Heat Pumps: Heating Cost Efficiency
This post has nothing to do with #vanlife.
TL;DR: You might not be saving money running your heat pump vs your Natural Gas furnace. You can calculate this, fairly easily. It would be nice if the Ecobee would allow you to set the crossover point based on the electricity TOU phase.
Preamble
- COP is Coefficient Of Performance. A COP of more than 1.0 means that for every unit of energy you are using, you are getting more than one energy unit worth of heat. A resistance heater is at best 1.0. A good Natural Gas furnace is ~0.96
- Energy efficiency is not the same as cost efficiency
- There is no doubt that heat pumps are energy efficient as long as the COP is above 1.0
- Assuming you will google any terms you don’t know
- Your mileage may vary
- You need to understand the COP of your heat pump at various ambient temperatures
- You need to know your true cost per unit of electricity and your auxiliary fuel (natural gas for me)
- Cooling is a different thing and is out of scope for this discussion
- I live in an area with cold winters and a heat pump alone is not recommended here
- The Canadian Government, as funded by Canadian tax payers, in partnership with certain energy providers recently had a program where you could get a heat pump pretty close to free
- Very few HVAC contractors were interested in just supplying the heat pump so you probably got and paid for a new auxiliary heat source
- Very few HVAC contractors were interested in just supplying the heat pump so you probably got and paid for a new auxiliary heat source
The cost efficiency of a heat pump is based on the energy efficiency of your heat pump vs your auxiliary heat source. Comparing the costs of these fuels and the efficiency at which the fuel is converted in to heat will give you information about the cost of each per common unit.
Cost of fuels
The Ontario Energy Board has great information on what is allowed to be on your energy bills. Please have a look there for more information. You should note that the advertised cost of your energy unit ($/m^3 for NG and $/kWh for Electricity) is far less than your full loaded cost. Here is a small table showing the energy cost vs the fully loaded variable cost per energy unit from my bills.
| Energy Type | Energy Unit | Time of Use | Base Cost | Loaded Variable Cost | Base % of Total Cost |
|---|---|---|---|---|---|
| Electricity | kWh | Off Peak | $0.087 | 0.134 | 64.9% |
| kWh | Mid Peak | $0.122 | 0.169 | 74.1% | |
| kWh | Peak | $0.182 | 0.229 | 79.43% | |
| Natural Gas | m^3 | Single Rate | $0.12 | $0.42 | 27.87% |
This table demonstrates that for my providers, the advertised rate of a cubic meter of Natural Gas is only 27.87% of the variable (based on consumption) rate advertised. It also indicates that for Electricity, the impact of the additional variable charges are more impactful on the lower Time Of Use (TOU) advertised rates.
Here is a look at the loaded electricity rates that could be used for determining the cross over temperature.
| Item | Base Rate | Loaded Rate |
|---|---|---|
| Off Peak | $0.087 | $0.134 |
| Mid Peak | $0.122 | $0.169 |
| Peak | $0.182 | $0.229 |
| Practical Blended* | $0.108 | $0.155 |
| TOU Blended** | $0.110 | $0.157 |
*Practical Blended was calculated by using the actual number of kWh used per billing period.
**TOU Blended was calculated by using the number of hours in each rate per day and multiplying that fraction by the rate for that period.
Energy Rates Change
Here is a table of our Natural Gas rates over the last 2 years.
| Billed To | Base $/m3 | Total $/m3 |
| 4/4/2024 | $0.12 | $0.42 |
| 3/5/2024 | $0.12 | $0.41 |
| 2/4/2024 | $0.12 | $0.42 |
| 1/5/2024 | $0.13 | $0.43 |
| 12/3/2023 | $0.13 | $0.45 |
| 11/6/2023 | $0.13 | $0.44 |
| 10/5/2023 | $0.12 | $0.42 |
| 9/6/2023 | $0.12 | $0.43 |
| 8/5/2023 | $0.12 | $0.43 |
| 7/5/2023 | $0.13 | $0.42 |
| 6/2/2023 | $0.13 | $0.42 |
| 5/5/2023 | $0.17 | $0.47 |
| 4/5/2023 | $0.20 | $0.49 |
| 3/7/2023 | $0.21 | $0.50 |
| 2/4/2023 | $0.21 | $0.50 |
| 1/6/2023 | $0.27 | $0.54 |
| 12/5/2022 | $0.28 | $0.55 |
| 11/3/2022 | $0.28 | $0.55 |
| 10/6/2022 | $0.28 | $0.53 |
| 9/7/2022 | $0.28 | $0.52 |
| 8/5/2022 | $0.28 | $0.52 |
| 7/6/2022 | $0.20 | $0.44 |
| 6/6/2022 | $0.18 | $0.42 |
| 5/5/2022 | $0.18 | $0.42 |
Let’s figure out the temperature at which it is cheaper to run the Natural Gas furnace vs the Heat Pump. This is often referred to as the balance point. But remember, I’m only looking at cost, not energy efficiency.
I found this video helpful for and overview and the formulas to use.
Calculating the cross over COP.
This is the formula: =(BTU/BTU per hour)*($per kWh/$per 1000 cubic feet)*Constant*SSE
The data we will need to do the calculations
| Item | Value | Words |
|---|---|---|
| BTU | 1000000 | BTUs in a therm |
| BTU/HR | 3414 | |
| $per kWh | 0.1553191677 | The electricity rate you will use (see above) – you must provide this |
| $ per 1000 cubic feet | 11.82 | rate for Natural Gas – you must provide this (note that Canadians will have to convert from $per meter cubed) |
| Constant | 0.9 | a constant (watch the linked video) |
| SSE | 0.96 | Steady state furnace efficiency – my furnace is 96% efficient |
| % for hot water | 0.17 | Amount of natural gas bill for hot water. Not needed, just informational. |
| Calculated COP | 3.325506522 | Result of the formula. Below this value, natural gas should be used. Above, the heat pump should be used. You will need to convert this into an outdoor temperature (see below) |
Turning the COP into an outdoor temperature
The COP is data is available for my heat pump in this link. It is important to have the CoP for a variety of temperatures as it is non-linear. Remember, this is for heating only.
| Outdoor Temp (C/F) | -30/-22 | -25/-13 | -20/-4 | -17/0 | -15/5 | -8/17 | -7/19.4 | -4/24.8 | 0/32 | 4/39 | 7/45 | 12/54 |
| COP | 1.81 | 1.89 | 2.26 | 2.45 | 2.51 | 2.8 | 2.81 | 2.9 | 3.14 | 3.31 | 4.18 | 4.85 |
If we plot this, we can get the formula for the best fit line and use said formula to enter a COP and determine the temperature at which we reach that COP. Please note that this graph is wrong, but is also right enough. Wrong because the independent value (temperature) should be on the x axis, but that makes a really yucky 5th degree polynomial. Also wrong as extrapolating beyond the known temperature values may result in nonsense.
Now that you know your cross over COP value for your rates, you can just look it up on the chart and get your outdoor temperature, or you cn use that formula in the chart to determine the t . More caveats, these are dry bulb temperatures, humidity can mess things up! Also note that the Ecobee uses a temperature for your area from the internet. Your local micro climate may be significantly different.
Revisit those different rates and cross over temperature
Chart below is based on natural gas rates from our most recent bill. That is a base cost of $0.12 per meter cubed and a loaded cost of $0.42 per meter cubed (or $11.82 per 1000 cubic feet). From the chart you can see that my default setting should be a cross over over 1.2 Degrees Celsius (34.2 F). But, I could be far more cost effective if I had 3 different cross over points I could set based on the TOU rate. The nice thing is that it is generally colder at night so our heating costs for the heat pump are generally lower when the climate requires more heat. But, we also like to sleep with a cooler house which is a bad pattern for heat pumps. As long as you start the ramp up before the electricity rates go up, you might be ok. Our night time offset is -2C.
| TOU | Electricity Base Rate | Loaded Rate | Cross over COP at rates | Cross over temp (C) | Cross over temp (F) |
| On Peak | 0.182 | 0.229 | 4.906 | 11.5 | 52.7 |
| Mid Peak | 0.122 | 0.169 | 3.621 | 4.9 | 40.8 |
| Off Peak | 0.087 | 0.134 | 2.872 | -5.9 | 21.4 |
| Practical Blended* | 0.108 | 0.155 | 3.326 | 1.2 | 34.2 |
| TOU Blended** | 0.110 | 0.157 | 3.369 | 1.8 | 35.3 |
When rates change, I can plug the new ones in and change my cross over temperature accordingly. Note that with Ecobee you must change your cross over temperature on the thermostat, not in the app. As of my last review of their API, you can’t change this parameter via the API. That sucks a bit because if we could, then I could dynamically set my cross over values with each TOU change.
Hopefully this was informative. Stay warm in there!