arXiv subjects

Iven Guzel

Publications and source records attributed to Iven Guzel.

3 recordsLinked to original sources

arXiv2026

Spectral Initialization and Certification for Power System Angle Estimation

Power System State Estimation (PSSE) is commonly formulated as a nonconvex weighted least-squares (WLS) problem, making global optimality difficult both to attain and to certify. Recent work has shown that, when voltage magnitudes are known to sufficient accuracy, the remaining angle estimation subproblem can be reduced to phase synchronization and solved effectively using spectral initialization and spectral certification. This paper explains why these spectral methods succeed. We prove that their behavior is governed by the measurement error, normalized against the usual observability margin from the classical literature. Below a fixed threshold, spectral initialization recovers the true voltage angles to first-order accuracy, and the WLS estimator is unique up to a global phase. Moreover, a zero-duality-gap spectral certificate verifies recovery of this unique WLS estimate. In the noiseless observable regime, spectral initialization exactly recovers the true angles and certification is exact without local refinement. Numerical experiments on standard benchmark systems support the theory and show that the spectral methods remain effective beyond the conservative regime covered by the guarantees.

math.OC↗

arXiv2024

Power System State Estimation by Phase Synchronization and Eigenvectors

To estimate accurate voltage phasors from inaccurate voltage magnitude and complex power measurements, the standard approach is to iteratively refine a good initial guess using the Gauss--Newton method. But the nonconvexity of the estimation makes the Gauss--Newton method sensitive to its initial guess, so human intervention is needed to detect convergence to plausible but ultimately spurious estimates. This paper makes a novel connection between the angle estimation subproblem and phase synchronization to yield two key benefits: (1) an exceptionally high quality initial guess over the angles, known as a \emph{spectral initialization}; (2) a correctness guarantee for the estimated angles, known as a \emph{global optimality certificate}. These are formulated as sparse eigenvalue-eigenvector problems, which we efficiently compute in time comparable to a few Gauss-Newton iterations. Our experiments on the complete set of Polish, PEGASE, and RTE models show, where voltage magnitudes are already reasonably accurate, that spectral initialization provides an almost-perfect single-shot estimation of $n$ angles from $2n$ moderately noisy bus power measurements (i.e. $n$ pairs of PQ measurements), whose correctness becomes guaranteed after a single Gauss--Newton iteration. For less accurate voltage magnitudes, the performance of the method degrades gracefully; even with moderate voltage magnitude errors, the estimated voltage angles remain surprisingly accurate.

math.OC↗

arXiv2023

Eliminating Media Noise While Preserving Storage Capacity: Reconfigurable Constrained Codes for Two-Dimensional Magnetic Recording

Magnetic recording devices are still competitive in the storage density race thanks to new technologies such as two-dimensional magnetic recording (TDMR). Error-prone patterns where a bit is surrounded by complementary bits at the four positions with Manhattan distance $1$ on the TDMR grid are called plus isolation (PIS) patterns. Recently, we introduced optimal plus LOCO (OP-LOCO) codes that prevent these patterns from being written. However, as the device ages, error-prone patterns where a bit is surrounded by complementary bits at only three positions with Manhattan distance $1$ emerge, and we call these incomplete PIS (IPIS) patterns. In this paper, we present capacity-achieving codes that forbid both PIS and IPIS patterns in TDMR systems with wide read heads. We collectively call these patterns rotated T isolation (RTIS) patterns, and we call the new codes optimal T LOCO (OT-LOCO) codes. We analyze OT-LOCO codes and derive their encoding-decoding rule. Simulation results demonstrate that OT-LOCO codes entirely eliminate media noise at practical TD densities. We suggest using OP-LOCO codes early in the device lifetime, then reconfiguring to OT-LOCO codes later on. Moreover, we introduce another coding scheme to remove RTIS patterns which offers lower complexity, lower error propagation, and track separation.

cs.IT↗