14-05-2012, 04:35 PM
Design of Decentralized Power System Stabilizers for Multimachine Power System using Model Reduction and Fast Output Sampling Techniques
Design of Decentralized Power System Stabilizers for Multimachine Power System ......pdf (Size: 291.97 KB / Downloads: 46)
Abstract
Power System Stabilizers (PSSs) are added to excitation
systems to enhance the damping during low frequency
oscillations. In this paper, the design of decentralized
PSSs for 10 machines with 39 buses using fast output
sampling feedback via reduced order model is proposed.
The nonlinear model of multimachine system is linearized
at a particular operating point and a linear model is
obtained. Using model reduction technique, lower order
model is obtained from the higher order model and for
this reduced model a stabilizing state feedback gain is
obtained. Using aggregation technique, state feedback gain
is obtained for the higher order model. A decentralized
fast output sampling feedback gain which realizes this
state feedback gain is obtained using LMI approach. This
method does not require state of the system for feedback
and is easily implementable. This decentralized fast output
sampling control via reduced order model is applied to
non-linear plant model of the multimachine. This method
gives very good results for the design of Power System
Stabilizers.
Keywords: Decentralized control, fast output sampling
feedback, multimachine system, nonlinear simulation,
power system stabilizer, reduced order model.
1 INTRODUCTION
Power System Stabilizers are added to excitation
systems to enhance the damping of electric power
system during low frequency oscillations. Several
methods are used for the design of PSSs. Tuning
of supplementary excitation controls for stabilizing
system modes of oscillations has been the subject of
much research during the past 35 years [1]. Two
basic tuning techniques have been successfully utilized
with power system stabilizer applications: Phase
compensation method and the Root locus method.
A commonly used approach is based around the
conventional PSS structure which is composed of
a wash out circuit and a cascade of two-phase
lead networks. A number of PSS input signals,
such as terminal voltage, rotor speed, accelerating
power, electric power etc., and linear combinations
of these have been extensively investigated and
recommendations regarding their use have been
reported in the literature. Phase compensation
consists of adjustment of the stabilizer to compensate
for the phase lags through the generator, excitation
system and power system, such that, the stabilizer
path provides torque changes which are in phase
with the speed changes [2] - [4]. This is the
most straightforward approach, easily understood and
implemented in the field and is most widely used.
The design of such PSSs requires the determination(or
tuning) of few parameters for each machine viz. the
overall dc gain, the wash out circuit time constant,
and the various constants for the two-lead networks.
A number of sequential and simultaneous approaches
for tuning of these parameters have been reported
in literature[5] - [7]. Although the above approaches
have been used and have produced satisfactory results
regarding the damping of local modes of oscillation,
their outcome may not be considered the best possible.
This is because of the restrictive assumptions made and
the intuitive nature of the design process [8].
Synthesis by root locus involves the shifting of
eigenvalues associated with power system modes
of oscillation, by adjusting the stabilizer pole and
zero locations in the s-plane [9]. This approach
gives an additional insight to the performance, by
working directly with the closed-loop characteristics
of the systems, as opposed to the open loop
nature of the phase compensation technique. But
it is more complicated to apply, particularly in
the field. Moreover, the performance of these
stabilizers considerably degrades with the changes in
p. 1
the operating condition during normal operation. It is
also known that for a multimachine system, eigenvalue
assignment is often too involved and complex for
simultaneous stabilization of multivariable systems
and may not provide satisfactory results for sequential
multivariable systems applied as SISO systems. Not
much attempts have been made for designing the power
system stabilizers for multimachine power system using
multivariable control theory. The complexity stems
from the fact that insufficient degree of freedom is
available to the designer in assigning eigenstructure by
fixed gain output feedback method. Moreover, even
if a sufficient degree is available or a dynamic output
feedback stabilizer is sought, numerical problems often
arise regarding the solution of sets of high dimensional
nonlinear algebraic equations, for which a solution
may or may not exist. It is also well known that,
in application of multivariable Nyquist array methods
to multimachine power system, many difficulties arive
for the attainment of necessary diagonal dominance
condition [10].
Since the eigenvalue assignment and Nyquist array
approaches have proved to be cumbersome, modern
control methods have been used by several researchers
to take advantage of the optimal control techniques.
These methods utilize a state space representation
of power system model and calculate a gain matrix
which when applied as a state feedback control will
minimize a prescribed objective function. Successful
application of the optimal control to power system
stabilizers requires that the constraints imposed by
power system nonlinearities be used effectively and
that a limited number of feedback signals be included
[11]. As a result, reports have appeared in the
literature concerning the application of LQR theory
for the design of power system stabilizers(PSSs). First
LQR theory was applied to single machine infinite
bus(SMIB) system. Later, this was extended to
multimachine case. It is quite easy to realize that
neither of these approaches can be successful while
dealing with real-life power systems which, in general,
may have thousands of state variables [12]- [13]. The
reason is that all the states may not be available for
measurement or may be difficult to measure. In this
case, the optimal control law requires to design the
state observer. This increases the implementation cost
and reduces the reliability of control system. Another
disadvantage of the observer based control system is
that, even slight variations of the model parameters
from their nominal values may result into significant
degradation of the closed loop performance. Hence,
it is desirable to go for an output feedback design
method.
In recent years there have been several attempts at
designing power system stabilizer using H∞ based
robust control techniques [14]- [15]. In this approach,
the uncertainty in the chosen system is modeled in
terms of bounds on frequency response. A H∞ optimal
controller is then synthesized which guarantees robust
stability of the closed loop system. Other performance
specifications such as disturbance attenuation criteria
are also imposed on the system. However, it should
be noted that the main objective of using a PSS is
to provide a good transient behaviour. Guaranteed
robust stability of the closed loop, though necessary, is
not adequate as a specification in this application. In
addition to this, the problem of the poorly damped
pole-zero cancellations and the choice of weighting
functions used in design, limit the usefulness of this
technique for PSS design. H∞ design, being essentially
a frequency domain technique does not provide much
control over transient behavior and closed loop pole
location. It would be more desirable to have a robust
stabilizer which, in addition guarantees an acceptable
level of small signal transient performance. Moreover,
this will lead to dynamic output feedback, which may
be feasible but leads to a higher order feedback system
[16].
The static output feedback problem is one of the
most investigated problems in control theory. The
complete pole assignment and guaranteed closed loop
stability is still not obtained by using static output
feedback [17]. Another approach to pole placement
problem is to consider the potential of time-varying
fast output sampling feedback. With Fast output
sampling approach proposed by Werner and Furuta
[18], it is generically possible to simultaneously realize
a given state feedback gain for a family of linear,
observable models. This approach requires to increase
the low rank of the measurement matrix of an
associated discretized system, which can be achieved
by sampling the output several times during one input
sampling interval, and constructing the control signal
from these output samples. Such a control law can
stabilize a much larger class of systems than the static
output feedback [19]-[22]. In fast output sampling
feedback technique gain matrix is generally full [20].
This results in the control input of each machine being
a function of outputs of all machines. Centralized fast
output sampling feedback PSSs require transmission of
signal among the generating units. This requirement
in itself no longer constitutes a problem from practical
and technical view points. This is due to the
rapid advancement in optical fiber communication
and their adoption by power utilities. However, if a
completely decentralized PSS can be found so that
no significant deterioration in the system performance
is experienced compared to state and centralized fast
output sampling feedback based schemes, then such
a scheme would be more advantageous, in terms of
practicability and reliability. In such schemes not
only is the cost implementation drastically reduced
but also the risk of loss of stability due to signal
transmission failure is minimized[23]. Also due to
p. 2
the geographically distributed nature of power system,
the decentralized control scheme may be more feasible
than the centralized control scheme. In decentralized
power system stabilizer, the control input for each
machine should be function of the output of that
machine only. This can be achieved by designing a
decentralized PSS using fast output sampling feedback
technique in which the gain matrix should have all
off-diagonal terms zero or very small compare to
diagonal terms. In decentralized PSS, to activate
the proposed controller at the same instant, proper
synchronization signal is required to be sent to all
machines. Thus, the decentralized stabilizer design
problem can be translated into a problem of diagonal
gain matrix design for multi machine power system[24].
For a large power system, the order of the state matrix
may be quite large. It would be difficult to work with
these complex systems in their original form [25]. In
particular to compute the state feedback gain needed
to obtain the decentralized fast output sampling
feedback based power system stabilizer becomes very
tedious for a large power system. One of the ways
to overcome this difficulty is to develop a reduced
order model for a large power system. Then a state
feedback gain can be computed from the reduced
model of the power system and using aggregation
techniques, a state feedback gain can be obtained for
the higher order (actual) model. This paper proposes
the design of a power system stabilizer for multi
machine system using fast output sampling feedback
via reduced order model. A brief outline of the paper
is as follows: Section 2 presents basics of power system
stabilizer whereas Section 3 contains the modeling of
multi machine system. Section 4 presents a brief
review on decentralized fast output sampling feedback
control method. Section 5 contains the simulations of
multi machine at different operating points with the
proposed controller followed by the concluding section.
2 Power System Stabilizers
Implementation of a power system stabilizer implies
adjustment of its frequency characteristic and gain to
produce the desired damping of the system oscillations
in the frequency range of 0.2 to 3.0 Hz. The transfer
function of a generic power system stabilizer may be
expressed as
PSS = Ks
Tws (1 + sT1) (1+sT3)
(1 + Tws) (1+sT2) (1+sT4)
(1)
where Ks represents stabilizer gain and the stabilizer
frequency characteristic is adjusted by varying the time
constant Tw, T1,T2,T3 and T4.
A power system stabilizer can be made more effective
if it is designed and applied with the knowledge
of associated power characteristics. Power system
stabilizer must provide adequate damping for the
range of frequencies of the power system oscillation
modes. To begin with, simple analytical models, such
as that of a single machine connected to an infinite
bus, can be useful in determining the frequencies
of local mode oscillations. Power system stabilizer
should also be designed to provide stable operation
for the weak power system conditions and associated
loading. Designed stabilizer must ensure for the
robust performance and satisfactory operation with an
external system reactance ranging from 20% to 80% on
the unit rating [26].