Stability of Real-Time Hybrid Simulation Using High-Order Unconditionally Stable and Explicit Algorithms

Abstract:

To provide high computational efficiency， accuracy and stability integration algorithms for real-time hybrid simulation （RTHS）， the high order accurate， unconditionally stable new dual-explicit （NDE）， and new semi-explicit （NSE） algorithms were developed based on the second-order accurate unconditionally stable and explicit Chen-Ricles （CR） and Chang algorithms. Based on the discrete control theory， the closed-loop discrete transfer function of the RTHS system using the two new algorithms were derived. The influences of time delay， damping ratio， stiffness proportional ratio， and integration algorithm on the stability of the RTHS system were investigated. Additionally， the approximation solution and accurate solution derived from the delay differential equation were also adopted for reference. The analytical results show that the time delay decreases the stability of the RTHS system. Increasing the stiffness proportional ratio reduces the difference between different analysis results. Increasing the damping ratio improves the stability of the RTHS system， enlarges the difference between the stability with and without considering the integration algorithm， and magnifies the difference between the stability using different integration algorithms. The stability of the RTHS system using the two high-order accurate integration algorithms is superior to that of the two second-order accurate integration algorithms.