Understanding Power-System Stability

Reviewed by: Gedef Yirgalem

ID.NO:BDU1200544
Michael J. Basler, Member, IEEE, and Richard C. Schaefer, Senior Member, IEEE
Abstract: This paper deals about power-system stability It will cover the effects of system impedance and
and instability including the importance of fast fault- excitation on stability. Synchronizing and damping
clearing performance to aid in reliable production of torques will be discussed, and a justification will be
power. An explanation regarding small-signal stability,
made for the need of supplemental stabilization. In
high-impedance transmission lines, line loading, and
the 1950s and into the 1960s, generating plants were
high-gain fast-acting excitation systems is provided.
equipped with continuously acting automatic voltage
Transient stability is discussed, including synchronizing
regulators (AVRs). As the number of power plants
and damping torques. The power-angle curve is used to
illustrate how fault-clearing time and high initial with AVRs grew, it became apparent that the high
response excitation systems can affect transient performance of these voltage regulators had a
stability. The term “power-system stability” has become destabilizing effect on the power system. Power
increasingly popular in generation and transmission. oscillations of small magnitude and low frequency
The sudden requirement for power-system stabilizers often persisted for long periods of time. In some
(PSS) has created confusion about their applicability,
cases, this presented a limitation on the amount of
Purpose, and benefit to the system. This paper discusses
power to be transmitted within the system. Power-
the fundamentals of the PSS and its effectiveness. In
system stabilizers (PSSs) were developed to aid the
today’s paper industry, PSSs are being applied on
larger machines in the world. damping of these power oscillations by modulating

Key words; Excitation, pole slip, stability, synchronous the excitation supplied to the synchronous machine.
machine, transient stability, voltage regulator
II. CLASSIFICATION OF POWER SYSTEM
I. TINTRODUCTION STABILITY
HIS paper will discuss the various types of power By depending on response of disturbance, power
system stability and instability. system stability can be classified as Steady state,
Power system stability involves the study of the dynamic and transient stability.
dynamics of the power system under disturbances. 1) Steady-state stability
Power system stability implies that its ability to Steady-state stability relates to the response of
return to normal or stable operation after having been synchronous machine to a gradually increasing load.
subjected to some form of disturbances. It is basically concerned with the determination of the

From the classical point of view power system upper limit of machine loading without losing

instability can be seen as loss of synchronism (i.e., synchronism, provided the loading is increased

some synchronous machines going out of step) when gradually.

the system is subjected to a particular disturbance. In an interconnected power system, the rotors of each
synchronous machine in the system rotate at the same

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average electrical speed. The power delivered by the decelerate, depending on the direction of the
generator to the power system is equal to the unbalance. As the rotor changes speed, the relative
mechanical power applied by the prime mover, rotor angle changes.
neglecting losses. The mechanical power input to the Fig. 2 shows the relationship between the rotor
shaft from the prime mover is the product of torque (torque) angle δ, the stator magneto motive force
and speed (PM = TMω). The mechanical torque is in (MMF) F1, and the rotor MMF F2. The torque angle
the direction of rotation. An electrical torque is δ is the angle between the rotor MMF F2 and the
applied to the shaft by the generator and is in a resultant of the vector addition of the rotor and stator
direction that is opposite of the rotation, as shown in MMFs R, as shown in Fig. 2.
Fig. 1 below.

Figure 1 Mechanical and electrical torques applied to the

shaft.
Fig. 3. Synchronous machine tied to infinite bus.

Figure 2 Stator, rotor, and resultant MMFs and torque angle

Fig 4. Phasor diagram, generator tied to infinite bus
When the system is disturbed due to a fault or when Fig. 3 shows a circuit representation of a synchronous
the load is changed quickly, the electrical power out generator connected through a transmission system to
of the machine changes. The electrical power out of an infinite bus. The synchronous machine is modeled
the machine can change rapidly, but the mechanical by an ideal voltage source Eg in series with
power into the machine is relatively slow to change. impedance Xg. The terminal voltage of the machine
Because of this difference in speed of response, there ET is increased to transmission system levels through
exists a temporary difference in the balance of power. a generator step-up (GSU) transformer, which is
This power unbalance causes a difference in torque represented by impedance XT. The high voltage side
applied to the shaft, which causes it to accelerate or of the GSU is connected to the infinite bus via a

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transmission line represented by reactance XL. The
real (MW) power output from the generator on a
steady-state basis is governed by
Eg ET
Pe = sin δ
xg
(1) where δ is the angle between the generator
terminal voltage and the internal voltage of the
machine. As the power transfer increases, the angle δ
increases. A fault in the system can result in a change
Fig. 5. Rubber band analogy
in electrical power flow, resulting in a change in the
power angle δ. This is shown in Fig. 4.
3) Transient stability
If a fault causes the current I to increase and the
terminal voltage to decrease, the electrical power out Transient stability involves the response to large
of the machine will decrease since the impedance disturbances, which may cause rather large changes
seen by the generator is now mainly inductive. This in rotor speeds, power angles and power transfers.
disturbance causes the rotor angle to increase, Transient stability is a fast phenomenon usually
perhaps beyond the limits of generator synchronous evident within a few second.
operation. The resulting variations in power flow as Suppose generators are connected to each other by a
the rotor accelerates will cause a well-designed loss network that behaves much like weights
of synchronism protective relaying (78 function) to interconnected by rubber bands (see Fig. 5). The
isolate that generator from the rest of the system. The weights represent the rotating inertia of the turbine
disturbance on the remaining system, which is due to generators, and the rubber bands are analogous to the
the loss of generation, may result in additional units inductance of the transmission lines. By pulling on a
tripping offline and, potentially, a cascading outage. weight and letting go, an oscillation is set up with
2) Dynamic Stability several of the weights that are interconnected by the
Dynamic stability involves the response to small rubber bands. The result of disturbing just one weight
disturbances that occur on the system, producing will result in all the weights oscillating. Eventually,
oscillations. The system is said to be dynamically the system will come to rest, which is based on its
stable if theses oscillations do not acquire more than damping characteristics. The frequency of oscillation
certain amplitude and die out quickly. If these depends on the mass of the weights and the
oscillations continuously grow in amplitude, the springiness of the rubber bands. Likewise, a transient
system is dynamically unstable. The source of this disturbance to the generator/network can be expected
type of instability is usually an interconnection to cause some oscillations due to the inability of the
between control systems. mechanical torque to instantaneously balance out the
transient variation in electrical torque. The
synchronous machine’s electrical power output can
be resolved into an electrical torque Te multiplied by

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the speed ω. Following a disturbance, the change in
electrical torque can further be resolved into two
components.
ΔTe = KsΔδ + KDΔω (2)
Where;
KsΔδ: component of torque that is in phase with the
rotor angle change. This is known as the
“synchronizing torque”.
KDΔω: component of torque that is in phase with the
speed change. This is known as the “damping
torque.”
Both components of torque act on each generator in
(b)
the system. A lack of sufficient synchronizing torque
Fig. 6 Transient-stability illustration (a) System (b) Power-angle
will result in loss of synchronism. Such a loss of curve
synchronism can only be prevented if sufficient The exciter system must increase the excitation by
magnetic flux can be developed when a transient applying a high positive voltage to the alternator field
change in electrical torque occurs. This is facilitated as quickly as possible. Conversely, when the rotor
by a high initial response excitation system (an angle is decreasing due to a mechanical torque that is
excitation system that will cause a change from the less than an electrical torque, the exciter system must
input to output within 1 s) that has a sufficient field- decrease the excitation by applying a high negative
forcing capability and a sufficiently fast response to voltage to the alternator field as quickly as possible.
resist the accelerating or decelerating rotor. In order Transient stability is primarily concerned with the
to be effective for both accelerating and decelerating immediate effects of a transmission line fault on
rotor responses, the excitation system must be generator synchronism. Fig. 6 shows the typical
capable of field forcing positively and negatively, behavior of a generator in response to a fault
particularly on generators with rotating exciters. condition.
When the rotor is accelerating with respect to the Starting from the initial operating condition (point 1),
stator flux, the rotor angle is increasing due to a a close-in transmission fault causes the generator’s
mechanical torque that is higher than an electrical electrical output power Pe to be extremely reduced.
torque. The resultant difference between the electrical power
and the mechanical turbine power causes the
generator rotor to accelerate with respect to the
system, increasing the power angle (point 2). When
the fault is cleared, the electrical power is restored to
a level corresponding to the appropriate point on the
power-angle curve (point 3).
(a)

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Clearing the fault necessarily removes one or more (b)
transmission elements from service and at least Fig. 7 Effect of fault-clearing time (a) slow fault-clearing time
(b) Fast fault-clearing time.
temporarily weakens the transmission system. After
clearing the fault, the electrical power out of the
In Fig. 7 shows this point. In the example of slower
generator becomes greater than the turbine power.
fault clearing (a), the time duration of the fault allows
This causes the unit to decelerate (point 4), reducing
the rotor to accelerate so far along the curve of PE
the momentum that the rotor gained during the fault.
that the decelerating torque comes right to the limit of
If there is enough retarding torque after fault clearing
maintaining the rotor in synchronism. The shorter
to make up for the acceleration during the fault, the
fault-clearing time (b) stops the acceleration of the
generator will be transiently stable on the first swing
rotor much sooner, assuring that sufficient
and will move back toward its operating point. If the
synchronizing torque is available to recover with a
retarding torque is insufficient, the power angle will
large safety margin. This effect is the demand placed
continue to increase until synchronism with the
on protection engineers to install the fastest available
power system is lost. Power-system stability depends
relaying equipment to protect the transmission
on the clearing time for a fault on the transmission
system.
system. Comparing the two examples
III. EFFECT OF THE EXCITATION SYSTEM
ON STABILITY
Maintaining power-system stability depends on the
speed of fault clearing, the excitation system speed of
response, and the forcing capacity. Increasing the
forcing capability and decreasing the response time
increase the margin of stability. This effect is shown
in Fig. 8, where the lower curve A represents the
power-angle curve of a lower forcing slower response
excitation system. Comparing the area under the
curve for acceleration when the electrical load is less
than the mechanical load to the area under curve A
(a) for deceleration clearly shows that a machine under
the example condition will lose synchronism.

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 Small-signal stability is defined as the ability of the
power system to remain stable in the presence of
small disturbances.
These disturbances could be minor variations in load
or generation on the system. If sufficient damping
torque does not exist, the result can be rotor angle
oscillations of increasing amplitude. Generators
connected to the grid utilizing high-gain AVRs can
experience insufficient damping to system

Fig. 8. Effect of high initial response excitation system oscillations.

For curve B representing a faster higher forcing To further understand the difference between the
exciter, the area under the curve where electrical good effect of high-performance excitation systems
power exceeds mechanical power is much greater, and the side effect of reduced damping torque,
which is sufficient to allow the generator to recover recalling (1), we discussed earlier the breaking down
from this swing. This effect is the source of the of the change in electrical torque ΔTe into the two
demand placed on generation engineers to install the components of synchronizing and damping torques.
fastest available excitation equipment with very high The synchronizing torque increases the pull between
levels of positive and negative forcing to secure the rotor and stator flux, decreasing the angle δ and
highest level of immunity to transient loss of reducing the risk of pulling out of step. The damping
synchronism. torque, on the other hand, results from the phase lag
While fast excitation systems help improve the or lead of the excitation current. Like the timing of
transient stability following large impact disturbances pushes to a swing, the excitation current acting to
to the system, the benefit may be outweighed by the improve the synchronizing torque normally is time
impact of the excitation system on damping the delayed by the characteristics of the excitation
oscillations that follow the first swing after the system: the time delay of the alternator field and the
disturbance. In fact, the fast-responding excitation time delay of the exciter field (if used).
system can contribute a significant amount of
negative damping to oscillations because it can
reduce damping torque. Thus, an excitation system
has the potential to contribute to small-signal
instability of power systems. With the very old
electromechanical excitation systems, the transient
response was relatively slow compared to systems Fig. 9 Inter unit oscillations

introduced today. This slow response has minimal

effect in reducing the damping torque.
IV. SMALL-SIGNAL STABILITY

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 power system. Interarea oscillations are normally in
Fig. 10 Local-mode oscillations
the frequency range of less than 0.5 Hz.
New fast excitation systems that are installed to aid in
improving transient stability can be a source of these
types of oscillations. These systems recognize a
change in voltage due to a load change of up to ten
Fig. 11. Interarea oscillations
times faster than older excitation systems. Thus,
These time delays cause the effect of a high initial
small oscillations of the unit cause the excitation
response excitation system to cause negative
system to correct immediately. Because of the high
damping, resulting in loss of Small-signal stability.
inductance in the generator field winding, however,
The loss of small-signal stability results in one or
the field current rate of change is limited. This
more types of oscillations, which are listed in the
introduces a considerable “lag” in the control
succeeding sections, involving rotor swings that may
function. Thus, from the time of recognition of a
grow without bound or may take a long time to
desired excitation change to its partial fulfillment,
dampen. Three types of oscillations that have been
there is an unavoidable time delay. During this delay
experienced with interconnected generators and
time, the state of the oscillating system will change,
transmission networks (shown in Figs. 9–11) include
causing a new excitation adjustment to be started.
as follows.
The net result is the excitation system that tends to
a. Interunit Oscillations
lag behind the need for a change, aiding the inherent
These oscillations involve typically two or more
oscillatory behavior of the generators interconnected
synchronous machines at a power plant or nearby
by transmission lines. The excitation system acts to
power plants. The machines swing against each other,
introduce energy into the oscillatory cycle at the
with the frequency of the power oscillation ranging
wrong time. Positive synchronizing torque can be
from 1.5 to 3 Hz.
provided to restore the rotor back to the steady-state
b. Local-Mode Oscillations
operating point if the excitation system can be made
These oscillations generally involve one or more to appropriately accelerate or decelerate the rotor.
synchronous machines at a power station swinging Positive damping torque damps out the rotor
together against a comparatively large power system oscillations of the torque angle loop to return the
or load center. The frequency of oscillation is in the system back to normal. For most power systems, the
range of 0.7–2 Hz. These oscillations become configuration of the network and the generator
troublesome when the plant is at high load with a control systems maintains stable damping forces that
high reactance transmission system. restore equilibrium to the power system. In some
c. Interarea Oscillations system configurations, however, unstable oscillations
These oscillations usually involve combinations of can result from the introduction of negative damping
many machines on one part of a power system torques caused by a fast-responding excitation
swinging against machines on another part of the system. This can occur when the system is connected
to a high-impedance transmission system as

7
compared to one connected to a low-impedance For small deviations in rotor speed, the mechanical
transmission system. and electrical torques is approximately equal to the
One solution to improve the dynamic performance of respective per-unit power values. The base value of
this system and large-scale systems in general would power is selected to be equal to the generator
be to add more parallel transmission lines to reduce nameplate megavolt amperes. The “swing equation”
the reactance between the generator and load center. dictates that, when disturbed from equilibrium, the
This solution is well known, but usually, it is not rotor accelerates at a rate that is proportional to the
acceptable due to the high cost of building net torque acting on the rotor divided by the
transmission lines. An alternative solution adds a PSS machine’s inertia constant. Equation (3) can be
acting through the voltage regulator. Working rewritten in terms of small changes about an
together, the excitation output is modulated to operating point
provide positive damping torque to the system. ΔTe = KsΔδ + KDΔω (4)
V. POWER SYSTEM STABLIZERS Where the expression for electrical-torque deviation
Power system stabilizers (PSSs) are a device that has been expanded into its synchronizing and
improves the damping of generator electromechanical damping components,
oscillations. Stabilizers have been employed on large Where
generators for several decades, permitting utilities Ks - Synchronizing coefficient;
to improve stability-constrained operating limits. In KD - damping coefficient;
order to describe the application of the PSS, it is Δδ -rotor angle change;
necessary to introduce general concepts of power- ω -angular speed of rotor;
system stability and synchronous generator operation. Δ- Change.
When disturbed by a sudden change in operating From (4), it can be seen that for positive values of Ks,
conditions, the generator speed and electrical power the synchronizing-torque component opposes
will vary around their steady-state operating points. changes in the rotor angle from the equilibrium point
The relationship between these quantities can be (i.e., an increase in rotor angle will lead to a net
expressed in a simplified form of the “swing decelerating torque, causing the unit to slow down,
equation”. relative to the power system, until the rotor angle is
2H d2δ restored to its equilibrium point Δδ = 0). Similarly,
Wo dt 2
= Tm – Te (3)
for positive values of KD, the damping-torque
component opposes changes in the rotor speed from
Where
the steady-state operating point.
δ -rotor angle in radians;
A generator will remain stable as long as there are
ωo - angular speed of rotor
sufficient positive synchronizing and damping
(The base or rated value ωo = 377 rad/s);
torques acting on its rotor for all operating
Tm - mechanical torque in per unit;
conditions.
Te - electrical torque in per unit;
A. Damping of Electromechanical Oscillations
H - Combined turbo generator inertia constant
expressed in megawatt seconds per megavolt ampere.

8
For positive values of the damping coefficient, and oscillations. The source of reduced damping is the
constant input power, the rotor angle’s response to phase lags due to the field time constants and the lags
small disturbances [i.e., the solution of (3)] will take in the normal voltage regulation loop. Thus, the PSS
the form of a damped sinusoid. The relationship uses phase compensation to adjust the timing of its
between rotor speed and electrical power following correction signal to oppose the oscillations it detects
small disturbances is shown in Fig. 12. A number of in the generator rotor. A PSS can increase a
factors can influence the damping coefficient of a generator’s damping coefficient, thus allowing a unit
synchronous generator, including the generator’s to operate under conditions where there is insufficient
design, the strength of the machine’s interconnection natural damping.
to the grid, and the setting of the excitation system.
While many units have adequate damping VI. PSS THEORY OF OPERATION
coefficients for normal operating conditions, they Modulation of generator excitation can produce
may experience a significant reduction in the value of transient changes in the generator’s electrical output
KD following transmission outages, leading to power. Fast responding exciters equipped with high-
unacceptably low damping ratios. In extreme gain AVRs use their speed and forcing to increase a
situations, the damping coefficient may become generator’s synchronizing torque coefficient (Ks),
negative, causing the electromechanical oscillations resulting in improved steady-state and transient-
to grow and, eventually, causing a loss of stability limits. Unfortunately, improvements in
synchronism. This form of instability is normally synchronizing torque are often achieved at the
referred to as dynamic small-signal or oscillatory expense of damping torque, resulting in reduced
instability to differentiate it from the steady-state levels of oscillatory or small signal stability. To
stability and transient stability. counteract this effect, many units that utilize high-
gain AVRs are also equipped with PSSs to increase
the damping coefficient (KD) and to improve
oscillatory stability (see Fig. 13).
VII. SPEED-BASED STABILIZERS
To supplement the unit’s natural damping after a
disturbance, the PSS must produce a component of
electrical torque that opposes changes in the rotor
speed. One method of accomplishing this is to
introduce a signal, which is proportional to a
Fig. 12 Response of speed and angle to small disturbances
measured rotor speed deviation, into the voltage-
By adding a PSS to a high initial response excitation
regulator input, as shown in Fig. 15.
system, the benefit of higher synchronizing torque is
Fig. 14 shows the steps used within the speed-based
available, and the possibility of a decreased damping
stabilizer to generate the output signal. These steps
torque can be corrected. The function of the PSS is to
are summarized in the following.
counter any oscillations by signaling to change
excitation at just the right time to dampen the

9
1) Measure the shaft speed using a magnetic-problem “PSS Out” changes abruptly during the disturbance to
and gear wheel arrangement. provide damping, but a constant modulation that is
2) Convert the measured speed signal into a dc being applied into the excitation system even during
voltage that is proportional to the speed. normal operation is also observed. Although field
3) High-pass filter the resulting signal to remove the voltage has not been recorded, one can conclude that
average speed level, producing a “change-in-speed” the field voltage is also moving aggressively in
signal; this ensures that the stabilizer reacts only to response to the “PSS Out” driving the voltage
changes in speed and does not permanently alter the regulator. The reason for the constant changing is the
generator terminal voltage reference. high noise content at the input of the speed-type
4) Apply a phase lead to the resulting signal to stabilizer. For years, the constant changes in the field
compensate for the phase lag in the closed-loop voltage have alarmed operators using this type of
voltage regulator. PSS. Notice in the example that, while the generator
5) Adjust the gain of the final signal applied to the active power is oscillatory for a few cycles after the
AVR input. disturbance, the terminal voltage and reactive power
With some minor variations, many of the early PSSs are very constant. Incremental improvements were
were constructed using this basic structure. made to the PSS by manipulating the swing equation
shown in (4) to derive a better method of improving
VIII. DUAL-INPUT STABILIZERS the damping signal input.
While speed-based stabilizers have proven to be d 1 1
Δω = (Tm − Te) = Tacc.
extremely effective, it is frequently difficult to dt 2H 2H
produce a noise-free speed signal that does not (5)
contain other components of shaft motion such as The simplified swing equation can be rearranged to
lateral shaft run-out (hydroelectric units) or torsional reveal the principle of operation of early power-based
oscillations (steam-driven turbo generators). The stabilizers. Based on (5), it is apparent that a speed
presence of these components in the input of a speed- deviation signal can be derived from the net
based stabilizer can result in excessive modulation of accelerating power acting on the rotor, i.e., the
the generator’s excitation and, for the case of difference between the applied mechanical power and
torsional components, in the production of potentially the generated electrical power.
damaging electrical-torque variations. These
electrical-torque variations led to the investigation of
stabilizer designs based upon the measured power.
Fig. 15 shows a 2% voltage step change introduced
into the voltage-regulator summing point that causes
the generator voltage to change by 2%. Here, a
speed-type PSS provides damping after the small-
signal disturbance to resolve the momentary MW
oscillation after the disturbance. Note that the

10
 Fig. 16. Block diagram of dual-input PSS.
Early attempts at constructing power-based stabilizers
used the aforementioned relationship to substitute the
measured electrical and mechanical power signals for
Fig. 13. Block diagram of excitation system and PSS. the input speed. The electrical power signal was
measured directly by using an instantaneous watt
transducer. The mechanical power could not be
measured directly and, instead, was estimated based
on the measurement of valve or gate positions. The
relationship between these physical measurements
and the actual mechanical power varies based on the
Fig. 14. Speed-based stabilizer
turbine design and other factors, resulting in a high
degree of customization and complexity.
This approach was abandoned in favor of an indirect
method that employed the two available signals:
electrical power and speed signals. The goal was to
eliminate the undesirable components from the speed
signal while avoiding a reliance on the difficult-to-
measure mechanical power signal. To accomplish
this, the relationship of (2) was rearranged to obtain a
derived integral-of-mechanical power signal from
electrical power and speed.
1
[ ΔT m dt -∫ ΔT e dt ]
2H ∫
Δω =

Fig. 15. Online step response, frequency-type PSS Ks = 6, 92-MW

Since mechanical power normally changes slowly
hydro turbine generator. relative to the electromechanical oscillation
frequencies, the derived mechanical power signal can
be band-limited using a low-pass filter. The low-pass
filter attenuates high-frequency components (e.g.,

11
torsional components and measurement noise) from there are normally several gear wheels already
the incoming signal while maintaining a reasonable provided for the purpose of speed measurement or
representation of mechanical power changes. The governing. The shaft location is not critical as long as
resulting band-limited derived signal is then used in it is directly coupled to the main turbo generator
place of the real mechanical power in the swing shaft. On vertical turbo generators (hydraulic), the
equation to derive a change-in-speed signal with direct measurement of shaft speed is considerably
special properties. more difficult, particularly when the shaft is
The swing equation has been written in the frequency subjected to large amounts of lateral movement
domain using the Laplace operator “s” to represent a (shaft run-out) during normal operation. On these
complex frequency. The final derived speed signal is units, speed is almost always derived from a
derived from both a band-limited measured speed compensated frequency signal.
signal and a high-pass filtered integral-of-electrical In either type of generator, the speed signal is
power signal. At lower frequencies, the measured plagued by noise, masking the desired speed-change
speed signal dominates this expression, whereas at information. The derivation of shaft speed from the
higher frequencies, the output is determined primarily frequency of a voltage phasor and a current phasor is
by the electrical power input. shown graphically in Fig. 18. The internal voltage
The integral-of-accelerating-power arrangement is phasor is obtained by adding the voltage drop
illustrated in the block diagram of Fig. 16. associated with a q-axis impedance (note that for
salient pole machines, the synchronous impedance
provides the required compensation) to the generator
terminal-voltage phasor. The magnitude of the
internal phasor is proportional to field excitation,
and its position is tied to the quadrature axis.
Therefore, shifts in the internal voltage phasor
position correspond with the shifts in the generator
rotor position. The frequency derived from the
compensated phasor corresponds to the shaft speed.
and can be used in place of a physical measurement.
Fig. 17. Speed derived from VT and CT signals
On round-rotor machines, the selection of the correct
IX. SPEED SIGNAL
compensating impedance is somewhat more
For the frequency or speed stabilizer, shaft speed was
complicated; simulations and site tests are normally
measured either directly or derived from the
performed to confirm this setting.
frequency of a compensated voltage signal obtained
from the generator terminal VT and CT secondary
voltages and currents (Fig. 17). If directly measured,
shaft speed is normally obtained from a magnetic
probe and gear-wheel arrangement. On horizontal
turbo generators operating at 1800 or 3600 rev/min,

12
 Fig. 18. Accelerating-power design (speed input) XI. DERIVED MECHANICAL POWER
SIGNAL
As previously described, the speed deviation and
integral of electrical power deviation signals are
combined to produce a derived integral-of
Fig. 19. Integral-of-electrical power block diagram. mechanical power signal. This signal is then low-pass
filtered, as shown in the block diagram of Fig. 20.
A low-pass filter can be configured to take on one of
the following two forms.
1) The first filter, which is a simple four-pole low-
pass filter, was used to provide attenuation of
Fig. 20. Filter configurations for derived mechanical torsional components appearing in the speed. For
power signal. thermal units, a time constant can be selected to
In either case, the resulting signal must be converted provide attenuation at the lowest torsional
to a constant level that is proportional to speed frequency of the turbo generator set.
(frequency). Two high-pass filter stages are applied Unfortunately, this design requirement conflicts
to the resulting signal to remove the average speed with the production of a reasonable derived
level, producing a speed deviation signal; this ensures mechanical power signal, which can follow
that the stabilizer reacts only to changes in speed and changes in the actual prime mover output. This is
does not permanently alter the generator terminal particularly problematic on hydroelectric units
voltage reference. Fig. 18 shows the high-pass filter where rates of the mechanical power change can
transfer-function blocks in the frequency-domain easily exceed 10% per second. Excessive band-
form (the letter “s” is used to represent the complex limiting of the mechanical power signal can lead
frequency or Laplace operator). to excessive stabilizer output signal variations
X. GENERATOR ELECTRICAL POWER during loading and unloading of the unit.
SIGNAL 2) The second low-pass filter configuration deals
The generator electrical power output is derived from with this problem. This filter, which is referred
the generator VT secondary voltages and CT to as a “ramp tracking” filter, produces a zero
secondary currents. The power output is high-pass steady-state error to ramp changes in the input
filtered to produce the required power deviation integral-of-electrical power signal. This limits
signal. This signal is then integrated and scaled the stabilizer output variation to very low levels
by using the generator inertia constant (2H) for for the rates of change of the mechanical power
combination with the speed signal. Fig. 19 shows the that are normally encountered during operation
operations performed on the power-input signal to of utility scale generators.
produce the integral-of-electrical power deviation
signal.

13
 system by applying a low-frequency signal into the
voltage-regulator auxiliary summing point input and
then by comparing to the generator output for phase
shift and gain over the frequency range applied.
These tests are normally performed with the
generator at 10% MW load. Fig. 22 shows the results
Fig. 21. Output stage of PSS to AVR
of a typical test performed to determine the phase lag
of the voltage regulator/generator interconnected to
the system without the PSS. Compensation is then
provided through the lead and lag of the PSS to
ensure that the voltage regulator will be responsive to
the frequency range desired. Here, phase lead is
needed above 1 Hz, as shown by the solid line in Fig.
22.

Fig. 22. Phase compensation denoted with and without the PSS

XII. STABILIZING SIGNAL SELECTION

AND PHASE COMPENSATION

As shown in the simplified block diagram of Fig. 16,

Fig. 23. Hydro generator without PSS
the derived speed signal is modified before it is
applied to the voltage-regulator input. The signal is
filtered to provide a phase lead at the
electromechanical frequencies of interest, i.e., 0.1 to
5.0 Hz. The phase-lead requirement is site specific
and is required to compensate for a phase lag
introduced by the closed-loop voltage regulator.
The diagram in Fig. 21 shows the phase-
compensation portion of the digital stabilizer. The Fig. 24. Hydro generator with PSS

transfer function for each stage of phase XIII. TERMINAL-VOLTAGE LIMITER

compensation is a simple pole-zero combination Since the PSS operates by modulating the excitation,
where the lead and lag time constants is adjustable. it may counteract the voltage regulator’s attempts to
Tests are performed to determine the amount of maintain a terminal voltage within a tolerance band.
compensation required for the generator/excitation To avoid producing an overvoltage condition, the

14
PSS may be equipped with a terminal-voltage limiter terminal voltage. The oscillations could be triggered
that reduces the upper output limit to zero when the by a step change in unit terminal voltage. The
generator terminal voltage exceeds the set point. waveforms in Fig. 23 illustrate the test results,
The level is normally selected such that the limiter indicating that the oscillations under the test
will operate to eliminate any contribution from the condition were damped but with significant duration.
PSS before the generator’s time-delayed overvoltage This condition occurred after the unit was upgraded
or V/Hz protection operates. The limiter will reduce from manual control to a modern static exciter
the stabilizer’s upper limit at a fixed rate until zero is system with high initial response characteristic.
reached or the overvoltage is no longer present. When the PSS, a dual-input-type PSS, was
The limiter does not reduce the AVR reference below implemented, the response of the turbine generator
its normal level; it will not interfere with the system was substantially improved, showing a much greater
voltage control during disturbance conditions. The damping capability compared to the performance in
error signal (terminal voltage minus limit start point) Fig. 23. In operation, with the settings of the PSS set
is processed through a conventional low pass as indicated in Fig. 24, the unit was able to deliver a
filter to reduce the effect of measurement noise. rated load once again, with no danger from power
oscillations threatening to damage the machine. This
is an example of a local area oscillation. The
combination of high-performance excitation and the
compensation of the PSS provide the best
combination of performance benefits for this hydro
turbine installation. The benefits of a newly installed
dual-input-type PSS (Fig. 25) versus those of the
existing single-input PSS (Fig. 15) for the same
machine can be seen in the online step response of a
92-MW turbine generator to system oscillations. The
speed based stabilizer produces a significant amount
of noise in the stabilizing signal. This noise limits the
maximum Ks gain to 6.2. With the dual-input type,
the noise is considerably less, allowing a higher gain,
Ks = 7.5 s, and more effective damping, as shown in
Fig. 25.
Fig. 25. Online step response, Basler PSS-100 Ks = 7.5, 92-MW
hydro turbine generator. XV. CHANGING TIMES FOR PSS
XIV. CASE STUDIES IMPLEMENTATION
A small turbine generator was experiencing Since the blackouts in the northwest United States in
potentially damaging power oscillations when the the late 1990s and the more recent blackout in the
unit load was increased to more than 0.5 pu, with northeast, the frailty of the transmission system has
oscillations triggered by small changes in load or become apparent. North American Reliability

15
Council has issued guidelines mandating testing to therefore, may require PSSs in the future if they do
verify hardware to improve the reliability of the not have them.
transmission system. These tests include the XVII. ACKNOWLEDGEMENT
verification of excitation models with excitation Praise to God for His guidance and blessing, this
system performance and the verification of excitation review was finally completed. First and foremost, I
limiters and protective relays to ensure coordination. would like to express my heartily gratitude to,
Today, the use of PSSs is being mandated in the Dr.Ing.Belachew Bantyirga for his guidance
western portion of the country for all machines of throughout the progress of this term paper review
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