Investigations in the Monte-Carlo sampling for interconnected power systems reliability evaluation

Abstract

This thesis makes three contributions to the methodology of multi-area reliability calculations. It examines the Simultaneous Decomposition-Simulation approach, and presents a technique to bound the approximation introduced by the simulation phase. The new approach keeps track of the probability of the unclassified states to keep the error under a specified fraction of the loss of load probability. There are two methods to select a sample state from a set, uniform sampling and proportional sampling. This study replaces uniform sampling with proportional sampling, so as to introduce a suitable convergence criterion. New algorithms are developed to use proportional sampling in the Simultaneous-Decomposition Simulation. A variance reduction technique is also introduced to make the sampling more efficient. The accuracy and efficiency of the improved Simultaneous Decomposition Simulation approach is demonstrated on the three area and ten area systems, where each area consists of an IEEE-RTS generation system. There is about 10 to 20 times reduction in the sample size for L and W sets. It is observed that with error bounding in the decomposition phase, simulation contribution from unclassified U sets can be negligible, resulting in considerable savings in the simulation CPU time. Finally, this thesis presents a comparison of two commonly used models in MonteCarlo simulation, random sampling and sequential sampling. They are both widely used in the industry. The mathematical analysis and system studies indicate that sequential sampling converges much slower than random sampling. However sequential sampling yields the index of frequency directly, and random sampling can only give index of frequency under the assumption of coherence.