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| Impedance Modeling of Hybrid MMC Considering Sub-Module Capacitor Voltage Dynamic Difference |
| Cao Chuanxu1, Hao Quanrui1, Qi Chen2, Wang Shuying1,3, Guo Meng1 |
1. Key Laboratory of Power System Intelligent Dispatch and Control Ministry of Education Shandong University Jinan 250061 China;
2. State Key Laboratory of Renewable Energy Grid-Integration China Electric Power Research Institute Beijing 100192 China;
3. State Grid Jinan Power Supply Company Jinan 250013 China |
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Abstract The accurate impedance model of hybrid modular multilevel converter (MMC) is the basis of stability analysis. However, the existing impedance model of hybrid MMC assumes the dynamics of half-bridge and full-bridge sub-modules (SMs) are identical, and ignores the difference in capacitance voltage between the two sub-modules during over modulation, which may lead to inaccurate impedance and wrong stability assessment result. To address this issue, this paper derives the accurate sequence model of hybrid MMC based on the improved arm average value model (AAVM), which represents the dynamics of half-bridge SMs and full-bridge SMs separately, analyzes the key parameters which mainly affect the overall stability of hybrid MMC, and proposes the parameter optimization strategy.
Firstly, the improved average value model of hybrid MMC is introduced briefly to show its advantage of representing the dynamics difference between full-bridge SMs and half-bridge SMs in overmodulation state. Based on the electric circuit of improved AAVM, the frequency domain harmonic equations of the electrical part considering the harmonics up to the kth order are derived in the multi-harmonic linearization theory. For the nonlinear reference voltage distribution in improved AAVM, the reference voltages of half-bridge and full-bridge SMs within one cycle are expressed in the piecewise function. The harmonics of the reference voltages are derived as the summation of harmonics of each piece in Fourier transform. Based on that, the small-signal relationship between voltage references and electrical quantities are obtained by linearized at the specific operating point. For the control loops, the frequency domain harmonics equations for the outer capacitor voltage control and dc current control loops are specially derived. The overall sequence impedance model is constructed by modularly cascading the frequency domain harmonic equations of electric circuit, nonlinear reference voltage distribution part and control loops. Secondly, the single-dimensional equivalent impedance model of hybrid MMC considering the the grid impedance is derived from the proposed 4×4 impedance to investigate the main influence frequency band and the influence extent of the capacitor voltage control and dc current control parameters on the impedance of hybrid MMC. Finally, the modal amplitude margin (MAM) is defined as the inverse of the intersection of the distance from (-1, j0) to the intersection point of Nyquist curve of one mode with real axis, and the parameter sensitivity is defined as the small disturbance value of MAM to quantify the influence of each parameter on the hybrid MMC grid-connected system overall stability. The control parameter optimization principle is pointed out.
Simulation results of hybrid MMC grid-connected system show that, the proposed impedance model with k≥4 agree well with the measure data, while the conventional impedance model obviously deviates from the measured data at key resonance frequency of 62 Hz. When the proportional coefficient of current inner loop kpIac changes from 2.4 to 2.1, the system real power starts to oscillate with the oscillation frequency of 27.26 Hz, which agree with the coupled oscillation frequencies of 77.26 Hz and 22.74 Hz in d-q frame predicted from the proposed impedance model. When the integral coefficient of current inner loop kiIac changes from 100 to 2 000, the system real power becomes stable gradually.
The following conclusion can be drawn from the simulation results: (1) The proposed sequence impedance model derived from improved AAVM is more accurate to predict the system stability compared with the conventional impedance model, and the voltage differences between half-bridge SMs and full-bridge SMs in over-modulation state cannot be neglected for stability analysis of hybrid MMC. (2) The capacitor voltage loop, the proportional coefficient and the integral coefficient of current inner loop mainly affect the impedances in sub-synchronous frequency band, low frequency band and the frequency band below 200 Hz, respectively. (3) The control parameters can be optimized by properly increasing the proportional and integral coefficient of current inner loop or decreasing the proportional coefficient of ac power control to increase the stability margin of hybrid MMC in sub-synchronous frequency band.
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Received: 09 May 2025
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2026, Vol. 41 
