1 synchronous machines two-pole,3-phase,wye-connected,salient-pole synchronous machine
TRANSCRIPT
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
Two-pole,3-phase,wye-connected,salient-pole synchronous machineTwo-pole,3-phase,wye-connected,salient-pole synchronous machine
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
In abc reference frame, voltage equations can be written as
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
flux linkage equations
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
flux linkage equations
Referring all rotor variables to the stator windingsReferring all rotor variables to the stator windings
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
Referring all rotor variables to the stator windingsReferring all rotor variables to the stator windings
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
Referring all rotor variables to the stator windingsReferring all rotor variables to the stator windings
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
TORQUE EQUATION IN MACHINE VARIABLES
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
SWING EQUATION
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Stator Voltage Equations in Arbitrary Reference-frame Variables
SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
The rotor voltage equations are expressed only in the rotor The rotor voltage equations are expressed only in the rotor reference frame:reference frame:
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
The flux linkage equations may be expressed as:The flux linkage equations may be expressed as:
The sinusoidal terms are constant, independent of The sinusoidal terms are constant, independent of and and rr only if only if = = rr
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
Therefore, the time-varying inductances are eliminated from the Therefore, the time-varying inductances are eliminated from the voltage equations only ifvoltage equations only if the the reference frame is fixed in the rotorreference frame is fixed in the rotor..
Voltage Equations In Rotor Reference-frame variables: park's Equations
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
Park's voltage equations are Park's voltage equations are often written in expanded form:often written in expanded form:
Flux linkages in expanded form:Flux linkages in expanded form:
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
The Equivalent q-axis Circuits:The Equivalent q-axis Circuits:
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
The Equivalent d-axis Circuits:The Equivalent d-axis Circuits:
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
The Equivalent 0-axis Circuits:The Equivalent 0-axis Circuits:
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
It is often convenient to express the voltage and flux linkage It is often convenient to express the voltage and flux linkage equations in terms of reactances rather than inductances:equations in terms of reactances rather than inductances:
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
Also, it is convenient to define:Also, it is convenient to define:
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
If we select the currents as independent variables:If we select the currents as independent variables:
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
If we select the flux linkages per second as independent If we select the flux linkages per second as independent variables:variables:
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
Torque Equations in Substitute Variables::
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
Rotor Angle :Rotor Angle :
it is convenient to relate the position of the rotor of a synchronous it is convenient to relate the position of the rotor of a synchronous machine to a voltage or to the rotor of another machine.machine to a voltage or to the rotor of another machine.
The electrical angular displacement of the rotor relative to its terminal The electrical angular displacement of the rotor relative to its terminal voltage is defined as the rotor angle,voltage is defined as the rotor angle,
The rotor angle is the displacement of the rotor generally referenced to The rotor angle is the displacement of the rotor generally referenced to the maximum positive value of the fundamental component of the the maximum positive value of the fundamental component of the terminal voltage of phase a:terminal voltage of phase a:
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
Rotor Angle :Rotor Angle :
It is important to note that the rotor angle is often used as the It is important to note that the rotor angle is often used as the argument in the transformation between the rotor and argument in the transformation between the rotor and synchronously rotating reference framessynchronously rotating reference frames
The rotor angle is often used in The rotor angle is often used in relating torque and rotor speed (if relating torque and rotor speed (if ee is constant): is constant):
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PER UNIT SYSTEMPER UNIT SYSTEM
SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
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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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
The torque expressed in per unit:The torque expressed in per unit:
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
ANALYSIS OF STEADY-STATE OPERATION:ANALYSIS OF STEADY-STATE OPERATION:
For balanced conditions:For balanced conditions:the 0s quantities are zero.the 0s quantities are zero.rr is constant and equal to is constant and equal to ee
the rotor windings do not experience a change of flux linkagesthe rotor windings do not experience a change of flux linkagesthe current is not flowing in the short-circuited damper windingsthe current is not flowing in the short-circuited damper windingsthe time rate of change of all flux linkages neglectedthe time rate of change of all flux linkages neglected
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
ANALYSIS OF STEADY-STATE OPERATION:ANALYSIS OF STEADY-STATE OPERATION:
For balanced conditions:For balanced conditions:
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SYNCHRONOUS MACHINESSYNCHRONOUS MACHINES
ANALYSIS OF STEADY-STATE OPERATION:ANALYSIS OF STEADY-STATE OPERATION:
Hence:
and if it is noted that:
Then:
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ANALYSIS OF STEADY-STATE OPERATIONANALYSIS 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 DYNAMIC PERFORMANCE DURING A SUDDEN CHANGE IN INPUT TORQUEIN INPUT TORQUE
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DYNAMIC PERFORMANCE DURING A SUDDEN CHANGE DYNAMIC PERFORMANCE DURING A SUDDEN CHANGE IN INPUT TORQUEIN INPUT TORQUE
Dynamic performance of a hydro turbine generator during a step increase in Dynamic performance of a hydro turbine generator during a step increase in input torque from zero to rated:input torque from zero to rated:
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DYNAMIC PERFORMANCE DURING A SUDDEN CHANGE DYNAMIC PERFORMANCE DURING A SUDDEN CHANGE IN INPUT TORQUEIN INPUT TORQUE
Torque versus rotor angle characteristicsTorque versus rotor angle characteristics
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DYNAMIC PERFORMANCE DURING A SUDDEN CHANGE DYNAMIC PERFORMANCE DURING A SUDDEN CHANGE IN INPUT TORQUEIN INPUT TORQUE
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DYNAMIC PERFORMANCE DURING A SUDDEN CHANGE DYNAMIC PERFORMANCE DURING A SUDDEN CHANGE IN INPUT TORQUEIN INPUT TORQUE
Dynamic performance of a steam Dynamic performance of a steam turbine generator during a step turbine generator during a step increase in input torque from zero increase in input torque from zero to 50% rated.to 50% rated.
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DYNAMIC PERFORMANCE DURING A SUDDEN CHANGE DYNAMIC PERFORMANCE DURING A SUDDEN CHANGE IN INPUT TORQUEIN INPUT TORQUE
Torque versus rotor angle characteristicsTorque versus rotor angle characteristics
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DYNAMIC PERFORMANCE DURING A 3 PHASE FAULT AT THE MACHINE TERMINALS
a hydro turbine generatora hydro turbine generator
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DYNAMIC PERFORMANCE DURING A 3 PHASE FAULT AT THE MACHINE TERMINALS
Torque versus rotor angle characteristics:Torque versus rotor angle characteristics:
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DYNAMIC PERFORMANCE DURING A 3 PHASE FAULT AT THE MACHINE TERMINALS
a steam turbine generatora steam turbine generator
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DYNAMIC PERFORMANCE DURING A 3 PHASE FAULT AT THE MACHINE TERMINALS
Torque versus rotor angle characteristics: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