Induction Motor Formulas: Power, Speed, and Efficiency

Posted on Jan 4, 2025 in Electronics

Induction Motor Formulas

COSy = R2/R1+SN / %((R1+R2/SN)^2+(X1+X2)^2)

Apparent Power

SN = (%3) * V1L * I1L

Reactive Power

QN = SN * SENy

Active Power

PN = SN * COSy

Motor Input Power

3 * (R2/S) * IF2

If Connected in Delta

IN,F = VF / %((R1 + R2/S)2 + (X1 X2 )2)

IN,F = IN,L = (%3) * IN,F

If Connected in Star

IN,F = VF/(%3) / %((R1 + R2/S)2 + ( X1 + X2 )2)

Efficiency

REND = P2 / (P2 + Pcu,1 + Pcu,2 + PFe + Pm) * 100

Pcu,1 = 3 * R1 * I1F2

Pcu,2 = 3 * R2 * I1F2

PFe = 3 * RFe * I1F2

P1 = (%) * V1,L * I1L * COSy

P2 = PN = Pi – Pm

Pi = 3 * Rc * I1F2

Pi = 3 * (1/s – 1) * R2 * IN,F2

2 * PI * fWs = ———–/p

Torque

TN = (3 * R2 / (Ws * S)) * (V1,F2 / ((R1 + R2 / S )2 + Xcc2))

TN = P2 / Wn = P2 / ((2*PI/60) * ns)

(WN = (1-SN) * WS)

WS = 2*PI * f / POLO

Full Load Speed

nN = (1 – SN ) * ns

R2SM = ——————-/%(R12 + Xcc2)

VCC,N = (%3) * VCC,N,F

VCC,N,F = Zcc * IN,F

Zcc = %((R1 + R2)2 + (X1 +X2)2)

Rad = (1 / mi * mv) * Rad’


COSy = R2/R1+SN / %((R1+R2/SN)^2+(X1+X2)^2)

Apparent Power

SN = (%3) * V1L * I1L

Reactive Power

QN = SN * SENy

Active Power

PN = SN * COSy

Motor Input Power

3 * (R2/S) * IF2

If Connected in Delta

IN,F = VF / %((R1 + R2/S)2 + (X1 X2 )2)

IN,F = IN,L = (%3) * IN,F

If Connected in Star

IN,F = VF/(%3) / %((R1 + R2/S)2 + ( X1 + X2 )2)

Efficiency

REND = P2 / (P2 + Pcu,1 + Pcu,2 + PFe + Pm) * 100

Pcu,1 = 3 * R1 * I1F2

Pcu,2 = 3 * R2 * I1F2

PFe = 3 * RFe * I1F2

P1 = (%) * V1,L * I1L * COSy

P2 = PN = Pi – Pm

Pi = 3 * Rc * I1F2

Pi = 3 * (1/s – 1) * R2 * IN,F2

2 * PI * fWs = ———–/p

Torque

TN = (3 * R2 / (Ws * S)) * (V1,F2 / ((R1 + R2 / S )2 + Xcc2))

TN = P2 / Wn = P2 / ((2*PI/60) * ns)

(WN = (1-SN) * WS)

WS = 2*PI * f / POLO

Full Load Speed

nN = (1 – SN ) * ns

R2SM = ——————-/%(R12 + Xcc2)

VCC,N = (%3) * VCC,N,F

VCC,N,F = Zcc * IN,F

Zcc = %((R1 + R2)2 + (X1 +X2)2)

Rad = (1 / mi * mv) * Rad’


COSy = R2/R1+SN / %((R1+R2/SN)^2+(X1+X2)^2)

Apparent Power

SN = (%3) * V1L * I1L

Reactive Power

QN = SN * SENy

Active Power

PN = SN * COSy

Motor Input Power

3 * (R2/S) * IF2

If Connected in Delta

IN,F = VF / %((R1 + R2/S)2 + (X1 X2 )2)

IN,F = IN,L = (%3) * IN,F

If Connected in Star

IN,F = VF/(%3) / %((R1 + R2/S)2 + ( X1 + X2 )2)

Efficiency

REND = P2 / (P2 + Pcu,1 + Pcu,2 + PFe + Pm) * 100

Pcu,1 = 3 * R1 * I1F2

Pcu,2 = 3 * R2 * I1F2

PFe = 3 * RFe * I1F2

P1 = (%) * V1,L * I1L * COSy

P2 = PN = Pi – Pm

Pi = 3 * Rc * I1F2

Pi = 3 * (1/s – 1) * R2 * IN,F2

2 * PI * fWs = ———–/p

Torque

TN = (3 * R2 / (Ws * S)) * (V1,F2 / ((R1 + R2 / S )2 + Xcc2))

TN = P2 / Wn = P2 / ((2*PI/60) * ns)

(WN = (1-SN) * WS)

WS = 2*PI * f / POLO

Full Load Speed

nN = (1 – SN ) * ns

R2SM = ——————-/%(R12 + Xcc2)

VCC,N = (%3) * VCC,N,F

VCC,N,F = Zcc * IN,F

Zcc = %((R1 + R2)2 + (X1 +X2)2)

Rad = (1 / mi * mv) * Rad’


COSy = R2/R1+SN / %((R1+R2/SN)^2+(X1+X2)^2)

Apparent Power

SN = (%3) * V1L * I1L

Reactive Power

QN = SN * SENy

Active Power

PN = SN * COSy

Motor Input Power

3 * (R2/S) * IF2

If Connected in Delta

IN,F = VF / %((R1 + R2/S)2 + (X1 X2 )2)

IN,F = IN,L = (%3) * IN,F

If Connected in Star

IN,F = VF/(%3) / %((R1 + R2/S)2 + ( X1 + X2 )2)

Efficiency

REND = P2 / (P2 + Pcu,1 + Pcu,2 + PFe + Pm) * 100

Pcu,1 = 3 * R1 * I1F2

Pcu,2 = 3 * R2 * I1F2

PFe = 3 * RFe * I1F2

P1 = (%) * V1,L * I1L * COSy

P2 = PN = Pi – Pm

Pi = 3 * Rc * I1F2

Pi = 3 * (1/s – 1) * R2 * IN,F2

2 * PI * fWs = ———–/p

Torque

TN = (3 * R2 / (Ws * S)) * (V1,F2 / ((R1 + R2 / S )2 + Xcc2))

TN = P2 / Wn = P2 / ((2*PI/60) * ns)

(WN = (1-SN) * WS)

WS = 2*PI * f / POLO

Full Load Speed

nN = (1 – SN ) * ns

R2SM = ——————-/%(R12 + Xcc2)

VCC,N = (%3) * VCC,N,F

VCC,N,F = Zcc * IN,F

Zcc = %((R1 + R2)2 + (X1 +X2)2)

Rad = (1 / mi * mv) * Rad’