The cost of dishonesty on optimal distributed frequency control of power networks

Optimal frequency controllers for power networks based on distributed averaging have previously been shown to be an effective means of distributing control authority among agents while maintaining a globally optimal operating point. Distributed control architectures however require an implicit trust between participating agents, in that each must faithfully communicate the appropriate control variables to neighboring agents. Here we study the case where some agents attempt to “cheat the system” by adding a bias to the averaging controller in order to lower their generation cost. We quantify the effect of this dishonesty on the resource allocation problem and introduce a “cost graph” whose weights measure the effect of the bias on the optimal equilibrium. Moreover, we propose an “honesty-enforcing” controller which counteracts the dishonest agents, and restores the optimal setpoint of the network.