This article describes the DC generator equations and formulas, including parameters for shunt and series generators, EMF calculations, armature and field current equations, power analysis, and efficiency calculation.
A DC generator converts mechanical energy into DC electrical energy. It has two main parts: the stator and the rotor. The stator has the field winding, which generates the magnetic flux. The armature is the rotating part of the generator the rotating part,
This guide describes the essential DC generator equations and explains parameters like terminal voltage, current flows, power, and efficiency for shunt and series generators in detail.
DC Generator Equations
EMF Equation for DC Generator
The EMF equation of a DC generator shows how these machines convert mechanical energy into electrical energy. The voltage generated in the armature winding can be calculated using the EMF equation The four factors that determine the EMF are generator construction, speed of armature, number of armature conductors. and magnetic flux.
The following equation shows the EMF generated per conductor in a DC generator,
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 a DC generator depends on the type of armature winding. There are two main types of windings-lap and wave. In lap winding, the number of parallel paths (A) is equal to the number of poles (P). In wave winding, the number of parallel paths (A) is 2.
The EMF equation for lap winding is,
The modified DC generator equation for wave winding is,
The general EMF equation for a DC generator is:
Torque Equation for DC Generator
Terminal Voltage of DC Generator
The voltage available at the output terminal of the generator is called the terminal voltage. The terminal voltage at no load and full load are not the same because voltage drop occurs in the armature when current flows through it.
Series DC Generator
The series generator has its field winding connected in the series with the armature winding and the same current flows in both the windings.
Where:
- Vt: Terminal voltage
- E: Generated EMF
- Ia: Armature current
- Ra: Armature resistance
- Rs: Series field resistance
Shunt DC Generator
The field and armature winding are connected in parallel in a shunt generator. The terminal voltage of the shunt generator can be expressed as,
Where:
- Vt: Terminal voltage
- E: Generated EMF
- Ia: Armature current
- Ra: Armature resistance
DC Generator Armature Current
The current flowing in the armature winding when the generator is connected to the load is called the armature current. The armature current for the series and shunt generator are different when these generators deliver power to the same load.
Series DC Generator
The armature current of a series DC generator is,
The same armature current flows in the field and armature winding.
Shunt DC Generator
The armature current in a shunt DC generator is,
Where,
- Ish: Shunt Field Current
- IL: Load Current
Field Current of DC Generator
The field current flows in the field winding and produces a magnetic field in the DC generators.
Series DC Generator
The field and armature windings are in a series connection, so an equal amount of current flows in both windings. As a result, the field current is equal to the armature current.
Shunt DC Generator
The field current is determined by the voltage across the field winding and its resistance.
Where Rsh is the shunt field winding.
Power Generated & Load Power
Power Generated
The power generated in a DC generator is the total electrical power produced in the armature winding. The generated power is the product of EMF and the armature current.
The total electrical power of the DC generator is:
Load Power (Output Power)
The terminal voltage and the EMF at no load are the same, but at load, the terminal voltage is less than the EMF. The product of terminal voltage and load current is the power delivered to the load. Mathematically, it can be expressed as.
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 input power of a DC generator is the mechanical power supplied to its shaft. The generator converts this mechanical power into electrical power in the armature.
The formula for input power is:
Where
- ω is the angular speed of the armature
- T is the torque applied
If the speed(N) is given in revolutions per minute (RPM), the angular velocity can be calculated as:
Where N is the rotational speed in RPM.
Converted Power
The converted power of a DC generator is the mechanical power supplied to the armature. It represents the total electrical energy supplied to the generator considering friction and windage loss.
The formula for converted power is:
The power converted from mechanical to electrical form is:
Efficiency of DC Generator
The generator receives the mechanical power and converts it into electrical power. The DC generator can not convert all the mechanical energy into electrical energy because of the losses in the conversion process. The ratio of the electrical power to mechanical power is the efficiency of the DC generator and mathematically it is expressed as,
Mechanical Efficiency
The mechanical efficiency of a DC generator indicates how effectively the generator transforms the mechanical power into electrical power. It is the ratio of the converted power to the input mechanical power.
Electrical Efficiency
The electrical efficiency of a DC generator indicates how effectively the DC generator delivers the electrical power generated in the armature to the external load. Electrical efficiency is the ratio of the output power to the converted power in the armature.
Overall Efficiency:
The ratio of output electrical power to the input mechanical power is the overall efficiency of the DC generator.
The mechanical input power is equal to the output electrical power and losses. The above equation can be written as,
Maximum Efficiency
you will get the maximum efficiency of the DC generator when variable losses become equal to the constant loss.
Conclusion
In this article, we covered DC generator equations and formulas. These equations are essential for the optimal design and efficient machine operation.