EE 303, Quiz 3, Fall, 2017, Dr. McCalley 20 minutes, closed book, closed notes, calculator allowed, no communication devices

1. (18 pts) For the circuit below, express (a) v1(t) and (b) v2(t) as a function of: mesh currents i1(t) and i2(t), associated current derivatives, and other parameters indicated on the diagram.

R2

i2(t)

v1(t)

M

L2 L1

R1

i1(t) v2(t)

Solution: a. Left loop: v1(t)=[i1(t)+ i2(t)]R2+L1di1(t)/dt-Mdi2(t)/dt+R1i1(t) b. Right loop : v2(t)=[i1(t)+ i2(t)]R2+L2di2(t)/dt-Mdi2(t)/dt

2. The “exact” equivalent circuit parameters of a 150-kVA, 2400volt/240volt single-phase transformer are R1=0.2Ω, R2=2mΩ,

X1=0.45Ω, X2=4.5mΩ, Rc=10kΩ, and Xm=1.55kΩ. R1, X1, Rc, and Xm are given referred to the primary side; R2 and X2 are given referred to the secondary side. A company purchases three of these single-phase transformers and connects them in a Y-Y configuration to a three-phase Y-connected load ZL.

a. (5 pts) Draw per-phase “exact” equivalent of the circuit (transformer and load) with all elements, except the load, referred to primary side.

b. (5 pts) Label all impedance elements on the diagram with their ohmic value (use letters and numerical value). c. (5 pts) Identify on the diagram the turns ratio (N1/N2)eff to be used in the per-phase circuit (identify numerical value). d. (5 pts) Label the secondary current referred to the primary, I’2 (do not need numerical value, just location &

directionality). e. (5 pts) Label the voltage across the secondary winding, referred to the primary, E’2 (do not need numerical value,

just location & directionality). Solution:

ZL

X’2=0.45

Xm= 1.55k

R’2=0.2 R1=0.2 I’2

Rc=10k E’2

10:1

X1=0.45

f. (6 pts) Would the effective turns ratio to be used in the per-phase circuit change from that identified in (c) if:

i. the transformers were connected Y-Δ? YES ii. the transformers were connected Δ-Y? YES

iii. the transformers were connected Δ- Δ? NO

Name (1 pt):___________________________________________________________________

3. (25 pts) Note: This problem is identical to Example B3.2 in Module B3 of the class notes. As indicated in our last class, you are allowed to respond to this quiz question using the work you did at home and brought with you to the exam (just staple your answers to the quiz question). Three balanced three-phase loads are connected in parallel. Load 1 is Y-connected with an impedance of 150 + j50 ; load 2 is delta-connected with an impedance of 900 + j600; and load 3 is 95.04 kVA at 0.6 pf leading. The loads are fed from a distribution line with an impedance of 3 + j24. The magnitude of the line-to-neutral voltage at the load end of the line is 4.8 kV.

4. (25 pts) Note: This problem is identical to the way Example B3.2 was worked during the last class. As indicated then, you are allowed to respond to this quiz question using the work you did at home and brought with you to the exam (just staple your answers to the quiz question). Rework problem #3 in per-unit.