HPAC Magazine

The Big Switch: Part 2

April 23, 2024 | By Curtis Bennett

An inside look at some of the math controls use to determine what energy source will be most cost-effective.

Getting the most out of your electrical and gas hook-ups when heating your home. (LifestyleVisuals/Getty Images)

I find it funny when I am helping my kids with their math homework, and I also find it unbelievably frustrating.

I am a very literal thinker. I presume that’s why ones and zeros work well in my head. With math there is one way to get to the answer (yes, I realize more complex math has more than one way to skin a cat). What I find frustrating with my kids’ homework is the way it’s presented. Confusing is an understatement.

So, what does that have to do with today’s topic? Well, we are going to do some equations, and because I am the teacher, I get to tell you how the math works.

In my last article (The Big Switch, HPAC February 2024), I went over the theory of switching between gas and electricity and wrote about why and when we might want to do this.

Today we will do a little empirical thinking as I walk through some real-world numbers to see how relevant switching can be.

We only touched on one topic that is pivotal to making this switch work properly and that is Time of Day pricing—where electricity utilities base pricing on supply and demand.

For instance, you could have peak day electricity costing you 40-cents per kWh and it’s only 3-cents per kWh in early morning off-peak times. This is going to get a little messy, but let’s do a couple of examples, and remember we’ll also be making a few assumptions along the way.


We need a couple of calculations to start. Coefficient of performance, or COP, is one way heat pump manufacturers rate their products. As a general rule, the COP is highest when outdoor temperatures are the highest and get worse as it gets colder outside.

The second calculation is for British thermal units (Btu). Normally in the hydronics world we would use something like 500 x Flow x Delta-T, but for our example we are going to use a single tank we’re heating up, so we will use Pounds (lbs.) of Water x Delta-T [remember, 1 Btu is the quantity of heat required to raise the temperature of one pound of water by 1-degree Fahrenheit (F)].

We are heating up one 40-gallon tank of water from 70F to 125F (Delta-T of 55F). The weight of water is 8.33 lbs. per gallon, so for our 40-gallon tank (40 x 8.33 = 332 lbs). So, 332 lbs. x 55F equals 18,260 Btu to heat up our 40-gallon tank from room temp (70F) to 125F.

Now, that calculation is assuming 100% efficiency. To be fair and derate that a bit based on the efficiency of the boiler we’ll use an 80% efficient situation. That puts us at 22,825 Btu.

To convert the Btu needed to heat the tank into electrical energy, we take the 18,260 Btu/h and divide that by 3.412 to get 5.531 kWh of electricity needed.

Wow, that’s a lot of numbers just to get started.

Time of Day Pricing in Ontario

For the next step I will use Ontario as our example, because we all know Alberta does not install heat pumps. LOL…

I’m just kidding. I chose Ontario because it has an easy to find Time-of-Day pricing system (see Figure 1).

Figure 1. Ontario time-of-day pricing, May-Oct. 2023. (source: EPCOR)

At this point we need to remember that a heat pump’s COP makes a big difference.

I am assuming a normal COP of 3, and peak summer COP of 4.

This means that if it takes 5.531 kWh of electricity to heat our 40 gallon tank (as we calculated), then a device with a COP of 3 will only use 5.531 kWh divided by 3 = 1.78KWh of electricity to heat the tank. And a COP of 4 would only use 5.531KWh/4 = 1.34KWh of electricity.

Remember that a normal resistive heating element has a COP of 1.

I almost forgot one conversion, Btu to gigajoule (GJ), so 22,825 Btu to GJ is 0.02408165.

Okay, that was a lot of prep work. Now for the actual math!

Our assumed price of natural gas will be set at $3.30 per GJ, which is $0.1191 per cubic-meter, and our electricity time-of-day rates (from ultra-low overnight to on-peak) are $0.024/$0.074/$0.102/$0.24 per kWh as in Figure 1.

Prices to heat our 40-gallon tank to 125F

Electric Element COP of 1 = 5.53 kWh x $0.102 = $0.56
Heat pump COP of 3 = 1.78kW x $0.24 = $0.42
Heat pump COP of 3 = 1.78kW x $0.102 = $0.178
Heat pump COP of 3 = 1.78kW x $0.074 = $0.13
Heat pump COP of 3 = 1.78kW x $0.024 = $0.04
Heat pump COP of 4 = 1.34kW x $0.074 = $0.10
Heat pump COP of 4 = 1.34kW x $0.024 = $0.03
(boiler) 22,825 (@80%) Btu = 0.627 m³ x $0.1191 = $0.074

One thing to keep in mind is the delivery cost on gas is out of control. If you factor that in, our price per GJ is around $11 per GJ delivered. This factor does change things enough to take a good look. But we won’t factor that in at this time.

If you look at the example you can see times of the day where it is more economical to heat with gas, or when electricity is the way to go. This is only a snapshot in time, and factors change seasonally as the cost of gas and the cost of electricity change.

So, these calculations can give us the information needed to determine the best value at different times of the day, and this is where controls come into play.

Controls can monitor these values in real time, and they also monitor electricity for the heat pumps, pump electricity usage, flow rates, incoming and outgoing temperatures and more.

With this information the controls can make a switch between heating with gas or heating with heat pumps.

You can only determine which source to use with algorithms and the proper data input. Other factors could be boiler efficiency or if there is a direct fire hot water tank, these change the calculations somewhat as well.

Time of Day programming

Another easy way to save on electricity current bills is to use an ECO-switch device.

We have had this in our controls for years. The essence of it is that you can program times of the day that the providers increase the price of electricity to prevent large electrical devices from running. If you don’t switch to gas at this point you pay astronomical pricing.

The ECO-switch feature only runs the boiler backup in this situation, until the control allows the heat pumps to come back on when they are in the allotted time slot.

A second way is to remember that your DHW tank is a battery—something that stores energy. If electricity is super cheap overnight, the DHW tank can be heated overnight and even overheated to a point (make sure you have proper scold protection on it) to store as much energy at the lowest price possible.

As a general rule we use a lot of hot water in the morning, so it makes the most sense to have the DHW tank ready at the least cost.

I will leave you with this. There are many reasons to save energy, and each of us has different values and different convictions for doing so. Controls are an easy solution to help with those decisions, whether you chose to avoid using gas most of the time or just prioritize saving money! <>

troubleCurtis Bennett C.E.T is product development manager with HBX Control Systems Inc. in Calgary. He formed HBX Control Systems with Tom Hermann in 2002. Its control systems are designed, engineered and manufactured in Canada to accommodate a range of hydronic heating and cooling needs.



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