On The Design of Robust Governors of Steam Power Systems Using Polynomial and State-Space Based H∞ Techniques: A Comparative Study

This work presents a comparison study between the state-space and polynomial methods for the design of the robust governor for load frequency control of steam turbine power systems. The robust governor is synthesized using the two approaches and the comparison is extended to include time and frequency domains performance, controller order, and uncertainty representation, weighting filters, optimality and sub-optimality. The obtained results are represented through tables and curves with reasons of similarities and dissimilarities. Keywords—Robust control, load frequency control, steam turbine, H∞-norm, system uncertainty, load disturbance. I. BACKGROUND AND MOTIVATION OWER system stability can be defined as that property of a power system that enables it to remain in state of operating equilibrium under normal operating conditions and to regain an acceptable state of equilibrium after being subjected to a disturbance. The quality of power supply must meet certain minimum standard requirements with special attention being given to the constancy of frequency [1], [2]. Our main concern in work paper concerns the above issue. Most universal method of electric generation is accomplished using thermal generation, and the most common machine for this production is the steam turbines. In the world most of the generation is powered by steam-turbine-driven generators [2]. Poor balancing between generated power and demand can cause the system frequency to deviate away from the nominal value, and create inadvertent power exchanges between control areas. to avoid such a situation, load frequency controllers (LFC) are designed and implemented to automatically balance between generated power and the demand power in each control area [1], [3], [4]. The problem of load frequency control has been investigated by many researchers. In [5] speed governors have been designed based on PID techniques with different philosophies because of its simplicity and ease of implementation. Fuzzy sliding mode controller for LFC has been designed in [6] to account for the system’s parameters variations and the governor backlash. Genetic algorithm (GA) is a global search optimization technique. The researchers in Rami A. Maher is with Isra University, Electrical Engineering Department, P.O. 11622, Amman, Jordan. (e-mail: [email protected]). Ibraheem K. Ibraheem is with the Department of Electrical Eng. Dept. / Engineering College / Baghdad University, Iraq (phone: 009647702562658; P.O.B: 47273; e-mail: [email protected]). [7] used GA for tuning the control parameters of the proportional-integral (PI) control subject to the ∞ H constraints in terms of LMI. Modern control techniques have been reported in [8], [9] in which a load frequency controller for power systems has been designed using LQR techniques. The work in [10] investigated the design problem or robust load frequency controller using LMI methods for solving the ∞ H control problem. This paper is organized as follows: Section II describes the modeling of steam turbine system, Section III presents the design formulation for the ∞ H governor using polynomial and state-space approaches, Section IV is devoted to the performance evaluation of the robust governors. The conclusions are summarized in Section V. II. STEAM TURBINES AND SPEED GOVERNING SYSTEM A steam turbine converts stored energy of high pressure and high temperature steam into mechanical energy, which is in turn converted into electrical energy by the generator. The heat source for the boiler supplying the steam may be a nuclear reactor or a furnace fired by fossil fuel (coal, oil, or gas) [1], [2]. A typical mechanical-hydraulic speed governing system consists of a Speed Governor (SG), a Speed Relay (SR), a Hydraulic Servomotor (SM), and Governor-Controller Valves (CVs). In steam turbine-generator system, the governing is accomplished by a speed transducer, a comparator, and one or more force-stroke amplifiers. Fig. 1 depicts the complete system block diagram of a steam turbine generator [2]. Speed Governor (SG):