A Contract Theory Approach to Dynamic Incentive Mechanism and Control Synthesis for Moral Hazard in Power Grids

Yasuaki Wasa*, Kenji Hirata, Kenko Uchida

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This article proposes a synthesis of a novel dynamic incentive mechanism and optimal control for moral hazard in power grids with real-time power balancing markets. For the liberalization of the balancing markets, it is an indispensable requirement to integrate dynamic subsystems controlled by individual agents into a stabilized power grid via an incentive mechanism. Meanwhile, without the proper use of the agents' private information, high-speed market-clearing achieving an appropriate social objective cannot be ensured. Consequently, a market mechanism is needed that contains some dynamic incentive mechanisms for eliciting their private information and proper controls under moral hazard, which is called incentivizing market in this article. Drawing on dynamic contract theory in microeconomics, a novel method for designing the incentivizing market is proposed on the basis of the integration of economic models and a dynamic grid model. Conventional contract problems have been analyzed for both static and dynamic systems whose control inputs are operated directly by an independent system operator. However, these analyses do not accord with the design for the dynamic incentive mechanism in the incentivizing market. The approach in this article requires adapting the dynamic contract problems to the market. To achieve this objective, the fundamental formulas for optimal design are established and the basic properties of the designed market based on a model-based approach are clarified. We next propose optimal pricing and control synthesis for social-objective designs. The performance of our proposed method is illustrated through simulations with an Institute of Electrical Engineers of Japan (IEEJ) East 30-machine system.

Original languageEnglish
Pages (from-to)2072-2083
Number of pages12
JournalIEEE Transactions on Control Systems Technology
Issue number5
Publication statusPublished - 2022 Sept 1


  • Dynamic contract theory
  • game theory
  • moral hazard
  • power balancing market
  • power grids
  • principal-agent problems
  • stochastic optimal control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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