Equilibrium modelling of beneficiary-pays transmission charges

Equilibrium modelling of beneficiary-pays transmission charges Prof. Andy Philpott, Dr. Anthony Downward EPOC Winter Workshop 2013

Background / Motivation • The EA has proposed that, in order to fund current/future investments in the transmission grid, a beneficiary-pays scheme ought to be introduced. • The fundamental aim of this scheme is that those who benefit from the investment will be required to pay for the investment (in proportion to their benefit). • While the aim of this pricing mechanism may be fair, problems arise in actually being able to compute the benefits created by adding an asset to the grid. • The key proposal was that SPD would be run, with and without an asset (e.g. a transmission line), and the difference in an offers’ infra-marginal rent would be treated as the benefit.

Overview • Beneficiary-pays Pricing • Computation of Rentals / Benefits • Incentives to Reduce Rentals / Benefits • Supply Function Modelling • Uniform Pricing • Pay-as-bid Pricing • Supply Function Equilibrium Examples • Single-node – tax on rentals • Two-node symmetric quadropoly– tax on benefits • Conclusions

Transmission Pricing Methodology Consultation Paper (2012) Beneficiary-pays Pricing • Run dispatch software with transmission asset and record dispatch and price. • Compute infra-marginal rental of agent , for each . • Re-run software with transmission asset derated to represent previous (counterfactual) state, recording new dispatch and price. • Compute counterfactual rent of agent , for each . • Charge a proportion of benefits to agent . Suppose the cost of the asset is . Then the proportion of benefits paid by agent is:

Transmission Pricing Methodology Consultation Paper (2012) Beneficiary-pays Pricing

Incentives to Reduce Charges • After the transmission pricing proposal was announced, there were concerns over the way the benefits would be computed. • Particularly, the ‘profit’ of a firm would be assumed to infra-marginal rental. Price P D Quantity (MW)

Price Price Incentives to Reduce Charges P P • Thus, in a context where firms are charged based on infra-marginal rentals, there may be incentive to mark-up infra-marginal offers so as to reduce these rents. • We will explore these incentives through a supply function equilibrium duopoly. D D Quantity (MW) Quantity (MW)

Incentives to Reduce Charges • EA TPM Consultation Presentation November 2012: • “Parties may be able to alter their offers to avoid the charge e.g. South Island generators could reduce their beneficiaries-pay charge for Pole 3 by offering as if only Pole 2 was available. • “To the extent parties can do this it would reveal the asset is not economically justified unless the SPD charge recovered costs from other beneficiaries e.g. costs of Pole 3 may be able to be recovered through the SPD charge from consumers.”

Supply Function Auction • Agents offer supply functions indicating how much they will supply at price . Let be the corresponding offer curve. • There is a demand curve and a random demand shock . • Demand realization occurs and all agents are paid: • a uniform price defined by the relation • for their respective dispatch quantity .

Price Supply Function Auction D(p) D(p)+h ∑S(p) p Quantity (MW)

Anderson and Philpott (2002), Wilson (1979) Market Distribution Function • The market distribution function defines the probability that a supplier is not fully dispatched if they offer the quantity at price . • It can be interpreted as the measure of residual demand curves that pass below and to the left of the point . • Random residual demand curves faced by a supplier. Here is the probability of a curve being red.

Anderson and Philpott (2002) Uniform Price Dispatch • The optimal offer curve for a supplier with profit • facing a market distribution function maximizes:

Anderson, Holmberg and Philpott (2013) Pay-as-Bid Dispatch • When the market clears at quantity for a supplier under a particular demand realization, the supplier receives payoff: • The expected payout earned from a offer curve is then

Inframarginal Rentals • When the market clears at quantity for a supplier at price then the regulator observes a rent of: • Given , the total expected rent earned by the curve is: • This is expected revenue from uniform pricing minus expected revenue from pay-as-bid pricing.

Modelling a Tax on Rentals • Suppose that some fraction of these rentals is paid to the regulator as a tax. The after-tax total expected payoff will be: • is a convex combination of uniform price and pay-as-bid payoffs.

Symmetric Duopoly • Suppose we examine a symmetric duopoly: • each firm has no costs, and capacity ; • there is no demand elasticity () and the demand shock . • At the limit as , the equilibrium can be found to be:

Symmetric Duopoly • Symmetric equilibrium with no tax (black) and with 25% tax on observed profit (blue). Generators mark-up low priced offers.

Symmetric Duopoly • Welfare with 25% tax on observed rentals (times 4860). • Taking into account the tax on rentals, suppliers offer to improve their actual after-tax payoffs. A side-effect of this is a transfer of some wealth to consumers.

Tax on Benefits • However, in the proposed transmission pricing methodology, the benefits would be computed based on the difference between the rentals in the current market, and those computed for a counterfactual without a transmission asset. • In this context, the incentive to increase one’s offer curve is reduced. Price P P’ D’ D Quantity (MW)

Price Price Incentives to Reduce Charges P P P’ P’ • However, in the proposed transmission pricing methodology, the benefits would be computed based on the difference between the rentals in the current market, and those computed for a counterfactual without a transmission asset. • In this context, the incentive to increase one’s offer curve is reduced. D’ D’ D D Quantity (MW) Quantity (MW)

Incentives to Reduce Charges • However, firms may be incentivised to mark-up supra-marginal offers. • Consider the situation where a transmission investment has allowed additional supply into a node. • In the current market, a generator at that node is unlikely to be dispatched for their final tranche; • whereas in the counter-factual they could be. Price D(p) counterfactual pc pc p Quantity (MW)

Transmission Example • Four (identical) suppliers. • Independent uniform demand shocks, and . • With a line capacity of the market distribution function is . • A grid investment increases the capacity to , changing the market distribution function to .

Predicted Behaviour? • The supplier benefit in a demand outcome giving , shown shaded for two candidate offer curves. The counterfactual (e.g. a lower capacity line) reduces dispatch to .

Transmission Example • We model line expansion as a change in market distribution function from to • Recall that the benefits are the difference in rentals. • Thus, the expected benefit is: • So the expected payoff will be

Transmission Equilibrium • Now let us consider the symmetric equilibrium: • each firm has no costs, and capacity ; • there is no demand elasticity () and the demand shock at each node is . • At the limit as , the equilibrium can be found to be:

Transmission Equilibrium • Supply function equilibrium when : • with no benefits tax (black) • 25% benefits tax (blue) • 100% benefits tax (green)

Conclusions • On the surface, if you consider a single dispatch point, clear incentives to avoid transmission charges exist. • However, since the charge is based on benefits, the incentive to increase infra-marginal offers is limited. • Ability of firms to mark-up in a supply function, with many demand realisations is restricted. • Furthermore, competition restricts ability of firms to mark-up to reduce transmission charges. • Asymmetric players • Demand response Future Extensions

Equilibrium modelling of beneficiary-pays transmission charges