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Scalable Reservoir Computing for Disturbance Localization and Identification in Power Grids
Erin Obermayer, Amir Sajadi, Bri-Mathias Hodge, Juan G. Restrepo
TL;DR
Power-grid disturbances are difficult to identify and localize quickly in complex, dynamic networks. This paper uses reservoir computing to localize and reconstruct disturbance waveforms from incomplete observations, with successful results across test systems and simultaneous disturbances.
Problem
Accurately identifying and responding to power-grid disturbances remains challenging because grids are large, fast, complex, and dynamic.
Source: §I · p. 1Method
A reservoir-computing framework localizes simultaneous disturbance sources and reconstructs their waveforms from incomplete measurements, using grid topology without an explicit model of system dynamics during inference.
Source: §I · p. 1Results
The method reconstructed disturbances across three systems, with mean RRMSE below 0.16 for the 1 Hz case, and accurately reconstructed simultaneous, distinct disturbance sources in the reduced WECC system.
Source: A. Scalability across power system… · p. 6, B. Disturbance localization and… · p. 7Takeaways & Limitations
Using only observed system data and grid topology supports fast, data-driven monitoring of large-scale power systems without requiring an explicit model of their governing dynamics during inference.
Source: §I · p. 1Validation used standard IEEE test systems and the reduced 240-bus WECC system; scaling to networks with more than 100 synchronous generators is left for future work.
Source: §V · p. 10
Abstract
from arXiv · showhide
In this paper, we present a novel method for the localization and temporal waveform reconstruction of disturbances in complex power grids using observations of system state variables. Although various methods exist for detecting these events, accurately identifying and responding to them remains a significant challenge due to the grid's size, speed, complexity, and inherently dynamic behavior. We formulate a method for disturbance localization and reconstruction based on reservoir computing, a recurrent neural network architecture. We show that our method is able to recover the time dependence of previously unobserved disturbances, is robust to missing information, and can operate online. The approach requires only observed system data and knowledge of the network topology, without requiring a physical model of the system dynamics, and can recover simultaneous disturbances occurring at multiple locations. We implement a scalable parallelized reservoir architecture and demonstrate our algorithm on test IEEE cases and a reduced WECC system.
I. INTRODUCTION
Many methods locate disturbances without reconstructing their waveforms, while often relying on detailed models, predefined event classes, or single-source settings. The paper formulates a reservoir-computing approach to localize and reconstruct multiple disturbances from incomplete observations using grid topology.
I. INTRODUCTION
- Many existing methods locate disturbances without reconstructing their waveforms, and often rely on detailed physical models, predefined event classes, or single-source settings.Waveforms can inform a disturbance’s origin, evolution, and physical characteristics.Source: §I · p. 1
- The framework simultaneously localizes multiple concurrent disturbance sources and reconstructs their waveforms from incomplete measurements, using grid topology without an explicit dynamics model during inference.The authors identify efficient, large-scale monitoring as a goal of this approach.Source: §I · p. 1
A. Problem Formulation
- The problem assumes significant disturbances affect a small set of nodes, typically at most three, and defines localization as identifying those nodes and reconstruction as approximating each disturbance’s time course.The approach seeks these outputs from state time series and general grid topology.Source: A. Problem Formulation · p. 2
B. Pseudo-Parallel Reservoirs
- Known forcing and state time series train each reservoir’s output to approximate a disturbance; during inference, observed states drive online disturbance estimates.Each reservoir estimates a scalar disturbance function.Source: B. Pseudo-Parallel Reservoirs · pp. 2–3
- Each of N separate reservoirs estimates one generator’s disturbance using measurements from that generator and its network neighbors, with transfer capacity and a threshold defining the local input set.The local architecture is intended to scale to large power grids.Source: B. Pseudo-Parallel Reservoirs · p. 3
C. Reservoir Architecture
The architecture uses a sparse recurrent reservoir for each generator and assigns observed inputs to reservoir nodes. A readout maps each reservoir’s internal state to an approximation of its generator’s disturbance.
C. Reservoir Architecture
- Each reservoir’s recurrent matrix is sparse and randomized, with its spectral radius rescaled to 0.9.Each entry is nonzero with probability 6/M; nonzero entries are sampled uniformly from [−1, 1].Source: C. Reservoir Architecture · p. 3
- Reservoir nodes are assigned among the inputs so each node receives exactly one input, with nodes distributed as evenly as possible.Input assignments are selected uniformly at random without replacement; S controls the average number of nodes assigned to each input.Source: C. Reservoir Architecture · pp. 3–4
- A readout matrix converts each reservoir’s internal state vector into an approximation of its corresponding generator’s disturbance.The readout matrices are computed using ridge regression with λ = 10^-10.Source: Figure 1 · p. 4, C. Reservoir Architecture · p. 4
- The reservoir activation uses the swish function with η = 0.001, which the authors found worked better than the hyperbolic tangent.Source: C. Reservoir Architecture · p. 4
D. Training forcing function
Training uses a piecewise-constant forcing function in three stages, progressing from single-generator pulses to simultaneous disturbances across groups and then all generators.
D. Training forcing function
- Training first forces each generator sequentially with a rectangular pulse whose amplitude is sampled uniformly from [−5, 5].The first-stage interval is divided into N equal subintervals, one per generator.Source: D. Training forcing function · p. 4
- The second stage applies random pulses to subsets of three or four generators simultaneously, with amplitudes sampled uniformly from [−5, 5].The simulations use LII = 50 subintervals unless otherwise specified.Source: D. Training forcing function · p. 4
- The third stage applies independently sampled [−5, 5] pulses to every generator simultaneously in each subinterval.The simulations use LIII = 75 subintervals unless otherwise specified.Source: D. Training forcing function · p. 4
- The three stages train reservoirs on both single-generator and multiple simultaneous disturbances; increasing LII and LIII generally improves recovery.More second- and third-stage subintervals provide a greater number of distinct training inputs.Source: D. Training forcing function · pp. 4–5, Figure 2 · p. 5
A. Test systems
The algorithm was tested on IEEE 9-bus and 39-bus systems and a reduced 240-bus WECC model, which correspond to aggregated systems with three, ten, and 49 synchronous machines.
A. Test systems
- The test systems were the IEEE 9-bus and 39-bus cases and a 240-bus reduced WECC model.Source: A. Test systems · p. 5
- After Kron reduction and generator aggregation, the IEEE 9-bus, IEEE 39-bus, and 240-bus WECC systems contain 3, 10, and 49 synchronous machines, respectively.The test systems vary in complexity.Source: A. Test systems · p. 5
B. Training Procedure
For each test system, the authors simulated the aggregated network under the training forcing functions, downsampled the generated time series, and used it to train the reservoirs and readouts.
B. Training Procedure
- Training data were generated by simulating each aggregated system over t ∈ [−T, 0] with T = 200 and time step Δt = 0.001.The swing-equation system was solved in MATLAB using Heun’s method.Source: B. Training Procedure · p. 5
- The simulated time series was downsampled so that only every 10th time step was supplied to the pseudo-parallel reservoirs.Source: B. Training Procedure · p. 5
- Training was completed by computing the readout matrices with the ridge-regression procedure.Source: B. Training Procedure · p. 5
C. Testing Procedure
The reservoirs were tested on previously unseen disturbances, beginning with conventional oscillations across three systems and then adding idealized and real-world nonlinear signals.
C. Testing Procedure
- After training, the reservoirs were evaluated on a range of previously unseen disturbances.Source: C. Testing Procedure · p. 5
1) Disturbance scenarios:
- Testing applied 1 Hz inter-area and 14.7 Hz sub-synchronous disturbances across all three systems; the most complex third system then received three idealized and three highly nonlinear disturbances derived from real-world grid events.Source: 1) Disturbance scenarios · p. 5
- Except for the square pulse, the tested disturbance types differed from those used to train the reservoir, and the reservoir successfully identified them.The real-world scenarios included NERC data-center load and forced-oscillation profiles and an AEMO event derived from measured West Murray Zone data.Source: 1) Disturbance scenarios · p. 5
2) Testing methodology:
The testing procedure averaged results over randomized realizations, and the method reconstructed disturbances across three systems without a clear system-size dependence. The remaining analyses focus on the reduced WECC 240-bus system.
2) Testing methodology:
- Each disturbance configuration was tested over 200 independent realizations with randomly selected disturbed generators and parameters, and reported statistics were averaged across realizations.Testing supplied the trained output matrices with simulated time series every tenth simulation step, using an effective input interval of 0.01 time units.Source: 2) Testing methodology · pp. 5–6
- The evaluation used five cases: one, two, or three generators sharing a disturbance type, and two or three generators receiving different types simultaneously.Source: 2) Testing methodology · pp. 5–6
IV. RESULTS AND DISCUSSIONS
- The results examined scalability, nonlinear-disturbance reconstruction, localization accuracy, reconstruction accuracy, partial information, model mismatch, and computational performance, with Sections B–G focused on the reduced WECC 240-bus system.Source: §IV · p. 6
- A quantitative comparison with prior methods was not possible because no existing method simultaneously localizes disturbances and reconstructs their temporal waveforms.Source: §IV · p. 6
A. Scalability across power system topologies
- Mean RRMSE was below 0.16 for 1 Hz disturbances across all three systems, with larger values for 14.7 Hz disturbances and no clear dependence on system size.In the 9-bus system, the dominant frequency was recovered exactly and its peak amplitude to within 17%, illustrating that higher RRMSE can reflect timing sensitivity rather than poor frequency-content recovery.Source: A. Scalability across power system… · p. 6
B. Disturbance localization and waveform reconstruction in the reduced WECC 240-bus System
In the reduced WECC system, the reservoir reconstructed three simultaneous disturbances of different types while distinguishing undisturbed generators. Spatial localization also achieved a range of tolerance values with no false positives or false negatives.
B. Disturbance localization and waveform reconstruction in the reduced WECC 240-bus System
- With three distinct disturbances applied simultaneously, the reservoir reconstructed each and correctly identified undisturbed generators; RRMSEs were 0.18, 0.13, and 0.03.The scenario used AEMO oscillatory, NERC forced-oscillation, and NERC data-center load-ramp signals; the corresponding PSD errors stayed below 1 × 10−4 through 20 Hz.Source: Figure 3 · p. 7, B. Disturbance localization and… · p. 7
- Fig. 4 plots PSD error by frequency for the three disturbed generators, showing accurate recovery of dominant frequency content within the examined range up to 20 Hz.Source: Figure 4 · p. 7, B. Disturbance localization and… · p. 7
C. Spatial localization accuracy
- The three-generator test produced a range of tolerance values with both false positive and false negative rates at zero, and its ROC curve had an AUC of 0.9981.The false positive rate approached 1 as ϵ approached zero, while the false negative rate approached 1 as ϵ increased, reaching that level for ϵ ≳1.Source: Figure 5 · p. 7, C. Spatial localization accuracy · p. 8
D. Disturbance reconstruction accuracy
Disturbance reconstruction error depends on disturbance type and reservoir size; under partial information, recovery remains accurate with few measurements and a restricted set of grid connections.
D. Disturbance reconstruction accuracy
- RRMSE is 0.14–0.21 for Ornstein-Uhlenbeck, NERC forced oscillation, and AEMO oscillatory disturbances, versus 0.03–0.05 for three other disturbance types.Despite higher RRMSE, PSD error remains below 1 × 10−4 for NERC and AEMO disturbances, indicating accurate recovery of dominant frequency content.Source: D. Disturbance reconstruction accuracy · p. 8
- RRMSE falls below 0.2 for M ≳50, with limited improvement from larger reservoirs.This corresponds to S = 2 and suggests moderate-sized reservoirs suffice under ideal operating conditions.Source: D. Disturbance reconstruction accuracy · p. 8, Figure 6 · p. 8
E. Robustness to partial information
- With measurements from only 9 of 49 generators available, the inferred disturbance remains close to the true disturbance, although RRMSE rises as more generators are masked.The evaluation targets disturbances at unmasked generators; recovery of disturbances applied to masked generators remains future work.Source: E. Robustness to partial information · pp. 8–9, Figure 7 · p. 8
- As the transfer-capacity threshold increases and the maximum connected generators falls from 23 to 9, reconstruction remains successful with RRMSE below 0.25, despite deteriorating performance.Using fewer connections also reduces computational cost.Source: E. Robustness to partial information · p. 9, Figure 8 · p. 9
F. Robustness to model mismatch
The paper tests robustness to parameter mismatch by training on nominal WECC parameters and recovering disturbances with perturbed parameters. It also reports experiment runtimes and describes validation scope.
F. Robustness to model mismatch
- A 5% mismatch (ν = 0.05) has little effect on reconstruction error, and even a 10% mismatch maintains low RRMSE.RRMSE increases as mismatch grows; the tested mismatch magnitude ν is added to inertia and damping parameters.Source: F. Robustness to model mismatch · p. 9, Figure 9 · p. 9
G. Computational Performance
- Mean training time was 25.5 seconds and mean testing time was 128.5 seconds across experiments.Computations used MATLAB R2024a on a 2023 14-inch MacBook Pro with an Apple M2 Pro processor and 16 GB of unified memory.Source: G. Computational Performance · p. 10
V. CONCLUSION
- Validation used standard IEEE test systems and the reduced 240-Bus WECC system; experiments indicate scaling beyond 100 synchronous generators, left for future work.The framework could be extended to inverter-based resource systems, according to the conclusion.Source: §V · p. 10