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International Journal of Trend in Scientific Research and Development (IJTSRD)
Volume 6 Issue 1, November-December 2021 Available Online: www.ijtsrd.com e-ISSN: 2456 – 6470
@ IJTSRD | Unique Paper ID – IJTSRD47776 | Volume – 6 | Issue – 1 | Nov-Dec 2021 Page 96
Development of Power System Stabilizer
Using Modern Optimization Approach
Mr. Qamar ul Zaman1
, Mr. Deepak Joshi2
, Mr. Yuvraj Ranawat2
1
M Tech Scholar, 2
Assistant Professor,
1,2
Department of Electrical Engineering, Mewar University, Rajasthan, India
ABSTRACT
The utilization of energy has increased manifold because of the
industrial revolution. The development of the induction motor by
Nikola Tesla in 1888 triggered the increasing demand of electrical
energy in the industrial world and also its usage for artificial lighting.
Higher amount of energy required for present society is provided by
means of electrical energy.
Highly complicated power systems have been constructed to deal
with the increasing demand. The development in electric power
production is focused on the interconnecting the transmission lines,
generators and loads into huge integrated systems, which helps in
providing reliable and quality power system to the consumers.
Power system stability is an idea that focuses on the way the system
adjusts with the occurrence of disorder. These disorders can result
because of switching-off a load or a modification in the mechanical
input to the system. Because of these disturbances oscillations may
happen in the system that could ultimately build up to a larger extent,
resulting in the synchronous generators to go out of step and lose
synchronism.
Due to the importance of the power system and its stability, there are
several techniques developed by various researchers for the
stabilization of the power systems. The paper addresses enhanced
Artificial Bee Colony (ABC) technique applied to design a robust
power system stabilizer (PSS) in order to improve transient and
dynamic stabilities of a turbo-alternator connected to an infinite bus
system comparisons wind, thermal and solar power generations the
design of the proposed controller initially is formulated as an
optimization problem and then enhanced ABC is employed for
obtaining optimal controller parameters. The results shows that the
proposed algorithm are better in performance than the conventional
methods.
KEYWORDS: Transmission lines, ABC (Artificial Bee Colony), power
system stabilizer (PSS), optimal controller, system stabilizer
How to cite this paper: Mr. Qamar ul
Zaman | Mr. Deepak Joshi | Mr. Yuvraj
Ranawat "Development of Power
System Stabilizer Using Modern
Optimization Approach" Published in
International Journal
of Trend in Scientific
Research and
Development (ijtsrd),
ISSN: 2456-6470,
Volume-6 | Issue-1,
December 2021,
pp.96-99, URL:
www.ijtsrd.com/papers/ijtsrd47776.pdf
Copyright © 2021 by author(s) and
International Journal of Trend in
Scientific Research and Development
Journal. This is an
Open Access article
distributed under the
terms of the Creative Commons
Attribution License (CC BY 4.0)
(http://creativecommons.org/licenses/by/4.0)
I. INTRODUCTION
The consumption of energy has increased extensively
due to the industrial revolution. The development of
the induction motor by Nikola Tesla in 1888
stimulated the improving demand of electrical energy
in the industrial world and also its usage for artificial
lighting. Higher amount of energy need for present
society is provided by electrical energy. A highly
complicated power system has been constructed to
deal with the increasing demand. The electric power
production development is mainly focused on the
interconnected transmission line network linking
generators and loads into huge integrated systems
which helps in better supply of power and a few of
which have the link of the entire continent. This huge
venture of providing electrical energy suffers various
engineering difficulties that pose the engineer with a
IJTSRD47776
International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470
@ IJTSRD | Unique Paper ID – IJTSRD47776 | Volume – 6 | Issue – 1 | Nov-Dec 2021 Page 97
range of challenges. The systems that are developed
according to this are highly complicated in their
planning, construction, and operation. These various
difficulties motivate the engineer's managerial
abilities their knowledge in designing a better system.
The complete design should be based on automatic
control without requiring any time consuming input
from the system operators. Power system’s
flourishing function is highly based on the engineer's
capability to afford continuous and dependable
service to the loads. The consistency of the supply
power refers greatly more than simply being
available. Preferably, the loads should be provided
with constant frequency and voltage every time.
Practically, this represents that both frequency and
voltage should be maintained within close tolerances
therefore the consumer's system may function
adequately. Consider an illustration that a voltage
drop of 10-15% or a reduction of the frequency of the
system by just a hertz may result in halting of the
motor loads on the system. Therefore it will be
perfectly indicated that the power system stabilization
should be maintained with higher standard for
uninterrupted power supply.
Stability of the Power system is an idea that focuses
on the way the system adjusts with the occurrence of
disorder. These disorders are the resulting of
switching-off a load or a modification in the
mechanical input to the system. Because of these
changes in the system, oscillations happen in the
system that could ultimately build up and bigger to
result in the synchronous generators to lose
synchronism and go out of step.
Because of using fast static excitation system, while
offering a gain in stability limits, can also cause poor
system damping in case of some loading conditions.
Methods of Power System Stabilization have been
suggested for a long period to enhance the power
system damping. Conventionally, lead-lag networks
have been used as power system stabilizers. Much has
been used on the manner to adjust the factors of the
lead lag controller. These controllers in the past have
been adjusted for both single and multiple operating
points of power system. The techniques used for
adjusting range from pole placement, to recent one
using the heuristic optimization technique for Particle
Swarm Optimization (PSO) has been proposed by
Mozafari et al, (2005).
One of the major problems in power system operation
is related to small signal instability caused by
insufficient damping in the system. The most
effective way of countering this instability is to use
auxiliary controllers called power system stabilizers,
to produce additional damping in the system.
The highly complicated, dynamic activities and
nonlinearity of power systems, along with their
approximately continuously time variant nature, have
led to a great challenge to power system control
engineers for several years. A critical factor stumble
upon the generating plant level is to maintain
synchronism or stability of synchronous generators
when exposed to rigorous variations at different
operating situations. An inexpensive and successful
ways to increase the power system stabilization is the
most important consideration in the present situation.
II. LITERATURE REVIEW:
When a disturbance takes place, introduced voltage
from the phase shifter is given to damping control of
generator swing. Consequently, this controller is
expected to enhance steady-state stability. This
apparatus is also estimated to be a potential fault
current limiter by utilizing the leakage reactance of a
series transformer. An uncomplicated and novel
control approach for damping electromechanical
oscillations through control of power converter firing
angles α1 and α2 of SMES unit was proposed by
(Rabbani et al, 1999). Both active and reactive power
modulations are exploited under uneven -mode of
operation. The option of uneven mode is discussed in
detail by this author. The gains of this SMES
controller are given once offline based on the power
system and the rating of the SMES unit. This control
Algorithm is uncomplicated and its realization will
necessitate very little hardware.
Katsuya et al, (2000) presented a technique to
stabilize a power system with elongated distance
mass power transmission from a remote huge power
plant through a synchronous condenser with rapid
excitation control. Excitation controls of a generator
have accomplished enormous success as a PSS.
Synchronous condensers have been implemented in
great numbers to power systems for the purpose of
controlling the system voltage and reactive power
with elevated consistency. In this technique the
synchronous condenser with a devised excitation
control has been implemented for the stabilization of
a generator power swing by establishing the
synchronous condenser at a bus in the transmission
line near the generator. A design based on the
damping and synchronizing torques was developed by
this author. The application of H-infinity control is
also taken into account to build up a robust control
system.
A control scheme of the Static Synchronous Series
Compensator (SSSC) for fault current limiting and
power system stabilization has been proposed by
(Duangkamol et al, 2000). The apparatus introduces a
voltage of variable magnitude in sequence with a
International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470
@ IJTSRD | Unique Paper ID – IJTSRD47776 | Volume – 6 | Issue – 1 | Nov-Dec 2021 Page 98
transmission line. This introduced voltage is in
quadrature with the line current. In normal condition,
it is controlled with the aim of compensating for
reactance of the transmission line.
When SSV of the augmented closed-loop system is
less than one, then the proposed approach is said to
achieve the robust performance. D-K iteration (open
and closed loop interconnected structure) technique is
used to provide solution to this problem, which gives
a lower and upper bound of synthesis.
Simulation results illustrated that the proposed
approach attains a better robust performance over a
wide range of operating conditions as compared to the
conventional power system stabilizers and H-infinity
control (achieving robust performance or
stabilization) power system stabilizer by (Soliman et
al, 2000). The electric energy of Plug-in Hybrid
Electric Vehicle (PHEV) is charged mainly during
night time when the electricity price is low.
Therefore, (Takagi et al, 2009) proposed a charging
power control of PHEVs to compensate the Load
Frequency Control (LFC) capacity in the night time.
The author proposes a control technique based on
Area Control Error (ACE) and frequency
characteristic of PHEV
III. MODELLING OF WIND POWER
SYSTEM WITH PSS
Power System experience low-frequency oscillations
due to disturbances. The oscillations may maintain
and grow to cause system separation if adequate
damping is not available. To increase system
damping, the generators are equipped with power
system stabilizers (PSSs) that provide supplementary
feedback stabilizing signals in the excitation systems.
In this work, a single synchronous generator
connected through a parallel transmission line to a
very huge network approximated by an infinite bus
(SMIB). The Power System Stabilizer (PSS) is an
additional excitation controller utilized to damp
generator, electro-mechanical oscillations is produced
in order to stabilize the grid and to protect the shaft
line.
In the proposed method, the H robust technique
named as Enhanced Artificial Bee Colony (EABC) is
implemented in order to improve the stability and the
damping performances in the exciter part of the
synchronous generator of wind turbine.
Fig 1:- 1 Block diagram of the modern SMIB
power system
The developed simulink model of the power system is
shown in the following figure Fig.2
Fig.2: Simulation Model of Power System
IV. Results & Analysis
Simulation results are carried out with EABC using
developed Simulink model and the responses are
recorded in the figure 3.3 active power, terminal
voltage, stator angle voltage, speed deviation. For the
comparative analysis, the same procedure is
performance measures such as damping coefficients,
static error, settling time and peak time are calculated
In this PSS design, an important subject is to evaluate
the designed PSS under power system condition
changing. The robustness of PSS should be evaluated
in various loading conditions and system operating
conditions.
The variation of operating conditions related to the
variation of transmission line parameters and the
active and reactive powers. Certain attention was
dedicated to the problem of the reactive power
consumption, which is very important for all electric
power systems and generating stations.
International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470
@ IJTSRD | Unique Paper ID – IJTSRD47776 | Volume – 6 | Issue – 1 | Nov-Dec 2021 Page 99
V. CONCLUSION
A standard technique for automated designing a
power system stabilizer using enhanced Artificial Bee
Colony Optimization technique applied on the AVR-
PSS system of a turbo alternator to increase transient
stability and its robustness for a single machine
infinite bus system. Three cases were considered,
control with conventional PSS, PSS with H∞
technique and using a robust PSS based on enhanced
ABC optimization. The method presented in this
work illustrate that the efficiency, performance,
reliability and robustness of the power system has
been increased.
VI. References
[1] J. Abonyi and R. Babuska. ˇ Local and global
identification and interpretation of parameters
in Takagi–Sugeno fuzzy models. In
Proceedings IEEE International Conference on
Fuzzy Systems, San Antonio, USA, May 2000.
[2] J. Abonyi and F. Szeifert J. A. Roubos, M.
Oosterom. Compact ts-fuzzy models through
clustering and OLS plus FIS model reduction.
In Proc. of IEEE international conference on
fuzzy systems, Sydney, Australia, 2001.
[3] J. Abonyi and F. Szeifert. Modified Gath-Geva
fuzzy clustering for identification of Takagi-
Sugeno fuzzy models. IEEE Transactions on
Systems, Man and Cybernetics, Part B., in
print, 2002.
[4] R. Babuska. ˇ Fuzzy Modeling for Control.
Kluwer Academic Publishers, Boston, 1998.
[5] R. Babuska, ˇ J. A. Roubos, and H. B.
Verbruggen. Identification of MIMO systems
by input–output TS fuzzy models. In
Proceedings FUZZ–IEEE’98, pages 657–662,
Anchorage, USA, 1998.
[6] R. Babuska ˇ and H. B. Verbruggen.
Constructing fuzzy models by product space
clustering. In H. Hellendoorn and D. Driankov,
editors, Fuzzy Model Identification: Selected
Approaches, pages 53–90. Springer, Berlin,
Germany, 1997.
[7] R. Babuska ˇ and H. B. Verbruggen. Fuzzy set
methods for local modeling and identification.
In R. Murray-Smith and T. A. Johansen,
editors, Multiple Model Approaches to
Nonlinear Modeling and Control, pages 75–
100. Taylor & Francis, London, UK, 1997.
[8] A. M. Bensaid, L. O. Hall, J. C. Bezdek, L. P.
Clarke, M. L. Silbiger, J. A. Arrington, and R.
F. Murtagh. Validity-guided (Re)Clustering
with applications to imige segmentation. IEEE
Transactions on Fuzzy Systems, 4:112–123,
1996.
[9] J. D. Bomberger and D. E. Seborg.
Determination of model order for NARX
models directly from input–output data.
Journal of Process Control, 8:459–468, Oct–
Dec 1998

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Development of Power System Stabilizer Using Modern Optimization Approach

  • 1. International Journal of Trend in Scientific Research and Development (IJTSRD) Volume 6 Issue 1, November-December 2021 Available Online: www.ijtsrd.com e-ISSN: 2456 – 6470 @ IJTSRD | Unique Paper ID – IJTSRD47776 | Volume – 6 | Issue – 1 | Nov-Dec 2021 Page 96 Development of Power System Stabilizer Using Modern Optimization Approach Mr. Qamar ul Zaman1 , Mr. Deepak Joshi2 , Mr. Yuvraj Ranawat2 1 M Tech Scholar, 2 Assistant Professor, 1,2 Department of Electrical Engineering, Mewar University, Rajasthan, India ABSTRACT The utilization of energy has increased manifold because of the industrial revolution. The development of the induction motor by Nikola Tesla in 1888 triggered the increasing demand of electrical energy in the industrial world and also its usage for artificial lighting. Higher amount of energy required for present society is provided by means of electrical energy. Highly complicated power systems have been constructed to deal with the increasing demand. The development in electric power production is focused on the interconnecting the transmission lines, generators and loads into huge integrated systems, which helps in providing reliable and quality power system to the consumers. Power system stability is an idea that focuses on the way the system adjusts with the occurrence of disorder. These disorders can result because of switching-off a load or a modification in the mechanical input to the system. Because of these disturbances oscillations may happen in the system that could ultimately build up to a larger extent, resulting in the synchronous generators to go out of step and lose synchronism. Due to the importance of the power system and its stability, there are several techniques developed by various researchers for the stabilization of the power systems. The paper addresses enhanced Artificial Bee Colony (ABC) technique applied to design a robust power system stabilizer (PSS) in order to improve transient and dynamic stabilities of a turbo-alternator connected to an infinite bus system comparisons wind, thermal and solar power generations the design of the proposed controller initially is formulated as an optimization problem and then enhanced ABC is employed for obtaining optimal controller parameters. The results shows that the proposed algorithm are better in performance than the conventional methods. KEYWORDS: Transmission lines, ABC (Artificial Bee Colony), power system stabilizer (PSS), optimal controller, system stabilizer How to cite this paper: Mr. Qamar ul Zaman | Mr. Deepak Joshi | Mr. Yuvraj Ranawat "Development of Power System Stabilizer Using Modern Optimization Approach" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-6 | Issue-1, December 2021, pp.96-99, URL: www.ijtsrd.com/papers/ijtsrd47776.pdf Copyright © 2021 by author(s) and International Journal of Trend in Scientific Research and Development Journal. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) (http://creativecommons.org/licenses/by/4.0) I. INTRODUCTION The consumption of energy has increased extensively due to the industrial revolution. The development of the induction motor by Nikola Tesla in 1888 stimulated the improving demand of electrical energy in the industrial world and also its usage for artificial lighting. Higher amount of energy need for present society is provided by electrical energy. A highly complicated power system has been constructed to deal with the increasing demand. The electric power production development is mainly focused on the interconnected transmission line network linking generators and loads into huge integrated systems which helps in better supply of power and a few of which have the link of the entire continent. This huge venture of providing electrical energy suffers various engineering difficulties that pose the engineer with a IJTSRD47776
  • 2. International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470 @ IJTSRD | Unique Paper ID – IJTSRD47776 | Volume – 6 | Issue – 1 | Nov-Dec 2021 Page 97 range of challenges. The systems that are developed according to this are highly complicated in their planning, construction, and operation. These various difficulties motivate the engineer's managerial abilities their knowledge in designing a better system. The complete design should be based on automatic control without requiring any time consuming input from the system operators. Power system’s flourishing function is highly based on the engineer's capability to afford continuous and dependable service to the loads. The consistency of the supply power refers greatly more than simply being available. Preferably, the loads should be provided with constant frequency and voltage every time. Practically, this represents that both frequency and voltage should be maintained within close tolerances therefore the consumer's system may function adequately. Consider an illustration that a voltage drop of 10-15% or a reduction of the frequency of the system by just a hertz may result in halting of the motor loads on the system. Therefore it will be perfectly indicated that the power system stabilization should be maintained with higher standard for uninterrupted power supply. Stability of the Power system is an idea that focuses on the way the system adjusts with the occurrence of disorder. These disorders are the resulting of switching-off a load or a modification in the mechanical input to the system. Because of these changes in the system, oscillations happen in the system that could ultimately build up and bigger to result in the synchronous generators to lose synchronism and go out of step. Because of using fast static excitation system, while offering a gain in stability limits, can also cause poor system damping in case of some loading conditions. Methods of Power System Stabilization have been suggested for a long period to enhance the power system damping. Conventionally, lead-lag networks have been used as power system stabilizers. Much has been used on the manner to adjust the factors of the lead lag controller. These controllers in the past have been adjusted for both single and multiple operating points of power system. The techniques used for adjusting range from pole placement, to recent one using the heuristic optimization technique for Particle Swarm Optimization (PSO) has been proposed by Mozafari et al, (2005). One of the major problems in power system operation is related to small signal instability caused by insufficient damping in the system. The most effective way of countering this instability is to use auxiliary controllers called power system stabilizers, to produce additional damping in the system. The highly complicated, dynamic activities and nonlinearity of power systems, along with their approximately continuously time variant nature, have led to a great challenge to power system control engineers for several years. A critical factor stumble upon the generating plant level is to maintain synchronism or stability of synchronous generators when exposed to rigorous variations at different operating situations. An inexpensive and successful ways to increase the power system stabilization is the most important consideration in the present situation. II. LITERATURE REVIEW: When a disturbance takes place, introduced voltage from the phase shifter is given to damping control of generator swing. Consequently, this controller is expected to enhance steady-state stability. This apparatus is also estimated to be a potential fault current limiter by utilizing the leakage reactance of a series transformer. An uncomplicated and novel control approach for damping electromechanical oscillations through control of power converter firing angles α1 and α2 of SMES unit was proposed by (Rabbani et al, 1999). Both active and reactive power modulations are exploited under uneven -mode of operation. The option of uneven mode is discussed in detail by this author. The gains of this SMES controller are given once offline based on the power system and the rating of the SMES unit. This control Algorithm is uncomplicated and its realization will necessitate very little hardware. Katsuya et al, (2000) presented a technique to stabilize a power system with elongated distance mass power transmission from a remote huge power plant through a synchronous condenser with rapid excitation control. Excitation controls of a generator have accomplished enormous success as a PSS. Synchronous condensers have been implemented in great numbers to power systems for the purpose of controlling the system voltage and reactive power with elevated consistency. In this technique the synchronous condenser with a devised excitation control has been implemented for the stabilization of a generator power swing by establishing the synchronous condenser at a bus in the transmission line near the generator. A design based on the damping and synchronizing torques was developed by this author. The application of H-infinity control is also taken into account to build up a robust control system. A control scheme of the Static Synchronous Series Compensator (SSSC) for fault current limiting and power system stabilization has been proposed by (Duangkamol et al, 2000). The apparatus introduces a voltage of variable magnitude in sequence with a
  • 3. International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470 @ IJTSRD | Unique Paper ID – IJTSRD47776 | Volume – 6 | Issue – 1 | Nov-Dec 2021 Page 98 transmission line. This introduced voltage is in quadrature with the line current. In normal condition, it is controlled with the aim of compensating for reactance of the transmission line. When SSV of the augmented closed-loop system is less than one, then the proposed approach is said to achieve the robust performance. D-K iteration (open and closed loop interconnected structure) technique is used to provide solution to this problem, which gives a lower and upper bound of synthesis. Simulation results illustrated that the proposed approach attains a better robust performance over a wide range of operating conditions as compared to the conventional power system stabilizers and H-infinity control (achieving robust performance or stabilization) power system stabilizer by (Soliman et al, 2000). The electric energy of Plug-in Hybrid Electric Vehicle (PHEV) is charged mainly during night time when the electricity price is low. Therefore, (Takagi et al, 2009) proposed a charging power control of PHEVs to compensate the Load Frequency Control (LFC) capacity in the night time. The author proposes a control technique based on Area Control Error (ACE) and frequency characteristic of PHEV III. MODELLING OF WIND POWER SYSTEM WITH PSS Power System experience low-frequency oscillations due to disturbances. The oscillations may maintain and grow to cause system separation if adequate damping is not available. To increase system damping, the generators are equipped with power system stabilizers (PSSs) that provide supplementary feedback stabilizing signals in the excitation systems. In this work, a single synchronous generator connected through a parallel transmission line to a very huge network approximated by an infinite bus (SMIB). The Power System Stabilizer (PSS) is an additional excitation controller utilized to damp generator, electro-mechanical oscillations is produced in order to stabilize the grid and to protect the shaft line. In the proposed method, the H robust technique named as Enhanced Artificial Bee Colony (EABC) is implemented in order to improve the stability and the damping performances in the exciter part of the synchronous generator of wind turbine. Fig 1:- 1 Block diagram of the modern SMIB power system The developed simulink model of the power system is shown in the following figure Fig.2 Fig.2: Simulation Model of Power System IV. Results & Analysis Simulation results are carried out with EABC using developed Simulink model and the responses are recorded in the figure 3.3 active power, terminal voltage, stator angle voltage, speed deviation. For the comparative analysis, the same procedure is performance measures such as damping coefficients, static error, settling time and peak time are calculated In this PSS design, an important subject is to evaluate the designed PSS under power system condition changing. The robustness of PSS should be evaluated in various loading conditions and system operating conditions. The variation of operating conditions related to the variation of transmission line parameters and the active and reactive powers. Certain attention was dedicated to the problem of the reactive power consumption, which is very important for all electric power systems and generating stations.
  • 4. International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470 @ IJTSRD | Unique Paper ID – IJTSRD47776 | Volume – 6 | Issue – 1 | Nov-Dec 2021 Page 99 V. CONCLUSION A standard technique for automated designing a power system stabilizer using enhanced Artificial Bee Colony Optimization technique applied on the AVR- PSS system of a turbo alternator to increase transient stability and its robustness for a single machine infinite bus system. Three cases were considered, control with conventional PSS, PSS with H∞ technique and using a robust PSS based on enhanced ABC optimization. The method presented in this work illustrate that the efficiency, performance, reliability and robustness of the power system has been increased. VI. References [1] J. Abonyi and R. Babuska. ˇ Local and global identification and interpretation of parameters in Takagi–Sugeno fuzzy models. In Proceedings IEEE International Conference on Fuzzy Systems, San Antonio, USA, May 2000. [2] J. Abonyi and F. Szeifert J. A. Roubos, M. Oosterom. Compact ts-fuzzy models through clustering and OLS plus FIS model reduction. In Proc. of IEEE international conference on fuzzy systems, Sydney, Australia, 2001. [3] J. Abonyi and F. Szeifert. Modified Gath-Geva fuzzy clustering for identification of Takagi- Sugeno fuzzy models. IEEE Transactions on Systems, Man and Cybernetics, Part B., in print, 2002. [4] R. Babuska. ˇ Fuzzy Modeling for Control. Kluwer Academic Publishers, Boston, 1998. [5] R. Babuska, ˇ J. A. Roubos, and H. B. Verbruggen. Identification of MIMO systems by input–output TS fuzzy models. In Proceedings FUZZ–IEEE’98, pages 657–662, Anchorage, USA, 1998. [6] R. Babuska ˇ and H. B. Verbruggen. Constructing fuzzy models by product space clustering. In H. Hellendoorn and D. Driankov, editors, Fuzzy Model Identification: Selected Approaches, pages 53–90. Springer, Berlin, Germany, 1997. [7] R. Babuska ˇ and H. B. Verbruggen. Fuzzy set methods for local modeling and identification. In R. Murray-Smith and T. A. Johansen, editors, Multiple Model Approaches to Nonlinear Modeling and Control, pages 75– 100. Taylor & Francis, London, UK, 1997. [8] A. M. Bensaid, L. O. Hall, J. C. Bezdek, L. P. Clarke, M. L. Silbiger, J. A. Arrington, and R. F. Murtagh. Validity-guided (Re)Clustering with applications to imige segmentation. IEEE Transactions on Fuzzy Systems, 4:112–123, 1996. [9] J. D. Bomberger and D. E. Seborg. Determination of model order for NARX models directly from input–output data. Journal of Process Control, 8:459–468, Oct– Dec 1998