Distributed transient frequency control for power networks with stability and performance guarantees

Abstract

This paper proposes a distributed strategy regulated on a subset of individual buses in a power network described by the swing equations to achieve transient frequency control while preserving asymptotic stability. Transient frequency control refers to the ability to maintain the transient frequency of each bus of interest in a given safe region, provided it is initially in it, and ii) if it is initially not, then drive the frequency to converge to this region within a finite time, with a guaranteed convergence rate. Building on Lyapunov stability and set invariance theory, we formulate the stability and the transient frequency requirements as two separate constraints for the control input. Our design synthesizes a controller that satisfies both constraints simultaneously. The controller is distributed and Lipschitz, guaranteeing the existence and uniqueness of the trajectories of the closed-loop system. We further bound its magnitude and demonstrate its robustness against measurement inaccuracies. Simulations on the IEEE 39-bus power network illustrate our results.

Distributed Bilayered Control for Transient Frequency Safety and System Stability in Power Grids

“…for certain matricesÃ,B 1 , andB 2 , withà stable [20]. Additionally, one can easily check that the linearized dynamics (15) and (16) preserve the locality of (2b) and (13). We consider the following three discretization methods with stepsize T > 0 to construct F, A, B 1 , and B 2 matrices in (6a) approximating the continuous dynamics (16).…”

“…Formally, for every i ∈ I ω , letγ i , γ i > 0, and ω thr i ,ω thr i ∈ R with ω i < ω thr i < 0 < ω thr i <ω i . We use the design from [13] for the top layer. For i ∈ I ω , α DF,i (x(t), p) takes the form…”

“…and for i ∈ I \I ω , simply α DF,i ≡ 0. The top-layer controller can be implemented in a decentralized fashion: for each α DF,i with i ∈ I ω on bus i, its implementation only requires the bus frequency ω i , aggregated power flow [D T ] i sin(Y b λ ), power injection p i , and ith component of the bottom-layer signal α BL,i , all of which are local to bus i. Additionally, similarly to [13], one can show that α T L is locally Lipschitz in x. For brevity, we may use α DF,i (x(t), p) (respectively, v i (x(t), p)) and α DF,i (t) (respectively v i (t)) interchangeably.…”

“…(Bilayered control with stability and frequency guarantees). Under condition (4), assume that ε i T i < 1 for every i ∈ I u , and x(0) ∈ T , then the system (2) with the bilayered controller defined by (5), (8), (12), (13), and (20) satisfies…”

“…However, these methods rely on some a-priori explicit frequency overshoot estimation based on reduced-order models, and hence only provide approximate transient frequency safety guarantees. Combining the notion of control barrier [11] and Lyapunov [12] functions, our previous work [13] proposes a feedback controller that meets both requirements of transient frequency safety and asymptotic stability. This controller is distributed and requires no communication, in the sense that each control signal regulated on an individual bus only depends on neighboring system information that can be directly measured.…”