## Improved genetic algorithm for distribution system performance analysis by taking advantage of essential spanning trees

##### Abstract

The smart grid initiative, increasing use of distributed generation, and classical distribution system reconfiguration (DSR) and restoration problems, have led to the search for efficient distribution automation tools. One such instrument, the Fast Non-Dominated Sorting Genetic Algorithm (FNSGA), has been shown to be very effective at finding Pareto optimal radial distribution systems that are optimized with respect to voltages, currents, and power losses. However, the original FNSGA is restricted by its use of the Newton-Raphson method and the need for large numbers of generations, which lead to burdensome memory requirements and long computation times. In the improved FNSGA, the Newton-Raphson load flow program was replaced with a revised version of the direct load flow method. Also, a parametric study was conducted to determine minimum values of N and Gen that lead to reasonably repeatable configurations of a distribution system that are optimized for the multiple objectives of voltages, currents, and power losses. To demonstrate the computation time efficiency of the proposed method, the central processor unit (CPU) times required for the program are considered; if we can further reduce the optimum values of N and Gen, then we can maintain reasonable CPU times in larger and larger test systems. By observing essential radial system topologies, we found that if the essential branches describe a radial system, branches chosen from each essential branch will also describe a radial system, which means we only need to consider the branches in essential branch sets. In this thesis, the method called essential spanning tree is expanded to improve the computational efficiency of the algorithm. This is accomplished by replacing the so-called M matrix and its associated process with the random selection of b essential branches, where b is the number of fundamental loops in the system. Essential branches are branches between essential nodes, where essential nodes are buses that connect at least three regular branches. The usual check for radiality is then made based on the b chosen essential branches. If the system is radial, then one regular branch within each essential branch is then chosen randomly. This switch set is then checked for repetition. Finally, this process is repeated N times to determine the initial population for application of the genetic algorithm. Results of the study show that for relatively small test systems, optimum system configurations are obtained using values of N and Gen that require very small CPU times. In larger systems, optimum values of N and Gen requiring reasonable CPU times can also be found, provided that certain carefully chosen branches are removed from the pool of possibilities when producing the initial population in the algorithm. By using essential trees, the efficiency of the calculation is further improved.

##### Degree

M.S.