Narrowing Frequency Probability Density Function for Achieving Minimized Uncertainties in Power Systems Operation – a Stochastic Distribution Control Perspective

Abstract

In this paper, the summary of the stochastic swing equation will be firstly given taking into account of DERs. This will then be followed by the development of stochastic distribution control model that links the power sources and the loads with the PDF of the frequency using Fokker Planck Kolmogorov (FPK) equations. A generic constrained optimization problem will be formulated, where the cost function is composed of a kind of “functional distance” between the actual and the desired PDFs of the frequency. A feasible solution using B-spine Neural Networks based stochastic distribution control model will be described. Using the obtained stochastic distribution control model, a feedback type control algorithm will be described that uses controllable power sources and the loads to shape the PDF of the frequency or to minimize the randomness of the frequency via minimized entropy approach. Future directions will be briefly discussed in the later part of the paper.