Voltampere reactive compensation using chance-constrained programming

Abstract

A new technique is developed for solving the voltampere reactive (VAR) compensation problem under uncertain operating conditions. The technique employs chance-constrained programming (CCP), and transforms the problem into a standard linear programming problem. In providing optimal allocation of VAR support, busbars with unacceptably high probability of violating voltage limits are identified and assigned appropriate chance-constraints. Two cases are considered using the new technique. In the first case, capacitive compensation is evaluated for peak load conditions. Inductive compensation is considered in the second case, assuming light load conditions. The method in its general form can be applied in cases where there is uncertainty with respect to equipment cost and/or the coefficients of the voltage-magnitude/reactive power relationships. Normal distributions are not necessary conditions and, if desired, dependent variates can be assumed. The method has been applied to the AEP 30-busbar test system for both heavy and light load conditions, and sample results are presented in the paper. IntroductionKiloVARs, as well as kilowatts, must be provided to the customer as part of a utility's electricity service, and the analysis of the technically most desirable and economically most attractive way to supply this reactive power requirement is one of the system planner's objectives. Whereas the kilowatts can be supplied only from an energy source or power plant, kilovars are automatically produced as well as consumed by the electric network itself. This, of course, results from the inherent shuntcapacitive and series-inductive characteristics of the transmission lines. For this reason planning of reactive power supply is subject to a greater range of system variables [1 ] . For long-range power system transmission planning, VAR compensation is an important aspect. In the past, load-flow studies, trial and error and engineering judgment have been combined in planning the reactive requirement. More recently optimisation techniques have been introduced to select the best alternative in supplying reactive power using linear, nonlinear, continuous or discrete programming [2][3][4].In long-range planning, there is uncertainty inherent in demand projections, equipment and fuel costs, and available rights of way. Recognising the importance of these uncertainties, the authors have found that chance-constrained programming [5-9] is a suitable technique for solving the VAR compensation planning problem. Although the technique in its general form can be applied to a problem with all the previous uncertainties, only voltage magnitude variation resulting from uncertainty in demand projection is considered in this paper.The significance of the new approach is that it accounts for those voltage deviations likely to occur because of uncertain operating conditions, and the probability levels provide a measure of the degree of confidence in meeting the voltage specifications. These advantages are not provided by the VAR allocation techniq...

Large-scale Unit Commitment under uncertainty

“…This explains why CCO (either Individual or Joint) models are the least employed in the literature on UC. However, it should be noted that these approaches have indeed been used in related problems such as power expansion and transmission ones (Sharaf and Berg 1982;Shiina 1999;Anders 1981), which need be formulated on a much longer time horizon than commonly considered in UC, and therefore crucially require taking uncertainty into account (Shiina 1999).…”

Large-scale unit commitment under uncertainty: an updated literature survey

“…This explains why CCO (either Individual or Joint) models are the least employed in the literature on UC. However, it should be noted that these approaches have indeed been used in related problems such as power expansion and transmission ones [16,466,474], which need be formulated on a much longer time horizon than commonly considered in UC, and therefore crucially require taking uncertainty into account [474].…”