基于精确反馈线性化的单相并联APF电流滑模控制

有源电力滤波器(active power filter,APF)作为一种谐波和无功补偿装置,能够实时动态地跟踪并补偿电网中的谐波。该文针对单极性调制的单相并联APF进行了分析和数学建模;基于精确反馈线性化理论,重新构造了单相APF仿射非线性系统的输出函数;在此基础上通过非线性坐标变换将原系统转化为完全能控的线性系统,并在映射的微分同胚系统中设计了一个相对阶为r(r=2)的滑模控制器实现了对补偿电流的精确控制。所提方法在实现对APF输出电流精确控制的同时,简化了控制系统的总体设计。在Matlab仿真试验中,通过与传统PI控制的单相APF的补偿效果进行对比:采用传统PI控制和该文所提控制方法的单相APF补偿后的电流总谐波失真(total harmonic distortion,THD)分别为3.83%和1.18%,后者的动态性能也优于前者,验证了基于精确反馈线性化的滑模控制方式的优越性。最后,搭建试验平台佐证了该文所研究控制方法具有良好的动态响应、稳态性能以及鲁棒性。该研究可为今后单相APF和三相APF的控制方式改进提供参考。

Sliding mode control of current of single-phase shunt APF based on exact feedback linearization

Harmonic compensations have become increasingly important in power systems due to the rapid proliferation of nonlinear loads in industrial, commercial, and residential applications. Harmonics not only increase the losses, but also produce unwanted disturbance to the communication network, more voltage and/or current stress, and so on. Different mitigation solutions, such as passive filter, active power line conditioner, and hybrid filter, have been proposed and used to solve the problems. Due to the excellent dynamic performance, shunt-type active power filter (APF) is used to eliminate the current harmonics. The aim of the paper is to apply the feedback linearization theory in the single-phase shunt-type APF via a sliding mode control approach. The control of the active filter is performed by 2 digital control loops: a sliding control surface in the inner loop, which linearizes the system dynamics and compensates the nonlinear load current distortion, and a conventional PI (proportion integration) control in the outer loop that regulates the level of the direct current side capacitor voltage. In this paper, firstly, the modeling of a single-phase APF is presented, which uses a standard full-bridge voltage-source inverter topology and a unipolar method, and the affine nonlinear model is obtained as well. Secondly, the APF’s system is linearized by means of a nonlinear coordinate transformation, deduced from the application of the differential geometry theorem to the system. The feedback linearization is achieved by the definition of an output function for the system that is based on the total energy stored in the APF. In the linearization process, any higher order nonlinear term is not ignored, and thus the linearized model can accurately reflect the real system. The feedback linearization of the system is performed without the need to transform the active filter model into a normal form, avoiding the tedious mathematical operations that are involved in this transformation, saving the computation space of the DSP (digital signal processor) and simplifying the final control configuration. Then, a sliding model controller is designed based on the linearized APF model, which guarantees the rapidity and accuracy of the compensation current and weakens the dependence on accurate mathematical mode at the same time. Finally, detailed simulation and experimental results were reported, demonstrating the validity of the proposed control scheme. In MATLAB simulations, the proposed controller was compared under the same control parameters and conditions with a conventional PI control scheme. The current total harmonic distortion (total harmonic distortion, THD) was 3.83% under conventional PI control and was 1.18% under control method proposed in this paper. This comparison showed that the proposed control approach achieved a strong harmonic attenuation all over the frequency spectrum of the supply current, leading to a significant reduction of the current THD. The THD of the grid current that was compensated was 2.71% in experiments. Thus, it can be seen that the proposed method employed in the paper is much more reasonable, and has a high value in practical applications.