Due to the recent surge in wind and solar installations in Europe (good), electricity prices have become significantly more volatile than in the past. Add to that the war in Ukraine (bad) and the reconfiguration of energy logistics (neutral), and you've got plenty of opportunities for optimization. In Estonia, it's not uncommon to see electricity prices vary by a factor of 100 within a single day. A tenfold difference between the daily maximum and minimum price is a daily occurrence. Naturally, this calls for some demand management - to save money and reduce CO₂ emissions. One effective method of consumption management is through heating, since heat can be stored far more easily than electricity. That is, assuming you're heating with electricity - say, by using a heat pump. In this case, you can heat (or even slightly overheat) your home when electricity is cheap, then rely on the thermal mass of your building's interior to "coast" through the expensive hours. The same principle can be applied to cooling, although there's less to optimize, as the outside temperature and desired inside temperature are more similar in the cooling case.

Below is a demo of using optimization methods to determine when and how much to heat to minimize spending, all while having to remain between comfortable upper and lower bound for inside temperature. The solver currently has price data for 3 days in December 2024



Aside from hourly electricity prices, the other inputs for the optimization model are provided in the form below. These fields are prefilled with sample values from my own place - a small two-room apartment with four exterior walls, built in 2007. This Heat Geek article is a great resource to better understand the assumptions behind these numbers. For my apartment, I've estimated a heat loss of around 3kW, though this could be off as I don't know the exact insulation details for the floor and walls. I've chosen a design indoor temperature of 21°C and an outdoor design temperature of –10°C that roughly corresponds to the regional average minimum in Estonia. The solver internally uses the heat loss in watts per kelvin (W/K), which means that a higher indoor temperature also results in higher heat loss. For even more precision, the model could incorporate weather forecasts or temperature-dependent heat pump efficiency - but for now, let's keep it simple(r).

The price data shown above isn't typically the final price for retail consumers. Often additional fees apply, for example distribution fees, green energy fees and the excise tax, which will be added to the market price before adding VAT. This is important, since for some low or negative market price periods, these fees still apply and might make it not worthwhile to overheat the property for low utility. The internal mass represents the thermal inertia inside the insulated envelope—floors, walls, furniture, etc. The more mass, the slower the temperature changes. That’s a good thing: more mass means more energy can be stored (in Joules), which increases the potential for optimization.

Another factor, that's only defined in the backend is the range of comfortable temperature. Clearly, having a wider spectrum of "comfortable" gives the solver more options to optimize, as the cheap hours can be used to a larger extent. Note that the comfortable level may depend on the time of the day, for example cooler temperatures at night are more acceptable and arguably even better for you and your sleep. These will be displayed alongside the results.

For comparison, let’s also look at two additional scenarios. The first is the "Always On" scenario, where the heating runs continuously, and the thermostat maintains a constant indoor temperature. In this case, the heating system compensates for heat loss every hour, resulting in steady energy use. The second scenario is based on a timer-controlled approach, which is quite common in real life. People often set timers to reduce heating during the night or when they’re away - such as during work hours - expecting to save money. This can be effective when electricity prices are stable. However, in a volatile pricing environment, this strategy has some drawbacks. The heating typically switches on during peak demand periods - early morning and around 5 PM - when prices are highest. Additionally, because the system needs to recover from several hours of inactivity, it has to work much harder during these peak hours, potentially offsetting any savings.