A Simplified Stability Analysis Method for Multi-Converter System Based on Complex-Valued Node Admittance Model

The zero points of the determinant of the node admittance model (NAM) have been applied to address the stability issues in power systems with high-penetration converters. Yet, the NAM generally relies on the rotations, i.e., the dynamic phase of each converter, moreover, the frequency coupling effect is neglected via NAM. To fill this gap, this paper presents the concept of a unified <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">αβ</i>-frame complex-valued NAM, with which different converters as well as the passive components can be incorporated to form an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i>-domain model for a complex system. Additionally, the intrinsic relationship among the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">αβ</i>-frame complex-valued NAM, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i>-frame NAM, and the sequence-domain NAM is revealed from a physical perspective. The proposed model merely relies on the initial phase of the voltage at each node and accurately reflects the frequency coupling effect. Furthermore, considering the frequency coupling, the consistency between the zero points of the determinant of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">αβ</i>-frame complex-valued NAM and the eigenvalues derived from the state-space model is demonstrated. Finally, the effectiveness of the modeling approach and stability criterion is validated by applying them to the 3-machine system with different types of converters. Besides, the effect of the placement and capacity of converters based on grid-forming control on the stability performance in the multi-converter system is revealed.