Discrete to Continuous Model Conversion of multiple time-delayed distributed power grid with A Singular Continuous-Time System Matrix

Transmission delay time can be neglected on traditional large-scale electricity system. However it is a serious issue in distributed power grid (DPG) system. In DPG system, electricity is propagated through highly related transmission line network and the impact of transmission delay will be amplified. This highly interconnected attribute will not only cause the power system less efficient but also make whole system unstable. Aimed at solving the above difficulty, we generate a matrix sign function. This method is good for multi-state, input delay DPG system. Using the proposed matrix sign function, a lagging and time discrete system with multiple lagging is turned up to an uninterrupted time system with multiple time lagging. We also provide a discrete time model to demonstrate how compelling of our new method.