A Photovoltaic System Investment Game for Assessing Network Hosting Capacity Allocations

The rapid rise of PV installations in low-voltage (LV) distribution networks means that they are likely to exceed network hosting capacity. For this reason, distribution network service providers (DNSP) have begun to mandate connection codes, such as inverter Volt/Var control and/or PV active power curtailment, to mitigate the resulting network problems. This approach manages the network state, but may cause an existing PV system to become inefficient as it is curtailed more often. This paper investigates the effects on overall economic efficiency and individual customer welfare of natural uncoordinated rooftop PV investment processes that arise when customers invest in PV systems independently to maximize their individual welfare. We develop a novel game-theoretic framework that computes the annual payoffs to customers for different PV investment sizes, given the installations of other customers. This calculation is based on an optimal AC power flow model that includes inverter connection standards that link customers' annual payoffs via their effects on AC network voltages and consequent PV curtailment responses. We show that the interaction of PV investments produces a concave potential game with continuous action sets, which has a pure Nash equilibrium that can be found using an adaptive learning process. Then, to evaluate the efficiency of the investments under the game model, we compute an centrally-coordinated PV investment profile, found by solving an optimal PV sizing problem that maximizes social welfare across all customers. Comparing the value of investment patterns for the game and the centrally-coordinated optimization shows: (i) the inefficiency of the Nash equilibrium is 1.4, which indicates the efficiency loss resulting from uncoordinated PV investments, and (ii) the inequity of a skewed distribution of benefits, penalising customers closer to the distribution transformer and benefiting those towards the end of the feeder. This model provides a quantitative tool for evaluating policies and regulations that improved coordination and allocation of PV hosting capacity (and that of other energy distributed energy resources) between customers on LV feeders.