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From an operational and planning perspective, it is important to quantify the impact of increasing penetration of photovoltaics on the distribution system voltage. Most existing impact assessment studies are scenario-based where derived results are scenario specific and not generalizable. Moreover, stochasticity in temporal behavior of multiple spatially distributed PVs requires a large number of scenarios to be simulated that increases with the size of the network and the level of penetration. Therefore, we propose a new computationally efficient analytical framework of voltage sensitivity analysis that allows for stochastic analysis of voltage change due to random changes in PV generation. We derive an analytical approximation for voltage change at any node of the network due to a change in power at other nodes in an unbalanced distribution network. Then, we derive the probability distribution of voltage change at a certain node due to random changes in power injections/consumptions at multiple locations of the network. The accuracy of the proposed method is illustrated using a modified version of IEEE 37 bus and IEEE 123 bus test systems. The proposed framework can serve as a powerful tool for proactive monitoring/control of voltage, and ease the computational burden associated with perturbation based cybersecurity mechanisms.

Probabilistic Voltage Sensitivity Analysis to Quantify Impact of High PV Penetration on Unbalanced Distribution System