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Building the conditional probability distribution of wind power forecasterrors benefits both wind farms (WFs) and independent system operators (ISOs).Establishing the joint probability distribution of wind power and thecorresponding forecast data of spatially correlated WFs is the foundation forderiving the conditional probability distribution. Traditional parameterestimation methods for probability distributions require the collection ofhistorical data of all WFs. However, in the context of multi-regionalinterconnected grids, neither regional ISOs nor WFs can collect the raw data ofWFs in other regions due to privacy or competition considerations. Therefore,based on the Gaussian mixture model, this paper first proposes aprivacy-preserving distributed expectation-maximization algorithm to estimatethe parameters of the joint probability distribution. This algorithm consistsof two original methods: (1) a privacy-preserving distributed summationalgorithm and (2) a privacy-preserving distributed inner product algorithm.Then, we derive each WF's conditional probability distribution of forecasterror from the joint one. By the proposed algorithms, WFs only need localcalculations and privacy-preserving neighboring communications to achieve thewhole parameter estimation. These algorithms are verified using the windintegration data set published by the NREL.

Privacy-Preserving Distributed Parameter Estimation for Probability Distribution of Wind Power Forecast Error