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| <html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Lossless nodal DC power flows · SpineOpt.jl</title><meta name="title" content="Lossless nodal DC power flows · SpineOpt.jl"/><meta property="og:title" content="Lossless nodal DC power flows · SpineOpt.jl"/><meta property="twitter:title" content="Lossless nodal DC power flows · SpineOpt.jl"/><meta name="description" content="Documentation for SpineOpt.jl."/><meta property="og:description" content="Documentation for SpineOpt.jl."/><meta property="twitter:description" content="Documentation for SpineOpt.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script data-outdated-warner src="../../assets/warner.js"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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Framework</a></li></ul></li><li><span class="tocitem">Standard model features</span><ul><li><a class="tocitem" href="../unit_commitment/">Unit Commitment</a></li><li><a class="tocitem" href="../investment_optimization/">Investment Optimization</a></li><li><a class="tocitem" href="../multi-year/">Multi-year Investments</a></li><li><a class="tocitem" href="../reserves/">Reserves</a></li><li><a class="tocitem" href="../ramping/">Ramping</a></li><li class="is-active"><a class="tocitem" href>Lossless nodal DC power flows</a><ul class="internal"><li><a class="tocitem" href="#key-concepts-advanced-nodal-DC"><span>Key concepts</span></a></li></ul></li><li><a class="tocitem" href="../powerflow/">PTDF-Based Powerflow</a></li><li><a class="tocitem" href="../pressure_driven_gas_transfer/">Pressure driven gas transfer</a></li><li><a class="tocitem" href="../user_constraints/">User Constraints</a></li></ul></li><li><span class="tocitem">Algorithms</span><ul><li><a class="tocitem" 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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">Standard model features</a></li><li class="is-active"><a href>Lossless nodal DC power flows</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Lossless nodal DC power flows</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/spine-tools/SpineOpt.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/spine-tools/SpineOpt.jl/blob/master/docs/src/advanced_concepts/Lossless_DC_power_flow.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="Lossless-nodal-DC-power-flows"><a class="docs-heading-anchor" href="#Lossless-nodal-DC-power-flows">Lossless nodal DC power flows</a><a id="Lossless-nodal-DC-power-flows-1"></a><a class="docs-heading-anchor-permalink" href="#Lossless-nodal-DC-power-flows" title="Permalink"></a></h1><p>Currently, there are two different methods to represent lossless DC power flows. In the following the implementation of the nodal model is presented, based of node voltage angles.</p><h2 id="key-concepts-advanced-nodal-DC"><a class="docs-heading-anchor" href="#key-concepts-advanced-nodal-DC">Key concepts</a><a id="key-concepts-advanced-nodal-DC-1"></a><a class="docs-heading-anchor-permalink" href="#key-concepts-advanced-nodal-DC" title="Permalink"></a></h2><p>In the following, it is described how to set up a connection in order to represent a nodal lossless DC power flow network. Therefore, key object - and relationship classes as well as parameters are introduced.</p><ol><li><strong><a href="../../concept_reference/Object Classes/#connection">connection</a></strong>: A connection represents the electricity line being modelled. A physical property of a connection is its <a href="../../concept_reference/Parameters/#connection_reactance">connection_reactance</a>, which is defined on the connection object. Furthermore, if the reactance is given in a p.u. different from the standard unit used (e.g. p.u. = 100MVA), the parameter <a href="../../concept_reference/Parameters/#connection_reactance_base">connection_reactance_base</a> can be used to perform this conversion.</li><li><strong><a href="../../concept_reference/Object Classes/#node">node</a></strong>: In a lossless DC power flow model, nodes correspond to buses. To use voltage angles for the representation of a lossless DC model, the <a href="../../concept_reference/Parameters/#has_voltage_angle">has_voltage_angle</a> needs to be <code>true</code> for these nodes (which will trigger the generation of the <a href="../../mathematical_formulation/variables/#node_voltage_angle">node_voltage_angle</a> variable). Limits on the voltage angle can be enforced through the <a href="../../concept_reference/Parameters/#max_voltage_angle">max_voltage_angle</a> and <a href="../../concept_reference/Parameters/#min_voltage_angle">min_voltage_angle</a> parameters. The reference node of the system should have a voltage angle equal to zero, assigned through the parameter <a href="../../concept_reference/Parameters/#fix_node_voltage_angle">fix_node_voltage_angle</a>.</li><li><strong><a href="../../concept_reference/Relationship Classes/#connection__to_node">connection__to_node</a> and <a href="../../concept_reference/Relationship Classes/#connection__from_node">connection__from_node</a></strong> : These relationships need to be introduced between the connection and each node, in order to allow power flows (i.e. <a href="../../mathematical_formulation/variables/#connection_flow">connection_flow</a>). Furthermore, a capacity limit on the connection line can be introduced on these relationships through the parameter <a href="../../concept_reference/Parameters/#connection_capacity">connection_capacity</a>.</li><li><strong><a href="../../concept_reference/Relationship Classes/#connection__node__node">connection__node__node</a></strong>: To ensure energy conservation across the power line, a fixed ratio between incoming and outgoing flows should be given. The <a href="../../concept_reference/Parameters/#fix_ratio_out_in_connection_flow">fix_ratio_out_in_connection_flow</a> parameter enforces a fixed ratio between outgoing flows (i.e. to_node) and incoming flows (i.e. from_node). This parameter should be defined for both flow direction.</li></ol><p>The mathematical formulation of the lossless DC power flow model using voltage angles is fully described <a href="@ref nodal-lossless-DC">here</a>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../ramping/">« Ramping</a><a class="docs-footer-nextpage" href="../powerflow/">PTDF-Based Powerflow »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Tuesday 26 November 2024 14:58">Tuesday 26 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> |
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