Measurement Points¶
In this example we showcase the functionality of adding measurement points to the model. Measurement points can be added to monitor the temperature at position $(x,y)$ in the environment.
Measurement points can be added to a StaticEnvSoil only. To add a measurement point, we start by constructing a static environment. Refer to the Example Calculation for a step by step guide on setting up a model.
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from datetime import datetime
import numpy as np
import pandas as pd
from cable_thermal_model import CableLayer, CablePosition, ModelFactory, StaticEnvSoil
from cable_thermal_model.cable.schemas.circuit_schemas import CircuitInSoilFromCableIdInputSchema
static_env = StaticEnvSoil()
circuit_input_1 = CircuitInSoilFromCableIdInputSchema(
x=0.0,
y=-1,
circuit_name="circuit_1",
cable_id="GPLK 10/10 kV 3x185 Al",
cable_source_file_path="../../data/example_cables.csv",
)
static_env.add_circuit_from_cable_id(circuit_input_1)
from datetime import datetime
import numpy as np
import pandas as pd
from cable_thermal_model import CableLayer, CablePosition, ModelFactory, StaticEnvSoil
from cable_thermal_model.cable.schemas.circuit_schemas import CircuitInSoilFromCableIdInputSchema
static_env = StaticEnvSoil()
circuit_input_1 = CircuitInSoilFromCableIdInputSchema(
x=0.0,
y=-1,
circuit_name="circuit_1",
cable_id="GPLK 10/10 kV 3x185 Al",
cable_source_file_path="../../data/example_cables.csv",
)
static_env.add_circuit_from_cable_id(circuit_input_1)
Out[ ]:
StaticEnvSoil Circuit circuit_1 Type: SingleCable BondingType: no_bonding x: 0.0 y: -1.0
With a static environment set, we can add one or multiple measurement points. The measurement keys can be used to retrieve the temperature profile after running the model.
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measurement_point_key1 = static_env.add_measurement_point(x=0.1, y=-1.0)
measurement_point_key2 = static_env.add_measurement_point(x=0.3, y=-1.0)
print(f"Measurement Point Key 1: {measurement_point_key1}")
print(f"Measurement Point Key 2: {measurement_point_key2}")
measurement_point_key1 = static_env.add_measurement_point(x=0.1, y=-1.0)
measurement_point_key2 = static_env.add_measurement_point(x=0.3, y=-1.0)
print(f"Measurement Point Key 1: {measurement_point_key1}")
print(f"Measurement Point Key 2: {measurement_point_key2}")
Measurement Point Key 1: ('measurement_point', 'x=0.100m', 'y=-1.000m')
Measurement Point Key 2: ('measurement_point', 'x=0.300m', 'y=-1.000m')
Now, a scenario and a model can be set up.
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# In this case we use a scenario that lasts for a week with a step size of 1 hour.
START_DATE = datetime(2026, 1, 1)
DAYS_TO_SIMULATE = 7
scenario = pd.DataFrame(
index=pd.date_range(start=START_DATE, end=START_DATE + pd.Timedelta(days=DAYS_TO_SIMULATE), freq="1h")
)
# We set the load of the circuit to oscillate between 50 and 350A with a period of 24 hours.
scenario["load_circuit_1"] = 200.0 + 150.0 * np.sin(2 * np.pi * scenario.index.hour / 24)
scenario["ambient_temperature"] = 15.0 # Ambient temperature is assumed to be constant at 15 degrees Celsius.
scenario["soil_thermal_resistivity"] = 0.75 # Soil thermal resistivity is assumed to be constant at 0.75 mK/W.
scenario["soil_thermal_capacity"] = 2.0e6 # Soil thermal capacity is assumed to be constant at 2e6 J/(m³K).
scenario.head()
# In this case we use a scenario that lasts for a week with a step size of 1 hour.
START_DATE = datetime(2026, 1, 1)
DAYS_TO_SIMULATE = 7
scenario = pd.DataFrame(
index=pd.date_range(start=START_DATE, end=START_DATE + pd.Timedelta(days=DAYS_TO_SIMULATE), freq="1h")
)
# We set the load of the circuit to oscillate between 50 and 350A with a period of 24 hours.
scenario["load_circuit_1"] = 200.0 + 150.0 * np.sin(2 * np.pi * scenario.index.hour / 24)
scenario["ambient_temperature"] = 15.0 # Ambient temperature is assumed to be constant at 15 degrees Celsius.
scenario["soil_thermal_resistivity"] = 0.75 # Soil thermal resistivity is assumed to be constant at 0.75 mK/W.
scenario["soil_thermal_capacity"] = 2.0e6 # Soil thermal capacity is assumed to be constant at 2e6 J/(m³K).
scenario.head()
Out[ ]:
| load_circuit_1 | ambient_temperature | soil_thermal_resistivity | soil_thermal_capacity | |
|---|---|---|---|---|
| 2026-01-01 00:00:00 | 200.000000 | 15.0 | 0.75 | 2000000.0 |
| 2026-01-01 01:00:00 | 238.822857 | 15.0 | 0.75 | 2000000.0 |
| 2026-01-01 02:00:00 | 275.000000 | 15.0 | 0.75 | 2000000.0 |
| 2026-01-01 03:00:00 | 306.066017 | 15.0 | 0.75 | 2000000.0 |
| 2026-01-01 04:00:00 | 329.903811 | 15.0 | 0.75 | 2000000.0 |
The model can be executed to compute the temperature profile over time.
The simulation output is stored in solution, and the temperature time series are available in temperature_result.
This includes cable temperatures (e.g., conductor and sheath) as well as temperatures at the added measurement points.
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model = ModelFactory.create_model(static_env=static_env)
solution = model.run(scenario=scenario)
temperature_result = solution.result
temperature_result.head()
model = ModelFactory.create_model(static_env=static_env)
solution = model.run(scenario=scenario)
temperature_result = solution.result
temperature_result.head()
Out[ ]:
| circuit_1 | measurement_point | |||
|---|---|---|---|---|
| single | x=0.100m | x=0.300m | ||
| Conductor | Sheath | y=-1.000m | y=-1.000m | |
| 2026-01-01 00:00:00 | 15.000000 | 15.000000 | 15.000000 | 15.000000 |
| 2026-01-01 01:00:00 | 24.553775 | 16.687167 | 15.262748 | 15.002660 |
| 2026-01-01 02:00:00 | 31.924032 | 18.656360 | 15.755784 | 15.013093 |
| 2026-01-01 03:00:00 | 38.759849 | 20.708081 | 16.407640 | 15.036851 |
| 2026-01-01 04:00:00 | 45.095192 | 22.765104 | 17.163937 | 15.078364 |
The temperature profile at a measurement point can be retrieved using the forementioned keys.
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import matplotlib.pyplot as plt
# Plot the measurement points together with conductor and sheath temperatures.
x = temperature_result.index
series = [
temperature_result["circuit_1"][CablePosition.Single][CableLayer.Conductor],
temperature_result["circuit_1"][CablePosition.Single][CableLayer.Sheath],
temperature_result[measurement_point_key1],
temperature_result[measurement_point_key2],
scenario["ambient_temperature"],
]
labels = [
"Conductor",
"Sheath",
"Measurement Point 1",
"Measurement Point 2",
"Ambient",
]
for y, label in zip(series, labels, strict=True):
plt.plot(x, y, label=label)
plt.ylabel("Temperature (°C)")
plt.title("Calculated Temperatures for Circuit 1 and Measurement Points")
plt.legend(loc="upper center", bbox_to_anchor=(0.5, 1.2), ncol=3)
plt.xticks(rotation=45)
plt.show()
import matplotlib.pyplot as plt
# Plot the measurement points together with conductor and sheath temperatures.
x = temperature_result.index
series = [
temperature_result["circuit_1"][CablePosition.Single][CableLayer.Conductor],
temperature_result["circuit_1"][CablePosition.Single][CableLayer.Sheath],
temperature_result[measurement_point_key1],
temperature_result[measurement_point_key2],
scenario["ambient_temperature"],
]
labels = [
"Conductor",
"Sheath",
"Measurement Point 1",
"Measurement Point 2",
"Ambient",
]
for y, label in zip(series, labels, strict=True):
plt.plot(x, y, label=label)
plt.ylabel("Temperature (°C)")
plt.title("Calculated Temperatures for Circuit 1 and Measurement Points")
plt.legend(loc="upper center", bbox_to_anchor=(0.5, 1.2), ncol=3)
plt.xticks(rotation=45)
plt.show()
