DC Machines - GATE Electrical Engineering Exam Preparation Quick Notes

• Mechanical Power: \(P_{mech} = T\omega = EI_a\)

• For lap winding: \(A = P\), For wave winding: \(A = 2\)

Effect of armature current on main field flux distribution

• Cross-magnetizing: Shifts magnetic neutral axis

• Demagnetizing: Reduces main field flux (when brushes shifted)

• Magnetizing: Increases main field flux (rare case)

• Interpoles: Eliminate reactance voltage

• Compensating windings: Cancel armature reaction

• Brush shifting: Temporary solution

• Separately Excited: \(V_t = E - I_a R_a\)

• Self Excited: Series, Shunt, Compound

• Separately Excited: Drooping (due to \(I_a R_a\) drop)

• Series: Rising initially, then drooping

• Shunt: Slightly drooping

• Compound: Flat, over-compound, or under-compound

• Residual magnetism must exist

• \(R_f < R_{cr}\) (field resistance < critical resistance)

• Field connections must aid residual flux

For shunt generator: \(R_L = \dfrac{E}{2I_a} - R_a\)

• \(I_f = I_a = I_L\)

• Poor voltage regulation

• Used for special applications (welding, constant current)

• Cumulative: Series field aids shunt field

• Differential: Series field opposes shunt field

• Level compound: \(V_{NL} = V_{FL}\)

• Over compound: \(V_{FL} > V_{NL}\)

• Under compound: \(V_{FL} < V_{NL}\)

• Input power: \(P_{in} = V_t I_L\)

• Mechanical power: \(P_{mech} = E_b I_a = T\omega\)

• Copper losses: \(P_{cu} = I_a^2 R_a + I_f^2 R_f\)

• Efficiency: \(\eta = \dfrac{P_{out}}{P_{in}} = \dfrac{E_b I_a - P_{rot}}{V_t I_L}\)

• Speed approximately constant (good speed regulation)

• \(T \propto I_a\) (since \(\phi\) is constant)

• Starting torque moderate

• No-load speed finite

Lathes, fans, pumps, machine tools (constant speed applications)

• \(T \propto I_a^2\) (unsaturated region)

• High starting torque

• Speed varies widely with load

• Dangerous at no-load (speed \(\rightarrow \infty\))

Traction motors, cranes, hoists, electric vehicles (high starting torque needed)

• Series field aids shunt field

• High starting torque + reasonable speed regulation

• Most common type of compound motor

• Series field opposes shunt field

• Speed increases with load (unstable)

• Rarely used

Elevators, compressors, rolling mills (variable torque with good speed control)

Three methods of speed control:

• Vary field current \(I_f\) using rheostat

• Speed above rated speed

• Constant torque operation

• Most economical method

• Speed range: 1:3 or 1:4

• Vary armature voltage (Ward-Leonard, chopper, controlled rectifier)

• Speed below rated speed

• Constant torque operation

• Smooth control, good efficiency

• Speed range: 1:10 or higher

• Add external resistance in armature circuit

• Speed below rated speed

• Poor efficiency (high \(I^2R\) losses)

• Used for temporary speed reduction

• Step-wise control

• Motor-generator set for voltage control

• Smooth speed control from zero to rated

• High initial cost but excellent performance

• Used in elevators, rolling mills

• Electronic switching for DC voltage control

• High efficiency, compact

• Used in modern DC drives

At starting: \(N = 0\), \(E_b = 0\), \(I_a = \dfrac{V_t}{R_a}\) (very high)

• 3-point starter: For shunt motors

• 4-point starter: For shunt motors (improved)

• Series starter: For series motors

• Resistance starting: Most common

• Voltage starting: Reduce applied voltage

• Current limiting: Electronic control

• No-volt protection (NVP)

• Overload protection (OLP)

• Motor runs at no-load

• Determines: rotational losses, \(I_0\), \(N_0\)

• \(P_{rot} = V_t I_0 - I_0^2 R_a\)

• Rotor blocked, reduced voltage applied

• Determines: \(R_a\), short-circuit characteristics

• \(R_a = \dfrac{V_{br}}{I_{br}}\) (approximately)

• No-load test on shunt machine

• Predicts efficiency at any load

• Assumption: rotational losses constant

• Copper losses: \(I_a^2 R_a + I_f^2 R_f\)

• Iron losses: Hysteresis + Eddy current

• Mechanical losses: Friction + Windage

• Brush losses: Brush contact drop

• Direct method: \(\eta = \dfrac{P_{out}}{P_{in}}\)

• Indirect method: \(\eta = \dfrac{P_{in} - \text{Losses}}{P_{in}}\)

Variable losses = Constant losses

1. Identify machine type (series, shunt, compound)

2. Draw equivalent circuit

3. Apply appropriate voltage equation

4. Use EMF and torque equations

5. Calculate power and efficiency

6. Check units and reasonableness

• EMF, torque, and power calculations

• Speed control and regulation

• Efficiency and losses

• Motor starting analysis

• Generator load characteristics

• Compound generator degree of compounding

• Series motor: High starting torque, variable speed, \(T \propto I_a^2\)

• Shunt motor: Constant speed, \(T \propto I_a\), good regulation

• Speed control: Flux control (above rated), voltage control (below rated)

• Efficiency: Maximum when variable losses = constant losses

• Armature reaction: Cross-magnetizing effect, use interpoles