Abstract

A modern power system faces daily challenges due to changes in load and gen-
eration patterns. These changes contribute significantly to the secure operation
of the electrical network and power system stability and small signal stability.
The work presented extends and contributes to research in power system stability
and focuses on the predicting inter-area low-frequency oscillations on the integ-
rated power system. Previous work in this area has made use of load flow models
and traditional machine learning techniques such as linear regression and support
vector machines to predict disturbances. The introduction of synchrophasor tech-
nology through the use of Phasor Measurement Units (PMUs) has, amongst other
benefits, contributed to the monitoring of low-frequency oscillations. However,
high resolution time series data provided by the PMUs require advanced meth-
ods of analysis to achieve the prediction target. In the research presented, data
from five different PMU devices on the Southern African power system is used
to predict eigenvalue locations on the eigenvalue plane using a Recurrent Neural
Network technique known as Long Short Term Memory (LSTM). It is shown that
the LSTM algorithm can accurately predict a small signal stability disturbance
using a preceding window length of 20 seconds before the actual event occurs.
Eigenvalues are estimated from the measured PMU data using the Matrix Pencil
Method of eigenvalue estimation. LSTM showed an 80% accuracy in predicting
the eigenvalues on the eigenvalue plane. Recommended future work would be to
investigate the use of PMU devices for power system inertia prediction and to
further determine the location of the disturbance on the network.


	Introduction
	Background
	Problem Statement
	Research Question
	Structure of the Dissertation
	Conclusion

	Power System Stability
	Voltage Stability
	Frequency Stability
	Rotor angle stability
	Large-disturbance or transient angle stability
	Small-disturbance or small-signal angle stability

	Characteristics of small signal stability problems
	Eigenvalue Analysis
	Conclusion

	Synchrophasor Technology
	Overview
	History
	Fundamentals of PMUs
	WAMS Applications
	Improved State Estimation
	Post Event Analysis
	Monitoring of the Power System Stability
	Model validation
	Re-synchronise islanded networks

	WAMS across the World
	PMU Case Studies - South Africa
	PMUs and Big Data
	Conclusion

	Machine Learning Algorithms
	Background
	Supervised Learning
	Unsupervised Learning
	Reinforced Learning
	Deep Learning
	Machine Learning Application in Power Systems
	Neural Networks
	Recurrent Neural Networks
	LSTM

	Conclusion

	Small-Signal Power System Stability Analysis using synchrophasor measurements
	Background
	Analysis Methods
	Mode Estimation Method
	Prony Analysis
	Matrix-Pencil Method

	Conclusion

	Evaluation of Machine Learning on PMU Data
	Data Collection
	Data Pre-processing
	Prediction Method
	Summary of the method
	Eigenvalue Region Prediction
	Conclusion

	Results and Discussion
	Prediction Method Verification
	Eigenvalue Area Prediction
	Real World Application

	Discussion
	Conclusion

	Conclusions
	Summary
	Conclusion
	Future Work

	References
	Appendices
	- About MATLAB R2020a
	- FFT MATLAB Code
	- Matrix Pencil Estimation Method MATLAB Code
	- Prony Estimation MATLAB Code
	- Power Calculation and Standardization Script
	- LSTM Machine Learning MATLAB Code
	- Eigenvalue estimation for train and test disturbances