Optimal Shunt Capacitors’ Placement and Sizing in Radial Distribution Systems using Multi-Verse Optimizer, Modified Loss Sensitivity Factors and Matlab Matrix Reduction Techniques

Abstract

The installation of shunt capacitors in radial distribution systems results in the reduction of branch power flows, currents, power losses and voltage drop. Consequently, this further results in improved voltage profiles and voltage stability margins. However, for efficient attainment of the aforementioned benefits, the installation of shunt capacitors needs to be carried out in an optimal manner, that is, optimally sized shunt capacitors need to be installed at the global optimum buses within a given electrical network. Identification of the global optimum buses at which to install shunt capacitors in radial distribution systems is one critical task that greatly affects the overall cost of total real power losses, shunt capacitors’ purchase, installation, operation, and maintenance (O&M). If an existing approach ably identifies the global optimum buses, then the overall cost of total real power losses, shunt capacitors’ purchase, installation, and O&M would be minimized to the least value possible. However, if an approach only identifies sub-optimal buses, then the minimization of the aforementioned overall cost would only be partial. There are two general approaches that are used to identify optimal buses on which to install shunt capacitors. These are: approaches for searching of optimal buses from unreduced search spaces and approaches for searching of optimal buses from reduced search spaces. The exhaustive search-based approach, which belongs to the former approach, gives the global optimum buses and consequently the global optimum overall cost of total real power losses, shunt capacitors’ purchase, installation, and O&M. However, its major shortfall is its high computation time. This is mainly so because under this approach, the search for the global optimum buses is carried out in unreduced search spaces. On the other hand, for approaches in which the search for optimal buses is carried out in reduced search spaces, the computation time is also reduced. However, this reduction in the search space, hence the computation time, results in reduced accuracy levels for the attained solutions. Consequently, in an attempt to counter shortfalls of existing approaches, i.e. high solutions’ accuracy at the expense of computation time; and shorter computation time at the expense of solutions accuracy, in this thesis a new optimal shunt capacitors’ placement and sizing approach has been developed, evaluated, and validated. The approach is based on Modified Loss Sensitivity Factors (MLSF), the Multi-Verse Optimizer (MVO) and MATLAB matrix or search space reduction techniques. In the developed approach, the MLSF and MATLAB’s matrix reduction techniques have been used to reduce the search space of optimal buses that require the provision of reactive power through the installation of shunt capacitors. Thereafter, MVO is used to do a concurrent search of the global optimum bus(es) from the reduced search spaces and the corresponding optimum shunt capacitor sizes to be installed. The developed approach was tested on the IEEE 10- and 33-bus radial distribution systems with the aim of minimizing the overall cost of total real power losses, shunt capacitors’ purchase, installation, and O&M while assuming fixed and variable system loading. Despite disregarding some bus combinations, the developed approach was still able to attain the same overall costs, real power losses, reactive power losses and bus voltages as the exhaustive search based algorithm. Additionally, the developed approach was able to attain the least overall cost than those obtained using approaches based on Artificial Bee Colony (ABC), Crow Search Algorithm (CrSA), Cuckoo Search Algorithm (CSA), Differential Evolution (DE), Dragonfly Optimizer (DFO), Genetic Algorithm (GA), Gravitational Search Algorithm (GSA), Grey Wolf Optimizer (GWO), Improved Crow Search Algorithm (ICrSA), Modified Cultural Algorithm (MCA), Moth Flame Optimizer (MFO) and Particle Swarm Optimization (PSO) algorithm. Consequently, because the search space becomes reduced after disregarding some bus combinations, the developed approach attains the global optimum results with relatively shorter computation times than the exhaustive search. In summary, the developed algorithm stands out as a potentially reliable tool for power system planners to adopt and use when solving the radial distribution systems’ optimal shunt capacitors’ placement and sizing problem for either minimization of the overall cost of total real power losses and shunt capacitors’ purchase or minimization of the overall cost of total real power losses, shunt capacitors’ purchase, installation, and O&M. This is so because, unlike available optimal shunt capacitors’ placement and sizing algorithms, the developed algorithm exactly matches the accuracy of the exhaustive search algorithm.