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Documenter.jl committed Feb 5, 2024
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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":"2024-02-05T05:35:19","documenter_version":"1.2.1"}}
{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2024-02-05T18:13:16","documenter_version":"1.2.1"}}
2 changes: 1 addition & 1 deletion dev/GTEP/index.html
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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="Monday 5 February 2024 05:35">Monday 5 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="Monday 5 February 2024 18:13">Monday 5 February 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
4 changes: 2 additions & 2 deletions dev/PCM/index.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></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">\[\begin{aligned}
\text{min} \quad
\min_{\Gamma} \quad
&amp;\sum_{g \in G, t \in T}VCG_{g} \times N_{t} \times \sum_{h \in H}p_{g,h} + \\
&amp;\sum_{s \in S, t \in T} VCS \times \sum_{h \in H} (c_{s,h} + dc_{s,h}) + \\
&amp;\sum_{d \in D, t \in T} VOLL_{d} \times \sum_{h \in H} p_{d,h}^{LS} + \\
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\ge \sum_{i \in I_{w},h \in H} \sum_{d \in D_{i}} p_{d,h} \times RPS_{w};\\
w \in W
\end{aligned}\]</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="Monday 5 February 2024 05:35">Monday 5 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="Monday 5 February 2024 18:13">Monday 5 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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