Andrzej Kłos

Network Solution Method Using Algebraic Network Model

Using the algebraic model of network derived in Part I, the general method of linear network solution is derived in this section. Suppose that the graph of b-branch network is known, and the topology is unrestricted, except that a tree includes voltage sources and a cotree includes current sources.

Current-Based Method of Load Flow Solution

Using classical input data, the process of finding the load flow in power system networks is done in two steps. First, the voltage state vector is calculated; second, the needed output quantities (branch power loads) are found.

Current–Voltage Functional Relations

Up to this point, the branch currents and branch voltages of a network system have been assumed to be unrelated, except that the current space ( overline{I} ) and the voltage space ( overline{V} ) are orthogonal and that individual current and voltage vectors obey the power law ( I^{*} V = 0 ) (see Chap. 6).

Algebraic Model of Network Graph

The important aspect of the mathematical modeling of network system is the representation of electrical network graph in terms of mathematical quantities (scalars, vectors, matrices, linear spaces), which represent the physical quantities of the network system graph (branches, node-sets, cut-sets, loop-sets) and algebraic relations representing these mathematical quantities. In this chapter, the electrical network graph is modeled in terms of linear algebra.

General Comments to Part I

The book presents a modern and non-conventional approach to the theoretical analysis and solution of electrical networks systems. The generally unknown interrelations of network quantities and the formulations of the fundamental network laws are derived. Some possibilities of its application in network analysis and solution are given.

Algebraic Model of Current–Voltage Vectors

The algebraic models of currents and voltages have been derived in the previous chapters. In this chapter, the important physical notion—the combined current–voltage vector—is defined and described.

Kirchhoff’s Laws Using Matrix T

One of the main results of the algebraic models of current and voltage states, derived in previous chapters, is the introduction of two b-dimensional linear spaces (b—number of network branches).

Method of Current and Voltage Sensitivity Analysis

It is intuitively known that the current or voltage values of a network branch depend on the current or voltage values of all other branches in the network (practically may depend on certain part of network only).

Algebraic Model of Network Voltages

Analogically as in the case of currents, the linear algebra model of network voltages can be derived starting from the model of branch voltage.

Applications of b-Dimensional Formulation of Kirchhoff’s Laws

The non-conventional formulations of Kirchhoff’s laws, given in the first part of book (see Chap. 7), may have various applications; some of them are given in this chapter.