XYLENE POWER LTD.

ELECTRICITY RATE ISSUES

By C. Rhodes

ELECTRICITY RATES:
Electricity rates should meet three fundamental objectives:
1. Provision of revenue sufficient to build, operate, maintain, replace and upgrade the electricity system;
2. Provision of fair compensation and fair cost allocation to parties that generate electricity, transmit electricity, distribute electricity, store and recover energy, consume electricity, operate the electricity system, regulate the electricity system and provide financing for the electricity system.
3. Provision of cost signals which indicate to all generators and load customers the manner in which they should change their equipment and operations to minimize their costs. If the electricity rates are properly set this change should enhance the electricity system.

APPLICATION:
The electricity rates discussed herein apply to grid customers that are non-dispatched generators or non-dispatched loads. The huge majority of grid customers fall into this category. Such grid customers act to maximize their profitability under the published rate structure and are not subject to direct control by the Independent Electricity system Operator (IESO).

ELECTRICITY RATE COMPONENTS:
An electricity rate has five principal components, a transmitted energy component, a received energy component, a transmission/distribution component, a congestion component and an administration component. The transmitted energy component reflects all the costs of energy generation. The received energy component is similar to the transmitted energy component but also reflects transmission/distribution system energy losses. The transmission/distribution component reflects all the non-energy costs of transmission/distribution. The congestion component is used to shift costs amongst customers in a manner that encourages the most efficient use of the available generation and transmission/distribution resources. The administration component reflects the account administration costs.

DEFINITIONS:
Let Er = total registered energy received by a customer from the grid;
Let Ert = total registered energy received via meters from the distribution system;
Let Et = total registered energy transmitted by the customer to the grid;
Let Ett = total registered energy transmitted via meters into the distribution system;
Let Cr = value per kWh of energy received by the customer from the grid;
Let Ct = value per kWh of energy transmitted by the customer to the grid;
Let T = time;
Let Era = value of Er at time T = Ta;
Let Erb = value of Er at time T = Tb;
Let Eta = value of Et at time T = Ta;
Let Etb = value of Et at time T = Tb;
Let Cd = transmission/distribution charge borne by each kWh received or transmitted by the customer;
Let Ca = administration charge that is the same for all customers in a rate group
Let B = the phase angle between the voltage and current waveforms if no harmonics are present. If harmonics are present B is as defined in the section titled Electricity Power Factor
Let cos(B) = power factor
Let F(B) = [Pi/((Pi - B)cos(B) + sin(B))]

At the commencement of a measurement interval T = Ta. At the end of the measurement interval T = Tb.
Let El = total electrical energy lost within the distribution system between T=Ta and T = Tb;
Let Es = total electical energy stored within the distribution system between T=Ta and T = Tb.
The law of conservation of energy requires that between times Ta and Tb:
Ett = El + Es + Ert

In most real transmission / distribution systems, over periods of time that are long compared to a few seconds, Es is negligibly small. Since El > 0, Ett > Ert. In order to evaluate El and hence compute the relative values of Ert and Ett it is necessary to measure all the components of Ert and all the components of Ett. Thus each electricity meter should have separate registers for the components Er and Et of Ert and Ett that it measures.

The kWh registers record the energy that flows through connections to the distribution system. However, net absorbed energy = (received energy - transmitted energy) is a poor indicator for apportioning transmission/distribution system costs. For example, a reactive load connected to a distribution system can cause substantial transmission/distribution costs even though the reactive load absorbs very little net energy. Similarly a residence with a behind the meter wind turbine can cause significant distribution costs while drawing little or no net energy from the electricity grid. The quantity:
(received energy - transmitted energy)/(power factor)
is a much better indication of transmission/distribution cost than is net energy.

The energy that a customer receives from the grid between time T = Ta and time T = Tb is:
(Erb - Era)
and the cost of that energy to the customer is:
Cr (Erb - Era).

The energy that a customer transmits to the grid between time T = Ta and time T = Tb is:
(Etb - Eta)
and the price that the customer receives for that transmitted energy is:
Ct (Etb - Eta)

The net energy absorbed by a customer between time T = Ta and time T = Tb is given by:
[(Erb - Era) - (Etb - Eta)]
and the net cost of that energy to the customer is:
[Cr (Erb - Era) - Ct (Etb - Eta)]

The purpose of a transmission/distribution system is to transport energy. Hence each customer should pay a transmission/distribution fee proportional to the transmission capacity that he/she uses. As shown in the section titled Electricity Power Factor, the transmission/distribution capacity used by the customer between time T = Ta and time T = Tb is given by:
|(Erb - Era) - (Etb - Eta)| / cos(B).
Hence between time T = Ta and time T = Tb the transmission distribution charge should be:
[Cd |(Erb - Era) - (Etb - Eta)| / cos(B)].
The rate Cd should be the same for all customers of a distribution system.

COST RECOVERY:
Any electricity utility has to recover its costs from its customers. Electricity utilites divide their customers into rate groups of similar customers. For each rate group the cost Cij allocated to customer i for the measurement period j between time T = Ta and T = Tb is given by adding the abovementioned rate components to get:
Cij = {[Cr(Erb - Era) - Ct(Etb - Eta)]ij + [Cd|(Erb-Era) - (Etb-Eta)|/ cos(B)]ij} + Ca

Note that for a load Cij is always a positive number and for a generator Cij should be a negative number.

CONSERVATION OF ENERGY:
Define:
Ett = sum of all (Etb - Eta) readings for all input/output meters of a transmission/distribution system;
Ert = sum of all (Erb - Era) readings for all input/output meters of a transmission/distribution system;
Then conservation of energy requires that for normal density customers served by Hydro One:
Ett = 1.092 Ert

NON-PROFIT ON ENERGY:
Conservation of cash related to energy requires that for all normal density customers served by Hydro One:
Cr Ert - Ct Ett = 0
Hence:
Cr / Ct = [Ett / Ert] = 1.092
or
Cr = 1.092 Ct

REFLECTED POWER:
For a load the reflected power ratio is:
[(Etb - Eta) / (Erb - Era)];
For a generator the reflected power ratio is:
[(Erb - Era) / (Etb - Eta)];
A transmission/distribution system operates most efficiently when the reflected power is close to zero at every termination. This condition is achieved by making the power factor at each termination close to unity. As the reflected power increases transmission/distribution losses increase.

RATE FACTORS:
Cd = a proportionality factor chosen such that the summation over all i of:
[Cd|(Erb - Era) - (Etb - Eta)|/ cos(B)]ij
recovers the utility's cost of transmission/distribution for measurement period j for the rate group.

Ct = a proportionality factor chosen such that:
Ct (Ett)j
recovers the total cost of generation for metering period j for the rate group.
Thus:
Ct = (total cost of generation for metering period j) / Ett

Recall that for Hydro One normal density customers:
Cr = 1.092 Ct

In 2006 the energy rate was:
Ct = $.067 / kWh
Hence:
Cr = Ct X 1.092
= $.067 X 1.092 kWh
= $.073164 / kWh

In 2006 for residential customers the quantity Cd was about:
Cd = $.0458 / kWh.

Ca = a constant chosen such that the summation over all i of (Ca)i recovers the total cost of account administration for metering period j.

FULL METERING FORMULA:
Recall that from the paragraph headed COST RECOVERY on this web page the full metering formula is:
Cij = {[Cr(Erb - Era) - Ct(Etb - Eta)]ij + [Cd|(Erb-Era) - (Etb-Eta)|/ cos(B)]ij} + Ca

Recall from the web page titled Power Factor for the condition:
(Erb - Era) > (Etb - Eta)
[Cd|(Erb-Era) - (Etb-Eta)|/ cos(B)]ij
= Cd[(Erb-Era) - (Etb-Eta)]/ cos(B)]ij
= Cd(Erb - Era)[1 - ((Etb - Eta)/(Erb - Era))]/ cos(B)
= Cd(Erb - Era)F(B)
where F(B) is a tabulated function of [(Etb - Eta) / (Erb - Era)] in the range:
1 < F(B) < 3.14159
Hence the metering formula becomes:
Cij = {[Cr(Erb - Era) - Ct(Etb - Eta)]ij + [Cd|(Erb-Era) - (Etb-Eta)|/ cos(B)]ij} + Ca
= Cij = {[Cr(Erb - Era) - Ct(Etb - Eta)]ij + [Cd(Erb-Era)F(B)]ij} + Ca

Recall from the web page titled Power Factor for the condition:
(Erb - Era) < (Etb - Eta)
[Cd|(Erb-Era) - (Etb-Eta)|/ cos(B)]ij
= Cd[(Etb-Eta) - (Erb-Era)]/ cos(B)]ij
= Cd(Etb - Eta)[1 - ((Erb - Era)/(Etb - Eta))]/ cos(B)
= Cd(Etb - Eta)F(B)
where F(B) is a tabulated function of [(Erb - Era) / (Etb - Eta)] in the range:
1 < F(B) < 3.14159
Hence the metering formula becomes:
Cij = {[Cr(Erb - Era) - Ct(Etb - Eta)]ij + [Cd|(Erb-Era) - (Etb-Eta)|/ cos(B)]ij} + Ca
= {[Cr(Erb - Era) - Ct(Etb - Eta)]ij + [Cd(Etb-Eta)F(B)]ij} + Ca

Hence interval measurements of Er, Et and T yeild values of
(Erb - Era) and (Etb - Eta) for each measurement interval which can be used to provide an exact solution to the full metering formula.

LOAD CUSTOMER METERING SIMPLIFICATION:
The full metering formula can be rewritten in the form:
Cij = {[Cr(Erb - Era) - Cr(Etb - Eta) + Cr(Etb - Eta) - Ct(Etb - Eta)]ij
+ [Cd|(Erb-Era) - (Etb-Eta)|/ cos(B)]ij} + Ca
= {[Cr((Erb - Era) - (Etb - Eta)) + (Cr - Ct)(Etb - Eta)]ij
+ [Cd|(Erb-Era) - (Etb-Eta)|/ cos(B)]ij} + Ca

For load customers with no behind the meter generation:
(Erb - Era) > (Etb - Eta)
Hence:
Cij = {[Cr((Erb - Era) - (Etb - Eta)) + (Cr - Ct)(Etb - Eta)]ij
+ [Cd((Erb-Era) - (Etb-Eta))/ cos(B)]ij} + Ca
or
Cij = [(Cr + (Cd / cos(B)))((Erb - Era) - (Etb - Eta))]ij + Ca + [(Cr - Ct)(Etb - Eta)]ij

LARGE LOAD CUSTOMERS:
A widely used simplification of the billing formula for large load customers with no behind the meter generation is to assume that:
(Etb - Eta)<<(Erb - Era)
and that:
(Cr - Ct) << (Cr + Cd).
Then the term:
[(Cr - Ct)(Etb - Eta)]ij
is negligibly small causing the metering formula to simplify to:
Cij = [(Cr + (Cd / cos(B)))((Erb - Era) - (Etb - Eta))]ij + Ca
Note that evaluating this formula requires measurement of absorbed energy and power factor. This electricity billing formula was used prior to the development of electronic meters that could separately register and cumulate Er and Et. This billing formula is still in commercial use today.

SMALL LOAD CUSTOMERS:
A further widely used simplification of the billing formula for small load customers with no behind the meter generation is to assume that:
cos(B) ~ 1.0
causing the metering formula to further simplify to:
Cij = [(Cr + Cd)((Erb - Era) - (Etb - Eta))]ij + Ca
This metering formula is used by residential smart meters in Ontario. The parameters Cd and Ca vary slightly from one local distribution company to another.

The advantage of this small customer simplification is that the methodology is conceptually simple and the electricity bill can be determined by interval recording of the quantity (Er - Et). The difference between two successive readings of (Er - Et) is:
((Erb - Etb) - (Era - Eta)) = ((Erb - Era) - (Etb - Eta)),
which is the absorbed energy for the metering interval, as required by the simplified metering formula.

GENERATOR METERING:
One of the problems with generator metering is that most generators have significant parasitic loads that continue even when the generator is not producing electricity. Hence generators should be subject to the full metering formula:
Cij = {[Cr(Erb - Era) - Ct(Etb - Eta)]ij + [Cd|(Erb-Era) - (Etb-Eta)|/ cos(B)]ij} + Ca
Note that when the generator is producing net power Cij is negative.

When the generator is not producing net power:
(Erb - Era) > (Etb - Eta), and the metering formula becomes:
Cij = {[Cr(Erb - Era) - Ct(Etb - Eta)]ij + [Cd(Erb-Era)F(B)]ij} + Ca

When a generator is producing net power:
(Erb - Era) < (Etb - Eta) and the metering formula becomes:
Cij = {[Cr(Erb - Era) - Ct(Etb - Eta)]ij + [Cd(Etb-Eta)F(B)]ij} + Ca
Note that when the generator is producing net power Cij is negative.

This formula reveals a major problem with the electricity rate structure in Ontario because at present operating generators are not charged for transmission/distribution or for generator power factor. At present for generators Cd = 0.

Artificially setting Cd = 0 for generators has removed the generator's compensation incentive for controlling F(B) and has caused the Ct values to be too small, which in turn has reduced marginal energy costs, reduced electricity rate based incentives for energy savings and has caused other price distortions throughout the electricity system. It is essential that generators to pay their share of transmission/distribution costs, so that each generator becomes responsible for its power factor.

When Ontario Hydro was the dominant generator, Ontario Hydro looked after generator power factor issues because Ontario Hydro also had responsibility for transmission/distribution costs. However, now that Hydro One is separate from Ontario Power Generation and is also separate from thousands of small independent generators, most of which are not under dispatch control, it is essential that every generator takes responsibility for maximizing its power factor in order to limit total system wide transmission/distribution costs. Thus, the generator compensation rate must be power factor dependent. The above metering formula shows that in order for generator compensation to be properly power factor dependent Cd must be the same for generators as for loads so that generators pay their share of transmission/distribution costs.

At present generation and transmission/distribution are performed by independent entities. Developers of new generation have no effective means of obtaining the transmission that they need when and where they need it because they lack cash flow with which to influence transmission/distribution planning and construction decisions. This problem has led to serious delays in electricity system expansion. There has been no attempt to address this problem under the Green Energy Act.

RE-ALLOCATION OF TRANSMISSION/DISTRIBUTION COSTS:
In order for generation to effectively influence transmission/distribution planning and construction it is crucial that generators pay for their share of the costs of the transmission/distribution network. Generators should pay for connection to transmission/distribution in the same manner as do load customers. The total net power flow through generator connections to transmission/distribution is slightly larger than the total net power flow through load customer connections. If generators pay for their connections to transmission/distribution the transmission/distribution rate charged to load customers can be reduced by about a factor of two but the energy charge to load customers must be increased to give generators the cash flow that they need to pay their share of the transmission/distribution costs. This cost re-allocation will increase the Hourly Ontario Electricity Price (HOEP).

INCENTING ENERGY STORAGE:
Another problem is that people applying the above rate formulae usually assume that Cr, Ct and Cd are constants. This assumption effectively says that all electricity kWh are worth the same, regardless of when they are consumed. However, displacing fossil fuels for load following requires energy storage. In order to financially enable energy storage the value of an on-peak kWh has to be about three times the value of an off-peak kWh. Hence, assuming that Cr, Ct and Cd are constant over time is not consistent with elimination of fossil fuels from the generation mix.

The issue of changing Cr, Ct and Cd with time is explored on other web pages on this web site.

This web page last updated July 5, 2009.