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Addition of distributed energy resources (DERs) in power systems (PS) coupled with uncertain loading has increased system uncertainties. The usual deterministic stability solution is no longer sufficient. While probabilistic methods (PM) have been explored before, their focus has mainly been on system events like faults or the realization of microgrids composed of DERs. Voltage stability (VS) analysis of a PS mixed with DERs has not received sufficient attention. In this work, a Bayesian parameter estimation (BPE) method is proposed. BPE works efficiently with efficient sampling techniques such as the Markov Chain Monte Carlo (MCMC) to accurately estimate uncertain parameters with good computation speed while using smaller data sample sizes. DERs and loads are represented by their respective statistical models. The models are then transformed into the Bayesian inferential framework. Using the BPE algorithm, uncertain parameters are estimated and their corresponding power outputs are obtained. The estimated powers are injected in the continuous power flow (CPF) to determine the VS of the PS. The proposed BPE has been tested on the 14 generator, 59 bus Australian IEEE benchmark. Test results show that with a 4.33% generation increase from DERs, leads to 11% enhancement in voltage stability margin of the PS.
Wanjoli et al. (Sun,) studied this question.