Smart Inverter Grid Probing for Learning Loads: Part II - Probing Injection Design

TL;DR

This paper develops a methodology for designing optimal inverter injection signals to probe power grids, improving load estimation accuracy while respecting system constraints, using linearized models and SDP relaxations.

Contribution

It introduces a systematic approach for creating probing injections that enhance load inference, considering inverter and network constraints, with validation on real and synthetic data.

Findings

Probing design improves load estimation accuracy.

SDP relaxation effectively handles noisy data.

Probing duration impacts estimation quality.

Abstract

This two-part work puts forth the idea of engaging power electronics to probe an electric grid to infer non-metered loads. Probing can be accomplished by commanding inverters to perturb their power injections and record the induced voltage response. Once a probing setup is deemed topologically observable by the tests of Part I, Part II provides a methodology for designing probing injections abiding by inverter and network constraints to improve load estimates. The task is challenging since system estimates depend on both probing injections and unknown loads in an implicit nonlinear fashion. The methodology first constructs a library of candidate probing vectors by sampling over the feasible set of inverter injections. Leveraging a linearized grid model and a robust approach, the candidate probing vectors violating voltage constraints for any anticipated load value are subsequently rejected. Among the qualified candidates, the design finally identifies the probing vectors yielding the most diverse system states. The probing task under noisy phasor and non-phasor data is tackled using a semidefinite-program (SDP) relaxation. Numerical tests using synthetic and real-world data on a benchmark feeder validate the conditions of Part I; the SDP-based solver; the importance of probing design; and the effects of probing duration and noise.