Set A Notation: Lower case, such as ‘v’, represents instantaneous quantity and bold upper case, such as ‘V’, represents phasor quantity. 1.A 3-phase balanced load is connected to a 3-phase balanced power supply through identical transformers of 1:1 turns ratio which are wye (Y)/delta connected as shown in Fig. 1. The load impedance is |Z|=10 ohms. The source voltage |E| (line-to ground) is 550 volt. E1E2E3S1ZZZILiLaiLbiLciaibiciAiBiCBCAbcaFig. 1 The switch S1 is closed, (a) What are the line-to-line voltages |Vab|= |Vbc|=|Vca|on the secondary sides ofthe transformers?(b) What is the phase voltage (line-to-neutral ), |Vph|, across each load Z? (c) What is the current |IL|of each load Z? (d) What are the magnitudes of |Ia|=|Ib|=|Ic|in the delta connection? (Hint: Draw current phasors to represent iLa=ia-ic, iLb=ib-ia, and iLc=ic -ib ). (e) What are the magnitudes of |IS|= |IA|=|IB|=|IC|on the primary side? (f) What is |SS|the complex power of the power source, 3|Eph||IS|, where |Eph|=|E1|=|E2|=|E3|? (g) What is |STs|the complex power of the secondary (load) side transformers, which are delta connected? From (f) and (g), it is clear that the complex power is independent of whether the transformers are connected in wye (Y) or delta. 2.One of the transmission lines is lost. This is represented by opening the switch S1. The current iA=0. (a) What is the current ia? The voltages with respect to ground across the primary transformers are vA, vB, vC. The b-phase is intact. (b) What is the voltage vbcin terms of vA, vB, vC? The c-phase is intact. (c) What is the voltage vbain terms of vA, vB, vC? Under balanced 3-phase operating conditions, vA+vB+vC=0 so that vA= -(vB+vC).
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