Adaptive Step Size Linear Multistep Method for Small Signal Stability Analysis in Power Systems with Time Delays

Distributed energy resources (DERs) offer a promising solution for enhancing the resilience and efficiency of modern power systems. However, the inherent time delays in their communication and control systems can degrade their small signal stability, affecting reliable operation. This paper presents an Adaptive Step Size Linear Multistep Method (AS-LMS), for analyzing small signal stability of the system in the presence of time delays. The AS-LMS automatically adjusts the step size based on the computed solution behavior, achieving a balance between accuracy and computational efficiency. The essential idea is to use smaller steps in regions where the dynamic is changing rapidly and larger steps in regions where it is relatively smooth. Two adaptive step size strategies are proposed. The first strategy compares the current step size to the initial step size, ensuring consistency across iterations. The second strategy compares the current step size with the previous step size, allowing for more local adjustments throughout the numerical integration process. We evaluate the performance of the proposed AS-LMS method on two standard testing systems, i.e., the IEEE 9-bus and IEEE 30-bus systems. Both systems are modified to converter-interfaced DER units and different delays are applied to each testing system. The results show that the proposed AS-LMS method improves computational efficiency while maintaining accuracy in stability assessments. By balancing the accuracy and computational efficiency, the AS-LMS method provides a potent tool to analyze the stability of power systems with time delay.