Gross margin and components to provide regulation FCAS
This page derives the gross margin gained from providing regulation services. The components as well as key variables are included in the Financial reports in FCAS-pays. Note that regulation FCAS cost recovery, i.e. the Area Portfolio Factors, are not included in this equation.
A derivation of Gross Margin
Assuming FCAS bids are not a function of energy bids (co-optimisation or stranded not withstanding) then a unit's gross margin equation for raise and lower services respectively follow.
| Raise Regulation Gross Margin (divide by 12 for a 5 minute dispatch interval) = | |||||
| Raise regulation revenue | + ∆ Electricity spot revenue | – Causer pays | – ∆ Fuel used | – Trip Risk (usually negligible) | – other terms |
| Raise enabled × RaiseRegRRP | + Utilisation1 × Raise enabled × RRP | – RaiseregRRP × Total Requirement × Causer pays participant factor | – Fuel cost × Utilisation × Raise enabled – Dynamic costs2 | – Cost of trip × ∆ Probability of trip | |
| Lower Regulation Gross Margin (divide by 12 for a 5 minute dispatch interval) = | |||||
| Lower regulation revenue | – ∆ Electricity spot revenue | – Causer pays | + ∆ Fuel used | – Trip Risk (usually negligible) | – other terms |
| Lower enabled × LowerRegRRP | – Utilisation × Lower enabled × RRP | – LowerregRRP × Total Requirement × Causer pays participant factor | + Fuel cost × Utilisation × Lower enabled – Dynamic costs | – Cost of trip × ∆ Probability of trip | |
Optimising gross margin is the objective of bidding into the spot market. Generally only the value of regulation revenue is considered however, as shown above, gross margin is a function of a number of other value components.
The change in the Electricity spot revenue is due to a unit's response to AGC (or other control systems) that results in a change in electricity generated and hence electricity revenue. This occurs even though there is no change to the energy bid.
1 Utilisation is defined as the proportion of a regulation service enablement that is actually used - that is to say the actual change in generator output caused by instructions to provide regulation FCAS. In theory this is a number between 0 and 1 and in practice is nearly always between 0 and 1 (there is a difference between a unit's instruction and response to that instruction).
Causer pays is the participants liability of the total cost of regulation services to the market (or regional component of the market). The portion of the total cost is represented by the participant's causer pays participation factor.
The change in the fuel used follows the same logic that electricity spot revenue changes.
2 Dynamic costs are derived from the change in the efficiency curve of the generator caused by the rate of change in generator output. Given an equal generation of energy, a unit with changing output will consume more fuel than a unit with steady output. This term is optional and requires information specific to the power station.
The cost of trip risk represents the cost of a trip multiplied by the change in the probability of a trip. The derivation of this value is very specific to the unit and often negligible. I shall provide two ways to consider this risk: first, providing regulation FCAS will increase wear on the unit. Power engineers have advised me that any change in wear of a units components is not material enough to change an outage schedule nor the maintenance programme therefore no cost can be directly derived from the impact on maintenance. However they advised that the reason for maintenance is partly to improve unit reliability and therefore the impact on value should be assessed on the increase in the probability of a unit trip. The second case is that providing FCAS will increase the risk of a trip due to vibration issues, this risk is likely to be only material for some units such as old hydro units.
Dynamic and trip costs are always negative.
Mathematics and Optimisation
This section symbolises the equations shown in "a derivation of Gross Margin (above)" and shows the terms as a function of utilisation and enablement. Regulation price is a function of enablement due to price elasticity.
Round brackets use the convention of x = x(y). That is to say for any particular point in time, x is a function of y. Square brackets will replace normal brackets so that 2[7 - 3] = 8. I will symbolise the lower regulation service. The same follows for the raise service except the sign on the change in spot revenue and the fuel used is opposite.
| Lower Regulation Gross Margin (divide by 12 for a 5 minute dispatch interval) = | |||||
| ML = EL PL(EL) – UL EL N – PL(EL) QL K + F UL EL – D(EL, UL) – C T(EL, UL) | |||||
Lower regulation revenue | – ∆ Electricity spot revenue | – Causer pays | + ∆ Fuel used | – Trip Risk (usually negligible) | – other terms |
Lower enabled × LowerRegRRP EL × PL(EL) | – Utilisation × Lower enabled × RRP – UL × EL × N | – LowerregRRP × Total Requirement × Causer pays participant factor – PL(EL) × QL × K | + Fuel cost × Utilisation × Lower enabled – Dynamic costs + F × UL × EL – D(EL, UL) | – Cost of trip × ∆ Probability of trip – C × T(EL, UL) | |
For simplicity I shall drop the Dynamic and Trip risk costs. However it is worth noting that both the first and second derivative of the dynamic and trip risk cost with respect to enablement are negative (at least that is my claim).
Summary of terms |
|---|
E = Enablement (MW) P(E) = Regulation Price as a function of Enablement ($/MW/hr) U = Utilisation, a value between 0 and 1 N = Electricity Price, RRP ($/MWhr) Q = Total regulation requirement (for the region(s)) (MW/hr) K = Causer Pays Participation Factor (%) F = Fuel Cost ($/MWhr) |
Removing the subscripts to denote raise and lower service, re-arranging the equations and dropping the dynamic and trip risk costs we get:
| Lower Regulation Gross Margin |
| ML = P(E) [E – QK] – E U [N – F] |
| Raise Regulation Gross Margin |
|---|
| MR = P(E) [E – QK] + E U [N – F] |
With negative signs in the equation one has to ask the question: when does providing regulation services result in negative gross margin?
P(E) is highly non-linear but for simplicity assume that P ≠ P(E), i.e. P = constant.
| Lower Regulation Gross Margin with P = constant |
ML = P [E – QK] – E U [N – F] to find when an increase in gross margin results with an increase in enablement find where dM/dE > 0, rearranging M, |
M = E [ P – UN + UF ] – QKP, taking the derivative dM/dE = P – UN + UF |
then dM/dE > 0 , when U < P / [ N – F ] |
| Raise Regulation Gross Margin with P = constant |
Very similar to Lower Reg but with a reversal of the sign, hence dM/dE > 0 when U < P / [ F – N ] |
Observation
Gross margin is a function of the utilisation of the service, U, the energy price, N, and the regulation price, P(E) (which also is a function of enablement of the regulation service). These terms are very dynamic. pdView has the algorithms and data to accurately estimate these values.
Example Chart and Simplified Gross Margin Equation
The chart plots an example of gross margin (and the components) for a single unit (or station) against the control variable being the enablement volume (which is controlled by the lower regulation bid).
| Lower Regulation Gross Margin |
|---|
| ML = E P(E) – U E N – P(E) Q K + F U E |
| ML = P(E) [E – Q K] + E U [F – N] |
Chart inputs
- E is the control variable shown as the x-axis.
- ML is the dependent variable shown as the y-axis.
- P(E) varies between $10 and $20 (to account for price elasticity). Shown as thin purple line on chart.
- U = 25%
- N = $250 /MWhr
- Q = 150 MW
- K = 2%
- F = $20 /MWhr
In this example the foregone energy revenue (in the spot market) dominates the components of the gross margin. In this scenario the lower regulation bid volume is considerably under priced in order to achieve a positive gross margin.
