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In the recent decades, the applications of semiconductor devices have increased manifold due their numerous advantages such as better controllability, higher efficiency, fast switching and better current handling capacity. But at the same time their inherent nonlinear characteristics introduce many undesirable features in the system, such as harmonics, poor voltage regulation, poor power factor, low system efficiency, and interference in nearby communication system etc. All these undesirable features affect the power quality. Shunt passive filters were traditionally used to provide current harmonic compensations. But these passive filters suffer from certain demerits such as fixed compensation, large size, detuning problems due to aging effect and resonance as pointed out by Singh, Al-Haddad, and Chandra (1999) in their review paper on active filters for power quality improvement. Shunt active power filters (APF) have emerged as an undisputed alternative over their passive counterparts for current harmonics mitigation and reactive power compensation.
The voltage source inverter (VSI) based shunt APF is preferred for harmonic and reactive power compensation as discussed by Akagi, Kanajawa, and Nabae (1984), Peng, Akagi, and Nabae (1990), Grady, Samotyj, and Noyola (1990), Singh, Chandra, and Al-Haddad (1999), and Singh, Al-Haddad, et al. (1999). A control scheme is proposed by Dixon, Contrado, and Morán (1999) which require sensing of line currents only for generation of reference current. The scheme is simple and easy to implement. Recently most of the reported work uses this scheme, which includes the papers of Jain, Agrawal, and Gupta (2002) on control of shunt APF using fuzzy logic controller (FLC) and Mishra and Bhende (2007) on bacterial foraging based optimized based control of shunt APF.
Artificial intelligence (AI) is getting popularity among control engineers due to its ability to handle complex problems at randomly varying operating conditions. Bose (1994) in his invited paper has explored the possibilities of expert system, fuzzy logic and neural network applications in power electronics and motion control. This work has provided a new space of opportunities for control engineers. Anis Ibrahim and Morcos (2002) focus on the effectiveness of AI and advanced mathematical tools for power quality applications. A fuzzy logic based shunt APF shows better dynamic response and higher control precision as compared with the PI controller as concluded by Dixon et al. (1999), Jain et al. (2002), An, Zhikang, Wenji, Ruixiang, and Chunming (2009), and Karuppanan and Mahapatra (2011). All these papers have proposed 49-rule FLC for the control of shunt APF. The 49-rule FLC has the drawback of a large number of fuzzy sets and control rules. Due to this the complexity of the controller increases, as large computational time and large memory is required to execute the desired control action. This drawback is overcome in this paper by approximating a 49-rule FLC with a simplest 4-rule FLC.
In the recent past some studies regarding reduction of rule base size have been reported. Bezine, Derbel, and Alimi (2002) explained some issues on design and rule base size reduction for the fuzzy control of robot manipulators. Ciliz (2005) explained some concepts regarding resizing of rule base by removing inconsistent and redundant rules for the application of vacuum cleaner. These two studies were application specific. Hampel and Chaker (1998) provided some conclusions for minimization of number of variable parameters for optimization of fuzzy controller. Moser and Navrata (2002) proposed a fuzzy controller with conditionally firing rules, in this work number of rules were not minimized only the conditions under which they will fire were reduced. Zeng and Singh (1994, 1995) proposed a mathematical description of approximation theory of fuzzy systems for single input single output (SISO) and multi input multi output (MIMO) cases. The main focus of these papers was the approximation capabilities of the fuzzy systems for approximating a mathematical polynomial rather than on rule reduction.