Bibliography

Full-Wave Rectifiers

4.9 Bibliography

S. B. Dewan and A. Straughen, Power Semiconductor Circuits, Wiley, New York, 1975.

J. Dixon, Power Electronics Handbook, edited by M. H. Rashid, Academic Press, San Diego, 2001, Chapter 12.

E. W. Kimbark, Direct Current Transmission, Wiley-Interscience, New York, 1971.

P. T. Krein, Elements of Power Electronics, Oxford University Press, 1998.

Y.-S. Lee and M. H. L. Chow, Power Electronics Handbook, edited by M. H. Rashid, Academic Press, San Diego, 2001, Chapter 10.

N. Mohan, T. M. Undeland, and W. P. Robbins, Power Electronics: Converters, Applications, and Design,3d ed., Wiley, New York, 2003.

M. H. Rashid, Power Electronics: Circuits, Devices, and Systems,3d ed., Prentice-Hall, Upper Saddle River, N.J., 2004.

B. Wu, High-Power Converters and AC Drives, Wiley, New York, 2006.

Problems

Uncontrolled Single-Phase Rectifiers

4-1. A single-phase full-wave bridge rectifier has a resistive load of 18 and an ac source of 120-V rms. Determine the average, peak, and rms currents in the load and in each diode.

4-2. A single-phase rectifier has a resistive load of 25 . Determine the average current and peak reverse voltage across each of the diodes for (a) a bridge rectifier with an ac source of 120 V rms and 60 Hz and (b) a center-tapped transformer rectifier with 120 V rms on each half of the secondary winding.

4-3. A single-phase bridge rectifier has an RLload with R15 and L60 mH.

The ac source is v_s100 sin (377t) V. Determine the average and rms currents in the load and in each diode.

4-4. A single-phase bridge rectifier has an RLload with R10 and L25 mH.

The ac source is v_s170 sin (377t) V. Determine the average and rms currents in the load and in each diode.

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Problems 165

4-5. A single-phase bridge rectifier has an RLload with R15 and L30 mH.

The ac source is 120 V rms, 60 Hz. Determine (a) the average load current, (b) the power absorbed by the load, and (c) the power factor.

4-6. A single-phase bridge rectifier has an RLload with R12 and L20 mH.

The ac source is 120 V rms and 60 Hz. Determine (a) the average load current, (b) the power absorbed by the load, and (c) the power factor.

4-7. A single-phase center-tapped transformer rectifier has an ac source of 240 V rms and 60 Hz. The overall transformer turns ratio is 3:1 (80 V between the extreme ends of the secondary and 40 V on each tap). The load is a resistance of 4 . Determine (a) the average load current, (b) the rms load current, (c) the average source current, and (d) the rms source current. Sketch the current waveforms of the load and the source.

4-8. Design a center-tapped transformer rectifier to produce an average current of 10.0 A in a 15-resistive load. Both 120- and 240-V rms 60-Hz sources are available. Specify which source to use and specify the turns ratio of the transformer.

4-9. Design a center-tapped transformer rectifier to produce an average current of 5.0 A in an RLload with R10 and L50 mH. Both 120- and 240-V rms 60-Hz sources are available. Specify which source to use and specify the turns ratio of the transformer.

4-10. An electromagnet is modeled as a 200-mH inductance in series with a 4- resistance. The average current in the inductance must be 10 A to establish the required magnetic field. Determine the amount of additional series resistance required to produce the required average current from a bridge rectifier supplied from a single-phase 120-V, 60-Hz source.

4-11. The full-wave rectifier of Fig. 4-3ahas v_s(t) 170 sin tV, R3 , L15 mH, V_dc48 V, and 2(60) rad/s. Determine (a) the power absorbed by the dc source, (b) the power absorbed by the resistor, and (c) the power factor. (d) Estimate the peak-to-peak variation in the load current by considering only the first ac term in the Fourier series for current.

4-12. The full-wave rectifier of Fig. 4-3ahas v_s(t) 340 sin tV, R5 , L40 mH, V_dc96 V, and 2(60) rad/s. Determine (a) the power absorbed by the dc source, (b) the power absorbed by the resistor, and (c) the power factor. (d) Estimate the peak-to-peak variation in the load current by considering only the first ac term in the Fourier series for current.

4-13. The peak-to-peak variation in load current in Example 4-1 based on I₂was estimated to be 6.79 A. Compare this estimate with that obtained from a PSpice simulation. (a) Use the default diode model Dbreak. (b) Modify the diode model to make n0.01 to approximate an ideal diode.

4-14. (a) In Example 4-3, the inductance is changed to 8 mH. Simulate the circuit in PSpice and determine whether the inductor current is continuous or discontinuous.

Determine the power absorbed by the dc voltage using PSpice. (b) Repeat part (a), using L4 mH.

4-15. The single-phase full-wave bridge rectifier of Fig. 4-5ahas an RL-source load with R4 , L40 mH, and V_dc24 V. The ac source is 120 V rms at 60 Hz.

Determine (a) the power absorbed by the dc source, (b) the power absorbed by the resistor, and (c) the power factor.

166 C H A P T E R 4 Full-Wave Rectifiers

4-16. The single-phase full-wave bridge rectifier of Fig. 4-5ahas an RL-source load with R5 , L60 mH, and V_dc36 V. The ac source is 120 V rms at 60 Hz.

Determine (a) the power absorbed by the dc source, (b) the power absorbed by the resistor, and (c) the power factor.

4-17. Simulate the circuit of Prob. 4-16 using L40 mH and again with L100 H.

Discuss the differences in the behavior of the circuits for the two inductors.

Observe steady-state conditions. Use the PSpice default diode model.

4-18. The full-wave rectifier of Fig. 4-6 has a 120-V rms 60 Hz source and a load resistance of 200 . Determine the filter capacitance required to limit the peak- to-peak output voltage ripple to 1 percent of the dc output. Determine the peak and average diode currents.

4-19. The full-wave rectifier of Fig. 4-6 has a 60-Hz ac source with V_m100 V. It is to supply a load that requires a dc voltage of 100 V and will draw 0.5 A.

Determine the filter capacitance required to limit the peak-to-peak output voltage ripple to 1 percent of the dc output. Determine the peak and average diode currents.

4-20. In Example 3-9, the half-wave rectifier of Fig. 3-11ahas a 120 V rms source at 60 Hz, R500 . The capacitance required for a 1 percent ripple in output voltage was determined to be 3333 F. Determine the capacitance required for a 1 percent ripple if a full-wave rectifier is used instead. Determine the peak diode currents for each circuit. Discuss the advantages and disadvantages of each circuit.

4-21. Determine the output voltage for the full-wave rectifier with an LCfilter of Fig. 4-8aif L10 mH and (a) R7 and (b) R20 . The source is 120 V rms at 60 Hz. Assume the capacitor is sufficiently large to produce a ripple-free output voltage. (c) Modify the PSpice circuit in Example 4-5 to determine V_ofor each case. Use the default diode model.

4-22. For the full-wave rectifier with an LCfilter in Example 4-5, the inductor has a series resistance of 0.5 . Use PSpice to determine the effect on the output voltage for each load resistance.

Controlled Single-phase Rectifiers

4-23. The controlled single-phase bridge rectifier of Fig. 4-10ahas a 20-resistive load and has a 120-V rms, 60-Hz ac source. The delay angle is 45. Determine (a) the average load current, (b) the rms load current, (c) the rms source current, and (d) the power factor.

4-24. Show that the power factor for the controlled full-wave rectifier with a resistive load is

4-25. The controlled single-phase full-wave bridge rectifier of Fig. 4-11ahas an RL load with R25 and L50 mH. The source is 240 V rms at 60 Hz.

Determine the average load current for (a) 15and (b) 75.

4-26. The controlled single-phase full-wave bridge rectifier of Fig. 4-11ahas an RL load with R30 and L75 mH. The source is 120 V rms at 60 Hz.

Determine the average load current for (a) 20and (b) 80. pfA1

sin(2) 2

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Problems 167

4-27. Show that the power factor for the full-wave rectifier with RLload where Lis large and the load current is considered dc is 2 /.

4-28. A 20-resistive load requires an average current that varies from 4.5 to 8.0 A.

An isolation transformer is placed between a 120-V rms 60-Hz ac source and a controlled single-phase full-wave rectifier. Design a circuit to meet the current requirements. Specify the transformer turns ratio and the range of delay angle.

4-29. An electromagnet is modeled as a 100-mH inductance in series with a 5- resistance. The average current in the inductance must be 10 A to establish the required magnetic field. Determine the delay angle required for a controlled single- phase rectifier to produce the required average current from a single-phase 120-V, 60-Hz source. Determine if the current is continuous or discontinuous. Estimate the peak-to-peak variation in current based on the first ac term in the Fourier series.

4-30. The full-wave converter used as an inverter in Fig. 4-14 has an ac source of 240 V rms at 60 Hz, R10 , L0.8 H, and V_dc100 V. The delay angle for the converter is 105. Determine the power supplied to the ac system from the dc source. Estimate the peak-to-peak ripple in load current from the first ac term in the Fourier series.

4-31. An array of solar cells produces 100 V dc. A single-phase ac power system is 120 V rms at 60 Hz. (a) Determine the delay angle for the controlled converter in the arrangement of Fig. 4-14 (V_dc100) such that 2000 W is transmitted to the ac system. Assume Lis large enough to produce a current that is nearly ripple-free. The equivalent resistance is 0.8 . Assume that the converter is lossless. (b) Determine the power supplied by the solar cells. (c) Estimate the value of inductance such that the peak-to-peak variation in solar cell current is less than 2.5 A.

4-32. An array of solar panels produces a dc voltage. Power produced by the solar panels is to be delivered to an ac power system. The method of interfacing the solar panels with the power system is via a full-wave SCR bridge as shown in Fig. 4-14 except with the dc source having the opposite polarity. Individual solar panels produce a voltage of 12 V. Therefore, the voltage from the solar panel array can be established at any multiple of 12 by connecting the panels in appropriate combinations. The ac source is12(120) sin (377t) V. The resistance is 1 .

12

Determine values of V_dc, delay angle , and inductance Lsuch that the power delivered to the ac system is 1000 W and the maximum variation in solar panel current is no more than 10 percent of the average current. There are several solutions to this problem.

4-33. A full-wave converter operating as an inverter is used to transfer power from a wind generator to a single-phase 240-V rms 60-Hz ac system. The generator produces a dc output of 150 V and is rated at 5000 W. The equivalent resistance in the generator circuit is 0.6 . Determine (a) the converter delay angle for rated generator output power, (b) the power absorbed by the ac system, and (c) the inductance required to limit the current peak-to-peak ripple to 10 percent of the average current.

Three-phase Uncontrolled Rectifiers

4-34. A three-phase rectifier is supplied by a 480-V rms line-to-line 60-Hz source. The load is a 50-resistor. Determine (a) the average load current, (b) the rms load current, (c) the rms source current, and (d) the power factor.

168 C H A P T E R 4 Full-Wave Rectifiers

4-35. A three-phase rectifier is supplied by a 240-V rms line-to-line 60-Hz source. The load is an 80-resistor. Determine (a) the average load current, (b) the rms load current, (c) the rms source current, and (d) the power factor.

4-36. A three-phase rectifier is supplied by a 480-V rms line-to-line 60-Hz source. The RLload is a 100-resistor in series with a 15-mH inductor. Determine (a) the average and rms load currents, (b) the average and rms diode currents, (c) the rms source current, and (d) the power factor.

4-37. Use PSpice to simulate the three-phase rectifier of Prob. 4-31. Use the default diode model Dbreak. Determine the average and rms values of load current, diode current, and source current. Compare your results to Eq. (4-41). How much power is absorbed by the diodes?

4-38. Using the PSpice circuit of Example 4-12, determine the harmonic content of the line current in the ac source. Compare the results with Eq. (4-46). Determine the total harmonic distortion of the source current.

Three-phase Controlled Rectifiers

4-39. The three-phase controlled rectifier of Fig. 4-20ais supplied from a 4160-V rms line-to-line 60-Hz source. The load is a 120-resistor. (a) Determine the delay angle required to produce an average load current of 25 A. (b) Estimate the amplitudes of the voltage harmonics V₆, V₁₂, and V₁₈. (c) Sketch the currents in the load, S₁, S₄, and phase Aof the ac source.

4-40. The three-phase controlled rectifier of Fig. 4-20ais supplied from a 480-V rms line-to-line 60-Hz source. The load is a 50-resistor. (a) Determine the delay angle required to produce an average load current of 10 A. (b) Estimate the amplitudes of the voltage harmonics V₆, V₁₂, and V₁₈. (c) Sketch the currents in the load, S₁, S₄, and phase Aof the ac source.

4-41. The six-pulse controlled three-phase converter of Fig. 4-20ais supplied from a 480-V rms line-to-line 60-Hz three-phase source. The delay angle is 35, and the load is a series RLcombination with R50 and L50 mH. Determine (a) the average current in the load, (b) the amplitude of the sixth harmonic current, and (c) the rms current in each line from the ac source.

4-42. The six-pulse controlled three-phase converter of Fig. 4-20ais supplied from a 480-V rms line-to-line 60-Hz three-phase source. The delay angle is 50, and the load is a series RLcombination with R10 and L10 mH. Determine (a) the average current in the load, (b) the amplitude of the sixth harmonic current, and (c) the rms current in each line from the ac source.

4-43. The six-pulse controlled three-phase converter of Fig. 4-20ais supplied form a 480-V rms line-to-line 60-Hz three-phase source. The load is a series RL combination with R20 . (a) Determine the delay angle required for an average load current of 20 A. (b) Determine the value of Lsuch that the first ac current term (n6) is less than 2 percent of the average current. (c) Verify your results with a PSpice simulation.

4-44. A three-phase converter is operating as an inverter and is connected to a 300-V dc source as shown in Fig. 4-23a. The ac source is 240 V rms line to line at 60 Hz.

The resistance is 0.5 , and the inductor is large enough to consider the load current to be ripple-free. (a) Determine the delay angle such that the output har80679_ch04_111-170.qxd 12/15/09 3:48 PM Page 168

Problems 169

voltage of the converter is V_o280 V. (b) Determine the power supplied or absorbed by each component in the circuit. The SCRs are assumed to be ideal.

4-45. An inductor having superconducting windings is used to store energy. The controlled six-pulse three-phase converter of Fig. 4-20ais used to recover the stored energy and transfer it to a three-phase ac system. Model the inductor as a 1000-A current source load, and determine the required delay angle such that 1.5 MW is transferred to the ac system which is 4160 V line-to-line rms at 60 Hz.

What is the rms current in each phase of the ac system?

4-46. A power company has installed an array of solar cells to be used as an energy source. The array produces a dc voltage of 1000 V and has an equivalent series resistance of 0.1 . The peak-to-peak variation in solar cell current should not exceed 5 percent of the average current. The interface between the solar cell array and the ac system is the controlled six-pulse three-phase converter of Fig. 4-23a. A three-phase transformer is placed between the converter and a 12.5-kV line-to-line rms 60-Hz ac line. Design a system to transfer 100 kW to the ac power system from the solar cell array. (The ac system must absorb 100 kW.) Specify the transformer turns ratio, converter delay angle, and the values of any other circuit components. Determine the power loss in the resistance.

Dc Power Transmission

4-47. For the elementary dc transmission line represented in Fig. 4-24a, the ac voltage to each of the bridges is 345 kV rms line to line. The total line resistance is 15 , and the inductance is large enough to consider the dc current to be ripple-free.

AC system 1 is operated with 45.0, and ac system 2 has 134.4. (a) Determine the power absorbed or supplied by each ac system. (b) Determine the power loss in the line.

4-48. For the elementary dc transmission line represented in Fig. 4-24a, the ac voltage to each of the bridges is 230 kV rms line to line. The total line resistance is 12 , and the inductance is large enough to consider the dc current to be ripple-free.

The objective is to transmit 80 MW to ac system 2 from ac system 1 over the dc line. Design a set of operating parameters to accomplish this objective.

Determine the required current-carrying capacity of the dc line, and compute the power loss in the line.

4-49. For the elementary dc transmission line represented in Fig. 4-24a, the ac voltage to each of the bridges is 345 kV rms line-to-line. The total line resistance is 20 , and the inductance is large enough to consider the dc current to be ripple-free.

The objective is to transmit 300 MW to ac system 2 from ac system 1 over the dc line. Design a set of operating parameters to accomplish this objective. Determine the required current-carrying capacity of the dc line, and compute the power loss in the line.

Design Problems

4-50. Design a circuit that will produce an average current that is to vary from 8 to 12 A in an 8-resistor. Single-phase ac sources of 120 and 240 V rms at 60 Hz are available. The current must have a peak-to-peak variation of no more than 2.5 A.

Determine the average and rms currents and maximum voltage for each circuit

170 C H A P T E R 4 Full-Wave Rectifiers

element. Simulate your circuit in PSpice to verify that it meets the specifications.

Give alternative circuits that could be used to satisfy the design specifications, and give reasons for your selection.

4-51. Design a circuit that will produce a current which has an average value of 15 A in a resistive load of 20 . The peak-to-peak variation in load current must be no more than 10 percent of the dc current. Voltage sources available are a single- phase 480 V rms, 60 Hz source and a three-phase 480 V rms line-to-line 60 Hz source. You may include additional elements in the circuit. Determine the average, rms, and peak currents in each circuit element. Simulate your circuit in PSpice to verify that it meets the specifications. Give alternative circuits that could be used to satisfy the design specifications, and give reasons for your selection.

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