Global Probabilistic Voltage Sensitivity Analysis of Active Distribution Networks Based on the Compound Gaussian Mixture Model

The stochasticity of the high penetration of distributed generations (DGs) exacerbates the voltage fluctuation of the active distribution networks (ADNs) and complicates its voltage safety analysis. Therefore, this paper proposes a global probability voltage sensitivity analysis method based on the compound Gaussian mixture model (GMM). Firstly, a shared node path impedance-based global voltage sensitivity analytical model of ADN is derived to quantify the impact of global power fluctuations on node voltage. Considering that the voltage fluctuation has the non-Gaussian characteristic under the superposition influence of power uncertainty injected by multiple nodes, the GMM is used to characterize the probability characteristics of DG and load forecasting errors. Then, based on the affine transformation of the global sensitivity matrix to the GMM of DG and load forecasting error, the probability analytic expression of the voltage fluctuation is constructed, which is caused by the uncertainty of DG and load. Finally, based on the GMM characteristic function, the compound GMM characteristic function of the combined influence of the uncertainty of DG and load on voltage fluctuation is derived, and the global probabilistic voltage sensitivity analysis model based on the compound GMM is established. The case study results show that the proposed method can reflect the probability characteristics of the impact of all node power fluctuations on node voltage, and can quickly and accurately calculate the probability of over-voltage in ADNs. © 2025 Power System Technology Press. All rights reserved.