6.2 DC Generators

6.2 DC Generators

Introduction to DC Generators

A DC generator is an electromechanical machine that converts mechanical energy into direct current (DC) electrical energy. It operates on the fundamental principle of electromagnetic induction discovered by Michael Faraday. When a conductor moves through a magnetic field, an electromotive force (EMF) is induced across it. In a DC generator, this induced alternating EMF is rectified into a unidirectional (DC) output through a mechanical commutator. Before the widespread adoption of AC power systems and solid-state rectifiers, DC generators were the primary source of DC power for industrial processes, traction systems, and battery charging. Understanding their operation, construction, and characteristics remains crucial for historical context, specialized applications, and grasping the fundamentals of rotating electrical machines.

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1. Operating Principle and Construction

1.1 Operating Principle (Faraday's Law and Commutation)

1. Basic Principle: When a conductor cuts magnetic flux (or when flux linking a conductor changes), an EMF is induced in it. The magnitude is given by the generator form of Faraday's law: $e = B \ l \ v$ where $B$ is flux density, $l$ is conductor length, and $v$ is velocity perpendicular to the field. In a rotating coil, this becomes a sinusoidal EMF.

2. Role of the Commutator: The induced voltage in the rotating armature coils is alternating. The commutator, a mechanical rotary switch, reverses the coil connections to the external circuit at the precise moment the coil EMF reverses polarity. This process, called commutation, converts the internal AC to a pulsating DC at the brushes.

3. Result: The output voltage across the brushes is unidirectional but has a ripple. Multiple armature coils and commutator segments are used to smooth this output, producing a nearly constant DC voltage.

1.2 Construction

A DC machine consists of two main assemblies: the Stator (stationary part) and the Rotor or Armature (rotating part).

A. Stator (Field System)

1. Yoke (Frame):

   • Outer cylindrical frame, usually made of cast steel or rolled steel.

   • Provides mechanical support and carries the magnetic flux (serves as part of the magnetic circuit).

2. Field Poles:

   • Bolted to the inner periphery of the yoke.

   • Made of laminated silicon steel to reduce eddy currents.

   • Carry the field winding which produces the main magnetic flux when excited by DC.

3. Field Windings:

   • Concentrated coils wound around the pole cores.

   • When energized, they create alternate North and South poles.

4. Interpoles (Commutating Poles):

   • Smaller poles placed midway between the main field poles.

   • Carry windings connected in series with the armature.

   • Their function is to improve commutation by neutralizing the reactance voltage in the coil undergoing commutation.

5. Brushes and Brush Gear:

   • Brushes (usually carbon or graphite) are held in brush holders and press against the commutator.

   • They collect current from the rotating commutator and conduct it to the external stationary circuit.

   • Brush gear allows for adjustment of brush position.

B. Rotor (Armature)

1. Armature Core:

   • Cylindrical, mounted on the shaft, made of laminated silicon steel to minimize hysteresis and eddy current losses.

   • Has slots on its periphery to hold the armature windings.

2. Armature Windings:

   • Pre-formed coils of copper conductors placed in the armature slots and properly interconnected.

   • Connected to the commutator segments. Types: Lap and Wave (explained in detail in Section 2).

3. Commutator:

   • The heart of the DC machine's rectification system.

   • A cylindrical assembly of hard-drawn copper segments (bars), insulated from each other by mica.

   • Mounted on the shaft, it rotates with the armature. The ends of armature coils are connected to these segments.

   • Brushes ride on its surface.

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2. Armature Windings (Lap and Wave)

The armature winding is a closed-circuit winding where the generated EMFs add up. The type of winding determines the machine's current and voltage ratings and the number of parallel paths.

2.1 Lap Winding

1. Connection Rule: The end of one coil is connected to the start of the next coil under the same pole, and the finishing end is connected to a commutator segment adjacent to the starting segment. It "laps" back on itself.

2. Parallel Paths (A): Number of parallel paths is equal to the number of poles ($P$). $A = P$

3. Conductor Current ($I_a$): Since total armature current ($I_a$) divides among $A$ paths, current per conductor/parallel path is: $I_{conductor} = \frac{I_a}{A} = \frac{I_a}{P}$

4. Generated EMF ($E_g$): Since many paths are in parallel, the generated EMF is the voltage available across any one path.

5. Characteristics:

   • Suitable for high-current, low-voltage machines.

   • Requires equalizer rings to prevent circulating currents between parallel paths due to magnetic asymmetry.

2.2 Wave Winding (Series Winding)

1. Connection Rule: The end of one coil is connected to the start of the next coil under the next pair of poles. After connecting all coils in series, it returns to a commutator segment adjacent to the starting one, "waving" forward around the armature.

2. Parallel Paths (A): Always 2, irrespective of the number of poles. $A = 2$

3. Conductor Current: $I_{conductor} = \frac{I_a}{A} = \frac{I_a}{2}$

4. Generated EMF ($E_g$): Since only two paths exist in parallel, the generated EMF is the sum of EMFs of half the total coils in series, resulting in a higher voltage per path compared to a lap winding for the same number of conductors.

5. Characteristics:

   • Suitable for high-voltage, low-current machines.

   • Does not require equalizer connections.

Comparison Summary:

Feature	Lap Winding	Wave Winding
Parallel Paths (A)	$A = P$	$A = 2$
Brush Sets	Equal to number of poles (P)	Only 2 are sufficient
Current Rating	High ($I_a = P \times I_{path}$)	Low ($I_a = 2 \times I_{path}$)
Voltage Rating	Low	High
Equalizers	Required	Not required
Application	Heavy current machines (e.g., electrolysis, steel mills)	High voltage machines (e.g., for distribution)

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3. Types of DC Generators

DC generators are classified based on the method of exciting the field windings (i.e., how the field current $I_f$ is supplied).

3.1 Separately Excited DC Generator

1. Excitation: The field winding is supplied from an independent external DC source (e.g., a battery or a small auxiliary generator called an exciter).

2. Circuit Diagram: Armature and field are two separate, isolated circuits.

3. Terminal Voltage ($V_t$): $V_t = E_g - I_a R_a$ where $I_a$ is armature current, $R_a$ is armature circuit resistance.

4. Characteristics: Output voltage can be controlled easily and widely by varying the independent field current. Used where precise voltage control is needed.

3.2 Self-Excited DC Generators

The field winding is excited by the generator's own output. For self-excitation to start, there must be residual magnetism in the pole cores.

A. Shunt Generator

1. Excitation: The field winding (shunt field) is connected in parallel with the armature. It has many turns of fine wire (high resistance).

2. Circuit Diagram: Shunt field across the armature terminals.

3. Relationships:

   • Armature Current: $I_a = I_L + I_{sh}$

   • Shunt Field Current: $I_{sh} = V_t / R_{sh}$

   • Terminal Voltage: $V_t = E_g - I_a R_a$

4. Voltage Build-Up: Depends on residual magnetism, field circuit resistance being less than the critical field resistance, and the direction of rotation.

B. Series Generator

1. Excitation: The field winding (series field) is connected in series with the armature. It has few turns of thick wire (low resistance).

2. Circuit Diagram: Load, armature, and series field are all in series.

3. Relationships:

   • $I_a = I_{se} = I_L$

   • Terminal Voltage: $V_t = E_g - I_a (R_a + R_{se})$

4. Characteristic: Voltage rises sharply with load current initially, then drops due to saturation and armature reaction. Never used in isolation for power supply; used as a booster or in series arc lighting.

C. Compound Generator

1. Excitation: Uses both a shunt field and a series field winding. This combines features of both.

2. Types:

   • Cumulatively Compound: Series field MMF aids the shunt field MMF.

     • Over-compounded: Series field is strong; terminal voltage increases with load (positive voltage regulation). Used for compensating line drop in distribution.

     • Flat-compounded: Terminal voltage remains approximately constant from no-load to full-load.

     • Under-compounded: Series field is weak; terminal voltage decreases with load, but less than a shunt generator.

   • Differentially Compound: Series field MMF opposes the shunt field MMF. Terminal voltage falls rapidly with load. Rarely used; can provide constant current output.

3. Connection: Series winding can be connected so that it carries armature current (long-shunt) or load current (short-shunt).

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4. Losses, Efficiency, and Characteristics

4.1 Losses in a DC Generator

1. Copper Losses (Electrical Losses):

   • $I^2R$ losses in the windings.

   • Armature Copper Loss: $I_a^2 R_a$.

   • Field Copper Loss: Shunt: $I_{sh}^2 R_{sh}$, Series: $I_{se}^2 R_{se}$.

   • Brush Contact Loss: Often approximated as $I_a \times$ constant voltage drop (≈ 2V total for carbon brushes).

2. Iron (Core) Losses:

   • Hysteresis Loss: $P_h \propto f B_m^{1.6}$.

   • Eddy Current Loss: $P_e \propto f^2 B_m^2 t^2$.

   • Occur in the armature core due to rotation in the magnetic field. Constant for constant speed and flux.

3. Mechanical Losses:

   • Friction Loss (bearings, brushes) and Windage Loss (air resistance).

   • Constant for constant speed.

4. Stray Load Losses: Additional losses due to load, difficult to measure directly (e.g., short-circuit currents in armature conductors). Usually taken as 1% of output.

4.2 Efficiency

1. Definitions:

   • Total Losses: $P_{loss} = P_{cu} + P_{iron} + P_{mech} + P_{stray}$.

   • Input (Mechanical) Power: $P_{in} = P_{out} + P_{loss}$.

   • Output (Electrical) Power: $P_{out} = V_t I_L$.

2. Efficiency Formulas:

   • Commercial Efficiency: $\eta = \frac{P_{out}}{P_{in}} \times 100\% = \frac{V_t I_L}{V_t I_L + \text{Losses}} \times 100\%$

   • Condition for Maximum Efficiency: Occurs when variable losses = constant losses. For a shunt generator, this is when Armature Copper Loss = Constant Iron + Mechanical Losses. $I_a^2 R_a = P_{constant}$

4.3 Characteristics of DC Generators

These are curves showing relationships between terminal quantities at constant speed.

1. No-Load / Open Circuit Characteristic (OCC):

   • Also called Magnetization Curve.

   • Plot: Generated EMF ($E_g$) vs. Field Current ($I_f$) at constant speed and no-load ($I_a=0$).

   • Shape: Initially linear (unsaturated region), then curves and flattens (saturated region).

   • Significance: Fundamental curve for all generators. Obtained by separately exciting the machine and running it as a generator on no-load.

2. Load Characteristics:

   • Internal Characteristic: $E_g$ vs. $I_a$. Shows the true generated EMF after accounting for armature reaction (which reduces effective flux).

   • External Characteristic (Performance Curve): $V_t$ vs. $I_L$.

     • Shunt Generator: $V_t$ falls with load due to (i) Armature drop ($I_aR_a$), (ii) Armature reaction (reduces flux), and (iii) Reduction in $I_{sh}$ as $V_t$ falls.

     • Series Generator: $V_t$ rises to a peak and then falls.

     • Compound Generator: Can be made flat or rising (over-compounded) by adjusting series field strength.

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5. Armature Reaction and Commutation

5.1 Armature Reaction

1. Definition: The effect of the magnetic field produced by the armature current on the main field flux produced by the field poles.

2. Consequences:

   • Distortion of Main Field Flux: The resultant flux density wave is distorted. It is strengthened at the leading pole tip and weakened at the trailing pole tip.

   • Demagnetizing Effect (if brushes are on Geometric Neutral Axis - GNA): Due to cross-magnetization, the flux per pole may slightly decrease if the magnetic circuit is saturated.

   • Shift of Magnetic Neutral Axis (MNA): The plane where the flux density is zero (and coil EMF is zero) shifts from the GNA in the direction of rotation for a generator.

3. Problems Caused:

   • Poor commutation (sparking at brushes) if brushes remain on GNA, as the coil undergoing commutation now has an induced EMF.

   • Reduction in generated EMF under load.

   • Possible flashover between brushes at heavy overloads.

4. Remedies:

   • Brush Shift: Shift brushes to the new MNA. For a generator, shift brushes forward in the direction of rotation. Disadvantage: Shifting introduces a demagnetizing component of armature reaction.

   • Use of Interpoles (Commutating Poles): Most effective modern solution. Interpoles placed midway between main poles produce a flux that exactly neutralizes the reactance voltage in the coil undergoing commutation. Their winding is in series with the armature, so their strength varies with load.

   • Compensating Windings: Embedded in pole faces and connected in series with the armature. They neutralize armature reaction under the pole faces, preventing field distortion. Used in large machines subject to heavy overloads (e.g., rolling mill motors).

5.2 Commutation

1. Definition: The process by which a coil short-circuited by the brushes has its current reversed from $+I_a$ to $-I_a$ (or vice-versa) as it moves from one parallel path to the next.

2. Ideal Commutation: Current reversal is linear and instantaneous, resulting in no sparking.

3. Practical Challenges & Causes of Sparking:

   • Reactance Voltage ($L \frac{di}{dt}$): The self-induced EMF in the coil due to the rapid reversal of current opposes the current change.

   • Armature Reaction: If MNA shifts, a small EMF may be induced in the short-circuited coil.

4. Methods to Improve Commutation:

   • Use of high-resistance brushes to limit the circulating current during commutation.

   • Brush Shift (as above).

   • Interpoles (as above) – they induce an EMF in the commutating coil to cancel the reactance voltage.

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6. Parallel Operation of DC Generators

Essential for increasing capacity, reliability, and maintenance flexibility in a power plant.

6.1 Conditions for Parallel Operation

For two or more DC generators (preferably identical) to be connected in parallel:

1. Polarities Must Be the Same: Terminal voltages must have the same polarity. This is checked by a voltmeter test across the open switch connecting the generators.

2. Voltages Should Be Equal: Terminal voltages should be approximately equal at the time of closing the paralleling switch to avoid a large circulating current.

3. For Shunt Generators: The external (drooping) characteristics should be similar to ensure proper load sharing. Generators with steeper droop characteristics take less share of the load.

6.2 Procedure for Paralleling Shunt Generators

1. Start the new generator (Generator #2) and bring it to rated speed using its prime mover.

2. Adjust its field rheostat until its terminal voltage is slightly higher than the busbar voltage (to ensure it takes some load immediately).

3. Close the main circuit breaker to connect Generator #2 to the busbars. At this moment, it may not supply any current if voltages are exactly matched.

4. To make Generator #2 share the load, increase its excitation (by reducing its field rheostat resistance) and/or increase the speed of its prime mover. This increases its generated EMF, causing it to deliver more current.

5. Load sharing is adjusted by varying the field excitation. Increasing excitation of one generator makes it take more load, and decreasing it shifts load to the other(s).

6.3 Load Sharing Between Compound Generators

• Requires special care because of their rising voltage characteristic.

• To ensure stable parallel operation, an equalizer busbar and equalizer connection are used.

• The equalizer connects the series field windings in parallel. This ensures that the total armature current divides between the machines in proportion to their shunt field strengths, preventing one machine from taking all the load and becoming over-compounded.

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7. Induced Voltage and Torque Equations

7.1 Generated EMF Equation ($E_g$)

The average EMF generated in a DC generator is derived from the fundamental law $e = Blv$ and considering all conductors ($Z$) and parallel paths ($A$). $E_g = \frac{P \phi Z N}{60 A}$ Where:

• $E_g$ = Generated EMF (Volts)

• $P$ = Number of poles

• $\phi$ = Flux per pole (Webers)

• $Z$ = Total number of armature conductors

• $N$ = Speed of rotation (RPM)

• $A$ = Number of parallel paths in armature ($A=P$ for lap, $A=2$ for wave)

Alternatively, in terms of angular velocity $\omega$ (rad/s): $E_g = \frac{P \phi Z \omega}{2\pi A}$

7.2 Torque Equation ($T_a$)

In a generator, mechanical torque is supplied by the prime mover. An opposing electromagnetic torque is developed due to the interaction of armature current and the magnetic field. $T_a = \frac{P \phi Z I_a}{2\pi A}$ Where:

• $T_a$ = Armature (Electromagnetic) Torque (Newton-meters)

• $I_a$ = Total armature current (Amperes)

Relationship between Power, Torque, and EMF:

• The electromagnetic power developed in the armature is: $P_{em} = E_g I_a = T_a \omega$ This shows the conversion of mechanical power ($T_a \omega$) into electrical power ($E_g I_a$).

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8. Equivalent Circuit and Magnetization Curve

8.1 Equivalent Circuit

The equivalent circuit provides a simplified model for analyzing performance.

1. General Form (for a Shunt Generator):

   • Armature Circuit: Modeled as a generated EMF source ($E_g$) in series with armature resistance ($R_a$) and brush contact drop (often modeled as a small fixed voltage or included in $R_a$).

   • Field Circuit: Shunt field winding represented by its resistance ($R_{sh}$) across the armature terminals.

   • Load: Connected across the terminals, drawing load current $I_L$.

2. Key Equations from Circuit:

   • Terminal Voltage: $V_t = E_g - I_a R_a$ (assuming brush drop included in $R_a$).

   • Armature Current: $I_a = I_L + I_{sh}$.

   • Shunt Field Current: $I_{sh} = V_t / R_{sh}$.

   • Generated EMF: $E_g = k \phi \omega$, where $k$ is the machine constant.

8.2 Magnetization Curve (OCC)

1. Definition: The graph of generated EMF ($E_g$) at no-load versus field current ($I_f$) at a constant rated speed. It is the B-H curve of the machine's magnetic circuit.

2. Procedure to Obtain: Run the machine as a separately excited generator at constant speed. With no load, vary $I_f$ from zero to a value giving about 25% above rated voltage, then back to zero. Plot $E_g$ vs. $I_f$. The curve for increasing $I_f$ lies slightly above the return curve due to hysteresis.

3. Key Features:

   • Residual Voltage ($E_r$): Small voltage (2-5% of rated) generated at $I_f=0$ due to residual magnetism.

   • Linear Region: At low flux, the curve is straight (unsaturated iron).

   • Knee Point: The bend where saturation of the iron begins.

   • Saturated Region: The curve flattens, requiring large increases in $I_f$ for small increases in $E_g$.

4. Significance:

   • Determines the critical field resistance for shunt generator voltage build-up.

   • Used to find the required field current for a given generated voltage.

   • Essential for analyzing performance under load when combined with the concept of armature reaction.

Conclusion: The DC generator, though largely superseded by AC generation and rectification for bulk power, encapsulates the core principles of electromechanical energy conversion. Its study provides an indispensable foundation for understanding more complex AC machines, the dynamics of torque production, and the challenges of commutation and magnetic saturation that are relevant across many types of electrical machinery.