Statistical Machine Learning Model for Stochastic Optimal Planning of Distribution Networks Considering a Dynamic Correlation and Dimension Reduction

TLDR

Distributed generation and reactive power allocation influence the economy and security of distribution networks, but deterministic scenario planning fails to address uncertainties from intermittent renewables and variable demand, and stochastic programming becomes computationally burdensome with many scenarios. The study proposes statistical machine learning theories to rapidly solve optimal capacitor planning in distribution networks. The approach employs Markov chains and copula functions to model weather variability and correlation, incorporates weather‑sensitive load modeling, applies nearest‑neighbor and nonnegative matrix decomposition for dimensionality and scenario reduction, uses a stochastic response surface for probabilistic power flow, and applies probabilistic inequality theory to estimate objective and constraints directly. The method’s effectiveness and efficiency are demonstrated by outperforming scenario‑reduction algorithms and Monte Carlo simulations on a 33‑bus distribution system.

Abstract

Distributed generation and reactive power resource allocation will affect the economy and security of distribution networks. Deterministic scenario planning cannot solve the problem of network uncertainties, which are introduced by intermittent renewable generators and a variable demand for electricity. However, stochastic programming becomes a problem of great complexity when there is a large number of scenarios to be analyzed and when the computational burden has an adverse effect on the programming solution. In this paper, statistical machine learning theories are proposed to quickly solve the optimal planning for capacitors. Various technologies are used: Markov chains and copula functions are formulated to capture the variability and correlation of weather; consumption behavior probability is involved in the weather-sensitive load model; nearest neighbor theory and nonnegative matrix decomposition are combined to reduce the dimensions and scenario scale of stochastic variables; the stochastic response surface is used to calculate the probabilistic power flow; and probabilistic inequality theory is introduced to directly estimate the objective and constraint functions of the stochastic programming model. The effectiveness and efficiency of the proposed method are verified by comparing the method with the scenario reduction algorithm and the Monte Carlo method in a 33-bus distribution system.