EMF Equation

Torque Equation

Power Relations

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

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

Definition

Effect of armature current on main field flux distribution

Effects

• Cross-magnetizing: Shifts magnetic neutral axis

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

• Magnetizing: Increases main field flux (rare case)

Compensation Methods

• Interpoles: Eliminate reactance voltage

• Compensating windings: Cancel armature reaction

• Brush shifting: Temporary solution

Classification by Excitation

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

• Self Excited: Series, Shunt, Compound

Load Characteristics

• 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

Voltage Regulation

Critical Field Resistance

Condition for Self-Excitation

• Residual magnetism must exist

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

• Field connections must aid residual flux

Maximum Power Condition

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

Series Generator

• \(I_f = I_a = I_L\)

• Poor voltage regulation

• Used for special applications (welding, constant current)

Compound Generator

• 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: \(V_{FL} < V_{NL}\)

Compounding Ratio

Voltage Equation

Speed Equation

Power Relations

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

Characteristics

• Speed approximately constant (good speed regulation)

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

• Starting torque moderate

• No-load speed finite

Speed Regulation

Applications

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

Characteristics

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

• High starting torque

• Speed varies widely with load

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

Speed-Torque Relation

Applications

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

Cumulative Compound

• Series field aids shunt field

• High starting torque + reasonable speed regulation

• Most common type of compound motor

Differential Compound

• Series field opposes shunt field

• Speed increases with load (unstable)

• Rarely used

Applications

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

From Speed Equation: \(N = \dfrac{V_t - I_a R_a}{K\phi}\)

Three methods of speed control:

1. Flux Control (Field 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

2. Armature Voltage Control

• 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

3. Armature Resistance Control

• Add external resistance in armature circuit

• Speed below rated speed

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

• Used for temporary speed reduction

• Step-wise control

Ward-Leonard System

• Motor-generator set for voltage control

• Smooth speed control from zero to rated

• High initial cost but excellent performance

• Used in elevators, rolling mills

Chopper Control

• Electronic switching for DC voltage control

• High efficiency, compact

• Used in modern DC drives

Need for Starter

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

Types of Starters

• 3-point starter: For shunt motors

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

• Series starter: For series motors

Starting Methods

• Resistance starting: Most common

• Voltage starting: Reduce applied voltage

• Current limiting: Electronic control

Protection Features

• No-volt protection (NVP)

• Overload protection (OLP)

No-Load Test

• Motor runs at no-load

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

• \(P_{rot} = V_t I_0 - I_0^2 R_a\)

Blocked Rotor Test

• Rotor blocked, reduced voltage applied

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

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

Swinburne’s Test

• No-load test on shunt machine

• Predicts efficiency at any load

• Assumption: rotational losses constant

Losses in DC Machines

• 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

Efficiency Methods

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

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

Condition for Maximum Efficiency

Variable losses = Constant losses

Fundamental Equations

Power & Efficiency

Speed Control Relations

Step-by-Step Approach

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

Common GATE Question Types

• EMF, torque, and power calculations

• Speed control and regulation

• Efficiency and losses

• Motor starting analysis

• Generator load characteristics

• Compound generator degree of compounding

Key Points to Remember

• 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