Improving Power Systems Controllability via Edge Centrality Measures

TL;DR

This paper tackles improving power-network controllability by moving beyond topology-only centrality to a control-theoretic edge centrality matrix (ECM) that uses controllability Gramian metrics $W_c$ to assess edge influence. It develops an ECM-based perturbation framework to identify influential transmission lines and designs near-optimal edge modifications under stability and budget constraints, using both non-convex and convex optimization strategies. Validation on IEEE 9-, 14-, and 68-bus networks shows improved reachability, damping, and energy efficiency, with ECM-based modifications often outperforming static nearest-neighbor centrality baselines, especially in low-cardinality scenarios. The work provides a dynamics-informed, scalable approach to enhancing power-system robustness and suggests directions for extending to nonlinear NDAEs and larger-scale systems.

Abstract

Improving the controllability of power networks is crucial as they are highly complex networks operating in synchrony; even minor perturbations can cause desynchronization and instability. To that end, one needs to assess the criticality of key network components (buses and lines) in terms of their impact on system performance. Traditional methods to identify the key nodes/edges in power networks often rely on static centrality measures based on the network's topological structure ignoring the network's dynamic behavior. In this paper, using multi-machine power network models and a new control-theoretic edge centrality matrix (ECM) approach, we: (i) quantify the influence of edges (i.e., the line susceptances) in terms of controllability performance metrics, (ii) identify the most influential lines, and (iii) compute near-optimal edge modifications that improve the power network controllability. Employing various IEEE power network benchmarks, we validate the effectiveness of the ECM-based algorithm and demonstrate improvements in system reachability, control, and damping performance.

Figures (6)

• Figure 1: Near-optimal topologies of $\Delta(\gamma^{\mathrm{ECM}_1})$, $\Delta(\gamma^{\mathrm{ECM}_2})$, $\Delta(\gamma^{\mathrm{ECM}_3})$ and the topology of $\Delta(\gamma^{\mathrm{NNEC}})$ (from left to right, respectively) where spectrum red lines represent the modified edges. The edges with darker colors correspond to the more influential edges. IEEE $68$-bus benchmark with $N = 16$ generators and $s=15$.
• Figure 2: $J_u$ and the average minimum energy $\mathrm{tr}(W_c(t_f)^{-1})$ associated with the minimum energy input in \ref{['umin']} for $t_f = -\frac{1}{\alpha(A(L))}$ and $t_f = \infty$ (lower bound) for these networks: IEEE $9$-bus, $s = 1$ (top-left) and $s=2$ (bottom-left), IEEE $14$-bus, $s = 1$ (top-middle) and $s=2$ (bottom-middle), IEEE $68$-bus, $s = 1$ (top-right) and $s=2$ (bottom-right).
• Figure 3: Relationship between the performance improvement $J(\gamma^{\mathrm{ECM}_i}(\beta))~(\%)$ and the budget/energy parameter $\beta$. IEEE $68$-bus benchmark, $i \in \{1,2,3\}$, $s = 1$ (left) and $s=15$ (right). $i = 1$: blue circle, $i=2$: red triangle, and $i = 3$: yellow square.
• Figure 4: Relationship between the near-optimality performance measures $J_V(\gamma^{\mathrm{ECM}_i}(\beta))~(\%)$ and $J_C(\gamma^{\mathrm{ECM}_i}(\beta))~(\%)$ and the budget/energy parameter $\beta$ for the IEEE $9$-bus benchmark with $\beta \le \min\{g_{ji}: (i,j) \in \mathcal{E}\}$, $s = 1$ and $i \in \{1,2,3\}$. $i = 1$: blue circle, $i=2$: red triangle, and $i = 3$: yellow square.
• Figure 5: Pole-zero maps with damping lines corresponding to the $A(L)$ and $A(L + \Delta (\gamma^{\mathrm{ECM}_i}))$ for $i \in \{1,2,3\}$ and $s = 2$. IEEE $14$-bus, from $i = 1$ (left) to $i = 3$ (right). The crosses in blue and red correspond to the poles of $A(L)$ and $A(L + \Delta (\gamma^{\mathrm{ECM}_i}))$.