Novel Compressed Sensing Reconstruction Algorithms for Power System Wide-Area Measurement Data Recovery Under Communication Outages in Nigeria

This research develops novel compressed sensing based reconstruction algorithms for recovering missing power system measurement data in Nigerian wide-area monitoring systems during communication outages, making original contributions to the mathematical theory of sparse signal recovery as applied to the structured sparsity characteristics of power system state trajectories. Wide-area monitoring systems rely on continuous communication channels from PMUs and SCADA remote terminal units to the control centre, but Nigerian communication infrastructure for power system telemetry is characterised by frequent and sometimes extended dropout events that create gaps in measurement records critical for state estimation, post-disturbance analysis, and contingency detection. The theoretical contribution originates from the observation that power system state trajectories exhibit low-rank and temporally sparse structure that is exploitable by matrix completion and compressed sensing methods, but that the specific structure of power system data including oscillatory dynamics, fault transients, and measurement noise requires algorithms beyond standard compressed sensing theory. Three novel algorithmic contributions are made: a structured nuclear norm minimisation formulation that incorporates the known oscillatory modes of the Nigerian grid as a prior into the matrix completion penalty, significantly improving recovery accuracy for inter-area oscillation monitoring; an adaptive measurement matrix design exploiting the graph topology of the Nigerian transmission network to maximise sensing efficiency given limited PMU placement; and a real-time iterative reconstruction algorithm with provable convergence guarantees for online deployment in the TCN Energy Management System. All algorithms are validated on actual Nigerian PMU event records. Keywords: compressed sensing, wide-area monitoring, PMU data recovery, communication outage, power systems.