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"(pq-example)=\n",
"# PQ curve limits\n",
"\n",
"## Introduction\n",
"This example demonstrates how PQ curves are built in SHOP, and how the PQ curves are affected by different limits on production and discharge.\n",
"\n",
"An introduction to PQ curves can be found [here](pq_curves).\n",
"\n",
"The model setup for this example is available in the following format:\n",
"\n",
"- pyshop\n",
" - [](pq_example_case.py)\n",
" \n",
"For saving PQ curves, use the command [save pq_curves /on](save_pq_curves). Note that only the PQ curves for the latest iteration is saved."
]
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"#Necessary imports\n",
"import pandas as pd\n",
"import plotly.graph_objs as go\n",
"import plotly.express as px\n",
"\n",
"from pyshop import ShopSession\n",
"\n",
"#Functions used in this example for building a basic SHOP model and running it\n",
"from pq_example_case import build_model, run_model"
]
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"id": "b62033cb",
"metadata": {},
"source": [
"## Create a SHOP session and import model\n",
"We will use a simple example model with one reservoir and one plant."
]
},
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"execution_count": 2,
"id": "1eadbe4f",
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"\n",
"\n",
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"#Create a standard ShopSession\n",
"shop=ShopSession()\n",
"#Build a basic SHOP model\n",
"build_model(shop)\n",
"#Display topology to the screen\n",
"display(shop.model.build_connection_tree())"
]
},
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"id": "00a07e39",
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"## Turbine efficiency curves\n",
"In addition to the net generator head, SHOP uses the generator attributes [gen_eff_curve](generator:gen_eff_curve) and [turb_eff_curves](generator:turb_eff_curves) to build the PQ curves. The [turb_eff_curves](generator:turb_eff_curves) is the most important of these attributes, and describe the turbine efficiency as a function of discharge for different net head values. The plot below shows the [turb_eff_curves](generator:turb_eff_curves) for our generator."
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"source": [
"for gen in shop.model.generator:\n",
" #Get generator turbine efficiency curves\n",
" turb_eff_curves=gen.turb_eff_curves.get() \n",
"\n",
" #Create figure \n",
" fig = go.Figure() \n",
" x_discharge = pd.DataFrame([], dtype=\"float64\")\n",
" y_net_head = pd.Series([], dtype=\"float64\")\n",
" z_efficiency = pd.DataFrame([], dtype=\"float64\")\n",
" \n",
" for curve in turb_eff_curves:\n",
" if (len(x_discharge) > 0):\n",
" x_discharge = pd.concat([x_discharge, pd.Series(curve.index)], axis=1)\n",
" else:\n",
" x_discharge = pd.concat([pd.Series(curve.index)], axis=1)\n",
" \n",
" if (len(y_net_head) > 0):\n",
" y_net_head = pd.concat([y_net_head, pd.Series(curve.name)])\n",
" else:\n",
" y_net_head = pd.concat([pd.Series(curve.name)])\n",
" \n",
" if (len(z_efficiency) > 0):\n",
" z_efficiency = pd.concat([z_efficiency, pd.Series(curve.values)], axis=1)\n",
" else:\n",
" z_efficiency = pd.concat([pd.Series(curve.values)], axis=1)\n",
" \n",
" title_name=\" Turbine efficiency curves of \"+gen.get_name()+\"\"\n",
" fig = go.Figure(data=[go.Surface(x=x_discharge.values.T, y=y_net_head.values, z=z_efficiency.values.T)])\n",
" fig.update_layout(scene = dict(\n",
" xaxis_title=\"Discharge (m3/s)\",\n",
" yaxis_title=\"Net head (meter)\",\n",
" zaxis_title=\"Efficiency (%)\"),\n",
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"cell_type": "markdown",
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"metadata": {},
"source": [
"## Run model and plot results\n",
"\n",
"We start by running the example model."
]
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{
"cell_type": "code",
"execution_count": 4,
"id": "c73399c2",
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"source": [
"In our example case, the reservoir goes from being full to being empty, so that the net head varies from its maximum to its minimum."
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"cell_type": "code",
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"for rsv in shop.model.reservoir: \n",
" # Reservoir water level trajectory\n",
" fig = go.Figure() \n",
" water_level=rsv.head.get()\n",
" fig.add_trace(go.Scatter(x=water_level.index, y=water_level.values, name=\"Reservoir water level\", marker_color=\"red\")) \n",
" \n",
" # Regulation max water level \n",
" max_level=rsv.hrl.get()\n",
" txy_max_level=pd.Series(index=water_level.index, dtype=\"float64\")\n",
" txy_max_level=txy_max_level.fillna(max_level)\n",
" fig.add_trace(go.Scatter(x=txy_max_level.index, y=txy_max_level.values, name=\"Reservoir regulation max water level\", marker_color=\"rgb(0, 0, 255)\", line=dict(width=3, dash=\"dot\"))) \n",
"\n",
" # Regulation min water level . \n",
" min_level=rsv.lrl.get()\n",
" txy_min_level=pd.Series(index=water_level.index, dtype=\"float64\")\n",
" txy_min_level=txy_min_level.fillna(min_level)\n",
" fig.add_trace(go.Scatter(x=txy_min_level.index, y=txy_min_level.values, name=\"Reservoir regulation min water level\", marker_color=\"rgb(0, 200, 0)\", line=dict(width=3, dash=\"dot\"))) \n",
"\n",
" change = water_level.values[-1] - water_level.values[0]\n",
" change = \"{:,.4f}\".format(change)\n",
" change_pencentage = (water_level.values[-1] - water_level.values[0])/(rsv.hrl.get() - rsv.lrl.get()) * 100\n",
" change_pencentage = \"{:,.2f}\".format(change_pencentage)\n",
" fig.update_layout(title=\"Reservoir water level trajectory of \"+rsv.get_name()+\"
(Change \"+str(change)+\" meter, \"+str(change_pencentage)+\"%)
\", xaxis_title=\"Time (Hour)\", yaxis_title=\"Water level (meter above sea level)\")\n",
" fig.update_layout(legend=dict(orientation=\"h\", yanchor=\"bottom\", y=-0.5, xanchor=\"center\", x=0.5))\n",
" fig.show()\n",
"\n",
"for plant in shop.model.plant:\n",
" eff_head=plant.eff_head.get()\n",
" fig = go.Figure() \n",
" fig.add_trace(go.Scatter(x=eff_head.index, y=eff_head.values, name=str(eff_head.name), mode=\"lines+markers\", line=dict(width=2))) \n",
" fig.update_layout(title=\"Effective head of \"+gen.get_name(), xaxis_title=\"Time\", yaxis_title=\"Eff head (m)\", colorway=px.colors.qualitative.Light24)\n",
" fig.show()\n",
" "
]
},
{
"cell_type": "markdown",
"id": "86b095ff",
"metadata": {},
"source": [
"The plots below show the generator's [original_pq_curves](generator:original_pq_curves), [convex_pq_curves](generator:convex_pq_curves) and [final_pq_curves](generator:final_pq_curves). Since no other limits have been set, the PQ curves are limited by the minimum and maximum discharge points from the [turb_eff_curves](generator:turb_eff_curves)."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "749d17fd",
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""
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"for gen in shop.model.generator: \n",
"\n",
" #Get generator discharge and production\n",
" discharge = gen.discharge.get()\n",
" production = gen.production.get()\n",
" \n",
" #Get PQ curves\n",
" original_pq_curve=gen.original_pq_curves.get()\n",
" convex_pq_curve=gen.convex_pq_curves.get()\n",
" final_pq_curve=gen.final_pq_curves.get()\n",
"\n",
" #Plot original PQ curves \n",
" fig = go.Figure() \n",
" for i, curve in enumerate(original_pq_curve): \n",
" if i%6==0: #plot every 6th hour only\n",
" fig.add_trace(go.Scatter(x=curve.index, y=curve.values, name=str(curve.name), mode=\"lines+markers\", line=dict(width=2))) \n",
" fig.update_layout(title=\"Original PQ curves of \"+gen.get_name(), xaxis_title=\"Discharge (m3/s)\", yaxis_title=\"Production (MW)\", colorway=px.colors.sequential.Plasma)\n",
" fig.show()\n",
" \n",
" #Plot convex PQ curves\n",
" fig = go.Figure() \n",
" for i, curve in enumerate(convex_pq_curve): \n",
" if i%6==0: #plot every 6th hour only\n",
" fig.add_trace(go.Scatter(x=curve.index, y=curve.values, name=str(curve.name), mode=\"lines+markers\", line=dict(width=2))) \n",
" fig.update_layout(title=\"Convex PQ curves of \"+gen.get_name(), xaxis_title=\"Discharge (m3/s)\", yaxis_title=\"Production (MW)\", colorway=px.colors.sequential.Plasma)\n",
" fig.show()\n",
" \n",
" #Plot final PQ curves\n",
" fig = go.Figure()\n",
" for i, curve in enumerate(final_pq_curve): \n",
" if i%6==0: #plot every 6th hour only\n",
" fig.add_trace(go.Scatter(x=curve.index, y=curve.values, name=str(curve.name), mode=\"lines+markers\", line=dict(width=2)))\n",
" \n",
" # Add working point for each time \n",
" current_discharge = discharge.loc[curve.name]\n",
" current_production = production.loc[curve.name]\n",
" if i%6==0: #plot every 6th hour only\n",
" fig.add_trace(go.Scatter(x=[current_discharge], y=[current_production], mode=\"markers\", marker_symbol=\"x\", marker=dict(color=\"Black\", size=5), name=\"working point\", showlegend=False))\n",
" fig.add_trace(go.Scatter(x=[current_discharge], y=[current_production], mode=\"markers\", marker_symbol=\"x\", marker=dict(color=\"Black\", size=5), name=\"working point\"))\n",
" fig.update_layout(title=\"Final PQ curves of \"+gen.get_name(), xaxis_title=\"Discharge (m3/s)\", yaxis_title=\"Production (MW)\", colorway=px.colors.sequential.Plasma)\n",
" fig.show()"
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"## Production limits"
]
},
{
"cell_type": "markdown",
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"metadata": {},
"source": [
"We will now run the example case again, but this time wih stricter limits on production; [p_min](generator:p_min) and [p_max](generator:p_max)."
]
},
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"cell_type": "code",
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"id": "febdeaeb",
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"source": [
"#Create a standard ShopSession\n",
"shop2=ShopSession()\n",
"#Build a basic SHOP model\n",
"build_model(shop2)\n",
"#Set the p_min and p_max attributes\n",
"for gen in shop2.model.generator:\n",
" gen.p_min.set(20)\n",
" gen.p_max.set(82)\n",
"#Run model\n",
"run_model(shop2)"
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"cell_type": "markdown",
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"Now the PQ curves are limited from below by the minimum production [p_min](generator:p_min). From above the curves are limited by the maximum production [p_max](generator:p_max) while the net head is high, while for lower net heads the PQ curve is still limited by the maximum discharge from the [turb_eff_curves](generator:turb_eff_curves)."
]
},
{
"cell_type": "code",
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"yaxis": {
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""
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"source": [
"for gen in shop2.model.generator: \n",
" original_pq_curve=gen.original_pq_curves.get()\n",
" fig = go.Figure() \n",
" for i, curve in enumerate(original_pq_curve): \n",
" if i%6==0: #plot every 6th hour only\n",
" fig.add_trace(go.Scatter(x=curve.index, y=curve.values, name=str(curve.name), mode=\"lines+markers\", line=dict(width=2))) \n",
" fig.add_trace(go.Scatter(x=[25,100], y=[gen.p_max.get()]*2, name=\"P_max\", mode=\"lines\", line=dict(dash=\"dash\",width=2,color=\"black\")))\n",
" fig.add_trace(go.Scatter(x=[25,100], y=[gen.p_min.get()]*2, name=\"P_min\", mode=\"lines\", line=dict(dash=\"dash\",width=2,color=\"black\")))\n",
" fig.update_layout(title=\"Original PQ curves of \"+gen.get_name(), xaxis_title=\"Discharge (m3/s)\", yaxis_title=\"Production (MW)\", colorway=px.colors.sequential.Plasma)\n",
" fig.show()\n",
" "
]
},
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"cell_type": "markdown",
"id": "4a52e9b4",
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"source": [
"## Discharge limits\n",
"\n",
"The default behaviour of SHOP is to find the discharge limits from the minimum discharge points of the [turb_eff_curves](generator:turb_eff_curves). Explicit discharge limits can be set using the head-dependent generator attributes [min_discharge](generator:min_discharge) and [max_discharge](generator:max_discharge). The same attributes are also available on the [needle_combination](needle_combination) object, which will take precedence over the generator attributes if both are defined. \n",
"\n",
"We define and plot head dependent discharge limits below:"
]
},
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"cell_type": "code",
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"id": "36273b5b",
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"q_min=pd.Series([45.0, 69.0], index=[90.0, 100.0])\n",
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"fig=go.Figure()\n",
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"fig.add_trace(go.Scatter(x=q_max.values, y=q_max.index, name=\"max discharge\"))\n",
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"build_model(shop3)\n",
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"q_max=pd.Series([85.0, 109.0], index=[90.0, 100.0])\n",
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" gen.max_discharge.set(q_max)\n",
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"Now we see that the PQ curves are limited by the head-dependent [min_discharge](generator:min_discharge) and [max_discharge](generator:max_discharge) attributes."
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"cell_type": "code",
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" original_pq_curve=gen.original_pq_curves.get() \n",
" fig = go.Figure() \n",
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" if i%6==0: #plot every 6th hour only\n",
" fig.add_trace(go.Scatter(x=curve.index, y=curve.values, name=str(curve.name), mode=\"lines+markers\", line=dict(width=2))) \n",
" fig.update_layout(title=\"Original PQ curves of \"+gen.get_name(), xaxis_title=\"Discharge (m3/s)\", yaxis_title=\"Production (MW)\", colorway=px.colors.sequential.Plasma)\n",
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"As shown in the figure below, the optimized discharge of the generator is limited by the set max_discharge limit when the effective generator head is low. For higher head values, the generator discharges 90 m3/s since this is the best operating point for the plant. \n",
"\n",
"Note that the max_discharge limit was not defined for head values lower than 90 m, but the effective head of the generator is lower than this for several time steps. SHOP assumes that the limits defined for the lowest and highest head values are valid for all head values outside the range covered by the input data, which can be seen in the figure below."
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