Optimum quantization and reconstruction of power flows from voltage measurements at dispersed buses

In this paper, optimum quantization and reconstruction is studied for a DC power flow model and voltage measurements taken at dispersed buses. Necessary conditions are provided for the optimum parameters that describe the quantization and reconstruction processes. Algorithms are described to employ these necessary conditions to search for the optimum parameters. When the voltage measurements are statistically independent, the necessary conditions decouple for each of the measurements, significantly simplifying the solution process. Suppose the sets of measurements at different buses can be broken into several groups. If all the measurements in a given group must be modeled as being statistically dependent but if measurements from different groups can be approximated as independent of one another, then it is shown that the necessary conditions are uncoupled from group to group. In this case, small problems, for each group, must be solved and then the solutions of the smaller problems can be combined to solve the overall problem. The resulting approach significantly reduces the complexity of finding the optimum quantization and reconstruction parameters. Further, this approximation appears reasonable in modeling power networks, where measurements at neighboring nodes may require a statistically dependent model but nodes where are far apart may not.