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. 2019 Nov 14;5(11):e02704.
doi: 10.1016/j.heliyon.2019.e02704. eCollection 2019 Nov.

Radial basis function for fast voltage stability assessment using Phasor Measurement Units

Jorge W Gonzalez  1 , Idi A Isaac  1 , Gabriel J Lopez  1 , Hugo A Cardona  1 , Gabriel J Salazar  1 , John M Rincon  1
Affiliations

Radial basis function for fast voltage stability assessment using Phasor Measurement Units

Jorge W Gonzalez et al. Heliyon. .

Abstract

A simple method, based on Machine Learning Radial Basis Functions, RBF, is developed for estimating voltage stability margins in power systems. A reduced set of magnitude and angles of bus voltage phasors is used as input. Observability optimization technique for locating Phasor Measurement Units, PMUs, is applied. A RBF is designed and used for fast calculation of voltage stability margins for online applications with PMUs. The method allows estimating active local and global power margins in normal operation and under contingencies. Optimized placement of PMUs leads to a minimum number of these devices to estimate the margins, but is shown that it is not a matter of PMUs quantity but of PMUs location for decreasing training time or having success in estimation convergence. Compared with previous work, the most significant enhancement is that our RBF learns from PMU data. To test the proposed method, validations in the IEEE 14-bus system and in a real electrical network are done.

Keywords: Electric power transmission; Electrical engineering; Electrical system planning; Machine learning; Phasor Measurement Units; Power engineering; Power system operation; Power system planning; Power system stability; Radial basis function networks; Voltage measurement.

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Figures

Fig. 1
Fig. 1
IEEE 14 bus bar system with PMU optimized placement.
Fig. 2
Fig. 2
Definitions for long-term voltage stability assessment.
Fig. 3
Fig. 3
Architecture of Radial basis function, RBF.
Fig. 4
Fig. 4
System with ANN and training process with matrices P and T.
Fig. 5
Fig. 5
Proposed Method for Voltage Stability training with RBF and a reduced set of Voltage Phasors.
Fig. 6
Fig. 6
Input matrix P for the RBF.
Fig. 7
Fig. 7
Target matrix T for the ANN.
Fig. 8
Fig. 8
Global voltage stability margin estimation in the modified 14 bus IEEE system with the trained RBF for three operating points (5, 710 and 1405) and different PMU locations.
Fig. 9
Fig. 9
Antioquia area grid.
Fig. 10
Fig. 10
Global voltage stability margin estimation in the Antioquia area grid with the trained RBF for three operating points (251, 3001, 5751). VSAT and optimum location.
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