Stability Analysis of Energy System with Grid-connected Converter

The structure of the energy system with a high share of renewable energy has changed. There will be more grid-connected converters in power generation and transmission stage. On the other hand, DC network, AC / DC hybrids and power electronic loads are increasing. This shows that the future energy system has a clear trend towards grid-connected converters. In contrast to conventional power system devices with well-known inherent characteristics, the operational behaviour of modern grid-connected converters strongly depends on implemented control and protection algorithms. This leads to fundamental changes in the theory of stability analysis and optimal operation of the power system.

Problem definition and approach
Due to the non-standardization and non-linearization of control strategy also the wide time-scale of dynamic characteristics (from microsecond class to second class), it is very difficult to analyze the energy system with grid-connected converter in a comprehensive and integrated stability. In addition, the interaction between the control strategies of multiple grid-connected converters exacerbates the difficulty of analysis.

Combining the modeling of grid-connected converters and the stability analysis of steady-state and transient-state, this project proposes a systematic, comprehensive and universal method for stability analysis of energy system with grid-connected converter. Based on this set of stability analysis methods, this project provides a theoretical basis and method for optimization and testing of converter.

Steady-state Stability Analysis
The steady-state stability analysis method linearizes the system near the operating point of the device, idealizing the grid-connected converter as a controlled current source or voltage source, and a series or parallel virtual impedance, as shown in Figure 1. In this project, the linearization of the grid synchronization control unit is carried out, such as phase-locked loops and P-f control loops. In the modeling and analysis process, the control unit coupled with the grid synchronization control unit is also considered. Using this analysis method can clearly explain the mechanism of instability phenomenon including sub-synchronous oscillation and harmonic oscillation, as shown in Figure 2. It can easily analyze the interaction between large-scale grid-connected converter.

Figure 1. The equivalent circuit diagram of the inverter-grid system

Figure 2. The measurement data for the Photovoltaic Charging Station

Transient-state Stability Analysis
The analysis object of the transient stability analysis method is the stability of grid-connected converter when the grid situation changes suddenly. In this process, the operation point of grid-connected converter is far away from its steady-state operation point, so a nonlinear analysis method must be used.
Qualitative analysis of the system can use a method similar to the phase portrait method, that is, the power-angle stability analysis method in a classic power system. The qualitative analysis method can intuitively judge the transient stability, as shown in Figure 3.

Figure 3. Analysis of phase-locked loop of converter based on phase portrait like method

The estimation of domain of attraction method is used for quantitative analysis of the system. According to the Lyapunov stability criterion, the system's domain of attraction is estimated, as shown in Figure 4, and the robustness of transient stability of the system is obtained. This analysis method can be used to explain and analyze the mechanism including LVRT failure (Figure 5) and voltage phase jump instability phenomenon.

Abbildung 4 Anziehungsbereich eines netzgekoppelten Konverters` PLL

Abbildung 5 Instabilität des Konverters nach LVRT


Zhang, Z., Schuerhuber, R., Chen, G., & Zhang, Y.
Stability and stability tests of inverter based power generation equipment.
In Energy Transition in Power Supply-System Stability and System Security; 13th ETG/GMA-Symposium (pp. 1-6). VDE.

Zhang, Z., Schürhuber, R., Fickert, L., Liu, X., Chen, Q., & Zhang, Y.
Hardware-in-the-loop Based Grid Compatibility Test for Power Electronics Interface.
In 2019 20th International Scientific Conference on Electric Power Engineering (EPE) (pp. 1-6). IEEE.

Zhang, Z., Gercek, C., Renner, H., Reinders, A., & Fickert, L.
Resonance instability of photovoltaic E-bike charging stations: Control parameters analysis, modeling and experiment.
Applied Sciences, 9(2), 252.

Zhang, Z., Schürhuber, R., Fickert, L., & Zhang, Y.
Stability of Grid-connected Photovoltaic Inverters During and After Low Voltage Ride Through.
In 8th Solar Integration Workshop: International Workshop on Integration of Solar into Power Systems.

Zhang, Z., & Fickert, L.
Power hardware-in-the-loop test of the energy feedback device in urban rail transportation system.
In 2018 19th International Scientific Conference on Electric Power Engineering (EPE) (pp. 1-4). IEEE.

Project Information


Dr. Ziqian ZHANG



  • Tongji University, China
  • Shanghai Dianji University, China