IMAC Team 2

- Improved Efficiency Final Report December 2006

Appendix G: Vehicle COP and Q Calculations Page 1 of 5 **Ap pendix IMA**  **C2**

**– G**  **: Vehicle COP and Capacity Calculations**  **COP, Capacity, and Compressor Power Calculation Method Comparison** The software model includes a real time ca lculation of COP, c apacit y , 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 plot s below show results from 3 main iterations calculated with vehicle data for the estimation of COP, capacit y, 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 ph ys icall y based approach implemented by EDS, the second was a linear regression approach implemented at CTS, and the third was a ph ys icall y based linear regression approach implemented at CTS. An enthalpy based method was also explored for COP calculation and a dry airside based calculation for capacit y was evaluated. The plots show estimated values for COP, capacit y, and compressor power using each of the 3 iterations with data taken in the vehicle at I25 b , L25 b , I 35 b , L35b as well as measured values for COP, capacit y, and compressor power taken for the same conditions on the bench. In addition the enthalpy

- based COP and airside capacit y were calculated using the vehicle data and shown for the 4 conditions tested. The final ph ys ically 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 rat e was calculated b y multipl yi ng compressor displacement (Disp) , duty cy cle, speed (V c ) , suction density ( ρ s ) and volumetric efficiency (η v ) as shown in the equation below . The duty cy cle was estimated based on the control signal to the compressor and the volumetric efficiency was estimated based o n discharge pressure

. Using the mass flow rate from this meth od predicted unreasonabl y high capacities originall y, 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 calculatio n gave reasonable capacit y values at the full displacement I25b point but performed poorly at reduced displacement points because there was no accounting for the loss in volumetric effi ciency at reduced displacements and because the dut y c yc le did not dire ctly 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 (AFR c ), the air temperature entering the condenser (T cai ), the average air temperature exiting the evaporator measured at the nozzle (T en ), the compressor speed (V c ), the discharge pressure (P cpro ), the compressor displacement control current (CompCurr) and the air flow rate over the evaporator (AFR e ) as shown in the following equations . The regression constants were fit using a limited amount of bench data . Th e results of this regression were poor because it was based on a small amount of data and because the variables used did not adequatel y represent the s ystem. Additional attempts were made with additional variables and additional bench data with limited re sults. I t was then decided to move to a more phy sically 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 displa cement, speed, suction density and volumetric efficiency was modified in this approach . The compressor duty cycle and volumetric efficiency were combined into one term (K v ) resulting in the mass flow rate equation shown below. The regression was performe d basing K v on a combination of pressure ratio ( P d /P s ) , compressor pressure difference *(P d - P s ) , compressor speed ( V c ) , and compressor displacement control signal current ( CompCurr) . The regression equation shown below was used with the full IMAC bench te st matrix data to calculate the constants C 1 through C 7 .

A regression for compressor power was done in the same fashion using a different term (K p ) shown in the equation s 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 compr essor 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 va lues 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. **Ai rside 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 (A FR c ) was multiplied by the specific heat and the change in air temperature across the evaporator as shown in the equation below.

The final ph ys icall y 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. IMA C Bench Data - COP Comparison** 

0 1 2 3 4 5 6 7 8

I35b L35b I25b L25b**C O** **P (** **- )** 

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** 

-4 -2 0 2 4 6 8 10 12 14 16

I35b L35b I25b L25b**C a** **p a** **c i** **t y** **( k** **W )** 

Vehicle EDS equations Vehicle original regression Vehicle final regression Capacity bench data Vehicle air side dryIMAC 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 0 0.5 1 1.5 2 2.5 3 3.5 4

I35b L35b I25b L25b**P o** **w e** **r (** **k W** **)**

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