PNNL

Abstract

This study examines the relationship between the topology of stable time-delay regions and the stability analysis of an LMTD (linear multiple time delay) system. To analyze the topology of stable time-delay regions, we construct a function with a value equal to zero for the time-delay points on the boundaries of stable time-delay regions. The function is continuous and differentiable in the whole defining field with a global minimum of zero so that we can locate the boundaries by minimizing the value of the function. Based the topology analysis, we proposed a performance validation approach for controllers that are designed to stabilize the system using feedback signals with varying time delays. The method based on the topology analysis is simple and reliable so that can deal with a linear time-invariant system with high order and multiple time delays (more than 3). The example case study shows that the above method is reliable and enables ultra-low latency coordination and control for the future power grid with ubiquitous power electronics.