Sairaj Dhople

Sachin Khoja, Kamlesh Sawant, Palak Jain et al.

This paper presents an automated software toolchain for synthesizing hardware-implementable analog circuits that solve constrained optimization problems. The proposed toolchain supports nonlinear objective functions with linear and quadratic constraints. It maps optimization variables to capacitor voltages, implementing dynamics that enforce Karush-Kuhn-Tucker conditions using operational amplifiers, resistors, capacitors, diodes, and analog multipliers. From high-level problem descriptions in AMPL or MPS, the toolchain generates a SPICE netlist for the analog circuit, simulates it, and verifies that the solutions converge. The projected settling time of the analog circuit depends on circuit parameters, gain-bandwidth product, and slew-rate limits of operational amplifiers, and leverages the inherent parallelism of analog circuits. The proposed toolchain successfully generates circuits with up to 10,000 variables and demonstrates large scalability improvements, achieving up to a 1,000X increase in solvable problem size over prior analog hardware demonstrations. Simulation studies further show that the automatically synthesized circuits converge to optimal solutions, achieving more than a 200X speedup compared to IPOPT, a state-of-the-art digital interior-point solver.

Damola Ajeyemi, Antonin Colot, Sairaj Dhople et al.

This paper develops a computationally efficient framework for reachability analysis of transmission-level power system dynamics with synchronous generators, grid-forming and grid-following inverters, and uncertain power injections/withdrawals. Starting from reduced-order device models and a frequency-divider representation, we derive a linear ordinary-differential-equation model suitable for efficient reachable-set computation under bounded disturbances across network buses. The proposed reachability method combines interval reachability and contraction-based bounds to construct certified over-approximations for the linear ordinary-differential-equation model. A real Jordan transformation separates non-oscillatory modes, handled through a linear embedding system, from oscillatory modes, enclosed using contraction-based ball bounds. Numerical experiments on a modified IEEE 39-bus system validate the reachable tubes against high-fidelity electromagnetic-transient (EMT) simulations, and demonstrate multi-second reachable sets computed in sub-second time.

Debjyoti Chatterjee, Nathan Baeckeland, Bala Kameshwar Poolla et al.

We present a swing-equation model with generalized and equilibria-dependent inertia, damping, and synchronization constants for energy conversion interfaces with second-order active-power versus voltage-phasor-angle dynamics connected to an infinite bus. The model is unified in that prudent parameterization of the second-order angle-to-power transfer function aligns with reduced-order models for synchronous generators, grid-following inverters with fast frequency-response capability, and droop- and virtual synchronous generator-based grid-forming inverters. Parametric necessary and sufficient conditions to examine small-signal stability of angle equilibria are derived from the unified swing-equation model.