arXiv subjects

Muhammad Hamza Ali

Publications and source records attributed to Muhammad Hamza Ali.

6 recordsLinked to original sources

arXiv2026

Dynamic Modeling of Transmission Networks, Grid-Following Inverters, and UPS-Based AI Data Centers

This document presents dynamic models of a transmission network and average models of power-electronic devices and loads in the synchronous $dq$ frame. We model the network in the positive sequence and its synchronous generators with the classical swing equation and a first-order turbine governor. The power-electronic models cover grid-following inverters and AI data centers. Each inverter has a phase-locked loop, a power controller, and a current controller. Each data center connects to the grid through two step-down transformers. Its low-voltage bus feeds an IT load, an induction-motor cooling load, and a constant-impedance load. A double-conversion uninterruptible power supply (UPS) serves the IT load. We model its rectifier, grid-forming output inverter, battery, and bidirectional DC-DC converter. A measured GPU power trace drives the IT demand. We replace every non-smooth operation with a smooth surrogate. This keeps the discretized model continuously differentiable for the nonlinear solver. We also show how we initialize each model at its power-flow operating point.

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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

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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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

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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