A modified geometric mean optimizer for integrating distributed photovoltaic power generation into radial distribution networks

This paper proposes a modified geometric mean optimizer (MGMO) based on nonlinear functions of the control parameter, the first being a logarithmic function (MGMOI) and the second being an exponential function (MGMOII), while the original geometric mean optimizer (OGMO) has a linear control parameter. To demonstrate the ef-fectiveness and efficiency of an MGMOI and MGMOII, they were implemented to benchmark functions, the results observed a best balance in exploration and exploitation and faster convergence to the best solution compared to the OGMO. On the other hand, the OGMO, MGMOI and MGMOII algorithms have been implemented on the standard IEEE 33 bus and the practical IRAQI 71 bus to obtain the optimal position and capacity of photovoltaic distributed generator (PV-DG), while the beta probability distribution func-tion (BPDF) is implemented to model the uncertainty of solar irradiation. Moreover, the performances of radial distribution networks (RDNs) are improved after incorporating a PV-DG into the RDN; the power losses are minimized (65.159%, 65.500%, and 65.505% for the OGMO, MGMOI, and MGMOII, respectively, in the IEEE 33 bus, 66.739%, 66.858%, and 67.490% for the OGMO, MGMOI, and MGMOII, respectively, in the IRAQI 71 bus), while the voltage profile and stability are maximized (15.205%, 15.205%, and 15.230% for the OGMO, MGMOI, and MGMOII, respectively, in the IEEE 33 bus, 12.813%, 12.997%, and 12.997% for the OGMO, MGMOI, and MGMOII, respectively, in the IRAQI 71 bus). Finally, the proposed modified algorithms proved their superiority and dominance over the original algorithm in converging to the optimal solution for find-ing the optimal position and sizing of a PV-DG (after 28, 25, and 19 iterations for the OGMO, MGMOI, and MGMOII, respectively, in the IEEE 33 bus, after 27, 23, and 20 it-erations for the OGMO, MGMOI, and MGMOII, respectively, in the IRAQI 71 bus), and the performance of the MGMOII is better than the performance of the MGMOI because it requires fewer iterations to reach the optimal solution.