IMAC Team 2 - Improved Efficiency Final Report December 2006

Appendix G: Vehicle COP and Q Calculations Page 1 of 5

Appendix IMAC2 – G: Vehicle COP and Capacity Calculations

COP, Capacity, and Compressor Power Calculation Method Comparison

The software model includes a real time calculation of COP, capacity, and compressor 

power. Various methods have been explored to estimate these values. The necessary

parameters to calculate these values are all recorded excluding compressor power and 

refrigerant mass flow rate. The plots below show results from 3 main iterations 

calculated with vehicle data for the estimation of COP, capacity, and compressor power

as well as bench test results at the same conditions and one additional method for COP 

calculation and another additional method for capacity calculation. The first iteration

was a physically based approach implemented by EDS, the second was a linear 

regression approach implemented at CTS, and the third was a physically based linear 

regression approach implemented at CTS. An enthalpy based method was also explored 

for COP calculation and a dry airside based calculation for capacity was evaluated. The 

plots show estimated values for COP, capacity, and compressor power using each of the 3 

iterations with data taken in the vehicle at I25b, L25b, I35b, L35b as well as measured 

values for COP, capacity, and compressor power taken for the same conditions on the 

bench. In addition the enthalpy-based COP and airside capacity were calculated using 

the vehicle data and shown for the 4 conditions tested. The final physically based 

regression showed a very good agreement with the bench as did the enthalpy based COP 

calculation. Each method of calculation is covered below.

EDS Physically Based Iteration

The compressor power was calculated using a normalized load calculation and the 

refrigerant flow rate was calculated by multiplying compressor displacement (Disp), duty

cycle, speed (Vc), suction density (ρs) and volumetric efficiency (ηv) as shown in the 

equation below. The duty cycle was estimated based on the control signal to the 

compressor and the volumetric efficiency was estimated based on discharge pressure. 

Using the mass flow rate from this method predicted unreasonably high capacities 

originally, however after some corrections to the implementation of this mass flow rate 

equation the prediction preformed better as is shown in the capacity plot as ‘EDS method 

corrected’. The corrected calculation gave reasonable capacity values at the full 

displacement I25b point but performed poorly at reduced displacement points because 

there was no accounting for the loss in volumetric efficiency at reduced displacements 

and because the duty cycle did not directly correlate to the displacement. The torque was 

estimated using a normalized load calculation which resulted in high predictions of 

compressor work.
IMAC Team 2 - Improved Efficiency Final Report December 2006

Appendix G: Vehicle COP and Q Calculations Page 2 of 5

CTS Original Linear Regression

A linear regression was provided to CTS which calculated mass flow rate and compressor 

power. The regression was based on the air flow rate on the condenser (AFRc), the air 

temperature entering the condenser (Tcai), the average air temperature exiting the 

evaporator measured at the nozzle (Ten), the compressor speed (Vc), the discharge 

pressure (Pcpro), the compressor displacement control current (CompCurr) and the air 

flow rate over the evaporator (AFRe) as shown in the following equations. The 

regression constants were fit using a limited amount of bench data. The results of this 

regression were poor because it was based on a small amount of data and because the 

variables used did not adequately represent the system. Additional attempts were made 

with additional variables and additional bench data with limited results. It was then 

decided to move to a more physically based regression approach.

CTS Final Physically Based Linear Regression

A physically based mass flow rate equation which calculates mass flow rate by 

multiplying duty cycle, compressor displacement, speed, suction density and 

volumetric efficiency was modified in this approach. The compressor duty cycle 

and volumetric efficiency were combined into one term (Kv) resulting in the mass 

flow rate equation shown below. The regression was performed basing Kv on a 

combination of pressure ratio (Pd/Ps), compressor pressure difference *(Pd-Ps), 

compressor speed (Vc), and compressor displacement control signal current 

(CompCurr). The regression equation shown below was used with the full IMAC 

bench test matrix data to calculate the constants C1 through C7.

A regression for compressor power was done in the same fashion using a 

different term (Kp) shown in the equations below.
IMAC Team 2 - Improved Efficiency Final Report December 2006

Appendix G: Vehicle COP and Q Calculations Page 3 of 5

This approach showed very good results as COP, capacity, and compressor 

power correlated well to the bench data for the 4 conditions tested. 

Enthalpy Based COP Calculation

An additional method for COP calculation was implemented using only the 

refrigerant enthalpies. The COP was calculated by dividing the change in

refrigerant enthalpy across the evaporator by the change in refrigerant enthalpy 

across the compressor as shown in the equation below. A constant, E1, was 

calculated using the bench data to account for compressor efficiency. 

This method output COP values close to the bench as can be seen in the COP 

comparison plot below. For very low displacements this method was less 

accurate due to the loss in compressor efficiency that is not captured with the 

constant E1.

Airside Capacity Calculation

A dry air side capacity measurement was also evaluated. As expected, this 

method outputs low values at the four conditions shown in the capacity plot 

below due to the lack of the latent load component. To calculate the capacities 

the air flow rate (AFRc) was multiplied by the specific heat and the change in air 

temperature across the evaporator as shown in the equation below.

The final physically based regression showed the best results and was implemented in the 

control software.
IMAC Team 2 - Improved Efficiency Final Report December 2006

Appendix G: Vehicle COP and Q Calculations Page 4 of 5

CTS Vehicle Tests vs. IMAC Bench Data - COP Comparison

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3

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6

7

8

I35b L35b I25b L25b

COP ( - ) COP vehicle EDS equations COP vehicle original regression COP vehicle final regression COP bench data COP vehicle enthalpy based

CTS Vehicle Tests vs. IMAC Bench Data - Capacity Comparison

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-2

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I35b L35b I25b L25b

Capacity ( kW )

Vehicle EDS equations Vehicle original regression Vehicle final regression Capacity bench data Vehicle air side dry
IMAC Team 2 - Improved Efficiency Final Report December 2006

Appendix G: Vehicle COP and Q Calculations Page 5 of 5

CTS Vehicle Tests vs. IMAC Bench Data - Compressor Power Comparison

-0.5

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I35b L35b I25b L25b

Power (kW)

Wcomp vehicle EDS equations Wcomp vehicle original regression Wcomp vehicle final regression Wcomp bench data