Modeling and Formulation of Delayed Cyber-Physical Power System for Small-Signal Stability Analysis and Control

Modeling and formulation of a delayed cyber-physical power system (DCPPS) are the basis of small-signal stability analysis and control synthesis of the system. First, a logic describing the interconnections between various systems of delayed differential algebraic equations (DDAEs) and delayed differential equations (DDEs) is established. It clearly shows the transformation of the most general DDAEs of the non-index-1 Hessenberg form to the widely used DDEs with finite terms of actual delays. Second, the DDAE model of the index-1 Hessenberg form is formulated in detail for DCPPS, which features in preserving the inherent sparsity in system's augmented state matrix. Exploiting the sparsity guarantees the scalability in stability analysis and controller design of a large DCPPS. Third, three delay merge properties are presented with complete proofs, which indicate that the feedback and control delays in one control loop can be treated as one single time delay. The properties facilitate modeling and formulating DCPPS. Last, numerical studies are carried out on a real-life large DCPPS with wide-area damping controllers embedded. Test results validate the correctness of the presented theoretical backgrounds.