Dissipativity of nonlinear ODE model of distribution voltage profile

TL;DR

This paper analyzes the dissipativity properties of a nonlinear ODE model of power distribution voltage profiles, revealing how dissipation relates to distribution losses and proposing a control strategy to reduce these losses.

Contribution

It demonstrates the dissipativity of subsystems in a nonlinear ODE model of distribution systems and links dissipation rates to power losses, offering a new control approach.

Findings

Dissipativity of active and reactive power subsystems is established.

Dissipation rates match the distribution losses proportional to current squared.

Control input based on dissipation rates can reduce distribution losses.

Abstract

In this paper, we consider a power distribution system consisting of a straight feeder line. A nonlinear ordinary differential equation (ODE) model is used to describe the voltage distribution profile over the feeder line. At first, we show the dissipativity of the subsystems corresponding to active and reactive powers. We also show that the dissipation rates of these subsystem coincide with the distribution loss given by a square of current amplitudes. Moreover, the entire distribution system is decomposed into two subsystems corresponding to voltage amplitude and phase. As a main result, we prove the dissipativity of these subsystems based on the decomposition. As a physical interpretation of these results, we clarify that the phenomena related to the gradients of the voltage amplitude and phase are induced in a typical power distribution system from the dissipation equalities. Finally, we discuss a reduction of distribution losses by injecting a linear combination of the active and reactive powers as a control input based on the dissipation rate of the subsystem corresponding to voltage amplitude.