Sizing

Abstract: A capacitor sizing problem for capacitors placed on a radial distribution system is formulated as a nonlinear programming problem, and a solution algorithm is developed. The object is to find the optimal size of the capacitors so that the power losses will be minimized for a given load profile while considering the cost of the capacitors. The formulation also incorporates the AC power flow model for the system and the voltage constraints. The solution algorithm developed for the capacitor sizing problem is based on a Phase I-Phase II feasible directions approach. Novel power flow equations and a solution method, called DistFlow, for radial distribution systems are introduced. The method is computationally efficient and numerically robust, especially for distribution systems with large r/x ratio branches. DistFlow is used repeatedly as a subroutine in the optimization algorithm for the capacitor sizing problem. The test results for the algorithm indicate that the method is computationally efficient and has good convergence characteristics. >

Abstract: This paper presents a new method based on the cost-benefit analysis for optimal sizing of an energy storage system in a microgrid (MG). The unit commitment problem with spinning reserve for MG is considered in this method. Time series and feed-forward neural network techniques are used for forecasting the wind speed and solar radiations respectively and the forecasting errors are also considered in this paper. Two mathematical models have been built for both the islanded and grid-connected modes of MGs. The main problem is formulated as a mixed linear integer problem (MLIP), which is solved in AMPL (A Modeling Language for Mathematical Programming). The effectiveness of the approach is validated by case studies where the optimal system energy storage ratings for the islanded and grid-connected MGs are determined. Quantitative results show that the optimal size of BESS exists and differs for both the grid-connected and islanded MGs in this paper.