Matrix Methods for Network Solutions
In the impedance matrix, the voltage equations are written in terms of known constant voltage sources, known impedances, and unknown loop currents. In the admittance matrix, current equations are written in terms of known admittances and unknown node voltages. The bus admittance matrix is formed by inspection. The bus impedance method demonstrates the ease of calculations throughout the distribution system, with simple manipulations. The size of the network is important. Even the most powerful computer may not be able to model all the generation, transmission, and consumer connections of a national grid, and the network of interest is ‘‘islanded’’ with boundary conditions represented by current injection or equivalent circuits. Linear network graphs help in the assembly of a network. The problem for large networks can be stated that a minimum number of linearly independent equations of zero redundancy must be selected to provide sufficient information for the solution of the network.