Financial transmission rights in convex pool markets

doi:10.1016/j.orl.2003.06.002

Operations Research Letters

Volume 32, Issue 2, March 2004, Pages 109-113

https://doi.org/10.1016/j.orl.2003.06.002 Get rights and content

Abstract

This paper studies financial transmission rights in electricity pool markets with nodal pricing. We prove that simultaneous feasibility entails revenue adequacy in a general framework of convex optimization, and show by counterexample as to how this result might fail in the absence of convexity.

Introduction

Electricity pool markets based on nodal pricing have emerged in a number of regions of North and South America, Australia, New Zealand, and the Nordic countries. In an electricity pool with a single node, all market participants trade (at any one point in time) at a single-system marginal price. In a full nodal pricing model, the price depends on location. In the absence of constraints and losses the price at every node is identical to the system marginal price. In practice, thermal constraints on the power flow in the lines, and power losses due to line impedance, result in a set of prices that vary with location. The variation of electricity spot prices with location in these markets has resulted in the development of market instruments to hedge the volatility in these price differences.

Financial transmission rights (FTRs) is one approach to solve this problem. An FTR is a financial instrument held by a market participant that pays an income stream based on the nodal prices observed in the transmission system over the course of the contract. An FTR can be specified by a vector of nodal loads and injections (where the loads are taken as positive) and the coupon payment at any time is equal to the inner product of the nodal price vector with the FTR. (In practice, most FTRs involve only two nodes.) FTRs were first proposed by Hogan [3], and have received a lot of attention in the literature under various names (they are called fixed transmission rights in the PJM market, transmission congestion contracts or TCCs in New York, and financial congestion contracts, or FCCs in New England).

In nodal electricity pools the prices are determined by the Independent System Operator (ISO), who solves an optimal dispatch problem. The prices at each node, which are paid by consumers and paid to generators at that node, are taken to be the Lagrange multipliers of the power flow balance constraints. In most circumstances the consumer payments exceed the payments to generators, and the ISO makes a surplus or rental that can be used to fund the coupon payments of the FTRs. A well-known result states that such revenue adequacy is guaranteed by the FTRs being simultaneously feasible for the network constraints, in the sense that they can be dispatched through the network without exceeding capacities. This result was first proved by Hogan [3] for lossless networks, extended to quadratic losses by Bushnell and Stoft [2], and further generalized to smooth nonlinear constraints by Hogan [4].

Our purpose in this paper is to place these results in a convex optimization setting, generalizing them where possible, and identifying counterexamples where appropriate. The paper is laid out as follows. In Section 2 we extend the revenue adequacy result proved by Hogan for smooth problem data to a general convex programme setting. This admits as a special case convex dispatch models with convex piecewise linear losses and piecewise linear benefit functions, as used in the New Zealand dispatch software SPD (see e.g. [1]). We then show by example how revenue adequacy can fail for dispatch models that are not convex.

Section snippets

Revenue adequacy

We formulate the dispatch problem as the following convex optimization problem in a transmission network with n nodes. $P_{I} : minimize ∑ i ∑ j∈O(i) c_{j} x_{j} subject to g_{i} (f)+ ∑ j∈O(i) x_{j} −z_{i} =d_{i}, i=1,2,…,n, z_{i} ⩾0, i=1,2,…,n, x∈X, f∈U.$ In this model each generator offers a piecewise constant nondecreasing supply function, made up of a finite set of tranches of power. The variable x_j is the level of dispatch of offer tranche j∈O(i), where O(i) is the set of tranches offered at node i, and each tranche j∈O(i) is offered at

Conclusion

Revenue adequacy is a key property desired of FTRs. The simultaneous feasibility condition will guarantee this as long as the network is unaffected by outages, and there are no negative nodal prices. It should be noted that the presence of FTRs might serve as an incentive for market participants to produce negative prices, so some methodology for dealing with these needs to be in place, in case they become a lot more frequent.

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A security-constrained bid-clearing system for the New Zealand wholesale electricity market
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There are more references available in the full text version of this article.

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This result was first proved by Hogan [5] for lossless networks, extended to quadratic losses by Bushnell and Stoft [3], and further generalised to smooth nonlinear constraints by Hogan [7]. A proof for the general convex case can be found in Ref. [9]. When the extant FTR contracts are simultaneously feasible as above, the rentals earned by the ISO are sufficient to fund the coupon payments to the FTR holders.

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¹: This work has been supported by the New Zealand Public Good Science Fund under Contract UOAX0004.

View full text

Financial transmission rights in convex pool markets

Abstract

Introduction

Section snippets

Revenue adequacy

Conclusion

A security-constrained bid-clearing system for the New Zealand wholesale electricity market

IEEE Trans. Power Systems

Electricity grid investment under a contract network regime

J. Regulatory Econom.