AC Power Generation and Voltage Regulation
AC Power Generation and Voltage Regulation
AC Power Generation and Voltage Regulation
AC Power Generation
Voltage Regulation
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AC main generation in aircraft
PMG : Permanent magnet generator
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Introduction
Figure : power rating of the main generators of some common aircraft (in red
medium to long range aircraft ,in black short to medium range aircraft)
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Introduction
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Synchronous generator construction
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Synchronous generator construction
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Synchronous generator construction
• The rate of rotation of the magnetic fields in the machine is related to the stator
electrical frequency by equation :
𝑛𝑚 𝑃
𝑓𝑠𝑒 =
120
𝑓𝑠𝑒 : electrical frequency, in Hz
𝑛𝑚 : mechanical speed of magnetic field, in r/min ( equals speed of rotor for synchronous
machines )
P : number of poles
• Since the rotor turn at the same speed as the magnetic field, this equation relates
the speed of rotor rotation to the resulting electrical frequency.
• Example :
To generate 60 Hz power in a two-pole machine, the rotor must turn at 3600 r/min
to generate 50 Hz power in a four-pole machine, the rotor must turn at 1500 r/min
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Internal generated voltage of a synchronous generator
Figure (a): Plot of flux versus field Figure (b) : The magnetization curve for the
current for a synchronous generator synchronous generator
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Equivalent circuit of a synchronous generator
Figure : generator equivalent circuit connected in Y Figure : generator equivalent circuit connected in Δ
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Equivalent circuit of a synchronous generator
• The fact that the three phase of a synchronous generator are identical in all aspects except of
phase angle normally leads to the use of a per-phase equivalent circuit.
Vϕ = EA − jIA X S − R A IA
Where EA : is the internal generated voltage produced in one phase of a synchronous generator
Vϕ : output voltage of a phase
XS : synchronous reactance
RA : stator resistance
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Phasor diagram of a synchronous generator
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Phasor diagram of a synchronous generator
Vϕ = EA − jIA XS − R A IA Vϕ = EA − jIA XS − R A IA
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Power and torque in synchronous generators
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Power and torque in synchronous generators
• The real electrical output power of the synchronous can be expressed in line quantities and
in phase quantities as :
𝑃𝑜𝑢𝑡 = 3𝑉𝐿 𝐼𝐿 𝑐𝑜𝑠θ = 3𝑉ϕ 𝐼𝐴 𝑐𝑜𝑠𝜃
• the reactive power output can be expressed in line quantities and in phase quantities as :
𝑄𝑜𝑢𝑡 = 3𝑉𝐿 𝐼𝐿 𝑠𝑖𝑛θ = 3𝑉ϕ 𝐼𝐴 𝑠𝑖𝑛𝜃
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Power and torque in synchronous generators
𝑃𝑐𝑜𝑛𝑣 3𝑉ϕ 𝐸𝐴
𝜏𝑖𝑛𝑑 = = 𝑠𝑖𝑛𝛿
𝜔𝑚 𝜔𝑚 𝑋𝑆
Figure : flow power diagram of a synchronous generator
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Measuring synchronous generator model parameters
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Measuring synchronous generator model parameters
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Synchronous generator operating alone
• The synchronous generator operating alone : to understand the operating characteristics of a synchronous
generator operating alone, examine a generator supplying a load.
• What happens when we increase the load in this generator ?
• The speed of generator will be assumed constant, and all terminal characteristics are drawn assuming
constant speed. Also, the rotor flux in the generators is assumed constant unless their field current is
explicitly changed.
• An increase in the load is an increase in the real and/or reactive power drawn from the generator. Such a
load increase increases the load current drawn from the generator. Because the field resistor has not been
changed, the field current is constant, and therefore the flux ϕ is constant. Since, the prime mover also
keeps a constant speed ω, the magnitude of the internal generated voltage EA =Kϕω is constant.
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Synchronous generator operating alone
• Conclusions :
If lagging loads (+Q or inductive reactive power loads) are added to a generator,
Vϕ and the terminal voltage VT decrease significantly.
If unity-power-factor loads (no reactive power) are added to a generator, there is a
slight decrease in Vϕ and the terminal voltage.
If leading loads (-Q or capacitive reactive power loads) are added to a generator,
Vϕ and the terminal voltage will rise.
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Voltage regulation
• A convenient way to compare the voltage behavior of two generators is by their voltage
regulation. The voltage regulation (VR) of a generator is defined by the equation :
𝑉𝑛𝑙 −𝑉𝑓𝑙
𝑉𝑅 = × 100%
𝑉𝑓𝑙
Vnl : is the no-load terminal voltage of generator
Vfl : is the full-load terminal voltage of generator
• A synchronous generator operating at a lagging power factor has a fairly positive
voltage regulation
• A synchronous generator operating at a unity power factor has a small positive
voltage regulation
• A synchronous generator operating at a leading power factor has a negative
voltage regulation
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Voltage regulation
• It is desirable to keep the voltage supplied to a load constant, even through the
load itself varies.
• The obvious approach is to vary the magnitude of EA to compensate for changes
in the load. Recall that 𝐸𝐴 = 𝐾ϕω. Since the frequency should not be changed in
a normal system, EA must be controlled by varying the flux in the machine.
• For example, suppose that a lagging load is adding to a generator. then Vϕ
decrease. To keep Vϕ in constant RF should be decreased. IF will increase
the flux ϕ will increase EA will increase Vϕ will be kept in constant.
Keep Vϕ in constant
under the variation of
load
• Example 1: A 480-V 60-Hz, Δ-connected, four-pole synchronous generator has the Open circuit
characteristic shown in Figure a. This generator has a synchronous reactance of 0.1 Ω and an
armature resistance of 0.015 Ω. At full load, the machine supplies 1200 A at 0.8 power factor
lagging. Under full-load conditions, the friction and windage losses are 40 kW, and the core losses
are 30 kW. Ignore any field circuit losses
a. What is the speed of rotation of this generator?
b. How much field current must be supplied to the generator to make the terminal voltage 480 V at
no load?
c. If the generator is now connected to a load and the load draws 1200 A at 0.8 power factor
lagging, how much field current will be required to keep the terminal voltage equal to 480 V?
d. Suppose that the generator is connected to a load drawing 1200 A at 0.8 power factor leading.
How much field current would be required to keep VT at 480 V?
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AC Generator
Solution :
This synchronous generator is Δ connected, so its phase voltage is equal to its line voltage Vϕ = VT ,
while its phase current is related to its line current by the equation IL = 3 Iϕ
a. The relationship between the electrical frequency produced by a synchronous generator and the
mechanical rate of shaft rotation is given by equation :
𝑛𝑚 𝑃 120𝑓𝑠𝑒 120(60 𝐻𝑧)
𝑓𝑠𝑒 = therefore 𝑛𝑚 = = = 1800 𝑟/𝑚𝑖𝑛
120 𝑃 4 𝑝𝑜𝑙𝑒𝑠
b. In this machine, Vϕ = VT . Since the generator is at no load , IA = 0 and Vϕ = EA . Therefore, Vϕ =
VT = EA = 480 V. and from the open circuit characteristic, IF = 4.5 A
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AC Generator
c. if the generator is now connected to a load draws 1200 A at 0.8 power factor lagging, then the
armature current in the machine is :
1200𝐴
𝐼𝐴 = = 692.8 𝐴
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The power factor lagging : cosθ = -0.8 so θ = -36.870
If the terminal voltage Vϕ is adjusted to be 480 V, the internal generated voltage EA is given by :
𝐸𝐴 = 𝑉ϕ + 𝑅𝐴 𝐼𝐴 + 𝑗𝑋𝑆 𝐼𝐴 = 480∠00 + 0.015Ω 692.8∠ −36.870 + 𝑗0.1Ω 692.8∠ −36.870
= 480∠00 + 10.39∠ −36.870 +692.8∠53.130 = 529.9 + j49.2 = 532∠5.30
To keep the terminal voltage at 480 V, EA must be adjusted to 532 V. Open circuit characteristic of
synchronous generator, the required field current is 5.7 A.
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AC Generator
d. The power that the generator is supplying can be found from the equation as below :
𝑃𝑜𝑢𝑡 = 3𝑉𝐿 𝐼𝐿 𝑐𝑜𝑠θ = 3 480𝑉 1200𝐴 cos 36.870 = 798 𝑘𝑊
To determine the power input to the generator, use the flow diagram. The mechanical input power is
given by :
Pin = Pout + Pelec loss + Pcore loss + Pmesh loss+ Pstray loss
The stray losses were not specified here, so they will be ignored. In this generator, the electrical
losses are :
𝑃𝑒𝑙𝑒𝑐 𝑙𝑜𝑠𝑠 = 3𝐼2 𝑅𝐴 = 3. 692.8 2
0.015 = 21.6 𝑘𝑊
The core losses are 30 kW, and the friction and windage losses are 40 kW, so the total input power to
the generator is :
Pin = Pout + Pelec loss + Pcore loss + Pmesh loss+ Pstray loss = 798 +21.6+30+40=889.6 kW
𝑃𝑜𝑢𝑡 798 𝑘𝑊
Therefore, the machine’s overall efficiency is : ƞ = . 100% = 100% = 89.75%
𝑃𝑖𝑛 889.6 𝑘𝑊
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AC Generator
e. If the generator’s load were suddenly disconnected from the line, the current IA would drop to zero,
making EA =Vϕ . Since the field current has not changed, so EA has not changed, and Vϕ must rise
to equal to EA .
Therefore, if the load is suddenly dropped, the terminal voltage of the generator would rise to 532 V.
d. If the generator were loaded down with 1200A at 0.8 power factor leading while the terminal
voltage was 480 V:
Cosθ =0.8 so θ=arccos (0.8)=36.870
then the internal generated voltage :
𝐸𝐴 = 𝑉ϕ + 𝑅𝐴 𝐼𝐴 + 𝑗𝑋𝑆 𝐼𝐴 = 480∠00 + 0.015Ω 692.8∠36.870 + 𝑗0.1Ω 692.8∠36.870
= 480∠00 + 10.39∠36.870 + 692.8∠126.870 = 446.7 + j61.7 = 451∠7.10
Therefore, the internal generated voltage EA must be adjusted to provide 451V if VT is to remain
480V. Using the open circuit characteristic, the field current would have to adjusted to 4.1 A.
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AC Generator
Example 2 : A three-phase Y-connected synchronous generator is rated 120 MVA, 13.2 kV, 0.8
power factor lagging, and 60 Hz. Its synchronous reactance is 0.9 Ω, and its resistance may be
ignored. What is its voltage regulation?
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AC Generator
• Solution :
𝑆 120 𝑀𝑉𝐴
the rated armature current is : 𝐼𝐴 = 𝐼𝐿 = = = 5249 𝐴
3𝑉𝑇 3(13.2 𝑘𝑉)
The power factor is 0.8 lagging, so cosθ = -0.8 and θ = -36.870 , the armature current 𝐼𝐴 = 5248∠ −
36.870
13.2𝑘𝑉
The phase voltage is : 𝑉ϕ = = 7621 𝑉
3
Therefore, the internal generated voltage is :
𝐸𝐴 = 𝑉ϕ + 𝑅𝐴 𝐼𝐴 + 𝑗𝑋𝑆 𝐼𝐴 = 7621∠00 + 𝑗0.9Ω 5249∠ −36.870 = 11120∠19.90 V
The resulting voltage regulation is :
11120 − 7621
𝑉𝑅 = 100% = 45.9%
7621
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AC main generation in aircraft
PMG : Permanent magnet generator
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AC main generation in aircraft
PMG : Permanent magnet generator
• Integrated drive generator (IDG)
consists of a constant speed drive
(CSD) and an AC generator mounted
side by side in a single housing. The
CSD components convert a variable
input speed to a constant output
speed.
• The CSD portion of the IDG is a
hydro mechanical device that adds or
subtracts from variable input speed of
the engine gearbox. The CSD
performs this operation by controlled
differential action to maintain the
constant output speed required to
drive the generator.
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AC main generation in aircraft
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Voltage regulation
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Voltage Regulation
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Voltage Regulation
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Thank you for your attention
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