- Electrical Machines - Home
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- DC Machines
- Construction of DC Machines
- Types of DC Machines
- Working Principle of DC Generator
- EMF Equation of DC Generator
- Derivation of EMF Equation DC Generator
- Types of DC Generators
- Working Principle of DC Motor
- Back EMF in DC Motor
- Types of DC Motors
- Losses in DC Machines
- Applications of DC Machines
- More on DC Machines
- DC Generator
- DC Generator Armature Reaction
- DC Generator Commutator Action
- Stepper vs DC Motors
- DC Shunt Generators Critical Resistance
- DC Machines Commutation
- DC Motor Characteristics
- Synchronous Generator Working Principle
- DC Generator Characteristics
- DC Generator Demagnetizing & Cross-Magnetizing
- DC Motor Voltage & Power Equations
- DC Generator Efficiency
- Electric Breaking of DC Motors
- DC Motor Efficiency
- Four Quadrant Operation of DC Motors
- Open Circuit Characteristics of DC Generators
- Voltage Build-Up in Self-Excited DC Generators
- Types of Armature Winding in DC Machines
- Torque in DC Motors
- Swinburne’s Test of DC Machine
- Speed Control of DC Shunt Motor
- Speed Control of DC Series Motor
- DC Motor of Speed Regulation
- Hopkinson's Test
- Permanent Magnet DC Motor
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- DC Servo Motor Theory
- DC Series vs Shunt Motor
- BLDC Motor vs PMSM Motor
- Induction Motors
- Introduction to Induction Motor
- Single-Phase Induction Motor
- 3-Phase Induction Motor
- Construction of 3-Phase Induction Motor
- 3-Phase Induction Motor on Load
- Characteristics of 3-Phase Induction Motor
- Speed Regulation and Speed Control
- Methods of Starting 3-Phase Induction Motors
- More on Induction Motors
- 3-Phase Induction Motor Working Principle
- 3-Phase Induction Motor Rotor Parameters
- Double Cage Induction Motor Equivalent Circuit
- Induction Motor Equivalent Circuit Models
- Slip Ring vs Squirrel Cage Induction Motors
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- Induction Motor Equivalent Circuits
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- Induction Motors Power Flow Diagram & Losses
- Determining Induction Motor Efficiency
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- 3-Phase Induction Motor Fault Types
- Synchronous Machines
- Introduction to 3-Phase Synchronous Machines
- Construction of Synchronous Machine
- Working of 3-Phase Alternator
- Armature Reaction in Synchronous Machines
- Output Power of 3-Phase Alternator
- Losses and Efficiency of an Alternator
- Losses and Efficiency of 3-Phase Alternator
- Working of 3-Phase Synchronous Motor
- Equivalent Circuit and Power Factor of Synchronous Motor
- Power Developed by Synchronous Motor
- More on Synchronous Machines
- AC Motor Types
- Induction Generator (Asynchronous Generator)
- Synchronous Speed Slip of 3-Phase Induction Motor
- Armature Reaction in Alternator at Leading Power Factor
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- Stationary Armature vs Rotating Field Alternator Advantages
- Synchronous Impedance Method for Voltage Regulation
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- Significance of Short Circuit Ratio in Alternator
- Hunting Effect Alternator
- Hydrogen Cooling in Synchronous Generators
- Excitation System of Synchronous Machine
- Equivalent Circuit Phasor Diagram of Synchronous Generator
- EMF Equation of Synchronous Generator
- Cooling Methods for Synchronous Generators
- Assumptions in Synchronous Impedance Method
- Armature Reaction at Unity Power Factor
- Voltage Regulation of Alternator
- Synchronous Generator with Infinite Bus Operation
- Zero Power Factor of Synchronous Generator
- Short Circuit Ratio Calculation of Synchronous Machines
- Speed-Frequency Relationship in Alternator
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- Max Reactive Power in Synchronous Generators
- Power Flow Equations for Synchronous Generator
- Potier Triangle for Voltage Regulation in Alternators
- Parallel Operation of Alternators
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- Constant Flux Linkage Theorem
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- Salient Pole Synchronous Machine Theory
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- Power-Angle of Salient Pole Machines
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- Power Input of Synchronous Generator
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- Hunting Synchronous Motor
- Self-Starting Synchronous Motor
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- Effect of Load Change on Synchronous Motor
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- Output Power of Synchronous Motor
- Input Power of Synchronous Motor
- V Curves & Inverted V Curves of Synchronous Motor
- Torque in Synchronous Motor
- Construction of 3-Phase Synchronous Motor
- Synchronous Motor
- Synchronous Condenser
- Power Flow in Synchronous Motor
- Types of Faults in Alternator
- Miscellaneous Topics
- Electrical Generator
- Determining Electric Motor Load
- Solid State Motor Starters
- Characteristics of Single-Phase Motor
- Types of AC Generators
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- Electrical Machines Basic Terms
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- CVT vs PT
- Metering CT vs Protection CT
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- Discussion
DC Generator
Here, we have listed all the important formulas and equations related to DC generators used in different electrical practices like design, simplify, and analysis. This page can serve as a DC generator formula handbook for electrical engineering students and professionals.
What is DC Generator?
An electromechanical energy conversion machine that converts rotational mechanical energy into DC electrical energy is referred to as a DC generator. A DC generator consists of two parts namely stator and rotor. The stator forms the field system of the machine, while the rotor acts as the armature.
Types of DC Generator
Based on armature and field winding connections, generators are classified into the following three types −
- Series DC Generator − The field winding is connected in series with the armature winding.
- Shunt DC Generator − The field winding is connected in parallel with the armature winding.
- Compound DC Generator − It has both series and shunt field windings connected with the armature winding.
Main Parts of a DC Generator
A typical DC generator consists of three-main parts namely magnetic field system, armature, and commutator and brushgear.
EMF Equation of DC Generator
The mathematical expression which helps to determine the induced or generated EMF of the DC generator is known as the EMF equation of the DC generator. It is given by,
$$\mathrm{E_{g} \: = \: \frac{NP \phi Z}{60A}}$$
Where, N is the speed of armature in RPM, P is the number of poles in the machine, φ is the magnetic flux per pole, Z is the number of armature conductors, and A is the number of parallel paths in armature winding.
The emf equation for wave wound DC generator (A = 2) is given by,
$$\mathrm{E_{g} \: = \: \frac{NP \: \phi \: Z}{120}}$$
The EMF equation for lap wound DC generator (A = P) is given by,
$$\mathrm{E_{g} \: = \: \frac{N \: \phi \: Z}{60}}$$
Generated Power and Load Power of DC Generator
The power developed in the armature of a DC generator is called generated power. The generated power by a DC generator is given by,
$$\mathrm{P_{g} \: = \: E_{g}I_{a}}$$
The amount of power that is supplied to the load by a DC generator is called load power. The load power of a DC generator is given by,
$$\mathrm{P_{L} \: = \: V_{T}I_{L}}$$
Where, VT is the terminal voltage, and IL is the load current.
Terminal Voltage of DC Generator
The part of total emf induced available at the load terminals of a DC generator is known as the terminal voltage of the DC generator.
Terminal Voltage of Series DC Generator
For a series DC generator, the terminal voltage is given by,
$$\mathrm{V_{T} \: = \: E_{g} \: - \: I_{a} \left( R_{a} \: + \: R_{se} \right)}$$
Where, Eg is the total generated emf, Ia is the armature current, Ra is the armature winding resistance, and Rse is the series field resistance.
Terminal Voltage of Shunt DC Generator
For a shunt DC generator, the terminal voltage is given by,
$$\mathrm{V_{T} \: = \: E_{g} \: - \: I_{a}R_{a}}$$
Armature Current of DC Generator
The total current that flows through the armature winding when a load is connected to a DC generator is known as the armature current of a DC generator.
Armature Current of Series DC Generator
The armature current of a series DC generator is given by,
$$\mathrm{I_{a} \: = \: I_{se} \: = \: \frac{E_{g} \: - \: V_{T}}{R_{a} \: + \: R_{se}}}$$
Armature Current of Shunt DC Generator
The armature current of a shunt DC generator is given by,
$$\mathrm{I_{a} \: = \: I_{sh} \: + \: I_{L}}$$
Where, Ish is the shunt field current, and IL is the load current.
Field Current of Shunt DC Generator
In the shunt DC generator, the electric current that flows through the shunt field winding to produce the working magnetic flux is known as its field current.
$$\mathrm{I_{sh} \: = \: \frac{V_{T}}{R_{sh}}}$$
Where, Rsh is the resistance of shunt field winding.
Total Output Power of DC Generator
The amount of electrical power that is delivered to the load by the DC generator is known as the total output power of the DC generator.
The output power of a DC generator is given by,
$$\mathrm{P_{out} \: = \: P_{in} \: - \: (core \: losses \: + \: copper \: losses \: + \: mechanical \: losses \: + \: stray \: losses)}$$
Where, Pin is the total input mechanical power, and Pout is the total output electrical power.
DC Generator Losses
The amount of generated power which is wasted in the form of heat and does not delivered to the load is called power loss. In a DC generator, the total power loss is given by,
$$\mathrm{Losses \: = \: P_{cu} \: + \: P_{i} \: + \: P_{m} \: + \: P_{stray}}$$
Where, Pcu is the copper loss in armature and field windings, Pi is the iron losses in iron cores of generator, Pm is the mechanical loss (friction and windage losses), and Pstray is the stray loss such as power loss in metal body due to induction.
Efficiency of DC Generator
The ratio of the output power to the input power to a DC generator is known as efficiency of the DC generator.
$$\mathrm{Efficiency, \: \eta \: = \: \frac{Output \: power}{Input \: power}}$$
For a DC generator, we have defined three efficiencies namely, mechanical efficiency, electrical efficiency, and overall efficiency.
Mechanical Efficiency of DC Generator
The ratio of mechanical power in the armature to the total input mechanical power is referred to as the mechanical efficiency of the DC generator. It is given by,
$$\mathrm{\eta_{mech} \: = \: \frac{\text{Mechanical power developed in armature}}{\text{Input mechanical power}}}$$
$$\mathrm{\Rightarrow \: \eta_{mech} \: = \: \frac{E_{g}I_{a}}{\omega \: \tau}}$$
Where, is the mechanical power input through the shaft.
Electrical Efficiency of DC Generator
The ratio of output electrical power to the armature power is known as electrical efficiency of the DC generator.
$$\mathrm{\eta_{elect} \: = \: \frac{\text{Output electrical power } \: ( V_{T}I_{L} )}{\text{Armature power} \: (E_{g}I_{a})}}$$
Overall Efficiency of DC Generator
The ratio of output electrical power to the input mechanical power is known as the overall efficiency of the dc generator.
$$\mathrm{\eta_{overall} \: = \: \frac{\text{Output electrical power} \: (V_{T}I_{L})}{\text{Input mechanical power } \: (\omega \: \tau)}}$$
$$\mathrm{\Rightarrow \: \eta_{overall} \: = \: \frac{V_{T}I_{L}}{V_{T}I_{L} \: + \: Losses }}$$
Condition for Maximum Efficiency of DC Generator
For the maximum efficiency of a DC generator, the variable losses (copper losses in field and armature windings) and the constant losses (core losses and mechanical losses) must be equal, i.e.,
$$\mathrm{\text{Variable losses }\: = \: \text{ Constant losses}}$$
Conclusion
In this article, we listed all the important formulae of DC generators used for design and analysis of the DC generator. All these formulae are very important for electrical engineering students and practicing electrical professionals.