240 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART C: APPLICATIONS AND REVIEWS, VOL. 41, NO. 2, MARCH 2011 Pareto-Optimal Design of Damping Controllers Using Modified Artificial Immune Algorithm Milad Khaleghi, Malihe M. Farsangi, Hossein Nezamabadi-pour, and Kwang Y. Lee, Fellow, IEEE Abstract—This paper presents two approaches for multiobjec- tive simultaneous coordinated tuning of damping controllers, a modified artificial immune network (MAINet) algorithm and a multiobjective immune algorithm (MOIA). The weighted-sum ap- proach is used to handle the multiobjective optimization problem in the MAINet, while the Pareto-optimization approach is used in the MOIA. To investigate the ability of the proposed algorithms in designing the damping controllers, one small and one large power systems are considered. Two power-system stabilizers (PSSs) are designed for the small power system, while one PSS for a genera- tor and one supplementary controller for a static var compensator (SVC) are designed for the large power system. The simulation studies show that the controllers designed by MOIA perform better than those by MAINet in damping the power-system low-frequency oscillations. Index Terms—Artificial immune network algorithm, low- frequency oscillations, Pareto optimization, power system stabiliz- ers (PSS), real immune algorithm, static var compensator (SVC). I. INTRODUCTION T O PROVIDE a secure operation for power systems, damp- ing of power-system oscillations has received a great deal of attention in power-system stability studies. It is known that the power-system stabilizers (PSSs) for generators and the supplementary controllers for flexible ac transmission system (FACT) devices are efficient tools for improving the stability of power systems through damping of low-frequency modes. Fre- quency of these modes ranges from 0.2 to 2.5 Hz, consisting of three main modes: local modes, interarea modes, and interplant modes. Several approaches have been applied to damping controller design in power system, such as [1]–[24]. Since 1981, sev- eral approaches based on modern control theory have been ap- plied to the PSS design problem, including adaptive control, pole-placement, optimal control, and variable-structure control [1]–[6]. Despite the potential use of modern control techniques with different control structures, power system utilities still pre- fer the conventional lead-lag power-system stabilizer structure. The reason is that the modern-control techniques may give a con- Manuscript received November 23, 2009; revised April 11, 2010; accepted May 27, 2010. Date of publication July 1, 2010; date of current version February 16, 2011. This paper was recommended by Associate Editor Z. Wang. M. Khaleghi, M. M. Farsangi, and H. Nezamabadi-pour are with the Depart- ment of Electrical Engineering, Shahid Bahonar University of Kerman, Kerman 76175-133, Iran (e-mail: khalegh.milad@gmail.co; mmaghfoori@mail.uk.ac.ir; nezam@mail.uk.ac.ir). K. Y. Lee is with the Department of Electrical and Computer Engineer- ing, Baylor University, Waco, TX 76798-7356 USA (e-mail: Kwang_Y_Lee@ baylor.edu). Digital Object Identifier 10.1109/TSMCC.2010.2052241 troller with higher order, which is difficult to implement. In addi- tion, solving problems by considering several different objective functions are difficult with an analytical method, especially to have good tradeoffs between different objective functions. Recently, there has been a growing interest in algorithms in- spired from the observation of natural phenomenon to seek the optimal design of PSS in a power system. It has been shown by many researches that these algorithms are viable candidates as tools to solve complex computational problems. In [7] and [8], neural network was used to design PSSs. In [9], Abido pro- posed a solution procedure employing simulated annealing to search for the solution. Evolutionary programming was used to optimal design of PSSs in [10]. The author in [11] presented an implementation using a particle-swarm optimization (PSO). Genetic algorithm (GA) in [12] was used to look for the PSS parameters. In [13], fuzzy theory and evolutionary algorithm were employed to solve the problem. Besides, different control efforts are reported for controlling the FACTs devices includ- ing modern control techniques as well as intelligent control [14]–[19]. In [20]–[23], different versions of immune algorithm (IA) were used to design PSSs for generators or supplementary con- trollers for static var compensators (SVCs) to damp oscillations. These different versions in [20]–[22] are: binary version of IA (BIA), real version of IA (RIA), and hybrid RIA with local search, e.g., as the modified real immune algorithm (MRIA). It was revealed that the RIA performs better than BIA, and the MRIA performs better than RIA in designing the controllers. Also, in [21], it was shown that the IA performs better than the conventional algorithm in terms of the control effort and precision. Furthermore, artificial immune network (AINet) is used in [23] for designing a supplementary controller for SVC to damp oscillations. Since there are some shortcomings with the AINet, a modified AINet (MAINet) algorithm is introduced in this pa- per to design coordinated damping controllers in two power systems, where the design problem is formulated as a multiob- jective optimization problem with the weighted-sum approach. As an alternative approach, a multiobjective immune algorithm (MOIA) is also proposed by using Pareto-optimal solutions to design damping controllers. To illustrate the feasibility of the proposed methods, numeri- cal results are presented on two study systems: a two-area four- machine system by designing two PSSs and a 5-area 16-machine system by designing a PSS for a generator and a supplemen- tary controller for the SVC. The obtained results show that the proposed methods not only solve the current problem but also could easily be extended to other similar engineering problems. 1094-6977/$26.00 © 2010 IEEE