# -*- coding: utf-8 -*-
# SPDX-FileCopyrightText: : 2020-2024 The PyPSA-Eur Authors
#
# SPDX-License-Identifier: MIT
from typing import Union
import numpy as np
import xarray as xr
from BaseCopApproximator import BaseCopApproximator
class CentralHeatingCopApproximator(BaseCopApproximator):
"""
Approximate the coefficient of performance (COP) for a heat pump in a
central heating system (district heating).
Uses an approximation method proposed by Jensen et al. (2018) and
default parameters from Pieper et al. (2020). The method is based on
a thermodynamic heat pump model with some hard-to-know parameters
being approximated.
Attributes:
----------
forward_temperature_celsius : Union[xr.DataArray, np.array]
The forward temperature in Celsius.
return_temperature_celsius : Union[xr.DataArray, np.array]
The return temperature in Celsius.
source_inlet_temperature_celsius : Union[xr.DataArray, np.array]
The source inlet temperature in Celsius.
source_outlet_temperature_celsius : Union[xr.DataArray, np.array]
The source outlet temperature in Celsius.
delta_t_pinch_point : float, optional
The pinch point temperature difference, by default 5.
isentropic_compressor_efficiency : float, optional
The isentropic compressor efficiency, by default 0.8.
heat_loss : float, optional
The heat loss, by default 0.0.
Methods:
-------
__init__(
forward_temperature_celsius: Union[xr.DataArray, np.array],
source_inlet_temperature_celsius: Union[xr.DataArray, np.array],
return_temperature_celsius: Union[xr.DataArray, np.array],
source_outlet_temperature_celsius: Union[xr.DataArray, np.array],
delta_t_pinch_point: float = 5,
isentropic_compressor_efficiency: float = 0.8,
heat_loss: float = 0.0,
) -> None:
Initializes the CentralHeatingCopApproximator object.
approximate_cop(self) -> Union[xr.DataArray, np.array]:
Calculate the coefficient of performance (COP) for the system.
_approximate_delta_t_refrigerant_source(
self, delta_t_source: Union[xr.DataArray, np.array]
) -> Union[xr.DataArray, np.array]:
Approximates the temperature difference between the refrigerant and the source.
_approximate_delta_t_refrigerant_sink(
self,
refrigerant: str = "ammonia",
a: float = {"ammonia": 0.2, "isobutane": -0.0011},
b: float = {"ammonia": 0.2, "isobutane": 0.3},
c: float = {"ammonia": 0.016, "isobutane": 2.4},
) -> Union[xr.DataArray, np.array]:
Approximates the temperature difference between the refrigerant and heat sink.
_ratio_evaporation_compression_work_approximation(
self,
refrigerant: str = "ammonia",
a: float = {"ammonia": 0.0014, "isobutane": 0.0035},
) -> Union[xr.DataArray, np.array]:
Calculate the ratio of evaporation to compression work based on approximation.
_approximate_delta_t_refrigerant_sink(
self,
refrigerant: str = "ammonia",
a: float = {"ammonia": 0.2, "isobutane": -0.0011},
b: float = {"ammonia": 0.2, "isobutane": 0.3},
c: float = {"ammonia": 0.016, "isobutane": 2.4},
) -> Union[xr.DataArray, np.array]:
Approximates the temperature difference between the refrigerant and heat sink.
_ratio_evaporation_compression_work_approximation(
self,
refrigerant: str = "ammonia",
a: float = {"ammonia": 0.0014, "isobutane": 0.0035},
) -> Union[xr.DataArray, np.array]:
Calculate the ratio of evaporation to compression work based on approximation.
"""
def __init__(
self,
forward_temperature_celsius: Union[xr.DataArray, np.array],
source_inlet_temperature_celsius: Union[xr.DataArray, np.array],
return_temperature_celsius: Union[xr.DataArray, np.array],
source_outlet_temperature_celsius: Union[xr.DataArray, np.array],
delta_t_pinch_point: float = 5,
isentropic_compressor_efficiency: float = 0.8,
heat_loss: float = 0.0,
) -> None:
"""
Initializes the CentralHeatingCopApproximator object.
Parameters:
----------
forward_temperature_celsius : Union[xr.DataArray, np.array]
The forward temperature in Celsius.
return_temperature_celsius : Union[xr.DataArray, np.array]
The return temperature in Celsius.
source_inlet_temperature_celsius : Union[xr.DataArray, np.array]
The source inlet temperature in Celsius.
source_outlet_temperature_celsius : Union[xr.DataArray, np.array]
The source outlet temperature in Celsius.
delta_t_pinch_point : float, optional
The pinch point temperature difference, by default 5.
isentropic_compressor_efficiency : float, optional
The isentropic compressor efficiency, by default 0.8.
heat_loss : float, optional
The heat loss, by default 0.0.
"""
self.t_source_in_kelvin = BaseCopApproximator.celsius_to_kelvin(
source_inlet_temperature_celsius
)
self.t_sink_out_kelvin = BaseCopApproximator.celsius_to_kelvin(
forward_temperature_celsius
)
self.t_sink_in_kelvin = BaseCopApproximator.celsius_to_kelvin(
return_temperature_celsius
)
self.t_source_out = BaseCopApproximator.celsius_to_kelvin(
source_outlet_temperature_celsius
)
self.isentropic_efficiency_compressor_kelvin = isentropic_compressor_efficiency
self.heat_loss = heat_loss
self.delta_t_pinch = delta_t_pinch_point
def approximate_cop(self) -> Union[xr.DataArray, np.array]:
"""
Calculate the coefficient of performance (COP) for the system.
Returns:
--------
Union[xr.DataArray, np.array]: The calculated COP values.
"""
return (
self.ideal_lorenz_cop
* (
(
1
+ (self.delta_t_refrigerant_sink + self.delta_t_pinch)
/ self.t_sink_mean_kelvin
)
/ (
1
+ (
self.delta_t_refrigerant_sink
+ self.delta_t_refrigerant_source
+ 2 * self.delta_t_pinch
)
/ self.delta_t_lift
)
)
* self.isentropic_efficiency_compressor_kelvin
* (1 - self.ratio_evaporation_compression_work)
+ 1
- self.isentropic_efficiency_compressor_kelvin
- self.heat_loss
)
@property
def t_sink_mean_kelvin(self) -> Union[xr.DataArray, np.array]:
"""
Calculate the logarithmic mean temperature difference between the cold
and hot sinks.
Returns
-------
Union[xr.DataArray, np.array]
The mean temperature difference.
"""
return BaseCopApproximator.logarithmic_mean(
t_cold=self.t_sink_in_kelvin, t_hot=self.t_sink_out_kelvin
)
@property
def t_source_mean_kelvin(self) -> Union[xr.DataArray, np.array]:
"""
Calculate the logarithmic mean temperature of the heat source.
Returns
-------
Union[xr.DataArray, np.array]
The mean temperature of the heat source.
"""
return BaseCopApproximator.logarithmic_mean(
t_hot=self.t_source_in_kelvin, t_cold=self.t_source_out
)
@property
def delta_t_lift(self) -> Union[xr.DataArray, np.array]:
"""
Calculate the temperature lift as the difference between the
logarithmic sink and source temperatures.
Returns
-------
Union[xr.DataArray, np.array]
The temperature difference between the sink and source.
"""
return self.t_sink_mean_kelvin - self.t_source_mean_kelvin
@property
def ideal_lorenz_cop(self) -> Union[xr.DataArray, np.array]:
"""
Ideal Lorenz coefficient of performance (COP).
The ideal Lorenz COP is calculated as the ratio of the mean sink temperature
to the lift temperature difference.
Returns
-------
np.array
The ideal Lorenz COP.
"""
return self.t_sink_mean_kelvin / self.delta_t_lift
@property
def delta_t_refrigerant_source(self) -> Union[xr.DataArray, np.array]:
"""
Calculate the temperature difference between the refrigerant source
inlet and outlet.
Returns
-------
Union[xr.DataArray, np.array]
The temperature difference between the refrigerant source inlet and outlet.
"""
return self._approximate_delta_t_refrigerant_source(
delta_t_source=self.t_source_in_kelvin - self.t_source_out
)
@property
def delta_t_refrigerant_sink(self) -> Union[xr.DataArray, np.array]:
"""
Temperature difference between the refrigerant and the sink based on
approximation.
Returns
-------
Union[xr.DataArray, np.array]
The temperature difference between the refrigerant and the sink.
"""
return self._approximate_delta_t_refrigerant_sink()
@property
def ratio_evaporation_compression_work(self) -> Union[xr.DataArray, np.array]:
"""
Calculate the ratio of evaporation to compression work based on
approximation.
Returns
-------
Union[xr.DataArray, np.array]
The calculated ratio of evaporation to compression work.
"""
return self._ratio_evaporation_compression_work_approximation()
@property
def delta_t_sink(self) -> Union[xr.DataArray, np.array]:
"""
Calculate the temperature difference at the sink.
Returns
-------
Union[xr.DataArray, np.array]
The temperature difference at the sink.
"""
return self.t_sink_out_kelvin - self.t_sink_in_kelvin
def _approximate_delta_t_refrigerant_source(
self, delta_t_source: Union[xr.DataArray, np.array]
) -> Union[xr.DataArray, np.array]:
"""
Approximates the temperature difference between the refrigerant and the
source.
Parameters
----------
delta_t_source : Union[xr.DataArray, np.array]
The temperature difference for the refrigerant source.
Returns
-------
Union[xr.DataArray, np.array]
The approximate temperature difference between the refrigerant and heat source.
"""
return delta_t_source / 2
def _approximate_delta_t_refrigerant_sink(
self,
refrigerant: str = "ammonia",
a: float = {"ammonia": 0.2, "isobutane": -0.0011},
b: float = {"ammonia": 0.2, "isobutane": 0.3},
c: float = {"ammonia": 0.016, "isobutane": 2.4},
) -> Union[xr.DataArray, np.array]:
"""
Approximates the temperature difference between the refrigerant and
heat sink.
Parameters:
----------
refrigerant : str, optional
The refrigerant used in the system. Either 'isobutane' or 'ammonia. Default is 'ammonia'.
a : float, optional
Coefficient for the temperature difference between the sink and source, default is 0.2.
b : float, optional
Coefficient for the temperature difference at the sink, default is 0.2.
c : float, optional
Constant term, default is 0.016.
Returns:
-------
Union[xr.DataArray, np.array]
The approximate temperature difference between the refrigerant and heat sink.
Notes:
------
This function assumes ammonia as the refrigerant.
The approximate temperature difference at the refrigerant sink is calculated using the following formula:
a * (t_sink_out - t_source_out + 2 * delta_t_pinch) + b * delta_t_sink + c
"""
if refrigerant not in a.keys():
raise ValueError(
f"Invalid refrigerant '{refrigerant}'. Must be one of {a.keys()}"
)
return (
a[refrigerant]
* (self.t_sink_out_kelvin - self.t_source_out + 2 * self.delta_t_pinch)
+ b[refrigerant] * self.delta_t_sink
+ c[refrigerant]
)
def _ratio_evaporation_compression_work_approximation(
self,
refrigerant: str = "ammonia",
a: float = {"ammonia": 0.0014, "isobutane": 0.0035},
b: float = {"ammonia": -0.0015, "isobutane": -0.0033},
c: float = {"ammonia": 0.039, "isobutane": 0.053},
) -> Union[xr.DataArray, np.array]:
"""
Calculate the ratio of evaporation to compression work approximation.
Parameters:
----------
refrigerant : str, optional
The refrigerant used in the system. Either 'isobutane' or 'ammonia. Default is 'ammonia'.
a : float, optional
Coefficient 'a' in the approximation equation. Default is 0.0014.
b : float, optional
Coefficient 'b' in the approximation equation. Default is -0.0015.
c : float, optional
Coefficient 'c' in the approximation equation. Default is 0.039.
Returns:
-------
Union[xr.DataArray, np.array]
The approximated ratio of evaporation to compression work.
Notes:
------
This function assumes ammonia as the refrigerant.
The approximation equation used is:
ratio = a * (t_sink_out - t_source_out + 2 * delta_t_pinch) + b * delta_t_sink + c
"""
if refrigerant not in a.keys():
raise ValueError(
f"Invalid refrigerant '{refrigerant}'. Must be one of {a.keys()}"
)
return (
a[refrigerant]
* (self.t_sink_out_kelvin - self.t_source_out + 2 * self.delta_t_pinch)
+ b[refrigerant] * self.delta_t_sink
+ c[refrigerant]
)