Download Synchronous generators

TEMPUS ENERGY: SYNCHRONOUS GENERATORS
1: TURBO GENERATORS AND SALIENT-POLE GENERATORS
In the majority of the synchronous generators, a sinusoidal voltage is induced in the stator by driving a
rotor. This rotor produces, with respect to this rotor, a fixed magnetic field. This fixed magnetic field is
due to permanent magnets mounted in the rotor or this magnetic field is due to electromagnets mounted in
the rotor and fed by a DC current. By controlling this DC current, the induction of this magnetic field can
be controlled (which is not possible when using permanent magnets).
Synchronous generators are commonly used in large electrical power stations (in nuclear power stations
and in power stations based on fossil fuels) where they inject their active power into the high voltage grid.
Synchronous generators can be turbo generators or salient-pole generators. Turbo generators are fast
rotating generators (for instance 1500 rpm or 3000 rpm) and have a rotor with a limited diameter with a
small number of pole pairs 𝑝. Turbo generators are mainly used in thermal power stations driven by steam
turbines. The high synchronous speed of rotation
𝑁𝑆 =
60 𝑓
𝑝
is inversely proportional with the number of pole pairs 𝑝 in the generator (and proportional with the
generated frequency 𝑓).
Figure 1: Synchronous turbo generator in an electrical power station
Salient-pole generators have a large rotor diameter which enables to realize a larger number of pole pairs.
This limits the synchronous speed. These slowly rotating salient-pole generators are commonly used in
hydraulic power stations (Figure 2 which visualizes a scale model of the pump station of Coo in Belgium
having salient-pole generators) and in wind turbines (Enercon wind turbine of Figure 3).
Figure 2: Scale model of the pump station of Coo with salient-pole generator
Figure 3: Synchronous generator in a wind turbine
2: EQUIVALENT CIRCUIT OF A TURBO GENERATOR AND THE POWER FLOW
A synchronous generator behaves as a non-ideal voltage source having the equivalent circuit visualized in
Figure 4. There is a generated voltage 𝑒(𝑡) and an internal ohmic inductive impedance containing 𝑅𝑖 and
𝐿𝑖 . Figure 4 also visualizes a switch which allows to connect and disconnect the generator with the grid
voltage 𝑢𝑔 𝑠𝑖𝑛(Ω𝑆 𝑡) (having an amplitude 𝑢𝑔 and pulsation Ω𝑆 ). Assume the generator is connected with a
strong grid meaning the generator is not able to change the grid voltage 𝑢(𝑡) = 𝑢𝑔 𝑠𝑖𝑛(Ω𝑆 𝑡).
The current 𝑖(𝑡) satisfies the differential equation
𝑢(𝑡) + 𝑅𝑖 𝑖(𝑡) + 𝐿𝑖
𝑑 𝑖(𝑡)
𝑑𝑡
= 𝑒(𝑡).
The solution of this differential equation mainly depends on the amplitude of 𝑒(𝑡) in comparison with the
amplitude of 𝑢(𝑡) and on the phase of 𝑒(𝑡) in comparison with the phase of 𝑢(𝑡). As visualized in Figure
5, the amplitude 𝐸 of 𝑒(𝑡) and the phase difference 𝜃 are very important to determine the power flow
between the generator and the grid.
Figure 4: Equivalent circuit of a synchronous generator
The instantaneous power 𝑃(𝑡) = 𝑢(𝑡) 𝑖(𝑡) contains two terms. The first term has an average value
𝑃=
1 𝑢𝑔 𝐸 𝑠𝑖𝑛(𝜃)
2
Ω𝑆 𝐿𝑖
and the second term has an amplitude
𝑄=−
𝑢𝑔 (𝑢𝑔 − 𝐸𝑐𝑜𝑠(𝜃))
Ω𝑆 𝐿𝑖
.
Here, 𝑃 is the active power injected into the grid by the generator for each phase (the three phase power is
three times larger)1. In case a synchronous machine is generating, the angle 𝜃 is positive. The voltage 𝑒(𝑡)
leads the grid voltage 𝑢(𝑡) = 𝑢𝑔 𝑠𝑖𝑛(Ω𝑆 𝑡) (in case the synchronous machine is motoring the angle 𝜃 is
negative and 𝑒(𝑡) lags the grid voltage).
3: REACTIVE POWER
The DC excitation of the rotor windings is very important. By increasing the excitation current in the rotor
windings, the amplitude of the induced voltage 𝑒(𝑡) increases. This implies the torque and therefore also
the active power can be larger.
The excitation also determines the reactive power (for each phase, the three phase power is three times
larger) as specified by2
𝑄=−
1
𝑢𝑔 (𝑢𝑔 − 𝐸𝑐𝑜𝑠(𝜃))
Ω𝑆 𝐿𝑖
.
In case of a salient-pole synchronous generator, another formula is valid but the main conclusions and the
philosophy remains the same.
2
In case of a salient-pole synchronous generator, another formula is valid but the main conclusions and the
philosophy remains the same.
By feeding the rotor windings by an excitation current which is sufficiently large (over excited generator
having a large 𝐸), this generator will generate reactive power (contrary to an asynchronous generator
which consumes reactive power). By feeding the rotor windings by an excitation current which is smaller
(under excited generator having a small 𝐸), this generator will consume reactive power (similar with an
asynchronous generator which also consumes reactive power). By adjusting the excitation current, the
generated or the consumed reactive power can be adjusted.
By having a sufficiently large excitation current, the synchronous generator is able to supply reactive
power to the loads, contrary to an asynchronous generator which has problems to supply reactive power.
3.1: REMARKS
Especially when considering smaller wind turbines, the synchronous generator can be grid connected
without the use of a power electronic converter (which reduces the capital investment). In this situation, a
strong grid with a fixed frequency gives the generator and the blades of the wind turbine a fixed speed of
rotation. Since the generator is grid connected, the excitation of the generator is important since this
excitation determines the reactive power generated or consumed by this generator.
When there is a frequency converter between the synchronous generator and the grid as visualized in
Figure 5, the speed of the generator and the rotor blades is not fixed. Due to the frequency converter, the
frequency of the voltage generated by the generator is allowed to depend on the wind speed. Moreover,
the frequency converter is able to inject reactive power into the grid or to consume reactive power
irrespective of the excitation of the synchronous generator.
4: BRUSHLESS SYNCHRONOUS MACHINE
The rotor of a classical synchronous machine (functioning as a motor or as a generator) is fed by an
excitation current. This requires slip rings and brushes which implies a lot of maintenance. Figure 5
visualizes a wind turbine equipped with a classical synchronous generator having slip rings and brushes.
Figure 5: Wind turbine equipped with a synchronous generator
In order to reduce the maintenance costs related with these slip rings and brushes, a brushless synchronous
generator can be used as visualized in Figure 6. Actually two generators, an auxiliary generator and a main
generator, are built in one single machine. The auxiliary generator contains an excitation winding in the
stator which is easily fed by a DC excitation current giving a fixed magnetic field. The rotor contains a
three phase winding which rotates in this fixed magnetic field and an AC voltage is induced in this three
phase winding. Diodes, mounted inside the rotor, rectify this generated voltage.
Using this rectified voltage, the excitation winding (in the rotor) of the main generator is fed giving a
synchronously rotating magnetic field. Due to this rotating magnetic field, a sinusoidal voltage is induced
in the three phase stator winding of the main generator.
Figure 6: Brushless synchronous generator
Figure 7: Rotors of brushless synchronous generators
Figure 8: Stator and rotor of a brushless synchronous generator (4 poles)