Calculating actual variable costs for energy

As a discussion related to the economics and cross-over points for dual-fuel heating (natural gas and heat pump) the topic came up how to calculate costs of each energy source.

While at first, it may seem obvious, there are a variety of costs that are variable (ie based on how much you consume) that are not easy to calculate, this is at least the case for us in Ottawa using natural gas from Enbridge and electricity from Hydro Ottawa (although I assume it would be similar for Hydro One). I will try and clarify how I calculated the variable costs and where they come from.

Advertised Rates vs Actual rates

Hydro Ottawa (Electricity)

Hydro Ottawa advertises rates per kWh, either through time-of-Use pricing (2 options) or tiered pricing. However, there are many additional charges (and rebates) that are added onto this advertised rate which makes the calculation a bit less straightforward. On the bill there are the advertised rates as well as Delivery fees, Regulatory Charges and an Electricity rebate (I am excluding the HST – provincial and federal taxes as they apply to both energy sources equally).

Delivery fees include a fixed cost (34.36$) and several variable costs (0.02025$/kWh + 3.38% of total)

  • Line Losses (3.38% of cost)
  • Low Voltage charge (0.00005$/kWh)
  • Rate adjustments 3 charges (0.0029$/kWh)
  • Network Service rate (0.011$/kWh)
  • Line and Transformation connection rate (0.0063$/kWh)

Regulatory fees include a fixed cost (0.25$) & variable (0.0059$/kWh)

  • Wholesale Market Service Rate (0.0041$/kWh)
  • Capacity Based Recovery (0.0004$/kWh)
  • Rural or Remote Electricity Rate Protection Charge (0.0014$/kWh)

The Electricity rebate is 19.3%

The list is available at the bottom of this page with more detail here

So after applying those extra fees and rebates, we get a fixed cost of 34.61$ and variable costs as below

Time of Use TierAdvertisedActual

Tiered rates

As we used tiered rates, I like to use an average to calculate my actual costs. This will tend to under estimate costs as the low tier is active at night, when temperature are lower and more heating is required while the high tier is active in the afternoon when the sun and temperatures are highest. The rate also is low for weekends and public holidays, to under estimate a bit more, I leave out the public holidays.

The tiered rate breaks down to 50% of the time is the low rate (overnight), 25% of the time medium and 25% of the time high. For 2 out of 7 days (weekends), the rate remains low all day. So if we put that together, 64% of the time we are at low rate, 18% at medium and 18% at high rates. With the numbers above, our blended average rate ends up being 0.1152 $/kWh

Enbridge (Natural Gas)

Similarly to above, there is a mix of fixed and variable costs, and an advertised rate and a number of of additional charges (Delivery, transportation, carbon tax, cost adjustment). Again I am leaving out HST as it applies equally to both energy sources.

Fixed costs are 22.88$

Gas supply rate (advertised rate) is 0.117575$/m3

Delivery is a tiered rate based on usage ranging from 0.1053$/m3 to 0.1212$/m3, the more gas you use, the lower the charge (first rate for 30m3, 2nd for next 55m3, 3rd for next 85m3 and 4th for anything above 170m3). (for the sake of calculation I took the average)

Transportation is charged at 0.047411$/m3

Carbon tax is currently set at 0.1239$/m3

Cost adjustment is 0.016344$/m3

So we have a fixed rate of 22.88$ and a variable rate:

Advertised rateActual rate


ElectricityNatural Gas
Variable (in Joules)32$/GJ11.22$/GJ

Note that a heat pump provides more heat than electricity it consumes, usually by a factor of 2-4 depending on the temperature. The cost per GJ is what is consumed by the heat pump, and would be divided by this factor for the actual heat output. (ie output is 2-4x less than cost above). On the other side, furnaces are not 100% efficient so some energy is lost (new furnaces are around 96% efficient), not a huge difference but it does have an impact on the output cost.

Both electricity and natural gas rates vary about every 3 months with natural gas currently being at the lowest point in 2 years, heat pumps are already less expensive when their efficiency is about 2.7 (most of the operating range). As time progresses, natural gas rates rise back up and carbon taxation increases, the economic advantage of heat pumps should only increase.






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