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"(plant-complex-ramping)=\n",
"# Complex ramping on plant discharge\n",
"This example shows the types of complex ramping constraints that can be applied to the plant discharge in SHOP under the SHOP_COMPLEX_RAMPING license. Similar constraints can also be applied to reservoir level, as shown in [this example](reservoir-complex-ramping). To understand the underlying concepts of rolling and period ramping better, the reader is referred to the complex ramping section in the brief [ramping tutorial](ramping).\n",
"\n",
"The model setup is available in the following formats:\n",
"\n",
"- pyshop\n",
" - [](complex_ramping.py)"
]
},
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"cell_type": "code",
"execution_count": 1,
"id": "944d8a31",
"metadata": {
"Collapsed": "false"
},
"outputs": [],
"source": [
"from pyshop import ShopSession\n",
"import pandas as pd\n",
"import plotly.graph_objs as go\n",
"import numpy as np\n",
"from complex_ramping import build_model, run_model"
]
},
{
"cell_type": "markdown",
"id": "06cc3d10",
"metadata": {},
"source": [
"## Baseline run without ramping constraints\n",
"The system used in the example is a single reservoir above a plant with one generator:"
]
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"source": [
"shop = build_model()\n",
"shop.model.build_connection_tree()"
]
},
{
"cell_type": "markdown",
"id": "08047796",
"metadata": {},
"source": [
"The reservoir starts half full, and has a constant inflow of 10 m3/s incoming during the 24 hour optimization horizon. The market price is above the constant water value in all hours, but the price is also linearly increasing in each hour.\n",
"\n",
"\n",
"First, we run the model without any complex ramping constraints. The resulting plant discharge is shown below, and we see that SHOP will wait a few hours before producing at best point."
]
},
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"source": [
"run_model(shop)\n",
"\n",
"plant = shop.model.plant[\"Plant1\"]\n",
"discharge_no_ramp = plant.discharge.get().asfreq('1min').ffill()\n",
"\n",
"fig = go.Figure()\n",
"fig.add_trace(go.Scatter(x=discharge_no_ramp.index, y=discharge_no_ramp.values, name=\"Plant discharge\"))\n",
"\n",
"fig.update_layout(title=\"Optimization without ramping constraints\", xaxis_title=\"Time\", yaxis_title=\"m3/s\")\n",
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"fig.show()"
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},
{
"cell_type": "markdown",
"id": "1f25ca87",
"metadata": {},
"source": [
"## Adding complex ramping constraints\n",
"Now we will add rolling and period ramping constraints to the plant discharge to limit how much the average, minimum, and maximum discharge can change over certain time windows. First, we create a new SHOP session."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "66f51db5",
"metadata": {
"Collapsed": "false"
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"source": [
"shop = build_model()\n",
"plant = shop.model.plant[\"Plant1\"]\n",
"\n",
"res = shop.get_time_resolution()\n",
"starttime = res[\"starttime\"]\n",
"endtime = res[\"endtime\"]"
]
},
{
"cell_type": "markdown",
"id": "759e7f13",
"metadata": {},
"source": [
"The plant discharge will be limited downwards by a *rolling* ramping constraint with a window size of 2 hours (120 min). This is a *limit* rolling ramping constraint in the downward direction, which means that the plant discharge in every time step is constrained by the maximal discharge value in the rolling window after subtracting the ramping limit.\n",
"\n",
"The [limit_discharge_rolling_ramping_down](plant:limit_discharge_rolling_ramping_down) attribute is of type XYT, which makes it possible to change the ramping limit inside the optimization horizon. Note that each XY attribute (in the form of a pd.Series object in the code below) has a reference time stamp. The time stamp specifies from when the ramping constraint is valid. In this example, the ramping limit is 20 m3/s for the first 6 hours of the optimization. It is then set to 'NaN', which deactivates the rolling ramping constraint for the remainder of the optimization horizon. Note that only a single rolling ramping constraint with a window size of 2 hours is defined in this example, which means that each XY table has a single point. The [reservoir level example](reservoir-complex-ramping) shows how to model multiple rolling ramping constraints with different rolling time windows."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "22b91025",
"metadata": {
"Collapsed": "false"
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"source": [
"rolling_window_sizes = [120]\n",
"limit_rolling_ramping_down_1 = pd.Series([20], index = rolling_window_sizes, name=starttime)\n",
"limit_rolling_ramping_down_2 = pd.Series([np.nan], index = rolling_window_sizes, name=starttime + pd.Timedelta(hours=6))\n",
"\n",
"plant.limit_discharge_rolling_ramping_down.set([limit_rolling_ramping_down_1, limit_rolling_ramping_down_2])"
]
},
{
"cell_type": "markdown",
"id": "ddd09783",
"metadata": {},
"source": [
"To limit the discharge in the upward direction, a *period* ramping constraint with 6 hour (360 min) long periods is added. Unlike the rolling ramping constraint, the period ramping constraint is constraining the *average* period discharge. This means that the average discharge in each 6 hour period is limited upward by the average discharge in the previous period.\n",
"\n",
"The [average_discharge_period_ramping_up](plant:average_discharge_period_ramping_up) attribute is used to add this constraint, and the ramping limit changes from 20 m3/s to 10 m3/s 12 hours into the optimization. Note that changing the ramping limit for period ramping constraints should only be done when a new period begins. Changing it in the middle of a period makes little sense, and an average ramping limit value will be used in those cases."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "568a0673",
"metadata": {
"Collapsed": "false"
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"source": [
"period_sizes = [360]\n",
"average_period_ramping_up_1 = pd.Series([20], index = period_sizes, name=starttime)\n",
"average_period_ramping_up_2 = pd.Series([10], index = period_sizes, name=starttime + pd.Timedelta(hours=12))\n",
"\n",
"plant.average_discharge_period_ramping_up.set([average_period_ramping_up_1, average_period_ramping_up_2])"
]
},
{
"cell_type": "markdown",
"id": "aa2285e3",
"metadata": {},
"source": [
"Since the optimization horizon is 24 hours and the ramping periods are 6 hours long, there will be no fractional ramping periods if the first period start at the start time of the optimization. It is not strictly necessary to define an offset for the period ramping when the offset from the start time is zero, but a warning will be printed to the log file. Therefore, the SY attribute [average_discharge_period_ramping_up_offset](plant:average_discharge_period_ramping_up_offset) is explicitly defined below, and the offset will be zero since the periods start at the optimization start time:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "d6a329b3",
"metadata": {
"Collapsed": "false"
},
"outputs": [],
"source": [
"offset = pd.Series(period_sizes, index = [starttime])\n",
"plant.average_discharge_period_ramping_up_offset.set(offset)"
]
},
{
"cell_type": "markdown",
"id": "541114f1",
"metadata": {},
"source": [
"Historical discharge values are needed to add both rolling and period ramping constraints at the beginning of the optimization. The period ramping constraint requires the most historical values since the rolling ramping window is only 2 hours long. There is no fractional ramping period at the beginning of the optimization since the specified offset is zero, so it is sufficient to include 6 hours of values to the [historical_discharge](plant:historical_discharge) attribute. However, there is no harm in giving in more historical values than strictly required. 24 hours of historical discharge is randomly generated below:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "fabe6b48",
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"source": [
"np.random.seed(5)\n",
"\n",
"#Generate random on/off status of generator\n",
"on_off = np.random.randint(0,2,size=24)\n",
"\n",
"#Generate random discharge between 25 and 100\n",
"discharge_level = 25 + 75*np.random.rand(24)\n",
"\n",
"discharge = on_off * discharge_level\n",
"t = [starttime - pd.Timedelta(hours=24-i) for i in range(24)]\n",
"\n",
"historical_discharge = pd.Series(discharge, index=t)\n",
"\n",
"plant.historical_discharge.set(historical_discharge)\n",
"\n",
"historical_discharge = historical_discharge.asfreq('1min').ffill()\n",
"\n",
"fig = go.Figure()\n",
"fig.add_trace(go.Scatter(x=historical_discharge.index, y=historical_discharge.values, name=\"Historical discharge\"))\n",
"fig.update_layout(title=\"Historical plant discharge values\", xaxis_title=\"Time\", yaxis_title=\"m3/s\")\n",
"\n",
"fig.show()"
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"source": [
"## Comparing results \n",
"Now we can optimize and compare the optimization results to the initial SHOP run without ramping constraints."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "50bece46",
"metadata": {
"Collapsed": "false"
},
"outputs": [],
"source": [
"run_model(shop)"
]
},
{
"cell_type": "markdown",
"id": "0cd82c07",
"metadata": {},
"source": [
"As seen in the figure below, the plant discharge can't ramp up from zero to 90 m3/s in the way the unconstrained solution suggests. Note that the historical discharge values have been appended to the optimized discharge results with ramping."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "e49a713b",
"metadata": {
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