Hierarchical algorithms of functional modelling for solution of optimal operation problems in electrical power systems

Abstract

This paper presents foundations of the optimization method intended for solution of power systems operation problems and based on the principles of functional modeling (FM). This paper also presents several types of hierarchical FM algorithms for economic dispatch in these systems derived from this method. According to the FM method a power system is represented by hierarchical model consisting of systems of equations of lower (subsystem) levels and higher level system of connection equations (SCE), in which only boundary variables of subsystems are present. Solution of optimization problem in accordance with the FM method consists of the following operations: (1) solution of optimization problem for each subsystem (values of boundary variables for subsystems should be determined on the higher level of model); (2) calculation of functional characteristic (FC) of each subsystem, pertaining to state of subsystem on current iteration (these two steps are carried out on the lower level of the model); (3) formation and solution of the higher level system of equations (SCE), which gives values of boundary and supplementary boundary variables on current iteration. The key elements in the general structure of the FM method are FCs of subsystems, which represent them on the higher level of the model as “black boxes”. Important advantage of hierarchical FM algorithms is that results obtained with them on each iteration are identical to those of corresponding basic one level algorithms.