M.Sc Thesis

M.Sc StudentRozenberg Igal
SubjectCompressed Sensing for Efficient Power System
DepartmentDepartment of Electrical and Computer Engineering
Supervisor ASSOCIATE PROF. Yoash Levron
Full Thesis textFull thesis text - English Version


This thesis addresses the challenge of fault location in power systems using a limited

number of sensors. Recent papers on fault location, suggest the use of a developing

mathematical tool, known as compressed sensing. Compressed sensing methods enable the finding of a unique solution to an under-determined linear system of equation when there exists an additional sparse prior on the solution. It was shown that various power system faults may be modeled by sparse vectors, and hence can be located efficiently using these techniques. This thesis extends the classical compressed sensing approach and proposes a sparse recovery algorithm that exploits both the sparsity constraints and additional structural constraints imposed by the fault physical models.

To this end, faults are represented by sparse vectors subjected to non-convex structural constraints. It is shown that these constraints provide additional information that is used for diminishing the necessary number of measurement for fault locations, and for improving the location accuracy. The proposed algorithm searches directly over these physical faults and therefore solves the problem by operating on a smaller solution space. The thesis also considers the conditions for unique location of sparse events in power networks with a given set of sensor measurements. It is argued, that the additional structural constraints on the sparse solution may guarantee unique solution, even in case the common sparse uniqueness condition (the spark) is not fulfilled. This result is demonstrated by deriving analytic conditions for the unique solution of a single short-to-ground in a power system.. With these additional structural constraints, the spark uniqueness condition happens to be sufficient but not necessary. The advantages of these new approaches are demonstrated by comparative simulations for several types of fault locations in different scenarios (signal-to-noise ratios, number of sensors and others).