Perfect competition vs. strategic behaviour models to derive electricity prices and the influence of renewables on market power

Abstract

A variety of fundamental modelling approaches exist using different competition concepts with and without strategic behaviour to derive electricity prices. To investigate the quality and practicability of these different approaches in energy economics, a perfect competition model, a Cournot model and a Bilevel model are introduced and applied to different situations in the German electricity market. The three electricity market approaches are analysed with respect to their ability to represent electricity prices and the possibility of market power abuse. Market prices are taken as a benchmark for model validity. As a result, the perfect competition model fits best to today’s market situation in most hours of the year. The Bilevel approach explains prices in high load hours sometimes better than the competition model. But complexity and calculation time increase disproportionately. In addition to the analysis of model quality, we use three scenarios to quantify how a high renewable feed-in influences the ability to abuse market power. Results show that the ability to address market power strongly depends on the amount of installed capacities.

Appendix: Social welfare calculation

The consumers surplus and the producers surplus added together is called the social welfare or the gain from trade and is a standard measure of market efficiency (Gabriel et al. 2013, p. 88). The consumers surplus is calculated by

$$\begin{aligned} \text{ consumers } \text{ surplus } = \int _0^{q^*} f_d^{-1}(q')dq'-p^*q^* \end{aligned}$$

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whereas $*$ stands for the equilibrium quantity and the resulting price. Since $q = \sum _{h,s}g(h,s)$ it is analogue $q^* = \sum _{h,s}dp^*(h,s)$ where $dp^*(h,s)$ is the produced quantity of power plant s in equilibrium. The symbols are declared in Sect. 3. The producer surplus is calculated by

$$\begin{aligned} \text{ producers } \text{ surplus } = p^*q^*-\sum _{h,s}\mathrm{oc}(h,s^*)dp^*(h,s). \end{aligned}$$

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Therefore, the social welfare will be obtained by

$$\begin{aligned} \text{ social } \text{ welfare }&= \int _0^{q^*}f_d^{-1}(q')dq'-\sum _{h,s}\mathrm{oc}(h,s^*)dp^*(h,s) \nonumber \\&= a(h)q^* + \frac{1}{2}b(h){q^*}^2 - \sum _{h,s}\mathrm{oc}(h,s^*)dp^*(h,s). \end{aligned}$$

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In Sect. 3.1, the quantity $q^*$ is found by maximisation of the social welfare.