# Fractional Sliding Mode Harmonic Control of an Active Power Filter
## 1 Introduction  
Today, in addition to the wide application of power electronic equipment and frequency conversion technology, new energy power generation is developing rapidly to improve energy quality. As a result, the nonlinear loads in the power grid have become more complex, which introduces challenges to the safe and stable operation of the power grid [1; 2; 3]. In recent years, with the development of the new energy industry, the importance of harmonic suppression has been emphasized. For example, both grid-connected wind and photovoltaic power systems are equipped with nonlinear power electronic devices, which produce certain harmonic and DC components. When the harmonic is injected into the power system, it causes the distortion of the voltage and current, which triggers the power system's relay protection and the misoperation of automatic devices, affecting the safe operation of the power system [4; 5; 6]. Therefore, it is urgent to deal with harmonics in a power grid. The common solutions are harmonic prevention and harmonic compensation. Harmonic compensation only requires a parallel or series compensation device on the load side. An active power filter (APF) has the advantages of great flexibility, excellent compensation, and superior controllability and has become the main equipment for harmonic compensation. The traditional harmonic current compensation tracking control is not good enough to give full play to the superior characteristics of the APF. The control strategy of the compensation current is the key point to the compensation capability of APF. Therefore, many studies have been carried out on the compensation current control strategy. At present, various control strategies, such as a neural network algorithm [7], fuzzy control [8], sliding mode control [9; 10], repetitive control [11; 12; 13], feedback linearization [14], digital control [15], model predictive control [16; 17], backstepping control [18], etc., have been proposed and have proved effective in numerous fields of industrial production. Sliding mode control (SMC) is a type of discontinuous nonlinear control with high robustness, which is usually used to deal with uncertainties and disturbances in the system [19; 20; 21; 22]. Since the advantage of sliding mode control is its robustness to external disturbances as well as changes and uncertainties in the internal parameters, it is very suitable for APF current control, which is difficult to model and requires high controlaccuracy. However, sliding mode control has a chattering problem. Therefore, over the years, some sliding mode controllers have been proposed to improve their performance. Fractional calculus is a form of research dating back centuries; the fractional-order integrator and differentiator can provide an extra degree of freedom to design a controller, and transfer energy more slowly than that of an integer-order counterpart, attenuating chattering [23; 24; 25]. [PERSON] et al. [26] presented a robust controller with fractional calculus for wind turbine generators. [PERSON] et al. [27] found that a fractional adaptive fuzzy controller had better dynamic properties than integer ones. [PERSON] et al. [28] presented a new adaptive FOSMC for a permanent magnet synchronous motor. Motivated by the above literature, an FOSMC for a three-phase APF is developed to achieve good working performance. The FOSMC has fast convergence and a small steady-state error in the phase of sliding mode. The contributions of this paper are as follows:  
1. A novel sliding mode control method combining a fractional-order method and sliding mode control is proposed in this paper. It not only has the characteristics of a small tracking error and reduced chattering but also ensures the tracking error converges fast. 2. This paper extends integer-order SMC to fractional ones. It is a challenge to combine the SMC together with fractional-order control and apply these to the three-phase APF. An FOSMC has more degrees of freedom to obtain the desired performance.