The existence and uniqueness of a power price equilibrium

TL;DR

This paper develops a game-theoretic power price model that accounts for non-storability, demonstrating the existence and conditions for the uniqueness of equilibrium prices in electricity markets.

Contribution

It introduces a novel equilibrium model for power prices that incorporates non-storable nature and strategic interactions between producers and consumers.

Findings

Equilibrium power prices exist under the proposed model.

Conditions for the uniqueness of the equilibrium are identified.

The model captures the non-storable characteristic of power markets.

Abstract

We propose a term structure power price model that, in contrast to widely accepted no-arbitrage based approaches, accounts for the non-storable nature of power. It belongs to a class of equilibrium game theoretic models with players divided into producers and consumers. The consumers' goal is to maximize a mean-variance utility function subject to satisfying an inelastic demand of their own clients (e.g households, businesses etc.) to whom they sell the power. The producers, who own a portfolio of power plants each defined by a running fuel (e.g. gas, coal, oil...) and physical characteristics (e.g. efficiency, capacity, ramp up/down times...), similarly, seek to maximize a mean-variance utility function consisting of power, fuel, and emission prices subject to production constraints. Our goal is to determine the term structure of the power price at which production matches consumption. In this paper we show that in such a setting the equilibrium price exists and also discuss the conditions for its uniqueness.