Time delay system control and application in electricity market

In many real-world engineering systems, the rate of variation in the system state depends on the past states, which characteristic is called delay or a time delay. As time delay will degrade the system dynamic performance and even destroy the system stability, the stability analysis of a system with a time delay has been investigated in many real control systems such as load frequency control scheme of power systems, genetic regulatory network, digital filter, electricity market and economic dispatch of the power system. Several improved stability criteria of time delay systems are proposed and applied in power system control with time delay such as load frequency control and electricity market. In this thesis, the Lyapunov-Krasovskii functional and the Wirtinger inequality have been investigated to establish several new stability criteria at first. The Wirtinger-based inequality used in a linear system with two additive time-varying delays is investigated and applied in load frequency control system in chapter 2. In chapter 3, an improved stability criterion based on Wirtinger-type double integral inequality was developed and applied in genetic regulatory networks. Then, in chapter4, the proposed method has been extended to a discrete system and applied in digital filters. Chapter 5 presents a further improve a stability criterion using Wirtinger-type three integral inequality and applied in the power system, including load frequency control system and economical dispatch system. In chapter 6, the stability analysis of an electricity market with a time-varying delay is studied. The dynamic model of an electricity market is presented to minimize the operation cost. The impact of a time delay on this dynamic model is analysed via a stability criterion developed in Chapter 5. The main contribution of the thesis is not only proposes several stability criteria based on the Lyapunov-Krasovskii functional and Wirtinger inequality but also applying the methods in power systems, genetic regulatory network and digital filter. Effectiveness of those new stability criteria has been verified via simulation studies based on numerical examples and those industry time-delay systems