Transcript synchronous machines

SYNCHRONOUS MACHINES
Two-pole,3-phase,wye-connected,salient-pole synchronous machine
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SYNCHRONOUS MACHINES

In abc reference frame, voltage equations can be written as
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SYNCHRONOUS MACHINES

flux linkage equations
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SYNCHRONOUS MACHINES

flux linkage equations
Referring all rotor variables to the stator windings
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SYNCHRONOUS MACHINES
Referring all rotor variables to the stator windings
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Referring all rotor variables to the stator windings
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SYNCHRONOUS MACHINES
TORQUE EQUATION IN MACHINE VARIABLES
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SYNCHRONOUS MACHINES
SWING EQUATION
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 Stator Voltage Equations in Arbitrary Reference-frame Variables
The rotor voltage equations are expressed only in the rotor
reference frame:
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SYNCHRONOUS MACHINES
The flux linkage equations may be expressed as:
 The sinusoidal terms are constant, independent of 
and r only if  = r
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 Therefore, the time-varying inductances are eliminated from the
voltage equations only if the reference frame is fixed in the rotor.
Voltage Equations In Rotor Reference-frame variables:
park's Equations
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Park's voltage equations are
often written in expanded form:
Flux linkages in expanded form:
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 The Equivalent q-axis Circuits:
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 The Equivalent d-axis Circuits:
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 The Equivalent 0-axis Circuits:
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 It is often convenient to express the voltage and flux linkage
equations in terms of reactances rather than inductances:
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 Also, it is convenient to define:
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 If we select the currents as independent variables:
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 If we select the flux linkages per second as independent
variables:
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 Torque Equations in Substitute Variables:
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 Rotor Angle :
it is convenient to relate the position of the rotor of a synchronous
machine to a voltage or to the rotor of another machine.
The electrical angular displacement of the rotor relative to its terminal
voltage is defined as the rotor angle,
The rotor angle is the displacement of the rotor generally referenced to
the maximum positive value of the fundamental component of the
terminal voltage of phase a:
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 Rotor Angle :
It is important to note that the rotor angle is often used as the
argument in the transformation between the rotor and
synchronously rotating reference frames
The rotor angle is often used in
relating torque and rotor speed (if
e is constant):
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SYNCHRONOUS MACHINES
PER UNIT SYSTEM
 Base voltage:
 the rms value ofthe rated phase voltage for the abc variables
 the peak value for the qd0 variables.
 Base power:
 When considering the machine separately, the power base is
selected as its volt-ampere rating.
 When considering power systems, a system power base
(system base) is selected
 Once the base quantities are established, the corresponding
base current and base impedance may be calculated.
Base torque is the base power divided by the synchronous
speed of the rotor:
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 The torque expressed in per unit:
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 ANALYSIS OF STEADY-STATE OPERATION:
For balanced conditions:
the 0s quantities are zero.
r is constant and equal to e
the rotor windings do not experience a change of flux linkages
the current is not flowing in the short-circuited damper windings
the time rate of change of all flux linkages neglected
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 ANALYSIS OF STEADY-STATE OPERATION:
For balanced conditions:
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 ANALYSIS OF STEADY-STATE OPERATION:
Hence:
and if it is noted that:
Then:
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 ANALYSIS OF STEADY-STATE OPERATION
It is convenient to define the last term on the right-hand side as
(excitation voltage):
if rs is neglected, the expression for the balanced steady-state
electromagnetic torque in per unit can be written as:
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DYNAMIC PERFORMANCE DURING A SUDDEN CHANGE
IN INPUT TORQUE
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DYNAMIC PERFORMANCE DURING A SUDDEN CHANGE
IN INPUT TORQUE
Dynamic performance of a hydro turbine generator during a step increase in
input torque from zero to rated:
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DYNAMIC PERFORMANCE DURING A SUDDEN CHANGE
IN INPUT TORQUE
Torque versus rotor angle characteristics
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DYNAMIC PERFORMANCE DURING A SUDDEN CHANGE
IN INPUT TORQUE
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DYNAMIC PERFORMANCE DURING A SUDDEN CHANGE
IN INPUT TORQUE
Dynamic performance of a steam
turbine generator during a step
increase in input torque from zero
to 50% rated.
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DYNAMIC PERFORMANCE DURING A SUDDEN CHANGE
IN INPUT TORQUE
Torque versus rotor angle characteristics
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DYNAMIC PERFORMANCE DURING A 3 PHASE FAULT
AT THE MACHINE TERMINALS
a hydro turbine generator
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DYNAMIC PERFORMANCE DURING A 3 PHASE FAULT
AT THE MACHINE TERMINALS
Torque versus rotor angle characteristics:
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DYNAMIC PERFORMANCE DURING A 3 PHASE FAULT
AT THE MACHINE TERMINALS
a steam turbine generator
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DYNAMIC PERFORMANCE DURING A 3 PHASE FAULT
AT THE MACHINE TERMINALS
Torque versus rotor angle characteristics:
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COMPUTER SIMULATION
Simulation in Rotor Reference Frame
Where:
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COMPUTER SIMULATION
Simulation in Rotor Reference Frame
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COMPUTER SIMULATION
Simulation of Saturation
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COMPUTER SIMULATION
Simulation of Saturation
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