Application of non-Euclidean metric in the electric power industry for reduction of measurement uncertainty

The paper proposes the use of the non-Euclidean metric to reduce the uncertainty that occurs when measuring voltage for the tasks of ongoing continuous control of electric power consumption in large, branched highvoltage electric networks. The problem is that for continuous control of electric power consumption, it is necessary to install the active and reactive power measuring equipment in each node of the electric network (at each substation) and to ensure the transmission of measurement information to dispatching control centers. For countries with large electric networks, long distances between electric grid nodes and dispatch control centers, this requires huge capital costs. Therefore, it is advisable to place equipment for measuring electric power and voltage only in individual nodes of the electrical network, and then calculate the parameters of the remaining nodes based on Kirchhoff's laws. But at the same time, there is a significant measurement uncertainty, because the complex value of the voltage is usually not measured, only the modulus of the voltage values is used for the calculation. The use of non-Euclidean metrics provides the reduction of the input data uncertainty, which are necessary to control the consumption of electric power in each node of the electric network.