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

Abstract

Abstract-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.

Gather-and-broadcast frequency control in power systems

“…A simulation of this scenario is shown in Figure 2 for the system parameters given in Section 5, where generator 10 follows the above cheating strategy to uniquely balance the system and exclusively receive compensation. We refer to [40] for further cheating mechanisms related to DAI control. To conclude this section, let us remark that all integral control mechanisms presented in Subsection 2.4 could also have been implemented also as proportional-integral (PI) controllers to improve the system performance and enhance its stability.…”

Stability and Optimality of Distributed Secondary Frequency Control Schemes in Power Networks

“…Remark 7: The dynamics in (16) eliminate the requirement to explicitly know p L within the power command dynamics by adding an observer that mimics the swing equation, described by (16c)-(16e). The dynamics in (16d)-(16e) ensure that the variable χ j is equal at steady state to the value 16 See also the use of observer dynamics in [26] as a means of counteracting agent dishonesty.…”

“…) ω j ∈ U j , p c j ∈ U c j for j ∈ N , and (x M,j , x c,j , x u,j ) ∈ X G j , (x c,j , x u,j ) ∈ X L j for j ∈ G, j ∈ L respectively 18 , 4) x M,j , x c,j , and x u,j all lie within their respective neighborhoods X 0 as defined in Section III-A. Recalling now (26), it is easy to see that within this neighborhood, V is a nonincreasing function of all the system states and has a strict local minimum at Q * . Consequently, the connected component of the level set {(η, ψ, ω G , x M , x c , x u , p c ) : V ≤ ǫ} containing Q * is guaranteed to be both compact and positively invariant with respect to the system (3)-( 6) for sufficiently small ǫ > 0.…”

“…We now consider this invariant set. If V = 0 holds at a point within Ξ, then (26) holds with equality, hence we must have ω = ω * and p c j = p c, * j at all buses j where Assumption 5(a) holds. The fact that ω is constant guarantees from (3a), (3d) that η and p are also constant.…”