Efficiency and Stability in Electrical Power Transmission Networks: a Partition Function Form Approach

Abstract

The users of electricity networks are organized into groups where the production and consumption of electricity is in balance. We study the formation of these balancing groups using a cooperative game in partition function form defined over an ideal (lossless) DC load flow model of the power grid. We show that such games contain widespread externalities that can be both negative and positive. We study the stability of certain partitions using the concept of the recursive core. While the game is clearly cohesive, we demonstrate that it is not necessarily superadditive. We argue that subadditivity may be a barrier to achieve full cooperation.

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Notes

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    In AC systems voltage is represented as a vector rotating on the complex plane. The angular speed of these vectors at the nodes is the same, but the actual angles may differ

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Acknowledgments

The authors thank Katalin Hangos, Dávid Raisz, Dániel Divényi, and seminar participants at IEHAS and LSU for their input. This work has been supported by the Fund PD 123900 of the Hungarian National Research, Development and Innovation Office, by the Momentum Program by the Hungarian Academy of Sciences (LP-004/2010), and by the Fund KAP17-61008-1.2-ITK of the Pázmány Péter Catholic University.

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Correspondence to Dávid Csercsik.

Appendix

Appendix

Partition Function of the Game Over the Network Depicted in Fig. 4a

The P values and flows corresponding to partitions 1, 2 + 3 + 4 + 5, 1, 2 + 3, 4 + 5 and 1, 2 + 3, 4, 5 are detailed in Example 1. The other values of the PFF are similarly derived.

Table 2 Partition function of the game over the network depicted in Fig. 4a

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Csercsik, D., Kóczy, L.Á. Efficiency and Stability in Electrical Power Transmission Networks: a Partition Function Form Approach. Netw Spat Econ 17, 1161–1184 (2017). https://doi.org/10.1007/s11067-017-9363-0

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Keywords

  • Partition function form games
  • Power transmission networks
  • Externalities
  • Game theory
  • Recursive core