The ratings of a three-phase, three-winding transformer

Consider a source of voltage vt_ _ 10 ffiffiffi2 p sin2t_V, with an internal resistance of 1800 W. A transformer that can be considered as ideal is used to couple a 50-W resistive loadto the source. (a) Determine the transformer primary-to-secondary turns ratio required to ensure maximum power transfer by matching the load and source resistances.(b) Find the average power delivered to the load, assuming maximum power transfer

For the circuit shown in Figure 3.31, determine voutt_.

A single-phase transformer has 2000 turns on the primary winding and 500 turns on the secondary. Winding resistances are R1 _ 2 W and R2 _ 0:125 W; leakage reactances are X1 _ 8 W and X2 _ 0:5 W. The resistance load on the secondary is 12 W. (a) If the applied voltage at the terminals of the primary is 1000 V, determine V2 at the load terminals of the transformer, neglecting magnetizing current. (b) If the voltage regulation is defined as the di_erence between the voltage magnitude at the load terminals of the transformer at full load and at no load in percent of full-load voltage with input voltage held constant, compute the percent voltage regulation.

A single-phase step-down transformer is rated 15 MVA, 66 kV/11.5 kV. With the 11.5 kV winding short-circuited, rated current flows when the voltage applied to the primary is 5.5 kV. The power input is read as 100 kW. Determine Req1 and Xeq1 in ohms referred to the high-voltage winding.

For the transformer in Problem 3.10, the open-circuit test with 11.5 kV applied results in a power input of 65 kW and a current of 30 A. Compute the values for Gc and Bm in siemens referred to the high- voltage winding. Compute the eciency of the transformer for a load of 10 MW at 0.8 PF lagging at rated voltage.

The following data are obtained when open-circuit and short-circuit tests are performed on a single-phase, 50-kVA, 2400/240-volt, 60-Hz distribution transformer. VOLTAGE(volts) CURRENT(amperes) POWER(watts) Measurements on low-voltage side with high-voltage winding open 240 4.85 173 Measurements on high-voltage side with low-voltage winding shorted 52.0 20.8 650 (a) Neglecting the series impedance, determine the exciting admittance referred to the high-voltage side. (b) Neglecting the exciting admittance, determine the equivalent series impedance referred to the high-voltage side. (c) Assuming equal series impedances for the primary and referred secondary, obtain an equivalent T-circuit referred to the high-voltage side.

A single-phase 50-kVA, 2400/240-volt, 60-Hz distribution transformer has a 1-ohm equivalent leakage reactance and a 5000-ohm magnetizing reactance referred to the high-voltage side. If rated voltage is applied to the high-voltage winding, calculate the open-circuit secondary voltage. Neglect I2R and G2 cV losses. Assume equal series leakage reactances for the primary and referred secondary.

A single-phase 50-kVA, 2400/240-volt, 60-Hz distribution transformer is used as a step-down transformer at the load end of a 2400-volt feeder whose series impedance is (1.0 + j2.0) ohms. The equivalent series impedance of the transformer is 1:0 _ j2:5_ ohms referred to the high-voltage (primary) side. The transformer is delivering rated load at 0.8 power factor lagging and at rated secondary voltage. Neglecting the transformer exciting current, determine (a) the voltage at the transformer primary terminals, (b) the voltage at the sending end of the feeder, and (c) the real and reactive power delivered to the sending end of the feeder.

Rework Problem 3.14 if the transformer is delivering rated load at rated secondary voltage and at (a) unity power factor, (b) 0.8 power factor leading. Compare the results with those of Problem 3.14.

A single-phase, 50-kVA, 2400/240-V, 60-Hz distribution transformer has the following parameters: Resistance of the 2400-V winding: R1 = 0:75 W Resistance of the 240-V winding: R2 = 0:0075 W Leakage reactance of the 2400-V winding: X1 = 1:0 W Leakage reactance of the 240-V winding: X2 = 0:01 W Exciting admittance on the 240-V side _ 0:003 - j0:02 S (a) Draw the equivalent circuit referred to the high-voltage side of the transformer. (b) Draw the equivalent circuit referred to the low-voltage side of the transformer. Show the numerical values of impedances on the equivalent circuits.

The transformer of Problem 3.16 is supplying a rated load of 50 kVA at a rated secondary voltage of 240 V and at 0.8 power factor lagging. Neglecting the transformer exciting current, (a) Determine the input terminal voltage of the transformer on the high-voltage side. (b) Sketch the corresponding phasor diagram. (c) If the transformer is used as a step-down transformer at the load end of a feeder whose impedance is 0:5 _ j2:0 W, find the voltage VS and the power factor at the sending end of the feede

Using the transformer ratings as base quantities, work Problem 3.13 in per-unit.

Using the transformer ratings as base quantities, work Problem 3.14 in per-unit.

Using base values of 20 kVA and 115 volts in zone 3, rework Example 3.4.

Rework Example 3.5, using Sbase3f _ 100 kVA and VbaseLL _ 600 volts.

A balanced Y-connected voltage source with Eag _ 277 0? volts is applied to a balanced-Y load in parallel with a balanced-D load, where ZY _ 20 _ j10 and ZD _ 30 ? j15 ohms. The Y load is solidly grounded. Using base values of Sbase1f _ 10 kVA and VbaseLN _ 277 volts, calculate the source current Ia in per-unit and in amperes.

Figure 3.32 shows the one-line diagram of a three-phase power system. By selecting a common base of 100 MVA and 22 kV on the generator side, draw an impedance diagram showing all impedances including the load impedance in per-unit. The data are given as follows: G: 90 MVA 22 kV x = 0:18 per unit T1: 50 MVA 22/220 kV x = 0:10 per unit T2: 40 MVA 220/11 kV x = 0:06 per unit T3: 40 MVA 22/110 kV x = 0:064 per unit T4: 40 MVA 110/11 kV x = 0:08 per unit M: 66.5 MVA 10.45 kV x = 0:185 per unit Lines 1 and 2 have series reactances of 48.4 and 65.43 W, respectively. At bus 4, the three-phase load absorbs 57 MVA at 10.45 kV and 0.6 power factor lagging.

For Problem 3.18, the motor operates at full load, at 0.8 power factor leading, and at a terminal voltage of 10.45 kV. Determine (a) the voltage at bus 1, the generator bus, and (b) the generator and motor internal EMFs.

Consider a single-phase electric system shown in Figure 3.33. Transformers are rated as follows: XY 15 MVA, 13.8/138 kV, leakage reactance 10% YZ 15 MVA, 138/69 kV, leakage reactance 8% With the base in circuit Y chosen as 15 MVA, 138 kV, determine the per-unit impedance of the 500 W resistive load in circuit Z, referred to circuits Z, Y, and X. Neglecting magnetizing currents, transformer resistances, and line impedances, draw the impedance diagram in per unit.

A bank of three single-phase transformers, each rated 30 MVA, 38.1/3.81 kV, are connected in YD with a balanced load of three 1 - W, wye-connected resistors. Choosing a base of 90 MVA, 66 kV for the high-voltage side of the three-phase transformer, specify the base for the low-voltage side. Compute the per-unit resistance of the load on the base for the low-voltage side. Also, determine the load resistance inohms referred to the high-voltage side and the per-unit value on the chosen base.

A three-phase transformer is rated 500 MVA, 220 Y/22 D kV. The wye-equivalent short-circuit impedance, considered equal to the leakage reactance, measured on the low-voltage side is 0.1 W. Compute the per-unit reactance of the transformer. In a system in which the base on the high-voltage side of the transformer is 100 MVA, 230 kV, what value of the per-unit reactance should be used to represent this transformer?

For the system shown in Figure 3.34, draw an impedance diagram in per unit, by choosing 100 kVA to be the base kVA and 2400 V as the base voltage for the generators.

Consider three ideal single-phase transformers (with a voltage gain of h) put together as a delta wye three-phase bank as shown in Figure 3.35. Assuming positive-sequence voltages for Van, Vbn, and Vcn, find Va0n0 , Vb0n0 , and Vc 0n0 in terms of Van, Vbn, and Vcn, respectively. (a) Would such relationships hold for the line voltages as well? (b) Looking into the current relationships, express I 0 a, I 0 b, and I 0 c in terms of Ia, Ib, and Ic, respectively. (c) Let S0 and S be the per-phase complex power output and input, respectively. Find S0 in terms of S.

Reconsider Problem 3.29. If Van, Vbn, and Vcn are a negative-sequence set, how would the voltage and current relationships change? (a) If C1 is the complex positive-sequence voltage gain in Problem 3.29, and C2 is the negative sequence complex voltage gain, express the relationship between C1 and C2.

If positive-sequence voltages are assumed and the wye-delta connection is considered, again with ideal transformers as in Problem 3.29, find the complex voltage gain C3. (a) What would the gain be for a negative-sequence set? (b) Comment on the complex power gain. (c) When terminated in a symmetric wye-connected load, find the referred impedance Z0L, the secondary impedance ZL referred to primary (i.e., the per-phase driving-point impedance on the primary side), in terms of ZL and the complex voltage gain C.

Determine the positive- and negative-sequence phase shifts for the three-phase transformers shown in Figure 3.36.

Consider the three single-phase two-winding transformers shown in Figure 3.37. The high-voltage windings are connected in Y. (a) For the low-voltage side, connect the windings in D, place the polarity marks, and label the terminals a, b, and c in accordance with the American standard. (b) Relabel the terminals a', b', and c' such that VAN is 9 out of phase with Va'n for positive sequence.

Three single-phase, two-winding transformers, each rated 450 MVA, 20 kV/288.7 kV, with leakage reactance Xeq _ 0:10 per unit, are connected to form a three-phase bank. The high-voltage windings are connected in Y with a solidly grounded neutral. Draw the per-unit equivalent circuit if the low- voltage windings are connected (a) in D with American standard phase shift, (b) in Y with an open neutral. Use the transformer ratings as base quantities. Winding resistances and exciting current are neglected.

Consider a bank of three single-phase two-winding transformers whose high-voltage terminals are connected to a three-phase, 13.8-kV feeder. The low-voltage terminals are connected to a three- phase substation load rated 2.1 MVA and 2.3 kV. Determine the required voltage, current, and MVA ratings of both windings of each transformer, when the high-voltage/low-voltage windings are connected (a) YD, (b) DY,(c) YY, and (d) DD.

Three single-phase two-winding transformers, each rated 25 MVA, 34.5/13.8 kV, are connected to form a three-phase DD bank. Balanced positive-sequence voltages are applied to the high-voltage terminals, and a balanced, resistive Y load connected to the low-voltage terminals absorbs 75 MW at 13.8 kV. If one of the single-phase transformers is removed (resulting in an open-D connection) and the balanced load is simultaneously reduced to 43.3 MW (57.7% of the original value), determine (a) the load voltages Van, Vbn, and Vcn; (b) load currents Ia, Ib, and Ic; and (c) the MVA supplied by each of the remaining two transformers. Are balanced voltages still applied the load? Is the open-D transformer overloaded?

Three single-phase two-winding transformers, each rated 25 MVA, 38.1/3.81 kV, are connected to form a three-phase YD bank with a balanced Y-connected resistive load of 0.6 W per phase on the low-voltage side. By choosing a base of 75 MVA (three phase) and 66 kV (line-to-line) for the high voltage side of the transformer bank, specify the base quantities for the low-voltage side. Determine the per-unit resistance of the load on the base for the low-voltage side. Then determine the load resistance RL in ohms referred to the high-voltage side and the per-unit value of this load resistance on the chosen base.

Consider a three-phase generator rated 300 MVA, 23 kV, supplying a system load of 240 MVA and 0.9 power factor lagging at 230 kV through a 330 MVA, 23 D/ 230 Y-kV step-up transformer with a leakage reactance of 0.11 per unit. (a) Neglecting the exciting current and choosing base values at the load of 100 MVA and 230 kV, find the phasor currents IA, IB, and IC supplied to the load in per unit. (b) By choosing the load terminal voltage VA as reference, specify the proper base for the generator circuit and determine the generator voltage V as well as the phasor currents Ia, Ib, and Ic, from the generator. (Note: Take into account the phase shift of the transformer.) (c) Find the generator terminal voltage in kV and the real power supplied by the generator in MW. (d) By omitting the transformer phase shift altogether, check to see whether you get the same magnitude of generator terminal voltage and real power delivered by the generator.

The leakage reactance of a three-phase, 300-MVA, 230 Y/23 D-kV transformer is 0.06 per unit based on its own ratings. The Y winding has a solidly grounded neutral. Draw the per-unit equivalent circuit. Neglect the exciting admittance and assume American standard phase shift.

Choosing system bases to be 240/24 kV and 100 MVA, redraw the per-unit equivalent circuit for Problem 3.39.

Consider the single-line diagram of the power system shown in Figure 3.38. Equipment ratings are: Generator 1: 1000 MVA, 18 kV, X00 = 0:2 per unit Generator 2: 1000 MVA, 18 kV, X00 = 0:2 Synchronous motor 3: 1500 MVA, 20 kV, X00 _ 0:2 Three-phase DY transformers T1, T2, T3, T4: 1000 MVA, 500 kV Y/20 kV D, X = 0:1 Three-phase YY transformer T5: 1500 MVA, 500 kV Y/20 kV Y, X _ 0:1 Neglecting resistance, transformer phase shift, and magnetizing reactance, draw the equivalent reactance diagram. Use a base of 100 MVA and 500 kV for the 50-ohmline. Determine the per-unit reactances.

For the power system in Problem 3.41, the synchronous motor absorbs 1500 MW at 0.8 power factor leading with the bus 3 voltage at 18 kV. Determine the bus 1 and bus 2 voltages in kV. Assume that generators 1 and 2 deliver equal real powers and equal reactive powers. Also assume a balanced three-phase system with positive-sequence sources.

Three single-phase transformers, each rated 10 MVA, 66.4/12.5 kV, 60 Hz, with an equivalent series reactance of 0.1 per unit divided equally between primary and secondary, are connected in a three- phase bank. The high-voltage windings are Y connected and their terminals are directly connected to a 115-kV three-phase bus. The secondary terminals are all shorted together. Find the currents entering the high-voltage terminals and leaving the low-voltage terminals if the low-voltage windings are (a) Y connected, (b) D connected.

A 130-MVA, 13.2-kV three-phase generator, which has a positive-sequence reactance of 1.5 per unit on the generator base, is connected to a 135-MVA, 13.2 D/115 Y-kV step-up transformer with a series impedance of 0:005 _ j0:1_ per unit on its own base. (a) Calculate the per-unit generator reactance on the transformer base. (b) The load at the transformer terminals is 15 MW at unity power factor and at 115 kV. Choosing the transformer high-side voltage as the reference phasor, draw a phasor diagram for this condition. (c) For the condition of part (b), find the transformer low-side voltage and the generator internal voltage behind its reactance. Also compute the generator output power and power factor.

Figure 3.39 shows a one-line diagram of a system in which the three-phase generator is rated 300 MVA, 20 kV with a subtransient reactance of 0.2 per unit and with its neutral grounded through a 0.4- W reactor. The transmission line is 64 km long with a series reactance of 0.5 W/km. The three-phase transformer T1 is rated 350 MVA, 230/ 20 kV with a leakage reactance of 0.1 per unit. Transformer T2 is composed of three single-phase transformers, each rated 100 MVA, 127/13.2 kV with a leakage reactance of 0.1 per unit. Two 13.2-kV motors M1 and M2 with a subtransient reactance of 0.2 per unit for each motor represent the load. M1 has a rated input of 200 MVA with its neutral grounded through a 0.4-W current-limiting reactor. M2 has a rated input of 100 MVA with its neutral not connected to ground. Neglect phase shifts associated with the transformers. Choose the generator rating as base in the generator circuit and draw the positive-sequence reactance diagram showing all reactances in per unit.

The motors M1 and M2 of Problem 3.45 have inputs of 120 and 60 MW, respectively, at 13.2 kV, and both operate at unity power factor. Determine the generator terminal voltage and voltage regulation of the line. Neglect transformer phase shifts.

Consider the one-line diagram shown in Figure 3.40. The three-phase transformer bank is made up of three identical single-phase transformers, each specified by Xl = 0:24 W (on the low-voltage side), negligible resistance and magnetizing current, and turns ratio h = N2=N1 = 10. The transformer bank is delivering 100 MW at 0.8 PF lagging to a substation bus whose voltage is 230 kV. (a) Determine the primary current magnitude, primary voltage (line-to-line) magnitude, and the three- phase complex power supplied by the generator. Choose the lineto- neutral voltage at the bus, Va'n1', as the reference. Account for the phase shift, and assume positive-sequence operation. (b) Find the phase shift between the primary and secondary voltages.

With the same transformer banks as in Problem 3.47, Figure 3.41 shows the one-line diagram of a generator, a step-up transformer bank, a transmission line, a step-down transformer bank, and an impedance load. The generator terminal voltage is 15 kV (line-to-line). (a) Draw the per-phase equivalent circuit, accounting for phase shifts for positivesequence operation. (b) By choosing the line-to-neutral generator terminal voltage as the reference, determine the magnitudes of the generator current, transmission-line current, load current, and line-to-line load voltage. Also, find the three-phase complex power delivered to the load.

Consider the single-line diagram of a power system shown in Figure 3.42 with equipment ratings given below: Generator G1: 50 MVA, 13.2 kV, x = 0:15 ru Generator G2: 20 MVA, 13.8 kV, x = 0:15 ru three-phase DY transformer T1: 80 MVA, 13.2 D/165 Y kV, X = 0:1 ru three-phase YD transformer T2: 40 MVA, 165 Y/13.8 D kV, X = 0:1 ru Load: 40 MVA, 0.8 PF lagging, operating at 150 kV Choose a base of 100 MVA for the system and 132-kV base in the transmission-line circuit. Let the load be modeled as a parallel combination of resistance and inductance. Neglect transformer phase shifts. Draw a per-phase equivalent circuit of the system showing all impedances in per unit.

A single-phase three-winding transformer has the following parameters: Z1 = Z2 = Z3 = 0 + j0:05, Gc = 0, and Bm =0:2 per unit. Three identical transformers, as described, are connected with their primaries in Y (solidly grounded neutral) and with their secondaries and tertiaries in D. Draw the per- unit sequence networks of this transformer bank.

The ratings of a three-phase three-winding transformer are: Primary (1): Y connected, 66 kV, 15 MVA Secondary (2): Y connected, 13.2 kV, 10 MVA Tertiary (3): D connected, 2.3 kV, 5 MVA Neglecting winding resistances and exciting current, the per-unit leakage reactances are: X12 = 0:08 on a 15-MVA; 66-kV base X13 = 0:10 on a 15-MVA; 66-kV base X23 = 0:09 on a 10-MVA; 13:2-kV base (a) Determine the per-unit reactances X1, X2, X3 of the equivalent circuit on a 15-MVA, 66-kV base at the primary terminals. (b) Purely resistive loads of 7.5 MW at 13.2 kV and 5 MW at 2.3 kV are connected to the secondary and tertiary sides of the transformer, respectively. Draw the per-unit impedance diagram, showing the per-unit impedances on a 15-MVA, 66-kV base at the primary terminals.

Draw the per-unit equivalent circuit for the transformers shown in Figure 3.34. Include ideal phase- shifting transformers showing phase shifts determined in Problem 3.32. Assume that all windings have the same kVA rating and that the equivalent leakage reactance of any two windings with the third winding open is 0.10 per unit. Neglect the exciting admittance.

The ratings of a three-phase, three-winding transformer are: Primary: Y connected, 66 kV, 15 MVA Secondary: Y connected, 13.2 kV, 10 MVA Tertiary: D connected, 2.3 kV, 5 MVA Neglecting resistances and exciting current, the leakage reactances are: XPS =0:07 per unit on a 15-MVA; 66-kV base XPT = 0:09 per unit on a 15-MVA; 66-kV base XST = 0:08 per unit on a 10-MVA; 13:2-kV base Determine the per-unit reactances of the per-phase equivalent circuit using a base of 15 MVA and 66 kV for the primary.

An infinite bus, which is a constant voltage source, is connected to the primary of the three-winding transformer of Problem 3.53. A 7.5-MVA, 13.2-kV synchronous motor with a subtransient reactance of 0.2 per unit is connected to the transformer secondary. A 5-MW, 2.3-kV three-phase resistive load is connected to the tertiary. Choosing a base of 66 kV and 15 MVA in the primary, draw the impedance diagram of the system showing per-unit impedances. Neglect transformer exciting current, phase shifts, and all resistances except the resistive load.

A single-phase 10-kVA, 2300/230-volt, 60-Hz two-winding distribution transformer is connected as an autotransformer to step up the voltage from 2300 to 2530 volts. (a) Draw a schematic diagram of this arrangement, showing all voltages and currents when delivering full load at rated voltage. (b) Find the permissible kVA rating of the autotransformer if the winding currents and voltages are not to exceed the rated values as a two-winding transformer. How much of this kVA rating is transformed by magnetic induction? (c) The following data are obtained from tests carried out on the transformer when it is connected as a two-winding transformer: Open-circuit test with the low-voltage terminals excited: Applied voltage _ 230 V, Input current _ 0:45 A, Input power _ 70 W. Short-circuit test with the high-voltage terminals excited: Applied voltage _ 120 V, Input current _ 4:5 A, Input power _ 240 W. Based on the data, compute the eciency of the autotransformer corresponding to full load, rated voltage, and 0.8 power factor lagging. Comment on why the eciency is higher as an autotransformer than as a two-winding transformer.

Three single-phase two-winding transformers, each rated 3 kVA, 220/110 volts, 60 Hz, with a 0.10 per-unit leakage reactance, are connected as a three-phase extended D autotransformer bank, as shown in Figure 3.31(c). The low-voltage D winding has a 110 volt rating. (a) Draw the positive- sequence phasor diagram and show that the highvoltage winding has a 479.5 volt rating. (b) A three- phase load connected to the low voltage terminals absorbs 6 kW at 110 volts and at 0.8 power factor lagging. Draw the per-unit impedance diagram and calculate the voltage and current at the high- voltage terminals. Assume positive-sequence operation.

A two-winding single-phase transformer rated 60 kVA, 240/1200 V, 60 Hz, has an effciency of 0.96 when operated at rated load, 0.8 power factor lagging. This transformer is to be utilized as a 1440/1200-V step-down autotransformer in a power distribution system. (a) Find the permissible kVA rating of the autotransformer if the winding currents and voltages are not to exceed the ratings as a twowinding transformer. Assume an ideal transformer. (b) Determine the effciency of the autotransformer with the kVA loading of part (a) and 0.8 power factor leading.

A single-phase two-winding transformer rated 90 MVA, 80/120 kV is to be connected as an autotransformer rated 80/200 kV. Assume that the transformer is ideal. (a) Draw a schematic diagram of the ideal transformer connected as an autotransformer, showing the voltages, currents, and dot notation for polarity. (b) Determine the permissible kVA rating of the autotransformer if the winding currents and voltages are not to exceed the rated values as a two-winding transformer. How much of the kVA rating is transferred by magnetic induction?

The two parallel lines in Example 3.13 supply a balanced load with a load current of 1:0 ?30? per unit. Determine the real and reactive power supplied to the load bus from each parallel line with (a) no regulating transformer, (b) the voltage-magnituderegulating transformer in Example 3.13(a), and (c) the phase-angle-regulating transformer in Example 3.13(b). Assume that the voltage at bus abc is adjusted so that the voltage at bus a0b0c0 remains constant at 1:0 0? per unit. Also assume positive sequence. Comment on the e_ects of the regulating transformers.

PowerWorld Simulator case Problem 3.60 duplicates Example 3.13 except that a resistance term of 0.06 per unit has been added to the transformer and 0.05 per unit to the transmission line. Since the system is no longer lossless, a field showing the real power losses has also been added to the one- line. With the LTC tap fixed at 1.05, plot the real power losses as the phase shift angle is varied from -10 to +10 degrees. What value of phase shift minimizes the system losses?

Repeat Problem 3.60, except keep the phase-shift angle fixed at 3.0 degrees, while varying the LTC tap between 0.9 and 1.1. What tap value minimizes the real power losses?

Rework Example 3.12 for a +10% tap, providing a 10% increase for the high-voltage winding.

A 23/230-kV step-up transformer feeds a three-phase transmission line, which in turn supplies a 150- MVA, 0.8 lagging power factor load through a step-down 230/23-kV transformer. The impedance of the line and transformers at 230 kV is 18 + j60 W. Determine the tap setting for each transformer to maintain the voltage at the load at 23 kV.

The per-unit equivalent circuit of two transformers Ta and Tb connected in parallel, with the same nominal voltage ratio and the same reactance of 0.1 per unit on the same base, is shown in Figure 3.43. Transformer Tb has a voltage-magnitude step-up toward the load of 1.05 times that of Tb (that is, the tap on the secondary winding of Ta is set to 1.05). The load is represented by 0:8 _ j0:6 per unit at a voltage V2 = 1.0/0 per unit. Determine the complex power in per unit transmitted to the load through each transformer. Comment on how the transformers share the real and reactive powers.

Reconsider Problem 3.64 with the change that now Tb includes both a transformer of the same turns ratio as Ta and a regulating transformer with a 3? phase shift. On the base of Ta, the impedance of the two components of Tb is j0:1 per unit. Determine the complex power in per unit transmitted to the load through each transformer. Comment on how the transformers share the real and reactive powers.