Sequential Least-Squares Estimation and the Electrical Network Problem

Fundamental relationships existing between the electrical network problem and least-squares estimation theory are illustrated and the theorems of least-power associated with the equilibrium conditions of physical systems are shown to correspond to the mathematical concepts of least-squares theory. Solution of the electrical network problem based on Kron's method of tearing and interconnection is considered and is shown to incorporate an iterative technique, similar to the algorithm developed for sequential least-squares data fitting. A formulation of the multi-machine power system problem is shown to incorporate inherently the form of a least-power theorem associated with a potential function related to machine power losses and network power. A piecewise solution of the transient problem is also developed based on a sequential connection of generators to the network nodes. Similar methods will have application for the decomposition of larger-scale system problems which can be identified with dynamic blocks connected to the nodes of a network structure. The techniques are also shown to apply for analysis of the multi-variable control system problem based on a sequential connection of control loops, analogous to the interconnection of link attendances in Kron's method of network tearing. Such analysis can simplify the procedure for control design based on a sensitivity analysis or by or by the application of conventional single-loop techniques. The physical significance of tearing and interconnection in the multi-machine and multi-variable control system problem and the resulting sequential formulations are illustrated in block diagram form.