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2 changes: 1 addition & 1 deletion dev/.documenter-siteinfo.json
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{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2024-02-08T19:33:20","documenter_version":"1.2.1"}}
{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2024-02-08T19:39:38","documenter_version":"1.2.1"}}
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\end{aligned}\]</p><p>(27) Cap &amp; Trade - State carbon allowance cap:</p><p class="math-container">\[\sum_{g \in (\bigcup_{i \in I_{w}} G_{i}) \cap G^{F}} a+{g,t} - em_{w}^{emis} \le ALW_{t,w}; w \in W, t \in T\]</p><p>(28) Cap &amp; Trade - Balance between allowances and emissions:</p><p class="math-container">\[N_{t} \sum_{h \in H_{t}} EF_{g} \times p_{g,t,h} = a_{g,t} + b_{g,t-1} = b_{g,t}; g \in (\bigcup_{i \in I_{w}} G_{i}) \cap G_{F}, w \in W, t \in T\]</p><p>(29) Cap &amp; Trade - No cross-year banking:</p><p class="math-container">\[b_{g,1} = b_{g,end} = 0; g \in G_{F}\]</p><p>(30) Binary variables:</p><p class="math-container">\[x_{g} = \{0,1 \}; \forall g \in G_{+}
y_{l} = \{0,1 \}; \forall l \in L_{+}
z_{s} = \{0,1 \}; \forall s \in S_{+}\]</p><p>(31) Nonnegative variable:</p><p class="math-container">\[a_{g,t}, b_{g,t}, p_{g,t,h}, p_{d,t,h}^{LS}, c_{s,t,h}, soc_{s,t,h}, pt^{rps}, pw_{g,w}, pwi_{g,w,w&#39;}, em^{emis} \\
\ge 0\]</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../notation/">« Notation</a><a class="docs-footer-nextpage" href="../PCM/">PCM »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Thursday 8 February 2024 19:33">Thursday 8 February 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
\ge 0\]</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../notation/">« Notation</a><a class="docs-footer-nextpage" href="../PCM/">PCM »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Thursday 8 February 2024 19:39">Thursday 8 February 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>PCM · HOPE.jl</title><meta name="title" content="PCM · HOPE.jl"/><meta property="og:title" content="PCM · HOPE.jl"/><meta property="twitter:title" content="PCM · HOPE.jl"/><meta name="description" content="Documentation for HOPE.jl."/><meta property="og:description" content="Documentation for HOPE.jl."/><meta property="twitter:description" content="Documentation for HOPE.jl."/><meta property="og:url" content="github.com/swang22/HOPE.git/PCM/"/><meta property="twitter:url" content="github.com/swang22/HOPE.git/PCM/"/><link rel="canonical" href="github.com/swang22/HOPE.git/PCM/"/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../search_index.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script><link href="../assets/favicon.ico" rel="icon" type="image/x-icon"/></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">HOPE.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><span class="tocitem">Home Page</span><ul><li><a class="tocitem" href="../">Introduction</a></li><li><a class="tocitem" href="../installation/">Installation</a></li><li><a class="tocitem" href="../run_case/">Run a case</a></li></ul></li><li><span class="tocitem">Model Mode and Formulation</span><ul><li><a class="tocitem" href="../model_introduction/">Model Introduction</a></li><li><a class="tocitem" href="../notation/">Notation</a></li><li><a class="tocitem" href="../GTEP/">GTEP</a></li><li class="is-active"><a class="tocitem" href>PCM</a><ul class="internal"><li><a class="tocitem" href="#Objective-Function"><span>Objective Function</span></a></li><li><a class="tocitem" href="#Constraints"><span>Constraints</span></a></li></ul></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Model Mode and Formulation</a></li><li class="is-active"><a href>PCM</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>PCM</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/swang22/HOPE" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/swang22/HOPE/blob/master/docs/src/PCM.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Introduction"><a class="docs-heading-anchor" href="#Introduction">Introduction</a><a id="Introduction-1"></a><a class="docs-heading-anchor-permalink" href="#Introduction" title="Permalink"></a></h1><h2 id="Objective-Function"><a class="docs-heading-anchor" href="#Objective-Function">Objective Function</a><a id="Objective-Function-1"></a><a class="docs-heading-anchor-permalink" href="#Objective-Function" title="Permalink"></a></h2><p>(1) Minimize total system cost:</p><p class="math-container">\[\begin{aligned}
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>PCM · HOPE.jl</title><meta name="title" content="PCM · HOPE.jl"/><meta property="og:title" content="PCM · HOPE.jl"/><meta property="twitter:title" content="PCM · HOPE.jl"/><meta name="description" content="Documentation for HOPE.jl."/><meta property="og:description" content="Documentation for HOPE.jl."/><meta property="twitter:description" content="Documentation for HOPE.jl."/><meta property="og:url" content="github.com/swang22/HOPE.git/PCM/"/><meta property="twitter:url" content="github.com/swang22/HOPE.git/PCM/"/><link rel="canonical" href="github.com/swang22/HOPE.git/PCM/"/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../search_index.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script><link href="../assets/favicon.ico" rel="icon" type="image/x-icon"/></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">HOPE.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><span class="tocitem">Home Page</span><ul><li><a class="tocitem" href="../">Introduction</a></li><li><a class="tocitem" href="../installation/">Installation</a></li><li><a class="tocitem" href="../run_case/">Run a case</a></li></ul></li><li><span class="tocitem">Model Mode and Formulation</span><ul><li><a class="tocitem" href="../model_introduction/">Model Introduction</a></li><li><a class="tocitem" href="../notation/">Notation</a></li><li><a class="tocitem" href="../GTEP/">GTEP</a></li><li class="is-active"><a class="tocitem" href>PCM</a><ul class="internal"><li><a class="tocitem" href="#Overview"><span>Overview</span></a></li><li class="toplevel"><a class="tocitem" href="#Problem-Formulation"><span>Problem Formulation</span></a></li><li><a class="tocitem" href="#Objective-function"><span>Objective function</span></a></li><li><a class="tocitem" href="#Constraints"><span>Constraints</span></a></li></ul></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Model Mode and Formulation</a></li><li class="is-active"><a href>PCM</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>PCM</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/swang22/HOPE" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/swang22/HOPE/blob/master/docs/src/PCM.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h2 id="Overview"><a class="docs-heading-anchor" href="#Overview">Overview</a><a id="Overview-1"></a><a class="docs-heading-anchor-permalink" href="#Overview" title="Permalink"></a></h2><p>The production cost model (PCM) is for system operation analysis under various policies and energy transition scenarios. This model is a Linear Programming Problem.</p><p>The objective of this model is to minimize the system&#39;s (given by the planning model) total cost, including variable operation costs and penalties for non-compliance with policies. The constraints of this model are power balance, transmission transfer limit, generator operation constraints, storage operation constraints, resource adequacy requirements, and policy constraints (i.e., renewable portfolio standards (RPS) and carbon emission limitations).  The continuous decision variables of the PCM model are hourly operations of resources for a target year.</p><h1 id="Problem-Formulation"><a class="docs-heading-anchor" href="#Problem-Formulation">Problem Formulation</a><a id="Problem-Formulation-1"></a><a class="docs-heading-anchor-permalink" href="#Problem-Formulation" title="Permalink"></a></h1><h2 id="Objective-function"><a class="docs-heading-anchor" href="#Objective-function">Objective function</a><a id="Objective-function-1"></a><a class="docs-heading-anchor-permalink" href="#Objective-function" title="Permalink"></a></h2><p>(1) Minimize total system cost:</p><p class="math-container">\[\begin{aligned}
\min_{\Gamma} \quad
&amp;\sum_{g \in G, t \in T}VCG_{g} \times N_{t} \times \sum_{h \in H}p_{g,h} + \\
&amp;\sum_{s \in S, t \in T} VCS \times \sum_{h \in H} (c_{s,h} + dc_{s,h}) + \\
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\ge \sum_{i \in I_{w},h \in H} \sum_{d \in D_{i}} p_{d,h} \times RPS_{w};\\
w \in W
\end{aligned}\]</p><p>(18) Cap &amp; Trade - State carbon allowance cap:</p><p class="math-container">\[\sum_{g \in (\bigcup_{i \in I_{w}} G_{i}) \cap G^{F}} a+{g,t} - \sum_{t \in T} N_{t} em_{w,h}^{emis} \le ALW_{t,w}; w \in W\]</p><p>(19) Cap &amp; Trade - Balance between allowances and emissions:</p><p class="math-container">\[\sum_{h \in H} EF_{g} \times p_{g,h} = a_{g,t} + b_{g,t-1} = b_{g,t}; g \in (\bigcup_{i \in I_{w}} G_{i}) \cap G_{F}, w \in W, t \in T\]</p><p>(20) Cap &amp; Trade - No cross-year banking:</p><p class="math-container">\[b_{g,1} = b_{g,end} = 0; g \in G_{F}\]</p><p>(21) Nonnegative variable:</p><p class="math-container">\[a_{g,t}, b_{g,t}, p_{g,h}, p_{d,h}^{LS}, c_{s,h}, soc_{s,h}, pt^{rps}, pw_{g,w}, pwi_{g,w,w&#39;}, em^{emis} \\
\ge 0\]</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../GTEP/">« GTEP</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Thursday 8 February 2024 19:33">Thursday 8 February 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
\ge 0\]</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../GTEP/">« GTEP</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Thursday 8 February 2024 19:39">Thursday 8 February 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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