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JuMP Model
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Decision variables
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Price-sensitive loads
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4.2.
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Objective function
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Constraints
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4.4.
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Inspecting and modifying the model
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Accessing decision variables
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Fixing variables, modifying objective function and adding constraints
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Adding new component to a bus
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References
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<div class="section" id="jump-model">
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<h1><span class="sectnum">4.</span> JuMP Model<a class="headerlink" href="#jump-model" title="Permalink to this headline">¶</a></h1>
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<p>In this page, we describe the JuMP optimization model produced by the function <code class="docutils literal notranslate"><span class="pre">UnitCommitment.build_model</span></code>. A detailed understanding of this model is not necessary if you are just interested in using the package to solve some standard unit commitment cases, but it may be useful, for example, if you need to solve a slightly different problem, with additional variables and constraints. The notation in this page generally follows [KnOsWa20].</p>
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<div class="section" id="decision-variables">
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<h2><span class="sectnum">4.1.</span> Decision variables<a class="headerlink" href="#decision-variables" title="Permalink to this headline">¶</a></h2>
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<div class="section" id="generators">
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<h3>Generators<a class="headerlink" href="#generators" title="Permalink to this headline">¶</a></h3>
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<table class="colwidths-auto docutils align-default">
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<thead>
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<tr class="row-odd"><th class="head"><p>Name</p></th>
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<th class="text-align:center head"><p>Symbol</p></th>
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<th class="head"><p>Description</p></th>
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<th class="text-align:center head"><p>Unit</p></th>
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</tr>
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</thead>
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<tbody>
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<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">is_on[g,t]</span></code></p></td>
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<td class="text-align:center"><p><span class="math notranslate nohighlight">\(u_{g}(t)\)</span></p></td>
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<td><p>True if generator <code class="docutils literal notranslate"><span class="pre">g</span></code> is on at time <code class="docutils literal notranslate"><span class="pre">t</span></code>.</p></td>
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<td class="text-align:center"><p>Binary</p></td>
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</tr>
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<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">switch_on[g,t]</span></code></p></td>
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<td class="text-align:center"><p><span class="math notranslate nohighlight">\(v_{g}(t)\)</span></p></td>
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<td><p>True is generator <code class="docutils literal notranslate"><span class="pre">g</span></code> switches on at time <code class="docutils literal notranslate"><span class="pre">t</span></code>.</p></td>
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<td class="text-align:center"><p>Binary</p></td>
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</tr>
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<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">switch_off[g,t]</span></code></p></td>
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<td class="text-align:center"><p><span class="math notranslate nohighlight">\(w_{g}(t)\)</span></p></td>
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<td><p>True if generator <code class="docutils literal notranslate"><span class="pre">g</span></code> switches off at time <code class="docutils literal notranslate"><span class="pre">t</span></code>.</p></td>
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<td class="text-align:center"><p>Binary</p></td>
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</tr>
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<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">prod_above[g,t]</span></code></p></td>
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<td class="text-align:center"><p><span class="math notranslate nohighlight">\(p'_{g}(t)\)</span></p></td>
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<td><p>Amount of power produced by generator <code class="docutils literal notranslate"><span class="pre">g</span></code> above its minimum power output at time <code class="docutils literal notranslate"><span class="pre">t</span></code>. For example, if the minimum power of generator <code class="docutils literal notranslate"><span class="pre">g</span></code> is 100 MW and <code class="docutils literal notranslate"><span class="pre">g</span></code> is producing 115 MW of power at time <code class="docutils literal notranslate"><span class="pre">t</span></code>, then <code class="docutils literal notranslate"><span class="pre">prod_above[g,t]</span></code> equals <code class="docutils literal notranslate"><span class="pre">15.0</span></code>.</p></td>
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<td class="text-align:center"><p>MW</p></td>
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</tr>
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<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">segprod[g,t,k]</span></code></p></td>
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<td class="text-align:center"><p><span class="math notranslate nohighlight">\(p^k_g(t)\)</span></p></td>
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<td><p>Amount of power from piecewise linear segment <code class="docutils literal notranslate"><span class="pre">k</span></code> produced by generator <code class="docutils literal notranslate"><span class="pre">g</span></code> at time <code class="docutils literal notranslate"><span class="pre">t</span></code>. For example, if cost curve for generator <code class="docutils literal notranslate"><span class="pre">g</span></code> is defined by the points <code class="docutils literal notranslate"><span class="pre">(100,</span> <span class="pre">1400)</span></code>, <code class="docutils literal notranslate"><span class="pre">(110,</span> <span class="pre">1600)</span></code>, <code class="docutils literal notranslate"><span class="pre">(130,</span> <span class="pre">2200)</span></code> and <code class="docutils literal notranslate"><span class="pre">(135,</span> <span class="pre">2400)</span></code>, and if the generator is producing 115 MW of power at time <code class="docutils literal notranslate"><span class="pre">t</span></code>, then <code class="docutils literal notranslate"><span class="pre">segprod[g,t,:]</span></code> equals <code class="docutils literal notranslate"><span class="pre">[10.0,</span> <span class="pre">5.0,</span> <span class="pre">0.0]</span></code>.</p></td>
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<td class="text-align:center"><p>MW</p></td>
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</tr>
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<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">reserve[r,g,t]</span></code></p></td>
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<td class="text-align:center"><p><span class="math notranslate nohighlight">\(r_g(t)\)</span></p></td>
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<td><p>Amount of reserve <code class="docutils literal notranslate"><span class="pre">r</span></code> provided by unit <code class="docutils literal notranslate"><span class="pre">g</span></code> at time <code class="docutils literal notranslate"><span class="pre">t</span></code>.</p></td>
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<td class="text-align:center"><p>MW</p></td>
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</tr>
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<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">startup[g,t,s]</span></code></p></td>
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<td class="text-align:center"><p><span class="math notranslate nohighlight">\(\delta^s_g(t)\)</span></p></td>
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<td><p>True if generator <code class="docutils literal notranslate"><span class="pre">g</span></code> switches on at time <code class="docutils literal notranslate"><span class="pre">t</span></code> incurring start-up costs from start-up category <code class="docutils literal notranslate"><span class="pre">s</span></code>.</p></td>
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<td class="text-align:center"><p>Binary</p></td>
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</tr>
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</tbody>
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</table>
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</div>
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<div class="section" id="buses">
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<h3>Buses<a class="headerlink" href="#buses" title="Permalink to this headline">¶</a></h3>
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<table class="colwidths-auto docutils align-default">
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<thead>
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<tr class="row-odd"><th class="head"><p>Name</p></th>
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<th class="text-align:center head"><p>Symbol</p></th>
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<th class="head"><p>Description</p></th>
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<th class="text-align:center head"><p>Unit</p></th>
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</tr>
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</thead>
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<tbody>
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<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">net_injection[b,t]</span></code></p></td>
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<td class="text-align:center"><p><span class="math notranslate nohighlight">\(n_b(t)\)</span></p></td>
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<td><p>Net injection at bus <code class="docutils literal notranslate"><span class="pre">b</span></code> at time <code class="docutils literal notranslate"><span class="pre">t</span></code>.</p></td>
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<td class="text-align:center"><p>MW</p></td>
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</tr>
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<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">curtail[b,t]</span></code></p></td>
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<td class="text-align:center"><p><span class="math notranslate nohighlight">\(s^+_b(t)\)</span></p></td>
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<td><p>Amount of load curtailed at bus <code class="docutils literal notranslate"><span class="pre">b</span></code> at time <code class="docutils literal notranslate"><span class="pre">t</span></code></p></td>
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<td class="text-align:center"><p>MW</p></td>
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</tr>
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</tbody>
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</table>
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</div>
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<div class="section" id="price-sensitive-loads">
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<h3>Price-sensitive loads<a class="headerlink" href="#price-sensitive-loads" title="Permalink to this headline">¶</a></h3>
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<table class="colwidths-auto docutils align-default">
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<thead>
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<tr class="row-odd"><th class="head"><p>Name</p></th>
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<th class="text-align:center head"><p>Symbol</p></th>
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<th class="head"><p>Description</p></th>
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<th class="text-align:center head"><p>Unit</p></th>
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</tr>
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</thead>
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<tbody>
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|
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">loads[s,t]</span></code></p></td>
|
|
<td class="text-align:center"><p><span class="math notranslate nohighlight">\(d_{s}(t)\)</span></p></td>
|
|
<td><p>Amount of power served to price-sensitive load <code class="docutils literal notranslate"><span class="pre">s</span></code> at time <code class="docutils literal notranslate"><span class="pre">t</span></code>.</p></td>
|
|
<td class="text-align:center"><p>MW</p></td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
<div class="section" id="transmission-lines">
|
|
<h3>Transmission lines<a class="headerlink" href="#transmission-lines" title="Permalink to this headline">¶</a></h3>
|
|
<table class="colwidths-auto docutils align-default">
|
|
<thead>
|
|
<tr class="row-odd"><th class="head"><p>Name</p></th>
|
|
<th class="text-align:center head"><p>Symbol</p></th>
|
|
<th class="head"><p>Description</p></th>
|
|
<th class="text-align:center head"><p>Unit</p></th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">flow[l,t]</span></code></p></td>
|
|
<td class="text-align:center"><p><span class="math notranslate nohighlight">\(f_l(t)\)</span></p></td>
|
|
<td><p>Power flow on line <code class="docutils literal notranslate"><span class="pre">l</span></code> at time <code class="docutils literal notranslate"><span class="pre">t</span></code>.</p></td>
|
|
<td class="text-align:center"><p>MW</p></td>
|
|
</tr>
|
|
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">overflow[l,t]</span></code></p></td>
|
|
<td class="text-align:center"><p><span class="math notranslate nohighlight">\(f^+_l(t)\)</span></p></td>
|
|
<td><p>Amount of flow above the limit for line <code class="docutils literal notranslate"><span class="pre">l</span></code> at time <code class="docutils literal notranslate"><span class="pre">t</span></code>.</p></td>
|
|
<td class="text-align:center"><p>MW</p></td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
<div class="admonition warning">
|
|
<p class="admonition-title">Warning</p>
|
|
<p>Since transmission and N-1 security constraints are enforced in a lazy way, most of the <code class="docutils literal notranslate"><span class="pre">flow[l,t]</span></code> variables are never added to the model. Accessing <code class="docutils literal notranslate"><span class="pre">model[:flow][l,t]</span></code> without first checking that the variable exists will likely generate an error.</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div class="section" id="objective-function">
|
|
<h2><span class="sectnum">4.2.</span> Objective function<a class="headerlink" href="#objective-function" title="Permalink to this headline">¶</a></h2>
|
|
<div class="math notranslate nohighlight">
|
|
\[\begin{split}
|
|
\begin{align}
|
|
\text{minimize} \;\; &
|
|
\sum_{t \in \mathcal{T}}
|
|
\sum_{g \in \mathcal{G}}
|
|
C^\text{min}_g(t) u_g(t) \\
|
|
&
|
|
+ \sum_{t \in \mathcal{T}}
|
|
\sum_{g \in \mathcal{G}}
|
|
\sum_{g \in \mathcal{K}_g}
|
|
C^k_g(t) p^k_g(t) \\
|
|
&
|
|
+ \sum_{t \in \mathcal{T}}
|
|
\sum_{g \in \mathcal{G}}
|
|
\sum_{s \in \mathcal{S}_g}
|
|
C^s_{g}(t) \delta^s_g(t) \\
|
|
&
|
|
+ \sum_{t \in \mathcal{T}}
|
|
\sum_{l \in \mathcal{L}}
|
|
C^\text{overflow}_{l}(t) f^+_l(t) \\
|
|
&
|
|
+ \sum_{t \in \mathcal{T}}
|
|
\sum_{b \in \mathcal{B}}
|
|
C^\text{curtail}(t) s^+_b(t) \\
|
|
&
|
|
- \sum_{t \in \mathcal{T}}
|
|
\sum_{s \in \mathcal{PS}}
|
|
R_{s}(t) d_{s}(t) \\
|
|
|
|
\end{align}
|
|
\end{split}\]</div>
|
|
<p>where</p>
|
|
<ul class="simple">
|
|
<li><p><span class="math notranslate nohighlight">\(\mathcal{B}\)</span> is the set of buses</p></li>
|
|
<li><p><span class="math notranslate nohighlight">\(\mathcal{G}\)</span> is the set of generators</p></li>
|
|
<li><p><span class="math notranslate nohighlight">\(\mathcal{L}\)</span> is the set of transmission lines</p></li>
|
|
<li><p><span class="math notranslate nohighlight">\(\mathcal{PS}\)</span> is the set of price-sensitive loads</p></li>
|
|
<li><p><span class="math notranslate nohighlight">\(\mathcal{S}_g\)</span> is the set of start-up categories for generator <span class="math notranslate nohighlight">\(g\)</span></p></li>
|
|
<li><p><span class="math notranslate nohighlight">\(\mathcal{T}\)</span> is the set of time steps</p></li>
|
|
<li><p><span class="math notranslate nohighlight">\(C^\text{curtail}(t)\)</span> is the curtailment penalty (in $/MW)</p></li>
|
|
<li><p><span class="math notranslate nohighlight">\(C^\text{min}_g(t)\)</span> is the cost of keeping generator <span class="math notranslate nohighlight">\(g\)</span> on and producing at minimum power during time <span class="math notranslate nohighlight">\(t\)</span> (in $)</p></li>
|
|
<li><p><span class="math notranslate nohighlight">\(C^\text{overflow}_{l}(t)\)</span> is the flow limit penalty for line <span class="math notranslate nohighlight">\(l\)</span> at time <span class="math notranslate nohighlight">\(t\)</span> (in $/MW)</p></li>
|
|
<li><p><span class="math notranslate nohighlight">\(C^k_g(t)\)</span> is the cost for generator <span class="math notranslate nohighlight">\(g\)</span> to produce 1 MW of power at time <span class="math notranslate nohighlight">\(t\)</span> under piecewise linear segment <span class="math notranslate nohighlight">\(k\)</span></p></li>
|
|
<li><p><span class="math notranslate nohighlight">\(C^s_{g}(t)\)</span> is the cost of starting up generator <span class="math notranslate nohighlight">\(g\)</span> at time <span class="math notranslate nohighlight">\(t\)</span> under start-up category <span class="math notranslate nohighlight">\(s\)</span> (in $)</p></li>
|
|
<li><p><span class="math notranslate nohighlight">\(R_{s}(t)\)</span> is the revenue obtained from serving price-sensitive load <span class="math notranslate nohighlight">\(s\)</span> at time <span class="math notranslate nohighlight">\(t\)</span> (in $/MW)</p></li>
|
|
</ul>
|
|
</div>
|
|
<div class="section" id="constraints">
|
|
<h2><span class="sectnum">4.3.</span> Constraints<a class="headerlink" href="#constraints" title="Permalink to this headline">¶</a></h2>
|
|
<p>TODO</p>
|
|
</div>
|
|
<div class="section" id="inspecting-and-modifying-the-model">
|
|
<h2><span class="sectnum">4.4.</span> Inspecting and modifying the model<a class="headerlink" href="#inspecting-and-modifying-the-model" title="Permalink to this headline">¶</a></h2>
|
|
<div class="section" id="accessing-decision-variables">
|
|
<h3>Accessing decision variables<a class="headerlink" href="#accessing-decision-variables" title="Permalink to this headline">¶</a></h3>
|
|
<p>After building a model using <code class="docutils literal notranslate"><span class="pre">UnitCommitment.build_model</span></code>, it is possible to obtain a reference to the decision variables by calling <code class="docutils literal notranslate"><span class="pre">model[:varname][index]</span></code>. For example, <code class="docutils literal notranslate"><span class="pre">model[:is_on]["g1",1]</span></code> returns a direct reference to the JuMP variable indicating whether generator named “g1” is on at time 1. The script below illustrates how to build a model, solve it and display the solution without using the function <code class="docutils literal notranslate"><span class="pre">UnitCommitment.solution</span></code>.</p>
|
|
<div class="highlight-julia notranslate"><div class="highlight"><pre><span></span><span class="k">using</span> <span class="n">Cbc</span>
|
|
<span class="k">using</span> <span class="n">Printf</span>
|
|
<span class="k">using</span> <span class="n">JuMP</span>
|
|
<span class="k">using</span> <span class="n">UnitCommitment</span>
|
|
|
|
<span class="c"># Load benchmark instance</span>
|
|
<span class="n">instance</span> <span class="o">=</span> <span class="n">UnitCommitment</span><span class="o">.</span><span class="n">read_benchmark</span><span class="p">(</span><span class="s">"matpower/case118/2017-02-01"</span><span class="p">)</span>
|
|
|
|
<span class="c"># Build JuMP model</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">UnitCommitment</span><span class="o">.</span><span class="n">build_model</span><span class="p">(</span>
|
|
<span class="n">instance</span><span class="o">=</span><span class="n">instance</span><span class="p">,</span>
|
|
<span class="n">optimizer</span><span class="o">=</span><span class="n">Cbc</span><span class="o">.</span><span class="n">Optimizer</span><span class="p">,</span>
|
|
<span class="p">)</span>
|
|
|
|
<span class="c"># Solve the model</span>
|
|
<span class="n">UnitCommitment</span><span class="o">.</span><span class="n">optimize!</span><span class="p">(</span><span class="n">model</span><span class="p">)</span>
|
|
|
|
<span class="c"># Display commitment status</span>
|
|
<span class="k">for</span> <span class="n">g</span> <span class="kp">in</span> <span class="n">instance</span><span class="o">.</span><span class="n">units</span>
|
|
<span class="k">for</span> <span class="n">t</span> <span class="kp">in</span> <span class="mi">1</span><span class="o">:</span><span class="n">instance</span><span class="o">.</span><span class="n">time</span>
|
|
<span class="nd">@printf</span><span class="p">(</span>
|
|
<span class="s">"</span><span class="si">%-10s</span><span class="s"> </span><span class="si">%5d</span><span class="s"> </span><span class="si">%5.1f</span><span class="s"> </span><span class="si">%5.1f</span><span class="s"> </span><span class="si">%5.1f</span><span class="se">\n</span><span class="s">"</span><span class="p">,</span>
|
|
<span class="n">g</span><span class="o">.</span><span class="n">name</span><span class="p">,</span>
|
|
<span class="n">t</span><span class="p">,</span>
|
|
<span class="n">value</span><span class="p">(</span><span class="n">model</span><span class="p">[</span><span class="o">:</span><span class="n">is_on</span><span class="p">][</span><span class="n">g</span><span class="o">.</span><span class="n">name</span><span class="p">,</span> <span class="n">t</span><span class="p">]),</span>
|
|
<span class="n">value</span><span class="p">(</span><span class="n">model</span><span class="p">[</span><span class="o">:</span><span class="n">switch_on</span><span class="p">][</span><span class="n">g</span><span class="o">.</span><span class="n">name</span><span class="p">,</span> <span class="n">t</span><span class="p">]),</span>
|
|
<span class="n">value</span><span class="p">(</span><span class="n">model</span><span class="p">[</span><span class="o">:</span><span class="n">switch_off</span><span class="p">][</span><span class="n">g</span><span class="o">.</span><span class="n">name</span><span class="p">,</span> <span class="n">t</span><span class="p">]),</span>
|
|
<span class="p">)</span>
|
|
<span class="k">end</span>
|
|
<span class="k">end</span>
|
|
</pre></div>
|
|
</div>
|
|
</div>
|
|
<div class="section" id="fixing-variables-modifying-objective-function-and-adding-constraints">
|
|
<h3>Fixing variables, modifying objective function and adding constraints<a class="headerlink" href="#fixing-variables-modifying-objective-function-and-adding-constraints" title="Permalink to this headline">¶</a></h3>
|
|
<p>Since we now have a direct reference to the JuMP decision variables, it is possible to fix variables, change the coefficients in the objective function, or even add new constraints to the model before solving it. The script below shows how can this be accomplished. For more information on modifying an existing model, <a class="reference external" href="https://jump.dev/JuMP.jl/stable/manual/variables/">see the JuMP documentation</a>.</p>
|
|
<div class="highlight-julia notranslate"><div class="highlight"><pre><span></span><span class="k">using</span> <span class="n">Cbc</span>
|
|
<span class="k">using</span> <span class="n">JuMP</span>
|
|
<span class="k">using</span> <span class="n">UnitCommitment</span>
|
|
|
|
<span class="c"># Load benchmark instance</span>
|
|
<span class="n">instance</span> <span class="o">=</span> <span class="n">UnitCommitment</span><span class="o">.</span><span class="n">read_benchmark</span><span class="p">(</span><span class="s">"matpower/case118/2017-02-01"</span><span class="p">)</span>
|
|
|
|
<span class="c"># Construct JuMP model</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">UnitCommitment</span><span class="o">.</span><span class="n">build_model</span><span class="p">(</span>
|
|
<span class="n">instance</span><span class="o">=</span><span class="n">instance</span><span class="p">,</span>
|
|
<span class="n">optimizer</span><span class="o">=</span><span class="n">Cbc</span><span class="o">.</span><span class="n">Optimizer</span><span class="p">,</span>
|
|
<span class="p">)</span>
|
|
|
|
<span class="c"># Fix a decision variable to 1.0</span>
|
|
<span class="n">JuMP</span><span class="o">.</span><span class="n">fix</span><span class="p">(</span>
|
|
<span class="n">model</span><span class="p">[</span><span class="o">:</span><span class="n">is_on</span><span class="p">][</span><span class="s">"g1"</span><span class="p">,</span><span class="mi">1</span><span class="p">],</span>
|
|
<span class="mf">1.0</span><span class="p">,</span>
|
|
<span class="n">force</span><span class="o">=</span><span class="kc">true</span><span class="p">,</span>
|
|
<span class="p">)</span>
|
|
|
|
<span class="c"># Change the objective function</span>
|
|
<span class="n">JuMP</span><span class="o">.</span><span class="n">set_objective_coefficient</span><span class="p">(</span>
|
|
<span class="n">model</span><span class="p">,</span>
|
|
<span class="n">model</span><span class="p">[</span><span class="o">:</span><span class="n">switch_on</span><span class="p">][</span><span class="s">"g2"</span><span class="p">,</span><span class="mi">1</span><span class="p">],</span>
|
|
<span class="mf">1000.0</span><span class="p">,</span>
|
|
<span class="p">)</span>
|
|
|
|
<span class="c"># Create a new constraint</span>
|
|
<span class="nd">@constraint</span><span class="p">(</span>
|
|
<span class="n">model</span><span class="p">,</span>
|
|
<span class="n">model</span><span class="p">[</span><span class="o">:</span><span class="n">is_on</span><span class="p">][</span><span class="s">"g3"</span><span class="p">,</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">model</span><span class="p">[</span><span class="o">:</span><span class="n">is_on</span><span class="p">][</span><span class="s">"g4"</span><span class="p">,</span><span class="mi">1</span><span class="p">]</span> <span class="o"><=</span> <span class="mi">1</span><span class="p">,</span>
|
|
<span class="p">)</span>
|
|
|
|
<span class="c"># Solve the model</span>
|
|
<span class="n">UnitCommitment</span><span class="o">.</span><span class="n">optimize!</span><span class="p">(</span><span class="n">model</span><span class="p">)</span>
|
|
</pre></div>
|
|
</div>
|
|
</div>
|
|
<div class="section" id="adding-new-component-to-a-bus">
|
|
<h3>Adding new component to a bus<a class="headerlink" href="#adding-new-component-to-a-bus" title="Permalink to this headline">¶</a></h3>
|
|
<p>The following snippet shows how to add a new grid component to a particular bus. For each time step, we create decision variables for the new grid component, add these variables to the objective function, then attach the component to a particular bus by modifying some existing model constraints.</p>
|
|
<div class="highlight-julia notranslate"><div class="highlight"><pre><span></span><span class="k">using</span> <span class="n">Cbc</span>
|
|
<span class="k">using</span> <span class="n">JuMP</span>
|
|
<span class="k">using</span> <span class="n">UnitCommitment</span>
|
|
|
|
<span class="c"># Load instance and build base model</span>
|
|
<span class="n">instance</span> <span class="o">=</span> <span class="n">UnitCommitment</span><span class="o">.</span><span class="n">read_benchmark</span><span class="p">(</span><span class="s">"matpower/case118/2017-02-01"</span><span class="p">)</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">UnitCommitment</span><span class="o">.</span><span class="n">build_model</span><span class="p">(</span>
|
|
<span class="n">instance</span><span class="o">=</span><span class="n">instance</span><span class="p">,</span>
|
|
<span class="n">optimizer</span><span class="o">=</span><span class="n">Cbc</span><span class="o">.</span><span class="n">Optimizer</span><span class="p">,</span>
|
|
<span class="p">)</span>
|
|
|
|
<span class="c"># Get the number of time steps in the original instance</span>
|
|
<span class="n">T</span> <span class="o">=</span> <span class="n">instance</span><span class="o">.</span><span class="n">time</span>
|
|
|
|
<span class="c"># Create decision variables for the new grid component.</span>
|
|
<span class="c"># In this example, we assume that the new component can</span>
|
|
<span class="c"># inject up to 10 MW of power at each time step, so we</span>
|
|
<span class="c"># create new continuous variables 0 ≤ x[t] ≤ 10.</span>
|
|
<span class="nd">@variable</span><span class="p">(</span><span class="n">model</span><span class="p">,</span> <span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="o">:</span><span class="n">T</span><span class="p">],</span> <span class="n">lower_bound</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">upper_bound</span><span class="o">=</span><span class="mf">10.0</span><span class="p">)</span>
|
|
|
|
<span class="c"># For each time step</span>
|
|
<span class="k">for</span> <span class="n">t</span> <span class="kp">in</span> <span class="mi">1</span><span class="o">:</span><span class="n">T</span>
|
|
|
|
<span class="c"># Add production costs to the objective function.</span>
|
|
<span class="c"># In this example, we assume a cost of $5/MW.</span>
|
|
<span class="n">set_objective_coefficient</span><span class="p">(</span><span class="n">model</span><span class="p">,</span> <span class="n">x</span><span class="p">[</span><span class="n">t</span><span class="p">],</span> <span class="mf">5.0</span><span class="p">)</span>
|
|
|
|
<span class="c"># Attach the new component to bus b1, by modifying the</span>
|
|
<span class="c"># constraint `eq_net_injection`.</span>
|
|
<span class="n">set_normalized_coefficient</span><span class="p">(</span>
|
|
<span class="n">model</span><span class="p">[</span><span class="o">:</span><span class="n">eq_net_injection</span><span class="p">][</span><span class="s">"b1"</span><span class="p">,</span> <span class="n">t</span><span class="p">],</span>
|
|
<span class="n">x</span><span class="p">[</span><span class="n">t</span><span class="p">],</span>
|
|
<span class="mf">1.0</span><span class="p">,</span>
|
|
<span class="p">)</span>
|
|
<span class="k">end</span>
|
|
|
|
<span class="c"># Solve the model</span>
|
|
<span class="n">UnitCommitment</span><span class="o">.</span><span class="n">optimize!</span><span class="p">(</span><span class="n">model</span><span class="p">)</span>
|
|
|
|
<span class="c"># Show optimal values for the x variables</span>
|
|
<span class="nd">@show</span> <span class="n">value</span><span class="o">.</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
|
</pre></div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div class="section" id="references">
|
|
<h2><span class="sectnum">4.5.</span> References<a class="headerlink" href="#references" title="Permalink to this headline">¶</a></h2>
|
|
<ul class="simple">
|
|
<li><p>[KnOsWa20] <strong>Bernard Knueven, James Ostrowski and Jean-Paul Watson.</strong> “On Mixed-Integer Programming Formulations for the Unit Commitment Problem”. INFORMS Journal on Computing (2020). <a class="reference external" href="https://doi.org/10.1287/ijoc.2019.0944">DOI: 10.1287/ijoc.2019.0944</a></p></li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
</div>
|
|
|
|
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