The economic loading of transmission systems

In several publications Kron, Kirchmayer and others have outlined methods for transforming power-system operating data in terms of complex voltages and currents into information concerning real generator powers and transmission losses. These losses are related to the individual generator loadings by a set of constants which are dependent only upon operating conditions at normal load. In the present paper Kron´s methods for establishing a transmission loss equation for a hypothetical 3-generator, 2-load system are described and the analysis is extended for application to an actual section of the British network. The coefficients of the loss equation are obtained from the basic impedance matrix of the system and various transformation matrices, which transform the basic matrix to the final loss matrix, based on certain operating assumptions. A method is developed for combining the loss formula with station fuel costs for economic system operation. The resulting loading equations are illustrated in nomograph form as an aid to system load dispatching. In the paper, owing to certain limitations of the required information regarding system loads, certain of the load-flow conditions have been estimated by calculation, and the accuracy of the loss analysis is correspondingly limited. However, the purpose of the paper is to illustrate available methods and not to formulate an accurate set of loading equations.