chapter 16: synchronous generators - oakland...
TRANSCRIPT
3/2/00 Electromechanical Dynamics 1
Chapter 16: Synchronous Generators
3/2/00 Electromechanical Dynamics 2
Generator under Load
• The behavior of a synchronous generator depends upon the connected load– two basic load categories
• isolated loads
• infinite bus
– isolated loads with a lagging pf
• current lags the terminal voltage, E
• the voltage drop across the synchronous reactance, EX, leads the current by 90°
• the induced voltage, E0, generated by the flux, Φ, is equal to the phasor sum of E and EX
3/2/00 Electromechanical Dynamics 3
Generator under Load
– isolated loads with a leading pf
• current leads the terminal voltage, E
• the voltage drop across the synchronous reactance, EX, leads the current by 90°
• the induced voltage, E0, generated by the flux, Φ, is equal to the phasor sum of E and EX
– note that E0 always leads E by the angle δ
• for lagging loads E0 is greater than E
• for leading loads E is greater than E0
3/2/00 Electromechanical Dynamics 4
Generator under Load
• Example– a 36 MVA, 20.8 kV, 3-phase
generator• synchronous reactance is 9 ohms
• nominal current is 1000 A
• no-load saturation curve is given
– adjust the excitation so that the terminal voltage is fixed at 21 kV
• calculate the excitation current
• draw the phasor diagrams for the following load conditions– no-load
– resistive load of 36 MW
– capacitive load of 12 MVAr
3/2/00 Electromechanical Dynamics 5
Regulation Curves
• Voltage regulation is the behavior of the generator’s terminal voltage as the load varies
• Regulation is a function of the load current– the regulation curve is a plot of the terminal voltage, VT, with
respect to load current, I, ranging from no-load to full-load• for a fixed field excitation current
• for a given load power factor
– family of curves are developed for various field excitation currents and for different load power factors
– percent regulation is defined as:
%100%,
,, ×−
=ratedT
ratedTNLT
V
VVVR
3/2/00 Electromechanical Dynamics 6
Regulation Curves
• Example– consider the regulation curves for a 36 MVA, 21 kV generator
– calculate the percent regulation corresponding to the unity power factor curve
3/2/00 Electromechanical Dynamics 7
Synchronization of a Generator
• Often two or more generators are connected in parallel to supply a common load in large utility systems– connecting a generator to other generators is called paralleling
– many paralleled generators behaves like an infinite bus• voltage and frequency are constant and can not be easily altered
– before connecting a generator to an electrical grid, it must be synchronized
• the generator frequency is equal to the system frequency
• the generator voltage is equal to the system voltage
• the generator voltage is in phase with the system voltage
• the phase sequence of the generator is the same as that of the system
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Synchronization of a Generator
• To synchronize a generator– adjust the speed regulator of the prime mover so that
frequencies are close
– adjust the excitation so that generator voltage and system voltage are equal
– observe the phase angle by means of a synchroscope, which indicates the phase angle between two voltages
• the pointer rotates proportional to the frequency difference
• a zero mark indicates a zero degree phase angle
• the speed regulator is adjusted so that the pointer barely creeps across the dial
– on the zero mark, the line circuit breaker is closed
3/2/00 Electromechanical Dynamics 9
Connecting to an Infinite Bus
• An infinite bus system is so powerful that it imposes its own– voltage magnitude and frequency
– once an apparatus is connected to an infinite bus, it becomes part of it
– for a synchronized generator, the operator can only vary two machine parameters
• the field excitation current, IX
• the prime-mover’s mechanical torque, T
3/2/00 Electromechanical Dynamics 10
Connecting to an Infinite Bus
• Varying the exciting current– impacts the induced voltage E0
– causes a current to flow that is 90 degrees out-of-phase due to the synchronous reactance
– does not affect the flow of active (real) power
– does cause reactive power to flow
SjX
EEI
−= 0
3/2/00 Electromechanical Dynamics 11
Connecting to an Infinite Bus
• Varying the mechanical torque– by opening up the control valve of the prime-mover, an
increase torque is developed
– the rotor will accelerate, E0 will increase in value and begin to slip ahead of phasor E, leading by a phase angle δ
– Although both voltages have similar values, the phase angle produces a difference of potential across the synchronous reactance
• a current will flow, but this time almost in phase with E
• real (active) power will flow
3/2/00 Electromechanical Dynamics 12
Active Power Delivered
• The active power delivered by a synchronous generator is given by
– PE = 3-phase power delivered by the generator
– E = induced generator voltage
– VT = generator terminal voltage
– XS = synchronous reactance, per phase
– δ = phase angle between E and VT
δsinS
TE X
VEP =
3/2/00 Electromechanical Dynamics 13
Active Power Delivered
0
0.5
1.0
1.5
2.0
P[pu]
0 30 60 180δ [degrees]
90 120 150
3/2/00 Electromechanical Dynamics 14
Active Power Delivered
• Example– a 36 MVA, 21 kV, 1800 rpm, 3-phase, 60 Hz generator is
connected to the power grid• synchronous reactance of 9 Ω per phase
• line-to-neutral exciting voltage is 12 kV
• line-to-line system voltage is 17.3 kV.
– calculate • the active power delivered when the power angle δ is 30°
• the peak power that the generator can deliver before losing synchronism
3/2/00 Electromechanical Dynamics 15
Transient Reactance
• A synchronous generator connected to a system is subject to switching events– short-circuits, load energization, etc.
• In many cases, the equivalent circuit doesnot reflect the behavior of the machine– the equivalent circuit is only valid
for steady-state operation
– for sudden, large current changes another reactance is needed
• reactance X' whose value varies as a function of time
– the reactance for a short circuit
• prior to the fault, the reactance equals the synchronous value
• at the instant of fault, the reactance falls to a much lower value, X'd
3/2/00 Electromechanical Dynamics 16
Transient Reactance
• The reactance X'd is called the transient reactance– can be as low as 15% of the synchronous reactance
– consequently, the initial short-circuit current is much higher than that corresponding to the synchronous reactance
3/2/00 Electromechanical Dynamics 17
Transient Model
• Example– a 250 MVA, 25 kV, 3-phase generator delivers its rated
output at unity power factor• a synchronous reactance of 1.6 pu
• a transient reactance of 0.23 pu
– a short circuit suddenly occurs on the connecting transmission line, close to the generator
– calculate• the induced voltage, E0, prior to the short circuit
• the initial value of the short-circuit current
• the final value of the short-circuit current if the circuit breaker should fail to open
3/2/00 Electromechanical Dynamics 18
Power Transfer
• We are often interested in the active power that can be transmitted between source A and source B– using Kirchhoff’s voltage law
– the active power absorbed at source B is
– applying the geometry law of the sines for a triangle
– substitution results in
ABBA IjXEE +=
BABBB IEP θcos=
θθψδ cos90sinsinsinAAAAB EEEIX =
+==
δsinX
EEP AB
B =
3/2/00 Electromechanical Dynamics 19
Power Transfer
• Example– a transmission line connects two generators
• generator A operates at E = 20 kV∠ 5°
• generator B operates at E = 15 kV∠ 42°
• the transmission line has a reactance of 14 ohms
– calculate the active power that flows over the line• which machine is receiving the power
3/2/00 Electromechanical Dynamics 20
Machine Efficiency
• The physical size of the synchronous machine has a profound effect upon:– efficiency, power output, relative cost, and temperature rise
– losses in the machine• I2R losses in the stator windings
• Idc2Rf losses in the rotor field winding
• iron core losses and mechanical losses
– keeping all machine parameters and materials the same• an increase in all linear dimensions causes
– voltage increases by the square
– output power increases by the 4th power
– losses increase by the 3rd power
3/2/00 Electromechanical Dynamics 21
Homework
• Problems 16-22, 16-23, and 16-24