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By William D. Stevenson

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4. Counting v in series with b v b b b v v v b b v g1 Fig. 4. Illustration for node equations. R\ as one branch, there are five branches and three nodes. Let us choose one of the nodes (any one) as a reference (or datum) node and consider the voltages between each of the other nodes and the reference node, with the voltage reference + away from the datum node. These voltages are the node voltages. Any branch voltage can be written as the difference between two node voltages. ) For the present example, 32 Loop and Node Systems of Equations [Ch.

Such an expression is incomplete unless we add to it a specification of i(0+), and in this sense is misleading. , which is certainly not true. Also, in many of the cases that we shall consider, the voltage may not be expressible in such a simple fashion for all t, the analytic expression for v(t) depending upon the particular interval of the axis on which the point t falls. In such a case the definite integral is certainly preferable. Some such waveshapes are shown in Fig. 9. Fig. 9. Voltage waveshapes.

The next step in the analysis is to substitute the v-i relationships of the branches into the K C L equations. Here we encounter some difficulty. The v-i re­ lationships for a simple transformer are (14) These expressions give the voltages in terms of the currents. In order to use these in the K C L equations we will have to invert them. Suppose we integrate both sides between the limits 0 and t. The result will be (15) Transposing the initial value terms leads to (16) Each of these equations contains both i and i .

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Solution manual of Power System Analysis by William D. Stevenson

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