Muhammad Hamza Ali

Muhammad Hamza Ali, Amritanshu Pandey

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.

Muhammad Hamza Ali, Amritanshu Pandey

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.