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access icon openaccess Optimal agency contract for incentive and control under moral hazard in dynamic electric power networks

This is an open access article published by the IET under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/)
Received 01/11/2018, Accepted 12/07/2019, Revised 14/03/2019, Published 18/07/2019

The authors propose an optimal contract mechanism under moral hazard in discrete-time dynamic electric power networks. As the utility (system operator) cannot adjust the control input of the agents (end-users) directly in real time out of respect for individual decision–making, the agents’ control input maximising their own profit does not always maximise social welfare. To avoid the issue, the authors introduce an aggregator as intermediary between the utility and the agents. The aggregator pays compensation for defective ancillary services, which are caused by random disturbance and the agents’ voluntary control. To reduce the compensation risk, the authors first present an optimal incentive/control contract problem for the aggregator's compensation. The problem is usually regarded as a principal-agent problem under moral hazard in contract theory. However, it is generally difficult to solve a contract problem with dynamics expressed as discrete-time simultaneous Bellman equations and a hierarchical control structure as a Stackelberg game. The authors next show that the problem can be solved by regarding it as a linear-exponential-quadratic-Gaussian dynamic game and employing a numerical optimisation technique. Due to the ex-ante appropriate payment contract, the agents select control inputs preferable for the aggregator. The effectiveness of the proposed contract mechanism is finally demonstrated through simulation.

Inspec keywords: game theory; discrete time systems; contracts; incentive schemes; optimisation

Other keywords: ex-ante appropriate payment contract; agents; defective ancillary services; principal-agent problem; contract theory; utility; optimal contract mechanism; discrete-time simultaneous Bellman equations; discrete-time dynamic electric power networks; individual decision–making; social welfare; aggregator; linear-exponential-quadratic-Gaussian dynamic game; optimal agency contract; compensation risk; control input; hierarchical control structure; system operator; moral hazard

Subjects: Other topics in statistics; Game theory; Optimisation techniques; Optimisation techniques; Discrete control systems; Optimal control

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