Abstract : This paper introduces the basic principles of excitation systems and applies iterative learning control theory to the design of excitation controllers. Based on a single-machine infinite bus system, the open-loop and closed-loop iterative learning control laws are compared with conventional PID control laws. Simulation results show that the iterative learning excitation controller has a strong ability to maintain the generator terminal voltage and can effectively improve the generator's power angle stability, demonstrating good application prospects. Keywords : power system; iterative learning control; generator excitation control[b][align=center]Iterative Learning Excitation Controller Design for Power Systems BAI Jing-cai, YU Shao-juan, HAN Ru-cheng (School of Electronic Information Engineering, Taiyuan University of science and technology, Taiyuan 030024, China)[/align][/b] Abstract : The principle of excitation system is introduced, and iterative learning control is applied to the design of excitation controller in the paper. Based on single machine to infinite system, the open-loop and closed-loop iterative learning control algorithms are compared with traditional PID control rule. Simulation results show that the designed iterative learning excitation controller can maintain the terminal voltage of generator on constant value, improve the generator angle stability greatly and would be applied in more fields. Key words : power system; iterative learning control; generator excitation controller Introduction The power system is a large-scale, nonlinear, dynamic system with multiple objectives and both continuous and discontinuous control. Currently, among the measures taken to improve power system stability, excitation control is one of the most effective and economical methods, offering advantages such as low investment, good results, and ease of implementation. Besides fulfilling its basic tasks, the excitation control system in a power system can also improve the dynamic quality of the generator excitation control system, thereby enhancing the operational stability of the power system. Among the many measures to improve the stable operation of synchronous generators, applying modern control theory to improve the control performance of the excitation system is recognized as one of the most economical and effective means. With the development of control theory and technology, optimal control, robust control, and variable structure control based on modern control theory have achieved remarkable results in excitation control systems. However, these control methods are designed based on precise mathematical models of the controlled object. Theoretically, these methods lack robustness to uncertainties in system parameters, and their application to solving problems arising from large systems, adaptability, and strong nonlinearity has significant limitations. Meanwhile, intelligent control, artificial neural network control, fuzzy control, and expert systems based on sample experiments, while effective, still struggle to address challenges posed by large systems, adaptability, and nonlinearity. At the same time, iterative learning control theory has made groundbreaking progress in the last 20 years and is gaining increasing attention in power system research. Iterative learning control continuously modifies the control inputs based on empirical information, gradually improving its future performance, and is independent of detailed models of the controlled system, making it highly adaptable to solving nonlinear problems in power systems. This paper introduces the working principle of the excitation system, analyzes two iterative learning excitation control schemes based on a third-order generator model, and establishes a simulation model of a typical single-machine infinite bus system using Matlab/Simulink. Simulation results show that the control scheme, which adds a power system stabilizer to the iterative learning excitation controller, enables the generator terminal voltage and power angle to converge rapidly to within the allowable range, effectively enhancing the damping of the generator excitation system and improving power system stability. Basic Model of Power System A single-machine infinite bus system is shown in Figure 1, where the voltage U[sub]S[/sub] of the infinite bus system is assumed to be constant, X[sub]τ[/sub] is the transformer reactance, and is the transmission line reactance. [align=center]Figure 1 Single-machine infinite bus system[/align] To perform dynamic analysis of the power system, it is first necessary to establish a mathematical model of the system for calculation. Power system models typically consist of the following types of models: ① Synchronous generator; ② Excitation power supply and its regulation system; ③ Prime mover and speed control system; ④ Load; ⑤ Power network. This paper takes the single-machine infinite bus system as the research object, mainly analyzing the mathematical model of the AC synchronous generator and excitation system, without considering the role of the prime mover and speed control system. Synchronous Generator Mathematical Model The mathematical model of the synchronous generator represents the mathematical expression of the relationship between electromagnetic quantities such as voltage, current, and flux linkage and mechanical quantities such as torque and speed of the synchronous motor. It is the foundation for dynamic analysis of synchronous motors and power systems. This paper only considers the change in excitation voltage and does not consider the effect of the rotor damping winding. The third-order mathematical model of the synchronous generator can be expressed as follows: Where: δ is the generator power angle; θ is the generator rotor angular velocity; θ0 is the generator steady-state angular velocity; H is the mechanical inertia constant; D is the damping coefficient; Eq is the q-axis transient electromotive force; Xd and Xsupd are the generator d-axis synchronous reactance and transient reactance, respectively; Xq is the generator q-axis synchronous reactance; Xr and Xz are the transformer and line reactance, respectively; T0 is the time constant of the excitation winding when the generator stator is open; U is the excitation control output voltage; Us is the infinite system voltage; Pm is the mechanical power of the generator. Excitation System Structure The excitation system of a synchronous generator consists of two parts. One is the excitation power supply, which provides DC excitation current to the excitation winding of the synchronous generator. The other is the excitation regulator, which controls the output of the excitation power supply according to requirements. The excitation system and the synchronous generator together form a closed-loop control system, called the generator excitation control system. This system is responsible for a series of tasks, including controlling the voltage ratio, distributing reactive power, and improving power system stability. By equipping each generator in the power system with a fast high-peak voltage thyristor excitation control system, the recovery of generator voltage after a power system fault and the transient stability of the system can be significantly improved. If a Power Stability System (PSS) device is further configured, the dynamic process of subsequent generator oscillations (referring to oscillations beyond the first oscillation cycle) after a short circuit in the power system can be greatly improved, allowing the oscillations to subside rapidly. The general functional block diagram of the excitation control system used for power system stability calculation and analysis is shown in Figure 2. Design of Iterative Learning Excitation Controller Iterative learning control is a novel intelligent control method, mainly targeting repetitive or periodic controlled objects. It utilizes prior control experience and measured tracking error signals, employing a certain learning law and repeated training process to feedforward the control quantity for the next iteration, thereby finding an ideal control input signal. This enables the controlled system to output a high-precision tracking trajectory within a finite time and interval. In recent years, the theoretical system of iterative learning control has become increasingly mature, and its application areas have become increasingly widespread. If we consider each swing of the power angle as a control cycle, then the electromechanical transient stability control of the power system can be viewed as periodic control. Rewriting the system described by equation (1) as an affine nonlinear system, for this dynamic process, if the desired control υ[sub]d[/sub](t) exists, then the objective of iterative learning control is: given the desired output y[sub]d[/sub](t) and the initial state x[sub]κ[/sub](0) for each run, within a given time t∈[0,t], according to a certain learning law, through multiple repeated runs, to make the control input equal to the system output. The output error is: Iterative learning control can be divided into two forms: open-loop control and closed-loop control. The basic structure is shown in Figures 3 and 4. In this design, open-loop PID and closed-loop PID iterative learning control algorithms are selected. The open-loop learning control method is that the control at the (K+1)th iteration is equal to the control at the Kth iteration plus the correction term of the output error at the Kth iteration. The closed-loop learning control method takes the error at the Kth iteration as the correction term for learning. In the formula, L is the open-loop or closed-loop PID learning operator. Open-loop iterative learning control has a large number of iterations and a long cycle. In the early stage of the iteration, it is prone to divergence and excessive overshoot, which limits the application of iterative learning control. The closed loop uses the control quantity of the previous iteration and the tracking error at the current iteration. As can be seen from the open-loop and closed-loop structure diagrams above, the open loop generates υ first and then obtains the state variable x; the closed loop, because it needs to use the tracking error e of the current iteration, generates x first and then obtains υ. Simulation Results and Analysis To study the control effect of open-loop and closed-loop PID iterative learning excitation control laws for generators, the single-machine infinite bus system shown in Figure 1 was simulated using MATLAB/Simulink simulation tools, and compared with conventional PID feedback control laws. The parameters of the single-machine infinite bus system shown in Figure 1 are: (1) Synchronous generator parameters; (2) Line and transformer parameters; (3) Parameters at the initial point of the system; (4) The infinite bus system is replaced by a three-phase power supply module, with the parameters set to the preset fault value of t=0.1s in the simulation: at t=0.1s, a three-phase short circuit to ground occurs at point k on the high-voltage side of the transformer; at t=0.2s, the protection system operates and disconnects the faulty line. During the simulation, it is assumed that the input mechanical power remains constant. The dynamic response curves of the system under the action of the three control laws are shown in Figure 5. From the simulation results in Figures (a), (b), and (c), it is easy to see that the two excitation controllers designed using the iterative learning control algorithm have a significantly better ability to maintain the generator terminal voltage than conventional PID control. Open-loop iterative learning control can maintain the terminal voltage within the specified range after 13 iterations, while closed-loop iterative learning control only requires 5 iterations to meet the requirements. Furthermore, the oscillation amplitudes of angular velocity ω and power angle β are much smaller than those of conventional PID control. Conclusion This paper applies iterative learning control theory to the design of an excitation control system, achieving good results through simulation. However, this is still in the exploratory stage. Because this method can handle strongly nonlinear and time-varying problems better than other control methods, its application prospects are limitless. In this design, the control objective is only the terminal voltage; therefore, it is difficult to solve the multi-objective control problem of the control system. Using multiple control variables in the design of the excitation controller will be a hot topic of our recent research. References [1] Wang Zhonghong, Wang Qiang, Zhang Dongxia, et al. Research on transient stability problem and iterative learning control of power system [J]. Automation of Electric Power System, 1999, 23 (8): 6-10. [2] Yuan Jixiu. Power system safety and stability control [M]. Beijing: China Electric Power Press, 1996. [3] Ding Zhidong, Liu Guohai. Research on the influence of synchronous generator excitation on stability [J]. Large Electric Machine Technology, 2007, 04: 60-64. [4] Yu Shaojuan, Qi Xiangdong. Iterative learning control theory and application [M]. Beijing: Machinery Industry Press, 2005. [5] Xu Min, Lin Hui. Simulation study on iterative learning excitation control based on PSB [J]. 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