Learn about DC Generator Equations and Formulas, including shunt and series generator parameters, EMF equation, armature and field current equations, power calculations, and efficiency.
DC generator converts mechanical energy into DC electrical energy. A DC generator has two main parts a stator and a rotor. The stator holds the field winding of the machine and produces flux, while the rotor is the rotating part that acts as the armature. This article provides a detailed explanation of DC Generator Equations and covers various parameters like terminal voltage, currents, efficiencies, power of shunt, and series generators.
DC Generator Equations
EMF Equation for DC Generator
The EMF (Electromotive force) generated in a DC generator is a function of its construction and speed. The EMF generated per conductor in a DC generator is:
Where:
- E: Generated EMF
- P: Number of poles
- ϕ: Flux per pole (in Weber)
- N: Speed of the armature (RPM)
- Z: Total number of armature conductors
- A: Number of parallel paths in the armature
The number of parallel paths(A) in lap winding and wave winding are equal to the number of poles(P) and 2, respectively. The DC generator equation(1) can be modified for lap winding as given below.
The DC generator equation(1) can be modified for wave winding as given below.
The generalized DC generator equation is,
Torque Equation for DC Generator
Terminal Voltage of DC Generator
The terminal voltage of a DC generator refers to the voltage available at the output terminals of the generator.
Series DC Generator
In a series generator, the field winding is connected in the series with the armature winding, and the entire armature current flows through the field.
Where:
- Vt: Terminal voltage
- E: Generated EMF
- Ia: Armature current
- Ra: Armature resistance
- Rs: Series field resistance
Shunt DC Generator
The field windings are connected in parallel (shunt) with the armature winding in a shunt generator. The terminal voltage of a shunt generator is given by:
Where:
- Vt: Terminal voltage
- E: Generated EMF
- Ia: Armature current
- Ra: Armature resistance
Armature Current of DC Generator
When the load is connected to a generator the entire current flows through the armature is known as the armature current.
Series DC Generator
The armature current of a series DC generator is,
Shunt DC Generator
The armature current of a shunt DC generator is,
Where,
- Ish: Shunt Field Current
- IL: Load Current
Field Current of DC Generator
The current flowing in the field winding that produces magnetic flux is called field current.
Series DC Generator
The field winding is connected in the series with the armature winding in the series DC generator, therefore the field current equals the armature current.
Shunt DC Generator
Where Rsh is the shunt field winding.
Power Generated & Load Power
Power Generated
The total electrical power generated in the armature is:
Load Power (Output Power)
The power delivered to the external load is:
Where:
- PL: Load power
- Vt: Terminal Voltage
- IL: Load Current
The difference between generated power and load power accounts for losses in the generator.
Input Power
The mechanical input power to the generator is:
Where
- ω is the angular speed of the armature
- T is the torque applied
Converted Power
The power converted from mechanical to electrical form is:
Efficiency of DC Generator
The efficiency of a DC generator is a measure of how effectively it converts mechanical input power into electrical output power. The ratio of the output power to the input power of a DC generator is known as the efficiency of the DC generator.
Mechanical Efficiency
The mechanical efficiency accounts for the losses in the mechanical system. The mechanical efficiency of a DC generator is defined as the proportion of the mechanical power converted in the armature to the total mechanical power supplied to the generator. Mathematically, it is expressed as:
Electrical Efficiency
The electrical efficiency of a DC generator is defined as the ratio of the electrical output power to the power developed in the armature.
Overall Efficiency:
The overall efficiency of the DC generator is equal to the ratio of output electrical power to the input mechanical power.
Mechanical input power equals the sum of output electrical power and losses. We can write the equation(17) as,
Maximum Efficiency
The maximum efficiency occurs when variable losses (copper losses in field and armature windings) equal constant losses (core and mechanical losses).
Summary: DC Generator Equations
| Equation Name | Series DC Generator | Shunt DC Generator |
| EMF Equation |  | |
| Terminal Voltage |  |  |
| Armature Current |  |  |
| Field Current |  |  |
| Generated Power |  | |
| Output Power |  | |
| Input Power |  | |
| Converted Power |  | |
| Mechanical Efficiency |  | |
| Electrical Efficiency |  | |
| Overall Efficiency |  | |
Conclusion
Understanding the key equations and parameters of DC generators, such as terminal voltage, currents, power, and efficiency, is important for designing and analyzing these machines effectively.