Optimizing flow rate for ideal COP

[Andre_K (André Kühne)]

Having an oversized heat pump, I recently wondered whether the high flow rate pump that goes along with it might also just be too much. Typically, everyone wants a high flow rate but at some point the electricity consumption of the pump will also become significant…the question is when.

To find this optimum, let’s have a look at what goes into it. We have our design heat loss P_heat and our radiators (or generally emitters) are chosen so they deliver this power into the house when they are at a specific temperature T_rad. Typically, this temperature is approximated as the mean of flow and return temperature, so T_rad = 1/2 (T_flow + T_return). Together with the mass flow heat equation, we can express the required flow temperature to reach our radiator temperature given a specific flow rate:

T_flow = T_rad + P_heat/(2 c flow_rate)

We see that the flow temperature is at least as high as the required radiator temperature, with an additional offset proportional to the required heating power and inversely proportional to the flow rate. For my house with 30°C radiator temperature (0°C outside) and heat loss of around 3 kW, the flow and return temperatures vs. flow rate look like this:

As flow rate increases, the flow and return temperature asymptotically approach the required radiator temperature, which would result in lower compressor electricity use due to higher COP at lower flow temperatures. If pumps didn’t need power, infinite flow rates would be best.

However, the required electrical power of the pump increases with flow rate. It appears this goes with the cube of flow rate, but I can’t confirm this. For simplicity I used a simple linear relationship that I approximated from my system’s pump, but the analysis works for more complex cases as well.

There were quite a few discussions on the forum how much of power put into the circulation pump ends up as usable heat in the house. For the sake of this analysis, I have assumed that all the electricity going into the pump is converted into heat. Here we can see how required compressor power decreases (due to increasing COP with lower flow temperatures) as pump power increases. The total heat being put into the house is constant. I did a simple linear approximation between compressor COP and (T_flow-T_outside) based on my Vaillant’s datasheet to get the compressor COP.

Adding those two up and dividing the required heat power by the sum gives us the total COP of the whole system. The next graph shows this for different total heat loss scenarios.

We can see that there’s an optimum point where we achieve the best possible COP. The higher the heat loss, the higher the optimum flow rate. It’s not a lot, but depending on where on the curve you’re sitting it can be up to 5% improvement. For the case that not all pump power ends up as heat and more realistic pump power vs flow rate curves, the peak will be more pronounced.

So back to my initial question - what about my oversized heat pump? My house is roughly represented by the orange line in the previous plot - 3 kW heat loss at 0°C. The optimum flow rate would be at around 12.5 l/min - which is lower than my heat pumps minimum speed. Hence, the flow rate capabilities are also significantly oversized. Originally I had my Vaillant set to full pump speed, which in my system translated to around 28 l/min. I dropped pump speed to 20 l/min, which is a bit above the minimum by lowering the max. remaining head setting. This drops pump power from 93 to 46 W, approximately halving it. Based on my simple model but using the actually recorded pump powers, COP (during compressor on time) would increase from 4.43 to 4.65 - around 5%. Interestingly, I didn’t even raise my flow temperatures and didn’t experience any appreciable drop in house temperature. The required flow temperature increase would be around 0.2 K, which is below the granularity of Vaillant’s controls. So probably the house got ever so slightly cooler, but noone noticed or cares .

I have uploaded my excel sheet to Google Sheets if anyone wants to play with their own values. It should be pretty much self explanatory. For the pump electrical use, four polynomial coefficients can be entered to approximate power vs flow rate. The percentage of pump power usable as heat can also be set.

[bringiton (David L)]

I’ve often wondered about this, but not enough to do the maths, so thanks for the worked example,

I think this reinforces my suspicion that my pumps are running too quick (18L/min for 4kW design heat loss)

It’s obviously worse than that because it’s not always - 2C (though it’s beginning to feel like it!) and there are times my pumps are 20% of the system power consumption, which just feels wrong.

Pump power is indeed the cube of the flow rate (Affinity Laws).

It’s also worth considering pump location. My pumps are in the basement, outside my thermal envelope (as is the water cylinder, which is a far bigger mistake on my part from an energy efficiency perspective), so heat loss from the motors is probably about 25% - pump heating COP ~= 0.75 (based on my rudimentary understanding of motor efficiencies).

The question then is whether it’s worth doing anything about it. In my case, pumps consume maybe 250kWh/ year. Maybe £50. Strategies would be to find the optimum set point (probably marginally to the low side of your optimum to give you a year around average optimal point) or to vary pump speed, based on compressor frequency or ambient temperature.

I’d be curious if anyone has done anything fancy with variable speed signals but I think the quick maths here has convinced me to try knocking the pumps back a touch.

[Andre_K (André Kühne)]

@bringiton

Pump power is indeed the cube of the flow rate (Affinity Laws).

Thanks for confirming and putting the Affinity Laws on my radar.

@bringiton

It’s also worth considering pump location. My pumps are in the basement, outside my thermal envelope (as is the water cylinder, which is a far bigger mistake on my part from an energy efficiency perspective), so heat loss from the motors is probably about 25% - pump heating COP ~= 0.75 (based on my rudimentary understanding of motor efficiencies).

Technically the kinetic energy of the water also ends up as heat via friction, so 100% of the electricity put into the pump ends up as heat somewhere. Will it really contribute to heating the house? I’ve got no clue.

@bringiton

The question then is whether it’s worth doing anything about it.

Well it costs me nothing to lower the flow rate and the little money saved each year does add up, even if it’s just an extra case of beer worth.

Generally, this should just be part of the heat pump controls. Maybe another inspiration for @langestefan and Advanced Heat Pump Controls.

[Ringi]

Unless flow temperature is automatically set to be as low it can be while still giving enough heat, there will be little to gain from trying to automatically optimise flow rate, as a lower dt only improves COP if flow temperature is reduced to take advantage.

But for DHW reheat I can see a case for controlling heatpump output so the water leaving the coil is always a few c above the temperature of the water in the DHW that is next to the coil. It should be possible for the heating software to change flow rate as a “square wave”, by swapping between two flow rate every few minutes along with monitoring COP then some advanced stats would indicate the best choose between the two flow rates.

DHW reheats in summer is a good target as many people don’t care how long they take provided they finish by the end of cheaprate.

With UFH outside of the coldest days, I am thinking that just stopping the pump for 2/3 of the time between the last two heatpump cycles could be an easy optimisation. Or just set the pump to lowest possible flowrate between heatpump cycles rather then keeping it at normal speed.

[Andre_K (André Kühne)]

@Ringi

Unless flow temperature is automatically set to be as low it can be while still giving enough heat, there will be little to gain from trying to automatically optimise flow rate, as a lower dt only improves COP if flow temperature is reduced to take advantage.

Of course, these need to be optimized in tandem.

@Ringi

With UFH outside of the coldest days, I am thinking that just stopping the pump for 2/3 of the time between the last two heatpump cycles could be an easy optimisation. Or just set the pump to lowest possible flowrate between heatpump cycles rather then keeping it at normal speed.

Vaillant automatically uses the minimum flow rate between cycles. For UFH you could stop the flow entirely as most volume is exposed to the living area but as soon as theres a volumizer you need to keep up the circulation as otherwise there’s unused hot water volume.

[Mikey_P]

Hi @Andre_K,
Thanks for this and the spreadsheet. I’m trying to work it out so I can use it with my details. I’ve filled in all the relevant parts but I’m unable to replicate the COP vs flow rate to get that graph. Am i missing something or is that just something you did for the post?

[Andre_K (André Kühne)]

Hi @Mikey_P,

welcome to the community! I imported my Excel sheet into Google sheets. The graphs look different, but essentially are the same. The only thing I manually created is the graph of COP vs flow rate for different heat losses in the same graph. The graph in the sheets version is only for the one set heat loss in the table.

[Mikey_P]

thank you so much @Andre_K
I will have a play later as I too and fascinated by the COP change due to the heat pump and delta T. I keep hearing different things and I honestly have no idea what is best for my unit. Doesn’t help the unit has no way to measure scop and cop but I have to do a bit of a manual calc to get a best idea.
If i wanted to update the data to min do i just change the bits that are relevant? ie my heat loss is 9.54 and the design ambiet temp of mine is -3.4. design flow as temp is 50 etc.

[Andre_K (André Kühne)]

Yes, you change those parameters. However, you’d also need to adjust the COP vs flow temp parameters and pump power draw parameters, which are likely unique to your heat pump. If you have a datasheet with COP figures I’d be happy to assist in getting the numbers.

[Mikey_P]

Hi Andre.
Sorry I never replied. I’ve been so busy with things but I’m back and appreciate your help.

What figures do you need from me. Pretend I’m a child

[Andre_K (André Kühne)]

Which heat pump make & model do you have, what’s the design outdoor temperature and flow temperature? Do you have any datasheet for the heat pump?

@Mikey_P

Pretend I’m a child

Hey buddy, find the datasheets and you’ll get your favorite cookies!

[Andre_K (André Kühne)]

I didn’t look up the exact COP vs temperature graphs for your heat pump, but it’s not necessary in this case. I just put in your heat loss, design temperature and an assumed radiator temperature of 45°C (assuming a dT of 10).

Due to the high temperature, the optimum is probably in a range you cannot reach, far in excess of what the pump can deliver. Your main point of attack for improved performance is to try to lower your flow temperatures, as 50°C is really quite high. Are you sure you need that?

Try to keep all TRVs on your radiators in the fully open position. You should just reach the desired temperature in your rooms. If you overshoot, then your weather compensation curve can be tweaked to yield lower flow temperatures. There are plenty of posts on the forums here how to optimize your heating like this - running a fully open loop, no TRVs, low flow temperature, maximum pump speed. As soon as you have the minimum temperature setup with maximum flow we can revisit this, but as designed there’s nothing to be gained with lower flow rates.

[Mikey_P]

Thank you so much Andre. My system isn’t balanced really, I bought a coupe of digital probes and was hoping to give it a go. My current delta t is 5/6c on the flow and return. I know gas and oil boilers want a 10c difference on the radiators but what shiuis that be fie hear pump systems wirh k2 panels?

[Andre_K (André Kühne)]

5-6K is an OK deltaT. Are you using thermostats on your radiators?

[Mikey_P]

Yea I have trvs installed and are set to just over 3 while the thermostat is at 19.5. As it’s not really balanced I thought this would help a bit. Push flow to other areas that aren’t warm. I’ve heard really it should all be open on 5 and control it that way and use the lockshield to reduce flow and balance that way. Is that right?

[bringiton (David L)]

There’s an argument for using TRVs as sequential balancers, I guess. Getting a proper balance will be marginally more efficient, but it depends how extreme the imbalance is. If the radiator is completely shutting off and on, that’s not great, but most TRVs provide proportional rather than on/off control.

If you’ve got whole radiators hardly flowing until others dial back, but then you reach a comfortable steady state in all rooms, I’d argue it’s fine for an “always on” system: The water doesn’t know which valve is throttling it at the end of the day. On the flip side, those throttled radiators can deliver more heat, so you might be flowing hotter than you need to because of a single undersized radiator elsewhere. Fixing that with a well balanced system may be worth considering.

[Andre_K (André Kühne)]

@Mikey_P

I’ve heard really it should all be open on 5 and control it that way and use the lockshield to reduce flow and balance that way. Is that right?

Yes that’s right!

@bringiton

TRVs provide proportional rather than on/off control.

If you have smart thermostats, you really need to look into how exactly they’re performing. Most of my Shelly TRVs were essentially operating in an on/off mode rather that proper proportional control. Those algorithms can be really finicky.

[Ringi]

@bringiton

There’s an argument for using TRVs as sequential balancers

But such setups hardy every have a correctly set weather compensation as it is not “visible” when the flow temperature is higher then required.

@bringiton

If you’ve got whole radiators hardly flowing until others dial back, but then you reach a comfortable steady state in all rooms, I’d argue it’s fine for an “always on” system:

It can take a very long time for such a system to stabilise and due to lower output until stabilised it may never get up to temperature. I leaned this the hardway when my wife was too hot on a below freezing day and totaly turn off the hallway thermostat on a gas system without telling me! The system did not wish to recover once thermostat set correctly,

[Andre_K (André Kühne)]

It’s time for some evidence!

Using the excellent “Compare” tool over at heatpumpmonitor.org, let’s have a look at how my heat pump performed. First, a comparison between the heating period Feb 7 2024 - Apr 30 2024 (Red) and Sep. 1st 2024 - Jan 4 2025 (blue) to see whether anything else changed over the summer. It doesn’t look like it:

Now, let’s compare Sep 1 - Jan 4 2025 to Jan 5 - Feb 26 - because I switched my flow rate to the lower target on Jan 5th.

There is a small but clearly discernible COP improvement visible. We can also see this in COP vs. outdoor temperature:

I’ll rerunthis at the end of the season when I have even more data, but I think it’s already quite visible. Not a huge effect by any means but still better than nothing.

[Blink47]

@Andre_K

Having an oversized heat pump, I recently wondered whether the high flow rate pump that goes along with it might also just be too much. Typically, everyone wants a high flow rate but at some point the electricity consumption of the pump will also become significant…the question is when.

To find this optimum, let’s have a look at what goes into it. We have our design heat loss P_heat and our radiators (or generally emitters) are chosen so they deliver this power into the house when they are at a specific temperature T_rad. Typically, this temperature is approximated as the mean of flow and return temperature, so T_rad = 1/2 (T_flow + T_return). Together with the mass flow heat equation, we can express the required flow temperature to reach our radiator temperature given a specific flow rate:

T_flow = T_rad + P_heat/(2 c flow_rate)

We see that the flow temperature is at least as high as the required radiator temperature, with an additional offset proportional to the required heating power and inversely proportional to the flow rate. For my house with 30°C radiator temperature (0°C outside) and heat loss of around 3 kW, the flow and return temperatures vs. flow rate look like this:

As flow rate increases, the flow and return temperature asymptotically approach the required radiator temperature, which would result in lower compressor electricity use due to higher COP at lower flow temperatures. If pumps didn’t need power, infinite flow rates would be best.

However, the required electrical power of the pump increases with flow rate. It appears this goes with the cube of flow rate, but I can’t confirm this. For simplicity I used a simple linear relationship that I approximated from my system’s pump, but the analysis works for more complex cases as well.

There were quite a few discussions on the forum how much of power put into the circulation pump ends up as usable heat in the house. For the sake of this analysis, I have assumed that all the electricity going into the pump is converted into heat. Here we can see how required compressor power decreases (due to increasing COP with lower flow temperatures) as pump power increases. The total heat being put into the house is constant. I did a simple linear approximation between compressor COP and (T_flow-T_outside) based on my Vaillant’s datasheet to get the compressor COP.

Adding those two up and dividing the required heat power by the sum gives us the total COP of the whole system. The next graph shows this for different total heat loss scenarios.

We can see that there’s an optimum point where we achieve the best possible COP. The higher the heat loss, the higher the optimum flow rate. It’s not a lot, but depending on where on the curve you’re sitting it can be up to 5% improvement. For the case that not all pump power ends up as heat and more realistic pump power vs flow rate curves, the peak will be more pronounced.

So back to my initial question - what about my oversized heat pump? My house is roughly represented by the orange line in the previous plot - 3 kW heat loss at 0°C. The optimum flow rate would be at around 12.5 l/min - which is lower than my heat pumps minimum speed. Hence, the flow rate capabilities are also significantly oversized. Originally I had my Vaillant set to full pump speed, which in my system translated to around 28 l/min. I dropped pump speed to 20 l/min, which is a bit above the minimum by lowering the max. remaining head setting. This drops pump power from 93 to 46 W, approximately halving it. Based on my simple model but using the actually recorded pump powers, COP (during compressor on time) would increase from 4.43 to 4.65 - around 5%. Interestingly, I didn’t even raise my flow temperatures and didn’t experience any appreciable drop in house temperature. The required flow temperature increase would be around 0.2 K, which is below the granularity of Vaillant’s controls. So probably the house got ever so slightly cooler, but noone noticed or cares .

I have uploaded my excel sheet to Google Sheets if anyone wants to play with their own values. It should be pretty much self explanatory. For the pump electrical use, four polynomial coefficients can be entered to approximate power vs flow rate. The percentage of pump power usable as heat can also be set.

The trade-off between pump power and compressor efficiency is definitely something worth considering, especially for those with oversized systems. Your findings—reducing pump speed while maintaining comfortable indoor temperatures and improving COP—align with what many users in heat pump forums have discussed.