XYLENE POWER LTD.

ELECTRICITY CONGESTION FACTOR

By C. Rhodes

IMPLICATION OF CLIMATE CHANGE:
One of the implications of reducing carbon dioxide emissions to the atmosphere is that much of the transportation energy and comfort heat presently provided by combustion of fossil fuels will instead have to be delivered or otherwise provided via electricity. It is reasonably anticipated that the required amount of electrical energy per capita per annum will more than double. Delivering this energy through the transmission/distribution system will require both increasing the transmission/distribution system size and increasing the effectiveness of transmission/distribution system utilization. The electricity rate payers of Ontario are facing a potentially enormous increase in both generation and transmission/distribution costs.

LOAD FACTOR:
One measure of the effectiveness of transmission/distribution system utilization by a load customer is the load factor. The Daily Load Factor is defined by:
Daily Load Factor = (daily average load) / (daily maximum load)
Thus, increasing the average amount of energy per day delivered via the transmission/distribution system to a load customer, without increasing the maximum load, requires increasing the Daily Load Factor. Increasing the Daily Load Factor generally involves use of a combination of load control and energy storage.

GENERATOR CAPACITY FACTOR:
One measure of the effectiveness of transmission/distribution system utilization by a generator is the generator capacity factor. The Daily Generator Capacity Factor is defined by:
Daily Generator Capacity Factor
= (daily average generator output) / (daily maximum generator output)
Thus, increasing the average amount of energy per day delivered to the transmission/distribution system from a generator, with a fixed maximum output, requires increasing the Daily Generator Capacity Factor. Increasing a generator's capacity factor generally involves the use of a combination of generation control and energy storage.

INCENTING BEHIND-THE-METER ENERGY STORAGE:
In order to minimize overall electricity system system costs it is important to build into the electricity rate structure financial rewards for high load factor and high generation capacity factor. These rewards should be sufficient to financially enable behind-the-meter energy storage.

HISTORY:
In the early 1960s Ontario Hydro recognized the importance to the electricity system of behind-the-meter energy storage and offered an electricity rate to developers and owners of major buildings that encouraged the construction and operation of thermal energy storage. This electricity rate relied on the use of monthly peak demand meters. This electricity rate was partially successful in achieving its objectives, but the degree of success was limited by the use of monthly peak demand meters. The practical difficulty was that once a monthly demand peak was established, the building owner had no financial incentive to reduce his demand on successive days in the month. The monthly demand peak was often established by random circumstances beyond the building owner's control. One of the most common of these circumstances was maintenance and repairs to the energy storage system itself, which consisted of a multiplicity of electric boilers, storage tanks, pumps, temperature controllers, motorized valves, pressure reducing valves, and isolation valves, as well as the feedwater system from the city of Toronto. There were further energy storage system shutdowns triggered by requirements for external electrical and plumbing maintenance. In summary, it was unrealistic for Ontario Hydro to expect that a complex load control and energy storage system would work 100% of the time. The overall result would have been better if the expectation was for the system to work 90% of the time. However, the peak demand meters that were readily available in the 1960s were not practical for daily peak demand measurements.

TODAY:
Today in 2009 there are electronic interval kWh meters that easily allow recording the daily peak demand. Use of such meters allows establishment of an electricity rate that encourages building owners to maximize their effectiveness of electricity system usage every day. Directional electronic interval kWh meters can be used to further incent high power factor, which increases electricity system efficiency.

CONGESTION FACTOR:
A congestion factor is a mathematical device used to reward high daily load factor and high daily generator capacity factor. A congestion factor increases electricity cost if the pattern of electricity usage increases congestion on the transmission/distributon system and reduces electricity cost if the pattern of electricity usage reduces congestion on the transmission/distribution system.

This web page derives electricity rate congestion factors that financially encourage high generator capacity factor and high customer load factor. These congestion factors are applicable to generators and load customers that are not dispatched by the Independent Electricity System Operator(IESO). These congestion factors are intended to financially enable behind the meter energy storage

The present electricity rate for residences and smaller businesses implicitly assumes that all electricity kWh are of equal value. The problem with this rate structure is that it does not convey to either generators or load customers the appropriate signal as to the equipment and operational changes that these parties should adopt to reduce both their own costs and overall electricity system costs.

The message that should be communicated via the electricity rate structure is that generators not subject to IESO dispatch should operate at very high net capacity factors and load customers not subject to IESO dispatch should operate at very high net load factors. Behind the meter energy storage should be used to increase net load factor or net generator capacity factor.

One of the properties of a balanced 3 phase constant resistive load is that its power drain from the grid is constant. Hence, for such a load, the instantaneous power is equal to the average power. This is the most efficient way of coupling to the grid and at any particular time should attract the lowest transmission/distribution charges per kWh of energy transferred.

Inefficient use of the transmission/distribution system should be financially penalized. If a customer presents a reactive impedance, harmonic distortion or a fluctuating load to the grid then that customer should be allocated a larger fraction of the transmission / distribution costs.

The higher the uncontrolled fluctuations in power transfer rate, the less efficiently the generation and transmission/distribution systems are utilized. If a customer presents a resistive load that varies from measurement interval to measurement interval that customer should be charged more per kWh for for generation and transmission/distribution than is a customer that draws energy at a constant rate.

A practical method of encouraging wide spread increases in generator capacity factor and customer load factor is introduction of congestion factors into the electricity rate structure.

Due to the daily electricity system load variation, which causes both expensive peaking generation and transmission/distribution congestion at on-peak times, the electricity rate congestion factors should encourage peak demand reduction and should encourage distributed generators to level their outputs. The congestion factors must be computed the same way for all parties.

The function of congestion factors is to financially reward parties that maintain high load factors or high generator capacity factors. Congestion factors operate by causing the average cost of net received energy per kWh to decrease as the load factor increases and by causing the average revenue per kWh from net transmitted energy to increase as the generator capacity factor increases.

Incorporation of congestion factors into electricity rates encourages wind generators and customers with highly variable loads to build energy storage behind their meters to reduce variations in the rate of power transfer to and from the grid. Congestion factors are calculated daily to minimize the financial impact of occasional random equipment shutdowns that affect the peak power transferred to or from the grid.

Congestion factor functions must meet the following criteria:
1. Shifting an average load from a non-congestion factor rate scheme to a congestion factor based rate scheme should not significantly change the electricity cost for that load;
2. Shifting an average generator from a non-congestion factor rate scheme to a congestion factor based rate scheme should not significantly change the revenue for that generator;
3. The congestion factor must reward high load factor sufficiently to financially enable behind the meter energy storage, but that reward must have a well defined upper limit;
4. The congestion factor must reward high generation capacity factor sufficiently to financially enable behind the meter energy storage, but that reward must have a well defined upper limit;
5. The congestion factor must not reward low power factor;
6. The congestion factor must not excessively penalize very low load factor;
7. The congestion factor mathematical functions should be continuous instead of in time blocks so that they do not cause power system instabilities;
8. The congestion factor mathematical functions must be readily understandable.

The congestion factor applied to electricity cost is:
[exp(-K Lf)]/[exp(-K Lfa)]
for load customers where Lf is the net load factor, Lfa is an industry average load factor and K is a constant chosen to financially enable behind the meter energy storage.Typically K is close to unity.

The congestion factor applied to the electricity price received by a generator is:
[1 - exp(-K Cf)]/[1 - exp(-K Cfa)]
where Cf is the net generator capacity factor and K is the constant chosen to financially enable behind the meter energy storage. Typically K is close to unity.

DEFINITIONS:
Let Er = cumulative energy received by the customer from the grid as registered by an electronic kWh meter with a sampling rate > 3600 power samples / second;
Let Et = cumulative energy transmitted by the customer to the grid as registed by an electronic kWh meter with a sampling rate > 3600 power samples / second;
Let Cr = cost per kWh of energy received by the customer from the grid;
Let Ct = price per kWh of energy transmitted by the customer to the grid;
Let Cd = transmission/distribution charge per kWh received or transmitted by the customer at a unity power factor;
Let T = time;
Let "measurement interval" refer to the time between successive recordings of Er, Et and T by an electricity meter;
Let T = Ta at the beginning of a measurement interval;
Let T = Tb at the end of a measurement interval;
Let Ero = value of Er at the beginning of a 24 hour day;
Let Erf = value of Er at the end of a 24 hour day;
Let Eto = value of Et at the beginning of a 24 hour day;
Let Etf = value of Et at the end of a 24 hour day;
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 Ca = administration charge that is the same for all customers in a rate group.
Let Pm = daily maximum value of [(Erb - Era) - (Etb - Eta)] / [Tb - Ta];
Let Gm = daily maximum value of [(Etb-Eta) - (Erb - Era)] / [Tb - Ta]
Let Ci = unadjusted daily electricity cost
Let Cia = adjusted daily electricity cost
Let Lf = load factor
Let Lfa = industry average load factor
Let Cf = generator capacity factor
Let Cfa = industry average generator capacity factor
Let F(B) = function of [(Etb-Eta)/(Erb-Era)] as set out in the section titled Electricity Power Factor, where:
B = phase angle, 1 < F(B) < 3.1415928, F(0) = 1.0, F(3.14/2) = 3.14

UNADJUSTED ELECTRICITY COST:
As shown in the section titled Electricity Rate Issues the general equation for the electricity cost for customer i in measurement interval j is:
Cij = {[Cr(Erb - Era) - Ct(Etb - Eta)]ij + [Cd|(Erb-Era) - (Etb-Eta)|/cos(B)]ij} + Ca

For each measurement interval either (Erb-Era) > (Etb - Eta) or (Erb - Era)< (Etb - Eta).

If (Erb - Era) > (Etb - Eta) and the general equation simplifies to:
Cij = [(Cr + (Cd F(B)))((Erb - Era) - Ct(Etb - Eta))]ij + Ca

and if (Erb - Era) < (Etb - Eta) and the general equation simplifies to:
Cij = [Cr(Erb - Era) + (-Ct+(Cd F(B)))(Etb - Eta)]ij + Ca

The metering system records the Er, Et and T values at the end of each measurement interval. After each 24 hour day the data is analysed. For each measurement interval the values (Erb - Era) and (Etb - Eta) are calculated. The relative sizes of (Erb - Era) and (Etb - Eta) are used to determine which of the above formulae is used to calculate Cij for the measurement interval.

The grid customer's daily unadjusted electricity cost Ci is the sum over all j of the individual measurement interval costs for that day. Note that net generation results in a negative electricity cost.

CONGESTION FACTOR CALCULATION PROCEDURE:
For each measurement interval the net received power P given by:
P = [(Erb - Era) - (Etb-Eta)]/(Tb - Ta)
is calculated. The daily maximum value of P = Pm is recorded.

For each measurement interval the net generated power G given by:
G = [(Etb - Eta) - (Erb-Era)]/(Tb - Ta)
is calculated. The daily maximum value of G = Gm is recorded.

The net daily energy consumption is given by:
[(Erf - Ero) - (Etf-Eto)]

The daily load factor Lf is given by:
Lf = ((Erf-Ero) - (Etf-Eto))/(Pm 24h)

The daily generation capacity factor Cf is given by:
Cf = ((Etf-Eto) - (Erf-Ero))/(Gm 24h)

If the unadjusted cost Ci is positive the grid customer is treated as a load for that day. If Ci is negative the grid customer is treated as a net generator for that day.

If Ci > 0 the grid customer is treated as a net load and the adjusted daily cost Cia is given by:
Cia = Ci [exp(-K Lf)]/[exp(-K Lfa)]
or
Cia = Ci exp(-K (Lf - Lfa))
where Lfa is an industry average daily load factor.

If the daily load factor is 1.0 the lowest possible average electricity cost is attained.
If Lf < Lfa and the consumption is unchanged the electricity cost increases.
If Lf > Lfa and the consumption is unchanged the electricity cost decreases.

If Ci < 0 the customer is a net generator and the payment, which is a negative cost, is:
Cia = Ci [1 - exp(-K Cf)] / [1 - exp(-K Cfa)]
where Cfa is an average generator capacity factor.

If Cf > Cfa the average electricity price realized by the generator increases.
If Cf < Cfa the average electricity price realized by the generator decreases.

If the generator capacity factor Cf = 1.0 the average electricity price achieved by the generator is maximized.

REACTIVE LOADS:
Pure reactive loads cause positive Cij values which cause the grid customer to be treated as a load. For a pure reactive load:
(Erb - Era) = (Etb - Eta)
which means that the grid customer is charged the high electricity rate corresponding to Lf = 0. This is a substantial disincentive for poor power factor.

CALCULATION OF K:
Recall that for a load:
Cia = Ci exp(-K (Lf - Lfa))

We can compare daily electricity cost Cia1 before installation of an energy storage system with daily electricity cost Cia2 after installation of an energy storage system avia the ratio:
Cia2/ Cia1 = (Ci2/Ci1) [exp(-K(Lf2 - Lfa))]/[exp(-K(Lf1 - Lfa))]
or
Cia2/Cia1 = (Ci2/Ci1) [exp(-K(Lf2 - Lf1)]

Initial monthly load factor = .30
Assume that the load customer is an office building which is open five days per week and is closed on the weekends. Assume that prior to installation of energy storage the monthly load factor from the electricity bills is 0.30. However, since there is no weekend consumption, the initial daily load factor Lf1 on occupied days is:
Lf1 = .30 (7/5) = .42
The theoretical best daily load factor improvement is:
1.0 - .42 = .58
Allowing for 10% downtime for the energy storage system, the economic model should work at a daily load factor improvement of:
Lf2 - Lf1 = 0.9(.58) = 0.53
Hence the load factor Lf2 after installation of the energy storage system is:
Lf2 = .42 + .53 = .95
Thus, without exceeding the previously set peak demand the electricity purchases from the grid can increase by a factor of:
Ci2/Ci1 = .95/.42 = 2.26
Assume that to financially enable energy storage the cost of the extra electricity purchased must be (1/4) the cost per kWh of the original electricity purchased. Hence the total cost of electricity increases by:
Cia2/Cia1 = 1 + (1.26/4) = 1.315.
Hence substituting into:
Cia2/Cia1 = (Ci2/Ci1) [exp(-K(Lf2 - Lf1)]
gives:
1.315 = 2.26 exp(-K(.53))
or
exp(.53K) = 2.26/1.315 = 1.719
or
.53K = Ln(1.719) = .5417
or
K =.5417/.53 = 1.022
If the storage system has an efficiency of .65, the fractional extra usable extra electricity is:
.65(1.26)=.819
Thus the available usable electricity has increased from 1 to 1.819. Hence, after installation of energy storage the peak demand setpoint can in principle be reduced by a factor of about (1 / 1.819).

Initial monthly load factor = .40
Assume that an office building is open five days per week and is effectively shut off on the weekends. Assume that the monthly load factor from the electricity bills is 0.40. However, since there is no weekend consumption, the initial daily load factor Lf1 on occupied days is:
.40 (7/5) = .56.
The theoretical best daily load factor improvement is:
1.0 - .56 = .44
Allowing for 10% energy storage downtime, the economic model should work at a daily load factor improvement of:
Lf2 - Lf1 = 0.40
Thus, without exceeding the previously set peak demand the electricity purchases from the grid can increase by a factor of:
Ci2/Ci1 = .96/.56 = 1.714
Assume that to financially enable energy storage the cost of the extra electricity purchased must be (1/4) the cost per kWh of the original electricity purchased. Hence the total cost of electricity increases by:
Cia2/Cia1 = 1 + (.714/4) = 1.1785
Recall that:
Cia2/Cia1 = (Ci2/Ci1) [exp(-K(Lf2 - Lf1)]
Substituting into this equation gives:
1.1785 = 1.714exp(-.40K)
or
exp(.4K) = 1.714/1.1785 = 1.454
or
.4K = Ln(1.454) = .375
or
K = .375/.4 = .936
If the storage system has an efficiency of .65, the usable extra fraction of electricity is:
.65(.714)=.4641
Thus the available usable electricity has increased from 1 to 1.4641.
Hence, in principle, after installation of the energy storage system the peak demand setpoint can be reduced by a factor of (1 / 1.4641).

Initial monthly load factor = .50
Consider an identical building that has an initial monthly load factor of 0.5. Since there is no weekend consumption, the daily load factor on occupied days is:
Lf1 = .50 (7/5) = .70
The theoretical best daily load factor improvement is:
1.0 - .70 = .30
Allowing for 10% downtime, the economic model should work at a daily load factor improvement of:
Lf2 - Lf1 = 0.26
Thus, without exceeding the previously set peak demand the electricity purchases from the grid can increase by a factor of:
Ci2/ci1 = .96/.70 = 1.371
Assume that to financially enable energy storage the cost of the extra electricity purchased must be (1/4) the cost per kWh of the original electricity purchased. Hence the total cost of electricity increases by:
Cia2/Cia1 = 1 + (.371/4) = 1.0928
Hence, substituting into:
Cia2/Cia1 = (Ci2/Ci1) [exp(-K(Lf2 - Lf1)]
gives:
1.0928 = 1.371exp(-.26K)
or
exp(.26K) = 1.371/1.0928 = 1.255
or
.26K = Ln(1.255) = .2271
or
K = .2271/.26 = .873
If the storage system has an efficiency of .65, the usable extra electricity is:
.65(.371)=.241
Thus the available usable electricity has increased by a factor of 1.241. Hence the peak demand setpoint can in principle be reduced by a factor of:
(1 / 1.241)

Various practical examples indicate that K should be in the range:
0.9 < K < 1.1

SUBMETERING:
Consider a building complex with ordinary kWh submeters. If in a one day period the bulk meter indicates [(Erf - Ero)-(Etf-Eto)] and if for the same day a submeter indicates [(Esf - Eso)], then the received energy cost allocated to the submetered zone is:
{[(Esf - Eso)]/[(Erf - Ero)-(Etf-Eto)]} Cia
where Cia is the value of Ci after congestion factor adjustment.
All of the submeters are permitted to share in the benefits of any energy storage or load management in the building.

NUMERICAL EXAMPLE:
Now numerically investigate the effect of Lf on average cost / kwh. Assume K = 1.0:
For Lf = 1.0:
[exp(-K Lf)] = .3678
 
For Lf = 0.9:
[exp(-K Lf)] = .4065
 
For Lf = 0.5:
[exp(-K Lf)] = .6065
 
For Lf = 0.4:
[exp(-K Lf)] = .6703
 
For Lf = 0.3:
[exp(-K Lf)] = .7408
Thus there is a significant electricity cost advantage in increasing load factor. However, part of this cost advantage will be offset by storage loss. A good rule of thumb is that the unit cost of energy that goes into the storage system must be less than one third of the cost of energy that does not go into the storage system in order to make the storage system financially viable.

RELATIVE VALUES OF GENERATION TYPES:
Recall that for a generator:
Cia = Ci [1 - exp(-K Cf)] / [1 - exp(-K Cfa)]

Compare generation type #1 with generation type#2. Then: Cia2/Cia1 = (Ci2/Ci1)[1 - exp(-K Cf2)] / [1 - exp(-K Cf1)]

If both generators output the same amount of electricity:
ci2 = Ci1
giving:
Cia2/Cia1 = [1 - exp(-K Cf2)] / [1 - exp(-K Cf1)]
With K = 1.0 the value of a kWh from nuclear at generator capacity factor:
Cf2 = 0.90
as compared to the value of a kWh from wind at generator capacity factor:
Cf1 = 0.30
is:
Cia2/Cia1 = (1 - exp(-K(.9))/ (1 - exp(-K(.3))
= (1 - .4065) / (1 - .7408)
=.5934/.2592
= 2.29
Significant departure from this relationship, unless justified by changes in generator capacity factor, will result in economically unsustainable electricity pricing.

Increasing the generator capacity factor increases the value of the generated energy. However, part of this increase in energy value may be offset by storage loss.

This web page last updated March 28, 2009.