# Understanding chiller performance curves

Recently I was tasked with some chiller-related tasks and I need to understand the performance model. More specifically, I am interested in the EIR EnergyPlus chiller model.

The chiller's performance in this model is characterized by three performance curves: CAPFT, EIRFT, and CAPFT.

Electric input to cooling output ratio (EIR)

EIR measures the ratio between the input power and the cooling output. For example, EIR 0.5 means that a chiller that produces 100KW cooling output does so with 50KW input electric power. EIR is the inverse of CoP.

Normalized EIR

EIR is often normalized to the rated EIR of the chiller. Say, a chiller's Rated EIR is 0.4 and we observe a noralized EIR 0.9 under some conditions. That means the EIR of the chiller under the observation condition is 0.9*0.4=0.36

Cooling capacity function of temperature curve (CAPFT):

This is a bi-quadratic curve where the two inputs are the evaporator's chilled water outlet temperature and the condenser's entering water temperature. The output of this function is measured in KW and denotes the chiller's power consumption.

Electric input to cooling output ratio function of temperature curve (EIRFT): This is a bi-quadratic curve where the two inputs are the evaporator's chilled water outlet temperature and the condenser's entering water temperature. The output of this function is the normalized EIR.

Electric input to cooling output ratio function of part load ratio curve (EIRfTPLR) This is meant to be again a Bi-quadratic curve but is often simplified to a quadratic curve by removing the temperature input. If simplified, it is often denoted as EIRPLR. The simplified quadratic curve input is the chiller's part load ratio, and the output is the chiller's normalized EIR.

And here comes the part that confuses me

The electric power consumption of the compressor is calculated using (source):

Q_compressor = (Q_ref / CoP_ref) * CAPFT * EIRFT * EIRPLR

Let's look at each part of this equation individually:

(Q_ref / CoP_ref): is the rated cooling power divided by the rated CoP. That gives the rated electrical input for the chiller that is a constant and measured in KW.

CAPFT * EIRFT: CAPFT is the cooling power at a given temperature that is multiplied by the EIR at the same temperature. This gives the input electrical power for the chiller under that temperature.

CAPFT * EIRPLR: CAPFT is the cooling power at a given temperature that is multiplied by the EIR at partial load.

My questions:

Question 1: To calculate EIRPLR we need to know the PLR. PLR is calculated by dividing the current cooling power by the maximum cooling power. It seems to be that the output of CAPFT should be used to calculate the PLR that is the input for the EIRPLR. But for some reason there is a multiplication. Why?

Question 2: EIRPLR and EIRFT both output normalized EIRs. multiplying those two gives us a squared normalized EIR. Similarly multiplying (Q_ref / CoP_ref) and CAPFT gives us squared KW. How does this whole multiplication end up with Q_compressor that should be the KW usage of the compressor?

Sources where I got this stuff: