Stochastic Power Generation Research Articles

Probabilistic load flow incorporating correlation between time-varying electricity demand and renewable power generation

The time-varying demand and stochastic power generation from renewable distributed generating resources necessitate an exhaustive assessment of distribution feeder parameters for the purpose of long-term planning. This paper proposes a novel formulation of probabilistic load flow for distribution feeders with high penetration of renewable distributed generation. The dependency between the load demand of different consumer classes and generation from different types of renewable resources is addressed in this study. In order to capture the coincidental variations of demand and generation, associated time series data for the same time instances are used. A transformation matrix based probabilistic load flow is formulated using the method of cumulants. Moreover, Pearson distribution functions are used to estimate the probability distribution of the line flows. The proposed load flow method is tested on a practical distribution feeder with high penetration of solar photovoltaic and wind energy conversion systems. The results demonstrate the aptitude of the proposed method for conducting probabilistic load flow studies with dependent non-Gaussian distribution of load and generation.

Scenario construction and reduction applied to stochastic power generation expansion planning

A challenging aspect of applying stochastic programming in a dynamic setting is to construct a set of discrete scenarios that well represents multivariate stochastic processes for uncertain parameters. Often this is done by generating a scenario tree using a statistical procedure and then reducing its size while maintaining its statistical properties. In this paper, we test a new scenario reduction heuristic in the context of long-term power generation expansion planning. We generate two different sets of scenarios for future electricity demands and fuel prices by statistical extrapolation of long-term historical trends. The cardinality of the first set is controlled by employing increasing length time periods in a tree structure while that of the second set is limited by its lattice structure with periods of equal length. Nevertheless, some method of scenario thinning is necessary to achieve manageable solution times. To mitigate the computational complexity of the widely-used forward selection heuristic for scenario reduction, we customize a new heuristic scenario reduction method named forward selection in wait-and-see clusters (FSWC) for this application. In this method, we first cluster the scenarios based on their wait-and-see solutions and then apply fast forward selection within clusters. Numerical results for a twenty year generation expansion planning case study indicate substantial computational savings to achieve similar solutions as those obtained by forward selection alone.

Stochastic Power Generation Unit Commitment in Electricity Markets: A Novel Formulation and a Comparison of Solution Methods

We propose a stochastic unit commitment model for a power generation company that takes part in an electricity spot market. The relevant feature of this model is its detailed representation of the spot market during a whole week, including seven day-ahead market sessions and the corresponding adjustment market sessions. The adjustment market sessions can be seen as an hour-ahead market mechanism. This representation takes into account the influence that the company's decisions exert on the market-clearing price by means of a residual demand curve for each market session. We introduce uncertainty in the form of several possible spot market outcomes for each day, which leads to a weekly scenario tree. The model also represents in detail the operation of the company's generation units. The model leads to large-scale mixed linear-integer problems that are hard to solve with commercial optimizers. This suggests the use of alternative solution methods. We test four solution approaches with a realistic numerical example in the context of the Spanish electricity spot market. The first is a direct solution with a commercial optimizer, which illustrates the mentioned limitations. The second is a standard Lagrangean relaxation algorithm. The third and fourth methods are two original variants of Benders decomposition for multistage stochastic integer programs. The first Benders decomposition algorithm builds approximations for the recourse function relaxing the integrality constraints of the subproblems. The second variant strengthens these cuts by performing one iteration of the Lagrangean of each subproblem. We analyze the advantages of these four methods and compare the results.