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

Hong Wang1, Zhihua Qu

  • 1Pacific Northwest National Laboratory



Invited Session


13:30 - 15:30 | Wed 22 Aug | Christiansborg | WeB2

Distributed Energy Resources

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With the increased penetration of renewables and other distributed energy resources (DERs), the frequency response in power systems exhibits stochastic nature, where the standard deterministic swing equation should be either represented or transferred into an Ito stochastic differential equation whose solution should be the non-stationary transient behavior of the probability density function (PDF) of the frequency. This transfers the frequency quality control for power systems into a stochastic distribution control problem, where the shape of the frequency distribution, namely the frequency PDF, needs to be directly controlled. In this context, this requires the development of control strategies via controlling the power balance so that the PDF of the frequency is made as narrow as possible whilst centered at its required mean value simple because such a sharp distribution shape means less uncertainties or randomness for the frequency response. In this paper, the summary of the stochastic swing equation will be given first taking into account of DERs. This will then be followed by the development of stochastic distribution control model that links the power sources 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 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 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.

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