Wide-Area Damping Controllers for Power System with Time Delays and Actuator Saturation

Abstract

Low-frequency Inter-area oscillations (0.2–0.8 Hz) have severe influence on the operation of an interconnected power system due to the involvement of numerous generators. The poorly damped inter-area oscillations are detrimental to the power system stability and meeting the goal of maximum power transfer capacity between the areas. Wide-area measurement system-based Wide-Area Damping controllers (WADC) for controlling devices such as FACTS, HVDC effectively damp out these oscillations. However, due to the usage of the communication network to transfer the wide-area signals and the physical limitations of the controller devices in the feedback loop, new problems are encountered in the design of WADC such as time delays and actuator saturation. These problems would degrade the control performance and even lead to the closed-loop instability, therefore it is necessary to consider time delays and actuator saturation limits in the design of WADC.

This thesis presents the design of WADC for Thyristor Controlled Series Capacitor (TCSC) device to improve the inter-area oscillation damping of power system subjected to time delay sand actuator saturation. To compensate the time delays, a WADC with prescribed degree of stability is proposed by using delay-dependent approach. Residue approach and Schur balanced model reduction methods are used to obtain input-output control signals and reduced order power system model to design a WADC. The α-stability region is considered to place all the poles of the closed-loop power system in the left of s = −α in the complex s-plane. The sufficient conditions ascertain the existence of the damping controller that guarantees the asymptotic stability of the closed-loop power system with time-delays are derived in Linear Matrix Inequality(LMI)form using Lyapunov-Krasovskii(L-K) functional with Free Weighting Matrix (FWM) approach. The proposed sufficient conditions are solved by using LMI solvers to obtain the parameters of the WADC and delay margin of the closed-loop power system.

Actuator saturation is an inevitable phenomenon in control system which degrades the system performance if it is not considered in the controller design. To reduce the influence of actuator saturation, direct and indirect approaches are used to design a WADC for the power system. A generalized sector condition is used to characterize the actuator saturation nonlinearity in the closed-loop formulation. Actuator saturation limits are symmetric and asymmetric in nature. Asymmetric actuator saturation limits needs to be converted into symmetric saturation limits which can be expressed in Linear Matrix Inequality (LMI) form for analysis. In this thesis, a Minimum Absolute Saturation Bound (MASB) and Normalized Saturation Bound (NSB) techniques are used to convert the asymmetric saturation limits into symmetric limits. Based on L–K functional with FWM approach, a delay-dependent stability and stabilization conditions via LMI formulation are derived to guarantee the asymptotic stability of the closed-loop power system with time delays and actuator saturation. The FWM approach provides less conservativeness results, however, it increases the complexity in the design of WADC. To reduce the complexity and conservativeness of the stability conditions, an appropriate L-K functional with Jensen’s integral inequality is proposed to derive a less conservative stability condition. These conditions are cast into the LMI-based convex optimization problem to calculate the delay margin and to determine the parameters of the WADC.

Small-signal analysis and time-domain simulations are carried out first using MATLAB/Simulink on a two-area four-machine power system to evaluate the performance of the proposed WADCs for different operating conditions. Then to validate the obtained simulations results in real-time environment, the proposed WADCs are implemented in real-time using an Opal-RT digital simulator. From the obtained results, it is observed that the proposed WADCs enhance the dynamic performance of the power system and provide sufficient damping to inter-area oscillations by compensating the effect of time delay and actuator saturation. Among the proposed WADCs, the DDAWC designed for HWADC using indirect approach exhibits superior performance compared to the WADCs designed using direct approach.