XYLENE POWER LTD.

INTERIM IES IMPLEMENTATION

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

INTRODUCTION:
The issue of proper use of Interruptible Power is crucial both for the Ontario electricity system and for mitigation of climate change.

Ontario has large amounts of intermittently available clean (non-fossil) electricity generation. One method of both decreasing the average cost of electricity and reducing provincial CO2 emissions is to sell this surplus clean electricity as interruptable power instead of curtailing (discarding) it or exporting it at a very low price as at present. Subject to appropriate pricing this interruptible power could be used at night for displacement of liquid fossil fuels in rural hybrid heating systems and for charging battery electric vehicles.

This web page addresses practical implementation of a simple interim method for exploiting part of the available Interruptible Electricity integrated with the existing Dependable Electricity Service (DES).
 

CONSUMER REQUIREMENT:
In order for a IES service to operate together with an existing DES service it is essential that the wiring at the consumer premises be modified such that the the IES load can be enabled or disabled by a timer without affecting the DES load. Usually this modification is realized by adding a contactor controlled pony panel at the premises main electrical panel and/or by use of low voltage or wireless appliance control signals.

In order for a consumer to use IES supplied electricity for an essential function such as winter space heating the consumer must have a fully functional automatic backup heating system, usually based on a liquid fossil fuel such as oil or propane. Most backup heating systems also need DES supplied electricity for proper control.
 

SIMPLE INTERIM SOLUTION:
At present (2022) in Ontario there is almost always interruptible electricity available daily between 11:00 PM and 7:00 AM. Thus, at least until the projected closure of the Pickering NGS, IES loads which will only operate during that time period can be enabled just by a timer. The consumer must have an interval electricty meter so that the Local Distribution Company (LDC) can apply a deep discount time-of-use rate to the interruptible load. A typical residential load is charging of a battery electric vehicle or displacing a liquid fossil fuel.

However, this simple time control methodology can only access part of the total available interruptible electricity and may only be valid for liquid fossil fuel displacement as long as the 3000 MWe clean electricity generation capacity of the Pickering NGS is available. Thereafter it may be important for LDCs to have the capability to selectively remotely disable interruptible electricity loads that are used for liquid fossil fuel displacement.

From a CO2 emissions perspective we should avoid use of electricity generated by combustion of natural gas for displacement of oil and propane in rural hybrid heating systems.

The situation is a bit different for Battery Electric Vehicle (BEV) charging because of the large difference in energy efficiency between a BEV and an Internal Combustion Engine (ICE) powered vehicle. Electricity generated by combustion of natural gas, when fed to a BEV, still results in less net CO2 emissions than an equivalent ICE powered vehicle.
 

PRACTICAL IMPLEMENTATION:
In order to have an IES Rate it is necessary to use a metering system that distinguishes IES electricity from DES electicity because IES electricity is provided at a different rate than DES electricity.

For practical reasons, both equipment and administrative, the IES should be implemented as an add-on rate to an existing DES account at the same address. Thus in reality there is no separate IES rate. Instead there is one combined rate that effectively provides the consumer the IES rate only during the period 11:00 PM to 7:00 AM. If the IES load operates at other times the consumer will be billed at the full DES rate for that out of specified period operation.
 

ELECTRICITY METER:
An important element of the proposed IES rate is that the IES metering system inherently prevents IES electricity being used to displace existing DES load. If a load actually runs when it is supposed to be disabled the electricity associated with that load is billed at the DES rate.
 

INTERRUPTIBLE ELECTRICITY RATE:
The cost of IES electrical energy rate should be about $0.02 / kWh. This price give the purchaser of the interruptible electricity various viable application options. This price is usually more than the IESO is able to realize via the spot export market.
 

CONDITIONS FOR SUPPLY OF INTERRUPTIBLE ELECTRICITY:
In order for an Interruptible Electricity Service to make financial sense for the participating parties, the marginal cost of providing IES energy must be close to zero. Hence:
1. Fossil fueled electricity generation should not be operating when use of interruptible electricity is permitted;
2. Provision of IES energy should not require any upgrade to the transmission/distribution system beyond normal upgrades required for providing reliable DES electricity;
 

POTENTIAL INTERIM IES CUSTOMERS:
Potential IES customers include:
1. Parties with hybrid electric/ fossil fuel heating systems;
2. Parties with thermal energy storage systems;
3. Parties with battery type energy storage systems.

The most easily accessible IES loads are charging of battery electric vehicles and displacement of fossil fuels by electricity for rural space and domestic hot water heating. It is contemplated that in the future many rural IES customers will likely have equipment such as large domestic hot water tanks for temporary storage of heat.
 

POLITICS AND HYBRID HEATING SYSTEMS:
One of the economic realities in Ontario during the past decade has been a substantial increase in the prices of both electricity and furnace oil, while the price of natural gas has fallen. Rising energy costs have more than doubled the cost of space and domestic hot water heating in rural areas that are not serviced by low cost piped natural gas while the cost of space and domestic hot water heating in urban areas with low cost piped natural gas service has decreased. This issue has contributed to a severe urban/rural split in elected members in the Ontario provincial legislature. If the provincial politicians want to remain in power it is essential that they offer electricity rate relief to rural property owners who presently have no economically viable automatic heating fuel options other than the liquid fossil fuels.

Offering rural property owners interruptible electricity at $.02 / kWh for space and domestic hot water heating, when that energy is otherwise going to waste via non-fossil generation constraint, would provide cost relief for rural property owners and would decrease liquid fossil fuel consumption and related CO2 emissions, all at no cost to anyone except the rural property owner who would have to fund the purchase and installation of an electric hot water heater in series his existing oil fired hot water heater and a furnace plenum electric duct heater and related wiring. With this equipment a typical home owner would likely experience a furnace oil cost saving of about $2000 per year, an increase in electricity cost of about $800 per year resulting in a net utility cost saving of about $1200 per year and would likely realize a two year to 3 year simple payback on his investment.

It is projected that over 100,000 single family homes and small businesses in Ontario would participate leading to a reduction in liquid fossil fuel purchases of over $200 million per year.

It is contemplated that the above described heating retrofits would be installed and maintained by the liquid fuel appliance field service technicians who are currently allied with rural oil and propane delivery firms such as Shell and Ultramar.
 

IMPLEMENTATION:
We need a IES rate that can be applied to any size building. Due to lack of customer knowledge this rate is not something that at present can be easily sold by an electricity utility. It needs to be sold by contractors who are already in the energy equipment service business. These contractors already have long standing business relationships with the target customers and would be responsible for the design, installation and maintenance of the hybrid heating system conversions. These contractors already provide periodic reports to the fire insurance companies relating to the system safety and good maintenance. These contractors are also responsible to MCCR/TSSA with respect to fuel safety and pressure vessel matters. They are responsible to ESA with respect to electrical safety matters.

Explaining the features of the interim IES electricity rate to unsophisticated consumers may not be simple. Thus the service contractors have an important role to play in explaining the relevant electricity rate issues to end users. Typically these contractors already have an earned trust relationship with their clients.

As a condition of obtaining the IES rate each customer must designate a technically qualified service contractor. Contractors that want to do this work must demonstrate to the local distribution company that they have the required expertise. One simple way of ensuring suitable competence is to have the work supervised by a licenced professional engineer with relevant experience.
 

EXECUTIVE SUMMARY:
The remainder of document contains a rigorous derivation of consistent formulae for interim implementation of a simple IES via a deep discount rate plan.

This author's practical experience is that while energy can be shifted from the day to the night periods, the process for shifting energy use within just the daytime period is much more complex and is not possible to effectively implement using just the simple methodology envisaged herein. Realizing significant benefits just within the day time period requires much more sophisticated control and metering equipment.

The system benefits are limited only by the amount of available interruptible energy. That amount is limited by the total amount of clean generation. In this respect every effort should be made to maximize the future output from all sources of clean generation.

The potential IES benefits are presently threatened by the projected closure of the Pickering NPP and by shutdown of other nuclear NPPs for refurbishment.
 

DEFINITIONS:
Dependable Power is the total grid supplied electric power that is used by all electricity consumers at least 99.7% of the time.

Interruptible Clean Power is the positive amount by which total instantaneous clean power generation exceeds the total instantaneous load requiring dependable electricity. Due to significant variations in both total clean generation and total load requiring dependable power Interruptible Clean Power is not always available.

The annual available Interruptible Clean Energy is the time integral over one year of positive clean Interruptible Power.

In the electricity export market the monetary value of Interruptible Clean Energy is usually less than $0.02 / kWh . However, the monetary value of Interruptible Clean Energy for liquid fuel displacement is presently over $0.14 /

In recent years the total amount of Interruptible Clean Energy in Ontario has been about 20 TWh / year. That is sufficient energy to power several million battery electric vehicles and to partially displace liquid fossil fuels in over two hundred thousand rural Ontario homes that cannot access low cost piped natural gas.

For consumers who need only dependable electricity Simple Rate Electricity Billing takes the form:
(Bill) = (Distribution Charge) + Kn En
where :
En = energy consumed during the billing period in kWh
Kn = Marginal Price per kWh

For consumers who need both dependable and interruptible electricity Combination Rate Electricity Billing takes the form:
(Bill) = (distribution charge )
+ (Kn )[1+ Kra (Ty / Tx)] [Ex] - Ky Kra (Ty / Tx) Ex + Ky Ey
which for the special case of 11:00 PM to 7:00 AM IES operation simplifies to: (Bill)
= (distribution charge) + Kn [Ex + Ey] - [9 Kn / 10] [ Ey – (Kra Ex / 2)]
Where the simple electricity rate component is:
= (distribution charge) + Kn [Ex + Ey]
and the discount component is:
= [9 Kn / 10][ Ey – (Kra Ex / 2)]
where:
Tx = time period when interruptible power is not available to consumers
Ty = time period when interruptible power is available to consumers
Ex = energy consumption during periods when interruptible power is not available to consumers
Ey = energy consumption during periods when interruptible power is available to consumers
Ky = Kn / 10 (An OEB experimental determination)
Kra = average value of {[Ey / Ty] / [Ex / Tx]} for consumers who are on Simple Rate Electricity Billing.

THIS DOCUMENT:
The 11:00 PM to 7:00 AM operating period is a special case of the more general issue of exploitation of Interruptible Power. This document derives the relationship between simple electricity billing and the billing algorithm that should be used for residential and small business consumers who wish to access the portion of the low cost interruptible power which presently is consistently available during the daily period 11 PM to 7 AM. That time period presently allows easy access to about half of the total available Clean Interruptible Energy.
 

SOURCE OF INTERRUPTIBLE POWER:
Most electricity consumers have an expectation of dependable electric power. Dependable power is power that is available to consumers in the amount that they want when they want it. It is normal for the total dependable power load on the electricity grid to vary over time.

However, the capacity of the electricity system to deliver dependable power depends on the peak generation capacity less a reserve margin always being greater than the peak dependable power load.

There is an additional complication that the clean generation capacity also varies with time.

The positive difference between the instantaneous clean generation capacity and the instantaneous dependable power load is potentially available clean interruptible power. Note that at certain times the available clean interruptible power goes to zero. Hence clean interruptible power can not be used for purposes that require dependable power.

When clean interruptible power is available the marginal cost of the delivered interruptible energy is relatively small. Hence interruptible power is an economic source of clean energy suitable for partial displacement of liquid heating fuels and for charging energy storage.(Battery Electric Vehicles).
 

MAKING EFFECTIVE USE OF INTERRUPTIBLE POWER:
The concept is to use this part of the available low cost interruptible energy to partially displace expensive liquid fossil fuels in rural comfort heating systems and to displace expensive gasoline in automotive transportation. A second benefit is to provide a significant monetary incentive for consumers to time shift their existing electrical loads from day time to night time operation.

The benefits of liquid fuel displacement are:
a) reduced heating costs for rural consumers who cannot access low cost natural gas
b) reduced charging costs for owners of battery electric vehicles
c) reduced Ontario provincial CO2 emissions
d) increased electricity system revenue
e) minimizing Ontario's requirement for construction of additional new clean generation

As the Ontario electricity system gradually evolves the availability profile of interruptible electricity will change. Hence the proposed new deep discount billing methodology should be expressed as a formula rather than being rigidly tied to a specific time frame. The rate and time frame proposed now by the OEB should be a special case of that more general billing formula.

At some point in the future many electricity consumers will likely have internet connected control boxes that will output a signal from the IESO / LDC which indicates time periods when interruptible power is available for that consumer. This general billing formula should be future compatible with that technology.

At some point in the future the global adjustment should be allocated to consumer demand rather than consumer energy consumption. The net effect of this rate fix on residential electricity rates should be very small. The proposed OEB deep discount plan provides a present means for residential consumers to access interruptible electricity at a marginal energy cost close to the cost that will apply after the global adjustment is allocated to consumer demand rather than consumer energy consumption.

Assuming that this deep discount electricity rate proposal is accepted it is almost certain that commercial parties will seek to access the remainder of the available interruptible power by use of more sophisticated control and metering equipment.

During the years to come the annual amount of available clean Interruptible Power is expected to first decrease on closure of the Pickering NPP and then gradually increase as other existing nuclear power plants are refurbished and as new clean generation is commissioned. As part of climate change mitigation the available Interruptible Energy in Ontario is projected to exceed 300 TWh / year by 2070. Thus long term proper application of Interruptible Power is of major importance.

The electricity billing plans available to consumers should include both a simple plan and a combination plan. The simple plan provides dependable power to consumers who do not need or want interruptible power and do not need or want a TOU rate. The combination plan provides both dependable power and low cost interruptible power to consumers who want to use interruptible power for partial displacement of liquid heating fuels and/or for charging of energy storage.(eg Battery Electric Vehicles)

While the current OEB proposal is for a particular time schedule, the methodology used to calculate the appropriate electricity rates should allow adoption of different time schedules in the future. That flexability will allow changing the interruptible power availability time schedule from time to time as the supply of available interruptible power changes.

For an average consumer who draws no interruptible power but who is billed according to the combination plan, that consumer's electricity bill should be identical to the bill for another average consumer who has the same load profile and who is on the simple rate plan.
 

ELECTRICITY METERING:
Most electricity consumers in Ontario have interval electricity metering. For the meters that cannot be remotely read in real time the interval data can be acquired by a human meter reader with a portable computer. The interruptible electricity billing is calculated from existing interval meter data.

Within the electricity system the monetary value of an interruptible kWh is much lower than the monetary value of dependable kWh. When both dependable power and interruptible power are simultaneously provided to the same consumer there must be a practical way of distinguishing between them.

At times when only dependable power is available to the consumer the metered energy consumption is all dependable power.

At times when both dependable power and interruptible power are both available to the consumer the measured total power is the sum of the dependable power plus the interruptible power. Calculation of the interruptible power requires a means of measuring or estimating the dependable power component.

The various methods of addressing this issue are:
a) Separate meters for dependable and interruptible loads. In cases where branch circuits contain both dependable and interruptible loads this method is prohibitively expensive to implement. Hence this method is not practical for wide spread implementation.

b) Pulse the interruptible power on/off during the period when interruptible power is available. The amplitude of the resulting power pulses indicates the interruptible power. The remainder is the dependable power. This method is accurate if suitable metering is available. This method might make sense for large users where the costs of the required metering equipment and billing software are justified but this method is not compatible with most existing residential interval meters.

c) Assume that the average dependable power during the period that interruptible power is available is the same as the average dependable power during the period when interruptible power is not available. This is the simplest and administratively the most easy method but the dependable power at night so calculated will be in error by the amount of the normal daily night/day fluctuation in dependable power. The advantage of this method is extreme simplicity. The disadvantage of this method is that that it will usually penalize parties who opt for combination billing but who then do not actually use interruptible power.

d) Prior to providing interruptible power service to a consumer measure the ratio of average dependable power during the period when interruptible power will in the future be available to this consumer to average dependable power during the period when interruptible power will not be available to this consumer. Then use this ratio to estimate the dependable power portion of the total power supplied during the period when interrupible power is available. This method, although it appears fair, is the administratively expensive to implement. In practical implementation there is significant manual work involved that cannot be automated. For that reason this author recommends against using this method for single family residential and small businesses consumers.

e) For a large number of consumers who are on simple Rate Billing, measure the ratio:
Kr = [Ey / Ty] / [Ex / Tx]

Find the average Kra of the Kr values. Then use Kra for all consumers on the combination billing plan to estimate the use of dependable power during times when both interruptible power and dependable power are available.. This method is an improvement on method (c). The advantage of this method is that for average combination plan consumers the small remaining errors in the estimate of dependable power during the period of interruptible power availability will approximately cancel out over a year.

f) Do the same as for method (e) above but develop a different Kra value for each month. This method is an improvement on method (e) which is appropriate if and only if the billing periods are identical for all consumers. The advantage of method (f) is that for average consumers there is little or no error in the estimate of dependable power during the period of interruptible power availability. Method (f) is essentially the same as method (e) except that the Kra value used changes from month to month. A disadvantage of method (f) is the likely necessity to have to explain it to inquisitive parties.

The following mathematical analysis applies to methods (c) to (f) inclusive.

A billing period Tn = Tx + Ty where:
Tx = number of hours in a billing period during which the consumer can access dependable electricity but cannot access interruptible electricity;
Ty = number of hours in a billing period during which the consumer can access both dependable electricity and interruptible electricity;
Ex = total energy consumption during time Tx;
Ey = total energy consumption during time Ty;
Px = Ex / Tx
= average power when the consumer can only access dependable electricity;
Py = Ey / Ty
= average power during periods when the consumer can access both interruptible and dependable electricity.

If the dependable power level is constant then the average interruptible power is given by:
Py – Px = [Ey / Ty] – [Ex / Tx];

If the dependable power fluctuates the dependable power Po during period Ty will be:
Po = Kr [Ex / Tx];
where unless a party is on shift work:
Kr < 1.0;

Thus the average interruptible power is given by:
Py – Po = [Ey / Ty] – Kr [Ex / Tx].

If there is no use of interruptible power then:
Py – Po = 0
which gives:
Kr = [Ey / Ty] / [Ex / Tx].

Each consumer, when not using interrupible power, can be characterized by the average power ratio referred to herein as Kr. The average Kr value for a large number of consumers is Kra.

If the averaging is done for each month Kra will take 12 different values during a year.

In theory, a Kr value for each consumer could be calculated from that consumer's historical electricity usage. However, as set out in (d) above, that procedure is administratively onerous. Instead the assumption is made that:
Kr = Kra,
where Kra is a average value of Kr obtained by calculating Kr for many consumers who do not use interruptible power and who are on the simple rate plan.

It is contemplated that consumers should be offered a choice of rate plans, two of which are simple rate billing and combination rate billing (deep discount at night) and that consumers should be free to change from one rate plan to another.

For method (c) above the combination rate billing plan constants are chosen such that for a consumer who has a constant dependable power load and who does not use interruptible power but who is on the combination rate plan, is billed the same amount as if he/she were on the simple rate plan.

Method (e) above, improves on method (c) by taking into account normal daily variations in average consumer dependable power.

Method (f) is essentially the same as method (e) except that the Kra value used changes from month to month. That may give slightly better monthly billing consistency for average consumers but is at the expense of 12 different monthly constants that may have to be explained to inquisitive parties.

THIS AUTHOR STRONGLY RECOMMENDS ADOPTION OF EITHER METHOD (e) or METHOD (f) DEPENDING ON EXISTING BILLING PERIOD STANDARDS.

The actual Kr value of a particular consumer will usually slightly deviate from Kra. If a consumer changes from a simple billing plan to the combination billing plan but does not use any interruptible power that consumer may experience a small change in his/her electricity bill caused by the deviation of his/her actual Kr value from the consumer average value Kra. However, if the consumer is dissatisfied he/she is free to adopt a different rate plan.

The practical field experience has been that the difference in electricity billing between the simple rate plan and the combination rate plan when interruptible power is not used is very small and the fraction of consumers who choose to jump back and forth between the different rate plans is negligible.

In summary, for consumers who choose the combination rate plan, the amount of their use of dependable power during the period when interruptible power is available is calculated using the assumption that
Kr = Kra.

Invoking this assumption is administratively much more practical than calculating each consumer's Kr value.

This methodology also avoids the issue of different consumers comparing their bills and finding that they are effectively on different rates. All consumers are treated identically.

There is another potential legal issue. The combination rate can be presented as being a simple rate less a discount. The merit of that approach is that then there is no necessity to legally defend the exact value of the marginal interruptible energy rate. Consumers are offered a simple electricity rate in an accepted format less a cost discount which discount is calculated in a consistent manner for all consumers in the rate group. The discount is expressed in dollars, not energy units, so should not be subject to federal legislation relating to weights and measures. It is a simply a financial offer that consumers are free to accept or reject.
 

BILLING FORMULA DERIVATION:
In a clean electricity system costs arise from three main sources: a) Distribution cost;
b) Fixed costs related to financing and maintaining capital equipment;
c) Variable costs reflecting the marginal cost of energy (fuel)
For clean energy generation the variable costs are small.

The distribution cost is a constant monthly charge common to every consumer in the rate group.

Usually the largest cost component that a consumer experiences is funding financing and maintaining the capital cost of generation and transmission required to dependably meet that consumer's peak coincident demand.

While peak coincident demand is difficult to measure, average demand is relatively easy to obtain from interval meter data. For residential consumers the rate group's average demand is proportional to the rate group's peak coincident demand.

Thus the monthly billing formula should consist of three terms, The fixed distribution cost, a term proportional to average power calculated at times when interruptible power is not available to the consumer and a term proportional to overall energy consumption.

A billing period Tn consists of the sum of two cumulative times Tx and Ty where:
Tx = number of hours in the billing period during which the consumer can only access dependable electricity
Ty = number of hours in the billing period during which the consumer can access both dependable electricity and interruptible electricity
Ex = energy consumption during time Tx
Ey = energy consumption during time Ty

The combination electricity bill should take the form:
Bill = (distribution charge ) + Kx [Ex / Tx] + Ky (Ex + Ey)
where Kx and Ky are rate constants. The term
Kx[Ex / Tx]
is proportinal to power and contributes to the electricity system fixed costs and the term
Ky [Ex + Ey]
is proportional to energy consumption and contributes to the electricity system variable costs.

Note that the units of Kx and Ky are different.

The OEB has experimentally demonstrated that for a deep discount residential rate to be successful:
Ky ~ Kn / 10

The Simple Rate bill for a non-TOU consumer who does not need or want interruptible power can be expressed as:
(Bill) = (distribution charge) + Kn En
where:
Kn = charge per kWh determined by the OEB via another rate setting process
En = monthly billing period energy consumption with no interruptible power

If an average consumer switches between the simple rate plan and the combination rate plan with no change in load profile his/her monthly bill should be almost unchanged.

Let Eyo be the value of Ey with no interruptible power.

For the special case of a consumer on the combination rate who actually uses no interruptible power:
Bill = (distribution charge) + Kn En
= (distribution charge) + Kx [Ex / Tx] + Ky (Ex+ Eyo)

This equation simplifies to:
Kn En = Kx [Ex / Tx] + Ky (Ex + Eyo)
or rearranging:
Kx = [Kn En – Ky (Ex + Eyo)] / [Ex / Tx]

For a consumer on the combination rate plan who uses no interruptible power:
Ex + Eyo = En

Hence: Kx = (En) (Kn – Ky) / [Ex / Tx]
= [En / Ex][Tx] (Kn - Ky)

For consumers on the combination rate plan:
En = Ex + Eyo

Hence:
Kx = [(Ex + Eyo) / Ex] [Tx ] (Kn - Ky)

Recall that:
[Eyo / Ty] / [Ex / Tx] = Kra

Thus:
Eyo = Kra Ty [Ex / Tx]

Hence:
Kx = [(Ex + Eyo) / Ex] [Tx] (Kn - Ky)
= [Tx](Kn – Ky) + Kra [Ty / Tx][Tx](Kn – Ky)
= (Kn – Ky)[ Tx + Kra Ty]

For commercial accounts the term:
Kx = (Kn – Ky)[ Tx + Kra Ty]
is known as the “cost of demand” and has units of $ / kW. This issue is of importance to commercial consumers who have [Ex / Tx] values comparable to or greater than 50 kW. Note that this cost of demand is significantly higher than present commercial demand charges because Ky should be significantly lower than the present marginal cost of energy.

This situation has arisen due to ill conceived provincial legislation that applies the global adjustment to kWh rather than to kW. This matter needs a legislative fix which we strongly recommend. Until there is a legislative fix the OEB is faced with having to undercharge commercial consumers for demand in order to compensate for over charging for energy. Under charging for demand sends the wrong message to commercial property owners in terms of peak demand minimization. The sooner that this faulty legislation is fixed, the better.

Thus in the case of the combination rate plan the billing formula is:
Bill = (distribution charge ) + Kx [Ex / Tx] + Ky (Ex + Ey)
= (distribution charge ) + {(Kn – Ky)[Tx + Kra Ty]} [Ex / Tx] + Ky (Ex + Ey)
= (distribution charge ) + (Kn – Ky)[1+ Kra (Ty / Tx)] [Ex] + Ky (Ex + Ey)
= (distribution charge ) + (Kn )[1+ Kra (Ty / Tx)] [Ex] - Ky Kra (Ty / Tx) Ex + Ky Ey

As a consumer increases his/her use of interruptible power, energy Ey increases.
 

FORMULA EVALUATION FOR THE OEB PROPOSED PARAMETERS:
For the OEB proposal:
Ty = 8 hours
Tx = 16 hours
Ty / Tx = 1 / 2
Ky = Kn / 10

Ex and Ey are both obtained from the interval meter. Thus:
Bill = (distribution charge ) + {(Kn )[1+ Kra (Ty / Tx)] [Ex] - Ky Kra (Ty / Tx) Ex + Ky ( Ey)
= (distribution charge ) + {(Kn )[1+ Kra (1 / 2)] [Ex] - (Kn / 10) Kra (1 / 2) Ex + (Kn / 10 )( Ey)
= (distribution charge) + Kn {Ex +( Kra Ex / 2) – Kra Ex / 20 + Ey / 10}
= (distribution charge) + Kn {Ex +( 9 Kra Ex / 20) + Ey / 10}

This formula can be expressed in the form:
(Bill) = (distribution charge) + Kn {Ex + ( 9 Kra Ex / 20) + (Ey / 10)}
= (distribution charge) + Kn {Ex + Ey} +Kn { - Ey + ( 9 Kra Ex / 20) + (Ey / 10)}
= (distribution charge) + Kn {Ex + Ey} - Kn { + Ey - ( 9 Kra Ex / 20) - (Ey / 10)}
= (distribution charge) + Kn {Ex + Ey} - Kn { (9 Ey / 10) - ( 9 Kra Ex / 20)}
= (distribution charge) + Kn {Ex + Ey} - [9 Kn / 10]{ Ey – (Kra Ex / 2)}
Where the simple rate charge is:
(distribution charge) + Kn {Ex + Ey}
and the discount is:
[9 Kn / 10]{ Ey – (Kra Ex / 2)}

The constant Kra is found by analysis of the load profiles of consumers who are on the simple rate plan.

For an average consumer:
[(Eyo / Ty) / (Ex / Tx)] = Kra

For the OEB case:
Ty = Tx / 2

Hence for an average consumer:
Eyo = Kra Ex / 2

Then for an average consumer with no interruptible load: Bill = (distribution charge) + Kn {Ex +( 9 Kra Ex / 20) + Eyo / 10}
= (distribution charge) + Kn {Ex +( 9 Kra Ex / 20) + Kra Ex / 20}
= (distribution charge) + Kn Ex {1 + Kra / 2}
= (distribution charge) + Kn Ex {1 + Eyo / Ex}
= (distribution charge) + Kn {Ex + Eyo}
which is the same charge that would result if this consumer was on the simple rate plan.
 

SUMMARY:
The general billing formula for consumers on the combination rate plan is:
Bill = (distribution charge ) + {(Kn )[1+ Kra (Ty / Tx)] [Ex] - Ky Kra (Ty / Tx) Ex + Ky Ey
which for the values of:
Ty / Tx = 1 / 2
and
Ky / Kn = 1 / 10
chosen by the OEB gives:
Bill = (distribution charge) + Kn {Ex +( 9 Kra Ex / 20) + Ey / 10}
= (distribution charge) + Kn {Ex + Ey} - [9 Kn / 10]{ Ey – (Kra Ex / 2)}
where Kn is the energy rate under simple billing and Kra is the average value of
Kr = (Ey / Ty) / (Ex / Tx)
for a large number of parties in the simple rate plan.

Typically $0.10 / kWh < Kn < $0.15 / kWh

For any real system utilizing Interruptible Power the energies Ex and Ey, can be measured using an interval meter.

In the unlikely event that the parties choose to rely on historical data Kra should be replaced by Kr, in which case at least one complete year of valid historical data is required to accurately determine Kr.
 

This web page last updated February 26, 2022.