The research archive

Publications

Research in robust estimation, uncertainty quantification, data fusion, and dynamical modeling. Each illustration explores the central idea behind a paper.

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01Typed sensor inputs
Sensor-Aware Joint Data Fusion and State Estimation under Sparse Multi-rate Distribution Grid Sensing: Typed sensor inputsMask each sensor catalog and encode with its sensor-specific adapter plus a type embedding 1Encode measurements by sensor type Measurements Sensor encoders Latent features PMUPMU adapterSCADASCADA adapterAMIAMI adapterDERDER adapter h(t)∥ eτ ● received sample × missing sample time → Shared latent features preserve sensor identity.
02Attention and continuous fusion
Sensor-Aware Joint Data Fusion and State Estimation under Sparse Multi-rate Distribution Grid Sensing: Attention and continuous fusionUse type-conditioned queries, keys and values with time gaps; aggregate by bus and time into q(z₀). Evolve a continuous latent trajectory on the feeder graph and decode a fused reconstruction 2aSensor-typed attention layers Typed features with observation time gaps Q: target + sensor type K, V: source + type + Δt α = softmax(QᵀK / √d)Weighted values + target skip Aggregate by bus + time → q(z₀) 2bContinuous latent evolution Latent graph ODEdzᵢ/dt = gᵢ(Z; τᵢ, G)Shared messages; typed readout Typed decoderz(t) → x̂DF(t)
03Residual state correction
Sensor-Aware Joint Data Fusion and State Estimation under Sparse Multi-rate Distribution Grid Sensing: Residual state correctionFeed fused reconstruction plus mask to the graph transformer and add its per-bus residual 3Correct the fused state Fused state x̂DF(t)Mask m(t); feeder graph G Graph-transformer estimator[x̂DF(t) ∥ m(t)] on GPer-bus residual Δ(t) Skip + x̂(t) Final state estimate x̂(t) = x̂DF(t) + Δ(t)
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2026NeurIPS 2026 Workshop: AI Foundations for Power Grids: From Models to Deployment at Scale

Sensor-Aware Joint Data Fusion and State Estimation under Sparse Multi-rate Distribution Grid Sensing

Pooja Algikar, Stefano Fenu, Kumarsinh Jhala, Siby Plathottam

Distribution grids combine sensors with different measurement types, reporting rates, and missing data. Het-ODE uses sensor-specific encoders and attention to learn a shared continuous-time graph representation, then refines fused reconstructions with a graph-transformer residual estimator. Tested on three IEEE feeders, the approach estimates states at sparsely observed buses while retaining the distinction between measured inputs and inferred states.

Explanation transcript
  1. Typed sensor encoders

    How can we estimate a changing system when its sensors measure different quantities, report at different rates, and leave gaps? In this work, each sensor type has its own encoder to handle its available measurement channels. An observation mask records which values are present. The encoders produce shared latent features, a common representation that also retains the identity of each sensor type.

  2. Sensor-typed attention

    The next challenge is deciding which observations should inform one another. Sensor-typed attention learns these relationships using the measurement features, sensor identities, and time between observations. A query represents the information being sought; keys and values represent the information other observations can contribute. Combining this evidence across observation times gives each bus a probability distribution for its initial latent state.

  3. Continuous graph ODE

    Between observations, the system continues to change. We represent that evolution with a graph ordinary differential equation, which describes how a compact latent state changes over time. Shared interaction functions exchange information between neighboring buses, while sensor-specific readouts determine their latent derivatives. A typed decoder converts the resulting trajectory into a fused reconstruction of electrical quantities for the state estimator.

  4. Residual state correction

    The fused reconstruction provides an initial estimate, which the state estimator then refines. A graph transformer learns a correction for each bus using that estimate, the observation mask, and connections between buses. The final state estimate is the fused estimate plus this learned correction. This residual formulation lets the estimator refine information already recovered by data fusion. In the three test feeders, the refinement improves accuracy over fusion alone.

Citation / BibTeX
@inproceedings{algikar2026sensoraware,
  title={Sensor-Aware Joint Data Fusion and State Estimation under Sparse Multi-rate Distribution Grid Sensing},
  author={Algikar, Pooja and Fenu, Stefano and Jhala, Kumarsinh and Plathottam, Siby},
  booktitle={NeurIPS Workshop: AI Foundations for Power Grids: From Models to Deployment at Scale},
  year={2026},
  eprint={2610.15156},
  archivePrefix={arXiv},
  primaryClass={cs.LG},
  url={https://arxiv.org/abs/2610.15156}
}
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01Probe evidence and attacker belief
Game-Theoretic Reinforcement Learning based Topology-Agnostic Defense for Virtual Power Plants: Probe evidence and attacker beliefCompare known perturbation footprints with measured responses. Update the attacker belief using GP inference and HMC 1aProbe-response evidence Known secret probeΔP, ΔQ + timestamps Measured voltageΔV at observer DERs Probe-footprint detectorConsistency decision + confidence 1bAttacker belief GP likelihood + HMC inferenceUncertain attacker type and behaviorPosterior mean + covariance Belief informs the next planning action.
02Planning guides the learned policy
Game-Theoretic Reinforcement Learning based Topology-Agnostic Defense for Virtual Power Plants: Planning guides the learned policyGuide RL through a Stackelberg action and reward alignment 2Plan + adapt Input: uncertain attacker-profile belief Stackelberg plannerBelief-weightedcandidate action RL policyVoltage + risk inputsRealized perturbation Policy input + alignment reward use the candidate. Chosen ΔP, ΔQ
03Physical probing and measured feedback
Game-Theoretic Reinforcement Learning based Topology-Agnostic Defense for Virtual Power Plants: Physical probing and measured feedbackApply small DER perturbations and observe the next response 3DER probing + feedback Policy-selected perturbation ΔP, ΔQ Actor DERsSmall feasible ΔP, ΔQ Observer DERsVoltage measurements Physical voltage response Measured-voltage feedback Next detector input: measured voltage DER-level feedback; feeder model not supplied.
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2026IEEE Transactions on Smart Grid

Game-Theoretic Reinforcement Learning based Topology-Agnostic Defense for Virtual Power Plants

Pooja Algikar, Stefano Fenu, Kumarsinh Jhala, Siby Plathottam

Virtual power plants often lack the feeder model needed by network-based cyber defenses. This method tests small, secret DER perturbations through measured voltage responses, updates a Bayesian belief over attacker profiles, and uses Stackelberg guidance within reinforcement learning. The learned policy balances informative probing with perturbation cost, adapting defense using DER-level observations rather than explicit feeder topology.

Explanation transcript
  1. Measured response

    A virtual power plant needs to detect interference even when it lacks a detailed feeder model. We test the integrity of its observations by applying small, secret power changes through selected distributed energy resources. These changes should create a recognizable voltage response at observing resources. A statistical detector compares the measured response with the expected signature, accounting for noise, and reports a decision with a measure of confidence.

  2. Bayesian attacker belief

    Detection evidence also helps us learn what kind of attacker may be present. A Gaussian process relates candidate attacker profiles to detection outcomes. Combining this likelihood with the previous belief produces an updated probability distribution over profiles. Hamiltonian Monte Carlo draws samples from that distribution. Their mean and covariance summarize the estimated attacker behavior and the uncertainty that the defender should consider when planning its next action.

  3. Stackelberg-guided RL

    The defender must choose a useful probe while anticipating how an attacker might respond. We model this as a Bayesian leader-follower game: the defender proposes an action, accounting for possible attacker responses under its current belief. The proposed action guides reinforcement learning through the policy input and a reward term penalizing deviation. Voltage and risk feedback help the policy adapt the final probing action.

  4. DER probing feedback

    The chosen action becomes a small adjustment to active and reactive power, subject to the resources' operating limits. Observing resources measure the voltage response, providing fresh evidence for detection and the attacker-belief update. Repeating this cycle links learning to physical feedback. The objective is useful detection information with limited probing effort and voltage disturbance. The strategy uses local voltage measurements and does not require explicit network connectivity.

Citation / BibTeX
@article{algikar2026gametheoretic,
  title={Game-Theoretic Reinforcement Learning based Topology-Agnostic Defense for Virtual Power Plants},
  author={Algikar, Pooja and Fenu, Stefano and Jhala, Kumarsinh and Plathottam, Siby},
  journal={IEEE Transactions on Smart Grid},
  year={2026},
  note={Early Access},
  doi={10.1109/TSG.2026.3741535},
  eprint={2610.15183},
  archivePrefix={arXiv},
  url={https://arxiv.org/abs/2610.15183}
}
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01Sensing constraints and method families
Real-Time Grid Visibility in Active Distribution Networks and Microgrids: A Review of Data Fusion, State Estimation, and Topology Identification: Sensing constraints and method familiesMap heterogeneous sensing and communication constraints. Organize data fusion, topology, and state-estimation methods 1aSensing + communication Sampling · latency · data quality Observation constraints Reporting intervalsCommunication delayMissingness + noise 1bCompare method families Classical + robust Probabilistic AI + graph learning Physics-informed Review criteria Modeling assumptionsUncertainty calibrationDeployment evidence
02The approved research-dependency map
Real-Time Grid Visibility in Active Distribution Networks and Microgrids: A Review of Data Fusion, State Estimation, and Topology Identification: The approved research-dependency mapReveal bidirectional structure, residual, and uncertainty feedback 2 Coupling as a research need DFTISE Data fusionTopologyState estimation Synthesis of dependencies and research needs.
03Uncertainty-aware decision support
Real-Time Grid Visibility in Active Distribution Networks and Microgrids: A Review of Data Fusion, State Estimation, and Topology Identification: Uncertainty-aware decision supportConnect evidence to decision support and fallback 3From estimates to decisions SE State estimates + uncertainty Decision support Uncertainty + fallback Check uncertainty against evidence Validate under changing operating conditions. Use fallback when observations are insufficient. Review synthesis; no new controller is claimed.
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IEEE Access

Real-Time Grid Visibility in Active Distribution Networks and Microgrids: A Review of Data Fusion, State Estimation, and Topology Identification

Pooja Algikar, Kumarsinh Jhala, Stefano Fenu, Siby Plathottam

Grid visibility depends on more than an accurate state estimator: sensing, communication, data fusion, and topology inference interact. This review organizes classical, probabilistic, learning-based, and physics-informed methods around their operational requirements. It examines how uncertainty and residual evidence should pass between these functions, and identifies gaps in field validation, adaptation, and decision support for active networks and microgrids.

Explanation transcript
  1. Sensing constraints

    Reliable grid operation requires knowing the system's electrical state and how its equipment is connected. Yet measurements are often sparse, noisy, delayed, and collected at different rates. This review examines how those sensing and communication constraints affect grid visibility. It brings data fusion, state estimation, and topology identification into one discussion, so methods can be assessed against the information actually available to an operator.

  2. Method families

    Different methods address different parts of this challenge. Classical estimators use electrical models to relate measurements to system states. Robust methods reduce the influence of unreliable observations, while probabilistic methods represent uncertainty explicitly. Learning and graph methods capture relationships in data, and physics-informed methods incorporate electrical constraints. The review compares these choices through their assumptions, data requirements, computational demands, and suitability for real-time operation.

  3. Coupled research needs

    Grid visibility depends on several interacting tasks. Data fusion combines heterogeneous observations for state and topology inference. The inferred network configuration determines how a state estimator interprets those observations. Disagreement between predicted and measured values can motivate checking data quality or connectivity. A central research need is to share uncertainty and residual evidence across these tasks, so each inference can benefit from the others.

  4. Decision support

    For operational decisions, an estimate must come with evidence of when it can be trusted. The review identifies field validation, adaptation to changing topology, uncertainty-aware fusion, and scalable computation as important research priorities. It also highlights the need for fallback when sensing or inference becomes unreliable. Its contribution is a coordinated view of what these methods must deliver before they can support dependable real-time decisions.

Citation / BibTeX
@article{algikar-grid-visibility-review,
  title = {Real-Time Grid Visibility in Active Distribution Networks and Microgrids: A Review of Data Fusion, State Estimation, and Topology Identification},
  author = {Pooja Algikar and Kumarsinh Jhala and Stefano Fenu and Siby Plathottam},
  journal = {IEEE Access},
  note = {Accepted; publication details pending}
}
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01Weight unusual input locations
Robust Gaussian Process Regression with Huber Likelihood and Projection Pursuit: Weight unusual input locationsLocate input outliers through projection statistics1Weight unusual input locations Training pairs(xᵢ, yᵢ) Input projectionsProjection distance PSᵢ Input leverage weightswᵢ = min(1, c / PSᵢ²) Larger projection distance → smaller input weight.
02Limit large residual influence
Robust Gaussian Process Regression with Huber Likelihood and Projection Pursuit: Limit large residual influenceScale residuals and apply the Huber likelihood2Limit large residual influence Residual rᵢ = yᵢ − f(xᵢ)Standardized residualzᵢ = rᵢ / (wᵢ σ s) Huber loss ρ_H(z) z Robust residual likelihoodQuadratic center; linear tails
03Infer the latent-function posterior
Robust Gaussian Process Regression with Huber Likelihood and Projection Pursuit: Infer the latent-function posteriorInfer the latent function with Laplace approximation or Gibbs sampling3Infer the latent-function posterior Gaussian-process prior× Huber likelihood Laplace approximationOR Gibbs sampling Posterior for f* at a new inputLatent-function uncertainty Posterior spread is not empirical prediction error.
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2025ECML PKDD 2025 · LNCS 16013, pp. 3–19

Robust Gaussian Process Regression with Huber Likelihood and Projection Pursuit

Pooja Algikar, Lamine Mili

Outliers in both inputs and responses can distort Gaussian process regression. This work combines projection pursuit weights for unusual inputs with a Huber likelihood that limits the influence of large residuals. Laplace approximation or Gibbs sampling then supports posterior inference and prediction. Experiments examine synthetic data, benchmark datasets, and transmission spectroscopy.

Explanation transcript
  1. Input leverage weights

    Gaussian process regression represents an unknown function probabilistically, using observed input–response pairs. Outliers can distort this learning through unusual responses or unusual input locations. We address input leverage with projection pursuit: examining the data along multiple directions and measuring robust distances from their central pattern. Larger projection distances receive smaller weights, limiting the influence of unusual input configurations before posterior inference.

  2. Huber residual likelihood

    A residual is the difference between an observed response and the latent function value. We standardize it using the input weight, noise scale, and a robust estimate of residual spread. The Huber likelihood applies a quadratic penalty to small standardized residuals and a linear penalty to large ones. This preserves squared-error behavior near the center while limiting the influence of extreme responses.

  3. GP posterior inference

    Combining this likelihood with a Gaussian process prior gives a posterior over the latent function, without a closed-form solution. We develop two inference routes. The Laplace route uses a smooth pseudo-Huber loss and a Gaussian approximation near the posterior mode. Gibbs sampling represents the tails through Gaussian distributions with random variances, then samples conditional distributions. Both support predictions and uncertainty at new inputs.

Citation / BibTeX
@inproceedings{algikar-gp-huber-2025,
  title = {Robust Gaussian Process Regression with Huber Likelihood and Projection Pursuit},
  author = {Pooja Algikar and Lamine Mili},
  year = {2026},
  booktitle = {ECML PKDD 2025 · LNCS 16013, pp. 3–19},
  doi = {10.1007/978-3-032-05962-8_1},
  url = {https://link.springer.com/chapter/10.1007/978-3-032-05962-8_1}
}
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01Robust process models
Robust and Data-Driven Uncertainty Quantification Methods as Real-Time Decision Support in Data-Driven Models: Robust process modelsRobust process models address contaminated observations1Robust process models Research thread 1 · Chapter 3 Contaminatedtraining pairs Robust mean +covariance fits Fittedprocess Reduce the influence of harmful observations. One of three parallel research threads.
02Bayesian Gaussian-process inference
Robust and Data-Driven Uncertainty Quantification Methods as Real-Time Decision Support in Data-Driven Models: Bayesian Gaussian-process inferenceGP-Huber provides likelihood-based Bayesian inference2Bayesian Gaussian-process inference Research thread 2 · Chapter 4 Inputs andresponses Huber likelihoodLaplace ORGibbs inference Posteriorfor f* A robust likelihood supports Bayesian uncertainty. A parallel thread, not output from the first pane.
03Quantify operator uncertainty
Robust and Data-Driven Uncertainty Quantification Methods as Real-Time Decision Support in Data-Driven Models: Quantify operator uncertaintyDMD and EDMD analysis propagates measurement uncertainty3Quantify operator uncertainty Research thread 3 · Chapters 5–6 Noisy statesnapshots DMD / EDMDMoment analysis Operatormoments Quantify uncertainty of learned operator entries. Parallel research threads; no sequential pipeline.
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2025Dissertation

Robust and Data-Driven Uncertainty Quantification Methods as Real-Time Decision Support in Data-Driven Models

Pooja Algikar

Reliable data-driven decisions require attention to both corrupted observations and propagated uncertainty. This dissertation connects robust Gaussian process modeling with uncertainty analysis of Koopman-operator approximations. Its chapters develop robust hyperparameter and likelihood approaches, then study measurement-noise propagation into DMD and extended-DMD operators. The organizing theme is quantifying reliability alongside learned predictions and dynamical representations.

Explanation transcript
  1. Robust process models

    Data-driven models must remain useful when observations are contaminated and learned quantities are uncertain. This dissertation addresses those problems through three complementary research threads. One thread develops robust Gaussian process models: probability models for an unknown response function. Projection statistics and residual weighting reduce harmful observation influence while the mean and covariance parameters are fitted iteratively for prediction.

  2. Bayesian GP inference

    A second thread takes a Bayesian approach to robust regression. A Gaussian process prior describes plausible latent functions, and a Huber likelihood models observations while limiting extreme residual influence. Projection-based weights also account for unusual inputs. The resulting posterior, the distribution updated by the data, is inferred using either Laplace approximation or Gibbs sampling. It represents the underlying response function and its uncertainty probabilistically.

  3. Operator moment analysis

    A third thread studies uncertainty in learned dynamical operators. Dynamic mode decomposition fits a linear evolution map from state snapshots; its extended form uses functions of the states as features. Under Gaussian modeling assumptions, random matrix theory propagates measurement uncertainty into first and second moments of individual operator entries. This complementary thread quantifies reliability in learned dynamics, alongside the dissertation's robust regression methods.

Manuscript dated December 2024; deposited at Virginia Tech in February 2025.

Citation / BibTeX
@phdthesis{algikar-dissertation-2025,
  title = {Robust and Data-Driven Uncertainty Quantification Methods as Real-Time Decision Support in Data-Driven Models},
  author = {Pooja Algikar},
  year = {2025},
  school = {Virginia Tech},
  url = {https://vtechworks.lib.vt.edu/items/2c689a22-9256-4e8f-a160-5f9036491bcb}
}
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01Specify noisy snapshot pairs
Statistical analysis and method to quantify the impact of measurement uncertainty on dynamic mode decomposition: Specify noisy snapshot pairsRepresent noisy snapshots by means and variances1Specify noisy snapshot pairs X = [x₁, …, xₘ]Current measurementsEntry means / variances Y = [x₂, …, xₘ₊₁]One step laterEntry means / variances X enters pseudoinversemoment analysis Y enters the operatormoment combination Assume normally distributed measurement uncertainty.
02Derive pseudoinverse moments
Statistical analysis and method to quantify the impact of measurement uncertainty on dynamic mode decomposition: Derive pseudoinverse momentsPropagate moments through the snapshot pseudoinverse2Derive pseudoinverse moments From snapshot matrix XEntry X†ᵢⱼ = s₁ / s₂Linear / quadratic formsIntegrate under normality Pseudoinverse momentsE[X†ᵢⱼ]E[(X†ᵢⱼ)²] The known moments of Y are retained separately. Output: first and second moments of each X† entry.
03Quantify learned operator entries
Statistical analysis and method to quantify the impact of measurement uncertainty on dynamic mode decomposition: Quantify learned operator entriesEstimate moments and confidence bounds for each DMD operator entry3Quantify learned operator entries Pseudoinverse momentsFrom X Shifted-snapshot momentsFrom Y Combine the momentsA ≈ X† Y E[aᵢⱼ]: entry mean Var(aᵢⱼ): entry variance Operator uncertainty, not a trajectory error band.
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202463rd IEEE Conference on Decision and Control (CDC), pp. 4373–4379

Statistical analysis and method to quantify the impact of measurement uncertainty on dynamic mode decomposition

Pooja Algikar, Pranav Sharma, Marcos Netto, Lamine Mili

Measurement noise affects the linear operator estimated by dynamic mode decomposition. This paper uses random matrix theory to propagate normally distributed measurement uncertainty through the pseudoinverse and into individual operator entries. Their first and second moments provide expectations and confidence bounds, evaluated against Monte Carlo simulations on spring–mass and power-system examples.

Explanation transcript
  1. Noisy snapshot pairs

    Dynamic mode decomposition estimates a linear map between consecutive measurements of a system's state. Measurement noise makes that fitted map uncertain. We organize the records into current and one-step-shifted snapshot matrices and model their entries as normal random variables with specified means and variances. This establishes the measurement uncertainty that must be carried through the operator calculation.

  2. Pseudoinverse moments

    The difficult step is the pseudoinverse: the generalized matrix inverse used in the least-squares fit. Its entries depend nonlinearly on the noisy snapshots. We express an entry as a ratio of linear and quadratic expressions, then use moment-generating functions and integration under normality to derive its first and second moments. These supply the information needed for its mean and variance.

  3. Operator-entry uncertainty

    The moments of the generalized inverse are combined with the moments of the shifted measurements to estimate a mean and variance for each fitted operator entry. The mean summarizes its central value; the variance measures its spread under the assumed noise model. Comparisons with repeated noisy simulations examine these calculations on spring–mass and power-system examples, connecting the statistical analysis to learned dynamical relationships.

Citation / BibTeX
@inproceedings{algikar-dmd-2024,
  title = {Statistical analysis and method to quantify the impact of measurement uncertainty on dynamic mode decomposition},
  author = {Pooja Algikar and Pranav Sharma and Marcos Netto and Lamine Mili},
  year = {2024},
  booktitle = {63rd IEEE Conference on Decision and Control (CDC), pp. 4373–4379},
  doi = {10.1109/CDC56724.2024.10886110},
  url = {https://doi.org/10.1109/CDC56724.2024.10886110}
}
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01Measure candidate dependence
Quantifying Non-linear Dependencies in Blind Source Separation of Power System Signals using Copula Statistics: Measure candidate dependenceMeasure nonlinear dependence with copula statistics1Measure candidate dependence Observed XMixture X = A S Apply current demixing WCandidate sources Y = W X Rank pairs → empirical copulaCompute dependence statistic CoS(yᵢ, yⱼ) Source dependence is modeled; independence is optional.
02Estimate the copula parameter
Quantifying Non-linear Dependencies in Blind Source Separation of Power System Signals using Copula Statistics: Estimate the copula parameterRegress the copula dependence parameter2Estimate the copula parameter CoS + suppliedcopula family Calibrated quadratic regressionα̂ = a₁ CoS² + a₂ CoS + a₃ Target dependence modelc_S(·; α̂) The copula family is supplied, not discovered here.
03Update the source estimates
Quantifying Non-linear Dependencies in Blind Source Separation of Power System Signals using Copula Statistics: Update the source estimatesUpdate the demixing matrix through KL-divergence minimization3Update the source estimates Candidate c_Y vs target c_SKL-gradient update of W Updated WY = W X Updated candidates → CoS and α̂Recompute the dependence model On convergence: estimated source signals.
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2024IEEE PES Innovative Smart Grid Technologies Conference (ISGT), pp. 1–5

Quantifying Non-linear Dependencies in Blind Source Separation of Power System Signals using Copula Statistics

Pooja Algikar, Lamine Mili, Kiran Karra, Akash Algikar, Mohsen Ben Hassine

Power-system signals may mix sources with nonlinear statistical dependencies. This method uses copula statistics to estimate a dependence parameter, then updates a demixing matrix by minimizing a copula-based Kullback–Leibler divergence. The resulting source estimates retain a modeled dependence structure rather than assuming independence. Tests include synthetic mixtures and coupled generator-speed signals.

Explanation transcript
  1. Candidate-source CoS

    Power-system observations can be linear mixtures of sources with nonlinear statistical dependence. Blind source separation seeks the underlying signals without knowing the mixing matrix. We allow dependent sources and apply a demixing matrix to form source candidates. Their ranks define an empirical copula, which describes dependence separately from each signal's individual distribution. A copula statistic then quantifies pairwise association among these candidates.

  2. Copula parameter regression

    Within a supplied copula family, the unknown dependence parameter controls the form of the source relationship. We calibrate a quadratic regression using simulated samples with known parameter values and their copula statistics. Applying that family-specific regression to the candidate-source statistic estimates the dependence parameter. This supplies a parameterized target copula for the separation procedure.

  3. KL-guided W update

    K L divergence measures the discrepancy between the candidate-source copula density and the target density. We minimize this discrepancy with gradient descent on the demixing matrix. Each update changes the candidate sources, so their copula statistics and estimated dependence parameters are recalculated. Iteration stops when the matrix stabilizes, producing source estimates guided by the supplied dependence model.

Citation / BibTeX
@inproceedings{algikar-ccca-2024,
  title = {Quantifying Non-linear Dependencies in Blind Source Separation of Power System Signals using Copula Statistics},
  author = {Pooja Algikar and Lamine Mili and Kiran Karra and Akash Algikar and Mohsen Ben Hassine},
  year = {2024},
  booktitle = {IEEE PES Innovative Smart Grid Technologies Conference (ISGT), pp. 1–5},
  doi = {10.1109/ISGT59692.2024.10454117},
  url = {https://doi.org/10.1109/ISGT59692.2024.10454117}
}
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01Build injection–voltage pairs
A Robust Data-Driven Process Modeling Applied to Time-Series Stochastic Power Flow: Build injection–voltage pairsUse time-series injection and voltage training pairs1Build injection–voltage pairs Same observation times t₁, …, tₙ Active + reactivepower injections (P, Q) Voltage magnitudeor phase angle at a bus Surrogate training setTime-aligned injection–voltage pairs Voltage targets: measurements or simulator outputs.
02Limit contamination during fitting
A Robust Data-Driven Process Modeling Applied to Time-Series Stochastic Power Flow: Limit contamination during fittingWeight leverage and residuals in robust hyperparameter estimation2Limit contamination during fitting Basis projectiondistances + Huberresidual weights Robust mean fit βKernel + noise fitAlternate until settled Recompute residuals and model parameters. Fitted robust process
03Predict bus voltages
A Robust Data-Driven Process Modeling Applied to Time-Series Stochastic Power Flow: Predict bus voltagesPredict voltage magnitude and angle with associated variance3Predict bus voltages New injections x*Use the fitted process Mean voltage μ*(x*)Predictive covariance Σ* Variance describes model uncertainty. Actual prediction error requires validation.
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2024IEEE Transactions on Power Systems 39(1), pp. 693–705

A Robust Data-Driven Process Modeling Applied to Time-Series Stochastic Power Flow

Pooja Algikar, Yijun Xu, Somayeh Yarahmadi, Lamine Mili

Corrupted power-injection and voltage data can undermine a learned power-flow model. This work estimates process-model hyperparameters with a Schweppe-type robust estimator, using projection statistics and residual weights to bound outlier influence. The trained surrogate predicts voltage phasors and quantifies associated variance. Studies include the IEEE 33-bus system and a real-world unbalanced 240-bus network.

Explanation transcript
  1. Injection–voltage training pairs

    Stochastic power flow asks how uncertain injections from loads and renewable generation affect grid voltages over time. We train a Gaussian process surrogate using power injections paired with voltage magnitudes or phase angles at matching times. The voltage targets come from measurements when available, or from a power-system simulator. These aligned examples let the model learn the injection-to-voltage relationship.

  2. Robust alternating GP fit

    Training data can be contaminated in both injections and voltage responses. We combine projection-based leverage weights with weights derived from the Huber loss for large residuals, the differences between observed and fitted voltages. Iteratively reweighted least squares updates the mean coefficients. With those coefficients fixed, likelihood fitting updates the kernel and noise parameters. Alternating these fits gives the robust process model.

  3. Voltage mean + covariance

    For new power injections, conditioning the fitted process on the training data gives a voltage prediction with a mean and covariance. The mean is the surrogate's voltage estimate. The covariance summarizes model uncertainty and correlations among predictions at the requested inputs. Applying this process across an injection time series yields a statistical surrogate that describes changing voltage behavior together with model-based uncertainty.

Issue year 2024; first published online in 2023.

Citation / BibTeX
@article{algikar-powerflow-2024,
  title = {A Robust Data-Driven Process Modeling Applied to Time-Series Stochastic Power Flow},
  author = {Pooja Algikar and Yijun Xu and Somayeh Yarahmadi and Lamine Mili},
  year = {2024},
  journal = {IEEE Transactions on Power Systems 39(1), pp. 693–705},
  doi = {10.1109/TPWRS.2023.3238385},
  url = {https://ieeexplore.ieee.org/document/10023983/}
}
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01Build time-delay coordinates
Identification of Power System Oscillation Modes using Blind Source Separation based on Copula Statistic: Build time-delay coordinatesBuild delay coordinates from an observed oscillation1Build time-delay coordinates Recorded signalx(t) Delayed copies of the signalx(t), x(t − τ),x(t − 2τ), … Coordinates for modal estimationd = 2m; candidate modal order m
02Estimate frequency and damping
Identification of Power System Oscillation Modes using Blind Source Separation based on Copula Statistic: Estimate frequency and dampingUse copula-based HOBI and the Hilbert transform2Estimate frequency and damping Copula-based whiteningDelayed dependencymatrices D_Z(τ) Joint diagonalization→ source estimates Y Hilbert transform of estimated sourcesFrequency f and damping σ
03Select the modal order
Identification of Power System Oscillation Modes using Blind Source Separation based on Copula Statistic: Select the modal orderRepeat embedding dimensions to identify modal order, frequency and damping3Select the modal order Candidate order mDelay coordinates Repeat HOBI + HilbertFrequency and damping Pair conjugate componentsMinimize pair divergenceacross candidate orders Modal orderFrequency fDamping σ Repeat the embedding and estimation for each m.
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2023IEEE Power & Energy Society General Meeting (PESGM), pp. 1–5

Identification of Power System Oscillation Modes using Blind Source Separation based on Copula Statistic

Pooja Algikar, Lamine Mili, Mohsen Ben Hassine, Somayeh Yarahmadi, Almuatazbellah Muataz Boker

A measured power-system oscillation can contain several coupled modes, even when few channels are available. The proposed method combines copula-based high-order blind identification with the Hilbert transform to estimate modal frequency and damping. Iterating over delay-embedding dimensions helps identify the modal order. Numerical and 11-bus simulations examine its performance under nonlinear coupling.

Explanation transcript
  1. Time-delay coordinates

    A recorded oscillation can contain several modes with different frequencies and damping, even when only one measurement channel is available. The method constructs delayed copies of the signal to expose its temporal structure. For each candidate number of modes, it uses twice as many delay coordinates, creating the observation matrix needed for modal estimation.

  2. Copula HOBI + Hilbert

    A copula statistic captures both linear and nonlinear dependence among the observations. This dependence information supports whitening and the construction of dependency matrices at several time delays. Joint diagonalization then estimates the underlying source signals. Applying the Hilbert transform to those estimates yields modal frequencies and damping coefficients, connecting statistical separation to the oscillation properties of interest.

  3. Modal-pair order selection

    Each oscillatory mode is associated with a pair of conjugate components whose frequency and damping estimates should agree. The method measures their divergence and repeats the analysis across candidate embedding dimensions. Comparing these pair divergences supports the selection of modal estimates and the number of modes, providing frequency and damping estimates together with an estimated modal order.

Citation / BibTeX
@inproceedings{algikar-hobmi-2023,
  title = {Identification of Power System Oscillation Modes using Blind Source Separation based on Copula Statistic},
  author = {Pooja Algikar and Lamine Mili and Mohsen Ben Hassine and Somayeh Yarahmadi and Almuatazbellah Muataz Boker},
  year = {2023},
  booktitle = {IEEE Power & Energy Society General Meeting (PESGM), pp. 1–5},
  doi = {10.1109/PESGM52003.2023.10252977},
  url = {https://doi.org/10.1109/PESGM52003.2023.10252977}
}
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01Diagnose input leverage
Robust Hyperparameter Estimation in Gaussian Process Regression Model: Diagnose input leverageProject basis-function points to assess leverage1Diagnose input leverage Training pairs (X, y)Mean-model basis F(X) Projection distances PSᵢLeverage weights wᵢ Residual scalingUse wᵢ with a robust spread estimate
02Fit the mean by reweighting
Robust Hyperparameter Estimation in Gaussian Process Regression Model: Fit the mean by reweightingIteratively reweight the mean-function fit2Fit the mean by reweighting Residuals r = y − FβHuber weights Q(r) IRLS update of βWeighted mean fit Recompute residuals and Huber weights. Output: robust mean coefficients β.
03Alternate kernel and mean fits
Robust Hyperparameter Estimation in Gaussian Process Regression Model: Alternate kernel and mean fitsAlternate mean and covariance hyperparameter updates before prediction3Alternate kernel and mean fits Fix β: kernel + noise fitProfile likelihood Robust mean updateUpdate β again Repeat the alternation to convergence. Fitted GP: prediction mean and covariance
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2023Research Square

Robust Hyperparameter Estimation in Gaussian Process Regression Model

Pooja Algikar, Lamine Mili

Outliers can bias Gaussian process hyperparameters and the uncertainty attached to predictions. This preprint develops a robust observational data-driven process using a Schweppe-type Huber estimator and projection-statistics weights. Iterative estimation limits the influence of unusual responses and harmful leverage points. Examples include thick-tailed synthetic data, coastal wind and water measurements, and stochastic power flow.

Explanation transcript
  1. Basis leverage weights

    Unusual input locations can exert disproportionate influence when fitting a Gaussian process. This method assesses the rows of the mean model's basis matrix using robust projection distances. Those distances inform leverage weights, which are combined with a robust estimate of residual spread. The resulting scaling prepares the fit to consider both input outlyingness and disagreement with the mean model.

  2. IRLS robust mean fit

    The mean coefficients are fitted through iteratively reweighted least squares. Residuals from the current mean are standardized using the leverage weights and robust scale, then Huber weighting limits the influence of large residuals. A weighted fit incorporating the current covariance updates the mean coefficients. Because that update changes the residuals, their weights are recalculated until this inner fit settles.

  3. Kernel–mean alternation

    The mean fit depends on the covariance, and covariance estimation depends on the fitted mean. An outer iteration therefore alternates between them: hold the mean coefficients fixed while fitting kernel and noise parameters through profile likelihood, then refit the robust mean with the updated covariance. At convergence, the fitted process provides prediction means and covariances describing uncertainty within the model.

Citation / BibTeX
@misc{algikar-hyperparameters-2023,
  title = {Robust Hyperparameter Estimation in Gaussian Process Regression Model},
  author = {Pooja Algikar and Lamine Mili},
  year = {2023},
  howpublished = {Research Square},
  note = {Preprint · journal publication not verified},
  doi = {10.21203/rs.3.rs-2584837/v1},
  url = {https://www.researchsquare.com/article/rs-2584837/v1}
}
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01Specify disturbance and grid
Electromechanical Wave Propagation for Disturbance Arrival Time Assessment in Power Systems: Specify disturbance and gridSeparate network parameters from disturbance frequency and initial/boundary values1Specify disturbance and grid Network inputsGenerator reactance XgLine admittances, inertia Disturbance inputsSinusoidal frequency fInitial / boundary values Inputs to the wave-propagation modelNetwork and disturbance quantities
02Include generator reactance
Electromechanical Wave Propagation for Disturbance Arrival Time Assessment in Power Systems: Include generator reactanceInclude generator reactance in rotor/terminal-angle coupling to obtain a frequency-dependent propagation speed2Include generator reactance Generator reactance XgRotor and terminal voltage angles Couple the angles in thewave-propagation equation Frequency-dependent wave speed v(f)
03Compute downstream arrival time
Electromechanical Wave Propagation for Disturbance Arrival Time Assessment in Power Systems: Compute downstream arrival timeCompute arrival times for two unspecified frequencies along the same path without asserting a universal ordering3Compute downstream arrival time Compare frequencies along the same path f₁ v(f₁) Arrival t₁ f₂ v(f₂) Arrival t₂ Line travel time = length / v(f) Frequency labels do not imply arrival order.
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20232023 IEEE Power & Energy Society General Meeting (PESGM)

Electromechanical Wave Propagation for Disturbance Arrival Time Assessment in Power Systems

Somayeh Yarahmadi, Pooja Algikar, Lamine Mili

When an electromechanical disturbance travels through a power system, its arrival depends on more than distance. This study includes generator reactances in a wave-propagation model, making propagation speed depend on disturbance frequency. Combined with admittance-based inertia distribution, the model examines how these effects alter estimated arrival times and rotor-angle behavior.

Explanation transcript
  1. Grid + disturbance inputs

    Assessing disturbance arrival requires a description of both the grid and the disturbance. The network contributes generator reactances, line admittances, and the distribution of inertia. The disturbance contributes its sinusoidal frequency and initial or boundary conditions. Together, these quantities define a physical propagation problem, allowing arrival time to reflect the system's dynamics as well as the distance traveled.

  2. Frequency-dependent wave model

    The key refinement is to account for the electrical reactance of each generator. In this model, the rotor angle and terminal voltage angle can differ, while their physical coupling is retained in the wave equation. This coupling makes the modeled wave speed depend on disturbance frequency. A fixed network can therefore have different propagation speeds for different sinusoidal disturbances.

  3. Downstream arrival time

    For each disturbance frequency, the model supplies a corresponding wave speed. The travel contribution of a line is its length divided by that speed, and these contributions determine arrival along the chosen path. Different frequencies can therefore produce different modeled arrival times on the same route. The arrival estimate therefore depends jointly on disturbance frequency and the physical parameters along the path.

Citation / BibTeX
@inproceedings{algikar-wave-arrival-2023,
  title = {Electromechanical Wave Propagation for Disturbance Arrival Time Assessment in Power Systems},
  author = {Somayeh Yarahmadi and Pooja Algikar and Lamine Mili},
  year = {2023},
  booktitle = {2023 IEEE Power & Energy Society General Meeting (PESGM)},
  doi = {10.1109/pesgm52003.2023.10252186},
  url = {https://doi.org/10.1109/pesgm52003.2023.10252186}
}
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01Distinguish three outlier types
A Measurement-Based Robust Non-Gaussian Process Emulator Applied to Data-Driven Stochastic Power Flow: Distinguish three outlier typesDistinguish vertical outliers, good leverage and bad leverage1Distinguish three outlier types Sample type Input Residual Regular sampleTypicalSmall Vertical outlierTypicalLarge Good leverageUnusualSmall Bad leverageUnusualLarge An unusual input can still provide useful information. Inform leverage + residual weighting
02Combine leverage and residual weights
A Measurement-Based Robust Non-Gaussian Process Emulator Applied to Data-Driven Stochastic Power Flow: Combine leverage and residual weightsCombine projection statistics with robust residual weighting2Combine leverage and residual weights Projection statistics+ Huber/SHGM residuals Downweight harmfulsamples; retain usefulgood-leverage points IRLS estimates mean coefficients βKernel parameters are fitted too
03Use the trained voltage emulator
A Measurement-Based Robust Non-Gaussian Process Emulator Applied to Data-Driven Stochastic Power Flow: Use the trained voltage emulatorUse the trained emulator for stochastic voltage predictions3Use the trained voltage emulator Trained model + newinjections P and Q Predict |V| or phase angleWith model covariance Evaluated on the renewable-integrated IEEE 33-bus system.
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2022IEEE Power & Energy Society General Meeting (PESGM), pp. 01–05

A Measurement-Based Robust Non-Gaussian Process Emulator Applied to Data-Driven Stochastic Power Flow

Pooja Algikar, Yijun Xu, Lamine Mili

Stochastic power-flow emulators trained on measurements are vulnerable to outliers. This paper uses projection-statistics weights and a Schweppe-type generalized maximum-likelihood estimator to limit the influence of vertical outliers and bad leverage points. The learned emulator produces voltage magnitude and angle predictions. A renewable-integrated IEEE 33-bus study tests the method using deliberately contaminated training data.

Explanation transcript
  1. Outlier taxonomy

    Robust training must distinguish unusual inputs from harmful observations. A vertical outlier has a large residual at a typical input location. Good and bad leverage points both have unusual inputs, but good leverage agrees with the fitted relationship while bad leverage has a large residual. This distinction matters because unusual inputs can still provide valuable information about the response.

  2. SHGM influence weighting

    The emulator combines projection statistics with a Schweppe-type Huber estimator. Projection statistics assess input outlyingness, while weighting based on scaled residuals limits harmful influence without discarding useful leverage. Iteratively reweighted least squares updates the mean coefficients; changing residuals require updated weights. The covariance parameters are also estimated, producing the trained process used to approximate the power-flow response.

  3. Voltage emulator output

    The trained emulator maps active and reactive power injections to predictions of voltage magnitude or phase angle at a target bus. Its mean gives the predicted response, while covariance describes uncertainty within the fitted model. Experiments use measured renewable injections in a thirty-three-bus system, with voltage magnitudes and phase angles from simulation, to evaluate the effect of contaminated training data.

Citation / BibTeX
@inproceedings{algikar-emulator-2022,
  title = {A Measurement-Based Robust Non-Gaussian Process Emulator Applied to Data-Driven Stochastic Power Flow},
  author = {Pooja Algikar and Yijun Xu and Lamine Mili},
  year = {2022},
  booktitle = {IEEE Power & Energy Society General Meeting (PESGM), pp. 01–05},
  doi = {10.1109/PESGM48719.2022.9916996},
  url = {https://ieeexplore.ieee.org/document/9916996}
}

Generator inertia is apportioned using connected-line admittances before computing propagation paths and arrival times; detailed sequence pending the full paper.

Full text needed to verify the method animation.

20222022 IEEE PES Generation, Transmission and Distribution Conference and Exposition – Latin America (IEEE PES GTD Latin America)

Electromechanical Wave Propagation Analysis in Power Systems

Somayeh Yarahmadi, Pooja Algikar, Lamine Mili

Electromechanical disturbances reach different parts of a power network at different times. This paper accounts for transmission-line admittances when distributing generator inertia in a continuum model. Simulations on a 39-bus system examine how that distribution changes propagation paths, wave velocities, and disturbance arrival estimates, providing information for the design of oscillation-damping controls.

Explanation transcript
  1. Paper overview

    Electromechanical disturbances travel through a power network, so different locations respond at different times. This study examines how representing generator inertia across transmission lines affects that propagation. It uses line admittances to distribute inertia in a continuum wave model. Simulations on a thirty-nine-bus system investigate propagation paths, wave velocities, and arrival times, with the aim of informing oscillation-damping control design. This overview draws on the published abstract; full text remains unavailable.

Citation / BibTeX
@inproceedings{algikar-wave-2022,
  title = {Electromechanical Wave Propagation Analysis in Power Systems},
  author = {Somayeh Yarahmadi and Pooja Algikar and Lamine Mili},
  year = {2022},
  booktitle = {2022 IEEE PES Generation, Transmission and Distribution Conference and Exposition – Latin America (IEEE PES GTD Latin America)},
  doi = {10.1109/ieeepesgtdlatinameri53482.2022.10037778},
  url = {https://doi.org/10.1109/ieeepesgtdlatinameri53482.2022.10037778}
}
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01Organize the reviewed literature
Distribution System Congestion Management: A Survey of Reliable Integration for Aggregated Resources and Microgrids: Organize the reviewed literatureOrganize decision horizons1Organize the reviewed literature Congestion-management studies Long-termplanning Operationalplanning Real-timeoperation Parallel review categories, not controller steps.
02Compare two solution families
Distribution System Congestion Management: A Survey of Reliable Integration for Aggregated Resources and Microgrids: Compare two solution familiesCompare congestion-management tools2Compare two solution families Market-basedPrices and contractsFlexibility auctions Technical controlsNetwork reconfigurationDirect resource control Choice depends on context and decision horizon.
03Map coordination requirements
Distribution System Congestion Management: A Survey of Reliable Integration for Aggregated Resources and Microgrids: Map coordination requirementsCoordinate constraints and flexibility3Map coordination requirements TSO / ISOMarkets DSONetwork limits Aggregator /microgrid DSO → TSO: network limits and flexibility TSO → DSO: prices and dispatch schedules DSO ↔ resources: requests and feasible offers Coordination roles differ across architectures.
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2026IEEE Access

Distribution System Congestion Management: A Survey of Reliable Integration for Aggregated Resources and Microgrids

Kumarsinh Jhala, Kiran Kumar Challa, Pooja Algikar, Prudhviraj Dhanapala

Flexible distributed resources can relieve grid congestion, but utilities and aggregators hold different information and control capabilities. This survey organizes market-based mechanisms and technical controls across planning, dispatch planning, and real-time operation. It compares distribution-operator architectures and coordination needs, clarifying how flexibility procurement and local network constraints must be considered together.

Explanation transcript
  1. Organize decision horizons

    Congestion management involves decisions at different time scales. Long-term planning considers future network and resource needs; operational planning prepares for anticipated conditions; real-time operation responds to current constraints. The survey organizes the literature by these horizons to clarify when decisions are made and what information and flexibility are available. This framework supports a consistent comparison of the reviewed approaches.

  2. Compare congestion-management tools

    The survey compares economic coordination with direct technical action. Market mechanisms use price signals, contracts, and auctions for flexibility to coordinate resource adjustments. Technical options include network reconfiguration and direct resource control. These approaches differ in the information they need and the participants authorized to act. Comparing those requirements helps identify suitable tools for planning, scheduling, or real-time operation.

  3. Coordinate constraints and flexibility

    Coordination matters because network constraints and resource flexibility are distributed across participants. The distribution operator can share local limits and available flexibility with the transmission side, which returns prices and dispatch schedules. Aggregators and microgrids exchange requests and feasible offers with the distribution operator. The survey compares coordination designs in terms of who exchanges information and who controls the resources.

Citation / BibTeX
@article{algikar-congestion-survey-2026,
  title = {Distribution System Congestion Management: A Survey of Reliable Integration for Aggregated Resources and Microgrids},
  author = {Kumarsinh Jhala and Kiran Kumar Challa and Pooja Algikar and Prudhviraj Dhanapala},
  year = {2026},
  journal = {IEEE Access},
  doi = {10.1109/access.2026.3709210},
  url = {https://doi.org/10.1109/access.2026.3709210}
}