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Blog 8 - Steady-state stability analysis of the power electronics system

Hao, 19 February 2024

In response to the UK government's commitment to bring all greenhouse gas emissions to net zero by 2050, converter-based renewable energy sources are gradually replacing conventional synchronous generators, resulting in a gradual transformation of the conventional power grid into a power electronics-based power system. Power electronic converter can be flexibly and quickly controlled to effectively realize the conversion between AC and DC [1], thus playing an important role in power generation, transmission and distribution, but it also brings challenges to the stability of the new power system. The oscillation phenomenon caused by wide timescale dynamics of converters can range from few Hertz to kiloHertz [2]. Therefore, stability analysis is especially important.

There are two main approaches for stability analysis: state-space based approach in time domain and impedance-based approach in the frequency domain [4].

The state-space based approach is commonly used in the analysis of conventional power systems, however, in power electronics-based power systems, control loops of converters introduce a large number of state variables, which leads to a high-order system model and is hard to solve. In addition, it requires detailed control strategies and parameters of converters to establish the system differential equations. This information is difficult to get due to the data confidentiality. 

Inverter-grid system and equivalent small-signal impedance model

The impedance-based modeling is an alternative approach, consisting of a frequency domain model built using transfer functions. The small signal conductance is used to represent the terminal dynamics of the power converter, thus simplifying the calculation process compared to the state-space approach. This is an example of “black-box” modeling because the control dynamics are characterised by using the input-output relationships of transfer functions, which can be easily measured with a frequency scan. The figure above shows an example of equivalent small-signal model of a power converter connected to a grid. 

The impedance models can be assessed for stability by applying the Nyquist stability criterion [4]. Furthermore, the impedance models can be analyzed with Bode diagrams to visually understand the interactions between grids and converters in the frequency domain. They can be used as guidelines for parameters’ design to enhance electronic power systems stability.

In conclusion, the impedance-based approach has been widely used to analyze system stability from single converter-based to multi-infeed power electronics systems. Further research is needed to improve the small-signal model so that it can cope with the flexible and realistic operation conditions that exist in real power systems, and to consider the implications of more practical grid-side models and different converter control schemes.



References: [1] F. Blaabjerg, R. Teodorescu, M. Liserre and A. V. Timbus, "Overview of Control and Grid Synchronization for Distributed Power Generation Systems," in IEEE Transactions on Industrial Electronics, vol. 53, no. 5, pp. 1398-1409, Oct. 2006, doi: 10.1109/TIE.2006.881997; [2 ] X. Wang and F. Blaabjerg, "Harmonic Stability in Power Electronic-Based Power Systems: Concept, Modeling, and Analysis," in IEEE Transactions on Smart Grid, vol. 10, no. 3, pp. 2858-2870, May 2019, doi: 10.1109/TSG.2018.2812712; [3] J. Sun, "Impedance-Based Stability Criterion for Grid-Connected Inverters," in IEEE Transactions on Power Electronics, vol. 26, no. 11, pp. 3075-3078, Nov. 2011, doi: 10.1109/TPEL.2011.2136439; [4] B. Wen, D. Boroyevich, R. Burgos, P. Mattavelli and Z. Shen, "Inverse Nyquist Stability Criterion for Grid-Tied Inverters," in IEEE Transactions on Power Electronics, vol. 32, no. 2, pp. 1548-1556, Feb. 2017, doi: 10.1109/TPEL.2016.2545871.

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