{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "kq1oXGHPbfFP"
},
"source": [
"```{index} single: solver; cbc\n",
"```\n",
"```{index} pandas dataframe\n",
"```\n",
"```{index} sample average approximation\n",
"```\n",
"```{index} stochastic optimization\n",
"```\n",
"```{index} chance constraints\n",
"```\n",
"```{index} mutable parameters\n",
"```\n",
"\n",
"# Economic dispatch in energy systems"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"ExecuteTime": {
"end_time": "2022-09-30T22:59:05.262585Z",
"start_time": "2022-09-30T22:59:04.962753Z"
},
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "lAvinyZKD5Vp",
"outputId": "0862459e-a608-4b16-8c17-fc377c563a4d",
"tags": []
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Using default Community Edition License for Colab. Get yours at: https://ampl.com/ce\n",
"Licensed to AMPL Community Edition License for the AMPL Model Colaboratory (https://colab.ampl.com).\n"
]
}
],
"source": [
"# install AMPL and solvers\n",
"%pip install -q amplpy pandas matplotlib numpy seaborn\n",
"\n",
"SOLVER = \"highs\"\n",
"\n",
"from amplpy import AMPL, ampl_notebook\n",
"\n",
"ampl = ampl_notebook(\n",
" modules=[\"highs\"], # modules to install\n",
" license_uuid=\"default\", # license to use\n",
") # instantiate AMPL object and register magics"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "M7WCjvp4FISI"
},
"source": [
"# Chance-constrained economic energy dispatch problem\n",
"\n",
"In this notebook, we will explore the applications of chance constraints to an area where high-probability guarantees on the system's functioning are required - the _economic dispatch (ED)_ problem.\n",
"\n",
"The problem considers the short-term determination of the optimal production of energy to meet all energy demands. Let $V$ denote a set of nodes, each of which is representing cities, industrial districts, power generators, or combinations of these. Each node $i \\in V$ may have:\n",
"- a certain energy demand $d_i \\geq 0$;\n",
"- a power generator whose energy production needs to be between $p_i^{min}$ and $p_i^{max}$ units of power. The cost of producing one unit of power at node $i$ is given by a variable cost $c_i \\geq 0$.\n",
"Importantly, not all the nodes have demand and generation, more specifically it is possible for a node to have only generation or only demand.\n",
"\n",
"The goal is to determine for each node $i \\in V$ the optimal production level $p_i$, such that\n",
"- the total energy demand is met\n",
"- no production limits are exceeded\n",
"- the total energy production costs are minimized.\n",
"\n",
"If we fully control the energy production and the customer demand is known, can formulate the problem as the following MILO problem:\n",
"\n",
"$$\n",
"\\begin{align}\n",
"\\begin{array}{llll}\n",
"\\min & \\sum_{i \\in V} c_i p_i\\\\\n",
"\\text{s.t.} & \\sum_{i \\in V} p_i = \\sum_{i \\in V} d_i,\\\\\n",
"& p_{i}^{min} \\leq p_{i} \\leq p_{i}^{max} & \\forall i \\in V.\n",
"\\end{array}\n",
"\\end{align}\n",
"$$\n",
"\n",
"Now, assume that we have built several offshore wind turbines. These wind turbines combined together produce a random non-negative amount of extra energy, denoted by $\\omega$. For a fixed value of $\\omega$, the optimization problem to be solved is thus to 'fill in' to the remaining energy demand not satisfied by wind power:\n",
"\n",
"$$\n",
"\\begin{align}\n",
"\\begin{array}{llll}\n",
"\\min & \\sum_{i \\in V} c_i p_i\\\\\n",
"\\text{s.t.} & \\omega + \\sum_{i \\in V} p_i = \\sum_{i \\in V} d_i,\\\\\n",
"& p_{i}^{min} \\leq p_{i} \\leq p_{i}^{max} & \\forall i \\in V.\n",
"\\end{array}\n",
"\\end{align}\n",
"$$\n",
"\n",
"The problem, however, is that $\\omega$ is a random variable and is typically not fully known before the generation levels $p_i$ of conventional generators have to be set. Because of stochastic fluctuations in wind power generation, the ED problem is best modeled as a stochastic optimization problem. The intermittency of wind generation makes it almost impossible to perfectly balance supply and demand on a real-time basis, but in practice there is some tolerance for error, i.e., certain degree of mismatch between supply and demand can be easily adjusted for.\n",
"\n",
"To formulate the problem under this assumption, let us denote by:\n",
"- $\\Delta \\geq 0$ the tolerance of the absolute power mismatch between supply and demand;\n",
"- $\\varepsilon \\in [0,1]$ is the risk level at which we are willing to accept for the supply to deviate from the demand more than $\\Delta$;\n",
"- $\\omega$ the non-negative random variable describing the total power production of offshore wind turbines.\n",
"\n",
"In this setting, instead of requiring that the supply and demand are matched perfectly, we require that the absolute difference remains below power threshold $\\Delta$ using the following chance constraint:\n",
"\n",
"$$\n",
"\\begin{align}\n",
" \\mathbb{P} \\Big ( \\Big | \\omega + \\sum_{i \\in V } p_i - \\sum_{i \\in V} d_i \\Big | \\leq \\Delta \\Big) \\geq 1 - \\varepsilon.\n",
"\\end{align}\n",
"$$\n",
"\n",
"To formulate the problem as an MILO, we can break up this absolute-value function including constraint into two individual chance constraints - note that in this way we relax the constraint because requiring that two one-sided constraints hold with probability $1 - \\varepsilon$ each is not the same as requiring that together they hold with probability $1 - \\varepsilon$, but in practice we can fine-tune the $\\varepsilon$ to adapt for this change.\n",
"\n",
"Such breaking up leads us to the following optimization problem with chance constraints:\n",
"\n",
"$$\n",
"\\begin{align}\n",
"\\begin{array}{llll}\n",
"\\min & \\sum_{i \\in V } c_i p_i\\\\\n",
"\\text{s.t.} & \\mathbb{P}(\\omega + \\sum_{i \\in V } p_i - \\sum_{i \\in V} d_i \\leq \\Delta) \\geq 1 - \\varepsilon\\\\\n",
"& \\mathbb{P}(\\omega + \\sum_{i \\in V } p_i - \\sum_{i \\in V} d_i \\geq -\\Delta) \\geq 1 - \\varepsilon\\\\\n",
"& p_{i}^{min } \\leq p_{i} \\leq p_{i}^{max } & \\forall i \\in V.\n",
"\\end{array}\n",
"\\end{align}\n",
"$$\n",
"\n",
"In this notebook, we will solve this problem using the SAA approach to chance constraints, with the wind power production using modeled with historical data of 500 outcomes of the total wind production."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "_SRQ2Y93bfFd"
},
"source": [
"## Data import\n",
"\n",
"We first import the necessary packages and define a function that reads all the necessary node and wind production random sample data."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"ExecuteTime": {
"end_time": "2022-09-30T22:59:07.200005Z",
"start_time": "2022-09-30T22:59:05.267305Z"
},
"id": "RE8rff0jD8Bd"
},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"id": "Im3hlIO4bfFf"
},
"outputs": [],
"source": [
"def read_economic_dispatch_data():\n",
" # Read local nodes.csv if exists\n",
" base_url = \"https://raw.githubusercontent.com/mobook/MO-book/main/notebooks/09/\"\n",
" nodes_df = pd.read_csv(base_url + \"nodes.csv\", index_col=0)[\n",
" [\"node_id\", \"d\", \"p_min\", \"p_max\", \"c_var\"]\n",
" ]\n",
" wind_production_samples_df = pd.read_csv(base_url + \"discrete_wind.csv\").T\n",
"\n",
" # Read data\n",
" nodes = nodes_df.set_index(\"node_id\").T.to_dict()\n",
" wind_production_samples = list(wind_production_samples_df.to_dict().values())\n",
" wind_production_samples = [sum(d.values()) for d in wind_production_samples]\n",
"\n",
" return nodes, wind_production_samples\n",
"\n",
"\n",
"nodes, wind_production_samples = read_economic_dispatch_data()"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "uwC5z8OLbfFg"
},
"source": [
"The wind production samples can be accessed through the `wind_production_samples` variable - a list of 500 equiprobable outcomes for the wind generation."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"id": "C2LJXBaabfFi",
"outputId": "a55e6fad-8d3f-4747-84f2-8ec059468fbc",
"colab": {
"base_uri": "https://localhost:8080/"
}
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"196.94632359541376"
]
},
"metadata": {},
"execution_count": 4
}
],
"source": [
"wind_production_samples[4] # fifth outcome"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "ZVX-Ar8ebfFk"
},
"source": [
"Let us take a look into the wind production data, including a Kernel Density Estimate.\n",
"We see that is has two modes.\n",
"This [paper](https://link.springer.com/article/10.1007/s40565-015-0172-5) explains what one could do with this."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"id": "983ygg2YbfFl",
"outputId": "511c9005-9c91-4b75-ae45-b7bce5f534f1",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 452
}
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
""
],
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\n"
},
"metadata": {}
}
],
"source": [
"sns.set_style(\"darkgrid\")\n",
"sns.histplot(\n",
" wind_production_samples, kde=True, stat=\"density\", kde_kws=dict(cut=1)\n",
").set_title(\"wind production\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "w37Ys2uQbfFn"
},
"source": [
"The `nodes` dictionary contains for every $i \\in V$ information about $p_i^{min}$, $p_i^{max}$, $c_i$, $d_i$. In our dataset, there is a clear separation of the nodes into nodes that only consume power, and nodes that only produce power, which can be seen by inspecting the node properties."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"id": "3O_YZrDnbfFo",
"outputId": "77e3f133-c6e3-4bfc-ade1-757bdcd2bac5",
"colab": {
"base_uri": "https://localhost:8080/"
}
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"{'d': 44.23034433319671, 'p_min': 0.0, 'p_max': 0.0, 'c_var': 0.0}"
]
},
"metadata": {},
"execution_count": 6
}
],
"source": [
"nodes[0] # first node properties"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "20nCg-lVbfFo"
},
"source": [
"Let us now provide some locations to our producers and consumers and visualize the data, using bubbles proportional to the size of demand (for consumers) and maximum generation capacity (for producers)."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"id": "izWpNSh2bfFp",
"outputId": "ec9b655c-6158-4955-c9e6-b91025543e0e",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 522
}
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
""
],
"image/png": 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\n"
},
"metadata": {}
}
],
"source": [
"df_nodes = pd.DataFrame.from_dict(nodes, orient=\"index\")\n",
"df_nodes[\"type\"] = \"consumer\"\n",
"df_nodes.loc[df_nodes.p_max > 0, \"type\"] = \"producer\"\n",
"np.random.seed(2023)\n",
"df_nodes[\"x\"] = np.random.randint(0, 100, len(nodes))\n",
"df_nodes[\"y\"] = np.random.randint(0, 100, len(nodes))\n",
"df_nodes[\"size\"] = df_nodes[[\"d\", \"p_max\"]].max(axis=1)\n",
"\n",
"\n",
"def ShowInstance(df_nodes):\n",
" # Define the size of the figure\n",
" fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
" # Set the scales of the x and y axes\n",
" ax.set_xlim([min(df_nodes[\"x\"]) - 10, max(df_nodes[\"x\"]) + 10])\n",
" ax.set_ylim([min(df_nodes[\"y\"]) - 10, max(df_nodes[\"y\"]) + 10])\n",
"\n",
" # Create a scatter plot with bubbles proportional to size\n",
" # ax.scatter(df_nodes['x'], df_nodes['y'], s=df_nodes['size']*1)\n",
" for (category, group), z, color in zip(\n",
" df_nodes.groupby(\"type\"), [2, 1], [\"red\", \"green\"]\n",
" ):\n",
" ax.scatter(\n",
" group.x,\n",
" group.y,\n",
" s=group[\"size\"] * 1,\n",
" label=category,\n",
" alpha=0.2,\n",
" zorder=z,\n",
" color=color,\n",
" )\n",
" if \"sol\" in group:\n",
" ax.scatter(\n",
" group.x,\n",
" group.y,\n",
" s=group[\"sol\"] * 1,\n",
" label=None,\n",
" alpha=1,\n",
" zorder=z,\n",
" color=color,\n",
" )\n",
"\n",
" plt.legend()\n",
" # Show the chart\n",
" plt.show()\n",
"\n",
"\n",
"ShowInstance(df_nodes)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "3W2UC7_hbfFr"
},
"source": [
"## MILO reformulation for the chance-constrained ED problem\n",
"\n",
"Since we have a discrete set of $N$ possible wind production outcomes, we can reformulate the chance-constrained ED problem as a mixed-integer linear optimization problem. More specifically, we introduce a binary variable $u_j$ for each sample $j$ of the wind production, which, thanks to the big-$M$ technique, determines whether the constraint related to the $j$-th sample is allowed to be violated or not, and add one constraint to ensure that the total probability that the constraint is violated is at most $\\varepsilon$, i.e.,\n",
"\n",
"$$\n",
"\\frac{1}{N} \\sum_{j=1}^{N} u_j \\leq \\varepsilon.\n",
"$$\n",
"\n",
"The resulting MILO is\n",
"\n",
"$$\n",
"\\begin{align}\n",
"\\begin{array}{llll}\n",
"\\min & \\sum_{i \\in V} c_i(p_i)\\\\\n",
"\\text{s.t.} & \\omega_j + \\sum_{i \\in V} p_i - \\sum_{i \\in V} d_i \\leq \\Delta + u_jM_j & \\forall j = 1, \\dots, N\\\\\n",
"& \\omega_j + \\sum_{i \\in V} p_i - \\sum_{i \\in V} d_i \\geq -\\Delta - u_jM_j & \\forall j = 1, \\dots, N\\\\\n",
"& \\sum_{j=1}^{N}u_j \\leq \\varepsilon N \\\\\n",
"& p_{i}^{min } \\leq p_{i} \\leq p_{i}^{max } & \\forall i \\in V, \\\\\n",
"& u_j \\in \\{0, 1\\} & \\forall j = 1, ..., N,\n",
"\\end{array}\n",
"\\end{align}\n",
"$$\n",
"\n",
"For each sample, the supply and demand constraints are deactivated when $u_j =1$ and $u_j=0$ otherwise. Note that we only use one single $u_j$ variable for each constraint. Indeed, having two separate $u^{(1)}_j$ and $u^{(2)}_j$ will yield the same objective value, but the model would be incorrect with respect to the violation of the supply and demand constraints introduced earlier.\n",
"\n",
"The constants $M_j$'s here should be selected based on the data: one reasonable choice for $M_j$ that will certainly work out is to take it equal to the left-hand side minus $\\Delta$ while replacing $p_i$ for $p_i^{max}$.\n",
"\n",
"We now define the Python function which implements this model. Note that the model is formulated with $\\varepsilon$ and $\\Delta$ as mutable model parameters, so that we can repeatedly solve the same model instance, upon modifying the parameters. In turn, this requires the $M_j$ constants to be expressions."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"id": "5M8Xn_MabfFs",
"outputId": "bafd6fd6-7413-44e7-c657-b4f77fdd8b56",
"colab": {
"base_uri": "https://localhost:8080/"
}
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Overwriting economic_dispatch.mod\n"
]
}
],
"source": [
"%%writefile economic_dispatch.mod\n",
"\n",
"param N; # number of samples\n",
"param samples{1..N};\n",
"\n",
"param eps;\n",
"param Delta;\n",
"\n",
"set V;\n",
"param c{V};\n",
"param d{V};\n",
"param p_min{V};\n",
"param p_max{V};\n",
"\n",
"param sum_pmax = sum{i in V} p_max[i];\n",
"param sum_d = sum{i in V} d[i];\n",
"\n",
"param M{j in 1..N} = samples[j] + sum_pmax + sum_d - Delta;\n",
"\n",
"var p{i in V} >= p_min[i], <= p_max[i];\n",
"var u{i in 1..N} binary;\n",
"\n",
"minimize my_objective: sum{i in V}(c[i] * p[i]);\n",
"\n",
"s.t. supply_demand_leq {j in 1..N}:\n",
" samples[j] + sum{i in V} p[i] - sum{i in V} d[i] <= Delta + M[j] * u[j];\n",
"s.t. supply_demand_geq {j in 1..N}:\n",
" samples[j] + sum{i in V} p[i] - sum{i in V} d[i] >= - Delta - M[j] * u[j];\n",
"s.t. success_probability: sum{j in 1..N} u[j] <= eps * N;"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"id": "KJ7q9D0MbfFt"
},
"outputs": [],
"source": [
"def economic_dispatch(nodes_df, samples, eps, Delta):\n",
" # Create AMPL instance and load the model\n",
" ampl = AMPL()\n",
" ampl.read(\"economic_dispatch.mod\")\n",
"\n",
" # Load the data\n",
" ampl.set[\"V\"] = nodes_df[\"node_id\"]\n",
" ampl.param[\"c\"] = nodes_df[\"c_var\"]\n",
" ampl.param[\"p_min\"] = nodes_df[\"p_min\"]\n",
" ampl.param[\"p_max\"] = nodes_df[\"p_max\"]\n",
" ampl.param[\"d\"] = nodes_df[\"d\"]\n",
"\n",
" ampl.param[\"N\"] = len(samples)\n",
" ampl.param[\"samples\"] = samples\n",
"\n",
" ampl.param[\"eps\"] = eps\n",
" ampl.param[\"Delta\"] = Delta\n",
"\n",
" # Set solver\n",
" ampl.option[\"solver\"] = SOLVER\n",
"\n",
" return ampl"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "hbtMq8mubfFv"
},
"source": [
"For demonstration purposes, we now solve the model for the provided instance and wind production outcomes and report the optimal objective value you obtain for $\\varepsilon = 0.02$ and $\\Delta=1000$."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"id": "8K2nP9fGbfFv",
"outputId": "0523f23c-4156-46dc-a4f2-ef3681ba8ba5",
"colab": {
"base_uri": "https://localhost:8080/"
}
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 7850.60066\n",
"12071 simplex iterations\n",
"1 branching nodes\n",
" \n",
"Total energy demand: 3007.112\n",
"Total optimal energy production: 1733.393\n",
"Total energy production cost: 7850.601\n"
]
}
],
"source": [
"# Data\n",
"eps = 0.20\n",
"Delta = 1000\n",
"N = 500\n",
"\n",
"base_url = \"https://raw.githubusercontent.com/mobook/MO-book/main/notebooks/09/\"\n",
"# Dataframe with node information\n",
"nodes_df = pd.read_csv(base_url + \"nodes.csv\", index_col=0)[\n",
" [\"node_id\", \"d\", \"p_min\", \"p_max\", \"c_var\"]\n",
"]\n",
"\n",
"# Solve model and report the solution\n",
"model = economic_dispatch(nodes_df, wind_production_samples, eps, Delta)\n",
"model.solve()\n",
"\n",
"sum_production = model.get_value(\"sum{i in V} p[i]\")\n",
"sum_demand = sum(nodes_df[\"d\"])\n",
"print(f\"Total energy demand: {sum_demand:.3f}\")\n",
"print(f\"Total optimal energy production: {sum_production:.3f}\")\n",
"print(f\"Total energy production cost: {model.obj['my_objective'].value():.3f}\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "d9-TlOdvbfFx"
},
"source": [
"# Visualizing and understanding the solution"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"id": "eXF6Jd2ZbfFy",
"outputId": "56e6996f-6429-4f96-9192-be38ceb4e1fd",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 522
}
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
""
],
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\n"
},
"metadata": {}
}
],
"source": [
"df_nodes[\"sol\"] = model.var[\"p\"].get_values().toPandas()\n",
"ShowInstance(df_nodes)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "G14B3dqsbfFz"
},
"source": [
"## Sensitivity analysis\n",
"Next, we will study the sensitivity of the optimal solution and value to the different risk guarantee levels - this helps the decision maker find a level that offers the best risk-reward tradeoff. To this end, we solve the same MILO varying the values first of $\\varepsilon \\in [0, 1]$ (for fixed $\\Delta=1000$) and then of $\\Delta \\in [0, 2000]$ (for fixed $\\varepsilon = 0.02$). "
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"id": "-kj9_ks0bfFz",
"outputId": "40302ada-2a1d-404c-8a5e-087ccd3d2f0a",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
}
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 13051.25426\n",
"1 simplex iterations\n",
"0 barrier iterations\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 13027.32641\n",
"2028 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 11790.73881\n",
"7076 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 9577.271586\n",
"9076 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 7461.511327\n",
"15901 simplex iterations\n",
"8 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 5270.132613\n",
"11448 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 2781.668242\n",
"2905 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 383.7998865\n",
"894 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0\n",
"0 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0\n",
"0 simplex iterations\n",
"0 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0\n",
"0 simplex iterations\n",
"0 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0\n",
"0 simplex iterations\n",
"0 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0\n",
"0 simplex iterations\n",
"0 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0\n",
"0 simplex iterations\n",
"0 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0\n",
"0 simplex iterations\n",
"0 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0\n",
"0 simplex iterations\n",
"0 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0\n",
"0 simplex iterations\n",
"0 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0\n",
"0 simplex iterations\n",
"0 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0\n",
"0 simplex iterations\n",
"0 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0\n",
"0 simplex iterations\n",
"0 branching nodes\n",
" \n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
""
],
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\n"
},
"metadata": {}
}
],
"source": [
"fixed_Delta = 1000\n",
"\n",
"feas_eps = []\n",
"feas_objs = []\n",
"\n",
"eps = 0\n",
"model = economic_dispatch(nodes_df, wind_production_samples, eps, fixed_Delta)\n",
"\n",
"for eps in np.linspace(0, 1, num=20):\n",
" model.param[\"eps\"] = eps\n",
" model.solve()\n",
"\n",
" if model.get_value(\"solve_result\") == \"solved\":\n",
" feas_eps.append(eps)\n",
" feas_objs.append(model.obj[\"my_objective\"].value())\n",
"\n",
"plt.plot(feas_eps, feas_objs, marker=\"o\", linestyle=\"--\")\n",
"plt.xlabel(\"$\\epsilon$\")\n",
"plt.ylabel(\"objective value\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"id": "AiuxqDjVbfF0",
"outputId": "f231f39f-a11f-4e8c-c81f-b78108dd4f4e",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
}
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: infeasible problem\n",
"120 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: infeasible problem\n",
"133 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: infeasible problem\n",
"150 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: infeasible problem\n",
"190 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: infeasible problem\n",
"423 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 25097.93105\n",
"444 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 22150.56263\n",
"814 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 19203.19421\n",
"908 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 16255.82579\n",
"2085 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 14051.25426\n",
"408 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 12051.25426\n",
"348 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 10051.25426\n",
"330 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 8051.254261\n",
"317 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 6051.254261\n",
"543 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 4053.447124\n",
"277 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 2158.710282\n",
"294 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 263.9734402\n",
"146 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0\n",
"0 simplex iterations\n",
"1 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0\n",
"0 simplex iterations\n",
"0 branching nodes\n",
" \n",
"HiGHS 1.5.3: \b\b\b\b\b\b\b\b\b\b\b\b\bHiGHS 1.5.3: optimal solution; objective 0\n",
"0 simplex iterations\n",
"0 branching nodes\n",
" \n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
""
],
"image/png": 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\n"
},
"metadata": {}
}
],
"source": [
"fixed_eps = 0.02\n",
"\n",
"feas_Deltas = []\n",
"feas_objs = []\n",
"\n",
"Delta = 0\n",
"model = economic_dispatch(nodes_df, wind_production_samples, fixed_eps, Delta)\n",
"\n",
"for Delta in np.linspace(0, 2000, num=20):\n",
" model.param[\"Delta\"] = Delta\n",
" model.solve()\n",
"\n",
" if model.get_value(\"solve_result\") == \"solved\":\n",
" feas_Deltas.append(Delta)\n",
" feas_objs.append(model.obj[\"my_objective\"].value())\n",
"\n",
"plt.plot(feas_Deltas, feas_objs, marker=\"o\", linestyle=\"--\")\n",
"plt.xlabel(\"$\\Delta$\")\n",
"plt.ylabel(\"objective value\")\n",
"plt.show()"
]
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"Based on the above plots, we can make the following observations:\n",
"\n",
"- Smaller values $\\varepsilon$ and $\\Delta$ lead to more infeasibilities, which is to be expected. Smaller $\\varepsilon$ allow for less constraint violations/relaxations, whereas smaller Delta make constraints tighter (and thus easier to violate).\n",
"- The reason why the plot becomes flat for high $\\varepsilon$ and $\\Delta$ values is because production is no longer needed. For instance, a high $\\varepsilon$ means we can ignore the $N\\varepsilon$ worst-case sample scenarios, whereas higher $\\Delta$ means that we do not need to produce to match demand."
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