于佳琪+李勇+曹一家+于晶荣+徐勇

摘 要：提出了一种基于Lyapunov函数的三相中点箝位型三电平并联有源电力滤波器（Neutral-Point Clamped Shunt Active Power Filter，NPC-SAPF）的控制策略.建立了NPC-SAPF的数学模型并在此基础上构建包含输出电流和直流电压误差项的能量函数；进一步推导出关于控制增益的特征方程，并绘制出其三维函数图，结合Lyapunov大范围渐进稳定条件和系统极点位置得到控制增益选取范围，在此区间选取合适的控制参数，保证系统在不同负载类型下动态和稳态性能.针对NPC特有的中点电位平衡问题，采用连接直流电压中点与配电变压器中点并引入中性点电位误差反馈控制的方法实现中点电位平衡.对电压源型和电流源型这两类非线性负载的动态和稳态性能进行了仿真和实验，结果表明：该控制策略对电流型和电压型非线性负载均取得较好的谐波补偿效果.

关键词：三电平；并联有源电力滤波器；Lyapunov函数法；电能质量

中图分类号：TM615；TP273 文献标志码：A

Lyapunov-function-based Control Strategy for Three-level SAPF

YU Jiaqi1， LI Yong1， CAO Yijia1， YU Jingrong2， XU Yong1

（1.College of Electrical and Information Engineering， Hunan University， Changsha 410082， China；

2. School of Information Science and Engineering， Central South University， Changsha 410083，China）

Abstract：A Lyapunov-function-based control strategy for NPC-SAPF was proposed. The mathematical model of NPC-APF was built， and Lyapunov energy function including the tracking error of compensation currents and DC voltage was also constructed. Characteristic equation including control permanents was derived and plotted. Linear range of control permanents were also obtained after the overall consideration of system globally asymptotically stable conditions and pole location. Error feedback control technique was then utilized to keep neutral point potential balanced. In order to verify the compensation performance of the proposed current control scheme， nonlinear loads including diode bridge rectifier with an inductive load and a capacitive load was simulated and tested. Simulation and experimental results show that the proposed control strategy is effective in the nonlinear loads of both current-source type and voltage-source type.

Key words： three-level technology； shunt active power filter； Lyapunov functions； power quality

并聯有源电力滤波器（Shunt Active Power Filter， SAPF）是用于抑制谐波、提高电能质量的有效手段之一[1-2].其中，三相中点箝位型并联有源电力滤波器（Neutral-Point Clamped， NPC-SAPF）与两电平APF相比具有系统容量大、补偿效果好、经济成本低等优点，受到了研究者的青睐.

然而由于NPC-SAPF系统是一个高阶强耦合的非线性系统，采用非线性控制器会取得更好的稳定性和指令跟踪控制效果.近年来，许多学者将非线性理论应用于APF控制系统的设计中[3-5].文献[3]提出基于滑模控制的混合型APF，该控制策略虽能……