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Infrastructure-Native Computing with Electric Power Grids

Yubo Song, Subham Sahoo, Freja Basse

arXiv:2610.08390v1cs.ETcs.SYeess.SY

TL;DR

The paper examines whether an electrical grid can serve as a fixed computational operator whose transformation is set by topology and governing equations. It uses the grid's voltage-to-current response as that operator; its representation has mean accuracy comparable to a 12,340-parameter digital replacement using a 933-parameter surrogate.

Abstract

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Computing is conventionally implemented by hardware engineered for information processing. Here we investigate infrastructure-native computing: the use of a physical system built for another primary function as a fixed computational operator. In time-domain simulations of an IEEE 14-bus electrical network, Kirchhoff's current law and Ohm's law relate voltage-reference perturbations applied at distributed controllable nodes interfaced by power electronics converters to current responses through a topology-dependent transformation. A trained digital encoder and decoder exploit this transformation for image classification, reaching 91.5% accuracy on MNIST and 82.25% on Fashion-MNIST. The modeled operator is represented by 933 surrogate parameters, compared with 12,340 task-trained parameters for an accuracy-matched fully connected core transformation. Current superposition further supports concurrent spatial sharing of the operator and sequential temporal reuse, with per-stream accuracies above 85% and 93%, respectively, in surrogate-model evaluations. Evaluations on CIFAR-10 and repeated 10-class tasks sampled from a Butterflies-and-Moths dataset show that the incremental utility of the physical operator depends on the representation supplied by upstream digital feature extraction. These results provide a simulation-based proof of concept for infrastructure-native computing with electrical networks and identify topology, accessible control channels, and input representation as determinants of its computational utility.

Results

The IEEE 14-bus grid maps voltage perturbations to current responses through a fixed, topology-dependent operator. A digital encoder and decoder use that response for image classification, with performance measured in time-domain simulations.

Electric Grids Implement a Fixed Topology-Dependent Physical Operator

  • Voltage-reference perturbations at converter-interfaced nodes produce current responses governed by grid topology, impedances, and modeled converter and network dynamics.The physical transformation is fixed by the electrical system rather than optimized using classification labels.Source: Electric Grids Implement a Fixed… · p. 3
  • The encoder maps images to voltage waveforms at four input nodes, and a linear decoder maps sampled current responses to class probabilities.The FIR encoder is kept lightweight to isolate the physical operator's contribution.Source: Electric Grids Implement a Fixed… · p. 3

DER 6

  • 91.50% accuracy on MNIST and 82.25% on Fashion-MNIST were achieved in PLECS time-domain simulations on 400 test images per dataset.Both datasets used the same physical layer and encoder architecture, with dataset-specific FIR kernel weights.Source: DER 6 · p. 5
  • A geometry-aware surrogate of the IEEE 14-bus system replicates the physical layer’s input-output behavior in software and supports offline encoder training; under ideal conditions, MNIST accuracy is 95.25%.This is a 3.75% difference from 91.5% for PLECS time-domain simulation of the network.Source: DER 6 · pp. 5–6

Network Topology Provides a Task-Independent Computational Prior

The grid's topology structures the physical operator before task-specific learning. In the tested MNIST comparison, its surrogate representation uses fewer parameters than an accuracy-matched fully connected replacement, while performance depends on accessible channels and their assignments.

Network Topology Provides a Task-Independent Computational Prior

  • The Jacobian's sparse structure follows network connectivity, with larger sensitivities on short, low-impedance paths and smaller ones on electrically distant or weakly coupled paths.KCL and Ohm's law constrain the admittance matrix to topology-consistent transformations, concentrating computational capacity along electrical coupling paths.Source: Network Topology Provides a… · p. 6
  • 0.915 mean per-class MNIST accuracy for the grid operator compares with 0.902 for a 30-hidden-unit fully connected network; their representations use 933 and 12,340 parameters, respectively.The 933 parameters represent the fixed grid operator, while the digital replacement's parameters are trained for classification.Source: Network Topology Provides a… · p. 6, Figure 2 · p. 7
  • The parameter comparison concerns the tested operator representations, not a universal advantage or a measurement of hardware complexity, energy use, or inference latency.The 933-parameter surrogate was fitted to reproduce the electrical response, not optimized for MNIST classification.Source: Network Topology Provides a… · p. 6
  • 0.910 mean accuracy with three active channels and 0.802 with two; swapping encoder kernels produced 0.917 and 0.910, close to the four-channel benchmark.The results indicate a range of encoder configurations, with progressive degradation as encoded-input dimensionality is reduced.Source: Network Topology Provides a… · p. 8

Physical Superposition Enables Multiplexed Inference

The grid's linearity supports sharing one fixed operator across multiple inference streams, either across node groups or across successive time windows. In surrogate evaluations, temporal reuse retains access to the full operator, while spatial sharing divides available coupling channels.

Physical Superposition Enables Multiplexed Inference

  • 0.784 and 0.851 mean per-task accuracies at 5 epochs rose to 0.858 and 0.881 at 20 epochs under spatial sharing, below the single-task benchmark of 0.915.Partitioning input nodes leaves each task with only a subset of the physical operator's coupling channels.Source: Physical Superposition Enables… · pp. 8–9, Figure 3 · p. 9
  • 0.965 and 0.938 mean accuracies after 5 epochs, and 0.962 and 0.941 after 20 epochs, were achieved with temporal multiplexing and full-operator access per task.Inputs occupy separate time windows and are decoded when adjacent windows are sufficiently separable.Source: Physical Superposition Enables… · p. 9, Figure 3 · p. 9
  • Spatial sharing applies simultaneous perturbations to distinct node groups, reducing each stream's available coupling channels; topology-dependent coupling also makes the two tasks asymmetric.Temporal reuse instead assigns successive inputs to low-to-non-overlapping windows, giving each stream access to the complete operator.Source: Physical Superposition Enables… · p. 9
  • These multiplexing tests are surrogate-model evaluations and do not establish zero crosstalk, intrinsic temporal memory, hardware throughput, or end-to-end energy savings.They demonstrate spatial sharing and time-division reuse of the fixed operator in the modeled system.Source: Physical Superposition Enables… · pp. 8–9

Computational Utility Persists within a Finite Operating Envelope

Perturbation tests delineate an operating envelope for the modeled operator: some parameter and measurement changes preserve classification performance, while removing a critical electrical path can substantially degrade it. The findings characterize tested conditions, not all possible grid operating conditions.

Computational Utility Persists within a Finite Operating Envelope

  • The tests characterize usability under selected line, load, and measurement perturbations, not robustness over all possible grid operating conditions.The tested setting is the IEEE 14-bus system with the classification pipeline unchanged.Source: Computational Utility Persists within… · p. 10
  • 0.922 mean accuracy followed a 10% increase in line 7 impedance, load 6 removal left accuracy at 0.915, and line 10 removal reduced it to 0.495.The contrasting responses indicate that disruption of a critical electrical path can strongly alter the operator.Source: Computational Utility Persists within… · p. 10
  • 0.917 to 0.910 mean accuracy was observed across AWGN levels of σ=0.001–0.05 pu; at σ=0.1 pu, accuracy fell to 0.810.The degradation near σ=0.05 pu was comparable to the 3.75% surrogate–simulation difference.Source: Computational Utility Persists within… · p. 10
  • Perturbations near σ=0.05 pu could account for a substantial part of the surrogate–simulation difference, but the analysis does not uniquely identify individual contributions.The passage compares read-out and simulation-related perturbations with the observed gap without assigning the gap to a single source.Source: Computational Utility Persists within… · p. 10

Computational Utility Depends on Input Representation

This section examines how an electrical network’s physical coupling and the input representation shape its computational utility, positioning the grid as a complement to digital feature extraction. It discusses superposition as a means of sharing the operator across tasks and notes simulation, hardware validation, and scaling as open limitations.

Computational Utility Depends on Input Representation

  • The physical pathway’s advantage over a static pass shows that grid responses add task-relevant computation beyond a learned linear recombination of the same encoded features.The comparison uses three pipelines: a direct feature classifier, a static pass bypassing the grid, and the physical pathway.Source: Computational Utility Depends on Input… · p. 10
  • Because the grid transformation is linear, additional nonlinear processing before it can increase feature linear separability and reduce the operator’s incremental benefit; less readily linearly separable task-relevant structure yields a larger contribution.Source: Computational Utility Depends on Input… · p. 11
  • On MNIST and Fashion-MNIST, the physical pathway outperformed the static pass and approached the direct classifier; stronger upstream extraction narrowed the physical–static gap on CIFAR-10.All three CIFAR-10 pipelines had lower accuracy than on MNIST and Fashion-MNIST, while stronger feature extraction improved separability.Source: Computational Utility Depends on Input… · pp. 10–11, Figure 5 · p. 12

Discussions

  • The fitted 933-parameter surrogate reached mean accuracy comparable to the 12,340-parameter digital replacement, a 13.2-fold difference in represented parameter count.The surrogate parameters identify the simulated electrical response rather than being trained on the classification task.Source: Discussions · pp. 12–13
  • Unlike programmable neuromorphic hardware, the grid’s operator is inherited from infrastructure topology and governing equations rather than designed backward from a computational task.Its fixed constraints limit arbitrary weight programming while providing a task-independent computational prior.Source: Discussions · p. 13
  • The grid provides a structured, interpretable transformation whose computational couplings can be related to network geometry and potentially influenced through topology or operating conditions.The operator is analytically related to topology and line impedances and can be characterized through the Jacobian ∂Irms/∂Vref.Source: Discussions · p. 13
  • The ±0.01 pu perturbations fall within voltage-flexibility ranges discussed for converter-interfaced resources, but this does not establish deployability without additional sensing, protection, communication, or control infrastructure.The proposed pathway superimposes computation on existing converter controllability without changing network topology.Source: Discussions · p. 14
  • More expressive upstream feature extraction and local contrast enhancement improve feature separability, an observation extended to 100-species Butterflies-and-Moths classification.Source: Discussions · p. 14
  • The physical operator adds most value when task-relevant structure remains beyond a direct linear mapping; its incremental contribution diminishes as upstream learning makes inputs more linearly separable.The discussion frames infrastructure-native computing as complementing, not replacing, learned digital feature extraction.Source: Discussions · p. 14
  • 0.858 and 0.881 were the spatial-multiplexing mean per-task accuracies after 20 epochs, versus 0.962 and 0.941 for temporal multiplexing.Spatial multiplexing is constrained by finite controllable nodes, while temporal multiplexing lets each task reuse the complete operator.Source: Discussions · p. 14
  • The study trains offline through a grid surrogate, leaving a simulation-to-reality gap, and its linear steady-state operator does not establish nonlinear physical extensions.Nonlinear cascaded layers remain a proposed extension, potentially using converter switching and saturation.Source: Discussions · p. 14
  • All results use time-domain simulation of the IEEE 14-bus benchmark; laboratory validation remains necessary to assess practical hardware constraints and variability.Source: Discussions · p. 15
  • The 14-bus comparison does not establish that the 13.2-fold advantage will grow with network size; scaling relationships remain an open empirical question.Larger IEEE 33-bus and 118-bus systems are proposed for testing scaling of representation, controllability, multiplexing capacity, and task performance.Source: Discussions · p. 15

Specifications of the IEEE Benchmark Grid

The study uses a three-phase IEEE 14-bus AC microgrid, with selected generator buses acting as distributed energy resources and a specified network of lines, shunts, and transformers. The benchmark defines the study’s electrical setting and nominal operating conditions.

Specifications of the IEEE Benchmark Grid

  • The study case is based on the IEEE 14-bus benchmark system, using raw data from, and is configured as a three-phase AC microgrid.Its nominal voltage is 138 kV and its nominal three-phase power is 100 MVA.Source: Specifications of the IEEE Benchmark… · p. 18
  • Buses 1, 2, 3, 6, and 8 are generator-connected DERs; buses 1, 2, 3, and 6 are inputs, while Bus 8 is the output.The remaining buses are passive, and the DER voltage magnitudes and phases are ideally regulated with source dynamics neglected.Source: Specifications of the IEEE Benchmark… · p. 18
  • Transmission lines are modeled as series RL elements, with shunt capacitances represented by the π model when present.Shunt susceptance is split into equivalent capacitances at the line terminals.Source: Specifications of the IEEE Benchmark… · p. 18
  • Three transformers connect Buses 4–7, 4–9, and 5–6, with turn ratios and equivalent reactances specified in the benchmark configuration.Loads are modeled as series RL, except the Bus 4 load, which is series RC.Source: Specifications of the IEEE Benchmark… · p. 18

Exemplary Computation Task

The image-classification task uses MNIST and Fashion-MNIST inputs encoded as time-varying voltage perturbations for the grid. A digital encoder and decoder surround a surrogate grid model that emulates the network’s dynamics and current responses.

Exemplary Computation Task

  • MNIST and Fashion-MNIST provide grayscale 28 × 28 images labeled in 10 classes for the classification task.Each dataset contains 60,000 training images and 10,000 test images.Source: Exemplary Computation Task · p. 18

Specifications of the Encoder and Decoder

  • The encoder applies parallel FIR convolution kernels, projects feature maps into 10-element vectors, then repeats each element over consecutive samples to form voltage-reference perturbations.The perturbations are applied at DERs 1, 2, 3, and 6; the four kernels target vertical edges, crosses, corners/endpoints, and loops.Source: Specifications of the Encoder and… · pp. 18–19
  • At DER 8, the decoder processes the time integral of sampled RMS current variation, forming 10 classification bins from segment increments before softmax.The output sequence is sampled over 0.1 s at 1 kHz; each bin has a learnable gain and bias.Source: Specifications of the Encoder and… · p. 19

Implementation of the Surrogate Grid Model

  • The surrogate models grid dynamics and coupling with learnable causal convolutions and projections, then aggregates the current-response states into an output sequence.Its hybrid training loss constrains signal fidelity, temporal dynamics, and energy consistency.Source: Implementation of the Surrogate Grid… · pp. 19–20

Data Acquisition

The data-acquisition and evaluation workflow generates surrogate-training examples through time-domain simulations, then trains and tests the encoder-decoder pipeline against the modeled grid. Classification statistics are calculated from predicted and ground-truth labels.

Data Acquisition

  • The workflow trains the encoder and decoder with the surrogate fixed, tests the surrogate, then evaluates the trained encoders through repeated PLECS simulations representing physical testing.The decoded responses are converted to class likelihoods, and the highest-likelihood class is recorded.Source: Data Acquisition · p. 21
  • Confusion matrices count predicted-label and ground-truth-label combinations, while per-class accuracy measures correct predictions among samples of each true class.The pipeline’s accuracy statistics evaluate classification under the modeled network conditions.Source: Data Acquisition · p. 21

Specifications of Multi-Tasking Cases

The supplementary cases specify how two inputs share the IEEE 14-bus system spatially or temporally, and compare physical-operator inference with direct and static-pass baselines on more complex datasets.

Specifications of Multi-Tasking Cases

  • Spatial multi-tasking applies two independently encoded inputs through spatially separated perturbation channels in the same electric network.Data 1 uses DERs 1 and 2; Data 2 uses DERs 3 and 6.Source: Specifications of Multi-Tasking Cases · p. 22
  • Temporal multi-tasking concatenates two 10-element encodings into one 20-element sequence and maps the outputs to separate 10-class prediction bins.Each input element is repeated over five samples, and the output is divided into 20 segments.Source: Specifications of Multi-Tasking Cases · p. 22

Supplementary Note S1: Evaluation on Generalization for More Complex Datasets

  • The comparisons test whether the physical-operator pipeline uses extracted features competitively and whether its fitted network transformation improves classification, but do not isolate a particular nonlinear component's contribution.The feature extractor, encoder, surrogate model, and readout procedure can each contribute to the overall mapping.Source: Conditions of the Evaluation · p. 27
  • The Butterflies-and-Moths evaluations average performance over 25 iterations, each training on 10 randomly selected species.The supplementary figure labels cases with and without local contrast enhancement or background removal, using feature extractors structured like the MNIST/Fashion-MNIST or CIFAR cases.Source: Evaluation with Butterflies-and-Moths… · p. 28, Figure S2 · p. 29

Supplementary Note S2: Incremental Network-Power Changes Induced by Encoded Perturbations

The note estimates how encoded perturbations change modeled network power flows and compares their load-delivery efficiency with the idle state. It does not provide an end-to-end energy-per-inference comparison with digital hardware.

Supplementary Note S2: Incremental Network-Power Changes Induced by Encoded Perturbations

  • The analysis excludes encoding, converter control, sensing, communication, and decoding energy, so it is not an end-to-end energy-per-inference comparison with digital hardware.It isolates the encoded perturbations' incremental effect on the modeled power-delivery network relative to idle operation.Source: Supplementary Note S2: Incremental… · p. 31
  • 94.99% and 95.03% are the energy efficiencies for the two exemplary MNIST test data, compared with 95.05% for the idle state.The passages identify the respective examples as Data 3 labeled “0” and Data 2 labeled “1”.Source: Supplementary Note S2: Incremental… · p. 31
  • 10^-3 pu is the order of the mean additional generated power and transmission losses for two illustrated MNIST samples, relative to nominal operation.The passage describes these variations as small relative to baseline power flow and says they do not substantially alter modeled power delivery under the stated assumptions.Source: Supplementary Note S2: Incremental… · p. 31

Supplementary Note S3: KCL Superposition as a Zero-Cost Physical Residual Primitive

The note explains how current conservation in the grid produces spatial and temporal residual aggregation. These physical effects support sharing inputs and accumulating responses across encoding time steps.

Supplementary Note S3: KCL Superposition as a Zero-Cost Physical Residual Primitive

  • Kirchhoff's current law sums simultaneous input-current contributions at the read-out node, implementing xout = f(xin) + xin without memory storage, retrieval, or additional hardware.The contributions are weighted by corresponding admittance-matrix elements.Source: Supplementary Note S3: KCL… · p. 32
  • Historical current responses also accumulate at the read-out node, creating temporal residual memory across the encoding window.The note describes spatial residual aggregation and temporal residual memory as emerging from conservation laws applied to the network.Source: Supplementary Note S3: KCL… · pp. 32–33
  • Spatial superposition preserves the linear separability of simultaneous inputs, while temporal accumulation supports time-division multiplexed inference across sequential encoding steps.Both capabilities arise from current conservation at each network node, enforced continuously by KCL.Source: Supplementary Note S3: KCL… · p. 33
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