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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Market clearing and LMPs · UnitCommitment.jl</title><meta name="title" content="Market clearing and LMPs · UnitCommitment.jl"/><meta property="og:title" content="Market clearing and LMPs · UnitCommitment.jl"/><meta property="twitter:title" content="Market clearing and LMPs · UnitCommitment.jl"/><meta name="description" content="Documentation for UnitCommitment.jl."/><meta property="og:description" content="Documentation for UnitCommitment.jl."/><meta property="twitter:description" content="Documentation for UnitCommitment.jl."/><script data-outdated-warner src="../../assets/warner.js"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 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href>Market clearing and LMPs</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Market clearing and LMPs</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/ANL-CEEESA/UnitCommitment.jl" 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/ANL-CEEESA/UnitCommitment.jl/blob/dev/docs/src/tutorials/market-old.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="Market-clearing-and-LMPs"><a class="docs-heading-anchor" href="#Market-clearing-and-LMPs">Market clearing and LMPs</a><a id="Market-clearing-and-LMPs-1"></a><a class="docs-heading-anchor-permalink" href="#Market-clearing-and-LMPs" title="Permalink"></a></h1><h2 id="Computing-Locational-Marginal-Prices"><a class="docs-heading-anchor" href="#Computing-Locational-Marginal-Prices">Computing Locational Marginal Prices</a><a id="Computing-Locational-Marginal-Prices-1"></a><a class="docs-heading-anchor-permalink" href="#Computing-Locational-Marginal-Prices" title="Permalink"></a></h2><p>Locational marginal prices (LMPs) refer to the cost of supplying electricity at a particular location of the netw0ork. Multiple methods for computing LMPs have been proposed in the literature. UnitCommitment.jl implements two commonly-used methods: conventional LMPs and Approximated Extended LMPs (AELMPs). To compute LMPs for a given unit commitment instance, the <code>compute_lmp</code> function can be used, as shown in the examples below. The function accepts three arguments – a solved SCUC model, an LMP method, and a linear optimizer – and it returns a dictionary mapping <code>(bus_name, time)</code> to the marginal price.</p><div class="admonition is-warning"><header class="admonition-header">Warning</header><div class="admonition-body"><p>Most mixed-integer linear optimizers, such as <code>HiGHS</code>, <code>Gurobi</code> and <code>CPLEX</code> can be used with <code>compute_lmp</code>, with the notable exception of <code>Cbc</code>, which does not support dual value evaluations. If using <code>Cbc</code>, please provide <code>Clp</code> as the linear optimizer.</p></div></div><h3 id="Conventional-LMPs"><a class="docs-heading-anchor" href="#Conventional-LMPs">Conventional LMPs</a><a id="Conventional-LMPs-1"></a><a class="docs-heading-anchor-permalink" href="#Conventional-LMPs" title="Permalink"></a></h3><p>LMPs are conventionally computed by: (1) solving the SCUC model, (2) fixing all binary variables to their optimal values, and (3) re-solving the resulting linear programming model. In this approach, the LMPs are defined as the dual variables' values associated with the net injection constraints. The example below shows how to compute conventional LMPs for a given unit commitment instance. First, we build and optimize the SCUC model. Then, we call the <code>compute_lmp</code> function, providing as the second argument <code>ConventionalLMP()</code>.</p><pre><code class="language-julia hljs">using UnitCommitment
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using HiGHS
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import UnitCommitment: ConventionalLMP
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# Read benchmark instance
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instance = UnitCommitment.read_benchmark("matpower/case118/2018-01-01")
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# Build the model
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model = UnitCommitment.build_model(
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instance = instance,
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optimizer = HiGHS.Optimizer,
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)
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# Optimize the model
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UnitCommitment.optimize!(model)
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# Compute the LMPs using the conventional method
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lmp = UnitCommitment.compute_lmp(
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model,
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ConventionalLMP(),
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optimizer = HiGHS.Optimizer,
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)
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# Access the LMPs
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# Example: "s1" is the scenario name, "b1" is the bus name, 1 is the first time slot
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@show lmp["s1","b1", 1]</code></pre><h3 id="Approximate-Extended-LMPs"><a class="docs-heading-anchor" href="#Approximate-Extended-LMPs">Approximate Extended LMPs</a><a id="Approximate-Extended-LMPs-1"></a><a class="docs-heading-anchor-permalink" href="#Approximate-Extended-LMPs" title="Permalink"></a></h3><p>Approximate Extended LMPs (AELMPs) are an alternative method to calculate locational marginal prices which attemps to minimize uplift payments. The method internally works by modifying the instance data in three ways: (1) it sets the minimum power output of each generator to zero, (2) it averages the start-up cost over the offer blocks for each generator, and (3) it relaxes all integrality constraints. To compute AELMPs, as shown in the example below, we call <code>compute_lmp</code> and provide <code>AELMP()</code> as the second argument.</p><p>This method has two configurable parameters: <code>allow_offline_participation</code> and <code>consider_startup_costs</code>. If <code>allow_offline_participation = true</code>, then offline generators are allowed to participate in the pricing. If instead <code>allow_offline_participation = false</code>, offline generators are not allowed and therefore are excluded from the system. A solved UC model is optional if offline participation is allowed, but is required if not allowed. The method forces offline participation to be allowed if the UC model supplied by the user is not solved. For the second field, If <code>consider_startup_costs = true</code>, then start-up costs are integrated and averaged over each unit production; otherwise the production costs stay the same. By default, both fields are set to <code>true</code>.</p><div class="admonition is-warning"><header class="admonition-header">Warning</header><div class="admonition-body"><p>This approximation method is still under active research, and has several limitations. The implementation provided in the package is based on MISO Phase I only. It only supports fast start resources. More specifically, the minimum up/down time of all generators must be 1, the initial power of all generators must be 0, and the initial status of all generators must be negative. The method does not support time-varying start-up costs. The method does not support multiple scenarios. If offline participation is not allowed, AELMPs treats an asset to be offline if it is never on throughout all time periods.</p></div></div><pre><code class="language-julia hljs">using UnitCommitment
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using HiGHS
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import UnitCommitment: AELMP
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# Read benchmark instance
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instance = UnitCommitment.read_benchmark("matpower/case118/2017-02-01")
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# Build the model
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model = UnitCommitment.build_model(
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instance = instance,
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optimizer = HiGHS.Optimizer,
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)
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# Optimize the model
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UnitCommitment.optimize!(model)
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# Compute the AELMPs
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aelmp = UnitCommitment.compute_lmp(
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model,
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AELMP(
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allow_offline_participation = false,
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consider_startup_costs = true
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),
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optimizer = HiGHS.Optimizer
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)
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# Access the AELMPs
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# Example: "s1" is the scenario name, "b1" is the bus name, 1 is the first time slot
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# Note: although scenario is supported, the query still keeps the scenario keys for consistency.
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@show aelmp["s1", "b1", 1]</code></pre></article><nav class="docs-footer"><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="Tuesday 21 May 2024 10:28">Tuesday 21 May 2024</span>. Using Julia version 1.10.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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