Minimize cost of electrical heating

Factual Questions
1

Electricity costs are getting really high in Norway right now and most homes are heated by electricity.

Prices vary througout the day, and you are given the price curve the day before. You could the heat your home when the prices are low and then turn the ovens off during the peaks in order to save on costs.

You would then have to live with some variations in temperature throughout the day.

What I am wondering is if there is some general algorithm/formula that takes price curve, min/max acceptable temperature and some value for how well the home retains heat and then gives you the optimal times to turn on/off the ovens to minimize costs.

2

Perhaps modern smart thermostats have that ability. I know here in the states many have the option to connect with the energy provider to lessen demand during peak periods for some rebate or some other incentive so they might have that. I would start with checking with your energy provider to see if such options exist.

3

It depends on the type of heating system too. Setting back your thermostat is almost always a good thing, but how much you set it back, and the way the system recovers, factors a great deal into how it should be programmed. Electric strip heaters in a forced-air system behave much differently than a heat pump with underfloor water loops, for example. The former can recover much faster than the latter, but also uses much more power in that short period as well. How well insulated the home is also makes a big difference as compared to the capacity of the heating system. We need more information to make an informed recommendation, because as far as I know, “ovens” are just kitchen cooking appliances, I have no idea what a home heating oven is.

4

This problem seems well-suited to a computer program that accepts several basic inputs:

  • the electricity cost curve for tomorrow
  • the weather forecast for tomorrow, including hour-by-hour wind, insolation, cloud cover, and ambient temp (sun adds heat, lower ambient temp increases the inside-outside temperature differential, clouds affect radiative losses and wind increases the exterior convection coefficient, further increasing heat loss rate)
  • upper and lower bounds for acceptable interior temp
  • the effective thermal mass of the house and its contents (more mass = can store more thermal energy for a given temp, decreasing the rate at which temp decreases during the course of the day)

An initial guess at when to start heating the house based on first principles probably won’t be optimal, so you’ll need to simulate a basic heating scenario and then try adjusting parameters back and forth to see if the total cost for the day gets any better. So before the day starts, your program would run a series of simulations.

Once all the input parameters are known, the program needs a starting point for its simulation. Assume the lowest acceptable interior temperature, turn on the virtual heat, and see how long it takes for the house to reach max acceptable temperature. Then see when and how much you need to heat it later in the day, when electricity is more expensive. Now you have a baseline cost. If costs vary in a gradual way throughout the day, then maybe you can shift your initial cheap heating period a little later; it’ll cost a little more, but if it facilitates buying less of the very expensive electricity later in the day, then your total costs for the day will improve. Repeat the sim again, but with the initial heating period shifted even later. Maybe now it’s getting more expensive for the whole day, so the software says “I’ve found the most optimal heating plan for tomorrow,” and it goes ahead and implements that when the new day starts.

A basic algorithm could start its life with assumed values for how well a house is insulated, how well it absorbs solar energy, how ambient winds affect the convection coefficient, and so on. A good algorithm would learn over time what these parameters are for your particular house, based on how the interior temperature changes when the heat is on versus when the heat is off (and the wind is/isn’t blowing, the sun is/isn’t shining, and the clouds are/aren’t covering).

Out of curiosity, how much is electricity in Norway these days? In the US, it’s around 15 cents per kilowatt-hour, and in Japan, it’s about twice this. Last time I looked, electricity in Norway was quite a bit cheaper than here in the US, and I read that this was part of why battery-electric cars were so popular there.

5

If it doesn’t exist, someone who studies/works in optimization research could create it. Answering that sort of question is exactly what this field is about.

6

There are different types of electric heat – there is the traditional use I^2R losses to get heat (basically how a toaster works), or heat pumps (basically air conditioners in reverse). heat pumps are MUCH more efficient as they move heat rather than create it. They tend not to work when the outside temperature gets really cold – for that ground source heat pumps (since deep underground the temp doesn’t get as cold)

Brian

7

If you watch Technology Connections he recently did a video in which he talked about just this. He cools his house far more than necessary during off-peak times and it’s enough to let him get through the day without having to run the AC again until night.
He did explain in his video that his savings are going to be unique to his house based on the local ambient temp, how much time the house is directly in the sun, how good his insulation is etc.

I can’t find the video right now, I’m fairly certain it was him, but it might have been part of a bigger video.

8

Norwegians pay around $0.135 compared to the US at $0.15 and the UK at $0.26. per kWh Residential electricity prices worldwide 2022 | Statista is a useful chart, although it excludes Norway for some reason.

9

Energy storage is an established method to shift your electricity demand. Two potential methods to store energy while electricity is cheap:

  • Charge a battery. A furnace rated for 80,000 BTU/hr works out to about 24 kilowatts. The battery on a Tesla Model S is about 85 kilowatt-hours, so if you had one of these in a corner of your home you could charge it up at night (while also electrically heating your home directly from the grid). Later, when electricity is expensive, you use the battery, which could supply 24 kilowatts for about 3.5 hours. Might not eliminate all of the expensive electricity consumption on the coldest days, but it would help.

  • Charge a thermal capacitor. Some commercial buildings in warm climates chill brine or make ice during the night with cheap electricity to economically meet their cooling needs during the daytime. The reverse could work in a cold climate: use cheap electricity to heat a tub of phase-change material, something that melts at maybe 50 degrees C (gallium melts at 30C, so maybe?). This can store heat energy without actually having to increase your home’s interior temperature. Later, when electricity is expensive, you pump this hot material through a heat exchanger to warm your home.

10

By ovens I meant regular electric space heaters. Ziberian is probably correct that this is an optimization problem. It could be made a bit simpler though, by assuming a constant outside temperature.

Norway has cheap hydro power, but the prices have begun fluctuating recently because of new power cables to other countries. Prices can be up to $0.50/kWh for short periods of time.

It would then make sense to overheat the house before those peaks occour. Currently my method is just to experiment by looking at a typical price curve throughout the day and try to set up a basic table for what settings I think are optimal.

11

I have smart thermostats and they only barely help.

In theory they can be good by learning a schedule of when you are away and when you are home but the reality is most families do not live perfectly scheduled lives. People are coming and going all the time and it is difficult for the thermostat to figure out an ideal schedule for heating/cooling.

Further, most people want the temperature of their home maintained with in a few degree window (say, 68-74F). There is no way around this. Your heating cooling needs to turn on and off whenever the temps you set stray from the window you want.

They do help at night, when you are sleeping, since you are likely to be ok with temps you do not want while awake. You will tolerate colder temps while sleeping since you are covered in blankets. That saves some money but not a lot (this is also the time of cheapest power).

Smart thermostats do have some nice features but you won’t save much having one in my experience.

The only real way I can think to save money is to buy a battery for your house (like Tesla’s PowerWall) and charge it over night when power is cheap and run the house on it during the day.

12

With those, or at least with the Nest, you can set them so even if your schedule is all over the place, it’ll still lower the temp in winter/raise the temp in summer, if it senses you’ve been gone for a certain length of time. Similarly, you can set up geofences so when you’re within, say, 5 miles of your house, it kicks back on.
Even with all the smart stuff turned off, it’s still nice to be able to pull up the app on your phone and turn on the heat/AC when you know you’ll be home soon.

13

I agree the smart thermostats have some nice features. I have two Nest and I would hate going back to a dumb thermostat.

That said, I don’t think they save you much money.

14

The very first question is - are the costs predictable? Can you safely say electricity is cheaper, say, 10PM to 7AM? If not, you need a communication with the utility company to assess this number.

The next question is - what is the heat loss of your house? Older houses are crap for insulation. Here in Canada, with similar issues, the first and biggest step is to properly insulate the house. do you have solid insulated doors? The old panel wood doors are not as good as solid insulation filled (metal) doors. Do you have triple-paned argon-filled window panes? (The best modern ones are as insulating as a regular wall). here in Canada, modern construction used 2x6 (inch) outer wall construction, rather than the old 2x4. The interior is also nowadays sealed with a plastic barrier to prevent air escaping. A big issue is ceilings. A common cheap upgrade for older houses is to blow up to a foot of insulation into the (unheated) attic space.

Then you can consider issues like wind and sun exposure. Adding an enclosed verandah/porch can add to the insulation value too. Older houses used to have a vestibule, so opening the outside door did not flood the whole house with cold air. Modern architecture seems to have ignored this, a byproduct of the 60’s mentality that energy was cheap and plentiful.

Another important point - how efficient are your appliances, which likely get used during peak periods. Many North American houses will have a freezer as well as a fridge. The freezer is rarely opened - but most do not have a external control to tell it - “Cool excessively during the cheap power times, so you don’t need to kick in during the daytime”. A good freezer, not opened too much, could probably go all day without need to cool - so maybe a timer that disables the freezer during the day? Also, use the microwave instead of the electric oven wherever possible, and those appliances like air fryers and induction pressure cookers, which use a lot less electricity and cook faster.

At the most extreme, is having computer controlled dampers and individual room thermostats - don’t push too much heat into a room that is not currently occupied. If you have individual room heaters, this control too is a good idea.

Tesla does make the PowerWall, which IIRC is 14kWh batteries intended to be charged by solar panels on the roof.

However, i would think any such algorithm would be heavily customized to the family’s specific needs. I would think an AI learning algorithm would work best. But - my Nest thermostat seems to have a mind of its own, doing things I don’t want it to do. (It alters the permanent schedule if I turn up the temperature too often, for example)

15

The house is new and really well insulated. The electricity prices throughout the day is made public at 1pm the previous day.

16

The house I live in in the UK had storage heaters when I moved in - these use an electric element to heat up iron-rich clay bricks inside a sealed insulated box, during the night time (on a special tariff that was much cheaper for night use). During the day, a timer would open a set of louvred vents at top and bottom of the storage heater, allowing air to flow through it and carry the stored heat into the room.

It didn’t work very well here in the UK because the weather can be wildly variable, so if there was an unusually warm day (it happens), the heat stored in the previous night still had to come out (even if the vents were not opened, it would radiate gradually into the room) making it sometimes unbearably warm.
In a climate with more predictable fluctuations, I imagine these might be a better fit.

17

The following is a question I have wondered about for a long time and never gotten a good answer on:

Do I use less energy maintaining a constant temperature or letting it dip 10 degrees and then warming the place back up?

Doubtless there is a point where letting it dip and stay there is more energy efficient if I am gone for a long time. But, what about leaving for work in the morning and heating the place back up seven hours later before I get home?

18

It’s always better to let it dip. The bigger the temperature differential between inside and outside you have to keep the bigger the losses.

The extra energy you spend heating it back is no more than what you save by not maintaing the temperature in the first place.

19

That sounds more like a poorly designed heater. Insulate that box better so the heat can be retained when not needed. I wouldn’t be surprised if they designed it that way since some of the radiant heat would need to come out into the room during the cold of night, so they figured they could cheap out and not bother insulating it too much, rather than relying on the vents and thermostats.

The cutaway of one of the storage heaters in the video below (starting at 18:13) doesn’t look well insulated at all, just a couple of metal panels and what looks like some reflective foil. It’s probably only just enough to prevent it from being dangerously hot to the touch.

The other issue with something like that is the more common it becomes, the less favorable those night tariffs will get. That’s doubly true as more people start to charge their electric cars at home at night.

20