Mathcad - Mech Char - En

This program is to calculate the mechnical characteristic . Programmer - bluephoenix ( http://engineer4myanmar.mmgeeks.com http://motor-design.blogspot.com) Last modified - 25-10-2007 6

MW := watt⋅ 10 s := sec

W := watt rev := 1

kV := V⋅ 10 meter := m

А := amp

kA := amp⋅ 10

unit := 0 + i

μ 0 := 4⋅ π ⋅ 10

3

3

min := 60⋅ sec

− 7 newton ⋅ 2

T := tesla

amp

−3

Wb := weber

milimeter := m⋅ 10

Given: rated values and parameters of equivalent ckt of induction motor n_phase := 3

P := 15000⋅ W

I1rated := 28.4⋅ A

n1 := 1500⋅

r1.pu := 0.046

r'2.pu := 0.023994

x12.pu := 5.11

r12.pu := 0.19

U1 := 380⋅ V

rev min

1.47⋅ 0.129 = 0.19

-1

n1 = 25 s

η := 0.892

x1.pu := 0.08643

x'2pu := 0.118

ORIGIN ≡ 1 slip := 0.0000 , 0.0001 .. 1 U1phase :=

U1

looping start here 2 -3

U1phase = 219.393 kg m s A

3

U1phase.pu := 1

Zbase :=

U1phase I1rated

⎛ r'2.pu ⎞ ⎟ + x'2pu⋅ unit ⎝ slip ⎠

( r12.pu + x12.pu⋅ unit) ⋅ Z'2.pu (slip) r12.pu + x12.pu ⋅ unit + Z'2.pu ( slip)

Zвх.pu ( slip) := ( r1.pu + x1.pu⋅ unit) + Zab.pu ( slip)

1

2 -3

Zbase = 7.725 kg m s A

Z'2.pu ( slip) := ⎜

Zab.pu ( slip) :=

-1

-2

I1.pu ( slip) :=

1 Zвх.pu ( slip)

⎡ ( Re ( I1.pu ( slip) ) ) 2 + ( Im ( I1.pu ( slip) ) ) 2 ⎤ ⎣ ⎦

I1mod.pu ( slip) :=

⎛ Im ( I1.pu ( slip) ) ⎞ ⎟ ⎝ Re ( I1.pu ( slip) ) ⎠

φ ( slip) := atan ⎜

φ deg ( slip) := φ ( slip) ⋅ 57.296 PF ( slip) := cos ( φ ( slip) )

⎡ U1phase.pu − I1.pu ( slip) ⋅ ( r1.pu + x1.pu⋅ unit) ⎤⎦ I'2.pu ( slip) := ⎣ Z'2.pu ( slip) 2 2 I'2.sq.pu ( slip) := ⎡⎣ ( Re ( I'2.pu ( slip) ) ) + ( Im ( I'2.pu ( slip) ) ) ⎤⎦

Pmech.pu ( slip) := n_phase⋅ I'2.sq.pu ( slip) ⋅ r'2.pu ⋅

( 1 − slip) slip

Pmech ( slip) := Pmech.pu ( slip) ⋅ ( I1rated) ⋅ Zbase 2

4 .10

4

3 .10

4

Pmech ( slip)2 .104

4

1 .10

0 0.005

0.25

0.5 slip

2

0.75

1

n2 ( slip) := n1⋅ ( 1 − slipω) 2 ( slip) := 2⋅ π ⋅ n2 ( slip) M ( slip) :=

Pmech ( slip)

Mkgm ( slip) := M ( slip) ⋅ 0.102

ω 2 ( slip) 25

18.75

Mkgm ( slip) 12.5

6.25

0

0

0.25

0.5

0.75

1

slip

ω 1 := 2⋅ π ⋅ n1

Mrated :=

P

2 -2

Mrated = 95.493 kg m s

ω1

2 -2

Mrated.kgm := Mrated⋅ 0.102 Mpu ( slip) :=

Mrated.kgm = 9.74 kg m s

M ( slip) Mrated 3

2.25

Mpu ( slip) 1.5

0.75

0

0

0.25

0.5 slip

3

0.75

1

I'2.mod.pu ( slip) :=

I'2.sq.pu ( slip) 5

4

3 I'2.mod.pu ( slip) 2

1

0

0

0.2

0.4

0.6 slip

4

0.8