Probabilistic Power Flow Analysis of DERs Integrated Power System From a Bayesian Parameter Estimation Perspective

The rise of distributed energy resources (DERs) in power systems demands efficient models for power flow analysis. Existing models often face challenges in balancing computation speed and accuracy. This paper presents a probabilistic power flow (PPF) method for systems with DERs, using Bayesian parameter estimation (BPE) to handle uncertainties in wind speed, solar irradiance, and loads. By applying Bayes' theorem, BPE estimates posterior distributions, refined by the Metropolis-Hastings algorithm. Validated on IEEE 39-bus and 59-bus test systems in MATLAB/Simulink, BPE outperformed the 2m+1 point estimate method (PEM) in terms of accuracy, computation speed and scalability. Simulation results demonstrate superior accuracy of BPE, yielding voltage profiles and congestion indices closely matching those of Monte Carlo Simulation (MCS) but with lower computation time. For instance, under heavy loading, BPE achieved a congestion index of 0.0617 (compared to PEM's 0.2228 and MCS's 0.0611). BPE also provided faster results as system size increased, averaging 3.477 hours, versus PEM's 6.837 hours and MCS's 11.524 hours. Statistical analyses confirmed BPE's consistent performance and minimal error, making it more efficient for large systems. Thus, BPE-based PPF is recommended for power system planning and operation under uncertain conditions, owing to its robustness, accuracy, and computational efficiency.