2.4.1 Example

As a slightly more complex example of reference frame theory it will be assumed now that the voltages are unbalanced. In particular consider the three-wire circuit shown in Figure 1.12. The three source voltages are expressed by eag = εEs cos θe

ebg=Es cos (θe2π3)

(2.113)

ecg=Es cos (θe+2π3)

(2.114)

eag=vas+vsg

(2.115)

where θe = ωet and ε is an arbitrary constant. Note that when ε is equal to unity the applied voltages are balanced.

Since the neutral return path in this case is absent, the load voltages are now not readily unknown but must be solved from the network equations. If vsg is defined as the voltage between neutral points, then clearly

eag=vas+vsg

(2.116)

Figure 2.11  Response of electric system for ...

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