978-1-4799-5776-7/14/$31.00 ©2014 IEEE Selective Harmonic Control for Power Converters Keliang Zhou 1 , Yongheng Yang 2 , Frede Blaabjerg 2 , Wenzhou Lu 3 , Danwei Wang 4 1 Department of Electrical and Computer Engineering, University of Canterbury, Christchurch, New Zealand, Email: eklzhou@ieee.org 2 Department of Energy Technology, Aalborg University, Aalborg, Denmark, Email: yoy@et.aau.dk; fbl@et.aau.dk 3 School of Electrical Engineering, Southeast University, Nanjing, China, Email: luwenzhou@126.com 4 School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Email: edwwang@ntu.edu.sg Abstract—This paper proposes an Internal Model Principle (IMP) based Selective Harmonic Controller (SHC) for power converters. The proposed SHC offers an optimal control solu- tion for power converters to mitigate power harmonics. It makes a good trade-off among cost, complexity and perfor- mance. It has high accuracy and fast transient response, and it is cost-effective, easy for real-time implementation, and com- patible for design rules-of-thumb. An application on a three- phase PWM converter has confirmed the effectiveness of the proposed control scheme in terms of harmonic mitigation. I. INTRODUCTION Today, a rapid growing amount of current harmonics and voltage harmonics due to non-linear electric loads frequently cause serious power quality problems in the electrical power systems [1], [2]. Power converters demand optimal control strategies for harmonics compensation, which should achieve high control accuracy, fast transient response, good robustness, and easy implementation [1]. In practical applications, harmonics usually concentrate on some particular frequencies [3]. For example, in the n-pulse converter systems, nk±1-order (k = 1, 2, 3, …) harmonics dominate the Total Harmonic Distortion (THD). Hence, it is possible to selectively compensate the harmonics according to the characteristic of the harmonic distributions in n-pulse power converters [4]-[6]. Based on the Internal Model Principle (IMP), classic Repetitive Controller (RC) [7]-[18] and ReSonant Controller (RSC) [19]-[21], which can achieve zero steady-state error in the control of any periodic signal and a sinusoidal signal respectively, and provide very simple but effective harmonic control solutions. However, a compact recursive RC can achieve zero tracking error at all harmonic frequencies, but yields typically slow total convergence rate. Paralleled Multiple ReSonant Controllers (MRSC) at selected harmonic frequencies can render fast transient response, but would increase the computational burden and design complexity in dealing with a large number of harmonics. The 6lr1 RC [10], [11] and the recursive odd harmonic RC [12], [13] offer an accurate, fast, and feasible Selective Harmonic Control (SHC) solution for single-phase power converters and three-phase power converters respectively. However, a universal selective harmonic control strategy is still open for exploration. Considering the above issues, in this paper, a universal SHC solution has been proposed in § II for the power converters to mitigate the harmonics selectively. The analysis and synthesis of the SHC systems are also addressed. The SHC solution has been applied to a three- phase Pulse Width Modulation (PWM) converter for case study in § IV. The results have verified the effectiveness of the proposed SHC solution for power converters in terms of harmonic mitigations. II. SELECTIVE HARMONIC CONTROL A. Classic Repetitive Control k rc   o c sT T e   c sT e  u rc e Fig. 1. Repetitive controller Grc(s). As it is shown in Fig. 1, a classic RC can be written as,  0 () () 1 c o sT sT rc rc rc sT u s k e G s e es e       (1) where krc is the control gain; To=2π/ωo=1/fo is the fundamental period of signals with fo being the fundamental frequency; ωo being the fundamental angular frequency; and Tc is the lead phase compensation time. The classic RC only consumes a little computation in its implementation. Eq. (1) for the classic RC can be expanded as [11]-[13],    2 2 0 0 1 1 2 c sT rc rc h o s G s k e T s h f  ｪ ｺ    ｫ ｻ  ｫ ｻ ｬ ｼ ｦ Z (2) which indicates that the RC is equivalent to the parallel combination of a proportional gain (i.e. -krc/2), an integrator and infinite resonant controllers (RSCs) (i.e. the internal models of DC and all harmonic signals). These RSC components, which will approach infinity at harmonic frequencies hZ0, enable the RC to compensate all harmonic frequencies. Since the control gains for all RSC controllers in (2) are identical, i.e. krc/To, it is impossible for the RC to optimize its transient response by tuning control gains independently for selected harmonic frequencies. Research supported by College Strategic Grants 2013, College of Engi- neering, University of Canterbury, New Zealand