Research on repetitive control strategy of high frequency link inverter

l Introduction

The bidirectional voltage source high frequency link inverter is currently a hot topic in the field of photovoltaic inverters due to its high conversion efficiency, high power density, and ease of use in high power applications. Based on the voltage source high frequency link inverter model, the mathematical models of the inverter in the continuous time domain and discrete time domain are established. The discrete repetitive control technology based on voltage feedback is studied, and the principle of repetitive control to eliminate the periodic waveform distortion of the output voltage is analyzed. Finally, the PSIM simulation software is used to conduct a system test and analyze the key test waveforms.

2 Establishment of the mathematical model of the inverter main circuit

The schematic diagram of the bidirectional voltage source high-frequency link inverter is shown in Figure 1. It is based on the forward as the basic unit. The DC input voltage is inverted by the high-frequency inverter, and high-frequency positive and negative pulses are obtained on the primary side of the transformer. The high-frequency transformer is used to adjust the transformation ratio and perform electrical isolation. The secondary side of the transformer obtains high-frequency positive and negative pulse waves with the same phase as the primary side. The frequency converter performs low-frequency demodulation on the high-frequency pulses, and obtains low-frequency AC pulse voltage at both ends of the output filter circuit, and then the filter circuit filters out high-order harmonics.

In the main circuit mathematical model of the high-frequency link inverter power supply, since the inverter switching frequency is much higher than the oscillation frequency of the LC filter, the dynamic characteristics of the inverter are mainly determined by the LC filter, which can be equivalent to a second-order system composed of the output LC filter link. Let the filter inductor be Lf, the filter capacitor be Cf, and the capacitor, inductor and other equivalent resistances be Rz:. The equivalent transfer function of the inverter is:

By using a zero-order holder and selecting a suitable sampling period T, the equivalent transfer function of the inverter can be discretized, and the discretized transfer function of the inverter is obtained as follows:

In the main circuit of the experiment, the carrier frequency of the inverter is 10 kHz. Considering that the cutoff frequency of the output filter is 1/10 to 1/5 of this frequency, Lf=2 mH, Cf=6μF, and Rz=1 Ω are selected.

Using MATLAB, the discrete form of the system transfer function can be obtained as:

The inverter has very small no-load damping and has a large resonance peak at the natural frequency. The output voltage error of the PWM inverter is mainly caused by factors such as load disturbance, DC side voltage fluctuation, and dead zone effect. Most of the error frequency components are located in the medium and low frequency bands. As long as the system has a strong suppression ability for these medium and low frequency error components, it can greatly improve steady-state indicators such as harmonic distortion (THD%) and voltage steady-state error. Therefore, its amplitude and phase compensation should be mainly concentrated in the medium and low frequency bands, that is, the amplitude at the natural frequency should be attenuated to below -3 dB.

3 Repeated control strategy

Repetitive control is a control strategy based on the internal model principle. Its function is that when the input signal repeats in the fundamental period, the output is the cycle-by-cycle accumulation of the input signal. Even if the input decays to zero, the internal model will continue to repeat the output of the same signal as the previous cycle waveform cycle by cycle. This periodic signal holder is introduced into the feedback control system, and the system is stabilized through the compensation link. It can track the given and eliminate disturbances within one cycle. The structure of the repetitive control system is shown in Figure 2, which includes the repetitive controller internal model, the periodic delay link and the compensator S(z).

3.1 Selection of cycle delay coefficient
The number of sampling times of the output voltage per fundamental wave cycle is N=fc/f. Where fc is the reference input fundamental frequency and f is the carrier frequency.
3.2 Design of compensator
From the amplitude-frequency characteristic curve of the controlled system P(z), it can be seen that there is a resonance peak at ω=4564 rad/s. The compensator S(z) is used to eliminate the resonance peak. The second-order oscillation link is selected to cancel with P(z) in the low and medium frequency bands and attenuate sharply in the high frequency band, where ζ=l, ωn=4600. In order to improve the compensation performance, the Notch function is introduced in the design to play a trapping role on the resonance peak. Then the complete compensator form is: S(z)=S1(z)F(z).
3.3 Design of zKKrQ(z)
Both the controlled object P(z) and the compensator S(z) have a large phase lag, so the phase compensation link Zk is used for compensation. By comparing the phase-frequency curve, it is determined that when k=10, S(z)P(z) and z-10 are consistent in the low and medium frequency bands, and the phase is compensated. The value range of Kr is 0~1, which is similar to the function of a proportional controller. In this example, Kr is 0.21 to obtain a satisfactory adjustment effect.
Q(z) should be a constant close to 1. When Q(z) is a constant less than 1, the unit circle with the origin as the end point of Q(z) is shifted to the left as a whole, which can ensure the stability of the system in the full frequency band. In this example, the empirical value is 0.95.
3.4 Simulation experiment
Under the conditions of resistive and resistive-inductive loads, the system is simulated, and the waveform results of comparing the output voltage and the reference input are shown in Figures 3 and 4.

As can be seen from Figure 3, after the introduction of the repetitive controller, the system has less harmonic content and better sinusoidal degree of the output voltage waveform under resistive load conditions; the phase is also consistent with the reference voltage. The waveform quality is good. As can be seen from Figure 4, the repetitive control is not as effective as the resistive load in regulating the waveform amplitude. The sinusoidal degree of the waveform is significantly deteriorated, and the harmonic content is large. This shows that repetitive control has certain difficulties in suppressing random interference and has the defect of poor dynamic performance. However, it can also be seen from the results that after the introduction of repetitive control, the phase adjustment effect is good, and the output waveform phase is basically consistent with the input reference, which provides a favorable condition for inverter waveform control and inverter parallel connection.

4 Conclusion

The structure and principle of the bidirectional voltage source high frequency link inverter commonly used in the inverter field are analyzed, and the discrete repetitive control technology based on voltage feedback is studied. Through experiments, it can be seen that after the introduction of the repetitive controller, the harmonic content of the system output waveform is significantly reduced, and the quality of the output voltage waveform is greatly improved; the effect is more obvious in the phase adjustment, so that the output waveform can be consistent with the input reference in phase, which provides favorable conditions for the parallel connection of inverters.