((joinpath(case,"settings/genx_settings.yml")), genx_settings_TZ) +``` + + +```julia + +``` diff --git a/docs/src/Tutorials/Tutorials_intro.md b/docs/src/Tutorials/Tutorials_intro.md index 014e215b39..62e59083c9 100644 --- a/docs/src/Tutorials/Tutorials_intro.md +++ b/docs/src/Tutorials/Tutorials_intro.md @@ -10,5 +10,7 @@ Here is a list of the tutorials: 4. [Tutorial 4: Model Generation](@ref) 5. [Tutorial 5: Solving the Model](@ref) 6. [Tutorial 6: Solver Settings](@ref) +7. [Tutorial 7: Policy Constraints](@ref) +8. [Tutorial 8: Outputs](@ref) diff --git a/docs/src/Tutorials/files/Julia.png b/docs/src/Tutorials/files/Julia.png new file mode 100644 index 0000000000..e881b2fa4b Binary files /dev/null and b/docs/src/Tutorials/files/Julia.png differ diff --git a/docs/src/Tutorials/files/LatexHierarchy.png b/docs/src/Tutorials/files/LatexHierarchy.png index 05981f99c0..9e7c7295f9 100644 Binary files a/docs/src/Tutorials/files/LatexHierarchy.png and b/docs/src/Tutorials/files/LatexHierarchy.png differ diff --git a/docs/src/Tutorials/files/OneZoneCase.png b/docs/src/Tutorials/files/OneZoneCase.png deleted file mode 100644 index f394e93853..0000000000 Binary files a/docs/src/Tutorials/files/OneZoneCase.png and /dev/null differ diff --git a/docs/src/Tutorials/files/addGenX.png b/docs/src/Tutorials/files/addGenX.png new file mode 100644 index 0000000000..e101cc2509 Binary files /dev/null and b/docs/src/Tutorials/files/addGenX.png differ diff --git a/docs/src/Tutorials/files/addIJulia.png 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a/docs/src/Tutorials/files/opennotebook.png b/docs/src/Tutorials/files/opennotebook.png new file mode 100644 index 0000000000..4d87a20dae Binary files /dev/null and b/docs/src/Tutorials/files/opennotebook.png differ diff --git a/docs/src/Tutorials/files/output_58_0.svg b/docs/src/Tutorials/files/output_58_0.svg deleted file mode 100644 index 41748d9d21..0000000000 --- a/docs/src/Tutorials/files/output_58_0.svg +++ /dev/null @@ -1 +0,0 @@ -05001,0001,5002,0002,5003,0003,5004,0004,5005,0005,5006,0006,5007,0007,5008,0008,5009,000Time Step (hours)02,0004,0006,0008,00010,00012,00014,00016,00018,000Load (MW)Total46121720232829344548WeekMW Load per hour with TDR Representative Weeks \ No newline at end of file diff --git a/docs/src/Tutorials/files/output_65_0.svg b/docs/src/Tutorials/files/output_65_0.svg deleted file mode 100644 index c66dee379a..0000000000 --- a/docs/src/Tutorials/files/output_65_0.svg +++ /dev/null @@ -1 +0,0 @@ -Extreme_Periods02,0004,0006,0008,00010,00012,00014,00016,00018,000Load (MW)Off02,0004,0006,0008,00010,00012,00014,00016,00018,000Load (MW)On05001,0001,5002,0002,5003,0003,5004,0004,5005,0005,5006,0006,5007,0007,5008,0008,5009,000Time Step (hours)Total47121520232534444849617282945WeekMW Load per hour with TDR Representative Weeks, Extreme Periods Off and On \ No newline at end of file diff --git a/docs/src/Tutorials/files/runcase.png b/docs/src/Tutorials/files/runcase.png index c7c80ed0ae..d92fe4068c 100644 Binary files a/docs/src/Tutorials/files/runcase.png and b/docs/src/Tutorials/files/runcase.png differ diff --git a/docs/src/Tutorials/files/statenames.csv b/docs/src/Tutorials/files/statenames.csv deleted file mode 100644 index ac48dd9087..0000000000 --- a/docs/src/Tutorials/files/statenames.csv +++ /dev/null @@ -1,2 +0,0 @@ - -Alabama Arkansas Arizona California Colorado Connecticut District of Columbia Delaware Florida Georgia Iowa Idaho Illinois Indiana Kansas Kentucky Louisiana Massachusetts Maryland Maine Michigan Minnesota Missouri Mississippi Montana North Carolina North Dakota Nebraska New Hampshire New Jersey New Mexico Nevada New York Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Virginia Vermont Washington Wisconsin West Virginia Wyoming diff --git a/docs/src/Tutorials/files/states.csv b/docs/src/Tutorials/files/states.csv deleted file mode 100644 index 6d499af7bf..0000000000 --- a/docs/src/Tutorials/files/states.csv +++ /dev/null @@ -1,50 +0,0 @@ -State Longitude Latitude -Alabama -86.902298 32.318231 -Arkansas -91.831833 35.20105 -Arizona -111.093731 34.048928 -California -119.417932 36.778261 -Colorado -105.782067 39.550051 -Connecticut -73.087749 41.603221 -District of Columbia -77.033418 38.905985 -Delaware -75.52767 38.910832 -Florida -81.515754 27.664827 -Georgia -82.907123 32.157435 -Iowa -93.097702 41.78003 -Idaho -114.742041 44.068202 -Illinois -89.398528 40.622125 -Indiana -85.602364 40.551217 -Kansas -98.484246 39.011902 -Kentucky -84.270018 37.839333 -Louisiana -92.145024 31.244823 -Massachusetts -71.382437 42.407211 -Maryland -76.641271 39.045755 -Maine -69.445469 45.2573783 -Michigan -85.602364 44.314844 -Minnesota -94.6859 46.729553 -Missouri -91.831833 37.9642553 -Mississippi -89.398528 32.354668 -Montana -110.362566 46.879682 -North Carolina -79.0193 35.759573 -North Dakota -101.002012 47.551493 -Nebraska -99.901813 41.492537 -New Hampshire -71.572395 43.193852 -New Jersey -74.405661 40.058324 -New Mexico -105.032363 34.97273 -Nevada -116.419389 38.80261 -New York -74.217933 43.299428 -Ohio -82.907123 40.417287 -Oklahoma -97.092877 35.007752 -Oregon -120.554201 43.804133 -Pennsylvania -77.194525 41.203322 -Rhode Island -71.477429 41.580095 -South Carolina -81.163725 33.836081 -South Dakota -99.901813 43.969515 -Tennessee -86.580447 35.517491 -Texas -99.901813 31.968599 -Utah -111.093731 39.32098 -Virginia -78.656894 37.431573 -Vermont -72.577841 44.558803 -Washington -120.740139 47.751074 -Wisconsin -88.787868 43.78444 -West Virginia -80.454903 38.597626 -Wyoming -107.290284 43.075968 diff --git a/docs/src/Tutorials/files/t3_TDR_demand.svg b/docs/src/Tutorials/files/t3_TDR_demand.svg new file mode 100644 index 0000000000..061d38acd0 --- /dev/null +++ b/docs/src/Tutorials/files/t3_TDR_demand.svg @@ -0,0 +1 @@ +05001,0001,5002,0002,5003,0003,5004,0004,5005,0005,5006,0006,5007,0007,5008,0008,5009,000Time Step (hours)02,0004,0006,0008,00010,00012,00014,00016,00018,000Demand (MW)Total48121724282930464851WeekMW Demand per hour with TDR Representative Weeks \ No newline at end of file diff --git a/docs/src/Tutorials/files/output_14_0.svg b/docs/src/Tutorials/files/t3_demand.svg similarity index 99% rename from docs/src/Tutorials/files/output_14_0.svg rename to docs/src/Tutorials/files/t3_demand.svg index 155924914a..fa35647fba 100644 --- a/docs/src/Tutorials/files/output_14_0.svg +++ b/docs/src/Tutorials/files/t3_demand.svg @@ -1 +1 @@ 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