Probabilistic voltage sensitivity analysis (PVSA) for random spatial distribution of active consumers

The future grid is expected to support many active consumers who will act as prosumers, and schedule their load as well as generation in accordance with real-time electricity prices. The impact of spatially distributed active consumers with rooftop photovoltaics on the distribution system must be quantified for operational planning. Most current studies are scenario-based, and derived results are scenario specific. Determining the impact of multiple active consumers with temporally variable behavior requires investigation of a large number of scenarios, which is computationally complex using current iterative power flow algorithms. This paper presents an upper bound for change in voltage at a particular bus due to change in power at other buses in a radial distribution network. Next, this bound is used to derive the probability distribution of voltage change at a bus due to random behavior of spatially distributed multiple active consumers. Results from the proposed probabilistic voltage sensitivity analysis (PVSA) are validated via traditional scenario based simulation of the IEEE 69 bus test system.