Supply Function Models in Electricity Markets Andy Philpott Energy - - PowerPoint PPT Presentation

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supply function models in electricity markets
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Supply Function Models in Electricity Markets Andy Philpott Energy - - PowerPoint PPT Presentation

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Supply Function Models in Electricity Markets Andy Philpott Energy Centre Workshop, February 22, 2007. Motivation Many pool markets use supply-function offers but most models are Cournot even though with uncertainty in

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Energy Centre Workshop, February 22, 2007.

Andy Philpott

Supply Function Models in Electricity Markets

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Energy Centre Workshop, February 22, 2007.

Motivation

  • Many pool markets use supply-function offers…
  • …but most models are Cournot…
  • …even though with uncertainty in demand the

SF model gives more realism.

  • Why? SFE models [Wilson (1979), K&M(1989)]

are difficult to work with.

  • Market distribution function is a powerful tool to

work with supply functions.

  • Aim to illustrate this by some examples.
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Energy Centre Workshop, February 22, 2007.

Residual demand curve

p q

Optimal dispatch point to maximize profit

S(p) = supply curve from other generators D(p) = demand function RDC = D(p) – S(p) R(q,p) = qp – C(q)

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Energy Centre Workshop, February 22, 2007.

A distribution of residual demand curves

p q

Optimal dispatch point to maximize profit

RDC shifted by random demand shock d

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p q

One supply curve optimizes for all demand realizations

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This doesn’t always work

p q

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Energy Centre Workshop, February 22, 2007.

p q

Suppose

  • these functions are log concave (e.g. qn)
  • generator cost function is convex

Then a monotonic optimal supply curve exists

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Energy Centre Workshop, February 22, 2007.

The monotonicity theorem

[Anderson and Philpott, 2002]

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Energy Centre Workshop, February 22, 2007.

The market distribution function

[Anderson and Philpott, 2002]

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Energy Centre Workshop, February 22, 2007.

Application: offer curve optimization

  • BOOMER (Pritchard)
  • Single period simulation/optimization model
  • Model (uncertain) generator stacks of competitors by

sampling from probability distributions

  • Solve pricing-dispatch problem for every sample
  • Construct optimal stack for particular objective in mind
  • Objective can include contracts, FTRs, retail load
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Energy Centre Workshop, February 22, 2007.

Contracts

A contract for differences (or hedge contract) for a quantity Q at a strike price f is an agreement for one party (the contract writer) to pay the

  • ther (the contract holder) the amount Q(f-p)

where p is the spot price. Having written a contract for Q, the generator seeks to maximize R(q,p) = qp - C(q) + Q(f-p)

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Energy Centre Workshop, February 22, 2007.

Example market distribution function

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Energy Centre Workshop, February 22, 2007.

Generator’s objective function

Owner of Huntly might have wanted to maximize Gross revenue at HLY + TKU + RPO –$35/MWh fuel cost at HLY –cost of purchases to cover retail base of

  • 25% at MDN/HND/OTA/WKM
  • 10% at ISL/HWB

accounting for hedge contracts at $50/MWh of

  • 250MW at OTA
  • 150MW at HAY
  • 50 MW at HWB

(Numbers are illustrative only!)

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Energy Centre Workshop, February 22, 2007.

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Energy Centre Workshop, February 22, 2007.

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Behaviour of optimal supply curves

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Application: the value of vertical integration

OTA S(p)=p q(p) ? d d (MRP) (Mercury) Other (competitive) generators Other retail

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Optimal offer of gentailer

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Optimal offer with vertical integration

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Compare a contract Q at price π

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Optimal offer with contract

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The best payoff obtainable by contracting

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Compare payoffs

The joint payoff when vertically integrated is The joint payoff when contracted optimally is The difference in expectation is

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Symmetric supply function equilibria

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Symmetric SFE when holding contracts

[Anderson and Xu 2001]

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Symmetric Cournot equilibrium with contracts

Assume constant marginal cost c and a linear inverse demand curve P(x) = A - Bx Nash equilibrium offer for each agent is 3B+c A+BQ q =

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Energy Centre Workshop, February 22, 2007.

Symmetric SFE (A=4, B=1, c=1, Q=2)

1 2 3 4 p 1 2 3 4 q

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SFE with transmission losses [P & Jofre (2006)]

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Strong and weak SFE

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Existence of weak SFE

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Example of strong SFE in network

1 S1(p) d-p 2 d-p S2(p) y y – 0.2y2 y + 0.2y2 Generation cost = 0.5q2

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Energy Centre Workshop, February 22, 2007.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

p S(p) S(p)=(√3-1)p

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Energy Centre Workshop, February 22, 2007.

Pay-as-bid auction models [Anderson & P (2007)]

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Behaviour of optimal curves

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Symmetric pay-as-bid SFE

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Comparison PABA and uniform

2000 4000 6000 8000 10000 200 400 600 800 1000 Source: Holmberg (2006)

Uniform price PABA average price PABA bid

Demand Price

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Example: uniform demand shock

q+p=1 Z>0 Z<0 Optimal offer (c=0)

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Mixed-strategy SFE

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Mixed-strategy SFE

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Conclusions

  • Supply function models are appropriate in

presence of uncertainty (e.g. demand)

  • Give qualitatively different answers to

Cournot models.

  • Analytical difficulties can be attacked

using market distribution functions.

  • Difficulties remain in general settings (but

these are not just SFE problems)