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| Large-Signal Stability Analysis for DC Microgrids Based on the Improved Equivalent Circuit Model |
| Wang Li1, Tan Zhenjie1, Zeng Xiangjun1, Zhao Bin1, Zheng Yueqiu2 |
1. School of Electrical and Information Engineering Changsha University of Science and Technology Changsha 410114 China;
2. Tibet East China Hydropower Equipment Co. Ltd Lhasa 851414 China |
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Abstract Simplified modeling has proven effective in analyzing the large-signal stability of high-order nonlinear DC microgrids (DCMGs). However, the traditional simplified models primarily focus on the parameters such as LC filters and line impedances, making it difficult to analyze the impact of converter control parameters. Additionally, the established criteria do not accurately reflect the stability region of DCMGs. To address these limitations, an improved equivalent circuit model with a complete set of state variables for DC voltage droop control converters was proposed. Compared to the traditional simplified models, this model provides a more accurate description of the system’s low-frequency response, enabling precise analysis of the large-signal stability of DCMGs.
The circuit model of the output impedance of DC voltage droop control converters is first derived from its output voltage dynamic equation. Subsequently, this model undergoes an equivalent transformation, resulting in an improved equivalent circuit model that incorporates a complete set of state variables for the DC voltage droop control converter. By combining the improved equivalent circuit model with constant power load (CPL) and parallel resistive load, an equivalent nonlinear circuit model is derived. The proposed model facilitates the construction of the mixed potential function, allowing for the derivation of both the large-signal stability criterion and stability region of the DCMGs. So that the parameters domain and power boundary of the system are calculated. Lastly, the energy indicator Q through the application of the LaSalle invariant set theorem is obtained, which helps to capture the trends in system stability changes. The large-signal stability of the system can be assessed based on the conditions of S<1 and PCPL<PCPLmax, along with the dynamic changes observed in the energy indicator. Additionally, the derived large-signal stability criterion can guide the optimization of control parameters.
The simulation results demonstrate the alignment between the DC voltage dynamic responses of the proposed model and those of the detailed model. The energy indicator reflects the degree of fluctuation in the DC voltage response. Enhancing the large-signal stability of DCMGs can be achieved by increasing the voltage loop proportional and integral gain, droop gain, filter capacitance and line resistance, while decreasing line inductance. Increasing the droop gain, line resistance, and parallel resistive load will result in a reduction of the CPL boundary. Comparing the large-signal stability criteria based on different modeling methods reveals errors in the analysis results obtained from traditional models. These errors occur due to the challenges in describing the dynamic response of the converters adequately or when the crucial parameters are overlooked during the calculations. Finally, based on the simulation results obtained for both two-terminal and five-terminal DCMGs, it can be seen that stability can be achieved in the event of large disturbances when the system satisfies the maximum singular value S<1 and when the CPL power value PCPL remains below the threshold of PCPLmax. Conversely, if the system fails to meet S<1 or PCPL<PCPLmax, instability occurs during large disturbances.
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Received: 01 April 2023
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2024, Vol. 39 
