Eur. Phys. J. Special Topics 223, 2549–2559 (2014)
https://doi.org/10.1140/epjst/e2014-02215-x

Regular Article

Node-wise robustness against fluctuations of power consumption in power grids

¹ Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
² Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan
³ FIRST, Aihara Innovative Mathematical Modelling Project, Japan Science and Technology Agency, The University of Tokyo, Tokyo 153-8505, Japan
⁴ Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
⁵ CREST, JST, Saitama 332-0012, Japan
⁶ Energy Engineering Research Laboratory, Central Research Institute of Electric Power Industry, Kanagawa 240-0196, Japan

^a e-mail: nagata@sat.t.u-tokyo.ac.jp

Received: 25 February 2014
Revised: 7 May 2014
Published online: 24 June 2014

Abstract

We propose a new concept of node-wise robustness of power grids under variation of effective power in one load node using a mathematical model that takes into account the change in voltage and reactive power of load nodes. We employ the topology of the power grid in eastern Japan. We define the robustness as the threshold value of the effective power, above which the steady state loses its stability. We show that the robustness is highly heterogeneous among the load nodes. We find that the shortest path length from generators is most highly correlated with the robustness of the load nodes. We numerically demonstrate that the supply of reactive power enhances the robustness.