Distributed bilayered control for transient frequency safety and system stability in power grids

TL;DR

This work tackles the challenge of guaranteeing transient frequency safety and overall stability in power networks described by swing dynamics under disturbances. It introduces a bilayered controller with a receding-horizon bottom-layer MPC for cooperative control and a real-time top-layer to enforce safety, aided by stability and smoothing filters. The distributed realization leverages strong convexification and saddle-point dynamics to achieve 2-hop information exchange while preserving locality. Theoretical guarantees show invariant and attractive frequency bounds and local asymptotic stability, with simulations on the IEEE 39-bus network validating robust performance under disturbances and forecast errors. The framework offers scalable, plug-and-play potential for grids with high renewable penetration.

Abstract

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.

Figures (8)

• Figure 1: Block diagram of the closed-loop system with the proposed controller architecture.
• Figure 2: IEEE 39-bus power network.
• Figure 3: Frequency and control input trajectories with and without transient frequency control. Plot \ref{['fig:frequency-response-open-loop']} shows the open-loop frequency responses at nodes 30, 31, 32, and 37, all exceeding the lower safe bound. The closed-loop system with the distributed control has all responses stay inside the safe region in plot \ref{['fig:frequency-response-closed-loop']}. Plot \ref{['fig:control-response-region1']} shows the corresponding control trajectories.
• Figure 4: Comparison of frequency and control trajectories with other approaches. Plot \ref{['fig:frequency-response-closed-loop-fully-decen']} and \ref{['fig:control-response-fully-decen']} employ the controller with regional coordination based on network decomposition proposed in YZ-JC:19-acc. Plot \ref{['fig:frequency-response-pure-df']} and \ref{['fig:control-response-pure-df']} correspond to the top-layer controller, a non-optimization-based control strategy proposed in YZ-JC:19-auto.
• Figure 5: Decomposition of the control signal at node 30. Plot \ref{['fig:control-response-30']}, \ref{['fig:control-response-30-smaller-penalty']}, and \ref{['fig:control-response-30-large-penalty']} show the signals generated by the two control layers at node $30$ using $d_{30} = 10^2$, $d_{30}=10$, and $d_{30}=10^3$, respectively, as values for the frequency safety violation penalty coefficient in the MPC component. With a larger penalty, the bottom layer plays a more significant role in the overall control signal.

Theorems & Definitions (18)

• Remark 3.1
• Remark 4.1
• Proposition 4.2
• proof
• Lemma 4.3
• proof
• Remark 4.4
• Remark 4.5
• Theorem 4.6
• proof