Intertemporal Considerations for Supply
Offer Development in Deregulated
Electricity Markets
P.A. Stewart, E.G. Read and R.J.W. James
Department of Management
University of Canterbury
New Zealand
[email protected]
Abstract
The literature refers to several methods for developing supply offers for generators in
wholesale electricity markets, all of which consider much more simplified
environments than those that occur in reality. In particular, we consider the approach
suggested by Anderson and Philpott, which involves forecasting and updating a
“market distribution function”. The market distribution function describes the
probability that a section of an offer curve at any point within the likely ranges of
(price, quantity) offering space will be accepted by the market. This function is then
used to produce an optimal offer.
The focus of this paper is the construction of offering strategies that consider
intertemporal linkages, such as those that may arise in hydroelectric systems or with
inflexible thermal units. The nature of these intertemporal linkages is diverse. Some
relate to linkages within a generating company, such as start-up and shut-down costs,
ramp-rate restrictions, limited water availability over time, hydro inflows, and hydro
reservoir storage bounds. A much more subtle set of linkages relate to the behaviours
of other participants in the offering process, including the patterns in rival offers as
time progresses. To date, the work of Philpott and Anderson produces offers for
single periods only. None of the intertemporal characteristics and restrictions of the
generation units are considered, and thus the offers may not be optimal when viewed
over several periods.
It can be shown, for example, that when stochastic intertemporal effects are taken into
account, the “optimal” offer from a hydro system will not necessarily be
monotonically non-decreasing, as generally is required by market rules. It is also
apparent that the optimal form of offers will change as real-time is approached and
various uncertainties are resolved. Clearly, these issues require modification of the
market distribution function approach, which doesn’t account for these intertemporal
characteristics. We therefore examine practical methods for forecasting market
distribution functions to account for these issues, in addition to investigating their
relation to the optimal offering strategy.
Intertemporal Considerations for Supply Offer Development in Deregulated Electricity Markets
Paul Stewart, Grant Read, Ross James
[email protected]
Intertemporal Considerations
1) Linkages within a generating company
•
•
Technical Costs and Constraints
Water Considerations
2) Effects due to forecasting of market clearing prices and system load
3) Reactions of other participants in the offering process
•
•
Rival forecasting
Repercussions from a generator’s offering strategy
New Zealand Market
BIG PICTURE OF NZ
The NZ Electricity Network
offers under uncertain prices
HydroHydro
offers
under uncertain prices
100
100
90
90
80
80
70
70
60
60
Price 50
Price 50
40
40
30
30
20
20
10
10
00
0.0
0.0
50.0
50.0
100.0
100.0
150.0
150.0
200.0
200.0
250.0
250.0
Quantity
Quantity
300.0
300.0
350.0
350.0
400.0
400.0
450.0
450.0
500.0
500.0
Hydro and Energy‐Limited Thermal Generation
For a single unit, the more they generate now, the less they can generate later (due to limited fuel resources). Marginal Costs ‐ Opportunity Costs
Optimal offer dependent on marginal costs and the position of any steps in the marginal cost curve Hydro and Energy‐Limited Thermal Generation
Residual Demand
For Hydro/ELT, don’t know marginal cost and its steps in advance
60
50
Price
40
($/MWh)
Optimal Offer Surfaces
Optimal price to offer for each quantity level, given the marginal cost at that level
Offer Stack
Residual Demand
30
Dispatch
20
Families of Offer Curves
10
Members = optimal offer for given uncertain residual demand curve for a constant marginal cost
0
0
20
40
Patch these together in real‐time with up‐to‐date marginal cost information Market Distribution Function
60
80
100
Quantity (MWh)
Stochastic Residual Demand
EPOC – Philpott, Anderson, Neame, Zakeri, Pritchard
EPOC ‐ Market Distribution Function (ψ)
50
Probability that an offer at any given (q, p) point will not be dispatched
Price
50
Constructing/Updating:
Anderson and Philpott (2001) – Bayesian Updating
Pritchard et al (2002) – Maximum Likelihood
20
Price
Expected
Residual
Demand
Expected Residual
Demand
50 Quantity
Offer Generation:
Anderson and Philpott (2002a), Anderson and Philpott (2002b), Neame
et al (2003), Philpott et al (2002)
20
50
Quantity
Optimal Offers – Numerical Examples
⎧30 − 0.5q
p=⎨
⎩44 − q
Optimal Offers – Numerical Examples
p ≥ 16
p < 16
MC = 2, 5, 25, BP = 8, 43
50
MC = 5
Price 45
MC = 2
40
MC = 25
35
30
σ=2
25
20
15
σ = 1 10
5
0
0
5
10
15
20
25
30
35
40
45
50
Quantity
Optimal Offer Form –
Concave Residual Demand
Marginal Revenue
Construction of the Optimal Offer
55
55
10
10
10
10
15
15
15
15
20
20
20
20
25
25
25
25
Quantity
Quantity
Quantity
Quantity
Quantity
30
30
30
30
35
35
35
35
40
40
40
40
45
45
45
45
45
Residual
Residual Demand
Demand
BP(Q)
BP(Q)
BP(P)
BP(P)
50
50
50
50
50
50
50
50
Optimal Offer
Optimal Dispatch Point
00
00
Marginal
Marginal Revenue
Revenue
Construction of the Optimal Offer
Residual Demand
BP(Q)
BP(P)
50
50
50
50
45
45
50
45
50
45
50
40
50
40
45
40
45
40
45
45
35
40
35
40
35
40
35
40
35
30
35
35
30
30
35
30
30
30
Price
30
Price 25
Price
25
Price
Price 25
25
20
20
20
20
15
15
15
15
10
10
10
10
5
555
0
0
00
Optimal Offer Form –
Convex Residual Demand
50
50
50
50
45
45
45
45
45
45
45
45
Optimal
Optimal Offer
Offer
Optimal
Optimal Dispatch
Dispatch Point
Point
40
40
40
40
40
40
40
40
50
35
35
35
35
35
35
35
35
45
30
40
30
30
30
30
30
30
30
3525
Price
25
Price
Price
Price
Price
25
25
25
25
Price
Price
25
Price 25
30
20
20
20
20
20
20
20
Price 25
20
15
15
15
15
15
15
20
15
15
15
10
10
10
10
10
10
10
10
1010
5555555
555
0000000
00
0
0000000
000
55
555
10
10
10
10
10
10
10
10
10
10
15
15
15
15
15
20
20
20
20
20
20
20
20
20
25
25
25
25
25
Quantity
Quantity
Quantity
Quantity
Quantity
Quantity
Quantity
Quantity
30
30
30
30
30
30
35
35
35
35
40
40
40
45
45
45
50
50
50
50
50
50
Optimal Offers – Numerical Examples
Optimal Offers – Numerical Examples
MC = 0, 10, 25, BP(Q) = 12, 31
MC = 0
50
MC = 10
Price 45
MC = 25
40
35
30
25
20
15
10
5
0
0
5
10
15
20
25
30
35
40
45
Quantity
Research Direction
Goal
Intertemporal Considerations for Supply Offer Development in Deregulated Electricity Markets
• Offering Strategy under uncertainty (intertemporal focus)
• Real‐time Optimal Offer Decisions • For reservoir level, marginal cost curve combination
Approach and Extensions
• Stochastic Dynamic Programming
• Limited Tranches, Thermal Applications, General Uncertainty
Paul Stewart, Grant Read, Ross James
[email protected]
50