UNIVERSITI MALAYSIA PERLIS
DET309 - Power Electronics
Tutorial Power Computations 1. The voltage and current for a device (using the passive sign convention) are periodic functions with T = 100 ms described by 5 ,
0,
0
70
70
0,
4 ,
0
50
50
100
100
Determine (a) the instantaneous power, (b) the average power, and (c) the energy absorbed by the device in each period. 2. The voltage and current for a device (using the passive sign convention) are periodic functions with T = 20 ms described by 5 ,
0,
0
14
14
20
7 ,
5 ,
4 ,
0
6
10
6
10
20
Determine (a) the instantaneous power, (b) the average power, and (c) the energy absorbed by the device in each period. 3. Voltage and current (consistent with the passive sign convention) for a device are shown in Figure 1(a) and 1 (b). (a) State the expression for the instantaneous voltage and current, (b) Sketch the waveform of the instantaneous power, vs time, , (c) Determine the instantaneous power absorbed by the device, (d) Determine the energy absorbed by the device in one period, (e) Determine the average power absorbed by the device. v (t)
20 V
0
(t)
10 ms
20 ms
(a)
i (t)
20 A
(t)
6 ms
20 ms
- 15 A
(b)
Figure 1 4. A non‐sinusoidal periodic voltage has a Fourier series of
10 20 cos 2 60
30 cos 4 60
20
25
. This voltage is connected to a load which is a 5 Ω resistor and a 15 mH inductor connected in series, as in below. Determine the power absorbed by the load. Vm cos (nω0t + θn)
V1 cos (ω0t + θ1)
LOAD
Vdc
Equivalent circuits for Fourier analysis 5. A sinusoidal voltage source of 100 cos 377
is applied to a nonlinear load, resulting in a non‐sinusoidal current which is expressed in Fourier series form as 8
15 cos 377
30
6 cos 2 377
Determine (a) the power absorbed by the load, (b) the power factor of the load, (c) the distortion factor of the load current, and (d) the total harmonic distortion of the load current. 45
2 cos 3 377
60
6. A sinusoidal voltage source of 170 cos 2 60 V is applied to a nonlinear load, resulting in a nonsinusoidal current which is expressed in Fourier series form as 10 cos 2 60
30
5 cos 4 60
45
2 cos 8π60t
20 A. Determine (a) the power absorbed by the load, (b) the power factor of the load, (c) the distortion factor, and (d) the total harmonic distortion of the load current. 7. Repeat Problem 3 with
12 cos 2 60
40
5 sin 4 60
4 cos 8π60t A. 8. A sinusoidal voltage source of resulting in a current 240√2 sin 2 60 V is applied to a nonlinear load, 10 sin 2 60
5 sin 4 60 A. Determine (a) the power absorbed by the load, (b) the power factor of the load, (c) he THD of the load current, (d) the distortion factor of the load current, and (e) the crest factor of the load current. 9. Repeat Problem 5 with 12 sin 2 60
9 sin 4 60 A. AC/DC Converters 10. For the controlled half‐wave rectifier with resistive load, the source is 120 Vrms at 60 Hz. The resistance is 100 Ω, and the delay angle is 60°. (a) Determine the average voltage across the resistor. (b) Determine the power absorbed by the resistor. (c) Determine the power factor as seen by the source. 11. A controlled half‐wave rectifier has an ac source of 240 V rms at 60 Hz. The load is a 30 Ω resistor. (a) Determine the delay angle such that the average load current is 3.0 A. (b) Determine the power absorbed by the load. (c) Determine the power factor. 12. A controlled half‐wave rectifier has a 120 Vrms, 60‐Hz ac source. The series R‐L load has R = 25 Ω and L = 50 mH. The delay angle is 25°. Determine (a) an expression for load current, (b) the average load current, and (c) the power absorbed by the load. 13. Design a circuit to produce an average voltage of 40V across a 100 ohm load from a 120Vrms, 60Hz supply. Determine (a)
(b)
(c)
(d)
the firing angle of the circuit, the rms voltage, the power absorbed by the resistance, the power factor. 14. A controlled half‐wave rectifier has a 120‐V rms, 60‐Hz ac source. The series R‐L load has R = 40 Ω and L = 15 mH. The delay angle is 50°. Determine (a) an expression for load current, (b) the average load current, and (c) the power absorbed by the load. 15. A single‐phase bridge rectifier has an R‐L load with R = 15 Ω and L = 45 mH. The ac source is 100 sin 377 V. Determine the average and rms currents in the load and in each diode. 16. A single‐phase bridge rectifier has an R‐L load with R = 25 Ω and L = 50 mH. The ac source is 120 Vrms, 60 Hz. Determine (a) the average load current, (b) the power absorbed by the load, and (c) the power factor. 17. The bridge rectifier circuit has an ac source with Vm = 100 V at 60 Hz and a series R‐L load with R = 10 Ω and L = 10 mH. (a) Determine the average current in the load, (b) Estimate the peak‐to‐peak variation in load current based on the first ac term in the Fourier series, (c) Determine the power absorbed by the load and the power factor of the circuit, (d) Determine the average and rms currents in the diodes. AC/AC Converter 18. The single‐phase ac voltage controller has a 240 Vrms source and a load resistance of 45 Ω. Determine the delay angle required to deliver 800 W to the load. 19. The single‐phase ac voltage controller has a 120
, 60‐Hz source. The load resistance is 15 Ω. Determine (a) The delay angle required to deliver 500 W to the load, (b) The rms source current, (c) The rms and average currents in the SCRs, (d) The power factor, and (e) The THD of the source current. 20. The single‐phase ac voltage controller has a 480 Vrms 60 Hz source and a load resistance of 50 Ω. The delay angle is 80°. Determine (a) the rms load voltage, (b) the power absorbed by the load, (c) the power factor, (d) the average and rms currents in the SCRs, and (e) the THD of the source current. DC/DC Converter 21. The buck dc‐dc converter has the following parameters: 50 , 0.4, 400
, 100
, 20
, 20Ω
Assuming ideal components, calculate (a) the output voltage Vo, (b) the maximum and minimum inductor current, and (c) the output voltage ripple. 22. The buck converter has the following parameters: VS = 24V, D = 0.65, L = 250 H, C = 15 F, and R = 10 Ω. The switching frequency is 25 kHz. Determine (a) the output voltage, (b) the maximum and minimum inductor currents, and (c) the output voltage ripple. 23. The buck converter has the following parameters: Vs = 15 V, D = 0.6, L = 50 H, C = 150 F and R = 5 Ω. The switching frequency is 50 kHz. Determine (a) the output voltage, (b) the maximum and minimum inductor currents, and (c) the output voltage ripple. 24. The boost converter has the following parameters: Vs = 20, D = 0.6, R = 12.5 Ω, L = 65 H, C = 200 F and switching frequency = 40 kHz. (a) Determine the output voltage. (b) Determine the average, maximum, and minimum inductor current. (c) Determine the output voltage ripple. (d) Determine the average current in the diode. POWER ELECTRONICS CONVERTERS AS MOTOR DRIVE 25. A 1 hp, DC shunt motor is loaded by a constant torque of 10 Nm. The armature resistance of the motor is 5 Ω, and the field constant
2.5
SCR converter. The power source is 120 , 60
. The motor is driven by a half‐wave . The triggering angle of the converter is 60 , and the conduction period is 150 . Calculate the motor speed and developed power? 26. For the motor in Problem 25, assume that the converter is a full‐wave type. The triggering angle of the converter is 60°, and the conduction period is 150°. Calculate the motor speed and the developed power delivered to the load.