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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 15, NO. 4, NOVEMBER 2000
Decentralized Stability-Enhancing Control of
Synchronous Generator
J. Machowski, S. Robak, J. W. Bialek, J. R. Bumby, and N. Abi-Samra
Abstract—This paper describes new structures for
stability-enhancing excitation controllers designed using a
nonlinear multi-machine system model and Lyapunov’s direct
method. Two control structures are presented: a hierarchical
structure in which the AVR is the master controller and the
PSS the slave controller and a traditional structure in which the
PSS constitutes a supplementary loop to the main AVR. Both
controllers are shown to be robust, as the damping they introduce
into the system is insensitive to changes in both the system
topology/parameters and the pattern of network flows. Each
individual controller contributes positively to the overall system
damping with no undesirable interaction between controllers.
These features should allow a decentralized approach to the design
of the AVR PSS. Such a design approach is compatible with the
new competitive market structures and should result in savings
on commissioning costs. Simulation results for a multi-machine
power system are presented that confirm the above and show that
the two control structures are very effective in damping both local
and inter-area power swings.
+
Index Terms—Power system control, power system stability, synchronous generator excitation.
I. INTRODUCTION
T
HE FUNCTIONAL diagram of a traditional excitation
control system is shown in Fig. 1. The excitation voltage
is supplied from the exciter and is controlled by the
Automatic Voltage Regulator (AVR). Its aim is to keep the
. Although
terminal voltage equal to the reference value
the AVR is very effective during normal steady-state operation,
it may have a negative influence on the damping of power
swings in the transient state [1], [2]. To compensate for this
a supplementary control loop, known as the Power System
Stabilizer (PSS), is often added as shown in Fig. 1.
Considerable research effort has been devoted to the design
of the AVR PSS system. Generally the properties of a particular PSS depend on the choice of the input quantities. The
, genermost commonly used quantities are speed deviation
ator real power , generator current , frequency deviation
or the transient emf . As each of these quantities has its own
Manuscript received February 12, 1999; revised December 21, 1999.
This work was supported by the Electrical Power Research Institute, Grant
WO8555-01.
J. Machowski and S. Robak are with the Warsaw University of Technology,
Instytut Elektroenergetyki, Koszykowa 75, 00-662 Warsaw, Poland.
J. W. Bialek and J. R. Bumby are with the University of Durham, School of
Engineering, Science Site, South Road, Durham DH 1 3LE, UK.
N. Abi-Samra is with the Electrical Power Research Institute, 3412 Hillview
Ave., Palo Alto, CA 94304-1395, USA.
Publisher Item Identifier S 0885-8950(00)10368-2.
Fig. 1.
Functional diagram of traditional excitation control system.
advantages and disadvantages, the PSS is often designed to operate on two or more input signals.
The main problems associated with the design of traditional
AVR PSS systems are:
1) the optimal settings usually depend on the power system
parameters and the system loading condition;
2) it is difficult to design an AVR PSS that damps efficiently multi-modal oscillations containing both local and
inter-area modes;
3) individual AVR PSS systems often cause harmful interactions in multi-machine systems.
Although the PSS itself is not expensive, the commissioning
costs can be quite high because of the need to undertake extensive system-wide studies in order to optimize the AVR and PSS
settings.
Many research centers are trying to develop improved
PSS systems that are robust and able to cope with
AVR
multi-modal power swings over a wide range of operating
conditions. Among the many approaches proposed so far are
those based on the use of adaptive systems [3], artificial intelligence tools [4], [5], robust control techniques [6], feedback
linearizing excitation control [7] and multi-loop controller [8].
This paper presents a novel approach to the design of power
system controllers based on the application of the Lyapunov’s
direct method. The design technique was originally applied to
a nonlinear single generator-infinite busbar model [9]–[11].
In this paper the approach is generalized to the nonlinear
multi-machine case.
II. THEORETICAL BACKGROUND
Point is the equilibrium point of the dynamic system deif
.
scribed by a set of nonlinear equations
Lyapunov’s stability theorem states that this equilibrium point
such that: i)
is stable if there is a Lyapunov function
is positive definite with a minimum value at , and ii) the time
0885–8950/00$10.00 © 2000 IEEE
MACHOWSKI et al.: DECENTRALIZED STABILITY-ENHANCING CONTROL OF SYNCHRONOUS GENERATOR
derivative
along the system trajectory
is neg. If
then the equilibrium
ative semi-definite, i.e.
point is asymptotically stable. The time derivative along the
can be calculated as:
system trajectory
1337
For the third order generator model [2]:
(5)
(6)
and , are the - and -axis components of the generwhere
, and
and
are the synator current,
chronous and transient -axis generator reactance, respectively.
B. Network
(1)
decreases with time and
If is negative then the function
tends toward its minimum value, the system equilibrium point
. The more negative the value of the faster the system returns
to the equilibrium point .
The automatic control of any system element, such as synchronous generators, turbines or FACTS devices, influences the
value of . Consequently any given control improves (in the
Lyapunov sense) the transient stability of the system if it maximizes the negative value of at each instant of the transient
state.
With these observations a design approach can be defined that
comprises of three stages:
find an appropriate
i) For given dynamic system
that is an explicit function of
Lyapunov function
the control variables.
ii) Select a control law that maximizes the negative value of
at all points along the system trajectory.
iii) Select locally available signals to execute the chosen control law.
III. SYSTEM MODEL
A. Generators
Lines and transformers are described by their -equivalents
whilst a load is replaced by a constant admittance. The generator
are added to the network model
transient reactances
to form fictitious generation nodes with the generator transient
emf as the nodal voltage. All the load nodes are eliminated so
that the original transmission network is reduced to a transfer
equivalent network connecting all the generation nodes [2]. For
such a system model, and noting that for the third order gener, the
-components of electric current
ator model
of the th generator can be expressed as [2]:
(7)
(8)
is the element of the transfer admittance matrix and
where
is the number of generators in the system. In deriving these
equations the conductance in the transfer equivalent network
. To account for power balhad been neglected, i.e.
in (8)
ance in the system model the equivalent conductance
includes the power losses that would have been present in the
. Substituting (7) and (8) into (5) and
transfer conductance
(6) gives:
The stability of electric power systems is usually assessed by
using a simplified synchronous generator model. In this paper
the third-order generator model is used [2]:
(9)
(2)
(10)
(3)
(4)
is the real power of the equivalent load
where
constant.
at the generation node. It is further assumed that
C. System
In these equations the subscript relates to the generator
number, is the power (rotor) angle and
is the speed deviation.
is the inertia
the mechanical time constant,
the rated
coefficient,
the mechanical power,
the electrical power,
power,
the damping coefficient,
the quadrature-axis component
the open-circuit transient time constant
of transient emf,
the excitation voltage. A “hat” on the top of a symbol
and
corresponds to the post-fault equilibrium point. Note that
.
The following notation is introduced:
(11)
(12)
(13)
(14)
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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 15, NO. 4, NOVEMBER 2000
Substituting (11)–(14) into (2)–(4) results in the following nonlinear multi-machine system model:
(15)
The time derivative of this function can be derived from (1) as
the sum of the time derivatives of the three components
, ,
. The component
given by (19) depends only on the
and
rotor speed deviation. Its time derivative is:
(16)
(17)
IV. LYAPUNOV’S DIRECT METHOD
If the flux variation in the generator is neglected (constant
transient emf) then the state-space system model defined by
(15)–(17) simplifies to the classical model with the generators
modeled by the swing (15) and (16) only. An energy-type Lyapunov function for such a system model comprises of the sum
of the system kinetic and potential energy with respect to the
equilibrium point [2], [12]:
(18)
(23)
, given by (20), depends on the rotor angles
The component
and the transient emfs, so that its time derivative must be calculated as:
(24)
Hence:
and
are proportional to the kinetic and
The functions
potential energy of the system such that:
(25)
(19)
in (21) depends only on the transient
As the component
emfs, its time derivative is:
(26)
(20)
Equations (23), (25) and (26) do not depend explicitly on the
. An implicit dependence is obtained using
control variables
and (17).
the time derivatives
gives:
Multiplying (17) by
and
are positive-definite around the equiBoth functions
librium point.
Lyapunov functions derived for higher-order power system
models usually contain some additional components. For the
third-order generator model a Lyapunov function derived by
Kakimoto et al. [13] included a component proportional to the
squared deviation of the transient emf
(27)
Re-arranging the terms in this equation results in:
(21)
is a
In this equation the subscript refers to “field.” As
square function it is positive-definite around the equilibrium
point. The candidate Lyapunov function is obtained as the sum:
(28)
(22)
MACHOWSKI et al.: DECENTRALIZED STABILITY-ENHANCING CONTROL OF SYNCHRONOUS GENERATOR
1339
is positive and maximum. This condition is satisfied by the control law
Substituting (28) into (26) gives:
(34)
(29)
Comparing (23), (25) and (29) shows that there are similar
components in these equations, but with opposite signs. One
,
and the other in
,
common component is in the pair
. These common components are due to the exchange of
energy between kinetic, potential and field energy. For example
the kinetic energy is converted into potential energy and vice
versa during power swings.
Substituting (23), (25) and (29) into the derivative
gives:
is the controller gain. Substituting (34) into (32) and
where
(31) gives, respectively:
(35)
(36)
Equation (36) shows that the control law given by (34) ensures
that the system is stable and tends toward the post-fault equilibrium point with maximum speed. Obviously this law is optimal
only for the Lyapunov function used. As Lyapunov functions are
nonunique, another formulation may result in a modified control law.
The control law defined by (34) can be re-written as
(30)
(37)
With manual excitation control the AVR is inactive,
constant, and the last component in (30) is zero. In this
case the time derivative is negative semi-definite, the function
, expressed by (22), is a Lyapunov function and the system is
stable.
Whether or not the derivative , given by (30), is negative
semi-definite when the excitation voltage is controlled by the
.
AVR depends on the control strategy chosen for
where
(38)
defines the post-fault steady-state synchronous emf. This emf
and the loading
depends on the required terminal voltage
condition.
The synchronous emf is induced by the field current and can
therefore be replaced by
V. CONTROL STRATEGIES
The excitation control law for
must maximize the negative value of at any instant in time. This control law will then
bring the system back to the equilibrium point as quickly as possible. Substituting the values obtained from (4) into (30) yields
(39)
(40)
is the -axis armature reaction reactance. Subwhere
stituting (38) and (39) into (37) gives the following control
strategy:
(41)
(31)
where
An alternative control strategy is obtained by substituting (38)
and (40) into (41) to give:
(42)
(32)
where
The first and the second components in (31) are negative semidefinite and always contribute to the overall system damping.
The third component is given by (32) and it is this component
that is influenced by the excitation control. Equation (32) is determined by the sum over all the generators of
(33)
Consequently (32) is negative maximum when each of the components of the sum is positive maximum. This means that at
any instant in the transient state the excitation voltage will en, (33)
sure that, after taking into account any constraints on
(43)
is the increment in the field current.
Obviously the control strategies defined by (41) and (42) are
valid only for the third order synchronous generator model used
in the derivation. For this generator model, the field current is
smooth as it contains only fluctuations at low swing frequencies. In reality, the dc offset in the armature current, which flows
during the subtransient state, will induce a rapidly decaying
50 Hz component in the field current. Moreover, a static exciter using commutation of an ac source will also produce persistent ripples in the field current. All these fast harmonics must
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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 15, NO. 4, NOVEMBER 2000
be “washed out” of the measured signal using a low-pass filter,
for example a Bessel filter.
VI. IMPORTANT FEATURES
The first important feature of the proposed control law defined by (34) is that the function , given by (36), is independent of the network parameters. It depends only on the controller
, the generator reactance
and
gain
, the speed deviation
and the deviation
time constant
. As determines the speed at which the
system trajectory tends toward the equilibrium point, it determines the system damping. This would suggest that, with the
proposed control strategy, the contribution of each generator
to the overall system damping is insensitive to changes in either tire network topology/parameters or the pattern of network
flows. This is very important as it suggests that the proposed
stabilizer is robust in that it does not need re-tuning following
network changes.
The second important feature is that each generator controlled
according to the control law (34) contributes an (38) independent component into given by (35), with no cross-coupling
terms between generators. In other words each individual controller contributes a damping term independent of all the other
controllers. This very important feature of the proposed controller is referred to as the additivity of damping. In traditional
AVR PSS systems the settings of individual controllers must
be coordinated as any controller may influence any other controller in the system. In contrast, the additivity of damping for
the proposed controllers suggests that their settings need not be
coordinated.
The robustness of the proposed stabilizer in conjunction with
the additivity of damping are very important features of the proposed control as they allow a decentralized approach to the design of stabilizing controllers. The parameters of the proposed
AVR PSS system can be determined in a decentralized way,
without considering the impact of other controllers or system
conditions. This feature of the proposed controller, which is
unique among competing AVR PSS design methodologies,
should reduce the commissioning costs. It is also compatible
with the new market structure in which individual generators
compete against each other and may be unwilling to disclose
detailed information about their generators and control systems.
Such information is necessary for optimal tuning of traditional
AVR PSS systems.
The features of the stabilizing control system discussed above
have been proved theoretically for the simplified system model.
The simulations described in Section X show the validity of the
control law (34) when applied to higher order, more realistic,
system models.
VII. CONTROLLER BLOCK DIAGRAMS
This section assumes the use of a static exciter. In the transient state, a static exciter can be represented as a proportional
and
shown in Fig. 1 are then problock [1], [2]. Voltages
.
portional to each other and, in per-unit,
Fig. 2.
Hierarchical structure.
This equality is valid only for the static exciter. For other types
of exciter an additional transfer function would have to be included in the block diagram to compensate for the equivalent
transfer function of the exciter.
A. Hierarchical Structure
Fig. 2 shows the functional block diagram of a hierarchical
excitation controller capable of executing the control strategy
(41). The symbol ST denotes a static exciter. The lower part
of this diagram, denoted as PSS, generates the signal
that is proportional to the change in the generator synchronous
. This
emf with respect to the post-fault equilibrium value
determined
signal is subtracted from the reference value
by the AVR shown in the upper part of the diagram. The AVR
acts with a classical voltage feedback loop and sets the reference
depending on the required
value of the synchronous emf
and the system loading condition.
terminal voltage
The structure of the hierarchical excitation controller is different to the traditional AVR PSS of Fig. 1. In the traditional
solution, the AVR is the main controller whilst the PSS is a
supplementary control loop. The structure of the proposed controller is hierarchical and of the master–slave type. The slave
(primary) controller is the PSS and the master (secondary) controller is the AVR. The PSS has two input signals: i) the reference value of the synchronous emf provided by the AVR and
ii) a feedback signal equal to the field current. The PSS does
not contain any phase compensation lead-lag elements. It is basically a proportional controller as the change in the excitation
voltage is proportional to the change in the synchronous emf (or
the field current). This hierarchical structure is similar to that of
the turbine governing system as discussed in [9].
The role of the additional TSEC block shown in the
right-hand part of Fig. 2 will be described in Section IX.
B. Structure with a Supplementary Loop
The alternative excitation control strategy (42) is executed
with a more traditional AVR PSS structure where the AVR
is the main control loop and the PSS is a supplementary loop.
Fig. 3 shows the functional block diagram of such an excitation
controller. The symbol ST denotes a static exciter.
A supplementary signal, proportional to the field current de, is subtracted from the signal generated by the AVR.
viation
MACHOWSKI et al.: DECENTRALIZED STABILITY-ENHANCING CONTROL OF SYNCHRONOUS GENERATOR
1341
Fig. 4. Diagram of the four-machine test system [1].
Fig. 3. Structure with supplementary loop.
In this more traditional structure a “wash-out” element provides
, determined by (43), by eliminating
from
the signal
.
the field current
The transfer function, and the parameters of the washout element, are chosen so that:
• The magnitude of the frequency response is zero at zero
frequency. This ensures that no constant signals are passed
through.
• Within the swing frequency range (0.2 to 2 Hz), signals
are passed with approximately unity gain and with a small
phase shift.
Typically the washout element consists of one differentiating
element and two lead-lag elements. It is important to note that
the “wash-out” element is part of the device measuring the field
current increment. Consequently its structure and parameters
are fixed in a similar way as are the parameters of the signal
sensor itself.
The role of the additional TSEC block shown in the
right-hand part of Fig. 2 will be described in Section IX.
VIII. FREQUENCY CHARACTERISTIC OF THE AVR
In both of the above control structures (Figs. 2 and 3) the
is set by the AVR in order to maintain the
reference value
. Thus
should not change as
desired terminal voltage
a consequence of voltage fluctuations following a power swing.
To achieve this, the AVR should have a low effective gain at the
swing frequency of typically 0.2–2 Hz. This can be achieved if
the AVR is a PI regulator, or a proportional regulator with an
appropriate transient gain reduction (TGR).
order to increase the available deceleration area [2]. However a
to sudshort-circuit causes the generator synchronous emf
denly increase and the proposed controllers would counteract
this by reducing the excitation voltage instead of increasing it.
In order to deal with such situations the controllers shown in
Figs. 2 and 3 are equipped with an additional logic circuit referred to as transient stability excitation control (TSEC).
In normal operation, or during power swings following a short
circuit, this additional control logic generates a signal TSEC
and the controllers execute the control strategy defined by (41)
or (42). During a short-circuit in the network a signal TSEC
is generated and the output of the PSS is blocked giving the
AVR absolute priority and, at the same time, the opportunity
to increase the excitation voltage. When the fault is cleared the
and the controllers operate
TSEC logic is again set to TSEC
according to the control law defined by (41) or (42).
The TSEC can also be used to improve the recovery of the
generator terminal voltage following a short circuit by modifying the output limits of the excitation system [10], [11].
There are many ways of designing the TSEC logic [10], [11].
In one simple version the TSEC detects the simultaneous presand a large acceleration power
ence of a large voltage error
. In the case of a short circuit in the network both the real
power and generator terminal voltage decrease rapidly and the
and
are both large and negative. The TSEC
increments
circuit recognizes the large deviation (with the same sign) in
. In the case of a power swing
both signals and sets TSEC
and
have op(forward or backward) the increments
posite sign. This enables the TSEC to distinguish between a
short-circuit and a power swing.
X. SIMULATION RESULTS
IX. TRANSIENT STABILITY EXCITATION CONTROL
The control law defined in (34) is valid only when the
dynamic system is time-invariant and its parameters do not
change with time. This is not the case during a short-circuit in
the network. As a result, the control action derived from (34)
may degrade the system stability during the fault instead of
improving it. This can be explained as follows using the equal
area criterion.
During a short-circuit the generator rotor accelerates and corin
rect control action should increase the excitation voltage
Simulation results are presented for the four-machine system
shown in Fig. 4 [1]. The system consists of two areas and each
area has two generators. The frequency of the two local modes
is about 1 Hz while the frequency of inter-area mode is about
0.5 Hz.
Four excitation control schemes have been simulated in
Figs. 5 and 6 with the first two schemes been taken from [1].
TGR corresponds to a static
The scheme denoted as ST
exciter with a proportional regulator plus transient gain reduc,
,
,
tion (TGR) with parameters
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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 15, NO. 4, NOVEMBER 2000
gain reduction (TGR) with parameters; gain
and time
and
whilst the Bessel filter has the
constants
same parameters as in the hierarchical structure. The transfer
function of the washout element is
For all the excitation control schemes the output limit of the
,
. The voltage
excitation voltage is
.
sensor has a time constant
The sixth-order generator model has been used in all the simulations so as to include sub-transient effects. The generator and
network resistances have also been included. The loads are modeled as constant real and reactive power demands. Three types
of disturbances have been studied:
deg)
• nonzero initial condition (
)
• a step change in the reference value (
• various network short-circuits.
In all the simulations the proposed excitation controllers have
demonstrated excellent performance producing fast damping of
power swings and small oscillations in the terminal voltage following the disturbance.
As an example, simulation results for the nonzero initial condegrees in the rotor angle of generator G1 are
dition
shown in Figs. 5–7. Additional results can be found in [10], [11].
Fig. 5. Damping of local swings: Generator G1.
A. Damping of Local and Inter-Area Swings
Fig. 6. Damping of inter-area swings.
. The second scheme denoted as ST
PSS corresponds to a static exciter with a proportional regulator. This
.
scheme includes a traditional PSS based on speed deviation
,
,
,
,
The data are:
,
,
,
. The third
scheme, denoted as “proposed (hierarchical),” corresponds
to a static exciter equipped with the hierarchical excitation
controller of Fig. 2. The low-pass Bessel filter has a transfer
where
,
. The
function
and an additional
primary controller (PSS) has a gain
. The secondary controller (AVR) is
,
and
a proportional-integral regulator with
. The final excitation control scheme,
an input limiter
denoted as “proposed (supplementary),” is a static exciter fitted
with proposed excitation controller with the supplementary
loop, Fig. 3. The AVR is a proportional controller with transient
To illustrate the damping of local swings, Fig. 5 shows the
, generator terminal voltage
variation of the real power
and excitation voltage
of generator G1 following
the disturbance. Similar results were obtained for generators
G2, G3 and G4. In these figures the dotted lines correspond
to the case when all the generators are equipped with the ST
TGR controller, the dashed lines when all the generators
are equipped with the ST PSS controller and the solid lines
to when all the generators are equipped with the proposed hiTGR is oscillatory
erarchical controller. The case with ST
unstable (as explained in [1]). Introducing the traditional PSS
makes the system stable but the proposed hierarchical controller
achieves significantly better damping in that both the first swing
power overshoot and the settling time are reduced by about
50%. Similar performance has been obtained for the proposed
controller with the supplementary loop. From the point of view
of the damping of local swings there is no difference between
either of the two, new, proposed structures.
Fig. 6 shows the power swings in the tie-line between node 7
and node 8, i.e. it illustrates the damping of inter-area swings.
The damping due to the traditional PSS and the proposed hierarchical structure is similar. However the performance of the
proposed supplementary structure is much better. It reduces the
first-swing overshoot by about 30% and the settling time by
about 50% when compared to the traditional PSS.
B. Additivity of Damping
One of the most important features of the two proposed stabilizing systems is the additivity of damping and the lack of potentially harmful interactions between individual stabilizers. To
illustrate this, Fig. 7 shows how the overall damping is improved
MACHOWSKI et al.: DECENTRALIZED STABILITY-ENHANCING CONTROL OF SYNCHRONOUS GENERATOR
1343
F. Asynchronous Operation
The optimization criterion of maximizing
is valid only
within the system stability area. When a generator loses
synchronism, the proposed control may not improve the
prospect of re-synchronization. Other AVR PSS systems also
tend to suffer from this problem. Any control aiming at fast
re-synchronization must coordinate the excitation control and
the turbine control [14].
Fig. 7. Damping of inter-area swings as the number of installed proposed
controllers increases.
as the number of generators equipped with the proposed stabilizer is increased.
The base case, shown by the dotted line, is when all the generators are quipped with ST TGR controllers and, as mentioned
earlier, it is unstable. The other lines show the cumulative effect
of adding, the proposed hierarchical controller to each generator in turn, i.e. first to G1 only, then to G1 and G4, then to
G1, G3 and G4, and finally to all the generators. Clearly, adding
each consecutive controller improves the damping of the power
swings.
C. Robustness of the Proposed Stabilizer
Section VI showed that the proposed controllers should force
the same rate of energy dissipation (i.e. damping) no matter
what the equivalent network reactance is, or what the pattern
of flows in the network are. In other words, the performance
of the controller should be robust and not be limited to the
assumed system operating conditions. Simulation studies for
various system loading and changes in network parameters reported in [10], [11] have confirmed this. While the damping of
the traditional PSS suffered when the system operating condition and/or network parameters changed, the performance of the
proposed stabilizer tended to be unaffected.
D. Comparison Between Two Control Structures
Both the controller structures in Figs. 2 and 3 correct the reby subtracting from
quired value of the synchronous emf
it a signal proportional to the field current increment. In the
two structures this increment is measured in a different way and
therefore the dynamic behavior of both controllers is slightly
different. A comparison of simulation results has shown that the
damping of the local swings (generator power) provided by both
controllers is very similar. The structure with the supplementary loop provides better damping for the inter-area oscillations
(power in the tielines) and generally results in a smaller overshoot in the generator terminal voltage.
E. Gain and Simplification of the Power System Model
Equations (35) and (36) suggest that the higher the gain
the better the damping. Simulations using the full Park’s
model have shown that there is a limit to the gain beyond which
the damping reduces. This may be due to the simplifications
in the power system model used in the derivation of the
theoretical control law. This problem is currently under further
investigation.
XI. CONCLUSION
A new synchronous generator excitation control law has been
derived using a nonlinear multi-machine system model. The
control law uses an energy-type Lyapunov function to maximize
the speed with which the system returns to the equilibrium point
following a disturbance. This control law is optimal only for the
particular Lyapunov function used.
The proposed control law possesses two important features.
First, the damping is insensitive to changes in both the system
topology/parameters and the pattern of flows in the network.
This means that the controllers are robust and do not need to
be re-tuned following any system changes. Secondly, each individual controller contributes positively to the overall system
damping without creating undesirable interactions between controllers. This would suggest that the settings of the proposed
controllers do not need to be coordinated.
Two different control structures have been discussed. The
first structure is a hierarchical structure of the master–slave type
where the master controller is the AVR and the slave controller
is the PSS. The second structure follows a more traditional approach where the PSS is added to the AVR as a supplementary
loop.
Simulation results for a multi-machine test system have
shown that both of the proposed excitation controllers are very
effective in damping both local and inter-area swings caused
by a variety of disturbances. With regards damping of the
inter-area modes, and the overshoot in the generator terminal
voltage, the structure with the PSS as a supplementary loop
shows marginally better performance.
The simulation results have confirmed that the damping provided by the proposed controllers is additive in a multimachine
system. This allows individual controllers to be designed and
operated in a decentralized way. This feature is especially important as it should reduce the AVR PSS commissioning costs.
It is also compatible with the new competitive market structures.
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