8. The house before renovation (gas boiler)¶
Question. Does FastSmoothBuildings also work with examples/residential_before_renovation.yaml: the same six-zone
semi-detached house with uninsulated cavity walls and attic, old double glazing, infiltration only (n50 = 12 1/h), a
non-condensing gas boiler at 75 degC, a pump, a three-way valve and six radiators with thermostatic valves?
Answer. Yes, without any change of the library. In closed loop it follows Buildings within 0.02 to 0.09 K per room hour by hour, its heating is 1.7 % above Buildings and its gas 1.9 %; every change of the YAML that moves the results moves both libraries alike, gas included. As an MPC model it exports in 45 s (160 states) and IPOPT solves its optimal control in 23 s (MPC).
Data: the residential_before rows of results/study_kpis.csv,
results/study_fidelity.csv, results/study_responses.csv,
results/study_verdicts.csv and results/study_hour_of_day.csv;
results/mpc_residential_before_renovation.json. The study case
residential_before is in study/buildings/cases.py; its runs are in study/buildings/results/residential_before.
Closed loop against Buildings, 28 days of January in Uccle¶
| Room | Hourly RMSE | Bias | Largest error | Heat of the radiators, CV(RMSE) | Heat, deviation |
|---|---|---|---|---|---|
| living | 0.02 K | +0.01 K | 0.22 K | 2.8 % | +2.3 % |
| kitchen | 0.03 K | +0.01 K | 0.32 K | 1.4 % | +1.0 % |
| bedroom 1 | 0.04 K | +0.01 K | 0.47 K | 2.6 % | +1.8 % |
| bedroom 2 | 0.04 K | +0.01 K | 0.45 K | 1.9 % | +1.5 % |
| bedroom 3 | 0.04 K | +0.01 K | 0.46 K | 1.8 % | +1.3 % |
| bathroom | 0.08 K | +0.01 K | 0.51 K | 3.1 % | +1.4 % |
The largest errors are in the first hours of the month, while both models settle from their initial temperatures; after the first day no room is more than 0.32 K from Buildings.
| Buildings | FastSmoothBuildings | ||
|---|---|---|---|
| Heat of the radiators | 2755 kWh | 2802 kWh | +1.7 % |
| Peak heating (hourly) | 8.70 kW | 8.78 kW | +0.9 % |
| Gas (energy meters) | 3391 kWh | 3454 kWh | +1.9 % |
| OpenModelica time | 268 s | 112 s | 2.4 times faster |
Responses to the YAML¶
| Change | Heating | Peak | Gas | Verdict |
|---|---|---|---|---|
| cavity of the walls filled (U 1.47 → 0.52 W/(m2.K)) | −23.3 % / −23.1 % (1.01) | −16.9 % / −16.9 % (1.01) | −22.2 % / −22.1 % (1.01) | alike |
| airtightness n50 x0.5 | −11.1 % / −11.0 % (1.00) | −8.0 % / −7.8 % (0.98) | −10.7 % / −10.5 % (1.01) | alike |
| airtightness n50 x1.5 | +11.2 % / +11.0 % (1.00) | +4.2 % / +3.7 % (0.88) | +10.7 % / +10.5 % (1.00) | alike |
| supply set point 65 instead of 75 degC | −11.8 % / −12.4 % (1.06) | −1.5 % / −1.6 % | alike | |
| radiators x0.7 | −12.0 % / −12.6 % (1.06) | −1.0 % / −1.0 % | alike | |
| living room and kitchen +1 K | +4.8 % / +4.7 % (0.99) | +4.6 % / +4.5 % (0.99) | alike | |
| air of the glazing gaps x0.5 | −1.0 % / −1.1 % | −0.8 % / −0.8 % | −1.0 % / −1.1 % | neither moves beyond 2 % |
| boiler 10 kW instead of 16 kW | −0.1 % / −0.1 % | −1.0 % / −1.3 % | −1.8 % / −1.8 % | neither moves beyond 2 % |
| radiator exponent 1.33 instead of 1.24 | 0 % / 0 % | −0.2 % / −0.4 % | 0 % / 0 % | neither moves beyond 2 % |
(Buildings / FastSmoothBuildings, and the ratio of the changes where a library moves by more than 2 %.) A smaller boiler saves
1.8 % of gas in both libraries for the same heat: the heat loss of the boiler to its room scales with its rating in
BoilerPolynomial and in FastSmoothBuildings's port of it.
The gas¶
The gas is 1.9 % above Buildings for 1.7 % more heat: per unit of heat the two libraries burn the same gas within 0.2 % (1.230 and 1.233), and both water loops close their energy balance within 0.15 % over the month. The study first reported +3.3 %, then +2.6 %: it read the gas of both libraries, then of Buildings only, from samples of the fuel power five minutes apart, which catch or miss the two-minute bursts of the boilers when the valves open in the morning. It now reads the energy meters of both. The boiler water loop has the balances and the restart.
MPC¶
160 states, 27 inputs; controls: the boiler, the three-way valve and the six radiator valves; the gas meter EFue is
the cost. IPOPT holds the six rooms at 20 degC through a 12-hour night at 0 degC with the boiler at 0.19 to 0.32 of its
power and 57 kWh of gas (MPC). The closed loop exports too (224 states), and every MPC
state is a closed-loop state of the same name.