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A New Decentralized Stabilization Approach with Application to Power System Stabilizer Design
Copyright © IFAC Large Scale Systems, London, UK, 1995
A NEW DECENTRALIZED STABILIZATION APPROACH WITH APPLICATION TO POWER SYSTEM STABILIZER DESIGN T. C. YANG· ·School of Engineering, Univer!itll of Suuex, Brighton , UK, BN! 9QT
Abstract , Power system stabilizer design for multi-machine power systems is studied in this paper. The difficulties of applying some existing design methods to stabilizers for day to day commercial operation are first discussed from the practical application point of view . Then, it is shown that whereas the design problem can be conveniently formulated as a large-scale system decentralized stabilization problem , it can also be translated into an equivalent one of feedback controller design for a multi-input multi-output system . The frequency response based sequential loop closure method is suggested for the design and it is applied to a model of 10 machine 54-th order power system . The results from computer analysis and simulation and the nature of the proposed method have showed that , the new design method may have some advantages in avoiding the difficulties discussed . Key Words. Large scale systems, Decentralized control, Stabilizing controllers, Power system stabilizers , Frequency response methods.
1. INTRODUCTION
the best possible damping effect . The allocation problem has been studied extensively in the literature, for example (Yang et al. , 1987) , and will not be addressed here. The focus of this paper is placed on stabilizer design when the PSS allocation has already been decided .
One of the stability problems in electrical power system operations is the steady-state stability, or in control terminology, the small-signal stability around a system operating point . Oscillations of small magnitude and low frequency, linked with the electromechanical modes in power systems , often persist for long periods of time and in some cases presented limitations on the power transfer capability. Power System Stabilizer (PSS) units have long been regarded as an effective way to enhance the damping of ElectroMechanical Oscillations (EMO) in power systems (Larsen and Swann , 1981) . One of the three signals: machine shaft speed , AC bus frequency or accelerating power can be used as the input to a conventional PSS . Of these , the most commonly used is machine shaft speed . The output of the PSS , as a supplementary control signal , is applied to the machine voltage regulator terminal.
Since the pioneering work of deMello and Con cordia in 1969 , control engineers, as well as power system engineers, have showed great interest and made significant contributions in PSS design and application . Most methods developed for multima.chine systems are based on well-developed modern control theory. However, the conventional design method is still important for the understanding of some useful concepts and the physical mechanism behind the theory. These concepts are used as the guidance for the PSS on-line tuning and are also used in this paper to decide the design details within the frame of frequency response based sequential loop closure approach . The transfer function for a conventional speedinput PSS has the basic form :
The earliest designs of PSSs were based on a single-machine infinite-bus representation of the power system . The concept of synchronising and damping torques in such a single-machine moJe! provided some very useful insights for stabilizer design . In the last decade , much attention has been paid on stabilizer design for multi-machine power systems . It is known that for such a system , it is neither necessary nor economical to equip every single machine with a PSS . This introduces the problem of PSS allocation in order to achieve
where K .• is the PSS gain ; Tw is the time constant for the wash-out stage which is to prevent steadystate voltage shift ; T 1 , T 2 , T3 and T4 are time constants for two phase-lead stages . There are some variations on (1) if the other two signals are employed as the PSS inputs . In most occasions , 173
a low-pass filter is also required to be added to the stabilizer to filter out noise and to prevent the excitation of other undesirable oscillations.
trol where the plant model is constantly identified and updated. However , the convergence of the identification is difficult to guarantee . Furthermore , since inclusion of a self-tuning controller produces an additional non-linear system , it is also difficult to prove stability, in particular , when some practical digital controller implementation issues are also taken into account .
State space models are commonly used for the analytical study of multi-machine power systems. The design of each individual stabilizer in a multimachine system must be coordinated due to the interactions between machines and controllers. The minimum requirement for the PSS design is that , when the open-loop system is closed by the stabilizers , the damping of the EMO modes concerned should be improved to a satisfactory degree and all system eigenvalues should have negative real parts. This still presents a challenge since the order of the system is high and information exchange between local plants (machines) is not allowed . Nevertheless, many design methods based on different approaches have been developed . These include: eigenvalue (pole) assignment (Zhou et al. , 1992) , optimal control (Vournas and Papadias, 1987), self tuning control (Wu and Hogg , 1990) , rule-based control (Hiyama, 1990) , etc. Results from computer simulations , laboratories and field tests have demonstrated the potential of these methods for practical applications . However, most methods , especially those methods leading to a controller structure different from the form of (1) , have not yet been widely adopted by utilities in their day to day commercial operation. This, from author 's point of view , is due to the following factors :
(d) to accommodate other power system engineering considerations ; A power system is a very complicated plant to operate . Whereas PSSs are mainly included to improve damping of EMO modes , their possible side effects on other system dynamics should also be considered . For example , the effect of PSS on the system transient stability and the possibility of other oscillations caused by stabilizers, etc. It is generally believed that , people have gained enough knowledge and experience on this aspect only for stabilizers in the form of equation (1) or its variations. (e) sequential commissioning of stabilizers ; It is logical and is also happened in practice that all stabilizers are not put into operation simultaneously but one by one. Therefore , the design should guarantee that the system is at least stable at each commissioning stage. In this paper, it is shown that , the design of PSS for mult.i-machine power systems can be translated into an equivalent one of feedback controller design for a multi-input multi-output system. The well-developed multi-variable frequency response approaches therefore can be applied to this problem . However, apart from some papers on applying them to the study of different control loops within a generating set (Anderson , 1987 ; Hamdan and Hughes, 1977) , there seems no publication on applying these approaches to the PSS design for multi-machine systems . The sequential loop closure method with a conventional PSS structure of equation (1) is suggested in this paper , among other considerations , for the practical application issues summarised above. In addition , since this design method naturally includes the dynamics of the interactions in the each design stage , it can be equally applied to both weak-linked systems and strong-linked systems , whereas some other design methods may have difficulties with strong-linked systems .
(a) on-line tuning; This is particularly important for practical applications since there are always modelling and other errors and one can not expect that controllers can be successfully put into operation for a complicated system without any final on-line tuning. If a design is based on a controller structure of equation (1) , then it will be possible to use the concept of synchronous and damping torques for the on-line parameter tuning; otherwise, as has happened in state-feedback based design , it is very difficult , if not impossible, to use such important concepts for the tuning . (b) robustness ; Although stabilizers are normally designed for the particular operating condition where they are most needed , they should also work satisfactorily under other operating conditions. The design method should also be insensitive to inaccurate data and un modelled system dynamics . It is difficult for eigenvalue based design approaches , perhaps also for some other approaches , to meet this requirement since eigenvalues are often quite sensitive to parameter disturbances .
The new design method is presented in the next section and the results on a test system are given in Section 3. In this paper , the design method is presented for the speed-input stabilizer only. However , the concepts and the procedures can also be applied if one of the other two signals , frequency or power , is used as the input .
(c) long term reliability; Theoretically, the above robustness issue can be solved by self-tuning con-
174
(1) The washout stage time constant Tw can be chosen , for example between 5 and 12, so that the frequency response of the washout stage can be considered as unity around the range of troublesome EMO frequencies (typically between 0.2Hz and 2Hz).
(b) The robustness of the design is achieved by providing a sufficient phase margin and gain margin in each design stage . This gives the restrictions on the value of K • . With the help of the concepts and the methods given in the literature, all PSS parameters can be finally tuned during commissioning.
(2) For the phase lead stages , an alternative representation is:
aTs+ 1 Ts+ 1
(a> 1)
(6)
3. APPLIED TO A TEST SYSTEM
It is well known that the maximum phase lead
a-I
a+l
A 10 machine 39 bus and 46 line power system (Figure 2) is used in this paper as a test system . This test system was developed as a representative of the power system in the Northeastern United States and is also called the NEW ENGLAND system. The detailed data can be found , for example in (Pai, 1989). This system has been used for the study of power system stabilities in a number of publications. These include dynamic equivalents for transient stability (Demello et al. , 1974) direct analysis of transient stability (Athay et al. , 1979), energy function analysis for power system stability (Pai, 1989), steady-state stability analysis (Verghese et al. , 1982) , power system stabilizer design (Lim and Elangovan, 1985) , and power system voltage stability (Gebreselassie and Chow, 1994) . In this system, Machine 10 can be considered as a reference machine (Busbar 39 considered as an infinity bus) and its dynamics are not required in the modelling. The dynamics of each of the other 9 machines can be modelled by 6 state variables for the study of PSS design . Therefore , the model established is a large scale system with 9 subsystems and 54 state variables (Yang, 1987).
(7)
at a frequency of
1
vaT
(8)
Since the function of the phase lead stages in the PSS is to compensate the phase lag caused by Generator, Exciter and Power system , the linearised transfer function of which is noted as GEP(s) in the literature, an a value of between 5 and 12 can be chosen as required and experience shows that to achieve a good stabilizing effect:
(9) where Wo is the frequency (in rad./sec.) of the EMO mode whose damping is to be improved by the stabilizer and {3 is a factor with a value of between 0.8 and 1.0. Once a and {3 have been chosen, the time constants for the phase lead stages can be calculated using the above equations. The above method of choosing the time constants for the phase lead stages is based on the assumption that , with suitable values of a and {3, the phase angle of P(jw o) = PSS(jwo)GEP(jw o) is a small negative value. This means that , at the EMO frequency, the electrical torque contributed by the PSS is mainly a positive damping torque plus a small positive synchronous torque as required . However, since it is difficult to obtain a linearised transfer function GEP(s) for multimachine systems, some trial and error may be required to obtain suitable values of a and {3. (3 ) The gain K. is selected in such a way that it is as big as practically possible subject to a stable system with a sufficient phase margin and gain margin . These margins can be obtained from the frequency response plot of PSSi(jW)qi(jW) (i = 1, 2, .. . I) . The selection of K. is based on following considerations :
Fig. 2. 10 Machine 39 Busbar test system
The system operating condition given in (Pai , 1989) with a load-flow result was considered as the "worst situation" for the steady-state stability. A 54-state small signal model based on this operating condition can be formed and is considered as a nominal model in this paper . Eigenstructure anal-
(a) If the time constants in the phase lead stages are correct , a large K. increases the magnitude of the useful torques contributed by the stabilizer. 176
when a small step disturbance of 0.05pu (per unit) is applied to the m-th machine voltage regulator terminal , for the system without PSS and with the four PSS on are given in Figure 5 as a full-line curve and a dotted-line curve, respectively. x 10'"
links with reported field trials. IEEE Trans. , PWRS-2, 189-196 . Athay, T.R., R. Podmore and S. Virmani (1979). A practical method for direct analysis of transient stability. IEEE Trans. , PAS-98, 573-584 . deMello , F .P. and C.Concordia (1969) . Concepts of synchronous machine stability as affected by excitation control. IEEE Trans. , PAS-88, 316325. Demello, R.W. , R. Podmore and K.N. Stanton (1974) . Coherency based dynamic equivalents for transient stability studies . Final report on EPRI project RP904-II . Gebreselassie , A. and J .H. Chow (1994) . Investigation of the effects of load models and generator voltage regulators on voltage stability. Int. J. Electrical Power and Energy Systems , 16 , 83-90 . Hamdan , A.M.A. and F .M. Hughes (1977) . Analysis and design of power system stabilisers . Int. J. Contr. , 26 , 769-782. Hiyama, T. (1990) . Rule-based stabilizer for multi-machine power system . IEEE Trans ., PS-5,403-41l. Larsen , E.V. and D.A . Swann (1981) . Applying power system stabilizers (three parts). IEEE Trans ., PAS-lOO, 3017-3046. Lim , C.M. and S. Elangovan (1985) . Design of stabilisers in multimachine power systems . lEE Proceedings, Part C, 132, 146-153. Pai , M.A. (1989) . Energy function analysis for power system stability Kluwer Academic Publishers. Verghese, G .C., I.J. Perez-Arriaga and F .C . Schweppe (1982) . Selective modal analysis with application to electric power systems (two parts) . IEEE Trans. , PAS-lOl , 3117-3134. Vournas, C.D. and B.C. Papadias (1987). Power system stabilization via parameter optimization - Application to the hellenic interconnected system . IEEE Trans. , PWRS-2, 615623 . WU. H.Q. and B.W . Hogg (1990) . Self tuning control for turbogeherat ors in multi-machine power systems. lEE Proceedings, Part C, 137 , 146-158 . Yang , T .C., N. Munro and A. Brameller (1987) . A new decentralised stabilisation method with application to power system stabiliser design for multimachime systems. Int. J. Electrical Power and Energy Systems , 9 , 206-216 . Yang, T .C. (1987). Power system stabilizer design PhD Thesis , UMIST , UK . Zhou , E.Z., O.P. Malik and G.S . Hope (1992) . Design of stabilizer for a multimachine power system based on the sensitivity of PSS effect . IEEE Trans. , EC-7, 606-613 .
Machine 3
ir--------,
X
ID.,)
Machine 4
2r--------,
Synem without PSS: _
; Systan with PSS on: . ••
Fig. 5. Machine speed deviation time responses in Per Unit This example also shows that if the state space model of the system is not available, some online frequency response identification method may be used to obtain qi(jW) required for the design. Therefore the design method proposed here , like many other frequency response based methods , can also be applied to applications where analytical models are difficult to obtain .
4. CONCLUSIONS A new power system stabilizer design method for multi-machine power systems is presented and applied to a model of a practical power system . Although the test system used is a small-median size one with weak interactions, judging from the nature of the design method and also taking into account today 's existing technology and experience, one could say that the suggested method and the stabilizers designed may have advantages in some practical application aspects discussed in the introduction , i.e. ease of on-line tuning , robustness , long term reliability and being able to accommodate other power system engineering considerations and to meet the sequential commiSSIOnIng requirement .
5. REFERENCES Anderson , J.H . (1987). A comparison of multivariable time and frequency domain design methods for power system stabilizers including 178
A NEW DECENTRALIZED STABILIZATION APPROACH WITH APPLICATION TO POWER SYSTEM STABILIZER DESIGN T. C. YANG· ·School of Engineering, Univer!itll of Suuex, Brighton , UK, BN! 9QT
Abstract , Power system stabilizer design for multi-machine power systems is studied in this paper. The difficulties of applying some existing design methods to stabilizers for day to day commercial operation are first discussed from the practical application point of view . Then, it is shown that whereas the design problem can be conveniently formulated as a large-scale system decentralized stabilization problem , it can also be translated into an equivalent one of feedback controller design for a multi-input multi-output system . The frequency response based sequential loop closure method is suggested for the design and it is applied to a model of 10 machine 54-th order power system . The results from computer analysis and simulation and the nature of the proposed method have showed that , the new design method may have some advantages in avoiding the difficulties discussed . Key Words. Large scale systems, Decentralized control, Stabilizing controllers, Power system stabilizers , Frequency response methods.
1. INTRODUCTION
the best possible damping effect . The allocation problem has been studied extensively in the literature, for example (Yang et al. , 1987) , and will not be addressed here. The focus of this paper is placed on stabilizer design when the PSS allocation has already been decided .
One of the stability problems in electrical power system operations is the steady-state stability, or in control terminology, the small-signal stability around a system operating point . Oscillations of small magnitude and low frequency, linked with the electromechanical modes in power systems , often persist for long periods of time and in some cases presented limitations on the power transfer capability. Power System Stabilizer (PSS) units have long been regarded as an effective way to enhance the damping of ElectroMechanical Oscillations (EMO) in power systems (Larsen and Swann , 1981) . One of the three signals: machine shaft speed , AC bus frequency or accelerating power can be used as the input to a conventional PSS . Of these , the most commonly used is machine shaft speed . The output of the PSS , as a supplementary control signal , is applied to the machine voltage regulator terminal.
Since the pioneering work of deMello and Con cordia in 1969 , control engineers, as well as power system engineers, have showed great interest and made significant contributions in PSS design and application . Most methods developed for multima.chine systems are based on well-developed modern control theory. However, the conventional design method is still important for the understanding of some useful concepts and the physical mechanism behind the theory. These concepts are used as the guidance for the PSS on-line tuning and are also used in this paper to decide the design details within the frame of frequency response based sequential loop closure approach . The transfer function for a conventional speedinput PSS has the basic form :
The earliest designs of PSSs were based on a single-machine infinite-bus representation of the power system . The concept of synchronising and damping torques in such a single-machine moJe! provided some very useful insights for stabilizer design . In the last decade , much attention has been paid on stabilizer design for multi-machine power systems . It is known that for such a system , it is neither necessary nor economical to equip every single machine with a PSS . This introduces the problem of PSS allocation in order to achieve
where K .• is the PSS gain ; Tw is the time constant for the wash-out stage which is to prevent steadystate voltage shift ; T 1 , T 2 , T3 and T4 are time constants for two phase-lead stages . There are some variations on (1) if the other two signals are employed as the PSS inputs . In most occasions , 173
a low-pass filter is also required to be added to the stabilizer to filter out noise and to prevent the excitation of other undesirable oscillations.
trol where the plant model is constantly identified and updated. However , the convergence of the identification is difficult to guarantee . Furthermore , since inclusion of a self-tuning controller produces an additional non-linear system , it is also difficult to prove stability, in particular , when some practical digital controller implementation issues are also taken into account .
State space models are commonly used for the analytical study of multi-machine power systems. The design of each individual stabilizer in a multimachine system must be coordinated due to the interactions between machines and controllers. The minimum requirement for the PSS design is that , when the open-loop system is closed by the stabilizers , the damping of the EMO modes concerned should be improved to a satisfactory degree and all system eigenvalues should have negative real parts. This still presents a challenge since the order of the system is high and information exchange between local plants (machines) is not allowed . Nevertheless, many design methods based on different approaches have been developed . These include: eigenvalue (pole) assignment (Zhou et al. , 1992) , optimal control (Vournas and Papadias, 1987), self tuning control (Wu and Hogg , 1990) , rule-based control (Hiyama, 1990) , etc. Results from computer simulations , laboratories and field tests have demonstrated the potential of these methods for practical applications . However, most methods , especially those methods leading to a controller structure different from the form of (1) , have not yet been widely adopted by utilities in their day to day commercial operation. This, from author 's point of view , is due to the following factors :
(d) to accommodate other power system engineering considerations ; A power system is a very complicated plant to operate . Whereas PSSs are mainly included to improve damping of EMO modes , their possible side effects on other system dynamics should also be considered . For example , the effect of PSS on the system transient stability and the possibility of other oscillations caused by stabilizers, etc. It is generally believed that , people have gained enough knowledge and experience on this aspect only for stabilizers in the form of equation (1) or its variations. (e) sequential commissioning of stabilizers ; It is logical and is also happened in practice that all stabilizers are not put into operation simultaneously but one by one. Therefore , the design should guarantee that the system is at least stable at each commissioning stage. In this paper, it is shown that , the design of PSS for mult.i-machine power systems can be translated into an equivalent one of feedback controller design for a multi-input multi-output system. The well-developed multi-variable frequency response approaches therefore can be applied to this problem . However, apart from some papers on applying them to the study of different control loops within a generating set (Anderson , 1987 ; Hamdan and Hughes, 1977) , there seems no publication on applying these approaches to the PSS design for multi-machine systems . The sequential loop closure method with a conventional PSS structure of equation (1) is suggested in this paper , among other considerations , for the practical application issues summarised above. In addition , since this design method naturally includes the dynamics of the interactions in the each design stage , it can be equally applied to both weak-linked systems and strong-linked systems , whereas some other design methods may have difficulties with strong-linked systems .
(a) on-line tuning; This is particularly important for practical applications since there are always modelling and other errors and one can not expect that controllers can be successfully put into operation for a complicated system without any final on-line tuning. If a design is based on a controller structure of equation (1) , then it will be possible to use the concept of synchronous and damping torques for the on-line parameter tuning; otherwise, as has happened in state-feedback based design , it is very difficult , if not impossible, to use such important concepts for the tuning . (b) robustness ; Although stabilizers are normally designed for the particular operating condition where they are most needed , they should also work satisfactorily under other operating conditions. The design method should also be insensitive to inaccurate data and un modelled system dynamics . It is difficult for eigenvalue based design approaches , perhaps also for some other approaches , to meet this requirement since eigenvalues are often quite sensitive to parameter disturbances .
The new design method is presented in the next section and the results on a test system are given in Section 3. In this paper , the design method is presented for the speed-input stabilizer only. However , the concepts and the procedures can also be applied if one of the other two signals , frequency or power , is used as the input .
(c) long term reliability; Theoretically, the above robustness issue can be solved by self-tuning con-
174
(1) The washout stage time constant Tw can be chosen , for example between 5 and 12, so that the frequency response of the washout stage can be considered as unity around the range of troublesome EMO frequencies (typically between 0.2Hz and 2Hz).
(b) The robustness of the design is achieved by providing a sufficient phase margin and gain margin in each design stage . This gives the restrictions on the value of K • . With the help of the concepts and the methods given in the literature, all PSS parameters can be finally tuned during commissioning.
(2) For the phase lead stages , an alternative representation is:
aTs+ 1 Ts+ 1
(a> 1)
(6)
3. APPLIED TO A TEST SYSTEM
It is well known that the maximum phase lead
a-I
a+l
A 10 machine 39 bus and 46 line power system (Figure 2) is used in this paper as a test system . This test system was developed as a representative of the power system in the Northeastern United States and is also called the NEW ENGLAND system. The detailed data can be found , for example in (Pai, 1989). This system has been used for the study of power system stabilities in a number of publications. These include dynamic equivalents for transient stability (Demello et al. , 1974) direct analysis of transient stability (Athay et al. , 1979), energy function analysis for power system stability (Pai, 1989), steady-state stability analysis (Verghese et al. , 1982) , power system stabilizer design (Lim and Elangovan, 1985) , and power system voltage stability (Gebreselassie and Chow, 1994) . In this system, Machine 10 can be considered as a reference machine (Busbar 39 considered as an infinity bus) and its dynamics are not required in the modelling. The dynamics of each of the other 9 machines can be modelled by 6 state variables for the study of PSS design . Therefore , the model established is a large scale system with 9 subsystems and 54 state variables (Yang, 1987).
(7)
at a frequency of
1
vaT
(8)
Since the function of the phase lead stages in the PSS is to compensate the phase lag caused by Generator, Exciter and Power system , the linearised transfer function of which is noted as GEP(s) in the literature, an a value of between 5 and 12 can be chosen as required and experience shows that to achieve a good stabilizing effect:
(9) where Wo is the frequency (in rad./sec.) of the EMO mode whose damping is to be improved by the stabilizer and {3 is a factor with a value of between 0.8 and 1.0. Once a and {3 have been chosen, the time constants for the phase lead stages can be calculated using the above equations. The above method of choosing the time constants for the phase lead stages is based on the assumption that , with suitable values of a and {3, the phase angle of P(jw o) = PSS(jwo)GEP(jw o) is a small negative value. This means that , at the EMO frequency, the electrical torque contributed by the PSS is mainly a positive damping torque plus a small positive synchronous torque as required . However, since it is difficult to obtain a linearised transfer function GEP(s) for multimachine systems, some trial and error may be required to obtain suitable values of a and {3. (3 ) The gain K. is selected in such a way that it is as big as practically possible subject to a stable system with a sufficient phase margin and gain margin . These margins can be obtained from the frequency response plot of PSSi(jW)qi(jW) (i = 1, 2, .. . I) . The selection of K. is based on following considerations :
Fig. 2. 10 Machine 39 Busbar test system
The system operating condition given in (Pai , 1989) with a load-flow result was considered as the "worst situation" for the steady-state stability. A 54-state small signal model based on this operating condition can be formed and is considered as a nominal model in this paper . Eigenstructure anal-
(a) If the time constants in the phase lead stages are correct , a large K. increases the magnitude of the useful torques contributed by the stabilizer. 176
when a small step disturbance of 0.05pu (per unit) is applied to the m-th machine voltage regulator terminal , for the system without PSS and with the four PSS on are given in Figure 5 as a full-line curve and a dotted-line curve, respectively. x 10'"
links with reported field trials. IEEE Trans. , PWRS-2, 189-196 . Athay, T.R., R. Podmore and S. Virmani (1979). A practical method for direct analysis of transient stability. IEEE Trans. , PAS-98, 573-584 . deMello , F .P. and C.Concordia (1969) . Concepts of synchronous machine stability as affected by excitation control. IEEE Trans. , PAS-88, 316325. Demello, R.W. , R. Podmore and K.N. Stanton (1974) . Coherency based dynamic equivalents for transient stability studies . Final report on EPRI project RP904-II . Gebreselassie , A. and J .H. Chow (1994) . Investigation of the effects of load models and generator voltage regulators on voltage stability. Int. J. Electrical Power and Energy Systems , 16 , 83-90 . Hamdan , A.M.A. and F .M. Hughes (1977) . Analysis and design of power system stabilisers . Int. J. Contr. , 26 , 769-782. Hiyama, T. (1990) . Rule-based stabilizer for multi-machine power system . IEEE Trans ., PS-5,403-41l. Larsen , E.V. and D.A . Swann (1981) . Applying power system stabilizers (three parts). IEEE Trans ., PAS-lOO, 3017-3046. Lim , C.M. and S. Elangovan (1985) . Design of stabilisers in multimachine power systems . lEE Proceedings, Part C, 132, 146-153. Pai , M.A. (1989) . Energy function analysis for power system stability Kluwer Academic Publishers. Verghese, G .C., I.J. Perez-Arriaga and F .C . Schweppe (1982) . Selective modal analysis with application to electric power systems (two parts) . IEEE Trans. , PAS-lOl , 3117-3134. Vournas, C.D. and B.C. Papadias (1987). Power system stabilization via parameter optimization - Application to the hellenic interconnected system . IEEE Trans. , PWRS-2, 615623 . WU. H.Q. and B.W . Hogg (1990) . Self tuning control for turbogeherat ors in multi-machine power systems. lEE Proceedings, Part C, 137 , 146-158 . Yang , T .C., N. Munro and A. Brameller (1987) . A new decentralised stabilisation method with application to power system stabiliser design for multimachime systems. Int. J. Electrical Power and Energy Systems , 9 , 206-216 . Yang, T .C. (1987). Power system stabilizer design PhD Thesis , UMIST , UK . Zhou , E.Z., O.P. Malik and G.S . Hope (1992) . Design of stabilizer for a multimachine power system based on the sensitivity of PSS effect . IEEE Trans. , EC-7, 606-613 .
Machine 3
ir--------,
X
ID.,)
Machine 4
2r--------,
Synem without PSS: _
; Systan with PSS on: . ••
Fig. 5. Machine speed deviation time responses in Per Unit This example also shows that if the state space model of the system is not available, some online frequency response identification method may be used to obtain qi(jW) required for the design. Therefore the design method proposed here , like many other frequency response based methods , can also be applied to applications where analytical models are difficult to obtain .
4. CONCLUSIONS A new power system stabilizer design method for multi-machine power systems is presented and applied to a model of a practical power system . Although the test system used is a small-median size one with weak interactions, judging from the nature of the design method and also taking into account today 's existing technology and experience, one could say that the suggested method and the stabilizers designed may have advantages in some practical application aspects discussed in the introduction , i.e. ease of on-line tuning , robustness , long term reliability and being able to accommodate other power system engineering considerations and to meet the sequential commiSSIOnIng requirement .
5. REFERENCES Anderson , J.H . (1987). A comparison of multivariable time and frequency domain design methods for power system stabilizers including 178