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Three-Phase Generator

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This guide covers three phase generator construction, voltage regulation, its rating, cooling methods, excitation control and several solved examples.

The three-phase generator has two main windings:

1. A three-phase AC winding
2. Another winding carrying DC.

In most cases the rotor has the DC winding and the stator the AC winding. A generator with a rotating AC winding and a stationary DC winding, while suitable for smaller outputs, is not satisfactory for the larger outputs required at power stations. With these machines the output can be in megawatts, a value too large to be handled with brushes and slip-rings. Because the terminal voltages range up to 33 kV, the only satisfactory construction is to have the AC windings stationary and to supply the rotor with DC.

This arrangement has the following advantages:

1. Extra winding space available for the AC windings
2. Easier to insulate for higher voltages
3. Simple, strong rotor construction
4. Lower voltages and currents in the rotating windings
5. High current windings have solid connections to the ‘outside’ circuit
6. Better suited to the higher speeds (and smaller number of poles) of turbine drives.


The stator of the three-phase synchronous machine consists of a slotted laminated core into which the stator winding is fitted. The stator winding consists of three separate windings physically displaced from each other by 120°E. Each phase winding has a number of coils connected in series to form a definite number of magnetic poles.

A four-pole machine, for example, has four groups of coils per phase or four pole-phase groups. The ends of the three-phase windings are connected in either the star or delta configuration to the external circuit.

The phase windings for a three-phase machine consist of three identical windings symmetrically distributed around the stator.

A typical three-phase stator is shown in Figure 1.

Stator for a four-pole 415 V three-phase 350 kVA generator

Figure 1 Stator for a four-pole 415 V three-phase 350 kVA generator


The three phase generator rotor can be of two types: low speed and high speed.

Low Speed (Salient Pole)

This type usually consists of a ‘spider’ similar to that used in DC machines, on which the field poles and the field coils are bolted (see Figure 2(a)). As the peripheral forces produced on the circumference of the rotor would be excessive at high speed, physical constraints limit the use of this type of rotor to low-speed machines.

ain types of generator rotors: (a) low speed, (b) high speed

Figure 2 Main types of generator rotors: (a) low speed, (b) high speed

High Speed (Cylindrical)

The cylindrical rotor was developed to meet the needs of higher-speed prime movers. To counteract centrifugal forces its diameter must be small compared to its length (see Figure 2(b)).

Prime Movers

Low speed

Most diesel engines used as prime movers for driving generators operate within the range 500–1000 rpm and this necessitates the use of rotors with many pairs of poles.

Hydroelectric turbines have water-driven impellers that operate at low speeds, consequently they also drive rotors with many poles. While the diesel-driven generator usually has its shaft in the horizontal plane, the hydroelectric unit has its shaft in the vertical plane. This method of construction means that special thrust bearings have to be fitted to take the end thrust of the rotating component.

High speed

Turbine prime movers, whether steam or gas, operate efficiently at speeds of about 3000 rpm. A three phase generator driven by a turbine and producing a frequency of 50 Hz at 3000 rpm must consist of only two poles.

The relationship between speed, frequency and the number of poles can be determined from:

relationship between speed, frequency and the number of poles in three phase generator

Example 1

At what speed would the governor of a 12-pole diesel-driven generator have to be set to enable a frequency of 60 Hz to be generated?

three phase generator frequency formula

A three phase generator in the speed range given in Example 1 will have a large diameter and a comparatively short axial length. With turbines, the extra expense and auxiliary machinery needed restricts their use to larger sizes. Higher outputs mean that the length of the generator must be increased, and the increase in length causes complications in cooling.

A typical standby motor-driven generator is shown in Figure 3 overleaf. This type of generator is used as a backup in the event of a power failure.

Skid mounted generating unit

Figure 3 Skid mounted generating unit

Three Phase Generator Cooling

Low Speed

With engine-driven or hydroelectric generators there is no great difficulty in providing adequate ventilation because of the characteristically large diameter and short axial length. In addition to the large surface area available for direct radiation of heat there is a fanning action due to the rotation of the fields, an action that can be increased by the addition of fan blades if necessary.

When the axial length is short, the heat developed in the imbedded windings is quickly conducted to the ends where it can be dissipated by the fanning action. As the machine size becomes larger it is often necessary to provide ventilation ducts within the core to provide paths through which the cooling air can flow.

High Speed

The provision of adequate cooling facilities is a problem in high-speed machines of large capacity, if the operating temperature of the windings is to be kept within safe limits. The surface area available for cooling in a high-speed machine is less than that in a low-speed machine of the same capacity.

The diameter of the rotor must be small enough to keep the surface speed down to a safe value, so for large capacities the length of the machine must be considerable. This long axial length causes difficulty in cooling the central portion of the core because the heat generated cannot be conducted away quickly enough to limit the temperature rise in the core to a value that will protect the windings and the insulation.

These considerations gave rise to the necessity for completely enclosing the generator and allowing the use of forced ventilation to carry away the heat produced. Where cooling air is used it must be filtered to keep it clean and sometimes washed by passing it through a spray chamber to prevent a build-up of dust within the machine. Washing the air has the added advantage of cooling it, and so further reducing the temperature of the generator, allowing the rating of the machine to be increased.

To increase generator ratings still more, hydrogen gas is used instead of air because of its greater ability to absorb heat. The machine is completely enclosed and the hydrogen is blown through the generator and then through a heat exchanger before being cycled through the generator again. The total exclusion of air from the fully sealed machine is necessary to prevent an explosive air/hydrogen mixture from forming.

Considerable care is taken to ensure the purity of the hydrogen gas. The oil pressure for the bearings is at a higher value than the pressure of the hydrogen being pumped through the machine. This ensures that the oil flow through the seal is towards the hydrogen gas so that it is retained in the machine. The oil may then be passed through a vacuum process to remove any hydrogen gas or air before being reused in the machine.

These cooling methods require considerable power and auxiliary equipment, so the output from the generator must be increased by an appreciable amount for the method to be economically feasible. Accordingly, it is used only on very large capacity machines.


The usual method for DC excitation of the rotor windings is for each machine to have its own DC generator called an exciter. The exciter can be belt driven or geared down from the synchronous machine but the usual practice is for the exciter to be directly coupled to the rotor shaft.

The exciter armature rotates within the influence of the exciter field, causing a DC voltage to be generated in the armature. The exciter output is fed into the field windings of the synchronous machine. By adjusting the rheostat in the exciter field circuit the strength of the magnetic field in the rotor can be varied.

The basic diagram of a generator and its exciter is shown in Figure 4.

Basic generator circuit and excitation system

Figure 4 Basic generator circuit

With very large three phase generators, the DC excitation requirements are substantial. This means that the DC generators have to be large also; so large that they might not be able to self-excite. Because of this, the DC generator might need an exciter of its own; one that is able to self-excite and provide power for the field of the main generator, which in turn supplies the rotor field of the generator.

Some generators use a brushless excitation system in which the exciter armature has been replaced by a small three-phase generator that rotates within the influence of a small residual magnetic field. This causes a small three-phase voltage to be generated in the exciter. When converted to DC by an internal rectifier, it supplies the main field of the generator, resulting in an AC output voltage.

A sensor unit connected to the output of the machine monitors the output voltage and load current of the generator and sends electrical signals to a controlled rectifier, which in turn controls the strength of the exciter field. The sensor unit and the controlled rectifier are in a sense the voltage regulator of the machine.

A basic circuit of a brushless generating system is shown in Figure 5.

Brushless excitation in three phase generator

Figure 5 Brushless excitation

Generated Voltage

The value of the generated AC voltage depends on the strength of the rotor flux and the speed at which it cuts the windings. Because the speed must be constant (and is linked to the frequency required) the sole remaining factor determining the value of the generated voltage is the strength of the rotor flux.

For a three phase generator, the generated voltage is found from:

three phase generator generated voltage formula

Example 2

Calculate the line voltage of a 50 Hz star-connected generator given the following details:

three phase generator line voltage calculation

Effect of Load on Generator Voltage

A three phase generator can be considered to consist of three components in series:

1. An AC Generating Source
2. A Resistor—Representing Iron And Copper Losses
3. An Inductor—Representing The Inductance Of The Windings And Magnetic Leakage.

Any load placed on the generator must be assumed to be in series with these components (see Figure 6 overleaf).

Equivalent circuit of a three phase generator

Figure 6 Equivalent circuit of a three phase generator

The series impedance of the resistance and inductance provides a drop in voltage before the generated voltage can reach the connected load. Additionally the load current in the AC windings produces an armature reaction, which also affects the output voltage.

With a unity power factor load, the armature reaction merely distorts the main field and the effect on voltage is minimal, the voltage drop is mainly due to the series impedance. Figure 7(a) shows that the resistive voltage drop IR is in phase with the load current I and the voltage drop due to the reactance IX is at 90°E to the IR drop.

voltage regulation phasor diagrams for three phase generator

Figure 7 Phasors for various power factor loads on a generator

These two values combine to form a voltage drop IZ due to the impedance of the generator windings. The phasor sum of the output voltage and IZ gives the generated voltage Vg.

For a load with a lagging power factor, however, the magnetic effect of the stator currents opposes that of the rotor (see Figure 7(b)). This results in a weakened rotor field and reduces the output voltage further than the resistive load alone did. As before, IR is in phase with the load current I. IX is at 90°E to IR, so placing IZ at a different angle to the previous case. In a similar manner, Vg is equal to the phasor sum of the output voltage and IZ.

For a load with a leading power factor, the flux caused by the stator currents assists that of the rotor, resulting in an increased output voltage (see Figure 7(c)).

The characteristics of the three types of loads are shown in Figure 8.

The effect of power factor on the output voltage of an generator

Figure 8 The effect of power factor on the output voltage of an generator

Three Phase Generator Voltage Regulation

A three phase generator is required to give a prescribed terminal voltage at full load. The difference in output between no load and full load is a measure of its voltage regulation. The difference is compared to the full-load value in a similar manner to that for DC machines.

Percent voltage regulation:

Percent voltage regulation: formula for three phase generator

Example 3

A three-phase star-connected generator has an output voltage of 3300 V at full load, with unity power factor. When the load is removed and the excitation is unchanged, the voltage rises to 3350 V. Find the percentage regulation.

voltage regulation example three phase generator

Note: The regulation must also be referred to the load power factor because at any other power factor these Figures would be different.

Three Phase Generator Ratings

A three phase generator is rated according to three basic factors:

1. Frequency
2. Voltage
3. Current.

The frequency fixes the speed at which the generator must be driven, the voltage rating sets the designed output voltage, and the rated current is the full-load current output. The last two factors help establish the volt-ampere rating, usually expressed in kVA.

The three phase generator rating cannot be given in kilowatts because the power factor of any load placed on the generator is beyond the control of the manufacturer, and because its value could vary considerably.

Example 4

A three-phase 415 V 50 Hz generator is rated at 150 kVA at 0.8 power factor.

Calculate the:

(a) Power Loading In Kilowatts When Fully Loaded With Power Factor Values Of 0.8 And 0.6
(b) Full Load Current Of The Generator.

(a) The machine is rated at 150 kVA and 0.8 power factor, so at this load:

three phase generator rating example

At 0.6 power factor:

generator rating at power factor

(b) In both cases, the current flowing will be the full-load current value, which should not be exceeded because of cooling problems within the windings.

At 0.8 power factor:

generator rating at 0.8 power factor

This is the full-load current rating for each phase winding of this particular generator and it applies irrespective of the load power or power factor.

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About Ahmad Faizan

Mr. Ahmed Faizan Sheikh, M.Sc. (USA), Research Fellow (USA), a member of IEEE & CIGRE, is a Fulbright Alumnus and earned his Master’s Degree in Electrical and Power Engineering from Kansas State University, USA.