Port-Hamiltonian System Modelling and Geometric Numerical Integrator for Synchronous Generators

Electromagnetic transient (EMT) simulation is of fundamental importance for the design and operation of modern power systems. The solution of EMT models relies on numerical integration methods whose performance depends on the structure, scale, and stiffness of the system models. In this paper, we develop a synchronous generator model that maintains the underlying physical structure. In particular, a synchronous generator is represented as the interconnection of energy storage ports, dissipation ports, and external ports, leading to a canonical port-Hamiltonian system formulation. By exploiting the port-Hamiltonian structure, we introduce an energy-related invariant quantity for the developed model and construct a geometric numerical integrator based on the discrete gradient. This geometric numerical integrator can exactly maintain the energy-related invariant in the discrete-time solution. Numerical experiments verify the energy-preserving property of the proposed geometric. Comparative analysis with the Runge-Kutta method and the implicit trapezoidal method shows that, the energy-preserving geometric numerical integrator has better long-term numerical stability and accuracy especially at relatively large integration steps.