{'fraction_non_alphanumeric': 0.014122394082044385, 'fraction_numerical': 0.0013449899125756557, 'mean_word_length': 5.497816593886463, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Probabilistic Voltage Sensitivity Analysis (PVSA)—A Novel Approach to Quantify Impact of Active Consumers

Active consumers will be integral to the future smart grid, scheduling their load and managing renewable generation in accordance with real-time pricing. The impact of spatially distributed renewable generation and active consumers on the distribution system must be quantified for operational planning. Most of the current studies are scenario-based and derived results are scenario specific. Determining the impact of spatially distributed active consumers with temporally variable behavior requires investigation of a large number of scenarios, which is computationally intractable using current iterative power flow algorithms. The objective of this work is to provide a new analytical method of voltage sensitivity analysis that allows for stochastic analysis of change in grid voltage due to change in consumer behavior (load and generation choices). This paper first derives an upper bound for change in voltage at a particular bus due to change in complex power at other buses in a radial distribution network. This bound is verified via simulations. 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 is validated via traditional-scenario-based simulation of the IEEE 69 bus test system.