Determine the water flow rate using the condenser capacity:

Q_c = Q_e + P
Q_c = Q_e + Q_e / COP
Q_c = Q_e * (1 + 1 / COP)

Where Q_c and Q_e are respectively the condenser and evaporator capacity, and P is the input power.

The calculation is done for both the heating and companion cooling coil and set to the maximum of the two.
Set the water flow rate to be the maximum of heating or cooling coil water flow rate

This doesn't seem right. RatedCapHeat is the condenser heat, it just happens to be the evaporator or load side. Yes, confusing. So heating flow rate sizing should simply be based on RatedCapHeat. So I think it should be simpleWatertoAirHP.RatedCapHeat for the heating object and just companionCoolingCoil.RatedCapCoolTotal for the cooling object. Probably need to talk this through more like we did for the Plant EIR HP. It matters which flow rate is being sized. If it's the load side then the flow should be the larger of flows to meet the load. Probably need to review how the PlantLoopHeatPumpEIR is sized.

@Nigusse made some changes to the Plant EIR HP on #10382:

    if (this->EIRHPType == DataPlant::PlantEquipmentType::HeatPumpEIRHeating) {
        designSourceSideHeatTransfer = tmpCapacity * (1 - 1 / this->referenceCOP);
    } else {
        designSourceSideHeatTransfer = tmpCapacity * (1 + 1 / this->referenceCOP);
    }

Oh, yes, that makes sense. I propagated the cooling coil adjustments to the heating coil but I see that it is incorrect. I'll push a correction. Thanks for catching that.

Repurpose existing test to let the rated water flow rate be autosized and test the outcome.

Here we're dealing with the heating coil so the evaporator is on the source side and the condenser is on the load side.

So if we start with Qc = Qe + P and because we're dealing with heating operation COP = Qc / P so Qe = Source Side Load = Qc - P = Qc (1 - 1 / COP) and Qc = simpleWatertoAirHP.RatedCapHeat. So I think that the + sign should be changed to -.

Instead of:

RatedWaterVolFlowRateDes =
(1 + 1 / RatedHeatCOP) * simpleWatertoAirHP.RatedCapHeat / (state.dataSize->PlantSizData(PltSizNum).DeltaT * Cp * rho);

We should have:

RatedWaterVolFlowRateDes =
(1 - 1 / RatedHeatCOP) * simpleWatertoAirHP.RatedCapHeat / (state.dataSize->PlantSizData(PltSizNum).DeltaT * Cp * rho);

I agree with the suggested change. See the equation below for reference:

The source side (evaporator coil) fluid mass flow rate can be calculated from the load side heating capacity and from the heating mode COP_h as follows:

m_dot_source = Q_load_side * (1 - 1/cop_h) / (cp_source * deltaT_source)

Alternatively:

m_dot_source = Q_source_side * / (cp_source * deltaT_source)

Where,

Q_source_side = Q_load_side * (1 - 1/COP_h)

Here we're dealing with the companion cooling coil so the evaporator is on the load side and the condenser is on the source side.

So if we start with Qc = Qe + P and because we're dealing with heating operation COP = Qe / P so Qc = Source Side Load = Qe + P = Qe (1 + 1 / COP) and Qe = companionCoolingCoil.RatedCapCoolTotal. So I think this is correct.

Then, we're taking the maximum of either the calculated heating coil evaporator flow rate or the cooling coil condenser flow rate.

We must be cautious about which COP value is used to relate the source-side and load-side heat transfer rates. In your equation, Qc = Qe + P = Qe (1 + 1/COP), the COP should be the cooling COP as shown below:

COP_c = Q_evap / P 
COP_h = Q_cond / P

So,

Q_cond = Q_evap + P = Q_evap * (1 + 1/COP_c)

Why do you have to take the maximum?

Right, cooling coil COP for the cooling coil calculations and heating coil COP for heating coil calculations.

If we have companion coils in the system (both water-to-air heating and cooling coils), we could end-up with different calculated water flow rates. Since we need only one value for the system, I assumed that we would want to keep the larger of the two. Do you have a suggestion?

I don't see a problem taking the maximum flow as long as the flow rates are determined based on their respective design loads, design delta T, and CP values appropriate for cooling and heating loops. In this case, it is how you arrive at the Design Load that leads to different flow rates.

Also, the assumption here for the companion coil is that it has already been sized. You might want to check if RatedCapCoolTotal == DataSizing::AutoSize before this calculation?

I do not think this is correct. Since when does Q = M * Cp * deltaT include COP? You have a load and a plant delta T, from those you calculate mass flow rate. I think this equation was correct to begin with. Also for the equation below for the companion coil, don't use (1 + 1/COP) but do use the correct plant Delta T from the Sizing:Plant object for the cooling plant. I believe PltSizNum here is for the heating plant. @Nigusse ?

COP comes into play because as @Nigusse pointed out above, for the heating coil we have m_dot_source = Q_load_side * (1 - 1/cop_h) / (cp_source * deltaT_source). Where simpleWatertoAirHP.RatedCapHeat is the load side capacity.

These are water to air coils, so the plant loop associated with them should be a condenser plant loop, meaning that both the heating and cooling coil should be on the demand side of that plant loop. So unless I'm missing something, the design dT should be the same for both coils. One thing I could do, to be safe, is to get the sizing plant object for the companion coil and use it to determine the cooling coil water flow rate instead of using the same value for both. I'll make that change.

If this is for source side sizing then this is fine. I see that RatedCapHeat is the air-side heating capacity on the load side. So these equations make sense for adjustment to the source side. Yes, use the correct Sizing:Plant information.

What happens if the companion cooling coil is hard-sized? There may not be a plant sizing object for the companion coil. And you couldn't then use the max of each if this coil's flow was less than that value. Not sure what to easily do about that. Up at line 2857 it's already determined that this coil's water flow rate is autosized so it's assumed that both flow rates are autosized? At the very least I think line 2890 should be protected with if (PltSizNumCompanionCoil > 0)

I assume that you mean that the companion cooling coil water flow rate is hard-sized by the user. If so, since we only need to have one value for the system, shouldn't we use the cooling coil water flow rate to not overwrite user inputs? If it is fine to overwrite user inputs we could perhaps take the maximum of the hard sized value and the value calculated for the heating coil, or, check if there's a plant loop sizing object and if so take the maximum of the three (heating coil value, hard-sized value, value determined using the dT of the plant loop).

Yes, companion cooling coil is hard-sized and this coil is autosized. I did say I couldn't think of an easy way to fix this. 1) I don't think we should ever overwrite a user input, 2) what happens if a user hard-sizes both coils and those values are different?, are there any example files that are hard-sized and these values are different? does real equipment always use the same flow rates? 3) if you really do want the flow rates to be the same, you could just use the companion value but then you need to know if it was hard-sized. This could also lead to very low or high delta T on the water side. So there is no easy answer. So unless you can think of something robust, you might just go with if (PltSizNumCompanionCoil > 0) and wait for these other issues to actually cause a problem. I do think it would be VERY rare that one is hard-sized and the other is autosized. The work-around for a future issue would be to use the same method for both coils.