Method of calculating COP and heat capacity in electrical heat pump

In energyPRO a simple Lorentz heat pump model is implemented for calculating the theoretical COP (coefficient of performance).

The theoretical COP is calculated by:

\[ C O P = \frac{T_{H i g h M e a n}}{\left( T_{H i g h M e a n} - T_{L o w M e a n} \right)} \]

Where \(T_{HighMean}\) is the mean temperature (K) of the Delivered hot water

            \(T_{LowMean}\) is the mean temperature (K) of the Heat source

The mean temperature of the Delivered hot water are calculated as:

\[ T_{H i g h M e a n} = \frac{T_{H i g h O u t l e t} - T_{H i g h I n l e t}}{\ln \left( \frac{T_{H i g h O u t l e t} + 2 7 3 . 1 5}{T_{H i g h I n l e t} + 2 7 3 . 1 5} \right)} \]

Where \(T_{HighOutlet}\) is the temperature (°C) of the delivered water out of the heat pump

            \(T_{HighInlet}\) is the temperature (°C) of the delivered water when entering the heat pump.

The mean temperature of the Heat source are calculated as:

\[ T_{L o w M e a n} = \frac{T_{L o w O u t l e t} - T_{L o w I n l e t}}{\ln \left( \frac{T_{L o w O u t l e t} + 2 7 3 . 1 5}{T_{L o w I n l e t} + 2 7 3 . 1 5} \right)} \]

Where \(T_{LowOutlet}\) is the temperature (°C) from which heat source is cooled from

            \(T_{LowInlet}\) is the temperature (°C) that the heat source is cooled down to

In the Heat pump specification the specified temperatures are used to calculate the theoretical COP. This COP is divided by the stated COP resulting in the heat pump efficiency, \(HP_{eff}\).

The actual temperatures are used to calculate a theoretical COP for each timestep. This theoretical COP is multiplied with the \(HP_{eff}\) giving the actual COP.

To calculate the heat capacity at the given time step, the actual COP is multiplied with the stated Electrical Capacity.

With very low temperature differences, the COP can become rather high. With fixed electricity capacity, the heat capacity of the heat pump than becomes high. However, often this is not realizable. When the calculated heat capacity exceeds the Max. Heat Capacity, the electricity capacity is reduced by dividing the Max. Heat Capacity with the calculated COP.