build based on 3014d49

dev/index.html

@@ -11,4 +11,4 @@
 author = "David M. Fobes and Sander Claeys and Frederik Geth and Carleton Coffrin",
 keywords = "Nonlinear optimization, Convex optimization, AC optimal power flow, Julia language, Open-source",
 abstract = "In this work we introduce PowerModelsDistribution, a free, open-source toolkit for distribution power network optimization, whose primary focus is establishing a baseline implementation of steady-state multi-conductor unbalanced distribution network optimization problems, which includes implementations of Power Flow and Optimal Power Flow problem types. Currently implemented power flow formulations for these problem types include AC (polar and rectangular), a second-order conic relaxation of the Branch Flow Model (BFM) and Bus Injection Model (BIM), a semi-definite relaxation of BFM, and several linear approximations, such as the simplified unbalanced BFM. The results of AC power flow have been validated against OpenDSS, an open-source “electric power distribution system simulator”, using IEEE distribution test feeders (13, 34, 123 bus and LVTestCase), all parsed using a built-in OpenDSS parser. This includes support for standard distribution system components as well as novel resource models such as generic energy storage (multi-period) and photovoltaic systems, with the intention to add support for additional components in the future."
-}</code></pre><p>The associated Power Systems Computation Conference talk can be found on <a href="https://youtu.be/S7ouz2OP0tE">YouTube</a>.</p><h2 id="License"><a class="docs-heading-anchor" href="#License">License</a><a id="License-1"></a><a class="docs-heading-anchor-permalink" href="#License" title="Permalink"></a></h2><p>This code is provided under a BSD license as part of the Multi-Infrastructure Control and Optimization Toolkit (MICOT) project, LA-CC-13-108.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="installation.html">Installation Guide »</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 18 September 2024 16:49">Wednesday 18 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+}</code></pre><p>The associated Power Systems Computation Conference talk can be found on <a href="https://youtu.be/S7ouz2OP0tE">YouTube</a>.</p><h2 id="License"><a class="docs-heading-anchor" href="#License">License</a><a id="License-1"></a><a class="docs-heading-anchor-permalink" href="#License" title="Permalink"></a></h2><p>This code is provided under a BSD license as part of the Multi-Infrastructure Control and Optimization Toolkit (MICOT) project, LA-CC-13-108.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="installation.html">Installation Guide »</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 18 September 2024 17:09">Wednesday 18 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/manual/formulations.html

@@ -48,4 +48,4 @@
 
 EN-ACR (AbstractExplicitNeutralIVRModel)
 |
-|-- ACRENPowerModel</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="eng2math.html">« Conversion to Mathematical Model</a><a class="docs-footer-nextpage" href="specifications.html">Problem Specifications »</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 18 September 2024 16:49">Wednesday 18 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+|-- ACRENPowerModel</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="eng2math.html">« Conversion to Mathematical Model</a><a class="docs-footer-nextpage" href="specifications.html">Problem Specifications »</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 18 September 2024 17:09">Wednesday 18 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/manual/load-model.html

@@ -3,4 +3,4 @@
 S^d&=\text{pd}+j.\text{qd} & S^\text{bus}&=\text{pd_bus}+j.\text{qd_bus}\\
 I^d&=\text{crd}+j.\text{cid} & I^\text{bus}&=\text{crd_bus}+j.\text{cid_bus}\\
 U^d&=\text{vrd}+j.\text{vid} & U^\text{bus}&=\text{vr}+j.\text{vi}\\
-\end{align}\]</p><h2 id="Voltage-dependency"><a class="docs-heading-anchor" href="#Voltage-dependency">Voltage dependency</a><a id="Voltage-dependency-1"></a><a class="docs-heading-anchor-permalink" href="#Voltage-dependency" title="Permalink"></a></h2><p>The general, exponential load model is defined as</p><p class="math-container">\[P^d_i = P^{d,0}_i \left(\frac{V^d_i}{V^{d,0}_i}\right)^{\alpha_i} = a_i \left(V^d_i\right)^{\alpha_i}\]</p><p class="math-container">\[Q^d_i = Q^{d,0}_i \left(\frac{V^d_i}{V^{d,0}_i}\right)^{\beta_i} = b_i \left(V^d_i\right)^{\beta_i}.\]</p><p>There are a few cases which get a special name: constant power (<span>$\alpha=\beta=0$</span>), constant current (<span>$\alpha=\beta=1$</span>), and constant impedance (<span>$\alpha=\beta=2$</span>).</p><h2 id="Wye-connected-Loads"><a class="docs-heading-anchor" href="#Wye-connected-Loads">Wye-connected Loads</a><a id="Wye-connected-Loads-1"></a><a class="docs-heading-anchor-permalink" href="#Wye-connected-Loads" title="Permalink"></a></h2><p>A wye-connected load connects between a set of phases <span>$\mathcal{P}$</span> and a neutral conductor <span>$n$</span>. The voltage as seen by each individual load is then</p><p class="math-container">\[U^d = U^\text{bus}_\mathcal{P}-U^\text{bus}_n,\]</p><p>whilst the current</p><p class="math-container">\[I^\text{bus}_\mathcal{P} = I^\text{d},\;\;\;I^\text{bus}_n=-1^TI^d\]</p><p>We now develop the expression for the power drawn at the bus for the phase conductors</p><p class="math-container">\[S^\text{bus}_\mathcal{P} = (U^d+U^\text{bus}_n)\odot(I^d)^* = S^d+U^\text{bus}_n S^d\oslash U^d.\]</p><p>From conservation of power or simply the formulas above,</p><p class="math-container">\[S^\text{bus}_n = -1^TS^\text{bus}_\mathcal{P}+1^TS^d.\]</p><h3 id="Grounded-neutral"><a class="docs-heading-anchor" href="#Grounded-neutral">Grounded neutral</a><a id="Grounded-neutral-1"></a><a class="docs-heading-anchor-permalink" href="#Grounded-neutral" title="Permalink"></a></h3><p>Note that when the neutral is grounded, i.e. <span>$U^\text{bus}_n=0$</span>, these formulas simplify to</p><p class="math-container">\[S^\text{bus}_\mathcal{P}=S^d,\;\;\;S^\text{bus}_n=0,\]</p><p>which is why in Kron-reduced unbalanced networks, you can directly insert the power consumed by the loads, in the nodal power balance equations.</p><h2 id="Delta-connected-Loads"><a class="docs-heading-anchor" href="#Delta-connected-Loads">Delta-connected Loads</a><a id="Delta-connected-Loads-1"></a><a class="docs-heading-anchor-permalink" href="#Delta-connected-Loads" title="Permalink"></a></h2><p>Firstly, define the three-phase delta transformation matrix</p><p class="math-container">\[M^\Delta_3 = \begin{bmatrix}\;\;\;1 &amp; -1 &amp; \;\;0\\ \;\;\;0 &amp; \;\;\;1 &amp; -1\\ -1 &amp; \;\;\;0 &amp; \;\;\;1\end{bmatrix},\]</p><p>which can be extended to more phases in a straight-forward manner. For loads connected between split-phase terminals of triplex nodes (usually located on the secondary side of center-tapped transformers), we define a single-phase delta transformation matrix</p><p class="math-container">\[M^\Delta_1 = \begin{bmatrix} 1 &amp; -1 \end{bmatrix}.\]</p><p>Now,</p><p class="math-container">\[U^d = M^\Delta U^\text{bus},\;\;\; I^\text{bus} = \left(M^\Delta\right)^T I^d.\]</p><p>We can related <span>$S^\text{bus}$</span> to <span>$U^\text{bus}$</span> and <span>$I^d$</span></p><p class="math-container">\[S^\text{bus} = U^\text{bus}\odot \left(I^\text{bus}\right)^* = U^\text{bus}\odot \left(M^\Delta\right)^T\left(I^d\right)^*,\]</p><p>and using the fact that <span>$\left(I^d\right)^*=S^d \oslash U^d$</span>, and the expression above for <span>$U^d$</span>,</p><p class="math-container">\[S^\text{bus} = U^\text{bus}\left(M^\Delta\right)^T S^d \oslash M^\Delta U^\text{bus}\]</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="specifications.html">« Problem Specifications</a><a class="docs-footer-nextpage" href="connections.html">Connecting Components »</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 18 September 2024 16:49">Wednesday 18 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+\end{align}\]</p><h2 id="Voltage-dependency"><a class="docs-heading-anchor" href="#Voltage-dependency">Voltage dependency</a><a id="Voltage-dependency-1"></a><a class="docs-heading-anchor-permalink" href="#Voltage-dependency" title="Permalink"></a></h2><p>The general, exponential load model is defined as</p><p class="math-container">\[P^d_i = P^{d,0}_i \left(\frac{V^d_i}{V^{d,0}_i}\right)^{\alpha_i} = a_i \left(V^d_i\right)^{\alpha_i}\]</p><p class="math-container">\[Q^d_i = Q^{d,0}_i \left(\frac{V^d_i}{V^{d,0}_i}\right)^{\beta_i} = b_i \left(V^d_i\right)^{\beta_i}.\]</p><p>There are a few cases which get a special name: constant power (<span>$\alpha=\beta=0$</span>), constant current (<span>$\alpha=\beta=1$</span>), and constant impedance (<span>$\alpha=\beta=2$</span>).</p><h2 id="Wye-connected-Loads"><a class="docs-heading-anchor" href="#Wye-connected-Loads">Wye-connected Loads</a><a id="Wye-connected-Loads-1"></a><a class="docs-heading-anchor-permalink" href="#Wye-connected-Loads" title="Permalink"></a></h2><p>A wye-connected load connects between a set of phases <span>$\mathcal{P}$</span> and a neutral conductor <span>$n$</span>. The voltage as seen by each individual load is then</p><p class="math-container">\[U^d = U^\text{bus}_\mathcal{P}-U^\text{bus}_n,\]</p><p>whilst the current</p><p class="math-container">\[I^\text{bus}_\mathcal{P} = I^\text{d},\;\;\;I^\text{bus}_n=-1^TI^d\]</p><p>We now develop the expression for the power drawn at the bus for the phase conductors</p><p class="math-container">\[S^\text{bus}_\mathcal{P} = (U^d+U^\text{bus}_n)\odot(I^d)^* = S^d+U^\text{bus}_n S^d\oslash U^d.\]</p><p>From conservation of power or simply the formulas above,</p><p class="math-container">\[S^\text{bus}_n = -1^TS^\text{bus}_\mathcal{P}+1^TS^d.\]</p><h3 id="Grounded-neutral"><a class="docs-heading-anchor" href="#Grounded-neutral">Grounded neutral</a><a id="Grounded-neutral-1"></a><a class="docs-heading-anchor-permalink" href="#Grounded-neutral" title="Permalink"></a></h3><p>Note that when the neutral is grounded, i.e. <span>$U^\text{bus}_n=0$</span>, these formulas simplify to</p><p class="math-container">\[S^\text{bus}_\mathcal{P}=S^d,\;\;\;S^\text{bus}_n=0,\]</p><p>which is why in Kron-reduced unbalanced networks, you can directly insert the power consumed by the loads, in the nodal power balance equations.</p><h2 id="Delta-connected-Loads"><a class="docs-heading-anchor" href="#Delta-connected-Loads">Delta-connected Loads</a><a id="Delta-connected-Loads-1"></a><a class="docs-heading-anchor-permalink" href="#Delta-connected-Loads" title="Permalink"></a></h2><p>Firstly, define the three-phase delta transformation matrix</p><p class="math-container">\[M^\Delta_3 = \begin{bmatrix}\;\;\;1 &amp; -1 &amp; \;\;0\\ \;\;\;0 &amp; \;\;\;1 &amp; -1\\ -1 &amp; \;\;\;0 &amp; \;\;\;1\end{bmatrix},\]</p><p>which can be extended to more phases in a straight-forward manner. For loads connected between split-phase terminals of triplex nodes (usually located on the secondary side of center-tapped transformers), we define a single-phase delta transformation matrix</p><p class="math-container">\[M^\Delta_1 = \begin{bmatrix} 1 &amp; -1 \end{bmatrix}.\]</p><p>Now,</p><p class="math-container">\[U^d = M^\Delta U^\text{bus},\;\;\; I^\text{bus} = \left(M^\Delta\right)^T I^d.\]</p><p>We can related <span>$S^\text{bus}$</span> to <span>$U^\text{bus}$</span> and <span>$I^d$</span></p><p class="math-container">\[S^\text{bus} = U^\text{bus}\odot \left(I^\text{bus}\right)^* = U^\text{bus}\odot \left(M^\Delta\right)^T\left(I^d\right)^*,\]</p><p>and using the fact that <span>$\left(I^d\right)^*=S^d \oslash U^d$</span>, and the expression above for <span>$U^d$</span>,</p><p class="math-container">\[S^\text{bus} = U^\text{bus}\left(M^\Delta\right)^T S^d \oslash M^\Delta U^\text{bus}\]</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="specifications.html">« Problem Specifications</a><a class="docs-footer-nextpage" href="connections.html">Connecting Components »</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 18 September 2024 17:09">Wednesday 18 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>