Question-and-Answer Resource for the Building Energy Modeling Community
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I think you may have just read the Input/Output Reference guide for Pump:VariableSpeed, because the Engineering reference for Variable Speed Pumps seems pretty clear in terms of explaining what these are. I'll take the key information out and format it here for convenience.
PLR is the current requested volume flow rate divided by the nominal volume flow rate:
$$PartLoadRatio = VolFlowRate / NomVolFlowRate$$
FracFullLoadPower is calculated from the equation you put in your question, based on PLR and the coefficients you have set (derived from the literature);
$$FracFullLoadPower= C1 + C2 \cdot PLR + C3 \cdot PLR^2 + C4 \cdot PLR^3$$
Then the power consumed by the pump is calculated:
$$Power = FracFullLoadPower * NomPowerUse$$
Where NomVolFlowRate and NomPowerUse are nominal = Design values you have entered in your pump object, respectively the Design Maximum Flow Rate and Design Power Consumption fields.
