Solutions Manual Power Electronics Circuits, Devices Applications 4th Edition Muhammad H. Rashid

Instant download and all chapters Solutions Manual Power Electronics Circuits, Devices Applications 4th Edition Muhammad H. Rashid https://testbankdata.com/download/solutions-manual-power-electronics-circuits-devices-_applications-4th-edition-muhammad-h-rashid/

Chapter 3-Diodes Rectifiers Prob 3-1

Vm := 170

R := 5

f := 60

Using Eq. (3-11) 2⋅ Vm Vdc :=

Vdc = 108.23

π

Vdc := 0.6366⋅ Vm

Prob 3-2

Vm := 170

Vdc = 108.22 −3

R := 10

Lc := 0.5⋅ 10

f := 60

Using Eq. (3-11) Vdc := 0.6366⋅ Vm Idc :=

Vdc Idc = 10.82

R

Using Eq. (3-83)

Vx := 2⋅ f ⋅ Lc⋅ Idc

Vx = 0.65

Vo := Vdc − Vx

Vo = 107.57

Prob 3-3 Vm := 170 R := 5 Using Eq. (3-25) 6 ⎛π⎞ Vdc := Vm⋅ ⋅ sin ⎜ ⎟ π ⎝6⎠ Prob 3-4

Vm := 170

f := 60

R := 5

Vdc = 162.34 f := 60

Using Eq. (3-25) 6

⎛π⎞ ⎟ ⎝6⎠

Vdc := Vm⋅ ⋅ sin ⎜ π Idc :=

Vdc = 162.34

Vdc Idc = 32.47

R

Using Eq. (3-83) Vx := 6⋅ f ⋅ Lc⋅ Idc

Vx = 5.84

Vo := Vdc − Vx

Vo = 156.49

Chapter 3-Diodes Rectifiers Page # 3 -1

−3

Lc := 0.5⋅ 10

Prob 3-5

Vs := 280

R := 5

2 3

Vm := 280⋅

f := 60 Vm = 228.62

Using Eq. (3-33) Vdc := 1.6542⋅ Vm

Prob 3-6

Vs := 280

Vdc = 378.18 R := 5

2 3

Vm := 280⋅

−3

f := 60

Lc := 0.5⋅ 10

Vm = 228.62

Using Eq. (3-33)

Vdc = 378.18

Vdc := 1.6542⋅ Vm Vdc

Idc :=

Idc = 75.64

R

Using Eq. (3-83) Vx := 6⋅ f ⋅ Lc⋅ Idc

Vx = 13.61

Vo := Vdc − Vx

Prob 3-7

Vdc := 240

0.6366

Vs = 266.58

2

Idc := Ip :=

Vm = 377

Vm

Vs :=

Diodes

R := 10 Vdc

Vm :=

Vo = 364.57

Vdc

Idc = 24

R

Vm

Ip = 37.7

R

Id :=

Idc

Id = 12

2

Chapter 3-Diodes Rectifiers Page # 3 -2

Ip

IR := Transformer

IR = 18.85

2 Vm

Vs :=

Vs = 266.58

2 Ip

Is :=

Is = 26.66

2

3

VI := Vs⋅ Is

Using Eq. (3-1) Pdc

Using Eq. (3-2)

2 0.6366⋅ Vm) ( :=

1 TUF

Prob 3-8 Vdc := 750 Using Eq. (3-33)

Diodes

3

Pac := Vs⋅ Is TUF :=

Vs :=

3

Pdc = 5.76 × 10

R

Using Eq. (3-8)

Vm :=

VI = 7.107 × 10

Pac = 7.11 × 10

Pdc

TUF = 0.8105

Pac = 1.23 Idc := 6000

Vdc

Vm = 453.39

1.6542 Vm

Vs = 320.6

2

Ip := Idc

Id :=

3

Ip = 6 × 10

Idc

IR :=

3

Id = 3 × 10

2 Ip

3

IR = 4.24 × 10

2

Chapter 3-Diodes Rectifiers Page # 3 -3

Transformer

Vs :=

Vm

Vs = 320.6

2 3

Is := Ip

Is = 6 × 10

VI := Vs⋅ Is

VI = 1.924 × 10

6

Using Eq. (3-1)

Pdc := Vdc⋅ Idc

Pdc = 4.5 × 10

Using Eq. (3-2)

Pac := 3Vs⋅ Is

Pac = 5.77 × 10

Using Eq. (3-8)

TUF

6

Pdc

TUF :=

1

6

TUF = 0.78

Pac = 1.28

Prob 3-9 Vm := 170

f := 60

R := 10

ω := 2⋅ π ⋅ f

ω = 376.99

RF := 0.04

Guess −3

L := 5⋅ 10 Given

Using Eq. (3-67)

2

⎛ 2⋅ ω⋅ L ⎞ RF⋅ 1 + ⎜ ⎟ − 0.481 = 0 ⎝ R ⎠ 3 Find ( L ) ⋅ 10 = 158.93

mH

Prob 3-10 Vm := 170

f := 60

R := 10

ω := 2⋅ π ⋅ f

ω = 376.99 RF := 0.02

Guess −3

L := 5⋅ 10

Chapter 3-Diodes Rectifiers Page # 3 -4

Given

Using Eq. (3-67) 2

2 ⎛ 6⋅ ω⋅ L ⎞ RF⋅ 2⋅ 1 + ⎜ = 0 ⎟ − ⎝ R ⎠ 35 3 Find ( L ) ⋅ 10 = 7.76

mH

Prob 3-11 E := 20

Vp := 120

Cap := 200

Vs = 60

Vm :=

Vp Vs := n ( a)

α := asin ⎛⎜

⎞ ⎟ ⎝ Vm ⎠ E

β := π − α

β⋅

δ := β − α

( b)

R :=

1 2π ⋅ Idc

α⋅

δ

180 π

180

2⋅ Vs

n := 2 Vm = 84.85

= 13.63

180

= 152.73

(

⋅ 2⋅ Vm⋅ cos ( α ) + 2⋅ E⋅ α − π ⋅ E

)

R = 1.776

( c)

Irms :=

2 ⎡⎛ V 2 ⎞ ⎤ Vm ⎢⎜ m ⎥ 2⎟ ⋅ ⎢⎜ + E ⎟ ⋅ ( π − 2⋅ α ) + ⋅ sin ( 2⋅ α ) − 4⋅ Vm⋅ E ⋅ cos ( α )⎥ 2 ⎠ ⎦ 2⋅ π ⋅ R 2 ⎣⎝ 2

1

Irms = 16.98 2 PR := Irms ⋅ R ( d)

( e)

PR = 512.06

Pdc := E⋅ Idc Cap ho := Pdc Pdc η := Pdc + PR

f := 60

= 166.37

π π

Idc := 10

Pdc = 200 ho = 1 η ⋅ 100 = 28.09

Chapter 3-Diodes Rectifiers Page # 3 -5

%

Ω

PIV := Vm + E

(f)

PIV = 104.85

Prob 3-12 E := 12

Cap := 100

Vp Vs := n ( a)

Vp := 120

Vs = 60

α := asin ⎛⎜

⎞ ⎟ V ⎝ m⎠ E

α⋅

β := π − α

β⋅

δ := β − α

( b)

( c) Irms :=

R :=

Vm :=

δ

1 2π ⋅ Idc

180 π

180

Idc := 5

2⋅ Vs

n := 2

f := 60

Vm = 84.85

= 8.13

= 171.87

π

180

= 163.74

π

(

⋅ 2⋅ Vm⋅ cos ( α ) + 2⋅ E⋅ α − π ⋅ E

)

R = 4.26

2 ⎡⎛ V 2 ⎞ ⎤ Vm ⎢⎜ m ⎥ 2⎟ ⋅ ⎢⎜ + E ⎟ ⋅ ( π − 2⋅ α ) + ⋅ sin ( 2⋅ α ) − 4⋅ Vm⋅ E ⋅ cos ( α )⎥ 2 ⎠ ⎦ 2⋅ π ⋅ R 2 ⎣⎝ 2

1

Irms = 8.21 2 PR := Irms ⋅ R ( d)

PR = 287.03

Pdc := E⋅ Idc

Pdc = 60

Cap ho := Pdc ( e)

η :=

(f)

ho = 1.67

Pdc

η ⋅ 100 = 17.29

Pdc + PR

PIV := Vm + E

%

PIV = 96.85

Prob 3-13 −3

L := 4.5⋅ 10

R := 4

f := 60

ω := 2⋅ π ⋅ 60

Chapter 3-Diodes Rectifiers Page # 3 -6

ω = 376.99

Ω

Vs := 120

E := 20

T :=

1

3 T⋅ 10 = 16.67

f

1 2 2 Z := ⎡⎣ R + ( ω⋅ L) ⎤⎦ θ := atan ⎛⎜ ω⋅

⎝

2

L⎞

⎟

R⎠

Z = 4.34 θ = 0.4

R ⎛π⎞ ⎡ − ⎛⎜ ⎞⎟ ⋅ ⎜ ⎟ ⎤ ⎢ ⎥ L Vs Vs 1 + e ⎝ ⎠ ⎝ ω ⎠⎦ E E ⎣ Y := 2⋅ ⋅ sin ( θ ) ⋅ − + − 2⋅ ⋅ sin ( θ ) R ⎛π⎞ R R Z Z ⎡ − ⎛⎜ ⎞⎟ ⋅ ⎜ ⎟ ⎤ ⎢ ⎥ L ⎝ ⎠ ⎝ω⎠ ⎣1 − e ⎦

( a)

Y = 0.02

iL ( t) :=

2⋅

Vs Z

⎛ R ⎞ ⋅⎛ π ⎞ − ⎛ R ⎞ ⋅t ⎜ ⎟⎜ ⎟ ⎜ ⎟ E L ω L ⋅ sin ( ω⋅ t − θ ) + ( Y) ⋅ e⎝ ⎠ ⎝ ⎠ ⋅ e ⎝ ⎠ −

R iL ( 0) = 10.27

( b)

The average diode current can be found from Equation 3-16 as: 1 ⌠ 120 1 ⎮ Id := ⋅ i ( t ) dt ⎮ T L ⌡ 0

( c)

Id = 11

The rms diode current can be found using Equation 3-16

⎞ ⎛ 1 ⎜ ⌠ 120 ⎟ 1 ⎮ 2 Ir := ⎜ ⋅ i ( t) dt⎟ ⎮ T L ⎜⌡ ⎟ ⎝ 0 ⎠ ( d)

1 2

Ir = 17.04

The rms output current can then be found by

Chapter 3-Diodes Rectifiers Page # 3 -7

Irms := Ir⋅ 2

Irms = 24.1

The max min values of output current R ⎛π⎞ ⎤⎤ ⎡ ⎡ − ⎛⎜ ⎞⎟ ⋅ ⎜ ⎟ ⎛ R ⎞ ⋅ ⎛ π − t⎞ ⎢ ⎢ ⎥⎥ L ω ⎝ ⎠ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ Vs⋅ 2 1 + e E L ω ⎝ ⎠ ⎝ ⎠⋅ ⎢ i1 ( t) := ⋅ ⎢ sin ( ω⋅ t − θ ) + sin ( θ ) ⋅ e − 1⎥ ⎥ − ⎢ ⎢ ⎥⎥ R Z R ⎛π⎞ − ⎛⎜ ⎞⎟ ⋅ ⎜ ⎟ ⎢ ⎢ ⎥⎥ L ⎝ ⎠ ⎝ω⎠ ⎣ ⎣1 − e ⎦⎦

Guess −3

t := 5⋅ 10 Given

R ⎛π⎞ ⎤⎤ ⎡ ⎡ ⎡ − ⎛⎜ ⎞⎟ ⋅ ⎜ ⎟ ⎛ R ⎞ ⋅ ⎛ π − t⎞ ⎢ ⎢V ⋅ 2 ⎢ ⎥⎥ L⎠ ⎝ω⎠ ⎝ ⎜ ⎟ ⎜ ⎟ 1 + e L ω d⎢ s ⎝ ⎠ ⎝ ⎠⋅ ⎢ ⋅ ⎢ sin ( ω⋅ t − θ ) + sin ( θ ) ⋅ e − 1⎥ ⎥ − R⎞ ⎛ π ⎞ ⎢ ⎢ ⎥⎥ dt ⎢ Z ⎛ − ⎜ ⎟ ⋅⎜ ⎟ ⎢ ⎢ ⎢ ⎥⎥ L ⎝ ⎠ ⎝ω⎠ ⎣ ⎣ ⎣1 − e ⎦⎦ −3

t1 := Find ( t)

t1 = 5.18 × 10

( )

Imax := i1 t1 tx := t1 −

Imax = 34.36

t1

at

1.15

( )

Imin := i1 tx

tx⋅ 1000 = 0.68

⎤ ⎥ E⎥ = 0 R⎥ ⎥ ⎦

180 π

⋅ ω⋅ t1 = 111.93

degrees

Imin = 6.04 ms

at

180 π

⋅ ω⋅ tx = 14.6

degrees

R ⎛π⎞ ⎤⎤ ⎡ ⎡ − ⎛⎜ ⎞⎟ ⋅ ⎜ ⎟ ⎛ R ⎞ ⋅ ⎛ π − t⎞ ⎢ ⎢ ⎥⎥ L ⎝ ⎠ ⎝ω⎠ ⎜ ⎟⎜ ⎟ Vs⋅ 2 E L ⎠ ⎝ ω ⎠ ⎢1 + e ⎝ ⎢ i1 ( t) := ⋅ sin ( ω⋅ t − θ ) + sin ( θ ) ⋅ e ⋅ − 1⎥ ⎥ − Z R ⎛π⎞ ⎢ ⎢ ⎥⎥ R − ⎛⎜ ⎞⎟ ⋅ ⎜ ⎟ ⎢ ⎢ ⎥⎥ ⎝L⎠ ⎝ω⎠ ⎣ ⎣1 − e ⎦⎦

Chapter 3-Diodes Rectifiers Page # 3 -8

ta := 0 , .0001 .. 2π

( )

i1 ta

40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0

0

9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144 153 162 171 180 180 π

Imin = 6.04 at 180

π

is the minimum current

⋅ ω⋅ tx = 14.6

Imax = 34.36 at 180

π

⋅ ω ⋅ ta

degrees is the maximum current

⋅ ω⋅ t1 = 111.93

degrees

Prob 3-14: Three-phase Diode Rectifier Input Phase Voltage

VS := 120

Load Resistance

R := 5

Load Inductance

L := 2.5⋅ 10

fs := 60 E := 20 −3

The ripple factor of the output voltage is to be limited to less than 5% of the average output voltage by an L-C filter.

Chapter 3-Diodes Rectifiers Page # 3 -9

1

VS = 120 VAB :=

ω := 2⋅ π ⋅ fs

2 2 Z := ⎡⎣ R + ( ω⋅ L) ⎤⎦

ω = 376.99

Z = 5.09

T :=

1 fs

2

⎛ ω⋅ L ⎞ ⎟ ⎝ R ⎠

θ := atan ⎜ 180.

θ π

= 10.67

T = 0.02 Vm :=

3⋅ VS

2⋅ VS

Vm = 169.71

VAB = 207.85 Line-to-Line RMS Input Voltage

I1 :=

iL ( t) :=

1.

⎤ ⎡ ⎡ ⎛ 2.⋅ π ⎞ ⎞⎤ ⎛π sin ⎜ − θ⎟ − sin ⎜ − θ⎟ ⎥ ⎛ R ⎞ ⋅ ⎛ π − t⎞⎥ ⎢ ⎢ ⎜ ⎟⎜ ⎟ 2⋅ VAB ⎝ 3 ⎠ ⎝3 ⎠ ⎥ ⋅ e⎝ L ⎠ ⎝ 3. ⋅ ω ⎠⎥ − E ⋅ ⎢ sin ( ωt − θ ) + ⎢ Z R ⎛ π ⎞ ⎢ ⎢ ⎥ ⎥ R − ⎛⎜ ⎞⎟ ⋅ ⎜ ⎟ ⎢ ⎢ ⎥ ⎥ L 1 − e ⎝ ⎠ ⎝ 3. ⋅ ω ⎠ ⎣ ⎣ ⎦ ⎦ Calculations for I1 using Equation on bottom of page 74

I1 :=

2.

R ⎛ π ⎞⎤ ⎡ − ⎛⎜ ⎞⎟ ⋅ ⎜ ⎟ ⎢ ⎛ 2⋅ π π ⎞ ⎛ − θ⎞ ⋅ e ⎝ L ⎠ ⎝ 3⋅ ω ⎠ ⎥ sin − θ − sin ⎟ ⎜ ⎟ ⎥ 2⋅ VAB ⎢ ⎜⎝ 3 3 ⎠ ⎝ ⎠ ⎢ ⎥−E ⋅ Z ⎢ ⎡− ⎛ R ⎞ ⋅ ⎛ π ⎞⎤ ⎥ R ⎢ ⎜ ⎟ ⎜ ⎟ ⎥ ⎢ ⎥ L 1 − e⎣ ⎝ ⎠ ⎝ 3⋅ ω ⎠⎦ ⎣ ⎦ I1 = 50.56

R ⎛ π ⎞⎤ ⎡ − ⎛⎜ ⎞⎟ ⋅ ⎜ ⎟ ⎢ ⎛ 2⋅ π ⎞ L ⎞ ⎛π 3⋅ ω ⎠ ⎥ sin ⎜ − θ⎟ − sin ⎜ − θ⎟ ⋅ e ⎝ ⎠ ⎝ ⎢ ⎥ 2⋅ VAB 3 3 ⎝ ⎠ ⎝ ⎠ ⎥−E ⋅⎢ Z ⎢ ⎡− ⎛ R ⎞ ⋅ ⎛ π ⎞⎤ ⎥ R ⎢ ⎜ ⎟ ⎜ ⎟ ⎥ ⎢ ⎥ L 1 − e⎣ ⎝ ⎠ ⎝ 3⋅ ω ⎠⎦ ⎣ ⎦

Calculations for Average Diode Current T ⎛ ⎜ ⌠3 2 ⎮ Id := ⎜ ⋅ ⎮ iL ( t) ⎜T ⎮ ⎜ ⌡T 6 ⎝

⎞ ⎟ dt⎟ ⎟ ⎟ ⎠

Id = 17.38

Chapter 3-Diodes Rectifiers Page # 3 -10

I1 = 50.56