# Coherence in Synchronizing Power Networks with Distributed Integral Control

## TL;DR

This paper analyzes frequency control in power networks, showing that distributed averaging PI control outperforms centralized and standard methods, especially as network size grows, with demonstrated benefits on the Nordic power grid.

## Contribution

It introduces and compares distributed averaging PI control with centralized and droop control, highlighting superior transient performance and scalability in power network synchronization.

## Key findings

- DAPI control outperforms CAPI and droop control in transient performance.
- Performance of CAPI and droop control worsens with larger networks.
- Simulations confirm advantages of DAPI on the Nordic power grid.

## Abstract

We consider frequency control of synchronous generator networks and study transient performance under both primary and secondary frequency control. We model random step changes in power loads and evaluate performance in terms of expected deviations from a synchronous frequency over the synchronization transient; what can be thought of as lack of frequency coherence. We compare a standard droop control strategy to two secondary proportional integral (PI) controllers: centralized averaging PI control (CAPI) and dis- tributed averaging PI control (DAPI). We show that the performance of a power system with DAPI control is always superior to that of a CAPI controlled system, which in turn has the same transient performance as standard droop control. Furthermore, for a large class of network graphs, performance scales unfavorably with network size with CAPI and droop control, which is not the case with DAPI control. We discuss optimal tuning of the DAPI controller and describe how inter- nodal alignment of the integral states affects performance. Our results are demonstrated through simulations of the Nordic power grid.