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DC Generator – Formulas and Equations
In this article, 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.
DC Generator Definition
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, Ï• 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,
$$\mathrm{\eta_{mech} = \frac{Mechanical\: power\: developed \: in\: armature}{Input\:mechanical\: power}}$$
$$\mathrm{\Rightarrow \eta_{mech} = \frac{E_{g}I_{a}}{\omega \tau }}$$
Where, ωτ 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.
$$\mathrm{\eta_{elect} = \frac{Output\: electrical\: power\left ( V_{T}I_{L} \right )}{Armature\: power\left ( E_{g}I_{a} \right ) }}$$
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.
$$\mathrm{\eta_{overall} = \frac{Output\: electrical\: power\left ( V_{T}I_{L} \right )}{Input\: mechanical\: power\left (\omega \tau \right) }}$$
$$\mathrm{\Rightarrow \eta_{overall} = \frac{V_{T}I_{L}}{V_{T}I_{L}+Losses }}$$
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.,
$$\mathrm{Variable\: losses = Constant\: losses}$$
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.
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