Multi-Period Sparse Optimization for Proactive Grid Blackout Diagnosis

TL;DR

The paper tackles grid survivability under correlated extreme events by introducing a multi-period sparse optimization framework that identifies persistent vulnerability locations as stress increases. It replaces hard persistency constraints with adaptive sparsity coefficients, solving each scenario via a circuit-theoretic formulation and the SparseFeas solver to enable scalability to large power systems. The method demonstrates reliable tracking of persistent failure sources across load-growth sequences and maintains sparsity and total compensation comparable to single-scenario baselines, while enabling projections to intermediate cases. Practically, this approach concentrates planning and operational interventions on enduring weak points, improving resilience with efficient, scalable analysis across wide stress ranges. $\min_{\bm{x},\bm{n}} \frac{1}{2}\|\bm{n}\|_2^2 + \sum_i c_i^{(t)}|\bm{n}_i|$ s.t. $\bm{g}(\bm{v})+\bm{n}=0$, $\mathcal{S}^{(1)}\subseteq\cdots\subseteq\mathcal{S}^{(T)}$, and adaptive $c_i^{(t)}$ encode persistency.$

Abstract

Existing or planned power grids need to evaluate survivability under extreme events, like a number of peak load overloading conditions, which could possibly cause system collapses (i.e. blackouts). For realistic extreme events that are correlated or share similar patterns, it is reasonable to expect that the dominant vulnerability or failure sources behind them share the same locations but with different severity. Early warning diagnosis that proactively identifies the key vulnerabilities responsible for a number of system collapses of interest can significantly enhance resilience. This paper proposes a multi-period sparse optimization method, enabling the discovery of {persistent failure sources} across a sequence of collapsed systems with increasing system stress, such as rising demand or worsening contingencies. This work defines persistency and efficiently integrates persistency constraints to capture the ``hidden'' evolving vulnerabilities. Circuit-theory based power flow formulations and circuit-inspired optimization heuristics are used to facilitate the scalability of the method. Experiments on benchmark systems show that the method reliably tracks persistent vulnerability locations under increasing load stress, and solves with scalability to large systems ({on average} taking {around} 200 s per scenario on 2000+ bus systems).

Figures (6)

• Figure 1: With the growing demand stress, the proposed method identifies a gradually expanding set of system vulnerabilities with severity quantified.
• Figure 2: Bayesian Network illustration of multi-period model
• Figure 3: Case30 Persistency: single-scenario (left) VS proposed multi-period (right) method. Subfigure (a) lists the key vulnerable locations at each scenario and plot the magnitude of key vulnerability sources $|n_i^{(t)}|$ by the size of the colored circle markers. Our proposed method (right) identifies bus #19 as the only vulnerable location starting from 1st and persists until the last scenario; the location is a 100% persistent failure location, i.e., the location persistency is 100%, and it lasts for 10 steps in total (as notified on the right with "100% / 10"). Whereas the baseline method (left) locates vulnerability sources to bus #22 in 1st and 2nd scenario; and later switched to bus #19, leading to lower persistency. The bottom plots (b) illustrate overall persistency by $\mathrm{SetPersistency}$ metric for baseline (left) and proposed (right) method. Bar plots show the number of locations $\vert\mathcal{S}^{(t)}\vert$ and the cumulative number of locations $\vert\sum_{j=1}^t \mathcal{S}^{(j)}\vert$ for $\forall t$; and red/blue line plot shows the ratio between the two, which is $\mathrm{SetPersistency(t)} = \vert\mathcal{S}^{(t)}\vert/\vert\sum_{j=1}^t \mathcal{S}^{(j)}\vert$ for $\forall t$.
• Figure 4: Case2383wp Persistency: single-scenario (left) VS proposed multi-period (right) method. (a): using single-scenario baseline, only 2 persistent vulnerability locations (No. 2219 and 2205) are identified No. 2320 and 2350, all other vulnerable locations do not persist well. Whereas using the proposed method, all identified vulnerability locations are persistent failure sources. (b): set persistency decreases with as we process more scenarios using baseline method; whereas our proposed method maintains high set persistency.
• Figure 5: Case2383wp: Proposed multi-period method and the single-scenario baseline achieve comparable level of sparsity (left) and total amount of compensation sources (right) to restore feasibility. I.e., our proposed work promotes persistency on multiple scenario analysis without significantly sacrificing sparsity and compensation resources.

Theorems & Definitions (3)

• definition 1: Ideal persistency of vulnerability locations
• definition 2: Location Persistency Metric
• definition 3: Set Persistency Metric