Comprehensive Analytical Expressions for Assessing and Maximizing Technical Benefits of Photovoltaics to Distribution Systems

The proliferation of photovoltaic (PV) can cause several operational problems in distribution systems. In this paper, comprehensive analytical expressions (CAEs) are proposed for maximizing the technical benefits of multiple PV units to distribution systems considering the uncertainty of PV generation and load profiles. Specifically, the proposed CAEs quantify and optimize the following five vital indices with multiple PV units: 1) active energy losses, 2) reactive losses, 3) voltage deviations, 4) line congestion margin, and 5) voltage stability index. The smart functions of the PV inverter (i.e., reactive power support and active power curtailment) are also incorporated in the CAEs, complying with the revised IEEE 1547:2018 standard. Further, various PV tracking options are considered, including fixed, one-axis, and two-axis trackers. Unlike existing approaches, the CAEs can simultaneously solve the optimal allocation problem of multiple PV units in a direct manner without needing optimization algorithms, iterative processes, or simplifying procedures. The calculated results reveal the high performance of the CAEs in terms of accuracy, flexibility and computational speed while providing further PV planning options. Moreover, CAEs are effectively utilized for two other applications with promising computational performance, i.e., rapid assessment of PV impacts with annual datasets and optimal centralized/decentralized inverter control.