  From an operational and planning perspective, it is important to quantify the
impact of increasing penetration of photovoltaics on the distribution system.
Most existing impact assessment studies are scenario-based where derived
results are scenario specific and not generalizable. Moreover, stochasticity in
the temporal behavior of spatially distributed PVs requires a large number of
scenarios that increase 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 first derive an
analytical approximation for voltage change at any node of the network due to
change in power at other nodes in an unbalanced distribution network. The
quality of this approximation is reinforced via bounds on the approximation
error. 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 PVSA is illustrated
using a modified version of the IEEE 37 bus test system. The proposed PVSA can
serve as a powerful tool for proactive monitoring/control and ease the
computational burden associated with perturbation based cybersecurity
mechanisms.
