Power System Controller Design using Multi- Population PBIL Komla Agbenyo Folly Department of Electrical Engineering University of Cape Town Cape Town, South Africa Komla.Folly@uct.ac.za Ganesh Kumar Venayagamoorthy Real-Time Power and Intelligent Systems Laboratory Holcombe Department of Electrical & Computer Eng. Clemson University, SC 29634, USA gkumar@ieee.org Abstract—The application of a multi-population based Population-Based Incremental Learning (PBIL) to power system controller design is presented in this paper. PBIL is a combination of evolutionary optimization and competitive learning derived from artificial neural networks. Single population PBIL has recently received increasing attention in various engineering fields due to its effectiveness, easy implementation and robustness. Despite these strengths, PBIL still suffers from issues of loss of diversity in the population. The use of multi-population is seen as one way of increasing the diversity in the population. The approach is applied to power system controller design. Simulations results show that the multi- population PBIL approach performs better than the standard PBIL and is as effective as PBIL where adaptive learning is used. Keywords— Adaptive learning rate; low-frequency oscillations; multi-population; PBIL; power system stabilizer I. INTRODUCTION In the past few decades, there has been an increasing interest in biologically motivated approaches to solving optimization problems, including Artificial Neural Networks (ANNs), Genetic Algorithms (GAs), and Evolution Strategies (ESs). GAs are one of the most used Evolutionary Algorithms (EAs) for function optimization. They are robust and can be applied to a wide range of problems [1]. However, GAs still have several limitations, such as genetic drift which prevents GAs from maintaining the diversity in the population, the difficulty in selecting optimal GA operators such as selection and mutation rates, crossover probability, and population size [2]-[4]. To cope with the above limitations, several other biological motivated algorithms have been proposed in the last few years. These include Differential Evolution (DE) [5]-[6], Artificial Immune Systems (AIS) [7], Bacterial Foraging Algorithm (BFA) [8], Ant Colony (ACO) [9], and Particle Swarm Optimization (PSO) [10] which belong to the family of Swarm intelligence. Among all these algorithms, PSO has been widely used for parameter optimization in controller design [11]-[12]. PSO is simple and easy to implement; however, the algorithm is very sensitive to some of its parameters such as inertia weights, and acceleration factors. In addition, the optimal selection of these parameters may be difficult to achieve. Recently, a new type of EA called Population-Based Incremental Learning (PBIL) has been proposed by Baluja [13], [14]. PBIL is simpler and more effective than GAs. In addition PBIL has less overhead than GAs [15]-[16]. There are few parameters to tune in PBIL as compared to GAs or PSO. This makes PBIL more attractive to a wide range of researchers. In PBIL, the crossover operator is abstracted away and the role of population is redefined [13], [14]. PBIL works with a probability vector (PV) instead of the whole population. One only needs to store a single PV and the solution being evaluated. The PV is used to control the random bit strings generated by PBIL and to create other individuals through learning. Learning in PBIL consists of using the current probability vector (PV) to create N individuals. The best individual is used to update the probability vector, increasing the probability of producing solutions similar to the current best individuals [14]. It has been shown that PBIL outperforms standard GAs approaches on a variety of optimization problems including commonly used benchmark problems [14]- [18]. In [19]-[22], the standard PBIL with fixed learning rate was used to design power system controllers known as power system stabilizers (PSSs). The main purpose of a PSS is to damp low frequency oscillations arising from small disturbances, such as gradual and small changes in loads or generations. However, a fixed learning rate may not be effective in dynamic environment to maintain the required trade-off between exploration and exploitation [23]-[25]. Also, the use of one probability vector (PV) to represent the whole population may reduce the diversity in the population and thereby degrading the global search ability of the algorithm [26]. Recently some authors have reported that PBIL suffers from diversity loss making the algorithm to converge to local optima [27]-[28]. Maintaining the diversity in PBIL’s population is directly linked to the learning rate. In [23], the authors investigated the effect of learning rate on the performance of PBIL. It was shown that using adaptive learning rate where the learning rate starts with a very small value and increases monotonically with the generation provides better results as compared to using a fixed learning rate. The authors in [24] used hyper-learning for PBIL where the The financial supports of the TESP and THRIP as well as the NSF EFRI # 1238097 grants are acknowledged. 37 978-1-4673-6002-9/13/$31.00 c 2013 IEEE