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DC Generator Formulas and Equations

DC Series and Shunt Generator Formulas & Efficiency, Power & EMF Equations

The following basic DC generator formulas and equations can be used to design, simplify, and analyze the basic generator circuits to determine the power, efficiency, voltage & current, generated EMF, torque, losses etc.

 

DC Generator Formulas and Equations

Shunt Generator:

Terminal Voltage:

V = E– Ia Ra

Where

Terminal Current:

Ia = If ­+ IL

where IIs the field current & Iis the load current

The Field Current:

­= V / Rsh

Where

  • Iis the field current
  • Rsh ­is the shunt field resistance

EMF Equation For DC Generator:

The EMF generated per conductor in a DC generator is:
EMF equation for DC generator
Where

  • Z = number of conductors
  • P = number of Poles
  • N = Speed of rotor in RPM
  • A = number of parallel paths

The EMF generated per path for a wave winding & lap-winding;
EMF generated per path for a wave winding & lap-winding
So the generalized equation for generated EMF of DC generator is:

E= kΦω

Where

  • K = ZP/2πA = constant of the DC machine
  • ω = 2πN/60 = angular speed in rads per second

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Torque of DC Generator:

the torque of generator is directly proportional to the armature current & it is given by:

T = kfΦIa

Where

  • Kis a constant based on machine construction
  • Φ is the magnetic flux
  • ω is the angular speed

angular speed of generator
Where N is the speed in Rotation Per Minute (RPM)

Power Generated & Load Power

The power generated by a shunt generator is given by:

P= ωT = EaIa

PL = VIL

Where Iis the load current

Series Generator:

Terminal Voltage:

V = E– (Ia R+ Ia Rse)

V = E– Ia(R+ Rse)

Where

  • is the armature induced voltage
  • Iis the armature current
  • R­­­is the armature resistance
  • Rse ­is the series field resistance

The series field current is equal to the armature current;

I= Ise

Armature Induced Voltage & Torque:

The armature induced voltage Eis proportional to the speed & armature current whereas the torque T of series generator is directly proportional to the square of armature current & it is given by:

E= kfΦωIa

T = kΦ Ia2

Where

  • Kis a constant based on machine construction
  • Φ is the magnetic flux
  • ω is the angular speed

angular speed of series generator
Where N is the speed in Rotation Per Minute (RPM)

Power Generated & Load Power

The power generated by a series generator is given by:

P= ωT = EaIa

PL = VIL

Where Iis the load current

Input Power:

Pin = ωT

Where

  • ω is the angular speed of armature
  • T is the torque applied
Converted Power:

Pcon = Pin – Stray losses – mechanical losses – core losses

Pcon = EaIa

Where

  • Ea is the induced voltage
  • Ia is the armature current
Output Power

Pout = Pcon – Electrical losses (I2R)

Pout = VIL

Where

  • V is the terminal voltage
  • Iis the load current

Efficiency of DC Generator:

Mechanical Efficiency:

Mechanical efficiency of DC generator

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Electrical Efficiency:

Electrical Efficiency of DC generator

Overall Efficiency:

Overall Efficiency of dc generator
Where

  • Pout is the useful output power
  • Pa ­­is the armature copper loss
  • Pf is the field copper loss
  • Pk is the constant losses that contains core losses & mechanical losses

Maximum Efficiency:

The efficiency of the dc generator is Maximum, when;

Variable power loss = Constant power loss

Copper loss = Core & mechanical loss

Copper loss (I2R) such as armature and field copper loss are variable loss because they depend on current. While the core loss such as hysteresis and eddy current loss, mechanical loss such as friction losses are all constant losses.

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