| dc.description.abstract | Energy loss and energy theft are two serious problems in modern grid which produce huge waste and cost. The smart grid with its ability to collect information about the behaviors of suppliers and customers is expected to be better equipped than the existing grid to detect loss and theft. The following two questions are the main focus of our works: 1). ``Can we locate the source of theft ?'' 2).``How much energy is stolen?" We deal with two types of theft: tampering with a smart meter and tapping a line.
For tampering, we propose a framework based on the measurement of energy, electric current and voltage to make theft detection feasible. In this framework, when measurements (of energy, electric current and voltage) are available everywhere, theft can be easily detected. The interesting case is, if measurements are not everywhere, theft detection is still feasible under some conditions. For different cases of measurement scenarios, we propose different solutions and provide
the conditions under which our solutions work. In particular, assuming that the smart grid has a tree structure and has a single source of energy, we show via simulation the following results:
1) With the measurement of electric current at the entry of each user and at the source of energy, we can locate the source of theft if the electric power is stolen in a constant rate and the measurement noise is comparatively small;
2) With the measurement of the energy production and each user's energy consumption plus the measurement of electric current at the entry of each user, we can accurately estimate the resistance of each link as long as the amount of stolen energy is comparatively small;
3) With the measurement of the voltage and electric current at the source of energy and at the entry of each user, we can accurately estimate the resistance of each transmission link if there is no theft.
For tapping, we apply clustering algorithms to analyze the anomalies in the usage data of all customers. We propose a hierarchical clustering algorithm which recursively bi-partitions the data along the principle eigenvector and separate the usage data of normal users and abnormal users.
Our theft detection framework employs the $\ell_1$ minimization under non-negative constraint, i.e., ${\underset{x \ge 0}{\text{min }}} \| Y-Ax \|_{\ell_1}$. As a theoretical verification of our work, we prove that under some suitable conditions on the matrix A, the $\ell_1$ minimization problem has a unique minimizer and the unique minimizer is equal to the real underlying result. | en |
