Sequential formulation of the multimachine-power-system and multivariable-control-system problems

A formulation of the multimachine-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 to the decomposition of large-scale system problems which can be represented with dynamic blocks connected to the nodes of a network structure. The techniques are also shown to apply to analysis of the multivariable-control-system problem based on a sequential connection of control loops, analogous to the interconnection of link admittances in Kron´s method of network tearing. Such analysis can simplify the procedure for control design based on a sensitivity analysis or by the application of conventional single-loop techniques.