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3) The Gauss-Seidel technique uses each value of voltage immediately after it is calculated. This is best illustrated using Eq. 3) in an 39 40 Chapter Five Input all parameters and form system admittance matrix Input system loading conditions and set initial busbar voltages Set busbar count Kto 1 n s· Calculate --4- and YlefVi i=1 vk #k L Yes No FLAG= 1 No Yes Solution converged. 1 Flowchart for Gauss-Seidel process. Gauss-Seidel Method 41 expanded form and employing iteration superscripts, where i repre­ sents the ith iteration.

1 5 Reference system. 02 Reference System 25 and the off-diagonal elements are Yki = - Ykj, k# j On this basis, the Y matrix may be assembled by inspection once all the line admittances have been calculated. 0097 = 1 = = . 534247 = . 278351 = . 154061 At this stage all the series line admittances for lines terminating at busbar 3 have been incorporated into the admittance matrix ele­ ments associated with busbar 3; however, the effects of the shunt line admittances have not been included. To do so, half of each line shunt admittance must be added to the diagonal element for busbar 3, in accordance with the line representation described in Sec.

To ensure that the resulting level of reactive power lies within the capa­ bility of the generator to supply it, the P, IVI busbar specification must be qualified by specifying also the machine maximum and minimum reactive power limits. Since a generator will supply current into a network, positive P and Q quantities conventionally represent lagging current supplied. 3 Transformers For transformers having a fixed transformation ratio, a simple series per-unit impedance representation is required.

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