Balanced Model Reduction for Nonlinear Power Network Models

Power systems transients are commonly modeled via a system of large nonlinear differential-algebraic equations (NDAEs). The complexity and size of power systems models are further increasing with the integration of renewables and other distributed energy resources. To allow scalable real-time monitoring and control, the field of model order reduction (MOR) is becoming more crucial. Although recent literature in power system MOR has proposed various MOR techniques, they simplify the NDAE models to often linear ODE ones. Consequently, the algebraic variables and constraints (power/current balance equations) are neglected and reduction is only carried out for dynamic variables. Ignoring algebraic states in the reduction process means a significant part of the system remains untouched, limiting the effectiveness of MOR. To that end, we propose MOR for complete NDAE power system models. The presented approach can significantly reduce the number of both dynamic and algebraic variables. Case studies on the IEEE 39-bus system validates the performance of the proposed approach. Numerical simulations show that the system can be represented using a far fewer number of states while providing input-output behavior similar to the original NDAE model.