Transformer thermal model

transformer-thermal-model is a library for modelling the transformer top-oil and hot-spot temperature based on the transformer specifications, a load profile and an ambient temperature profile. The model is an implementation according to the standard IEC 60076-7, also known as de Loading Guide.

Check out our documentation page, the technical documentation, the quick start or one of the many other examples!

Installation

Install from PyPI

You can directly install the package from PyPI.

pip install transformer-thermal-model

Structure of the code

This package contains the following modules to work with:

• transformer_thermal_model.model: the core of the package to calculate a temperature profile of a transformer using the thermal model;
• transformer_thermal_model.transformer: a module containing multiple transformer classes to be used to define a transformer;
• transformer_thermal_model.cooler: a module containing the enumerators to define the cooler type of the transformer;
• transformer_thermal_model.schemas: in schemas one can find a.o. the definition of the model interfaces and how the transformer specificitations should be specified;
• transformer_thermal_model.hot_spot_calibration: a module that is used to determine the transformer hot-spot factor to be used in the thermal model.

The following modules contain elements that are not required for thermal modelling but are used to get more insight in aging and load capacity:

• transformer_thermal_model.aging: a module to calculate the aging of a transformer according to IEC 60076-7 paragraph 6.3;
• transformer_thermal_model.components: a module containing enumerators to define components of a power transformer if one wants to calculate the relative load capacity of each component in the transformer.

How to create a transformer

Before performing a calculation, a transformer object must be created with all necessary details about the transformer. Default values will be used for any attribute not specified by the user.

transformer_thermal_model.transformer: This module has multiple Transformer children, which will be elements used for the temperature calculation inside Model.

• PowerTransformer: A power transformer class, child of the Transformer class.
• DistributionTransformer: A distribution transformer class, also child of the Transformer class.
• ThreeWindingTransformer: A three winding transformer, also child of the Transformer class.
• TransformerType (Enum): For easily checking all available types. Does not have any use in our code, but might be useful for your use-case.

Transformer specifications

A Transformer needs a couple of specifications (user_specs) and a cooling type (in cooling_type). The specifications are defined in transformer_thermal_model.schemas.UserTransformerSpecifications, and are a composition of some mandatory specifications and some optionals. When the optionals are left unchanged, the default values per class will be used. These can be found by defaults, e.g. PowerTransformer.defaults will show you the default specifications.

An example on how to initialise a PowerTransformer:

from transformer_thermal_model.cooler import CoolerType
from transformer_thermal_model.transformer import PowerTransformer
from transformer_thermal_model.schemas import UserTransformerSpecifications

tr_specs = UserTransformerSpecifications(
   load_loss=1000,  # Transformer load loss [W]
   nom_load_sec_side=1500,  # Transformer nominal current secondary side [A]
   no_load_loss=200,  # Transformer no-load loss [W]
   amb_temp_surcharge=20,  # Ambient temperature surcharge [K]
)
transformer = PowerTransformer(user_specs=tr_specs, cooling_type=CoolerType.ONAF)

It is recommended to adjust the following parameters when modelling a specific transformer as these influence the thermal modelling and are transformer-specifically defined (the ones with a '*' are mandatory):

• load_loss*: load loss of the transformer.
• no_load_loss*: no load loss of the transformer.
• nom_load_sec_side*: nominal current of the secondary side of the transformer.
• amb_temp_surcharge*:
  • PowerTransformer: temperature surcharge on ambient temperature due to installation conditions.
  • DistributionTransformer: Building or placement thermal classification.
• top_oil_temp_rise: top-oil temperature increase under nominal conditions.
• winding_oil_gradient: temperature difference between the average winding and average oil temperature under nominal conditions
• hot_spot_fac: factor determining the temperature difference between top-oil and hot-spot. Only specify when known, otherwise see hot-spot factor calibration.

Cooler

transformer_thermal_model.cooler: Similarly, you must provide the type of cooling of your transformer. This is only for a PowerTransformer, since a DistributionTransformer is always ONAN. To adjust the cooler type for a PowerTransformer, you can do the following:

from transformer_thermal_model.transformer import PowerTransformer
from transformer_thermal_model.cooler import CoolerType
from transformer_thermal_model.schemas import UserTransformerSpecifications

tr_specs = UserTransformerSpecifications(
                load_loss=10000,
                nom_load_sec_side=1000,
                no_load_loss=1000,
                amb_temp_surcharge=0,
            )

# You can create a power transformer with ONAF cooling.
onaf_trafo = PowerTransformer(user_specs = tr_specs, cooling_type = CoolerType.ONAF)
# Or you can create a power transformer with ONAN cooling
onan_trafo = PowerTransformer(user_specs = tr_specs, cooling_type = CoolerType.ONAN)

Hot-spot factor calibration for power transformers

When the hot-spot factor of a transformer is known, it can be given as a specification as hot_spot_fact in a UserTransformerSpecifications object.

It often occurs, however, that a transformer hot-spot factor is not known. If this is the case, a hot-spot factor calibration can be performed to determine the hot-spot factor of a given PowerTransformer object. Note that for DistributionTransformer objects, hot-spot calibrations should not be performed and the default value can be used. For both the PowerTransformer and the DistributionTransformer the hot_spot_fac in the specification is set to the default value of no hot-spot factor is provided via the UserTransformerSpecifications.

The following example shows how to calibrate a PowerTransformer object.

from transformer_thermal_model.cooler import CoolerType
from transformer_thermal_model.schemas import UserTransformerSpecifications
from transformer_thermal_model.transformer import PowerTransformer
from transformer_thermal_model.hot_spot_calibration import calibrate_hotspot_factor

tr_specs = UserTransformerSpecifications(
   load_loss=1000,  # Transformer load loss [W]
   nom_load_sec_side=1500,  # Transformer nominal current secondary side [A]
   no_load_loss=200,  # Transformer no-load loss [W]
   amb_temp_surcharge=20,  # Ambient temperature surcharge [K]
)
uncalibrated_transformer = PowerTransformer(user_specs=tr_specs, cooling_type=CoolerType.ONAF)
calibrated_trafo = calibrate_hotspot_factor(
   uncalibrated_transformer=uncalibrated_transformer,
   ambient_temp=20.0,
   hot_spot_limit=98, # in most cases a hot-spot temperature limit of 98 can be used
   hot_spot_factor_min=1.1,
   hot_spot_factor_max=1.3,
)

The new hot-spot factor is available via calibrated_trafo.specs.hot_spot_fac, and from now on used in the thermal model.

>>> print(calibrated_trafo.specs.hot_spot_fac)
1.1

Component capacities of a power transformer

For load capacity calculations it can be required to take into account the capacity of the different components of a power transformers. Therefore a functionality is available to calculate the relative capacity of the tap changers, the bushings (primary and secondary) and the internal current transformer. The capacity is defined as the ratio of the component capacity and the nominal load of the transformer.

The capacities are properties of the PowerTransformer and require the TransformerComponentSpecifications to be given during initiating a PowerTransformer object.

In the following example for all components the required information is provided.

from transformer_thermal_model.components import BushingConfig, TransformerSide, VectorConfig
from transformer_thermal_model.cooler import CoolerType
from transformer_thermal_model.schemas import (
    TransformerComponentSpecifications,
    UserTransformerSpecifications,
)
from transformer_thermal_model.transformer import PowerTransformer

comp_specs = TransformerComponentSpecifications(
        tap_chang_capacity=600,  # Tap changer nominal current [A]
        nom_load_prim_side=550,  # Transformer nominal current primary side [A]
        tap_chang_conf=VectorConfig.TRIANGLE_OUTSIDE,  # Tap Changer configuration
        tap_chang_side=TransformerSide.SECONDARY,  # Tap changer side
        prim_bush_capacity=600,  # Primary bushing nominal current [A]
        prim_bush_conf=BushingConfig.SINGLE_BUSHING,  # Primary bushing configuration
        sec_bush_capacity=1800,  # Secondary bushing nominal current [A]
        sec_bush_conf=BushingConfig.SINGLE_BUSHING,  # Secondary bushing configuration
        cur_trans_capacity=1300,  # Current transformer nominal current [A]
        cur_trans_conf=VectorConfig.STAR,  # Current transformer configuration
        cur_trans_side=TransformerSide.PRIMARY,  # Current transformer side
    )
user_specs = UserTransformerSpecifications(
        load_loss=1000,  # Transformer load loss [W]
        nom_load_sec_side=1500,  # Transformer nominal current secondary side [A]
        no_load_loss=200,  # Transformer no-load loss [W]
        amb_temp_surcharge=20,
    )
power_transformer = PowerTransformer(
        user_specs=user_specs, cooling_type=CoolerType.ONAF, internal_component_specs=comp_specs
    )

The resulting component capacities are available in power_transformer.component_capacities:

>>> print(power_transformer.component_capacities)
{'tap_changer': 0.4, 'primary_bushings': 1.0909090909090908, 'secondary_bushings': 1.2, 'current_transformer': 2.3636363636363638}

Note that it is also possible to only define a subset of the components if not all components are present. Then only the component capacities of the provided components are available:

comp_specs = TransformerComponentSpecifications(
    tap_chang_capacity=600,  # Tap changer nominal current [A]
    nom_load_prim_side=550,  # Transformer nominal current primary side [A]
    tap_chang_conf=VectorConfig.TRIANGLE_OUTSIDE,  # Tap Changer configuration
    tap_chang_side=TransformerSide.SECONDARY,  # Tap changer side
)
power_transformer = PowerTransformer(
        user_specs=user_specs, cooling_type=CoolerType.ONAF, internal_component_specs=comp_specs
    )

This will generate the following result:

>>> print(power_transformer.component_capacities)
{'tap_changer': 0.4, 'primary_bushings': None, 'secondary_bushings': None, 'current_transformer': None}

Thermal modelling

When a Transformer object is completely defined, the temperatures can be calculated using transformer_thermal_model.model: the core of the package. The Model is built as follows:

import pandas as pd

from transformer_thermal_model.model import Model
from transformer_thermal_model.cooler import CoolerType
from transformer_thermal_model.schemas import UserTransformerSpecifications, InputProfile
from transformer_thermal_model.transformer import PowerTransformer

# In this example the model is used to calculate the transformer temperature based on a load and ambient
# profile with a period of one week. Any duration can be chosen preferably with timestamps with an interval of
# 15 minute or lower. Larger timesteps will result in incorrect results but it *is* possible to calculate with them.
one_week = 4*24*7
datetime_index = pd.date_range("2020-01-01", periods=one_week, freq="15min")

# For the load (in A) and ambient temperature (in C) arbitrary constants profiles are chosen.
# It is also possible to use a realistic profile.
nominal_load = 100
load_points = pd.Series([nominal_load] * one_week, index=datetime_index)
ambient_temp = 21
temperature_points = pd.Series([ambient_temp] * one_week, index=datetime_index)

# Create an input object with the profiles
profile_input = InputProfile.create(
   datetime_index = datetime_index,
   load_profile = load_points,
   ambient_temperature_profile = temperature_points
)

# Initialise a power transformer with cooling type ONAF and, besides the mandatory user specifications, default values.
tr_specs = UserTransformerSpecifications(
   load_loss=1000,  # Transformer load loss [W]
   nom_load_sec_side=1500,  # Transformer nominal current secondary side [A]
   no_load_loss=200,  # Transformer no-load loss [W]
   amb_temp_surcharge=20,  # Ambient temperature surcharge [K]
)
transformer = PowerTransformer(user_specs=tr_specs, cooling_type=CoolerType.ONAF)
model = Model(
   temperature_profile = profile_input,
   transformer = transformer
)

results = model.run()

# Get the results as pd.Series, with the same datetime_index as your input.
top_oil_temp_profile = results.top_oil_temp_profile
hot_spot_temp_profile = results.hot_spot_temp_profile

>>> top_oil_temp_profile.head(3)
2020-01-01 00:00:00    41.000000
2020-01-01 00:15:00    43.639919
2020-01-01 00:30:00    45.801302

>>> hot_spot_temp_profile.head(3)
2020-01-01 00:00:00    41.000000
2020-01-01 00:15:00    44.381177
2020-01-01 00:30:00    46.443459

You can use the Model to run a calculation with either a PowerTransformer or a DistributionTransformer. The model will return results with the top_oil_temperature and hot_spot_temperature as pd.Series. More specifically, the output will be in the form of OutputProfile, as defined in transformer_thermal_model.schemas. The reason for using pd.Series as output, is that the model uses the index of the series that you have provided to run the calculation, which also creates the benefit for you that you can relate the result to your provided input for eventual cross-validation or analysis.

Three winding Transformer modelling

The model also supports thermal modeling of three-winding transformers. To use this feature, provide both a ThreeWindingTransformer and a ThreeWindingInputProfile as input to the Model. The ThreeWindingInputProfile requires a separate load profile for each winding (high, medium, and low voltage sides), all sharing the same length and datetime index.

With UserThreeWindingTransformerSpecifications, you can specify the nominal load and winding oil gradient for each winding, as well as the load losses between windings. The resulting hot-spot temperature profile is returned as a DataFrame with columns for each winding, making it easy to analyze the results for each part of the transformer.

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

# Define the time range for your simulation
one_week = 4 * 24 * 7
datetime_index = pd.date_range("2020-01-01", periods=one_week, freq="15min")

# Create ambient temperature profile (can be a constant or a realistic profile)
ambient_temp = 21
temperature_points = pd.Series([ambient_temp] * one_week, index=datetime_index)

# Create load profiles for each winding (high, medium, low voltage sides)
load_profile_high_voltage_side = pd.Series([2000] * one_week, index=datetime_index)
load_profile_middle_voltage_side = pd.Series([1500] * one_week, index=datetime_index)
load_profile_low_voltage_side = pd.Series([1000] * one_week, index=datetime_index)

# Create the input profile for the three-winding transformer
profile_input = ThreeWindingInputProfile.create(
    datetime_index=datetime_index,
    ambient_temperature_profile=temperature_points,
    load_profile_high_voltage_side=load_profile_high_voltage_side,
    load_profile_middle_voltage_side=load_profile_middle_voltage_side,
    load_profile_low_voltage_side=load_profile_low_voltage_side,
)

# 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)

# Run the thermal model
model = Model(
    temperature_profile=profile_input,
    transformer=transformer
)
results = model.run()

# The results are returned as pandas Series/DataFrame, indexed by your datetime_index
top_oil_temp_profile = results.top_oil_temp_profile
hot_spot_temp_profile = results.hot_spot_temp_profile

top_oil_temp_profile = results.top_oil_temp_profile
hot_spot_temp_profile = results.hot_spot_temp_profile

>>> top_oil_temp_profile.head()
2020-01-01 00:00:00    31.000000
2020-01-01 00:15:00    40.212693
2020-01-01 00:30:00    48.198972
2020-01-01 00:45:00    55.122101
2020-01-01 01:00:00    61.123609

```text
>>> hot_spot_temp_profile.head()
                          low_voltage_side   middle_voltage_side   high_voltage_side
2020-01-01 00:00:00           31.000000           31.000000           31.000000
2020-01-01 00:15:00           84.991214          116.068422           84.991214
2020-01-01 00:30:00           90.234413          119.407866           90.234413
2020-01-01 00:45:00           94.756639          122.263816           94.756639
2020-01-01 01:00:00           98.676844          124.739555           98.676844

Using the top oil temperature as an input to the model

Optionally, you can provide the top oil temperature as an input parameter to the InputProfile to use it in place of the ambient temperature as an input to the model:

import pandas as pd

from transformer_thermal_model.model import Model
from transformer_thermal_model.cooler import CoolerType
from transformer_thermal_model.schemas import UserTransformerSpecifications, InputProfile
from transformer_thermal_model.transformer import PowerTransformer

one_week = 4*24*7
datetime_index = pd.date_range("2020-01-01", periods=one_week, freq="15min")

nominal_load = 100
load_points = pd.Series([nominal_load] * one_week, index=datetime_index)
ambient_temp = 21
temperature_points = pd.Series([ambient_temp] * one_week, index=datetime_index)
top_oil_temp = 42
top_oil_points = pd.Series([top_oil_temp] * one_week, index=datetime_index)

profile_input = InputProfile.create(
   datetime_index = datetime_index,
   load_profile = load_points,
   ambient_temperature_profile = temperature_points,
   # Here is where we add the top oil temperature as an input. It has the same shape as the ambient temperature.
   top_oil_temperature_profile = top_oil_points
)

tr_specs = UserTransformerSpecifications(
   load_loss=1000,  # Transformer load loss [W]
   nom_load_sec_side=1500,  # Transformer nominal current secondary side [A]
   no_load_loss=200,  # Transformer no-load loss [W]
   amb_temp_surcharge=20,  # Ambient temperature surcharge [K]
)
transformer = PowerTransformer(user_specs=tr_specs, cooling_type=CoolerType.ONAF)
model = Model(
   temperature_profile = profile_input,
   transformer = transformer
)

# As we have provided the top oil temperature as an input, this is now being used in place of the ambient temperature.
# If you still want to use the top oil temperature you can do so using model.run(force_use_ambient_temperature=True)
results = model.run()

top_oil_temp_profile = results.top_oil_temp_profile
hot_spot_temp_profile = results.hot_spot_temp_profile

>>> top_oil_temp_profile.head(3)
2020-01-01 00:00:00    42.0
2020-01-01 00:15:00    42.0
2020-01-01 00:30:00    42.0

>>> hot_spot_temp_profile.head(3)
2020-01-01 00:00:00    42.000000
2020-01-01 00:15:00    42.741258
2020-01-01 00:30:00    42.938711

Note, how the top oil temperature we receive as the output results.top_oil_temp_profile exactly matches the top oil temperature we provided as the input.

License

This project is licensed under the Mozilla Public License, version 2.0 - see LICENSE for details.

Licenses third-party libraries

This project includes third-party libraries, which are licensed under their own respective Open-Source licenses. SPDX-License-Identifier headers are used to show which license is applicable.

The concerning license files can be found in the LICENSES directory.

Contributing

Please read CODE_OF_CONDUCT, CONTRIBUTING and PROJECT GOVERNANCE for details on the process for submitting pull requests to us.

Contact

Please read SUPPORT for how to get in touch with the Transformer Thermal Model project.