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"(reservoir-complex-ramping)=\n",
"# Complex ramping on reservoir level\n",
"This example shows the types of complex ramping constraints that can be applied to the reservoir level in SHOP under the SHOP_COMPLEX_RAMPING license. Similar constraints can also be applied to plant discharge, as shown in [this example](plant-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)."
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"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"
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"## 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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"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 reservoir level is shown below, and we see that SHOP will wait a few hours before producing heavily and almost emptying the reservoir."
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"## Adding complex ramping constraints\n",
"Now we will add rolling and period ramping constraints to the reservoir level to limit how much the reservoir level can change over certain time windows. First, we create a new SHOP session:"
]
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"shop = build_model()\n",
"rsv = shop.model.reservoir[\"Reservoir1\"]\n",
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"res = shop.get_time_resolution()\n",
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"The reservoir level will be constrained upwards by two *rolling* ramping constraints with different rolling window lengths. One has a 6 hour (360 min) rolling window and the other has a 12 hour (720 min) rolling time window. The ramping limits are 4 cm and 5 cm, respectively, and this limit is calculated upward from the *average* level in the rolling time windows. The appropriate attribute to use for these constraints is therefore [average_level_rolling_ramping_up](reservoir:average_level_rolling_ramping_up). This is an XYT attribute, which makes it possible to specify several rolling ramping constraints with different window sizes. An XY table (represented by a pd.Series object in the code below) is defined where the window sizes in minutes are the x-values and the corresponding ramping limits are the y-values. Since this is an XYT attribute the XY table is valid from the specified time stamp, which is the start time of the optimization in this case. The ramping limits don't change during the optimization horizon in this example, so a single XY table is used in the XYT. The [plant discharge example](plant-complex-ramping) shows how the XYT can be defined when the ramping limits change."
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"rolling_window_sizes = [360, 720]\n",
"ramping_limits = [0.04,0.05]\n",
"average_rolling_ramping_up = pd.Series(ramping_limits, index = rolling_window_sizes, name=starttime)\n",
"\n",
"rsv.average_level_rolling_ramping_up.set([average_rolling_ramping_up])"
]
},
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"For downwards ramping, a *period* ramping constraint with 10 hour (600 min) long periods is added. This periodic ramping constraint limits the change from the highest reservoir level in one period to the lowest reservoir level in the next period to 75 cm. Since the ramping is applied between extreme values, from max to min in downward ramping and from min to max in upward ramping, the constraint is called *limit* period ramping. The [limit_level_period_ramping_down](reservoir:limit_level_period_ramping_down) attribute is defined in a similar way to the rolling ramping constraints. It is possible to specify multiple period constraints with different period lengths, but a single period constraint is used in this example."
]
},
{
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"period_sizes = [600]\n",
"ramping_limits = [0.75]\n",
"limit_period_ramping_down = pd.Series(ramping_limits, index = period_sizes, name=starttime)\n",
"\n",
"rsv.limit_level_period_ramping_down.set([limit_period_ramping_down])"
]
},
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"The default behaviour in SHOP is to assume that the first fixed ramping period starts at the beginning of the optimization horizon. Since the ramping periods are 10 hours long and the optimization horizon is 24 hours, the four last hours of the optimization will therefore be part of an incomplete ramping period. No constraints will be built from the last full ramping period to the final ramping period if it is too short. However, it is also possible to specify an offset to signal that the first full ramping period should start after the start time of the optimization. This is done below with the SY attribute [limit_level_period_ramping_down_offset](reservoir:limit_level_period_ramping_down_offset) so that the 4 first hours are fractional instead of the last four:"
]
},
{
"cell_type": "code",
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"id": "cdb20e31",
"metadata": {
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"offset = pd.Series(period_sizes, index = [starttime + pd.Timedelta(hours=4)])\n",
"rsv.limit_level_period_ramping_down_offset.set(offset)"
]
},
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"Historical reservoir level values should be supplied to SHOP when running with complex ramping constraints since both rolling and periodic constraints look backwards in time. Historical values will therefore allow SHOP to add proper ramping constraints for the first hours of the optimization, and can be defined using the TXY attribute [historical_level](reservoir:historical_level). \n",
"\n",
"For simplicity, hourly values for the first day before the optimization start time is used in this example. To cover all rolling ramping constraints in this example, it is sufficient to define historical reservoir levels that begin 12 hours before optimization start. Historical values must be defined for 16 hours before the optimization start time to properly initialize the periodic ramping constraints, 6 hours to complete the initial fractional period and another 10 hours to add a full and purely historical ramping period before that."
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"source": [
"np.random.seed(0)\n",
"\n",
"#We generate 24 historic hourly reservoir values by going on a random walk backwards from the start level 95 masl\n",
"#Each value is within 5 cm of the previous one\n",
"prev_level = 95\n",
"level = []\n",
"for i in range(24):\n",
" l = prev_level + 0.05*(1-2*np.random.rand())\n",
" level.append(l)\n",
" prev_level = l\n",
" \n",
"#Flip values so that the oldest comes first\n",
"level = level[::-1] \n",
"t = [starttime - pd.Timedelta(hours=24-i) for i in range(24)]\n",
"historical_level = pd.Series(level, index=t)\n",
"\n",
"rsv.historical_level.set(historical_level)\n",
"\n",
"fig = go.Figure()\n",
"fig.add_trace(go.Scatter(x=historical_level.index, y=historical_level.values, name=\"Historical reservoir level\"))\n",
"fig.update_layout(title=\"Historical reservoir level values\", xaxis_title=\"Time\", yaxis_title=\"masl\")\n",
"\n",
"fig.show()"
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"id": "16ba7312",
"metadata": {},
"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": "142346ae",
"metadata": {
"Collapsed": "false"
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"outputs": [],
"source": [
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]
},
{
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"id": "b6ce7b08",
"metadata": {},
"source": [
"As seen in the figure below, it is no longer possible to drain the reservoir without violating the ramping constraints. Note that the historical reservoir levels have been appended to the optimized reservoir level results."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "462c852e",
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"level = rsv.head.get()\n",
"\n",
"#Combine historical and optimized reservoir levels to one Series\n",
"total_level = pd.concat((historical_level,level))\n",
"total_level = total_level.asfreq('1min').interpolate()\n",
"\n",
"fig = go.Figure()\n",
"fig.add_trace(go.Scatter(x=total_level.index, y=total_level.values, name=\"With ramping\"))\n",
"fig.add_trace(go.Scatter(x=level_no_ramp.index, y=level_no_ramp.values, name=\"Without ramping\"))\n",
"\n",
"fig.update_layout(title=\"Reservoir level comparison\", xaxis_title=\"Time\", yaxis_title=\"masl\")\n",
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"source": [
"To further visualize the different ramping constraints, we will validate that they are not broken by post-calculating the average reservoir levels in the fixed ramping periods and as a rolling average.\n",
"\n",
"### Period ramping validation\n",
"The figure below includes the reservoir level in addition to the maximum reservoir level reached within each fixed ramping period. The lower reservoir limit due to the ramping constraint is also calculated and shown as a black dashed line. The vertical dotted lines show the beginning of each fixed ramping period."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "efaf7d1d",
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