State Identification of Underdetermined Grids

Abstract

Methods of grid state identification are mathematical algorithms to obtain information on state variables of electric power system grids. These procedures are based fundamentally on the acquisition of measured, forecasted or estimated values, which are universally referred to as influencing variables, or, more simply, as measurands. In combination with knowledge of grid topology and electrical equipment parameters, identification methods aim at the best possible determination of the grid state. Depending on the ratio of the number of available independent measurands and the quantity of state variables, the equation system to be solved is either overdetermined, determined or underdetermined. Thus, different procedures of grid state identification are applied. Independent of the identification approach the basic proceeding of grid state determination remains the same. Starting at an initial guess the grid state identificator returns a nodal voltage vector which is used to calculate secondary grid values like nodal currents, nodal powers or terminal currents and powers. Calculation results are compared to the available information on influencing variables. The grid state identificator now iteratively adjusts the voltages to minimize the difference between measured and calculated values. If the input vector is redundant and contains more (real-valued) measurands than twice the number of nodes, the equation system is overdetermined. This sort of problem is characteristic of high voltage and ultra high voltage transmission grids. Recording of more measurands than needed for uniquely solving the equation system is used to protect grid state identification against measurement uncertainties and outages of measurement facilities. Typically, the number of measurands is more than twice as high as the amount which would have been necessary to uniquely calculate a grid state. To solve an overdetermined equation system state estimation algorithms based on Gaussian Least-Squares-Optimization or artificial neural networks are applied which find a solution vector of nodal voltages that minimizes the mean square error. If the number of independent (real-valued) measurands is exactly twice the number of nodes, the equation system is uniquely solvable. In case of measuring only voltages and currents, a direct solution without any iteration is possible. If powers are used as influencing variables, an iterative solution approach is applied using a Newton-Raphson or fixed-point 17