Research On The Stability And Compensation Strategy For LC-Type Voltage-source-inverter Under Digital Control

Voltage-controlled Voltage-Source-Inverters with LC filter(LC-type VSIs)present strong suppression of high-frequency harmonics,they also present high-quality characteristics at AC voltage output,therefore,it is very common in applications such as distributed power generation units,uninterruptible power supplies,and AC motor drives.However,the inherent delay in digital control system which leads to the reduction of phase margin and the LC filter resonance in the digital control system both threaten the stability of LC-type inverter.This paper takes single closed-loop control and double closed-loop control LC-type inverter as research objects,research on the stability and compensation methods of LC-type inverter with different control strategy.First of all,a mathematical model of a single closed-loop LC-type inverter is established in this paper,the mechanism of digital control delay is then analyzed,thus,the open-loop transfer function of the single-loop control system in the discrete domain can be derived.The crossover frequency of the open-loop gain of the single-loop inverter system is 1/3 of the sampling frequency,Therefore,the system can meet the stability requirements by adjusting the controller proportional parameters to make the system amplitude gain lower than 0d B at 1/3 of the sampling frequency when the resonance frequency of the LC filter is higher than 1/3 of the sampling frequency.Aiming at the single-loop unstable region where the LC filter resonance frequency is lower than 1/3 of the sampling frequency,a damping strategy based on the second-order notch filter is proposed and applied to the LC-type inverter to improve the stability of system.the system with notch filter damping can effectively suppress the harmonic components of high-frequency switching,which also improve the output power quality,meanwhile the hardware experiment is used to verify the practical feasibility of the notch filter damping strategy.However,the notch damping strategy that enabled in single-loop system exhibits the shortcomings such as sensitivity to system parameters and poor robustness,the dual-loop control system formed by using state variable feedback is also an important method to improve the stability of the inverter,which leads to the analysis of system stability under the dual-closed-loop strategy.Secondly,according to the mathematical model of the double-loop LC type inverter,this paper compares and analyzes the stability and anti-disturbance ability of the dual-loop control system under different control strategies.Such double-loop system includes capacitor current feedback and inductor current feedback.It is revealed that the inner loop of the capacitor current under the influence of control delay is equivalent to the virtual impedance which connected in parallel to capacitor.The virtual impedance is a positive resistance when the resonant frequency is lower than 1/6 of the sampling frequency,and a negative resistance from 1/6 sampling frequency to 1/2 sampling frequency,it also revealed that the unstable poles appear when virtual impedance exhibits negative resistance characteristics.The unstable poles of the system can be solved by Routh criterion,combined with the Nyquist stability criterion,the stability conditions of different frequency bands of the dual closed-loop inverter control system and the optimization design method of the voltage controller parameters are obtained.The active damping effect of the system is the best after the controller parameters are optimized.Experimental results verify the correctness of stability analysis.Furthermore,this paper analyzes the stability of the system when the LC filter resonant frequency is close to 1/6 of the sampling frequency in the double closed-loop control system of the LC inverter with active damping of the capacitive current.The contradiction between the number of unstable poles and the number of crossings which causes the system to be unstable,the all-pass filter lag phase angle compensation strategy is proposed and the parameter design method is given by taking advantage of the lag phase characteristics of the all-pass filter,which also has no effect on the amplitude gain of system,Experimental results prove that the system is stable again at f_s/6 and has good stability and robustness when all-pass-filter is enabled.Finally,the model of capacitor voltage active damping of LC-type inverter is established according to the relationship between capacitor current and capacitor voltage.the drawbacks of traditional differentiator frequency characteristics are analyzed in this paper,an improved digital differentiator design method is proposed to compensate for the lagging phase angle problem introduced by the backward differential differentiator.Theoretical analysis shows the frequency characteristics of improved differentiator and ideal differentiator are basically the same.Then,the improved differentiator is applied to capacitor voltage active damping control,and the experiment are used to verify the feasibility of the proposed method.