We formulate a stochastic security-constrained multi-period electricity market-clearing problem with unit commitment. The stochastic security criterion accounts for a pre-selected set of random generator and line outages with known historical failure rates and involuntary load shedding as optimization variables. Unlike the classical deterministic reserve-constrained unit commitment, here the reserve services are determined by economically penalizing the operation of the market by the expected load not served. The proposed formulation is a stochastic programming problem that optimizes, concurrently with the pre-contingency social welfare, the expected operating costs associated with the deployment of the reserves following the contingencies.

The behavior of electricity differs from other commodity prices. One reason for that is that electricity is a non-storable good, implying that inventories cannot be used to arbitrage prices over the time. The aim of this paper is to propose a diffusion process with a Levy process as a jump process to model electricity spot price that can reproduce the main characteristics of the electricity prices that are seasonality, mean reverting, fat tails, volatility clustering and spikes. There are various reasons for spikes: for example, changing weather conditions such as a heat wave, or the outage of a major power plant. To understand spikes, one should be aware that the marginal cost of generation of power increases sharply beyond a certain production level. Beyond that level, additional electricity can only be produced by adding generators with a high fixed cost.

Suppliers of electricity in competitive markets regularly respond to prices that change hour by hour or even more frequently, but most consumers respond to price changes on a very different time scale, i.e. they observe and respond to changes in price as reflected on their monthly bills. The presentation will outline nonlinear complementarity programming models of equilibrium that can bridge the speed of response gap between suppliers and consumers, yet adhere to the principle of marginal cost pricing of electricity. It is intended that the models will be useful (a) in the regular exercise of setting consumer prices by a body such as the Ontario Energy Board, (b) in evaluation of the economic benefit due to time-of-day pricing compared with a single price, and (c) in the estimation of the degree of market power that can be exercised by large suppliers.