Radial distribution power systems (RDPSs) are essential in the power system to supply electricity to loads for developing industries, commerce, and services in countries. However, RDPSs have many distribution lines with high resistance, causing high active power loss. So, the core target of the study is to reduce the total active power loss, considering the highest penetration level of installed PVUs. Photovoltaic units (PVUs) are placed optimally by implementing the Coot optimization algorithm (COOA), the archimedes optimization algorithm (AOA), the transient search optimization algorithm (TSOA), the crystal structure algorithm (CrSA), the war strategy optimization algorithm (WSA), and the average and subtraction-based optimizer (ASBO). Two test RDPSs with 33 and 69 nodes are employed for four different study cases, including (1) the number of PVUs is three and the power factor is 1.0; (2) the number of PVUs is three, and the power factor is optimally determined; (3) the number of PVUs is determined optimally while the power factor is 1.0; and (4) the number of PVUs and the power factor of PVUs are optimally determined. For the first system, COOA can reach smaller power losses than others by 0.14% to 13.059% for Case 1, 0.5% to 77.89% for Case 2, 0.101% to 10.126% for Case 3, and 11.818% to 88.492% for Case 4. For the second system, COOA can reach a lower loss than others by 0.164% to 15.511% for Case 1, 0.774% to 78.6% for Case 2, 0.173% to 15.104% for Case 3, and 46.201% to 95.389% for Case 4. Especially in Case 4, the power loss is approximately equal to zero. The loss reduction is the first significant contribution of the study. In addition, the study also investigated the difference between the four cases for obtaining power loss reduction, the maximum penetration level of active and reactive power of PVUs, and the improvement of load voltage. As a result, Case 4 is superior to the three other cases. Thus, the number, peak power, power factor, and location of added PVUs in RDPSs should be simultaneously optimized, and one of the most effective optimization tools is COOA.