The classical closed-loop feedback control scheme of the shunt active power filter (SAPF) includes indirect [

3,

4,

5,

6,

7,

8,

9] and direct current control methods [

10,

11,

12,

13,

14]. Proportional-resonant (PR) controllers are the most popular method for SAPF, as they guarantee zero-state errors and achieve the required total harmonic distortion (

THD) performance at each specified frequency. The systematical design method of PR controllers is described in [

3] and the effects of different discretization methods are considered, but the output harmonic order is below the 20th. An LCL-filter-based SAPF with PR controllers is proposed in [

4], and the grid current spectrum shows that it has good compensation performance below the 25th harmonics but poor performance on eliminating switching frequency harmonics. A sensorless control strategy with multiple quasi-resonant compensators for SAPF was presented in [

5], which is able to track an unknown grid frequency, reducing its sensitivity to this variable. However, the SAPF only outputs the 1st–15th harmonics and the

THD of grid currents is up to 9.8%. In [

6], a fixed-point processor-based PR current control scheme in synchronous reference frame (SRF) is proposed. It has a better response time compared with other frequency-selective current control methods, but it only outputs 1st–19th harmonics. Repetitive controllers just designed below 1.25 kHz are described in [

7,

8,

9]. An improved repetitive controller which adds a proportional link in parallel with the original repetitive control loop for SAPF is proposed in [

7]. The SAPF obtains good performance in simulation results, but only compensates to the 25th harmonics under experimental conditions. A two-layer structure controller is designed in [

8]. The outer layer uses a repetitive control algorithm to provide good tracking of periodic signals and the inner layer achieves practically-decoupled control of d-axis and q-axis currents, while the compensation current order only reaches to 19th harmonic. A current control strategy integrating PR and odd-harmonic repetitive control (OHRC) is proposed in [

9]. The OHRC method provides better performance than the multiple resonant control scheme, however these two methods only consider 1st–13th harmonics. SAPFs adopted hysteresis controllers are presented in [

10,

11,

12], which only output 1st–21st harmonics, moreover the output currents are magnified between the 21st–33rd harmonics in [

11,

12].

The aforementioned SAPFs with closed-loop control methods only have good compensation performance below the 25th harmonics. The reason for this is that the output bandwidth is determined jointly by the control parameters, output inductance and switching frequency. The general switching frequency of insulated gate bipolar transistors (IGBT) is 10–20 kHz. Under the specified switching frequency, the output bandwidth is determined by the proportional gain of the controller and output inductance. From their open-loop Bode plots, it can be concluded that a larger proportional gain and smaller inductance means a wider output bandwidth, however this situation leads to worse current ripple inhibition ability [

16]. This compromise between system stability and harmonic current compensation ability indicates that they cannot deal with the high-frequency harmonics. However, in the metal processing industry, the Intermediate Frequency Induction Heating Device (IFIHD) typically generate about 1st–49th harmonics. The high-frequency harmonics cannot satisfy the requirements of IEEE Standard 519-2014 [

17], which may cause interference with communication circuits and increase total losses of transformers.

Lyapunov stability theory was introduced in inverters [

18,

19,

20,

21,

22,

23,

24], since it can ensure the globally asymptotical stability of nonlinear systems. Lyapunov stability theory-based method uses the reference currents and system mathematical model to obtain gate signals, which overcomes the disadvantage of the classical closed-loop feedback control method. As a result, Lyapunov stability theory is suitable for improving the compensation ability on the premise of system stability.

In a neutral-point-clamped shunt active power filter (NPC-SAPF) system, the upper and lower DC-capacitor voltages have to be maintained at half of the DC-link voltage, because the balance of upper and lower DC-capacitor voltages is related to the system stability and compensation performance. The carrier based pulse width modulation (CB-PWM) in [

25,

26,

27] achieves the voltage-balancing task and mitigates the voltage oscillations of neutral-point (NP) with lower switching losses than other PWM methods. Moreover, it is easy to realize and saves more storage space in digital implementation than the NP voltage balance method based on space-vector PWM (SVPWM). Therefore it is adopted in this paper. A LCL type filter is usually employed to suppress the switching frequency harmonics. An improved LLCL filter is proposed in [

28,

29,

30,

31], which can decrease the total inductance and eliminate the switching harmonic currents preferably due to the only one tuned trap. Thus, the improved LLCL filter is used in this paper.

The rest of this paper is organized as follows.

Section 2 deduces the mathematical model of the NPC-SAPF.

Section 3 discusses the Lyapunov stability theory-based control strategy. The system stability is analyzed and compared with the PR controllers in

Section 4. The simulation results in MATLAB/Simulink are given in

Section 5.

Section 6 describes experimental results on a 6.6 kVA NPC-SAPF laboratory prototype. Finally, the conclusions are presented in

Section 7.