Inverse Stability Problem and Applications to Renewables Integration

IEEE Trans. Control Netw. Syst.

2020

This paper considers power networks governed by swing nonlinear dynamics and subject to disturbances. We develop a bilayered control strategy for a subset of buses that simultaneously guarantees transient frequency safety of each individual bus and asymptotic stability of the entire network. The bottom layer is a model predictive controller that, based on periodically sampled system information, optimizes control resources to have transient frequency evolve close to a safe desired interval. The top layer is a real-time controller assisting the bottom-layer controller to guarantee transient frequency safety is actually achieved. We show that control signals at both layers are Lipschitz in the state and do not jeopardize stability of the network. Furthermore, we carefully characterize the information requirements at each bus necessary to implement the controller and employ saddle-point dynamics to introduce a distributed implementation that only requires information exchange with up to 2-hop neighbors in the power network. Simulations on the IEEE 39-bus power network illustrate our results.

Section: Frequency Safety and Local Asymptotic Stabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

IEEE Trans. Control Netw. Syst.

2020

“…We establish a stability constraint by identifying an energy function and restricting the input so that its evolution along every trajectory of the closed-loop dynamics is monotonically nonincreasing. We select the following energy function [Vu et al, 2017]…”

Section: Constraint Ensuring Stability and Convergencementioning

confidence: 99%

“…On the other hand, although it is easy to check if a given initial state belongs to Φ, it is difficult to characterize its geometric shape. The work [Vu et al, 2018] shows that, for suitable c > 0 determined via a convex quadratic program, the ellipsoid…”

Section: Constraint Ensuring Stability and Convergencementioning

confidence: 99%

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

2019

Automatica

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.

“…Let G ∈ I denote the collection of node indexes with strictly positive inertia, and ω g ∈ R |G| be the corresponding collection of frequencies of these nodes. Consider the energy function [Zhang and Cortés, 2019, Vu et al, 2018, Monshizadeh and Persis, 2017]…”

Section: Open-loop Finite-horizon Optimal Controlmentioning

confidence: 99%

Model predictive control for transient frequency regulation of power networks

2019

Preprint

This paper introduces a control strategy to simultaneously achieve asymptotic stabilization and transient frequency regulation of power networks. The control command is generated by iteratively solving an open-loop control cost minimization problem with stability and transient frequency constraints. To deal with the non-convexity of the stability constraint, we propose a convexification strategy that uses a reference trajectory based on the system's current state. We also detail how to employ network partitions to implement the proposed control strategy in a distributed way, where each region only requires system information from neighboring regions to execute its controller.