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<li class="first-level active"><a href="#linear-sensitivity-factors">Linear Sensitivity Factors</a></li>
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<li class="second-level"><a href="#injection-shift-factors">Injection Shift Factors</a></li>
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<h1 id="linear-sensitivity-factors">Linear Sensitivity Factors</h1>
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<p>UnitCommitment.jl includes a number of functions to compute typical linear sensitivity
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factors, such as <a href="@ref">Injection Shift Factors</a> and <a href="@ref">Line Outage Distribution Factors</a>. These sensitivity factors can be used to quickly compute DC power flows in both base and N-1 contigency scenarios.</p>
|
||||
<h2 id="injection-shift-factors">Injection Shift Factors</h2>
|
||||
<p>Given a network with <code>B</code> buses and <code>L</code> transmission lines, the Injection Shift Factors (ISF) matrix is an <code>L</code>-by-<code>B</code> matrix which indicates much power flows through a certain transmission line when 1 MW of power is injected at bus <code>b</code> and withdrawn from the slack bus. For example, <code>isf[:l7, :b5]</code> indicates the amount of power (in MW) that flows through line <code>l7</code> when 1 MW of power is injected at bus <code>b5</code> and withdrawn from the slack bus.
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This matrix is computed based on the DC linearization of power flow equations and does not include losses.
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To compute the ISF matrix, the function <code>injection_shift_factors</code> can be used. It is necessary to specify the set of lines, buses and the slack bus:</p>
|
||||
<pre><code class="julia">using UnitCommitment
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instance = UnitCommitment.load("ieee_rts/case14")
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isf = UnitCommitment.injection_shift_factors(lines = instance.lines,
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buses = instance.buses,
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slack = :b14)
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@show isf[:l7, :b5]
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</code></pre></div>
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<li class="first-level active"><a href="#benchmark-model">Benchmark Model</a></li>
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<li class="second-level"><a href="#building-and-solving-the-model">Building and Solving the Model</a></li>
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<li class="second-level"><a href="#decision-variables">Decision Variables</a></li>
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<li class="second-level"><a href="#accessing-the-solution">Accessing the Solution</a></li>
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<h1 id="benchmark-model">Benchmark Model</h1>
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<p>UnitCommitment.jl includes a reference Mixed-Integer Linear Programming
|
||||
(MILP), built with <a href="https://github.com/JuliaOpt/JuMP.jl">JuMP</a>, which can
|
||||
either be used as-is to solve instances of the problem, or be extended to
|
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build more complex formulations.</p>
|
||||
<h2 id="building-and-solving-the-model">Building and Solving the Model</h2>
|
||||
<p>Given an instance and a JuMP optimizer, the function <code>build_model</code> can be used to
|
||||
build the reference MILP model. For example:</p>
|
||||
<pre><code class="julia">using UnitCommitment, JuMP, Cbc
|
||||
instance = UnitCommitment.load("ieee_rts/case118")
|
||||
model = build_model(instance, with_optimizer(Cbc.Optimizer))
|
||||
</code></pre>
|
||||
|
||||
<p>The model enforces all unit constraints described in <a href="@ref">Unit Commitment
|
||||
Instances</a>, including ramping, minimum-up and minimum-down times. Some
|
||||
system-wide constraints, such as spinning reserves, are also enforced. The
|
||||
model, however, does not enforce transmission or N-1 security constraints,
|
||||
since these are typically generated on-the-fly.</p>
|
||||
<p>A reference to the JuMP model is stored at <code>model.mip</code>. After constructed, the model can
|
||||
be optimized as follows:</p>
|
||||
<pre><code class="julia">optimize!(model.mip)
|
||||
</code></pre>
|
||||
|
||||
<h2 id="decision-variables">Decision Variables</h2>
|
||||
<p>References to all decision variables are stored at <code>model.vars</code>.
|
||||
A complete list of available decision variables is as follows:</p>
|
||||
<table>
|
||||
<thead>
|
||||
<tr>
|
||||
<th align="left">Variable</th>
|
||||
<th align="left">Description</th>
|
||||
</tr>
|
||||
</thead>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td align="left"><code>model.vars.production[gi,t]</code></td>
|
||||
<td align="left">Amount of power (in MW) produced by unit with index <code>gi</code> at time <code>t</code>.</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="left"><code>model.vars.reserve[gi,t]</code></td>
|
||||
<td align="left">Amount of spinning reserves (in MW) provided by unit with index <code>gi</code> at time <code>t</code>.</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="left"><code>model.vars.is_on[gi,t]</code></td>
|
||||
<td align="left">Binary variable indicating if unit with index <code>gi</code> is operational at time <code>t</code>.</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="left"><code>model.vars.switch_on[gi,t]</code></td>
|
||||
<td align="left">Binary variable indicating if unit with index <code>gi</code> was switched on at time <code>t</code>. That is, the unit was not operational at time <code>t-1</code>, but it is operational at time <code>t</code>.</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="left"><code>model.vars.switch_off[gi,t]</code></td>
|
||||
<td align="left">Binary variable indicating if unit with index <code>gi</code> was switched off at time <code>t</code>. That is, the unit was operational at time <code>t-1</code>, but it is no longer operational at time <code>t</code>.</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="left"><code>model.vars.unit_cost[gi,t]</code></td>
|
||||
<td align="left">The total cost to operate unit with index <code>gi</code> at time <code>t</code>. Includes start-up costs, no-load costs and any other production costs.</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="left"><code>model.vars.cost[t]</code></td>
|
||||
<td align="left">Total cost at time <code>t</code>.</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="left"><code>model.vars.net_injection[bi,t]</code></td>
|
||||
<td align="left">Total net injection (in MW) at bus with index <code>bi</code> and time <code>t</code>. Net injection is defined as the total power being produced by units located at the bus minus the bus load.</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
<h2 id="accessing-the-solution">Accessing the Solution</h2>
|
||||
<p>To access the value of a particular decision variable after the
|
||||
optimization is completed, the function <code>JuMP.value(var)</code> can be used. The
|
||||
following example prints the amount of power (in MW) produced by each unit at time 5:</p>
|
||||
<pre><code class="julia">for g in instance.units
|
||||
@show value(model.vars.production[g.index, 5])
|
||||
end
|
||||
</code></pre>
|
||||
|
||||
<h2 id="modifying-the-model">Modifying the Model</h2>
|
||||
<p>Prior to being solved, the reference model can be modified by using the variable references
|
||||
above and conventional JuMP macros. For example, the
|
||||
following code can be used to ensure that at most 10 units are operational at time 4:</p>
|
||||
<pre><code class="julia">using UnitCommitment, JuMP, Cbc
|
||||
instance = UnitCommitment.load("ieee_rts/case118")
|
||||
model = build_model(instance, with_optimizer(Cbc.Optimizer))
|
||||
|
||||
@contraint(model.mip,
|
||||
sum(model.vars.is_on[g.index, 4]
|
||||
for g in instance.units) <= 10)
|
||||
|
||||
optimize!(model.mip)
|
||||
</code></pre>
|
||||
|
||||
<p>It is not currently possible to modify the constraints included in the
|
||||
reference model.</p>
|
||||
<h2 id="reference">Reference</h2>
|
||||
<p><code>@docs
|
||||
UnitCommitment.build_model</code></p></div>
|
||||
|
||||
|
||||
</div>
|
||||
|
||||
<footer class="col-md-12 text-center">
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|
||||
<hr>
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<p>
|
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<small>Copyright © 2020, UChicago Argonne, LLC. All Rights Reserved.</small><br>
|
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|
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<small>Documentation built with <a href="http://www.mkdocs.org/">MkDocs</a>.</small>
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@ -1,15 +1,15 @@
|
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<?xml version="1.0" encoding="UTF-8"?>
|
||||
<urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9"><url>
|
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<loc>None</loc>
|
||||
<lastmod>2020-11-03</lastmod>
|
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<lastmod>2020-11-06</lastmod>
|
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<changefreq>daily</changefreq>
|
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</url><url>
|
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<loc>None</loc>
|
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<lastmod>2020-11-03</lastmod>
|
||||
<lastmod>2020-11-06</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url><url>
|
||||
<loc>None</loc>
|
||||
<lastmod>2020-11-03</lastmod>
|
||||
<lastmod>2020-11-06</lastmod>
|
||||
<changefreq>daily</changefreq>
|
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</url>
|
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</urlset>
|
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