# XYLENE POWER LTD.

## ELECTRICITY RATE PROPOSAL

#### By C. Rhodes, P.Eng., Ph.D.

OSPE RETAIL ELECTRICITY RATE PROPOSAL:
The OSPE retail electricity rate proposal has been under discussion for several years. The objective of this rate proposal is to make better use of non-fossil electricity generated in Ontario that is presently either curtailed (wasted) or is exported to other jurisdictions at a very low price (~ \$0.02 / kWh).

The contemplated OSPE retail electricity rate can be expressed either as an energy rate plus a monthly charge for average daily peak demand or as an energy rate plus a surcharge for daily maximum consumption per hour. The surcharge can also be expressed in terms of a maximum daily hourly consumption deviation from its mean value.

These expression alternatives are shown to be mathematically equivalent. In all cases an electrical load controller is required to realize maximum benefit from the proposed OSPE retail electricity rate.

The OSPE retail electricity rate has two components. The first component is a daily charge for the number of kWh consumed. Thus the energy consumption on day number i is Eci where Eci is in units of kWh. In a typical home on a typical day Eci ~ 24 kWh.

If the daily consumption pattern is uniform over a month with N = 30 days then the monthly electrical energy consumption for a representative home is given by:
Sum from i = 1 to i = N of Eci
= N X Eci = 30 X 24 kWh = 720 kWh

The energy cost per marginal kWh is Ca. Under the OSPE rate plan a typical value for Ca is \$0.02 / kWh. Thus a typical daily charge for marginal energy consumption is:
Ca X Eci = \$0.02 / kWh X 24 kWh day = \$0.48 / day

The second OSPE rate component is a daily charge in proportion to the maximum number of kWh consumed during any one hour of each day. This daily peak energy consumption per hour = Pi. A typical value for Pi in a representative home is:
Pi ~ 5 (kWh / h).

The charge per (kWh / h) is Cb. A typical value for Cb is \$0.60 / (kWh / h).

Thus a typical daily charge for peak hourly number of kWh consumed is:
Cb X Pi = \$0.60 / (kWh / h) X 5 (kWh / h) /day = \$3.00 / day

Note that Pi may be expressed as Pi = [Pi – (Eci / 24 h)] + (Eci / 24 h)
where:
[Pi – (Eci / 24) ] is the maximum daily deviation of the hourly consumption from its average value of (Eci / 24 h).

Hence the electricity cost for one day is:
\$0.48 / day + \$3.00 / day = \$3.48 / day

The monthly electricity bill is the sum of the daily electricity costs. If the daily electricity consumption pattern is constant for a 30 day month the monthly electricity bill will be:
30 days / month X \$3.48 / day = \$104.40 / month

The corresponding blended cost of electricity is:
\$104.40 / (30 days X 24 kWh / day) = \$0.145 / kWh

The equivalent monthly peak demand charge is:
(\$3.00 / day X 30 days ) / 5 kW = \$18.00 / kW

The cost of a marginal increase in energy consumption which does not affect the peak demand is \$0.02 / kWh.

For example, if a 5 kW electric hot water tank is added to a home without a load controller the daily peak demand may increase from 5 kW to 10 kW and the daily energy consumption may increase by 12 kWh.
Hence the monthly energy consumption may increase by:
12 kWh / day X 30 days = 360 kWh
and the monthly cost of marginal electrical energy will rises by:
360 kWh X \$0.02 / kWh = \$7.20

Without a load controller the monthly cost of peak demand may increase by as much as:
\$18.0 / kW-month X 5 kW = \$90.00 / month
whereas with a load controller the additional monthly cost of peak demand is zero.

With a properly set load controller the cost of heating the water is:
\$0.02 / kWh.

Without a load controller the cost of heating the water rises from \$0.02 / kWh to:
(\$7.20 + \$90.00) / (730 h X 0.5 kW) = \$.2663 / kWh.

Hence without a load controller adoption of the OSPE retail electricity rate may cause the blended cost of electricity per kWh to rise instead of fall.

Thus it is essential for consumers to grasp that a properly designed, installed and adjusted load controller is required to take advantage of the OSPE retail electricity rate.

This web page last updated February 15, 2019.