Generation Capacity Expansion in a Risky Environment: A Stochastic Equilibrium Analysis

Abstract

We cast models of the generation capacity expansion type formally developed for the monopoly regime into equilibrium models better adapted for a competitive environment. We focus on some of the risks faced today by investors in generation capacity and thus pose the problem as a stochastic equilibrium model. We illustrate the approach on the problem of the incentive to invest. Agents can be risk neutral or risk averse. We model risk aversion through the CVaR of plants' profit. The CVaR induces risk-adjusted probabilities according to which investors value their plants. The model is formulated as a complementarity problem (including the CVaR valuation of investments). An illustration is provided on a small problem that captures several features of today's electricity world: a choice often restricted to coal and gas units, a peaky load curve because of wind penetration, uncertain fuel prices, and an evolving carbon market. We assess the potential of the approach by comparing energy-only and capacity market organizations in this risky environment. Our results can be summarized as follows: a deterministic analysis overlooks some changes of capacity structure induced by risk, whether in the capacity market or energy-only organizations. The risk-neutral analysis also misses a shift towards less capital-intensive technologies that may result from risk aversion. Last, risk aversion also increases the shortage of capacity compared to the risk-neutral view in the energy-only market when the price cap is low. This may have a dramatic impact on the bill to the final consumer. The approach relies on mathematical programming techniques and can be extended to full-size problems. The results are illustrative and may deserve more investigation.

Equilibrium, uncertainty and risk in hydro-thermal electricity systems

“…We have also computed equilibria for incomplete market models in which specific financial instruments (such as contracts for differences) are included. Similar computational experiments have been carried out by [6] for models with thermal plant and two-stage uncertainty. Such incomplete market models are currently of small scale, but we expect that before too long improvements in computation will provide regulators and market analysts with a methodology to test the welfare gains that might be realized by introducing practical hedging instruments into markets in which these are absent.…”

“…Now let {u s a (n) : n ∈ N , a ∈ A} be a solution to SP with risk sets D s (n) = ∩ a∈A D a (n). Suppose this gives rise to µ and prices {π(n) : n ∈ N } where π(n)σ(n) are the Lagrange multipliers for constraints (6). These prices and quantities form a multistage risk-trading equilibrium in which agent a solves SPM(a) with a policy defined by u a (·) together with a policy of trading Arrow-Debreu securities defined by {W a (n), n ∈ N \ {0}}.…”

An approximation scheme for a class of risk-averse stochastic equilibrium problems

“…For the natural gas market, the deterministic MCP model from [15] and [23] was revisited in a stochastic risk-neutral setting in [14]. For electricity markets, game-theoretical and MCP formulations have been considered in [27] and [17], respectively. Regarding the merits of the two modelling approaches, it is sometimes argued that the MCP formulation provides an adequate framework for imperfect markets.…”

“…In this work, we adopt the modeling of [32]. Our approach is comprehensive enough to include the electricity generation-capacity expansion model [17] and the European natural gas market model in [23], set in a stochastic environment.…”

Risk Aversion and Technology Portfolios

“…With regard to the technology mix, Roques et al (2008) compared portfolios containing combined cycle gas turbine (CCGT), coal and nuclear plants. 4 Fan et al (2010) and Ehrenmann and Smeers (2011) used numerical simulations of an electricity industry equilibrium to assess the influence of generators' risk aversion on the total capacity built and on the technology mix.…”