We present a two-stage stochastic programming model for committing reserves in systems with large amounts of wind power. We describe wind power generation in terms of a representative set of appropriately weighted scenarios, and we present a dual decomposition algorithm for solving the resulting stochastic program. We test our scenario generation methodology on a model of California consisting of 122 generators, and we show that the stochastic programming unit commitment policy outperforms common reserve rules.

In this paper we present a unit commitment model for studying the impact of large-scale wind integration in power systems with transmission constraints and system component failures. The model is formulated as a two-stage stochastic program with uncertain wind production in various locations of the network as well as generator and transmission line failures. We present a scenario selection algorithm for selecting and weighing wind power production scenarios and composite element failures, and we provide a parallel dual decomposition algorithm for solving the resulting mixed-integer program. We validate the proposed scenario selection algorithm by demonstrating that it outperforms alternative reserve commitment approaches in a 225 bus model of California with 130 generators and 375 transmission lines. We use our model to quantify day-ahead generator capacity commitment, operating cost impacts, and renewable energy utilization levels for various degrees of wind power integration. We then demonstrate that failing to account for transmission constraints and contingencies can result in significant errors in assessing the economic impacts of renewable energy integration.

Low-voltage distribution networks are emerging as an increasingly important component of power system operations due to the deployment of distributed renewable resources (e.g., rooftop solar supply) and the need to mobilize the flexibility of consumers that are connected to the low-voltage grid. The pricing of electric power at distribution nodes follows directly from the theory of spot pricing of electricity. However, in contrast to linearized lossless models of transmission networks, an intuitive understanding of prices at the distribution level presents challenges due to voltage limits, reactive power flows, and losses. In this paper, we present three approaches toward understanding distribution locational marginal prices by decomposing them: 1) through a duality analysis of the problem formulated with a global power balance constraint; 2) through a duality analysis of a second-order cone program relaxation; and 3) through an analysis of the impact of marginal losses on price. We discuss the relative strengths and weaknesses of each approach in terms of computation and physical intuition, and demonstrate the concepts on a 15-bus radial distribution network.

We present a parallel implementation of Lagrangian relaxation for solving stochastic unit commitment subject to uncertainty in renewable power supply and generator and transmission line failures. We describe a scenario selection algorithm inspired by importance sampling in order to formulate the stochastic unit commitment problem and validate its performance by comparing it to a stochastic formulation with a very large number of scenarios, that we are able to solve through parallelization. We examine the impact of narrowing the duality gap on the performance of stochastic unit commitment and compare it to the impact of increasing the number of scenarios in the model. We report results on the running time of the model and discuss the applicability of the method in an operational setting.

This paper presents a multistage stochastic programming formulation of a transmission-constrained economic dispatch subject to multiarea renewable production uncertainty, with a focus on optimizing the dispatch of storage in real-time operations. This problem is resolved using stochastic dual dynamic programming. The applicability of the proposed approach is demonstrated on a realistic case study of the German power system calibrated against the solar and wind power integration levels of 2013-2014, with a 24-h horizon and 15-min time step. The value of the stochastic solution relative to the cost of a deterministic policy amounts to 1.1%, while the value of perfect foresight relative to the cost of the stochastic programming policy amounts to 0.8%. The relative performance of various alternative real-time dispatch policies is analyzed, and the sensitivity of the results is explored.

We present a stochastic unit commitment model for assessing the impacts of the large-scale integration of renewable energy sources and deferrable demand in power systems in terms of reserve requirements. We analyze three demand response paradigms for assessing the benefits of demand flexibility: the centralized co-optimization of generation and demand by the system operator, demand bids and the coupling of renewable resources with deferrable loads. We motivate coupling as an alternative for overcoming the drawbacks of the two alternative demand response options and we present a dynamic programming algorithm for coordinating deferrable demand with renewable supply. We present simulation results for a model of the Western Electricity Coordinating Council.