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

## TL;DR

This paper introduces a privacy-preserving distributed algorithm based on Gaussian mixture models to estimate joint and conditional wind power forecast error distributions without sharing raw data.

## Contribution

It develops novel privacy-preserving distributed expectation-maximization algorithms using local computations and neighbor communications for wind power error modeling.

## Key findings

- Algorithms successfully estimate joint distribution parameters.
- Preserves data privacy during distributed estimation.
- Validated with NREL wind data set.

## Abstract

Building the conditional probability distribution of wind power forecast errors benefits both wind farms (WFs) and independent system operators (ISOs). Establishing the joint probability distribution of wind power and the corresponding forecast data of spatially correlated WFs is the foundation for deriving the conditional probability distribution. Traditional parameter estimation methods for probability distributions require the collection of historical data of all WFs. However, in the context of multi-regional interconnected grids, neither regional ISOs nor WFs can collect the raw data of WFs in other regions due to privacy or competition considerations. Therefore, based on the Gaussian mixture model, this paper first proposes a privacy-preserving distributed expectation-maximization algorithm to estimate the parameters of the joint probability distribution. This algorithm consists of two original methods: (1) a privacy-preserving distributed summation algorithm and (2) a privacy-preserving distributed inner product algorithm. Then, we derive each WF's conditional probability distribution of forecast error from the joint one. By the proposed algorithms, WFs only need local calculations and privacy-preserving neighboring communications to achieve the whole parameter estimation. These algorithms are verified using the wind integration data set published by the NREL.