rahman tutorial 1

ELEC 4240/9240 Power Electronics

Tutorial 1 T1-1 M. F. Rahman/March 2003

School of Electrical Engineering & Telecommunications University of New South Wales

ELEC4240/9240 - Power Electronics

Tutorial 1 - Basic Concepts in Power Electronics

1. Find the dc and the rms values of the fundamental and the first few harmonics of the

waveforms (a)-(i), in Figure T1-1. The waveforms in figures T1-1(f), (h) and (i) consist of parts of sine waves.

π π

I di( t )

– I d

(a) Input current waveform of a single-phase bridge rectifier with negligible source inductance

ddc n

4IAns : I 0, I

n 2π= = for n = 1, 3, 5, …..

(b) Input current waveform of a 3-phase bridge rectifier with negligible source inductance.

ddc n

4I nAns : I 0, I sin3n 2π

π = =

for n = 1, 3, 5, ….

(c) Input current waveform of a single-phase bridge rectifier with source inductance

ddc n 2

8I nAns : I 0, I sin2n 2µ

πµ = =

for n = 1, 3,5, …

2 π /3 2π /3

I d

π /3

− Id

µ /2 µ /2 µ /2 µ /2 µ /2 µ /2

Id

π - µ − Id

i(t)



(d) Input current waveform of a 3-phase bridge converter with source inductance.

ddc n 2

8I n nAns : I 0, I sin cos2 6n 2µ π

πµ = =

(e) Magnetic flux in the inductor of a rectifier or a DC-DC converter.

maxdc n 2 2

8IAns : I 0, I

n 2π= = for n = 1, 3, 5, …

(f) Output voltage waveform of a full-wave rectifier

( )

max maxdc n 2

2V 4VAns : V , V

n 1 2π π= =

− for n = 2, 4, 6, …

(g) Output voltage waveform of a DC-DC converter.

( )ddc d n

2 VAns : V DV , V sin nD

nπ

π×

= = for n = 1, 2, 3, ….

Id

µµ

µ µ 2π /3

π /3 π/3

π

− Id

π/2 π/2

π/2 π/2Imax

– Imax

π π

Vmax

π

D T

V d c

T0 t



(h) Output voltage waveform of a 3-phase (3-pulse)C-T AC-DC rectifier.

maxdc

3 3VAns : V

2π= ;

( ) ( )maxn

sin 3n 1 / 3 sin 3n 1 / 33VV

3n 1 3n 12π π

π+ −

= + + − for n = 1,2,3,…

(i) Output voltage waveform of a 3-phase bridge (3-pulse) AC-DC rectifier.

Ans: maxdc

3VV

π= ;

( ) ( )maxn

sin 6n 1 / 6 sin 6n 1 / 66VV

6n 1 6n 1π π

π+ −

= + + − for n = 1, 2, 3, …

Figure 1. Waveforms typically occurring in power electronic circuits.

2. Calculate the THD for the waveforms (a)-(e) in figure T1-1. Assume that µ = 20° for the

waveforms in 1(c) & (d). Ans: THD = (a) 48%, (b) 31%, (c) 39%, (d) 48%, (e) 12% 3. For the waveforms (f)-(i) in Figure 1, calculate the total ripple component as a ratio of

the dc value (the Ripple Factor).

Ans: RF = (f) 48%, (g) 1 DD− , (h) 18%, (i) 4%.

4. A non sinusoidal periodic voltage of frequency f = 50 Hz is expressed in a Fourier series as

v( t ) 10 20 cos( 2 ft 25 ) 30 cos( 4 ft 20 )π π= + − + + Volts The voltage is applied to a load resistor of 5Ω in series with and inductor of 15 mH.

Calculate the power absorbed by the load. Ans: P = 60.94 W.

2π/3 2π/3

Vmax

π /3 π /3

V m ax



5. A sinusoidal voltage source of v( t ) 340 cos tω= volts is applied to a converter which draws and input current given by

i( t ) 8 15 cos( 314t 30 ) 6 cos( 3 314t 45 ) 2 cos( 5 314t 60 )= + − + × + + × + A Calculate

(i) the power absorbed by the load, assuming that the converter absorbs no power (ii) the distortion factor of the input current (iii) the THD of the input current (iv) the input power factor of the converter.

Ans: (i) P = 2209 W, (ii) IDF = 0.76, (iii) THD = 86%, (iv) IPF = 0.68 (lagging).

6. A sinusoidal voltage of 340× sinωt V is applied to a single-phase converter, the input

current of which is represented by the waveforms (a)-(e) of figure T1-1. Assume that the zero crossing of each waveform is 30° behind that of the input voltage waveform. Assume that the peak value of these waveforms is 10 A. Calculate

(i) the average power drawn by the converter, (ii) its input displacement factor (iii) the input distortion factor and (iv) the power factors for each of these waveforms.

Ans: (i) P = 1463 W, (ii) IDispF = 0.866, (iii) IDistF = 0.956, (iv) THD = 30.95%

for the waveform of figure 1(b). 7. A transformer is wound with on a toroidal core. The primary winding is supplied with a

square-wave voltage of ±50 Volts amplitude and frequency of 100 kHz. Assuming an uniform flux density B in the core, calculate the minimum number of turns required in the primary winding to keep the peak flux density in the core below 0.35 T. Assume that the core area of cross-section is 1.2 cm2.

Plot the voltage and the flux density waveforms as a function of time.

Ans: Np = 6. 8. The switching times for a device, as specified in its data sheet, are as follows: tri = 100 ns; tfv = 50 ns; trv = 100 ns; and tfi = 200 ns. These switching times are explained in Figure 2-6 in your text book (Mohan's). Assume that the device switches a clamped inductive circuit as indicated in Figure 2-6(a)

(Mohan's). Calculate and plot the switching power loss as a function of switching frequency in the range of 25 - 100 kHz, assuming Vd = 300 V, Io = 4 A in the circuit of figure 2-6(a) in your textbook.

Ans: Ps = 6.75 W @ 25 kHz, Ps = 27 kW @ 100 kHz.



9. Consider the resistive switching circuit of figure T1-2. Vd = 300 V, fs = 100 kHz and R = 75 Ω. Assume that the turn-on time ton is given by the sum of tri and tfv and the turn-off time toff by the sum of trv and tfi, as in problem 8.

R

+vT

¯

iTV d

Figure T1-2

Assuming linear voltage and current switching characteristics, plot the switch voltage and

current waveforms and the switching power loss as a function of time. Compare the average power loss with the power loss in problem 8.

Ans: Ps = 9 W or 1/3 of the power loss in problem 8.

rahman tutorial 1

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