## Abstract

Voltage source converters (VSCs) are becoming more and more popular in the power electronic-based (PE-based) power systems. Using PE-based units in the system introduces some facilities like more controllability of the system states, while it brings some challenges regarding the stability and reliability of the grid operation. Accordingly, although conventional stability concepts are eligible for the PE-based power systems, it needs more detailed assessment in order to analyze the stability of the VSCs.

Regarding the stability analysis of the grid-connected VSCs, there are a couple of points to be considered. First, an appropriate model of the VSC based on the case study is required. A small signal model of the system using linearization techniques is credible for the small signal assessment, while a large signal model including nonlinear parts of the system is suited when a large signal disturbance happens like when a large such as a big change in the load and this is the subject of the study. Second, as the scale of the PE-based units become large, it is not adequate to model the main grid as a stiff voltage source. Therefore, the main grid will act as a weak grid, which needs a relevant model to be applied to the analysis. Modelling of the weak grid condition is one of the main challenges of the current PE-based power systems, specifically in island power systems with high penetration of distributed.

In this paper, a large signal model of the grid-connected VSC considering the weak grid condition is presented. To do so, the converter is considered as a voltage source in which its output active power can be controlled. Then, in order to evaluate the large signal stability, the nonlinear part of the system should be considered in the model without using the linearization techniques. In order to

overcome this challenge, the Lyapunov function of the system is used for the stability assessment. The Lyapunov function is defined based on the VSC parameters, the grid parameter, and the phase angle difference between the VSC and the main grid. It is shown that as long as the proposed Lyapunov

function is positive and its derivative with respect to the time is negative, the system works in its stable mode.

To verify the proposed model, time domain simulations are considered for a grid-connected VSC. In the case studies, the DC-link voltage of the VSC is considered to be constant for the sake of simplicity and in order to focus on the proposed method. It is shown that the stability boundaries can be predicted by using the proposed model, and the proposed method is valid both for the small signal and large signal stability assessments.

Regarding the stability analysis of the grid-connected VSCs, there are a couple of points to be considered. First, an appropriate model of the VSC based on the case study is required. A small signal model of the system using linearization techniques is credible for the small signal assessment, while a large signal model including nonlinear parts of the system is suited when a large signal disturbance happens like when a large such as a big change in the load and this is the subject of the study. Second, as the scale of the PE-based units become large, it is not adequate to model the main grid as a stiff voltage source. Therefore, the main grid will act as a weak grid, which needs a relevant model to be applied to the analysis. Modelling of the weak grid condition is one of the main challenges of the current PE-based power systems, specifically in island power systems with high penetration of distributed.

In this paper, a large signal model of the grid-connected VSC considering the weak grid condition is presented. To do so, the converter is considered as a voltage source in which its output active power can be controlled. Then, in order to evaluate the large signal stability, the nonlinear part of the system should be considered in the model without using the linearization techniques. In order to

overcome this challenge, the Lyapunov function of the system is used for the stability assessment. The Lyapunov function is defined based on the VSC parameters, the grid parameter, and the phase angle difference between the VSC and the main grid. It is shown that as long as the proposed Lyapunov

function is positive and its derivative with respect to the time is negative, the system works in its stable mode.

To verify the proposed model, time domain simulations are considered for a grid-connected VSC. In the case studies, the DC-link voltage of the VSC is considered to be constant for the sake of simplicity and in order to focus on the proposed method. It is shown that the stability boundaries can be predicted by using the proposed model, and the proposed method is valid both for the small signal and large signal stability assessments.

Original language | English |
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Title of host publication | Proceedings of CIGRE Symposium Aalborg 2019 |

Number of pages | 13 |

Publisher | CIGRE (International Council on Large Electric Systems) |

Publication date | Jun 2019 |

Article number | 18 |

Publication status | Published - Jun 2019 |

Event | CIGRE Symposium Aalborg 2019 - Aalborg, Denmark Duration: 4 Jun 2019 → 7 Jun 2019 |

### Conference

Conference | CIGRE Symposium Aalborg 2019 |
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Country | Denmark |

City | Aalborg |

Period | 04/06/2019 → 07/06/2019 |

## Keywords

- Power electronic stability
- Grid-connected voltage source converters
- Large-signal stability assessment
- Lyapunov stability analysis