7.1. C ONCLUSIONS
In this thesis, a survey of the fundamentals and history of SMC and time delay sys-tems with application to power syssys-tems have been presented. The syssys-tems structure with non-linear delayed disturbances were fully considered and it’s applications have been tested on power system models. Although the issue of communication delays in wide area network remains an open problem for multi-area power systems integration, the re-sults presented in this thesis has improved several rere-sults in this domain. This thesis has been presented in seven chapters.
In the first and second chapters of this thesis, an introductory knowledge and liter-ature reviews have been presented alongside main contributions of the thesis, followed by the mathematical preliminaries which have been used. The third chapter presents a general introductory knowledge and concepts of controllability, linear feedback control system, SMC, time delay systems, interconnected systems and power systems with sim-plified illustrative examples have been presented.
systems with non-linear disturbances is proposed. The objective of the designed delay dependent smc controller is to force the system position to track a desired trajectory. The systems stability is analysed based on Lyapunov Razumikhin method combined with ba-sic LMI technique to achieve a less conservative result such that the developed uncertainty bounds can be fully applied in the controller design for rejecting the effect of uncertainty in the system. In order to make the system more robust to uncertainties, much focus has been placed on disturbance tolerability, and matched and mismatched uncertainty is also considered which involve time-varying delay. The simulation result indicate that the proposed controller works well for the AVR system and the numerical example. More so, the simulation studies indicate that the proposed control scheme is robust to bounded uncertainties.
A load frequency SMC for reheat turbine system with turbine-end delays and multi-ple delayed non-linear term is proposed in the fifth chapter. The objective is to introduce turbine-end delays which will account for unnecessary delays in the turbine region, and also consider multiple delay around the input which may result in increased oscillation.
Various Lyapunov stability methods have been used to achieve sufficient results such that the multiple delays and non-linearities within the modified time delay system are sta-ble within bounds and a sufficient ultimate bound is achieved for step load disturbances.
Load frequency SMC with reduced chattering effects have been developed, and simula-tion is conducted using matlab/simulink tool for a single area reheat turbine generating unit, such that the closed-loop performance of the considered system is ensured. Result obtained from simulation shows a robust and effective designed controller. This technique is useful for protecting the turbine further in real application, and also reduced oscillations caused by input delays.
The sixth chapter considers the multi-area power systems. It presents a systematic approach for dealing with large constant and time-varying communication delays and un-certain non-linear interconnection in the multi-area power system. Robustness has been achieve by dealing with the interconnection as a separate non-linear uncertain term. The parameter uncertainties are assumed to be matched and based on Lyapunov-Razumikhin
approach. There is no limitation to the size of the delay. In addition, the system allows the bounds on the uncertainties not only have more general non-linear form but also involve time delay. A two area LFC model is simulated to show the feasibility of the developed results and the effectiveness of the proposed method. Furthermore, the technique devel-oped here is robust and sufficient to adapt future growing network delays and uncertain interconnection.
7.2. F UTURE W ORK
Future research interest is shaped by the emerging trend towards the increase in size and complexity of interconnected systems due to renewable energy integration. Many challenging issues associated with time delay such as stabilisation, robust performance analysis etc., are still open areas in almost every engineering application and cannot be ignored. Therefore, it is meaningful to explore further ways to improve systems structure and applications.
Although, this thesis have only considered single input single output (SISO) systems, multi input multi output (MIMO) systems will be considered in the future. In order to show the reliability and validity of the proposed method, further comparative studies will be conducted in future work. As wide area network communication time delay increases due to large-scale industrial processes. It is important to understand that certain systems may be at risk of unknown delays and parameters, thereby increasing its likelihood to risk of uncertainties. Therefore, it will be interesting to extend my research to delay independent control cases, a phenomenon of unknown delays as compared with known delay cases in previous works. Also, the use of Lyapunov Krasovskii methods of time delay stability will be studied as compared with Razumikhin in this thesis. More so, if unknown parameters exists in considered system, adaptive technique may be employed in the future.
From application perspective, a much more integrated approach to SMC design will be studied and the developed results will be applied to broad areas of power systems network and other energy related applications.