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# VOLTAGE STABILITY Computer Science Engineering (CSE) Notes | EduRev

## Computer Science Engineering (CSE) : VOLTAGE STABILITY Computer Science Engineering (CSE) Notes | EduRev

``` Page 1

6.6 Voltage stability
Voltage collapses usually occur on power system which are heavily loaded or faulted or have shortage
of reactive power. Voltage collapse is a system instability involving many power system components.
In fact, a voltage collapse may involve an entire power system.
Voltage collapse is typically associated with reactive power demand of load not being met due to
shortage in reactive power production and transmission.
Voltage collapse is a manifestation of voltage instability in the system. The de?nition of voltage
stability as proposed by IEEE/CIGRE task force is as follows:
Voltage stability refer to the ability of power system to maintain steady voltages at all buses in
the system after being subjected to a disturbance from a given initial operating point. The system
state enters the voltage instability region when a disturbance or an increase in load demand or
alteration in system state results in an uncontrollable and continuous drop in system voltage.
A system is said to be in voltage stable state if at a given operating condition, for every bus in
the system, the bus voltage magnitude increases as the reactive power injection at the same bus is
increased.
A system is voltage unstable if for at least one bus in the system, the bus voltage magnitude
decreases as the reactive power injection at the same bus is increased. It implies that if, V-Q
sensitivity is positive for every bus the system is voltage stable and if V-Q sensitivity is negative
for at least one bus, the system is voltage unstable. The term voltage collapse is also often used for
voltage instability conditions. It is the process, by which, the sequence of events following voltage
instability leads to abnormally low voltages or even a black out in a large part of the system.
stability is sometimes also called load stability. In response to a disturbance, the power consumed
by the loads tends to be restored by load dynamics. This in turn increases the stress on the high
voltage network by increasing the reactive power consumption and further reducing the voltage.
A major factor contributing to voltage instability is the voltage drop in the line impedances when
active and reactive powers ?ow through it. As a result, the capability of the transmission network
for power transfer and voltage support reduces. Voltage stability of a system is endangered when
a disturbance increases the reactive power demand beyond the sustainable capacity of the available
reactive power resources.
The voltage stability has been further classi?ed into four categories: Large disturbance voltage
stability, small disturbance voltage stability, short term voltage satiability and long term voltage
stability. A summary of these classi?cations is as follows:
• Large disturbance voltage stability: It refers to the system’s ability to maintain steady voltage
following large disturbances such as, system faults, loss of generation or circuit contingencies.
This ability is determined by the system load characteristics and interaction of both continuous
and discrete controls and protections. The study period of interest may be from few seconds
to tens of minutes. This requires long term dynamic simulation study of the system to capture
the interactions of under-load tap changer and generator ?eld current limiter.
298
Page 2

6.6 Voltage stability
Voltage collapses usually occur on power system which are heavily loaded or faulted or have shortage
of reactive power. Voltage collapse is a system instability involving many power system components.
In fact, a voltage collapse may involve an entire power system.
Voltage collapse is typically associated with reactive power demand of load not being met due to
shortage in reactive power production and transmission.
Voltage collapse is a manifestation of voltage instability in the system. The de?nition of voltage
stability as proposed by IEEE/CIGRE task force is as follows:
Voltage stability refer to the ability of power system to maintain steady voltages at all buses in
the system after being subjected to a disturbance from a given initial operating point. The system
state enters the voltage instability region when a disturbance or an increase in load demand or
alteration in system state results in an uncontrollable and continuous drop in system voltage.
A system is said to be in voltage stable state if at a given operating condition, for every bus in
the system, the bus voltage magnitude increases as the reactive power injection at the same bus is
increased.
A system is voltage unstable if for at least one bus in the system, the bus voltage magnitude
decreases as the reactive power injection at the same bus is increased. It implies that if, V-Q
sensitivity is positive for every bus the system is voltage stable and if V-Q sensitivity is negative
for at least one bus, the system is voltage unstable. The term voltage collapse is also often used for
voltage instability conditions. It is the process, by which, the sequence of events following voltage
instability leads to abnormally low voltages or even a black out in a large part of the system.
stability is sometimes also called load stability. In response to a disturbance, the power consumed
by the loads tends to be restored by load dynamics. This in turn increases the stress on the high
voltage network by increasing the reactive power consumption and further reducing the voltage.
A major factor contributing to voltage instability is the voltage drop in the line impedances when
active and reactive powers ?ow through it. As a result, the capability of the transmission network
for power transfer and voltage support reduces. Voltage stability of a system is endangered when
a disturbance increases the reactive power demand beyond the sustainable capacity of the available
reactive power resources.
The voltage stability has been further classi?ed into four categories: Large disturbance voltage
stability, small disturbance voltage stability, short term voltage satiability and long term voltage
stability. A summary of these classi?cations is as follows:
• Large disturbance voltage stability: It refers to the system’s ability to maintain steady voltage
following large disturbances such as, system faults, loss of generation or circuit contingencies.
This ability is determined by the system load characteristics and interaction of both continuous
and discrete controls and protections. The study period of interest may be from few seconds
to tens of minutes. This requires long term dynamic simulation study of the system to capture
the interactions of under-load tap changer and generator ?eld current limiter.
298
If following a large disturbance and subsequent system control actions, voltages at all the buses
in the system settle down at acceptable levels, the system is said to be large disturbance voltage
stable.
• Small-disturbance voltage stability: This stability is concerned with the ability of the system
to maintain acceptable level of steady voltages, when subjected to small perturbations such as
incremental changes in system load. This form of stability is also in?uenced by the character-
istics of loads, continuous controls, and discrete controls at a given instant of time. The basic
processes contributing to small disturbance stability are essentially of a steady state nature.
Therefore, static analysis can be e?ectively used to estimate stability margins.
• Short term voltage satiability: It involves dynamics of fast acting load components such as
induction motors, electronically controlled loads and HVDC converters. The study period of
interest is in the order of several seconds and the analysis requires solution of appropriate
system di?erential equations.
• Long term voltage stability: The study of long term voltage stability involves the dynamics of
slower acting equipment such as tap changing transformers, thermostatically controlled loads
and generator current limiters. The study period of interest may extend to several or many
minutes, and requires long term dynamics system simulation.
Voltage instability may arise due many reasons, but some signi?cant contributors are:
? Generators, synchronous condensers, or SVC reaching reactive power limits
? Action of tap changing transformers
? Line tripping or generator outages
Most of these changes have a signi?cant impact on the reactive power production, consumption
and transmission in the system.
Some counter measures to prevent voltage collapse are:
? Switching of shunt capacitors
? Blocking of tap-changing transformers
? Redispatch of generation
299
Page 3

6.6 Voltage stability
Voltage collapses usually occur on power system which are heavily loaded or faulted or have shortage
of reactive power. Voltage collapse is a system instability involving many power system components.
In fact, a voltage collapse may involve an entire power system.
Voltage collapse is typically associated with reactive power demand of load not being met due to
shortage in reactive power production and transmission.
Voltage collapse is a manifestation of voltage instability in the system. The de?nition of voltage
stability as proposed by IEEE/CIGRE task force is as follows:
Voltage stability refer to the ability of power system to maintain steady voltages at all buses in
the system after being subjected to a disturbance from a given initial operating point. The system
state enters the voltage instability region when a disturbance or an increase in load demand or
alteration in system state results in an uncontrollable and continuous drop in system voltage.
A system is said to be in voltage stable state if at a given operating condition, for every bus in
the system, the bus voltage magnitude increases as the reactive power injection at the same bus is
increased.
A system is voltage unstable if for at least one bus in the system, the bus voltage magnitude
decreases as the reactive power injection at the same bus is increased. It implies that if, V-Q
sensitivity is positive for every bus the system is voltage stable and if V-Q sensitivity is negative
for at least one bus, the system is voltage unstable. The term voltage collapse is also often used for
voltage instability conditions. It is the process, by which, the sequence of events following voltage
instability leads to abnormally low voltages or even a black out in a large part of the system.
stability is sometimes also called load stability. In response to a disturbance, the power consumed
by the loads tends to be restored by load dynamics. This in turn increases the stress on the high
voltage network by increasing the reactive power consumption and further reducing the voltage.
A major factor contributing to voltage instability is the voltage drop in the line impedances when
active and reactive powers ?ow through it. As a result, the capability of the transmission network
for power transfer and voltage support reduces. Voltage stability of a system is endangered when
a disturbance increases the reactive power demand beyond the sustainable capacity of the available
reactive power resources.
The voltage stability has been further classi?ed into four categories: Large disturbance voltage
stability, small disturbance voltage stability, short term voltage satiability and long term voltage
stability. A summary of these classi?cations is as follows:
• Large disturbance voltage stability: It refers to the system’s ability to maintain steady voltage
following large disturbances such as, system faults, loss of generation or circuit contingencies.
This ability is determined by the system load characteristics and interaction of both continuous
and discrete controls and protections. The study period of interest may be from few seconds
to tens of minutes. This requires long term dynamic simulation study of the system to capture
the interactions of under-load tap changer and generator ?eld current limiter.
298
If following a large disturbance and subsequent system control actions, voltages at all the buses
in the system settle down at acceptable levels, the system is said to be large disturbance voltage
stable.
• Small-disturbance voltage stability: This stability is concerned with the ability of the system
to maintain acceptable level of steady voltages, when subjected to small perturbations such as
incremental changes in system load. This form of stability is also in?uenced by the character-
istics of loads, continuous controls, and discrete controls at a given instant of time. The basic
processes contributing to small disturbance stability are essentially of a steady state nature.
Therefore, static analysis can be e?ectively used to estimate stability margins.
• Short term voltage satiability: It involves dynamics of fast acting load components such as
induction motors, electronically controlled loads and HVDC converters. The study period of
interest is in the order of several seconds and the analysis requires solution of appropriate
system di?erential equations.
• Long term voltage stability: The study of long term voltage stability involves the dynamics of
slower acting equipment such as tap changing transformers, thermostatically controlled loads
and generator current limiters. The study period of interest may extend to several or many
minutes, and requires long term dynamics system simulation.
Voltage instability may arise due many reasons, but some signi?cant contributors are:
? Generators, synchronous condensers, or SVC reaching reactive power limits
? Action of tap changing transformers
? Line tripping or generator outages
Most of these changes have a signi?cant impact on the reactive power production, consumption
and transmission in the system.
Some counter measures to prevent voltage collapse are:
? Switching of shunt capacitors
? Blocking of tap-changing transformers
? Redispatch of generation
299
Figure 6.9: Simple radial power system
Voltage stability may occur in di?erent ways. A simple case of voltage stability can be explained
by considering the two terminal network of Fig. 6.9.
In this system, the network is represented by an equivalent generator that can be modeled in the
steady state by an equivalent voltage source
¯
E behind the equivalent impedance
¯
Z
g
.In general, the
generator, transformer and line impedances are combined together and represented as
¯
Z
L
impedance is
¯
Z
D
and
¯
V is the receiving end or load voltage. The current
¯
I in the circuit is given
by:
¯
I =
¯
E
¯
Z
L
+
¯
Z
D
=
¯
E
Z
L
??+Z
D
?f
=
¯
E
(Z
L
cos?+Z
D
cosf)+j(Z
L
sin?+Z
L
sinf)
(6.173)
The magnitude of current is
I =
E
»
(Z
L
cos?+Z
D
cosf)
2
+(Z
L
sin?+Z
L
sinf)
2
which may be written as:
I =
E
Z
L
v
F
L
(6.174)
300
Page 4

6.6 Voltage stability
Voltage collapses usually occur on power system which are heavily loaded or faulted or have shortage
of reactive power. Voltage collapse is a system instability involving many power system components.
In fact, a voltage collapse may involve an entire power system.
Voltage collapse is typically associated with reactive power demand of load not being met due to
shortage in reactive power production and transmission.
Voltage collapse is a manifestation of voltage instability in the system. The de?nition of voltage
stability as proposed by IEEE/CIGRE task force is as follows:
Voltage stability refer to the ability of power system to maintain steady voltages at all buses in
the system after being subjected to a disturbance from a given initial operating point. The system
state enters the voltage instability region when a disturbance or an increase in load demand or
alteration in system state results in an uncontrollable and continuous drop in system voltage.
A system is said to be in voltage stable state if at a given operating condition, for every bus in
the system, the bus voltage magnitude increases as the reactive power injection at the same bus is
increased.
A system is voltage unstable if for at least one bus in the system, the bus voltage magnitude
decreases as the reactive power injection at the same bus is increased. It implies that if, V-Q
sensitivity is positive for every bus the system is voltage stable and if V-Q sensitivity is negative
for at least one bus, the system is voltage unstable. The term voltage collapse is also often used for
voltage instability conditions. It is the process, by which, the sequence of events following voltage
instability leads to abnormally low voltages or even a black out in a large part of the system.
stability is sometimes also called load stability. In response to a disturbance, the power consumed
by the loads tends to be restored by load dynamics. This in turn increases the stress on the high
voltage network by increasing the reactive power consumption and further reducing the voltage.
A major factor contributing to voltage instability is the voltage drop in the line impedances when
active and reactive powers ?ow through it. As a result, the capability of the transmission network
for power transfer and voltage support reduces. Voltage stability of a system is endangered when
a disturbance increases the reactive power demand beyond the sustainable capacity of the available
reactive power resources.
The voltage stability has been further classi?ed into four categories: Large disturbance voltage
stability, small disturbance voltage stability, short term voltage satiability and long term voltage
stability. A summary of these classi?cations is as follows:
• Large disturbance voltage stability: It refers to the system’s ability to maintain steady voltage
following large disturbances such as, system faults, loss of generation or circuit contingencies.
This ability is determined by the system load characteristics and interaction of both continuous
and discrete controls and protections. The study period of interest may be from few seconds
to tens of minutes. This requires long term dynamic simulation study of the system to capture
the interactions of under-load tap changer and generator ?eld current limiter.
298
If following a large disturbance and subsequent system control actions, voltages at all the buses
in the system settle down at acceptable levels, the system is said to be large disturbance voltage
stable.
• Small-disturbance voltage stability: This stability is concerned with the ability of the system
to maintain acceptable level of steady voltages, when subjected to small perturbations such as
incremental changes in system load. This form of stability is also in?uenced by the character-
istics of loads, continuous controls, and discrete controls at a given instant of time. The basic
processes contributing to small disturbance stability are essentially of a steady state nature.
Therefore, static analysis can be e?ectively used to estimate stability margins.
• Short term voltage satiability: It involves dynamics of fast acting load components such as
induction motors, electronically controlled loads and HVDC converters. The study period of
interest is in the order of several seconds and the analysis requires solution of appropriate
system di?erential equations.
• Long term voltage stability: The study of long term voltage stability involves the dynamics of
slower acting equipment such as tap changing transformers, thermostatically controlled loads
and generator current limiters. The study period of interest may extend to several or many
minutes, and requires long term dynamics system simulation.
Voltage instability may arise due many reasons, but some signi?cant contributors are:
? Generators, synchronous condensers, or SVC reaching reactive power limits
? Action of tap changing transformers
? Line tripping or generator outages
Most of these changes have a signi?cant impact on the reactive power production, consumption
and transmission in the system.
Some counter measures to prevent voltage collapse are:
? Switching of shunt capacitors
? Blocking of tap-changing transformers
? Redispatch of generation
299
Figure 6.9: Simple radial power system
Voltage stability may occur in di?erent ways. A simple case of voltage stability can be explained
by considering the two terminal network of Fig. 6.9.
In this system, the network is represented by an equivalent generator that can be modeled in the
steady state by an equivalent voltage source
¯
E behind the equivalent impedance
¯
Z
g
.In general, the
generator, transformer and line impedances are combined together and represented as
¯
Z
L
impedance is
¯
Z
D
and
¯
V is the receiving end or load voltage. The current
¯
I in the circuit is given
by:
¯
I =
¯
E
¯
Z
L
+
¯
Z
D
=
¯
E
Z
L
??+Z
D
?f
=
¯
E
(Z
L
cos?+Z
D
cosf)+j(Z
L
sin?+Z
L
sinf)
(6.173)
The magnitude of current is
I =
E
»
(Z
L
cos?+Z
D
cosf)
2
+(Z
L
sin?+Z
L
sinf)
2
which may be written as:
I =
E
Z
L
v
F
L
(6.174)
300
where,
F
L
= 1+
Z
D
Z
L

2
+ 2
Z
D
Z
L
cos (?-f)
Where
The magnitude of the receiving and voltage is given by:
V = Z
D
I
=
E
v
F
L

Z
D
Z
L
 (6.175)
The power supplied to the load is
P
L
=VIcosf
P
L
= ?
Z
D
F
L

E
Z
L

2
cosf (6.176)
The plots of I,V andP
L
are shown in Fig. 6.10 as a function of
Z
L
Z
D
ratio for a speci?c value of
? andf.
Figure 6.10: Receiving end voltage, Current and Power as a function of Load
An explanation of the chracteristics of Fig. 6.10 is as follows:
• As the load demand is increased by reducingZ
D
L
increases rapidly at ?rst
and then slowly, before reaching a maximum value and then starts decreasing. There is thus, a
maximum value of active power that can be transmitted through an impedance from a constant
voltage source.
301
Page 5

6.6 Voltage stability
Voltage collapses usually occur on power system which are heavily loaded or faulted or have shortage
of reactive power. Voltage collapse is a system instability involving many power system components.
In fact, a voltage collapse may involve an entire power system.
Voltage collapse is typically associated with reactive power demand of load not being met due to
shortage in reactive power production and transmission.
Voltage collapse is a manifestation of voltage instability in the system. The de?nition of voltage
stability as proposed by IEEE/CIGRE task force is as follows:
Voltage stability refer to the ability of power system to maintain steady voltages at all buses in
the system after being subjected to a disturbance from a given initial operating point. The system
state enters the voltage instability region when a disturbance or an increase in load demand or
alteration in system state results in an uncontrollable and continuous drop in system voltage.
A system is said to be in voltage stable state if at a given operating condition, for every bus in
the system, the bus voltage magnitude increases as the reactive power injection at the same bus is
increased.
A system is voltage unstable if for at least one bus in the system, the bus voltage magnitude
decreases as the reactive power injection at the same bus is increased. It implies that if, V-Q
sensitivity is positive for every bus the system is voltage stable and if V-Q sensitivity is negative
for at least one bus, the system is voltage unstable. The term voltage collapse is also often used for
voltage instability conditions. It is the process, by which, the sequence of events following voltage
instability leads to abnormally low voltages or even a black out in a large part of the system.
stability is sometimes also called load stability. In response to a disturbance, the power consumed
by the loads tends to be restored by load dynamics. This in turn increases the stress on the high
voltage network by increasing the reactive power consumption and further reducing the voltage.
A major factor contributing to voltage instability is the voltage drop in the line impedances when
active and reactive powers ?ow through it. As a result, the capability of the transmission network
for power transfer and voltage support reduces. Voltage stability of a system is endangered when
a disturbance increases the reactive power demand beyond the sustainable capacity of the available
reactive power resources.
The voltage stability has been further classi?ed into four categories: Large disturbance voltage
stability, small disturbance voltage stability, short term voltage satiability and long term voltage
stability. A summary of these classi?cations is as follows:
• Large disturbance voltage stability: It refers to the system’s ability to maintain steady voltage
following large disturbances such as, system faults, loss of generation or circuit contingencies.
This ability is determined by the system load characteristics and interaction of both continuous
and discrete controls and protections. The study period of interest may be from few seconds
to tens of minutes. This requires long term dynamic simulation study of the system to capture
the interactions of under-load tap changer and generator ?eld current limiter.
298
If following a large disturbance and subsequent system control actions, voltages at all the buses
in the system settle down at acceptable levels, the system is said to be large disturbance voltage
stable.
• Small-disturbance voltage stability: This stability is concerned with the ability of the system
to maintain acceptable level of steady voltages, when subjected to small perturbations such as
incremental changes in system load. This form of stability is also in?uenced by the character-
istics of loads, continuous controls, and discrete controls at a given instant of time. The basic
processes contributing to small disturbance stability are essentially of a steady state nature.
Therefore, static analysis can be e?ectively used to estimate stability margins.
• Short term voltage satiability: It involves dynamics of fast acting load components such as
induction motors, electronically controlled loads and HVDC converters. The study period of
interest is in the order of several seconds and the analysis requires solution of appropriate
system di?erential equations.
• Long term voltage stability: The study of long term voltage stability involves the dynamics of
slower acting equipment such as tap changing transformers, thermostatically controlled loads
and generator current limiters. The study period of interest may extend to several or many
minutes, and requires long term dynamics system simulation.
Voltage instability may arise due many reasons, but some signi?cant contributors are:
? Generators, synchronous condensers, or SVC reaching reactive power limits
? Action of tap changing transformers
? Line tripping or generator outages
Most of these changes have a signi?cant impact on the reactive power production, consumption
and transmission in the system.
Some counter measures to prevent voltage collapse are:
? Switching of shunt capacitors
? Blocking of tap-changing transformers
? Redispatch of generation
299
Figure 6.9: Simple radial power system
Voltage stability may occur in di?erent ways. A simple case of voltage stability can be explained
by considering the two terminal network of Fig. 6.9.
In this system, the network is represented by an equivalent generator that can be modeled in the
steady state by an equivalent voltage source
¯
E behind the equivalent impedance
¯
Z
g
.In general, the
generator, transformer and line impedances are combined together and represented as
¯
Z
L
impedance is
¯
Z
D
and
¯
V is the receiving end or load voltage. The current
¯
I in the circuit is given
by:
¯
I =
¯
E
¯
Z
L
+
¯
Z
D
=
¯
E
Z
L
??+Z
D
?f
=
¯
E
(Z
L
cos?+Z
D
cosf)+j(Z
L
sin?+Z
L
sinf)
(6.173)
The magnitude of current is
I =
E
»
(Z
L
cos?+Z
D
cosf)
2
+(Z
L
sin?+Z
L
sinf)
2
which may be written as:
I =
E
Z
L
v
F
L
(6.174)
300
where,
F
L
= 1+
Z
D
Z
L

2
+ 2
Z
D
Z
L
cos (?-f)
Where
The magnitude of the receiving and voltage is given by:
V = Z
D
I
=
E
v
F
L

Z
D
Z
L
 (6.175)
The power supplied to the load is
P
L
=VIcosf
P
L
= ?
Z
D
F
L

E
Z
L

2
cosf (6.176)
The plots of I,V andP
L
are shown in Fig. 6.10 as a function of
Z
L
Z
D
ratio for a speci?c value of
? andf.
Figure 6.10: Receiving end voltage, Current and Power as a function of Load
An explanation of the chracteristics of Fig. 6.10 is as follows:
• As the load demand is increased by reducingZ
D
L
increases rapidly at ?rst
and then slowly, before reaching a maximum value and then starts decreasing. There is thus, a
maximum value of active power that can be transmitted through an impedance from a constant
voltage source.
301
• The transmitted power reaches a maximum when the voltage drop in the line is equal to the
D
is equal to line impedance Z
L
. As
Z
D
is gradually reduced, current in the line I increases and load voltage V decreases. Initially,
for high values of Z
D
, the enhancement in I is more than the reduction in V, and hence load
power P
L
increases rapidly with reduction in Z
D
. As Z
D
approaches Z
L
, the e?ect of the
enhancement in I is only slightly greater than that of the reduction in V, hence increase inP
L
is slow. Finally, whenZ
D
is quite less thanZ
L
the reduction in V dominates over increase in
I and hence,P
L
decreases.
• The critical operating condition, corresponding to maximum power, is the limiting point of
satisfactory operation. For higher load demand, control of power by varying load would be
unstable, as a reduction in load impedance will reduce power. The load characteristics decides
whether the system voltage decreases progressively and the system will become unstable. With
lower than the desired values. For a constant power load characteristic, the system becomes
unstable through collapse of load bus voltage. If the load is supplied by transformers with
automatic under load-tap- changing (ULTC), the tap changer will try to raise the e?ective
D
as seen from the system. This will lower the load bus voltage still further
and lead to a progressive reduction of voltage. This is the ease of simple voltage instability.
From the study of voltage stability the relationship betweenP
L
and V is important and this will
be discussed in the next lecture.
302
```
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