The Price of Synchrony: Resistive Losses due to Phase Synchronization in Power Networks

TL;DR

This paper quantifies the resistive losses in power networks due to phase synchronization, revealing that increased connectivity does not reduce losses and that costs grow with network size, especially with distributed generation.

Contribution

It derives a topologically invariant expression for synchronization losses, contrasting with traditional stability measures, and highlights the cost implications of network connectivity and distributed generation.

Findings

Resistive losses scale with network size and generator properties, independent of topology.

Highly connected networks do not reduce total resistive losses for synchronization.

Losses increase unboundedly with the number of generators in distributed networks.

Abstract

We investigate the total resistive losses incurred in returning a power network of identical generators to a synchronous state following a transient stability event or in maintaining this state in the presence of persistent stochastic disturbances. We formulate this cost as the input-output $H^2$ norm of a linear dynamical system with distributed disturbances. We derive an expression for the total resistive losses that scales with the size of the network as well as properties of the generators and power lines, but is independent of the network topology. This topologically invariant scaling of what we term the price of synchrony is in contrast to typical power system stability notions like rate of convergence or the region of attraction for rotor-angle stability. Our result indicates that highly connected power networks, whilst desirable for higher phase synchrony, do not offer an advantage in terms of the total resistive power losses needed to achieve this synchrony. Furthermore, if power flow is the mechanism used to achieve synchrony in highly-distributed-generation networks, the cost increases unboundedly with the number of generators.