L1 norm minimization applied to power system state estimation

Contact: Konstantina Christakou

The static state of a power system is defined as the magnitude and phase of the voltage at all network buses. State estimation (SE) is a systematic procedure which provides estimates of this state by processing sets of remotely captured real-time measurements. SE is considered nowadays a basic module of energy management systems that facilitates monitoring and control of power systems, and serves as the real-time database for several applications.

One of the most commonly used state estimation methods in power systems is the weighted least squares method. This method relies on the assumption that the available measurements contain errors that have a Gaussian distribution and tries to minimize the weighted sum of the squares of the errors to obtain the system state.

The goal of this project is to explore the use and evaluate the performance of ℓ1 norm minimization for power system state estimation. ℓ1 norm minimization is a less traditional method that tries to minimize the absolute deviation of the errors and implicitly assumes that these errors follow a Laplace distribution. In general ℓ1 norm minimization is less simple than least squares, but is considered more robust to outliers or wrong distributional assumptions.

Specific tasks of the project are the formulation and implementation of the SE problem as an ℓ1 norm minimization problem and the comparison with the traditional weighted least squares algorithm in different test scenarios.