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| Voltage Source Converter Input Admittance Model Considering Frequency Coupling of Sideband Components |
| Xu Shaobo1, Xu Yonghai1, Tao Shun1, Wang Yingxin1, Zhang Huaying2 |
1. School of Electrical and Electronic Engineering North China Electric Power University Beijing 102206 China;
2. New Smart City High-Quality Power Supply Joint Laboratory of China Southern Power Grid Shenzhen Power Supply Co. Ltd Shenzhen 518020 China |
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Abstract Under the background of high proportion of renewable energy and high proportion of power electronic equipment access, the harmonic pollution and coupling resonance characteristics in the distribution grid gradually expand to the high frequency band. The controller sampling process and pulse width modulation (PWM) process of voltage source converter (VSC) have sideband effect. When the frequency of the disturbance signal exceeds the Nyquist frequency, the amplitude of the sampling and PWM sideband components will be higher than the original disturbance due to the influence of spectrum aliasing and the low-pass filtering characteristics of the controller, resulting in an obvious frequency coupling effect between the sideband components and the disturbance, thus affecting the VSC input admittance characteristics. In the analysis of high-frequency resonant characteristics, the existing single frequency impedance model of VSC based on switching cycle averaging is difficult to meet the impedance modeling accuracy requirements above Nyquist frequency. Therefore, this paper analyzes the frequency coupling mechanism between the sideband component and disturbance generated by VSC controller sampling and PWM link; Considering the frequency coupling of two kinds of sideband components, the VSC multi-frequency coupling input admittance model above Nyquist frequency is established.
Firstly, the generation mechanism of VSC sampling sideband component and PWM sideband component and the frequency coupling mechanism with disturbance are analyzed. Under the action of sideband effect, sampling sideband component, PWM sideband component and disturbance signal realize frequency coupling through feedback loop between VSC control system and physical circuit, thus affecting VSC port impedance characteristics. Considering the suppression effect of ZOH and filter on high frequency components in the sideband, the model can only retain ωs–ωp and ωc–ωp–ω0 sideband component. Considering the influence of current inner loop control, system voltage feedforward control, controller calculation delay effect, the sampling procedure and PWM modulation, the multi-frequency input admittance model of VSC is established. A grid connected VSC hardware in the loop simulation platform is built to verify the theoretical analysis result. The input admittance model which takes into account the frequency coupling of sidebands is basically consistent with the frequency scanning results of hardware in the loop simulation. When the frequency coupling effect of sampling and PWM sidebands is ignored, the amplitude and phase angle characteristics of the input admittance model have certain errors in the frequency bands near and above the Nyquist frequency, which proves the necessity of this study.
The following conclusions can be drawn from the simulation analysis: (1) The VSC multi-frequency coupling input admittance model considering the coupling effect of sampling and PWM sideband components has higher accuracy in the high frequency band above Nyquist frequency. (2) Both the sampling sideband component and PWM sideband component will affect the admittance characteristics of VSC in the high frequency band, but the influence of sampling sideband component on the admittance characteristics of VSC in the high frequency band is more significant. (3) The anti-aliasing filter can significantly suppress the frequency coupling effect of sampling and PWM sideband components. When the cut-off frequency of the anti-aliasing filter is low, the influence of sideband frequency coupling effect on VSC input admittance can be ignored. (4) The sampling mode of PWM modulation has a significant impact on the impedance characteristics of VSC. On the one hand, the delay effect caused by different sampling modes is different, and on the other hand, the nonlinear characteristics of PWM modulation are different due to different sampling modes.
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Received: 31 October 2022
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2023, Vol. 38 
