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Keep the heating in a house all day on?

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Marco:
Now get it to 21 degrees 50% of the time, starting early enough to get it there 50% of the time, and let it coast for the rest of the time. Which power bill would you rather pay?

Siwastaja:
OK, I'll run the sim. But hold on a bit, I want to make sure it goes right. I'm happy to be shown wrong so if necessary I can fix my understanding, because long term I can't afford putting a biased opinion ahead of facts, because this simulation and understanding the subtleties of the control is the basis of the business and I need the model to correctly represent and control many different types of houses, including very low and very high thermal capacity.

Siwastaja:
OK, here are some results.

Now in the model, heating is arranged with simple electronic thermostat, which senses current indoor temperature and provides a variable heating power using a steep P controller (Google "heat anticipator" for explanation of the classic mechanical PWM device), capping max power to 10kW.

Again, at the top/blue is the calculated "required" heating/cooling power if steady 21degC would be desired. This info is not used in calculation, just for reference. Top/orange is the solar irradiance power. Again, second graph is outdoor temp. Third graph is simulated room temp. Fourth graph is cumulative output energy.

Blue is low thermal capacity house (3kWh/K), orange is high thermal capacity house (15kWh/K). Insulation (i.e., average heat flow through envelope) is the same.

First, bear with me, without hourly cutting of power
see thermo1.png

As you can see, the cumulative energy drifts apart whenever there is overheating due to solar irradiance. Higher thermal capacity house shows reduced consumption right after such sunny days as it stores the energy. This is even with a "dumb" thermostat which does not understand the thermal capacity. Two month consumption, 1015.8kWh vs. 976.53kWh in favor of higher thermal capacity house.

Now let's cut the power to both houses. Let's cut it for 12 hours per day, say between 6am to 6pm when going to work and, in very non-Finnish way, eat out after work.
see thermo2.png

Two month consumption is now to 948.45 and 948.56 kWh, basically the same result. As you can see, the average temperature of the low-C house dropped, which also dropped its consumption, but not very much. With high-C house, consumption also dropped, but not as much; but it's still as good.

You asked to "start early enough to get it there". Now this expectation comes from the mindset of low thermal capacity. I didn't implement such logic in the model, but as you can see the high thermal house keeps decent nice indoor temperature without such trickery. Here's a zoom-in on transient response:
see thermo3.png

So while you can see that high-C house heats up slower, it starts from higher temperature. You decide which one is better, especially if you miss-schedule and fail to predict your living patterns.

This example data was not cherry picked. I'm sure I could find examples of both high-C building showing significantly better result (now the difference was marginal), but also could find data to prove your point where low-C building shows better result.

Siwastaja:
... I made one more simulation where I swapped the on/off time, turning heat off overnight, from 6pm to 6am. With such case, lower C house wins, probably because the reduction now coincides with the time of highest demand so there is potential to drop the average temperature so much it obviously finally does what was discussed in this thread.

Consumption:
ans =  818.80
ans =  924.00

But who wants to wake up in such cold rooms. If heating is started already at 4 a.m., the difference reduces:

ans =  885.60
ans =  942.45

Marco:
I thought high performance windows we're pretty much energy neutral in cold weather on a sunny day? (ie. no solar heating in winter.)

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