# Solving the Synchronization Problem in Power Networks

*October 30th, 2013*

**Scientists find a concise formula to predict stable synchronization in complex
power networks.**

Despite its large scale, heterogeneity, and complexity, the power grid reliably provides energy to most parts of the world. Recent political and societal developments are leading to the deregulation of energy markets and the increasing adoption of renewable energy sources. Together with the ever-increasing power demand, these developments are also leading to more stressed and heavily loaded power networks operating near their dynamic stability margins, as documented by recent power outages.

With the complexity of future smart grids and the integration challenges posed by renewables, a deeper understanding of the grid’s dynamic network interactions as well as the control of those interactions is increasingly important.

In order to address this challenge, Institute faculty member Francesco Bullo and former PhD student Florian Dörfler, together with Michael Chertkov from Los Alamos National Laboratory, have developed a closed-form condition that predicts synchronization in complex power networks. Their findings, published in the Proceedings of the National Academy of Sciences, are summarized below.

**The Synchronization
Problem in Power Networks**

All power sources connected to an AC power grid are electro-mechanical oscillators coupled through a complex electrical network. All of these oscillators need to operate in strict frequency synchrony despite volatile renewable sources, fluctuating loads, and major disturbances in the transmission network.

Because synchronization is pervasive in the operation of an interconnected power grid, central questions that must be answered are, “Under which conditions does there exist a synchronous operating point? When is it optimal, when is it stable, and how robust is it?" A local loss of synchrony can trigger cascading failures and possibly result in widespread blackouts.

*Right: A system of spring-interconnected particles
rotating on a ring serves as a mechanical analog that illustrates the
synchronization dynamics in a multi-machine power system.*

**Research Findings**

In order to analyze synchronization in coupled oscillators, the authors explored connections between synchronization phenomena in different scientific disciplines and made use of recent mathematical advances in network sciences.

The authors studied an accurate yet tractable mathematical model and developed a surprisingly simple closed-form condition that predicts synchronization in a complex and highly nonlinear power grid as a function of the topology and parameters of the underlying electrical network.

The authors’ findings significantly improve upon the existing conditions advocated by theorists and practitioners thus far. They are provably exact for various interesting network topologies and parameters, and are statistically correct for a broad set of random network models.

The authors used different randomized complex network models and 10 IEEE power system benchmark test cases to examine the correctness and the predictive power of their analytic conditions.

The researchers validated the synchronization condition in a volatile smart grid scenario that included fluctuating loads with random power demand, renewable energy sources with severely fluctuating power outputs, and controllable loads. In this test case, a series of events triggered by the loss of a generator and imbalanced power demand, caused a loss of synchronization and a series of line outages leading to a blackout. The numerical findings confirmed the validity, accuracy, and practical applicability of the researchers' analytic synchronization conditions in complex power network scenarios.

**Research
Applications **

In their subsequent work, the authors have leveraged the insights gained from their synchronization analysis for the following design problems:

- Distributed control strategies in microgrids

- Power flow optimization schemes with stability constraints

- Advanced power flow approximations

In each case, the proposed novel solution strategy significantly improves upon conventional methods advocated in industry and academia.

Each of the above schemes could be readily implemented by utilities, and the authors and their collaborators have already conducted some first hardware experiments. The authors’ results could also be used in multiple other smart grid problems such as monitoring strategies in volatile power networks, wide-area control design, and remedial action schemes.

Author: Florian Dorfler

(former PhD student at UC Santa Barbara)

To read the full published paper click here.

**Publication details**: F. Dörfler, M. Chertkov, and F. Bullo. Synchronization in Complex Oscillator Networks and Smart Grids. Proceedings of the National Academy of Sciences, 110(6):2005-2010, February 2013. **Authors**: Florian Dörfler (UCLA), Michael Chertkov (LANL), Francesco Bullo (UCSB)