Losses in Electrical Machines – Formulas and Equations

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Losses in Machines Equations and Formulas

The following formulas and equations can be used to calculate and measure the different kinds of losses in an electrical machine such as eddy current and hysteresis as iron core losses and armature and field losses as copper losses.

Table of Contents

Copper Losses:

Armature Loss:

Armature Cu Losses = P_a = I_a²R_a

Where

I_ais the armature current
R_a is the armature resistance

Field Loss:

Field Cu Losses = P_f = I_f²R_f

Where

I_fis the field current
R_fis the field resistance

For Shunt Field:

Where

I_shis the shunt field current
R_sh is the shunt field resistance

For Series Field:

Where

I_seis the series field current
R_se is the series field resistance

Hysteresis Loss:

Where

η = hysteresis or Steinmetz’s constant
B_max= maximum value of the magnetic flux density
f = frequency of magnetization
V= volume of the core

Also

Where

P is the number of poles
N is the speed in RPM

Eddy Current Loss:

W_e = PB²_max f²t²Watts

Where

K_eis the electrical constant of the core material
B_maxis the maximum flux density
f is the frequency of magnetization
t is the thickness of lamination
V is the volume of the core

Brush Losses in DC Machine:

P_BD = V_BD x I_a

Where:

P_BD = Power loss due to brush drop
V_BD = Voltage drop due to brush drop
I_a = Armature Current

Other machinal loss and stray loss in a machine depends on multiple factors and different for each case and machine such as transformer, motor, alternator etc.

Losses in Electrical Machines – Formulas and Equations