SCHOOL OF ELECTRICAL, ELECTRONIC AND COMPUTER ENGINEERING
Electrical Machines 3
(ENEL4MA)
Practical Assignment – Transient Behaviour of
Synchronous Machines
i|Page
,Abstract
The power system stability of synchronous machines is primarily concerned with transient
behaviour, which is defined as the ability of a power system to maintain a state of operating
equilibrium under normal operating conditions and to re-establish an acceptable state of
equilibrium after being subjected to a disturbance. The main goal of this practical project is to
examine synchronous machines' transient behaviour. The mathematical description, electrical
transient performance, and electrical output of synchronous machines are examined, as well
as their theory and modelling. A Single Machine Infinite Bus System (SMIBS) Model was
created using PDCAD as the simulation tool to study the transient behaviour of synchronous
machines. The SMIBS was designed with an Automatic Voltage Regulator (AVR) to keep
the system voltage constant and a Power System Stabilizer (PSS) to keep the system stable
after faults or when it loses synchronism. The SMIBS was simulated in PSCAD, and it began
with the start-up stages of Source2Machine and Unlock Rotor, which took t=0.3 s and t=0.5
s, respectively. The generator, AVR, PSS, and Infinite Bus settings were then initialized. A
three-phase short-circuit fault was applied at the generator terminals at t=5 s, and lasted for
300 ms. The instantaneous stator currents were measured, and their response was as
expected, since they showed the unidirectional and fundamental frequency components
during the fault. The three-phase generator line current and terminal voltage were also
measure. So the rotor speed increased during the fault, the terminal voltage dropped, and
when the fault grew to be greater than the pre-fault condition value, the AVR and PSS
stabilized it to its original value. During the fault, the generator current rose. In terms of
active and reactive power, the rotor speed rose when the fault was applied, therefore some
power was stored. The machine produced more active and reactive power after the fault than
it had before, because it was now delivering the input power as well as the power that had
been stored during the problem.
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,Table of Contents
Abstract.................................................................................................................................................ii
Table of Figures.....................................................................................................................................iv
List of symbols.......................................................................................................................................v
Acronyms...........................................................................................................................................v
Synchronous generator symbols........................................................................................................v
Automatic Voltage Regulator............................................................................................................vi
System symbols.................................................................................................................................vi
General.............................................................................................................................................vii
.........................................................................................................................................................vii
Per-unit............................................................................................................................................vii
.........................................................................................................................................................vii
Small chance operator.....................................................................................................................vii
1. Introduction.......................................................................................................................................1
2. Theory................................................................................................................................................2
2.1. Synchronous machine characteristics.........................................................................................2
2.2. Synchronous machine theory and modelling..............................................................................2
2.2.1. Physical description.............................................................................................................3
2.2.2. Mathematical description of a synchronous machine.........................................................6
2.2.3. Electrical transient performance characteristics..................................................................9
2.3. Synchronous machine electrical output....................................................................................12
2.3.1. Swing equation..................................................................................................................14
2.3.2. Power-angle curve.............................................................................................................15
2.3.3. Equal-area criterion...........................................................................................................18
2.3.4. Response to a short-circuit fault........................................................................................19
2.4. The stability criteria in synchronous machines.........................................................................20
2.4.1. Transient stability in synchronous machines.....................................................................21
3. System Modelling............................................................................................................................22
3.1. Automatic Voltage Regulator (AVR)..........................................................................................23
3.2. Power System Stabilizer (PSS)...................................................................................................24
3.3. PSCAD Model of the SMIBS.......................................................................................................25
4. Simulation results and discussion....................................................................................................28
4.1. Instantaneous stator currents and field current.......................................................................29
4.2. Three-phase rms generator line voltage and current...............................................................31
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, 4.3. Three-phase generator active and reactive power...................................................................32
5. Conclusion.......................................................................................................................................34
6. References.......................................................................................................................................35
Appendix A – Synchronous generator parameters..............................................................................36
Appendix B – Automatic Voltage Regulator parameters.....................................................................37
Appendix C – Infinite Bus parameters..................................................................................................37
Table of Figures
Figure 1: Schematic diagram of a three-phase synchronous machine [1].............................................3
Figure 2: MMF waveform due to a single coil [1]..................................................................................4
Figure 3: MMF waveform due to a number of coils [1].........................................................................4
Figure 4: Spatial mmf wave of phase a [1].............................................................................................5
Figure 5: Stator and rotor mmf wave shapes [1]...................................................................................6
Figure 6: Stator and rotor circuits of a synchronous machine [1]..........................................................7
Figure 7: Variation of permeance with rotor position [1]......................................................................8
Figure 8: RL circuit [1]............................................................................................................................9
Figure 9: Short-circuit currents in the three phases [1].......................................................................11
Figure 10: Field current response following a stator short-circuit [1]..................................................11
Figure 11: Fundamental frequency component of armature current [1].............................................12
Figure 12: Per phase equivalent of synchronous machine [1].............................................................13
Figure 13: Per-phase vector equivalent of synchronous generator delivering lagging current [6]......13
Figure 14: Rotor shaft direction of rotation with mechanical and electrical torque [6].......................14
Figure 15: Single-machine infinite bus system.....................................................................................15
Figure 16: (a) Equivalent circuit, (b) reduced circuit [1].......................................................................16
Figure 17: Power-angle relationship....................................................................................................16
Figure 18: Response to a step change in mechanical power input [1].................................................17
Figure 19: (a) Single-line diagram, (b) Equivalent circuit [1]................................................................19
Figure 20: (a) Response to a fault cleared in tc1 sec -stable case, (b) Response to a fault cleared in tc2
sec- unstable case [1]..........................................................................................................................20
Figure 21: Rotor angle response to a transient disturbance [1]...........................................................22
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Electrical Machines 3
(ENEL4MA)
Practical Assignment – Transient Behaviour of
Synchronous Machines
i|Page
,Abstract
The power system stability of synchronous machines is primarily concerned with transient
behaviour, which is defined as the ability of a power system to maintain a state of operating
equilibrium under normal operating conditions and to re-establish an acceptable state of
equilibrium after being subjected to a disturbance. The main goal of this practical project is to
examine synchronous machines' transient behaviour. The mathematical description, electrical
transient performance, and electrical output of synchronous machines are examined, as well
as their theory and modelling. A Single Machine Infinite Bus System (SMIBS) Model was
created using PDCAD as the simulation tool to study the transient behaviour of synchronous
machines. The SMIBS was designed with an Automatic Voltage Regulator (AVR) to keep
the system voltage constant and a Power System Stabilizer (PSS) to keep the system stable
after faults or when it loses synchronism. The SMIBS was simulated in PSCAD, and it began
with the start-up stages of Source2Machine and Unlock Rotor, which took t=0.3 s and t=0.5
s, respectively. The generator, AVR, PSS, and Infinite Bus settings were then initialized. A
three-phase short-circuit fault was applied at the generator terminals at t=5 s, and lasted for
300 ms. The instantaneous stator currents were measured, and their response was as
expected, since they showed the unidirectional and fundamental frequency components
during the fault. The three-phase generator line current and terminal voltage were also
measure. So the rotor speed increased during the fault, the terminal voltage dropped, and
when the fault grew to be greater than the pre-fault condition value, the AVR and PSS
stabilized it to its original value. During the fault, the generator current rose. In terms of
active and reactive power, the rotor speed rose when the fault was applied, therefore some
power was stored. The machine produced more active and reactive power after the fault than
it had before, because it was now delivering the input power as well as the power that had
been stored during the problem.
ii | P a g e
,Table of Contents
Abstract.................................................................................................................................................ii
Table of Figures.....................................................................................................................................iv
List of symbols.......................................................................................................................................v
Acronyms...........................................................................................................................................v
Synchronous generator symbols........................................................................................................v
Automatic Voltage Regulator............................................................................................................vi
System symbols.................................................................................................................................vi
General.............................................................................................................................................vii
.........................................................................................................................................................vii
Per-unit............................................................................................................................................vii
.........................................................................................................................................................vii
Small chance operator.....................................................................................................................vii
1. Introduction.......................................................................................................................................1
2. Theory................................................................................................................................................2
2.1. Synchronous machine characteristics.........................................................................................2
2.2. Synchronous machine theory and modelling..............................................................................2
2.2.1. Physical description.............................................................................................................3
2.2.2. Mathematical description of a synchronous machine.........................................................6
2.2.3. Electrical transient performance characteristics..................................................................9
2.3. Synchronous machine electrical output....................................................................................12
2.3.1. Swing equation..................................................................................................................14
2.3.2. Power-angle curve.............................................................................................................15
2.3.3. Equal-area criterion...........................................................................................................18
2.3.4. Response to a short-circuit fault........................................................................................19
2.4. The stability criteria in synchronous machines.........................................................................20
2.4.1. Transient stability in synchronous machines.....................................................................21
3. System Modelling............................................................................................................................22
3.1. Automatic Voltage Regulator (AVR)..........................................................................................23
3.2. Power System Stabilizer (PSS)...................................................................................................24
3.3. PSCAD Model of the SMIBS.......................................................................................................25
4. Simulation results and discussion....................................................................................................28
4.1. Instantaneous stator currents and field current.......................................................................29
4.2. Three-phase rms generator line voltage and current...............................................................31
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, 4.3. Three-phase generator active and reactive power...................................................................32
5. Conclusion.......................................................................................................................................34
6. References.......................................................................................................................................35
Appendix A – Synchronous generator parameters..............................................................................36
Appendix B – Automatic Voltage Regulator parameters.....................................................................37
Appendix C – Infinite Bus parameters..................................................................................................37
Table of Figures
Figure 1: Schematic diagram of a three-phase synchronous machine [1].............................................3
Figure 2: MMF waveform due to a single coil [1]..................................................................................4
Figure 3: MMF waveform due to a number of coils [1].........................................................................4
Figure 4: Spatial mmf wave of phase a [1].............................................................................................5
Figure 5: Stator and rotor mmf wave shapes [1]...................................................................................6
Figure 6: Stator and rotor circuits of a synchronous machine [1]..........................................................7
Figure 7: Variation of permeance with rotor position [1]......................................................................8
Figure 8: RL circuit [1]............................................................................................................................9
Figure 9: Short-circuit currents in the three phases [1].......................................................................11
Figure 10: Field current response following a stator short-circuit [1]..................................................11
Figure 11: Fundamental frequency component of armature current [1].............................................12
Figure 12: Per phase equivalent of synchronous machine [1].............................................................13
Figure 13: Per-phase vector equivalent of synchronous generator delivering lagging current [6]......13
Figure 14: Rotor shaft direction of rotation with mechanical and electrical torque [6].......................14
Figure 15: Single-machine infinite bus system.....................................................................................15
Figure 16: (a) Equivalent circuit, (b) reduced circuit [1].......................................................................16
Figure 17: Power-angle relationship....................................................................................................16
Figure 18: Response to a step change in mechanical power input [1].................................................17
Figure 19: (a) Single-line diagram, (b) Equivalent circuit [1]................................................................19
Figure 20: (a) Response to a fault cleared in tc1 sec -stable case, (b) Response to a fault cleared in tc2
sec- unstable case [1]..........................................................................................................................20
Figure 21: Rotor angle response to a transient disturbance [1]...........................................................22
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