Stochastic Equilibrium Models for Generation Capacity Expansion

Abstract

Capacity expansion models in the power sector were among the first applications of operations research to the industry. We introduce stochastic equilibrium versions of these models that we believe provide a relevant context for looking at the current very risky market where the power industry invests and operates. We then look at the insertion of risk related investment practices that developed with the new environment and may not be easy to accommodate in an optimization context. Specifically we consider the use of plant specific discount rates that we derive by including stochastic discount rates in the equilibrium model. Linear discount factors only price systematic risk. We therefore complete the discussion by inserting different risk functions (for different agents) in order to account for additional unpriced idiosyncratic risk in investments. These different models can be cast in a single mathematical representation but they do not have the same mathematical properties. We illustrate the impact of these phenomena on a small but realistic example.

Does risk aversion affect transmission and generation planning? A Western North America case study

“…An alternative is to assume complete financial markets, such that investors can trade all types of risk (e.g., there exist Arrow-Debreu securities for all future scenarios). This reduces the complexity of the problem and, like the assumption of perfect competition in energy markets, can make risk-averse planning problems much more tractable (see, e.g., Ehrenmann and Smeers, 2011b). It may, however result in an overestimation of investment levels and in an underestimation of the strategic interactions between market participants, including the need for individual investors to hold diversified portfolios, although it is unclear what the practical implications of the latter would be for aggregate investment levels.…”

“…As mentioned above, this is an obvious simplification since modeling of financial markets is outside the scope of this work, but it would be even less appropriate to ignore their (beneficial) effects altogether. It has been shown that, given these assumptions, the generation dispatch and generation expansion equilibrium is equivalent to the solution of a risk-adjusted cost minimization problem (Ralph and Smeers, 2010;Ehrenmann and Smeers, 2011b) 5 . This is intuitive -complete financial markets ensure that the worst-case scenario is the worst case for every market participant; perfect competition then restores the market equilibrium to its risk-averse social optimum.…”

Risk Trading and Endogenous Probabilities in Investment Equilibria

“…The electricity investment model proposed in [11] is of this type and was one of the inspirations for the work presented here. Our paper, or rather the first version of it [26], is cited in work on two-stage capacity equilibria [12] and two-stage hydropower equilibria [25]. It is also cited in [22], which combines a market in financial instruments with a spot electricity market, Downloaded 01/05/16 to 131.111.184.102.…”

“…. , N) and (12) in statement B of Theorem 7 can be equivalently written as the Nash game that combines (16) (for i = 1, . .…”

$$\Gamma $$-Robust electricity market equilibrium models with transmission and generation investments

“…In many of these studies, bilevel or trilevel problems are cast as mathematical programs with equilibrium constraints (MPECs) or equilibrium problems with equilibrium constraints (EPECs) and are solved by equivalent single-level reformulations of the multilevel problem. In [9], the author shows that a hierarchical bilevel model formulated as an MPEC and a simultaneous model formulated as an MCP lead to the same results in a perfectly competitive market structure and under some mild conditions; see also, e.g., [13,17] for similar results in comparable settings. Hence, in this paper, we resort our attention to MCP formulations.…”