No, it doesn't work like that at all. There seems to be fundamental confusion here between rates and volumes. The heat load of your house is a volume - and your heating system can supply heat at a certain rate. So lets use a 10 gallon bucket as an analogy.

The bucket represents your heatload - you have to fill the bucket each hour to keep your house at a certain temperature. You have two sets of hoses to fill the bucket with - one comes from a supplier that charges 10c per gallon, but you can only get 6 gallons out of that pipe per hour. The other comes from a supplier that charges 40c per gallon and you can get 10 gallons per hour. Now say you have a 10 gallon bucket. How would you choose to fill it? If the cheap supplier broke down, you'd have to use the 40c per gallon guy but at least he could supply enough water to fill your bucket every hour. It would be expensive but your bucket would be full.  Normally, you'd use the 10c per gallon guy, but this would leave you short 4 gallons, so you'd have to buy 4 gallons from the expensive guy, but you'd still fill your bucket. Since he can supply 10 gallons per hour, you'd only need to run that pipe 4/10 to fill your bucket. Now lets say the 40c guy could supply you 20 gallons per hour at the same 40c per gallon. You'd still need 4 gallons, but now you'd only have to run the pipe for half as long because the water would be coming out twice as fast. You'd still use 4 gallons, though, and so you'd still pay 4x40c. In other words, the rate of supply has no effect on the cost, assuming you're filling your bucket first with the cheap guy with as much water as he can supply. The expensive guy says ok, I can supply as much as you want at a certain price per gallon and you can have it as quickly or as slowly as you want. The salient point is how much water you need, not how fast you fill the bucket, so long as you can completely fill your bucket per hour. Now hopefully you've sized your bucket so that the cheap guy can completely fill it per hour (i.e. this is the design load). But sometimes it's cold and the bucket ends up bigger so you need to buy water from the expensive guy. In this case, it doesn't matter how fast you fill, the amount of water is the same.

You also have to think what happens if the cheap guy can't give you any water at all - do you want a big enough pipe from the expensive guy to completely fill your bucket per hour? If not, you will be cold if the cheap guy breaks.

This is exactly how auxiliary heat works. It is there to make up the difference when the heat load is higher than what the heatpump can supply. But it should also be capable of completely supplying your worst case load if the heatpump breaks - i.e. emergency heat. This will mean that it is sized much larger than the difference between the heatpump capacity and the required worst case normal load - but this doesn't make any difference to the cost of operation when the heatpump is filling the bucket as fast as it can. It is nice, though, to have sufficient auxilliary heat that you can still keep warm for the time your heatpump breaks on the coldest day of the year.

Hope this helps make sense of the apparent contradiction that 20kW auxiliary heat will cost no more to run than 10kW, so long as the heatpump is running at full output and 10kW is enough, in combination with the heatpump, to meet your load. Of course, this is why you need a two stage thermostat so that it only runs the aux heat when it has to and, as soon as the bucket is full, switches it off. As far as I am aware, this is exactly what two stage thermostats do (and 3 stage for that matter where the 3rd stage is auxiliary heat).

Paul in Montreal.

Given the house is only 1500 sq ft, and the Backup heat is 20 Kw, You could indeed heat the house really quick... Anyone ever heard of a flash fire :) Now that's quick.

 

 

thanks Paul you have a very interesting way of describing this backup heat usage and others for their thoughts too.

I think what Geo Fan was pointing out is that if the "cheap" system is running for 30 minutes and then the resistance kicks in and runs 10 minutes, then both the geo and resistance shuts off for 20 minutes, then you’re better off running the geo system the whole time. Or if the resistance heating element is smaller and it takes 20 minutes to run then the geo ran another 10 minutes longer in this case, thus lowering the overall COP.

Correct me if I am wrong, but I believe in most cases the resistance is only running when say your 2F below the set point and kicks back off when you get to 1F below the set point and the geo runs the whole time, then it won’t matter what the size of the resistance heat is, unless it could actually overshoot and cause the geo to cycle off for a bit. If this is truly the case then resistance size wouldn’t matter again.

That was a great explanation and analogy.

My auxiliary heat only comes on if the GSHP can't keep up with the heat demand. In January this year the GSHP ran pretty much continuously for the whole month as the temperature was at or below the design temp for the whole time. When it was below design temp, the aux heat came on to make up the difference. The only other time aux heat comes on is if you try to recover too quickly from a set back - this is the main reason that setbacks are often not economically viable with GSHP systems - though, of course, it depends on the heat load at the time and how smart a thermostat you have. It is so consistently cold where I am located that it makes no sense to have any setbacks at all - plus I work from home.

Paul in Montreal.

Paul,

Your bucket analogy is correct if you have control on the rate at which you buy from the expensive pipes. Or as you said "assuming you're filling your bucket ""FIRST"" with the cheap guy with as much water as he can supply." For a gshp system, running on aux, the supply heat is a mix from the heat pump and from the strip, simultaneously. If you can not control the expensive share of the out put by small increments, you end up using more than what is absolutely necessary from the expensive source in a shorter time, as compared to the optimized mix still within the limits of the time constraint.

In your bucket example, with fixed rates of flow at 6, 10, and 20 gals per hour, it will cost 287.5 cents to fill the bucket from the first and second supply sources simultaneously running vs 330.8 cents from the first and third supply sources, in less time, but still within the one hour time limit for each case.

Regards, Masou

In your bucket example, with fixed rates of flow at 6, 10, and 20 gals per hour, it will cost 287.5 cents to fill the bucket from the first and second supply sources simultaneously running vs 330.8 cents from the first and third supply sources, in less time, but still within the one hour time limit for each case.

No, you're wrong I'm afraid. There's no difference in cost between the 10 and 20 gals per hour case. The only requirement is that the bucket has to have 10 gallons put in it each hour. You have 6 gallons from the cheap supply and 4 gallons from the expensive supply - but it's still 4 gallons and is still charged at the same price per gallon no matter if you put it in quickly or slowly.

The way it works in reality is that your bucket is continually emptying at a a certain rate. The GSHP is supplying a certain amount of "water" and the auxiliary heat the rest, controlled by the thermostat (which is actually sensing the rate). Since the aux is either fully on or fully off, its rate is more than needed by the rate the bucket is emptying so you essentially have let the bucket run down somewhat (thermostat sees this as not keeping up) and then you turn on the big pipe of the aux and the bucket starts to fill. If you use a really big pipe (the 20 gallon per hour analogy) the bucket fills really fast, but the thermostat turns off this big pipe before the bucket overflows (which would be equivalent to exceeding the setpoint of the thermostat and having to switch everything off - this is the bad case that you want to avoid and I don't know of any thermostats that would cause this - unless they are very badly sited). Either way, you're still putting in an extra 4 gallons per hour on average - so the cost is the same no matter if it's a fat pipe or not. Of course, it is good to have a fat pipe to keep your bucket full for the worst-case scenario of your heatpump breaking down completely. If not, you'll have to accept a lower temperature.

If I need 10 gallons per hour and have 6@10c and 4@40c, then I will never spend more than 220c per hour. The flaw in your logic is that you have the expensive sources running for the whole time - a 2 stage thermostat does not work like that at all.

Paul

Paul,

I have a ClimateMaster 3 stage thermostat that does work just like that. There are thermostats that destage the aux heat or step back from 2nd stage as the room temperature APPROACHES the setpoint. However, in real world many do not, and the system stays in the higher stage until the set point is reached, then the system stops all together. This is the reason for placing large aux heat coils on multiple stages, making smaller aux increments available as needed for overall higher system economy.

For your bucket example, it is not true that you put in 6 gallons of cheap water FIRST, and then top it off with 4 gallons more of the expensive water. It is a case of buying water @ 16, or 26 gallons per hour RATES until the bucket is full. Your cost per bucket of water increases, as the cheap water is "diluted" in the total flow rate which fills the bucket.

Regards, Masoud

For your bucket example, it is not true that you put in 6 gallons of cheap water FIRST, and then top it off with 4 gallons more of the expensive water. It is a case of buying water @ 16, or 26 gallons per hour RATES until the bucket is full. Your cost per bucket of water increases, as the cheap water is "diluted" in the total flow rate which fills the bucket.

Masoud,

with respect, you're wrong again. The whole reason I came up with the analogy was to break the confusion between quantity and rate. The GSHP can only supply 6  gallons. That's it, that's all. You need 10 gallons - so you have to find 4 gallons from somewhere. The 4 gallons cost 40c per gallon. You need 4 gallons - it doesn't matter how I give you those 4 gallons: it could be in dollops of 1 gallon every 15 minutes, or in dollops of 4 pints every 7.5 minutes - the volume (i.e. number of BTUs) is the same. The GSHP only gives me 6 gallons flat out - it can't give me any more. Now if I only needed 4 gallons total (for that hour in the analogy) then I would stop the heatpump after 40 minutes. I would only ever agree to buy the expensive water if I needed it - I would never be mixing the expensive (i.e. aux heating) and the cheap (i.e. GSHP heating) "waters" together. Of course, in my analogy I picked an arbitrary period of 1 hour. In reality the 2 stage thermostat is monitoring the rate of change of temperature over some time period (I don't know what this period is). If the 1st stage is running but the temperature is declining, rather than increasing, then it switches on the aux until the rate of change is below its threshold (note that the stage 1 heat is still running at that point). There is some hysteresis so the temperature can again start to fall until the thermostat says OK, we're not supplying enough heat, turn on stage 2 again. And so on. But note that the thermostat (assuming it is properly designed and I have no reason to suspect otherwise) tries to stay out of stage 2 (or stage 3 or whatever the "expensive" stage is) as much as possible.

Now if you have a 3-stage thermostat (2 stages of heatpump and 1 of aux) there's not such an economic penalty to staying in stage 2 (as you're still running with a high COP) so there's no problem staying in that stage until setpoint is reached. What do you don't want is the aux to come on and then the thermostat to reach setpoint and switch everything off. I don't know of any that do that - mine certaintly doesn't -  as soon as the rate of change is right it switches off the aux but keeps the heatpump running.

Hope this is clear for everyone else that made it through the analogy. I don't think there's much point me writing anymore about this now.

Paul.

My understanding with the way the aux works is that you either have the geo compressor running and producing heat or the aux running and producing heat not both and that they programmed my system so that it only comes on if the aux heat is selected and not
coming on automatically, I have a honeywell 8000 pro thermostat. however your analogy Paul seems to make sense the aux should
produce enough heat to turn the thermostat off once it hits the set point. You sure opened a can of worms, now I am not sure this method of not using the aux until i manually select is the most cost effective way.
It would seem as long as I am asleep and the geo is running and not producing any heat I am losing all the way around until I wake up and turn the aux on. :(

Thank you Paul.

Regards, Masoud

Let me try another explanation

Suppose, in an example hour of winter weather, your geo makes 40,000 btu but your house needs 50,000 btu

That's a 10,000 btu deficit for the hour. A 5 KW strip would need to run 35.2 minutes during that hour to make up the difference and it would use 2.93 extra kwh during the 35.2 minutes.

A 20 KW strip would only need to run for 8.8 minutes during that same hour to provide the extra 10,000 btu needed. It would use 4 times as much electricity for 1/4 the time, but at the end of the hour, the same extra 2.93 kwh would have been used.

I think that in actuality the 20 KW strip would come on in stages.

Bottom line is that in the example 10,000 btu are supplied by strips at the same added cost, regardless of strip rating.

Of course if the needed extra heat exceeds what the strip can add during continuous operation, house temp won't be maintained at thermostat setpoint.

Hope that helps

My geo design report indicates the backup heat is used starting at 2 deg F outside and my Space Btu/hr
is 49,311 with the geo furnishing 47,445 btu/h perhaps the difference is made up with the aux and I don't
know it but as I mentioned before it supposedly is optioned not to come on ( i  don't know and dont see that
option in my instruction book for the tstat) Im not looking to change that but am only mentioning it as a observation.
Your example is a good one and perhaps will help others who have questions about their auxilary heat.

Where are you? (I'll check town / state in my weather database and then comment on the 2 degree balance point)

CM aux is staged. Unit and aux in this case are over sized.
J

We are in Michigan the "land of opportunity" and un-employed captial of the US.

gimme a nearby city

sorry, try Howard city, Lakeview or perhaps Cedar springs, one of those should show up on your lists.

Ill thow some numbers at that one

lets say in your 5KW example the system runs with the aux turning on at the 25 minuet mark
hence giving you all the possible heat from the geo
Now in the second example lets say that the aux turns on again at 25 min and satisfies the t-stat 35 min into the hour

OK now the % of geo heat has ben dropped off because of the speed the aux can can supply
required back up in unknown to the equip it only knows on or off 

basically the more aux you use above what you need , decreases the system running time ( deceasing the btu output of the geo)

Hope this helps out engineer

In examples where auto down stageing takes place it doesnt matter
But time delay it WOULD