Equilibrium, uncertainty and risk in hydro-thermal electricity systems

Abstract

The correspondence of competitive partial equilibrium with a social optimum is well documented in the welfare theorems of economics. These theorems can be applied to single-period electricity pool auctions in which price-taking agents maximize profits at competitive prices, and extend naturally to standard models with locational marginal prices. In hydro-thermal markets where the auctions are repeated over many periods, agents seek to optimize their current and future profit accounting for future prices that depend on uncertain inflows. This makes the agent problems multistage stochastic optimization models, but perfectly competitive partial equilibrium still corresponds to a social optimum when all agents are risk neutral and share common knowledge of the probability distribution governing future inflows. The situation is complicated when agents are risk averse. In this setting we show under mild conditions that a social optimum corresponds to a competitive market equilibrium if agents have time-consistent dynamic coherent risk measures and there are enough traded market instruments to hedge inflow uncertainty. We illustrate some of the consequences of risk aversion on market outcomes using a simple two-stage competitive equilibrium model with three agents.

Strategic bidding for price-maker producers in predominantly hydroelectric systems

“…2. 1 A mathematical proof of the existence of a Nash equilibrium is beyond the scope of this study. 2 Feasible arc interior point algorithm for nonlinear constrained optimization. The second (and more complex) system comprises one thermal and seven hydro plants in different cascades, as depicted in Fig.…”

“…The electricity industry has undergone a restructuring process over the last three decades, which led to the establishment of wholesale electricity markets in most industrialized regions of the world [1,2]. Despite inherent characteristics and differences of each region, the fundamental goal of this process is the implementation and development of electricity markets to stimulate competition and market efficiency on behalf of the society.…”

Impact of Risk Aversion on the Operation of Hydroelectric Reservoirs in the Presence of Renewable Energy Sources

“…The most obvious one is the possible exercise of market power due to a strategic behavior of generation companies that might not reflect the true generation costs in their offers. However, even in the absence of such strategic behavior, the existence of uncertainty can lead also to a market inefficiency as demonstrated in [16,17]. In both works, it is proved that risk trading (for instance, by signing forward markets with risk-neutral agents such as the aggregated demand), can lead again to the optimum centralized solution even in case of risk-averse agents.…”

“…This ratio is named as the energy coefficient, and for a given hydro plant h, it is denoted by E h . Instead of assuming a static representation (as in [17]), this paper considers its dependency on the stored volume of water given that the net head changes with respect to the volume of water stored accordingly to the shape of the pond.…”

“…Regarding [17], the presented model does not require to build in advance the extreme points of the polyhedron that define the risk set of each agent, and it takes into account the net-head dependency. In addition, the implemented model in the example-case section is not just a two-stage scenario tree, but a multi-stage scenario tree with 12 time periods (months) that can be used to analyze the impact of the risk aversion on the annual evolution of the main variables.…”