A Novel Reduced Model for Electrical Networks with Constant Power Loads

TL;DR

This paper introduces a new reduced modeling approach for electrical power networks with constant power loads, utilizing a novel matrix decomposition to derive simpler ODE-based models that handle nonlinearities and algebraic constraints.

Contribution

The paper presents a new reduced model for power networks with constant power loads using the projected incidence matrix, extending Kron reduction to nonlinear and algebraic constraints.

Findings

Derived explicit reduced models as ODEs for complex power networks.

Introduced the projected incidence matrix for better decomposition.

Provided a new approach to handle nonlinear power flow equations.

Abstract

We consider a network-preserved model of power networks with proper algebraic constraints resulting from constant power loads. Both for the linear and the nonlinear differential algebraic model of the network, we derive explicit reduced models which are fully expressed in terms of ordinary differential equations. For deriving these reduced models, we introduce the "projected incidence" matrix which yields a novel decomposition of the reduced Laplacian matrix. With the help of this new matrix, we provide a complementary approach to Kron reduction which is able to cope with constant power loads and nonlinear power flow equations.