Ian Petersen

Norak Rin, Iman Shames, Ian Petersen et al.

Recent advances in precise phasor measurement units are enabling new approaches to estimate distribution and transmission grid parameters in real-time. In this paper, we investigate voltage and current phasor measurement requirements to estimate the electric grid topology and admittance parameters. We show necessary and sufficient conditions for the number of independent operating points (measurements) required to determine the topology and admittance of a completely unknown electric grid. With prior topology information, we also show that there is a minimum number of measurements required to uniquely determine the admittance matrix and corresponding grid topology. In the presence of noisy phasor measurements, we show that the admittance matrix can be estimated using a structured total least squares approach. By means of numerical simulations on the IEEE 13-node distribution feeder, the IEEE 14-node transmission network, and the IEEE 123-node distribution feeder, we demonstrate our approach is suitable for applications in radial and mesh grid topologies in the presence of measurement noise.

Subhransu Bhattacharjee, Ian Petersen

We introduce a novel adaptive damping technique for an inertial gradient system which finds application as a gradient descent algorithm for unconstrained optimisation. In an example using the non-convex Rosenbrock's function, we show an improvement on existing momentum-based gradient optimisation methods. Also using Lyapunov stability analysis, we demonstrate the performance of the continuous-time version of the algorithm. Using numerical simulations, we consider the performance of its discrete-time counterpart obtained by using the symplectic Euler method of discretisation.