arXiv subjects

Amritanshu Pandey

Publications and source records attributed to Amritanshu Pandey.

At least 19 recordsLinked to original sources

arXiv2026

Steady-State Equivalent Circuit Model for Data Center Loads

Planners currently represent data centers as aggregate constant-PQ or ZIP loads in steady-state interconnection and contingency studies. These aggregate models are computationally convenient. However, they obscure the electrical relationship between computational workloads, server utilization, and grid-side demand. They ignore the internal power-electronic conversion stages of IT loads and assume homogeneous workload distributions across the compute clusters. This hides operating-point-dependent converter losses and efficiency variations. We propose a steady-state equivalent-circuit model (ECM) for data centers, which explicitly builds circuit models for IT loads, power supply units, cooling, and auxiliary systems. For power supply units, the equivalent circuit model explicitly represents internal power-electronic conversion stages. For IT loads, we develop a utilization-dependent server power model, and we combine it with loss-aware ECMs of power supply units. This approach captures the grid-side impact of heterogeneous workload distributions while preserving compatibility with conventional power-flow analysis. We evaluate this data center ECM in large-scale transmission power flows, using Monte Carlo simulations under heterogeneous and homogeneous cluster utilization. In comparison with the fixed-efficiency constant-PQ model, the ECM predicts that the most stressed line exceeds its thermal limit in about 30% of Monte Carlo samples. The results further show that homogeneous server utilization overstates line-loading variability by 17%-46% relative to heterogeneous server utilization, depending on the intra-cluster workload correlation.

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arXiv2026

Analysis of Circuit-based Per-Panel Diode Model of Photovoltaic Array

Solar photovoltaic systems are increasing in size and number on the grid. In regions with high penetration, such as California, PV systems serve multiple functions, including peak shaving and demand response. Therefore, the criticality of PV systems to grid operations calls for accurate models. The current practice is to represent the PV array, composed of multiple PV panels, with an aggregated single-diode model (SDM). The highly abstract model has a limited ability to capture real-world behaviors, such as partial shading and hotspots. Thus, we develop a circuit-based per-panel PV array model that uses a single diode model for each panel and interconnects them to form an array. This approach bridges the tradeoff between cell-level physics and control-dependent system-level behavior. We establish conditions for mathematical equivalence between the proposed per-panel array circuit model and the aggregated single-diode array model. We generate empirical evidence by running simulations using parameters derived from real-world PV panels. Results indicate that the proposed per-panel array model can represent the electrical behavior of the array under non-ideal conditions, such as partial shading, more accurately. With maximum power point tracking control, the proposed model is 21.2% more accurate when estimating the real power output of an array under a partial shading scenario and 8.1% more accurate under a hot spot scenario.

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arXiv2026

PowerDAG: Supervisory Agentic AI System for Automating Distribution Grid Analysis

Distribution grid analyses include tasks such as network information retrieval, power-flow analysis, hosting-capacity assessment, DER planning, and state estimation. Completing these tasks often requires long-horizon, stateful workflows in which an engineer retrieves data, loads a feeder, runs simulations, evaluates results, and exports outputs. The growing volume of these analyses is outpacing the limited engineering workforce, causing suboptimal outcomes and delays. Large Language Model (LLM)-orchestrated agents can help, but they often struggle for two reasons: (i) they lack algorithms to determine the right context for an unseen grid task, and (ii) they cannot verify proposed actions against the environment state beforehand and instead rely on feedback after execution. We propose PowerDAG, an agentic artificial intelligence (AI) system that formalizes workflows as directed acyclic graphs (DAGs) and addresses current gaps in this formalism through two mechanisms, adaptive retrieval and Just-in-Time supervision. To dynamically retrieve relevant context, it curates and ranks expert exemplars using an adaptive score-decay cutoff that matches the query complexity. For supervision, it evaluates prerequisites before every tool call. If an agent proposes an invalid action, the supervisor blocks execution, preserves the environment, and returns a corrective advisory. We evaluate PowerDAG on 150 held-out queries from a 200-record expert-verified benchmark that covers 10 of the most commonly performed distribution-grid analyses, comparing 6 agentic systems across 10 LLMs for a total of 9,000 runs. PowerDAG reaches a success rate of 98.0% with GPT-5.5, 97.3% with Gemini 3.1 Pro, and 92.7% with Qwen3.6-27B, improving success rates by 6 to 50 percentage points over baselines.

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arXiv2026

AC Dynamics-aware Trajectory Optimization with Binary Enforcement for Adaptive UFLS Design

The high penetration of distributed energy resources, resulting in backfeed of power at the transmission and distribution interface, is causing conventional underfrequency load shedding (UFLS) schemes to become nonconforming. Adaptive schemes that update UFLS relay settings recursively in time offer a solution, but existing adaptive techniques that obtain UFLS relay settings with linearized or reduced-order model formulations fail to capture AC nonlinear network behavior. In practice, this will result in relays unable to restore system frequency during adverse disturbances. We formulate an adaptive UFLS problem as a trajectory optimization and include the full AC nonlinear network dynamics to ensure AC feasibility and time-coordinated control actions. We include binary decisions to model relay switching action and time-delayed multi-stage load-shedding. However, this formulation results in an intractable MINLP problem. To enforce model tractability, we relax these binary variables into continuous surrogates and reformulate the MINLP as a sequence of NLPs. We solve the NLPs with a homotopy-driven method that enforces near-integer-feasible solutions. We evaluate the framework on multiple synthetic transmission systems and demonstrate that it scales efficiently to networks exceeding 1500+ nodes with over 170k+ continuous and 73k+ binary decision variables, while successfully recovering binary-feasible solutions that arrest the frequency decline during worst-case disturbance.

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arXiv2026

Tutorial: Grid-Following Inverter for Electrical Power Grid

The growing use of inverter-based resources in modern power systems has made grid-following inverters a central topic in power-system modeling, control, and simulation. Despite their widespread deployment, introductory material that explains grid-following inverter operation from first principles and connects control design to time-domain simulation remains limited. To address this need, this tutorial presents a circuit-theoretic introduction to the modeling and simulation of a grid- following inverter connected to an electrical power grid. We describe the inverter synchronization with the grid (PLL), power control, and current control structure and show how these elements can be represented within an electromagnetic transient (EMT) simulation framework using companion model-based formulations similar to those used in circuit simulators such as SPICE and Cadence. In this tutorial, we use the grid-following inverter as the primary example to illustrate how its governing equations, control loops, and network interface can be formulated and simulated from first principles. By the end of the document, readers should gain a clear introductory understanding of how to model and simulate a grid-following inverter in an EMT platform.

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arXiv2026

Frequency-Aware Sparse Optimization for Diagnosing Grid Instabilities and Collapses

This paper aims to proactively diagnose and manage frequency instability risks from a steady-state perspective, without the need for derivative-dependent transient modeling. Specifically, we jointly address two questions (Q1) Survivability: following a disturbance and the subsequent primary frequency response, can the system settle into a healthy steady state (feasible with an acceptable frequency deviation $Δf$)? (Q2) Dominant Vulnerability: if found unstable, what critical vulnerabilities create instability and/or full collapse? To address these questions, we first augment steady-state power flow states to include frequency-dependent governor relationships (i.e., governor power flow). Afterwards, we propose a frequency-aware sparse optimization that finds the minimal set of bus locations with measurable compensations (corrective actions) to enforce power balance and maintain frequency within predefined/acceptable bounds. We evaluate our method on standard transmission systems to empirically validate its ability to localize dominant sources of vulnerabilities. For a 1354-bus large system, our method detects compensations to only four buses under N-1 generation outage (3424.8 MW) while enforcing a maximum allowable steady-state frequency drop of 0.06 Hz (otherwise, frequency drops by nearly 0.08 Hz). We further validate the scalability of our method, requiring less than four minutes to obtain sparse solutions for the 1354-bus system.

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arXiv2026

Grid-ECO: Grid Aware Electric Vehicle Charging Stations Placement Optimizer

The paper develops a methodology, Grid-ECO, to optimally allocate electric vehicle charging stations (EVCS) within a distribution feeder, while considering EV charging demand at census-level granularity. The underlying problem is NP-hard and requires satisfying nonlinear, nonconvex, three-phase unbalanced AC network constraints while including integer decision variables. Existing works cannot guarantee AC feasibility nor optimality of this problem without either i) relaxing the integer decision variable space or ii) convexifying AC constraints. Proposed Grid-ECO exactly solves the underlying mixed-integer nonlinear program (MINLP) to near-zero optimality gap while prioritizing candidate locations based on grid voltage and current sensitivities. To solve the MINLP exactly, Grid-ECO exactly reformulates it into mixed-integer bilinear program (MIBLP), enabling global optimization using the spatial branch-and-bound algorithm (sBnB). To ensure computational tractability for large-scale feeders, we develop and include a novel presolving strategy based on Sequential Bound Tightening (SBT) with variable filtering and decomposition. Case studies demonstrate that Grid-ECO outperforms the off-the-shelf Gurobi sBnB solver by solving cases where no feasible solution is found within 167 hours. When feasible solution is found by off-the-shelf solver, Grid-ECO reduces solution time by up to 73\% and sBnB node exploration by up to 97\%, while achieving a 0\% optimality gap and guaranteed AC feasibility.

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arXiv2026

Two-Stage Bidirectional Inverter Equivalent Circuit Model for Distribution Grid Steady-State Analysis and Optimization

This paper presents a \textit{physics-based} steady-state equivalent circuit model of a two-stage bidirectional inverter. These inverters connect distributed energy resources (DERs), such as photovoltaic (PV) and battery systems, to distribution grids. Existing inverter models have technical gaps on three fronts: i) inadequate modeling of inverter losses; ii) use of mathematical abstractions for bidirectional flow of power; and iii) inability to integrate different control modes into nonlinear solvers without loss of generality. We propose a physics-first model that explicitly captures losses in passive circuit components based on circuit-level principles. We enable bidirectional power flow without binary or complementarity constraints by formulating loss terms as smooth, sign-aware expressions of current. We introduce and parameterize controlled current sources with twice-differentiable continuous functions to enable inverter control modes without loss of generality. We integrate DERs with the proposed inverter model at the load buses of distribution networks to perform power flow and optimization studies on real-world distribution networks with over 20,000 nodes. We demonstrate that the proposed model is more accurate, integrates seamlessly with various control modes without loss of generality, and scales robustly to large optimization problems. Index Terms: bidirectional inverter model, circuit-based modeling, DERs, inverter efficiency, power control, steady-state analysis.

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arXiv2025

Stochastic framework for scheduling preemptive upgrades of distribution transformers

Electrification of residential heating and transporta- tion has the potential to overload transformers in distribution feeders. Strategic scheduling of transformer upgrades to antici- pate increasing loads can avoid operational failures and reduce the risk of supply shortages. This work proposes a framework to prioritize transformer upgrades based on predicted loads at each meter, including heat pumps and electric vehicle chargers. The framework follows a Monte Carlo approach to forecasting, generating many possible loading instances and collecting a distribution of failure probabilities for each transformer. In each loading instance, heat pumps and EVs are added stochastically to each meter over time, based on an overall estimated growth rate and factors specific to each customer. We set heat pump load profiles by temperature and EV load profiles based on a stochastic driving model and charging pattern. The load profiles feed into network topology and transformer failure models to calculate failure probabilities.We formulate a cost optimization based on these failure probabilities to schedule transformer upgrades. We demonstrate this approach on a real-world distribution feeder in rural Vermont under low, medium, and high-electrification scenarios. We find generally less than 20% of transformers having substantial risk of failure over a 20-year simulation. Lastly, we develop an optimization routine to schedule upgrades and discuss the expected number of failures.

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arXiv2025

PowerChain: A Verifiable Agentic AI System for Automating Distribution Grid Analyses

Rapid electrification and decarbonization are increasing the complexity of distribution grid (DG) operation and planning, necessitating advanced computational analyses to ensure reliability and resilience. These analyses depend on disparate workflows comprising complex models, function calls, and data pipelines that require substantial expert knowledge and remain difficult to automate. Workforce and budget constraints further limit utilities' ability to apply such analyses at scale. To address this gap, we build an agentic system PowerChain, which is capable of autonomously performing complex grid analyses. Existing agentic AI systems are typically developed in a bottom-up manner with customized context for predefined analysis tasks; therefore, they do not generalize to tasks that the agent has never seen. In comparison, to generalize to unseen DG analysis tasks, PowerChain dynamically generates structured context by leveraging supervisory signals from self-contained power systems tools (e.g., GridLAB-D) and an optimized set of expert-annotated and verified reasoning trajectories. For complex DG tasks defined in natural language, empirical results on real utility data demonstrate that PowerChain achieves up to a 144/% improvement in performance over baselines.

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arXiv2025

Solving Three-phase AC Infeasibility Analysis to Near-zero Optimality Gap

Recent works have shown the use of equivalent circuit-based infeasibility analysis to identify weak locations in distribution power grids. For three-phase power flow problems, when the power flow solver diverges, three-phase infeasibility analysis (TPIA) can converge and identify weak locations. The original TPIA problem is non-convex, and local minima and saddle points are possible. This can result in grid upgrades that are sub-optimal. To address this issue, we reformulate the original non-convex nonlinear program (NLP) as an exact non-convex bilinear program (BLP). Subsequently, we apply the spatial branch-and-bound (SBnB) algorithm to compute a solution with near-zero optimality gap. To improve SBnB performance, we introduce a bound tightening algorithm with variable filtering and decomposition, which tightens bounds on bilinear variables. We demonstrate that sequential bound tightening (SBT) significantly improves the efficiency and accuracy of Gurobi's SBnB algorithm. Our results show that the proposed method can solve large-scale three-phase infeasibility analysis problems with >5k nodes, achieving an optimality gap of less than 10e-4. Furthermore, we demonstrate that by utilizing the developed presolve routine for bounding, we can reduce the runtime of SBnB by up to 97%.

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arXiv2025

Circuit-theoretic Joint Parameter-State Estimation -- Balancing Optimality and AC Feasibility

AC State Estimation (ACSE) is widely recognized as a practical approach for determining the grid states in steady-state conditions. It serves as a fundamental analysis to ensure grid security and is a reference for market dispatch. As grid complexity increases with rapid electrification and decarbonization, there is a growing need for more accurate knowledge of the grid operating state. However, existing ACSE algorithms have technical gaps. Critically, current ACSE algorithms are susceptible to erroneous system parameters, which are assumed to be fixed in traditional approaches. In this paper, we build a novel circuit-theoretic joint parameter-state estimation algorithm to address this limitation. The innovative algorithm builds an analogous equivalent circuit of the grid with states and certain parameters unknown. It solves a circuit-constrained optimization to estimate the most likely grid states and parameters given a set of measurements. Further, it quantifies the goodness of the estimated output by formulating tight convex envelopes around the original non-convex problem to quantify the quality of estimates. We compare the various proposed approaches on systems with up to 2869 nodes while demonstrating a tradeoff between solution optimality and model fidelity.

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arXiv2025

Large-scale Grid Optimization: The Workhorse of Future Grid Computations

Purpose: The computation methods for modeling, controlling and optimizing the transforming grid are evolving rapidly. We review and systemize knowledge for a special class of computation methods that solve large-scale power grid optimization problems. Summary: Large-scale grid optimizations are pertinent for, amongst other things, hedging against risk due to resource stochasticity, evaluating aggregated DERs' impact on grid operation and design, and improving the overall efficiency of grid operation in terms of cost, reliability, and carbon footprint. We attribute the continual growth in scale and complexity of grid optimizations to a large influx of new spatial and temporal features in both transmission (T) and distribution (D) networks. Therefore, to systemize knowledge in the field, we discuss the recent advancements in T and D systems from the viewpoint of mechanistic physics-based and emerging data-driven methods. Findings: We find that while mechanistic physics-based methods are leading the science in solving large-scale grid optimizations, data-driven techniques, especially physics-constrained ones, are emerging as an alternative to solve otherwise intractable problems. We also find observable gaps in the field and ascertain these gaps from the paper's literature review and by collecting and synthesizing feedback from industry experts.

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arXiv2025

AC-aware Optimization Framework for Under-Frequency Load Shedding

Under-frequency load shedding (UFLS) prevents system collapse during large disturbances. Increased penetration of distributed energy resources (DERs) and reduced system inertia makes it challenging to design a static UFLS scheme, which relies on preset frequency thresholds and load shed fractions to meet design criteria across all possible operating conditions. Due to non-linearity and traceability issues, previous adaptive UFLS schemes use simplified tractable frequency models that overlook AC network effects such as voltage-dependent load/generation. This paper leverages model order reduction techniques to obtain a higher fidelity low-order model of system frequency dynamics that captures AC network effects while incorporating turbine governor action and their associated limits. The model is then used in a new AC-aware predictive optimization framework to adapt UFLS setpoints periodically based on current operating conditions while minimizing load shed. Validated on a 1,648-bus system with PSS/E simulations, the proposed method meets design criteria under various operating conditions and disturbance scenarios. Furthermore, the framework outperforms conventional static UFLS schemes and adaptive UFLS schemes based on simplified dynamic models.

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arXiv2024

Circuit-Theoretic Joint Parameter-State Estimation of Utility-Scale Photovoltaic, Battery, and Grid Systems

Solar PV and battery storage systems have become integral to modern power grids. Therefore, bulk grid models in real-time operation must include their physical behavior accurately for analysis and optimization. AC state estimation is critical to building real-time bulk power systems models. However, current ACSE techniques do not include detailed physics and measurements for battery and PV systems. This results in sub-optimal estimation results and subsequent less accurate bulk grid models for real-time operation. To address these challenges, we formulate a circuit-theoretic AC state estimator with accurate PV and battery systems physics and corresponding measurements. First, we propose an aggregated equivalent circuit model of the solar PV, battery, and traditional grid components. Next, we add measurements from PV and battery systems to the traditional measurement set to facilitate accurate estimation of the overall grid model. Finally, we develop a circuit-theoretic joint parameter-state estimation algorithm that can accurately estimate grid, PV, and battery system states and is robust against erroneous parameters. To demonstrate the efficacy of the proposed framework, we estimate the states of 10k node transmission networks with hundreds of battery+PV-tied systems. We compare the accuracy against the estimation of stand-alone grid, battery, and PV systems.

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arXiv2024

Distributed Primal-Dual Interior Point Framework for Analyzing Infeasible Combined Transmission and Distribution Grid Networks

The proliferation of distributed energy resources has heightened the interactions between transmission and distribution (T&D) systems, necessitating novel analyses for the reliable operation and planning of interconnected T&D networks. A critical gap is an analysis approach that identifies and localizes the weak spots in the combined T\&D networks, providing valuable information to system planners and operators. The research goal is to efficiently model and simulate infeasible (i.e. unsolvable in general settings) combined positive sequence transmission and three-phase distribution networks with a unified solution algorithm. We model the combined T&D network with the equivalent circuit formulation. To solve the overall T&D network, we build a Gauss-Jacobi-Newton (GJN) based distributed primal dual interior point optimization algorithm capable of isolating weak nodes. We validate the approach on large combined T&D networks with 70k+ T and 15k+ D nodes and demonstrate performance improvement over the alternating direction method of multipliers (ADMM) method.

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arXiv2024

ANOCA: AC Network-aware Optimal Curtailment Approach for Dynamic Hosting Capacity

With exponential growth in distributed energy resources (DERs) coupled with at-capacity distribution grid infrastructure, prosumers cannot always export all extra power to the grid without violating technical limits. Consequently, a slew of dynamic hosting capacity (DHC) algorithms have emerged for optimal utilization of grid infrastructure while maximizing export from DERs. Most of these DHC algorithms utilize the concept of operating envelopes (OE), where the utility gives prosumers technical power export limits, and they are free to export power within these limits. Recent studies have shown that OE-based frameworks have drawbacks, as most develop power export limits based on convex or linear grid models. As OEs must capture extreme operating conditions, both convex and linear models can violate technical limits in practice because they approximate grid physics. However, AC models are unsuitable because they may not be feasible within the whole region of OE. We propose a new two-stage optimization framework for DHC built on three-phase AC models to address the current gaps. In this approach, the prosumers first run a receding horizon multi-period optimization to identify optimal export power setpoints to communicate with the utility. The utility then performs an infeasibility-based optimization to either accept the prosumer's request or dispatch an optimal curtail signal such that overall system technical constraints are not violated. To explore various curtailment strategies, we develop an L1, L2, and Linf norm-based dispatch algorithm with an exact three-phase AC model. We test our framework on a 1420 three-phase node meshed distribution network and show that the proposed algorithm optimally curtails DERs while guaranteeing the AC feasibility of the network.

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arXiv2024

A Convex Method of Generalized State Estimation using Circuit-theoretic Node-breaker Model

An accurate and up-to-date topology is critical for situational awareness of a power grid; however, wrong switch statuses due to physical damage, communication error, or cyber-attack, can often result in topology errors. To maintain situation awareness under the possible topology errors and bad data, this paper develops ckt-GSE, a circuit-theoretic generalized state estimation method using node-breaker (NB) model. Ckt- GSE is a convex and scalable model that jointly estimates AC state variables and network topology, with robustness against different data errors. The method first constructs an equivalent circuit representation of the AC power grid by developing and aggregating linear circuit models of SCADA meters, phasor measurement units(PMUs), and switching devices. Then based on this circuit, ckt-GSE defines a constrained optimization problem using weighted least absolute value (WLAV) objective to form a robust estimator. The problem is a Linear Programming (LP) problem whose solution includes accurate AC states and a sparse vector of noise terms to identify topology errors and bad data.This paper is the first to explore a circuit-theoretic approach for an AC-network constrained GSE algorithm that is: 1) applicable to the real-world data setting, 2) convex without relaxation, scalable with our circuit-based solver; and 3) robust with the ability to identify and reject different data errors

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