Thermal modelling of a three winding transformer¶
In this example the following concepts are shown:
- Creating a ThreeWindingTransformer, and setting its parameters
- Creating a ThreeWindingInputProfile, that holds the profiles for a three winding transformer
- The the thermal modelling of a three winding transformer
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import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from transformer_thermal_model.cooler import CoolerType
from transformer_thermal_model.model import Model
from transformer_thermal_model.schemas import (
ThreeWindingInputProfile,
UserThreeWindingTransformerSpecifications,
WindingSpecifications,
)
from transformer_thermal_model.transformer import ThreeWindingTransformer
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from transformer_thermal_model.cooler import CoolerType
from transformer_thermal_model.model import Model
from transformer_thermal_model.schemas import (
ThreeWindingInputProfile,
UserThreeWindingTransformerSpecifications,
WindingSpecifications,
)
from transformer_thermal_model.transformer import ThreeWindingTransformer
The creation of a ThreeWindingInputProfile is similar to the creation of a normal InputProfile, except that the load_profile is now replaced with a seperate profile for the low, medium and high voltage side of the transformer. These profiles should all have the same length.
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# Define the time range for your simulation
datetime_index = [pd.to_datetime("2025-07-01 00:00:00") + pd.Timedelta(minutes=15 * i) for i in np.arange(0, 288)]
load_series_high = pd.Series(
data=np.sin(np.arange(0, 288) * 900 * 2 * np.pi * 1 / 43200) * 500 + 500, index=datetime_index
)
load_series_middle = pd.Series(
data=np.sin(np.arange(0, 288) * 900 * 2 * np.pi * 1 / 43200) * 500 + 500, index=datetime_index
)
load_series_low = pd.Series(
data=np.sin(np.arange(0, 288) * 900 * 2 * np.pi * 1 / 43200) * 500 + 500, index=datetime_index
)
ambient_series = pd.Series(data=20, index=datetime_index)
# Create the input profile for the three-winding transformer
profile_input = ThreeWindingInputProfile.create(
datetime_index=datetime_index,
ambient_temperature_profile=ambient_series,
load_profile_high_voltage_side=load_series_high,
load_profile_middle_voltage_side=load_series_middle,
load_profile_low_voltage_side=load_series_low,
)
# Define the time range for your simulation
datetime_index = [pd.to_datetime("2025-07-01 00:00:00") + pd.Timedelta(minutes=15 * i) for i in np.arange(0, 288)]
load_series_high = pd.Series(
data=np.sin(np.arange(0, 288) * 900 * 2 * np.pi * 1 / 43200) * 500 + 500, index=datetime_index
)
load_series_middle = pd.Series(
data=np.sin(np.arange(0, 288) * 900 * 2 * np.pi * 1 / 43200) * 500 + 500, index=datetime_index
)
load_series_low = pd.Series(
data=np.sin(np.arange(0, 288) * 900 * 2 * np.pi * 1 / 43200) * 500 + 500, index=datetime_index
)
ambient_series = pd.Series(data=20, index=datetime_index)
# Create the input profile for the three-winding transformer
profile_input = ThreeWindingInputProfile.create(
datetime_index=datetime_index,
ambient_temperature_profile=ambient_series,
load_profile_high_voltage_side=load_series_high,
load_profile_middle_voltage_side=load_series_middle,
load_profile_low_voltage_side=load_series_low,
)
Next, we create an ThreeWindingTransformer object, this is a Child class of the Transformer object. To create this, a user needs to pass specifications in the UserThreeWindingTransformerSpecifications class, in this class the following inputs are mandatory:
- The no-load loss [W]
- The ambient temperature surcharge [K]
- Specifications of the low voltage winding, these are set with a
WindingSpecificationscontaining:- the nominal load [A]
- temperature difference between the average winding and average oil temperature under nominal conditions [K]
- mv_winding (again with a
WindingSpecificationsclass) - hv_winding (again with a
WindingSpecificationsclass) - The load loss between high-voltage and low-voltage winding [W]
- The load loss between high-voltage and middle-voltage winding [W]
- The load loss between middle-voltage and low-voltage winding [W]
Similar to UserTransformerSpecifications, you can also specify a lot off other optional parameters, if these are not set, the default values are used.
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# Define the transformer specifications for each winding
user_specs = UserThreeWindingTransformerSpecifications(
no_load_loss=20,
amb_temp_surcharge=10,
lv_winding=WindingSpecifications(
nom_load=1000, winding_oil_gradient=20, hot_spot_fac=1.2, time_const_winding=1, nom_power=1000
),
mv_winding=WindingSpecifications(
nom_load=1000, winding_oil_gradient=20, hot_spot_fac=1.2, time_const_winding=1, nom_power=1000
),
hv_winding=WindingSpecifications(
nom_load=2000, winding_oil_gradient=20, hot_spot_fac=1.2, time_const_winding=1, nom_power=2000
),
load_loss_hv_lv=100,
load_loss_hv_mv=100,
load_loss_mv_lv=100,
)
# Create the transformer object
transformer = ThreeWindingTransformer(user_specs=user_specs, cooling_type=CoolerType.ONAN)
# Define the transformer specifications for each winding
user_specs = UserThreeWindingTransformerSpecifications(
no_load_loss=20,
amb_temp_surcharge=10,
lv_winding=WindingSpecifications(
nom_load=1000, winding_oil_gradient=20, hot_spot_fac=1.2, time_const_winding=1, nom_power=1000
),
mv_winding=WindingSpecifications(
nom_load=1000, winding_oil_gradient=20, hot_spot_fac=1.2, time_const_winding=1, nom_power=1000
),
hv_winding=WindingSpecifications(
nom_load=2000, winding_oil_gradient=20, hot_spot_fac=1.2, time_const_winding=1, nom_power=2000
),
load_loss_hv_lv=100,
load_loss_hv_mv=100,
load_loss_mv_lv=100,
)
# Create the transformer object
transformer = ThreeWindingTransformer(user_specs=user_specs, cooling_type=CoolerType.ONAN)
The specifications that are used in the thermal model can consulted in the specs property.
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transformer.specs
transformer.specs
Out[47]:
ThreeWindingTransformerSpecifications(no_load_loss=20.0, amb_temp_surcharge=10.0, time_const_oil=210.0, top_oil_temp_rise=60.0, oil_const_k11=0.5, winding_const_k21=2, winding_const_k22=2, oil_exp_x=0.8, winding_exp_y=1.3, end_temp_reduction=0.0, lv_winding=WindingSpecifications(nom_load=1000.0, winding_oil_gradient=20.0, time_const_winding=1.0, hot_spot_fac=1.2, nom_power=1000.0), mv_winding=WindingSpecifications(nom_load=1000.0, winding_oil_gradient=20.0, time_const_winding=1.0, hot_spot_fac=1.2, nom_power=1000.0), hv_winding=WindingSpecifications(nom_load=2000.0, winding_oil_gradient=20.0, time_const_winding=1.0, hot_spot_fac=1.2, nom_power=2000.0), load_loss_hv_lv=100.0, load_loss_hv_mv=100.0, load_loss_mv_lv=100.0, load_loss_total_user=None)
Now we can create a model based on the transformer and the profiles and run the model to create a temperature profile of the top-oil and the hot-spot. This is exactly the same as for Power- and Distribution transformers.
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model = Model(temperature_profile=profile_input, transformer=transformer)
results = model.run()
top_oil_temp_profile = results.top_oil_temp_profile
hot_spot_temp_profile = results.hot_spot_temp_profile
model = Model(temperature_profile=profile_input, transformer=transformer)
results = model.run()
top_oil_temp_profile = results.top_oil_temp_profile
hot_spot_temp_profile = results.hot_spot_temp_profile
A three winding transformers has three hotspot temperature profiles, one for each winding. The return profile of results.hot_spot_temp_profile is therefor a pandas Dataframe with 3 columns:
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hot_spot_temp_profile
hot_spot_temp_profile
Out[49]:
| low_voltage_side | middle_voltage_side | high_voltage_side | |
|---|---|---|---|
| 2025-07-01 00:00:00 | 30.000000 | 30.000000 | 30.000000 |
| 2025-07-01 00:15:00 | 53.641883 | 53.641883 | 40.974417 |
| 2025-07-01 00:30:00 | 57.846068 | 57.846068 | 44.054824 |
| 2025-07-01 00:45:00 | 62.012581 | 62.012581 | 47.126624 |
| 2025-07-01 01:00:00 | 66.084285 | 66.084285 | 50.166824 |
| ... | ... | ... | ... |
| 2025-07-03 22:45:00 | 41.734443 | 41.734443 | 39.717655 |
| 2025-07-03 23:00:00 | 43.754966 | 43.754966 | 40.581056 |
| 2025-07-03 23:15:00 | 46.117911 | 46.117911 | 41.670329 |
| 2025-07-03 23:30:00 | 48.804771 | 48.804771 | 42.988857 |
| 2025-07-03 23:45:00 | 51.784651 | 51.784651 | 44.532525 |
288 rows × 3 columns
It only has one top oil temperature, so results.top_oil_temp_profile is still a pandas series
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top_oil_temp_profile
top_oil_temp_profile
Out[50]:
2025-07-01 00:00:00 30.000000
2025-07-01 00:15:00 32.311651
2025-07-01 00:30:00 34.623552
2025-07-01 00:45:00 36.946722
2025-07-01 01:00:00 39.281517
...
2025-07-03 22:45:00 38.338455
2025-07-03 23:00:00 38.410548
2025-07-03 23:15:00 38.628808
2025-07-03 23:30:00 39.011589
2025-07-03 23:45:00 39.573090
Length: 288, dtype: float64
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# Plot the top-oil temperature profile
fig1, ax1 = plt.subplots()
results.top_oil_temp_profile.plot(ax=ax1, label="Top-oil temperature")
ax1.set_title("Top-oil Temperature")
ax1.set_ylabel("Temperature [C]")
ax1.legend()
plt.show()
# Plot the hot-spot temperature profiles
fig2, ax2 = plt.subplots()
results.hot_spot_temp_profile.plot(ax=ax2)
ax2.set_title("Hot-spot Temperatures")
ax2.set_ylabel("Temperature [C]")
ax2.legend()
plt.show()
# Plot the top-oil temperature profile
fig1, ax1 = plt.subplots()
results.top_oil_temp_profile.plot(ax=ax1, label="Top-oil temperature")
ax1.set_title("Top-oil Temperature")
ax1.set_ylabel("Temperature [C]")
ax1.legend()
plt.show()
# Plot the hot-spot temperature profiles
fig2, ax2 = plt.subplots()
results.hot_spot_temp_profile.plot(ax=ax2)
ax2.set_title("Hot-spot Temperatures")
ax2.set_ylabel("Temperature [C]")
ax2.legend()
plt.show()
