Study On Modeling And Solution Algorithms Of Capacitor Optimization With Harmonic Consideration In Distribution Systems

Optimization of capacitor in distribution systems is an important measure to ensuresecurity and economy of system operation. Optimal capacitor placement and switching canresult in voltage profile improvement, system loss reduction, power factor correction, andfeeder capacity release. However, due to the wide-spread use of nonlinear loads indistribution networks, there is a significant amount of harmonic distortion in voltage andcurrent waveforms, which may cause capacitor failure or out of work. On the other hand,shunt capacitors may lead to harmonic amplification caused by resonance conditions.Therefore, it is of great significance to study on capacitor optimization in distributionsystems with harmonic consideration, aiming to achieve the maximum system lossreduction and prevent harmonic amplification as well. This dissertation devotes to the interrelated problems of capacitor optimization indistribution systems with harmonic consideration, including the research on efficientalgorithms of fundamental and harmonic power flow calculations for radial distributionsystems, the research on a practical optimization algorithm and its improvement, theresearch on problem formulations and solution algorithms of optimal capacitor placementand switching in distribution systems, and the research on problem formulation andsolution algorithm of optimal reactance rate selection of serial reactors in capacitor banksinstalled in substations. As essential calculations in capacitor optimization with harmonic consideration,fundamental and harmonic power flow calculations influence the efficiency of the wholeoptimization procedure to a great extent. In the aspect of fundamental power flowcalculation, an improved back/forward sweep algorithm based on branch and bus layeringis proposed. In this algorithm, the branches and buses are sorted by layers, and the branchcurrents and bus voltages in the same layer can be parallel computed, so as to improve thecalculation efficiency greatly. In the aspect of harmonic power flow calculations, byborrowing the solution method used in fundamental power flow calculation, a novel IIIback/forward sweep distribution harmonic flow algorithm is presented, which helps tocalculate harmonic currents, harmonic voltages and total harmonic distortion (THD)rapidly even for a large-scale distribution system. As a representative swarm-intelligence based optimization algorithm, Particle SwarmOptimization (PSO) algorithm is applied to capacitor optimization in the dissertation.Aiming to overcome the limitations of standard PSO algorithm, a modified PSO algorithmis proposed by adjusting key parameters to improve the convergence and introducingnon-uniform mutation mechanism to enhance the global search ability of the algorithm andhence achieve better-quality solutions. Test results on a typical function optimizationproblem and several constrained optimization problems show that the proposed modifiedPSO algorithm can achieve a significant improvement on the convergence and searchquality compared with the standard PSO algorithm. Optimal capacitor placement and optimal capacitor switching are formulated withharmonic distortion consideration respectively. In the problem formulation of optimalcapacitor placement, the objective function includes the energy loss cost, the cost of peakpower loss, and the total capacitor cost which comprises the installment cost and thepurchase cost. In the problem formulation of optimal capacitor switching, the switchingoperation cost is considered as one part of the objective function so as to avoid frequentswitchings which may shorten the capacitors' life expectancies. In doing so, the large-scaleoptimization problem during a day can be decoupled into numbers of small-scaleoptimization problems at each hour, thus the computational complexity could besignificantly reduced. Mathematically, the two problems are both formulated as nonlinearinte...