Data-driven dictionaries to enhance the performance of compressive sensing-based state estimators

Smart grids utilize sensing, communication, and computation infrastructure to perform state estimation and obtain the situational awareness necessary for safety and control. However, an increase in metering deployments increases the strain on the communication infrastructure. Therefore, techniques for data compression such as compressive sensing (CS) have been developed. CS exploits the inherent sparsity of real-world data in certain transformation bases to compress and decompress measurements with low reconstruction errors. Previous works on compressing smart meter data have utilized the Haar, Hankel, and Toeplitz transformation bases to achieve sub-Nyquist compression. However, the transformation matrices can be tailored to the data using techniques such as dictionary learning to reduce reconstruction errors. Dictionary learning aims to find transformation matrices that generate sparse representations of the data. These dictionaries can provide superior reconstruction performance compared to deterministic trasformation bases. Therefore, this work proposes to generate data-driven dictionaries to learn the sparsifying basis for smart meter data and utilize them with 1-D and 2-D CS-based distribution state estimators. These estimators utilize compressed measurements and the Newton-Raphson method to obtain the system states. The performance of the generated dictionaries with CS-based state estimators has been evaluated on the IEEE 33-node distribution system and a 100-node test system. The data-driven dictionaries provided superior state estimation performance compared to conventional transformation bases such as Haar. Voltage magnitude and angle estimation error less than 0.3% mean absolute percentage error and 0.04 degree mean absolute error, respectively, were achieved at compression ratios as high as eight.