Transactions Template JOURNAL OF ENGINEERING RESEARCH AND TECHNOLOGY, VOLUME 1, ISSUE 2, JUNE 2014 66 A robust PSS Based Advanced H2 Frequency Control to Improve Power System Stability – Implementation under GUI/MATLAB GHOURAF Djamel Eddine1 and NACERI Abdellatif1 1Department of Electrical Engineering University of SBA, IRECOM Laboratory BP 98 22000 Algeria E-mail: jamelbel22@yahoo.fr Abstract— This article present a comparative study between two control strategies, a classical PID regulator, and a robust H2 controller based on LQG control with KALMAN filter applied on automatic excitation control of powerful synchronous generators, to improve transient stability and its robustness of a single machine- infinite bus system (SMIB). The computer simulation results have proved the efficiency and robustness of the robust H2 approach, in comparison with using classical regulator PID, showing stable system responses almost insensitive to large parameter variations. This robust control possesses the capability to improve its performance over time by interaction with its environment. The results proved also that good performance and more robustness in face of uncertainties (test of robustness) with the linear robust H2 controller (optimal LQG controller with Kalman Filter) in comparison with using the classical regulator PID. Our present study was performed using a GUI realized under MATLAB in our work. Index Terms— powerful synchronous generators and Excitations, AVR and PSS, LQG control , Kalman filter, stability and robustness. I INTRODUCTION Power system stability continues to be the subject of great interest for utility engineers and consumers alike and remains one of the most challenging problems facing the power community. Power system oscillations are damped by the introduction of a supplementary signal to the excitation system of a power system. This is done through a regulator called power system stabilizer. Classical PSS rely on math- ematical models that evolve quasi-continuously as load conditions vary. Conventional PSS based on simple design principles such as PI control and eigenvalue assignment techniques have been widely used in power systems [1, 2]. Such PSS ensure optimal performance only at their nominal operating point and do not guarantee good performance over the entire oper- ating range of the power system. This is due to external disturbances such as changes in loading conditions and fluc- tuations in the mechanical power. In practical power systems networks, a priori information on these external disturbances is always in the form of certain frequency band in which their energy is concentrated. Remarkable efforts have been devoted to design appro- priate PSS with improved performance and robustness. These have led to a variety of design methods using optimal and output feedback methods [3, 5]. The shortcoming of these model-based control strategies is that uncertainties cannot be considered explicitly in the design stage. The stabilizer of this new generation for the system AVR – PSS, aimed-at improving power system stability, was developed using the robust controller H2 based on LQG. This has been advantage of maintaining constant terminal voltage and frequency irrespective of conditions variations in the system study. The H2 control design problem is de- scribed and formulated in standard form with emphasis on the selection of the weighting function that reflects robust- ness and performances goals [6]. The proposed system has the advantages of robustness against model uncertainty and external disturbances (electrical and mechanical), fast re- sponse and the ability to reject noise. Simulation results shown the evaluation of the proposed linear control methods based on this advanced frequency techniques applied in the automatic excitation regulator of powerful synchronous generators: the robust H2 linear stabi- lizer and conventional PID control schemes against system variation in the SMIB power system, with a test of robust- ness against parametric uncertainties of the synchronous machines (electric and mechanic), and make a comparative study between these two control techniques for AVR – PSS systems. II DYNAMIC POWER SYSTEM MODEL A Power System Description In this paper the dynamic model of an IEEE - standard of power system, namely, a single machine connected to an infinite bus system (SMIB) was considered [4]. It consists of a single synchronous generator (turbo-Alternator) connected through a parallel transmission line to a very large network approximated by an infinite bus as shown in figure 1. mailto:jamelbel22@yahoo.fr A robust PSS Based Advanced H2 Frequency Control to Improve Power System Stability – Implementation under GUI/MATLAB, GHOURAF Djamel Eddine and NACERI Abdellatif (2014) 67 '' q E '' d X d I q U Figure 1 Standard system IEEE type SMIB with excitation control of powerful synchronous generators B The Park-Gariov modeling of powerful synchronous generators This paper is based on the Park-Gariov modeling of powerful synchronous generators for eliminating simplifying hypotheses and testing the control algorithm. The PSG mod- el is defined by equations (1to 5) and Figures 2 and 3 below [4]: Vf I1d Vd Vq I1q ‘’q’’ Xq X1q Xf X1d Xd ‘’d’’ I2q X2q Figure 2. PARK Transformation of the synchronous machine '' d E '' q X q I d U Figure 3. Equivalent diagrams simplifies of the synchronous machine with damping circuits (PARK-GARIOV model)  Currants equations: sradffsrdaddd qsraqqqqddd qsraqqqdqqq XIXI XIXEUI XIXEUI /)( /)( /)( /)( /)( /)( 11 222 '''' 111 ''''    sfdsfad fq ad fd sfd q ad f sf q XXX E X X X E X X X E 111 .1.1 '' ''    sfqad fd aq fq sfq d XX E X X X E 11 .1 ' ''    Flow equations   dsdqad IXXE  '''' ;   qsqdaq IXXE  ''''  dtIR q qqsq . 1 0 111      dtIR q qqsq . 2 0 222      dtUIR f fffsf    0 0   dtIR d ddsd . 1 0 111      Mechanical equations   , s s s sdtd                dt d jMMavecMMM jjejT  inertied'moment 0 :   eTjTdaqqadj MMs dt d TMIIs dt d T -ou ..  T s e M P dt d j    C Models of regulators AVR and PSS: The AVR (Automatic Voltage Regulator), is a controller of the PSG voltage that acts to control this voltage, thought the exciter .Furthermore, the PSS was developed to absorb the generator output voltage oscillations [1]. In our study the synchronous machine is equipped by a voltage regulator model "IEEE" type – 5 [7, 8], as is shown in Figure 4. Vref  pT pK A A 1 + - VT VE VR Efdmax Efdmin Efd Figure 4. A simplified” IEEE type-5” AVR FrefE A REA R VVV T VVK V    , In the PSS, considerable’s efforts were expended for the development of the system. The main function of a PSS is to modulate the SG excitation to [1, 2, and 4]. Figure 5. A functional diagram of the PSS used [8] In this paper the PSS signal used, is given by: [9] SEE AVR SE GS Xe T Δfu fu’ If’ ΔP  P Δu u’ Uref P S S (1) (2) (4) (3) (5) (6) PSS K W W pT pT 1 2 1 1 1 pT pT   V1 V2 V3 VPSSmax VPSS- max VPSS Δ input A robust PSS Based Advanced H2 Frequency Control to Improve Power System Stability – Implementation under GUI/MATLAB, GHOURAF Djamel Eddine and NACERI Abdellatif (2014) 68 inputKVV T V V V T T T VV V V T T T VV V PSS W        . . 1 . 1 3 . 3 . 2 2 3 2 23 . 2 . 2 1 2 1 12 . 1 ; ; ; D Simplified model of system studied SMIB We consider the system of Figure 6. The synchronous machine is connected by a transmission line to infinite bus type SMIB. With: Re: A resistance and Le: an inductance of the transmission line [4]. Va Re V∞ Le Figure 6. Synchronous machine connected to an infinite bus net- work We define the following equation of SMIB system                                 i iXILSinVPvV d qeodqeabcodq 0 ' cos 0 2   THE III ROBUST H2-PSS DESIGN BASED ON LQG CONTROL AND KALMAN FILTER The control system design method by means of modern FSM algorithms is supposed to have some linear test regula- tor. It is possible to collect various optimal adjustment of such a regulator in different operating conditions into some database. Linear – Quadratic – Gaussian (LQG) control technique is equivalent to the robust H2 regulator by mini- mizing the quadratic norm of the integral of quality [13]. In this work, the robust quadratic H2 controller (corrector LQG) was used as a test system, which enables to trade off regulation performance and control effort and to take into account process and measurement noise [11,5]. LQG design requires a state-space model of the plant:        DuCxy BuAx dt dx Where x, u, y is the vectors of state variables, control in- puts and measurements, respectively. Figure 7. Optimal LQG regulated system with Kalman filter. The goal is to regulate the output y around zero. The plant is driven by the process noise w and the controls u, and the regulator relies on the noisy measurements yv = y+v to generate these controls. The plant state and measurement equations are of the form: Both w and v are modeled as white noise. In LQG control, the regulation performance is meas- ured by a quadratic performance criterion of the form: The weighting matrices Q, N and R are user specified and define the trade-off between regulation performance and control effort. The LQ-optimal state feedback u=–kx is not implement- ed without full state measurement. However, a state esti- mate x̂ can b e d er ived such that u = −kx̂ remains optimal for the output-feedback problem. This state estimate is generated by the Kalman filter: Thus, the LQG regulator consists of an optimal state- feedback gain and a Kalman state estimator (filter), as shown in figure 7. On the basis of investigation carried out, the main points of fuzzy PSS automated design method were formu- lated [6]. The nonlinear model of power system can be represented by the set of different linearized model shown in equations (7). For such model, the linear compensator in the form of u = –Kx can be calculated by means of LQG method. The family of test regulators is transformed into united fuzzy knowledge base with the help of hybrid learn- ing procedure (based variable structure sliding mode). In order to solve the main problem of the rule base design, which is called “the curse of dimensionality”, and decrease the rule base size, the scatter partition method [13] is used. In this case, every rule from the knowledge base is associated with some optimal gain set. The ad- vantage of this method is practically unlimited expansion of rule base. It can be probably needed for some new oper- ating conditions, which are not provided during learning process. Finally, the robust H2 stabilizer was obtained by minimizing the quadratic norm 2 2 M of the integral of quality J(u) in (11), where   ., )()( 2/12/1 0 jsRuQxZandxsMsZ TT  [6]. A Structure of the power System with Robust H2 Con troller The basic structure of the control system of a powerful synchronous generator with the robust controller is shown in Figure 8.                         UUU and III and or pP input fff fff mach 0 0 0 ,  (7) (8) Kalman Filter LQG regulator (9)      )()()()( )()()()()()( twtxtCty tvtutBtxtAtx v  dtNuxRuuQxxuJ TTT    0 )2()( )ˆ(ˆ ˆ DuxCyLBuxA dt xd v  (13) (12) (10) (11) A robust PSS Based Advanced H2 Frequency Control to Improve Power System Stability – Implementation under GUI/MATLAB, GHOURAF Djamel Eddine and NACERI Abdellatif (2014) 69 g1 g le glissment erreur % delta delta Ug la tension Ug To Workspace y TBB 720 TBB 720 TBB 500 TBB 500 TBB 200 TBB 200 TBB 1000 TBB 1000 Step Réseau Pe PEM Cliques deux fois ci-dessous pour visualiser les courbes et les parametres déssirées Math Function 1 u MS Goto 9 [delta ] Goto 8 [eif ] Goto 7 [If ] Goto 6 [Iq ] Goto 5 [Ud ] Goto 4 [Ug ] Goto 3 [Id ] Goto 2 [Uq ] Goto 13 [eug ] Goto 12 [Wr] Goto 11 [Pe ] Goto 10 [g ] Goto 1 [DUf ] Gain 1 100 From 9 [G1000 ] From 8 [G500 ] From 7 [Id ] From 6 [G200 ] From 5 [delta ] From 4 [Pe] From 3 [Ug ] From 20 [Ug ] From 2 [delta ] From 19 [eug ] From 18 [DUf] From 17 [g] From 16 [If ] From 15 [Ud ] From 14 [Uq ] From 13 [Iq ] From 12 [eif ] From 11 [delta ] From 10 [G720 ] From 1 [Ug ] Dot Product Constant 5 Ug Constant 4 If Constant 3 Ug Clock1 AVR-FA 0 2 4 6 8 0.94 0.96 0.98 1 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 1 2 3 4 5 6 7 8 0.94 0.96 0.98 1 1.02 50 100 150 200 250 300 20 40 60 80 100 20406080100120 20 40 60 80 100 120 20 40 60 80100 20 40 60 80 100 120 0 2 4 6 8 0.995 1 1.005 0 2 4 6 8 0.96 0.98 1 1.02 Figure 10.The realised GUI / MATLAB As command object, we have synchronous generator with regulator AVR-FA (PID with conventional PSS), an excita- tion system (exciter), an information block and measures (BIM) of output parameters to regulated. Figure 8. Structure of the power system withe robust H2 controller [3] IV THE SIMULATION RESULT UNDER GUI/ MATLAB A Creation of a calculating code under MATLAB / SIMULINK The “SMIB” system used in our study includes:  A powerful synchronous generator (PSG) ;  Two voltage regulators: AVR and AVR-PSS con- nected to;  A Power Infinite network line The SMIB mathematical model based on Park-Gariov model is used for simulation in this paper and is shown in Figure 9. Figure 9. Structure of the synchronous generator (PARK-GARIOV model) with the excitation controller under [10]. B A Created GUI/MATLAB To analyzed and visualized the different dynamic behav- iors, we have created and developed a “GUI” (Graphical User Interfaces) under MATLAB. This GUI allows as to:  Perform control system from PSS controller;  View the system regulation results and simulation;  Calculate the system dynamic parameters;  Test the system stability and robustness;  Study the different operating regime (under- excited, rated and over excited regime). The different operations are performed from GUI that was realized under MATLAB and shown in Figure 10. '' q E '' d X d I q U Régulateur SG AVR+PSS Robust Controller H2 Exciter BIM Uref ∆f, f’, ∆u, u’, ∆if, if’, ∆P I G UG A robust PSS Based Advanced H2 Frequency Control to Improve Power System Stability – Implementation under GUI/MATLAB, GHOURAF Djamel Eddine and NACERI Abdellatif (2014) 70 Damping coefficient α The static error Q OL AVR PSS H2-PSS OL AVR PSS H2-PSS -0.1372 Unstable -0.709 -1.761 -2.673 Unstable 2.640 1.620 negligible -0.4571 Unstable -0.708 -1.731 -2.593 Unstable 2.673 1.629 negligible 0.1896 -0.0813 -0.791 -1.855 -2.766 5.038 2.269 1.487 negligible 0.3908 -0.1271 -0.634 -1.759 -2.695 5.202 1.807 1.235 negligible 0.5078 -0.1451 -0.403 -1.470 -2.116 3.777 0.933 0.687 negligible 0.6356 -0.1588 -0.396 -1.442 -2.099 3.597 0.900 0.656 negligible The setting time for 5% The maximum overshoot % Q OL AVR PSS H2-PSS OL AVR PSS H2-PSS -0.1372 Unstable 4,231 1,704 rapid 9.572 9,053 7,892 3.682 -0.4571 Unstable 4,237 1,713 rapid 9.487 9,036 7,847 3.482 0.1896 - 3,793 1,617 rapid 10,959 9,447 8,314 3.915 0.3908 - 4,732 1,706 rapid 10,564 8,778 7,883 3.737 0.5078 14,320 7,444 2,041 rapid 9,402 6,851 6,588 2.290 0.6356 14,423 7,576 2,080 rapide 9,335 6,732 6,463 2,012 0 1 2 3 4 5 6 7 8 0.94 0.95 0.96 0.97 0.98 0.99 1 1.01 Ug le temps en sec U g BO PSS-H2 PSS 0 1 2 3 4 5 6 7 8 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 Pem le temps en sec P e m BO PSS-H2 PSS 0 1 2 3 4 5 6 7 8 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 Delta le temps en sec D e lt a BO PSS-H2 PSS 0 1 2 3 4 5 6 7 8 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 x 10 -3 la courbe de glissment le temps en sec g BO PSS-H2 PSS 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 1.28 1.3 1.32 1.34 1.36 1.38 1.4 1.42 1.44 1.46 Delta le temps en sec D e lt a BO PSS-H2 PSS 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0.98 0.985 0.99 0.995 1 1.005 1.01 1.015 Ug le temps en sec U g BO PSS-H2 PSS 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 x 10 -3 la courbe de glissment le temps en sec g BO PSS-H2 PSS 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 Pem le temps en sec P e m BO PSS-H2 PSS 0 1 2 3 4 5 6 7 8 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 x 10 -3 la courbe de glissment le temps en sec g BO PSS-H2 PSS 0 1 2 3 4 5 6 7 8 0.92 0.925 0.93 0.935 0.94 0.945 0.95 0.955 0.96 0.965 Ug le temps en sec U g BO PSS-H2 PSS 0 1 2 3 4 5 6 7 8 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 Delta le temps en sec D e lt a BO PSS-H2 PSS 0 1 2 3 4 5 6 7 8 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 Pem le temps en sec P e m BO PSS-H2 PSS C Simulation result and discussion  Study of the stability We performed perturbations by abrupt variations of tur- bine torque ΔTm of 15% at t = 0.2s, The following results (Table 1 and Figure 11, 12) were obtained by studying the “SMIB” static and dynamic per- formances in the following cases: 1. SMIB in open loop (without regulation) (OL) 2. Closed Loop System with the conventional stabilizer PSS-FA and robust control H2-PSS [10]. We simulated three operations: the under-excited, the rated and the over-excited. Our study is interested in the synchronous power genera- tors of type: TBB-200, TBB-500 BBC-720, TBB-1000 (pa- rameters in Appendix 1) [10]. Table 1 presents the BBC -720 static and dynamic per- formances results in (OL) and (CL) with PSS and H2-PSS, for an average line (Xe = 0.3 pu), and an active power P=0.85 p.u , for more details about the calculating parame- ters see GUI-MATLAB in Appendix 3. Where: α: Damping coefficient ε %: the static error, d%: the maximum overshoot, ts: the setting time Table 1 The “SMIB “static and dynamic performances Figures 11,12 and 13 show simulation results for : 's' var- iable speed , 'delta' the internal angle, 'Pe' the electromagnet- ic power system, 'Ug' the stator terminal voltage; for power- ful synchronous generators BBC -720 with P = 0.85, Xe = 0.3, Q1 = -0.1372 (pu)  Tests of robustness In a first step we performed variations of the electrical parametric (increase 100% of R). Then, we performed varia- tions of the mechanical parametric (lower bound 50% of inertia J) The simulation time is 8 seconds. We present in Figure 12 (electrical uncertainties) and Figure 13 mechanical uncertainties) Figure 11. functioning system in the under-excited used of BBC 720 connected to a average line with PSS , H2-PSS and OL (Study of the stability) Figure 12.functioning system in the under-excited used of BBC 720 connected to a average line with PSS , H2-PSS and OL (Tests of robustness) A robust PSS Based Advanced H2 Frequency Control to Improve Power System Stability – Implementation under GUI/MATLAB, GHOURAF Djamel Eddine and NACERI Abdellatif (2014) 71 Figure 13. functioning system in the under-excited used of BBC 720 connected to a average line with PSS , H2-PSS and OL (Tests of robustness) The electromechanical damping oscillations of parameters of the synchronous power generators under-excited mode in controllable power system, equipped by H2-PSS (Black), PSS (Blue) and open loop (green) are given in figures 11-13. Results of time domain simulations, with a test of robustness (electrical uncertainties (figure 12) and mechanical uncer- tainties (figure 13)), confirm both a high effectiveness of test robust H2-PSS Regulator in comparison with using the clas- sical regulator PID and open loop. For study of the stability the simulation results (figure 11), it can be observed that the use of H2-PSS improves considerably the dynamic perfor- mances (static errors negligible so better precision, and very short setting time so very fast system (table 1), and we found that after few oscillations, the system returns to its equilibri- um state even in critical situations (specially the under- excited regime) and granted the stability and the robustness of the studied system. V CONCLUSION This paper proposes an advanced control method based on advanced frequency techniques: robust H2 approach’s (an optimal LQG controller with Kalman Filter), applied on the system AVR - PSS of synchronous power generators, to improve transient stability and its robustness of a single machine- infinite bus system (SMIB). This concept allows accurately and reliably carrying out transient stability study of power system and its controllers for voltage and speeding stability analyses. It considerably increases the power transfer level via the improvement of the transient stability limit. The computer simulation results (with test of robustness against electric and mechanic machine parameters uncertain- ty), have proved a high efficiency and more robustness with the Robust H2- PSS, in comparison using a conventional stabilizer (with a strong action) realized on PID schemes, showing stable system responses almost insensitive under different modes of the station. This robust H2 generator volt- age controller has the capability to improve its performance over time by interaction with its environment. As perspective, to study the effectiveness of the robust control H2 realized a comparative study between a robust control H∞ and H2 applied to power system stability REFERENCES [1] LA. GROUZDEV, A.A. STARODEBSEV, S.M. OUSTINOV "Conditions for the application of the best amortization of transient processes in energy systems with numerical optimization of the controller parame- ters AVR-FA" Energy-1990-N ° ll-pp.21-25 (translated from Russian). [2] DEMELLO F.P., FLANNETT L.N. and UNDRILL J.M., « Practical approach to supplementary stabilizing from accelerating power », IEEE Trans., vol. PAS-97, pp, 1515-1522, 1978. [3] DEMELLO F.P. and CONCORDIA C., « Concepts of synchronous machine stability as affected by excitation control », IEEE Trans. on PAS, vol. PAS-88, pp. 316– 329, 1969. [4] S.V. SMOLOVIK « mathematical modeling Method of transient processes synchronous generators most usual and non-traditional in the electro-energy systems "PhD Thesis State, Leningrad Polytechnic Institute, 1988 (translated from Russian). [5] G. STEIN and M. ATHANS “The LQG/LTR procedure for multivariable feedback control design” , IEEE Transaction on Automatic Control, vol. 32, No 2, 1987. [6] NACERI A., “"Study and Application of the ad- vanced methods of the robust H2 and H∞ control theo- ry in the AVR-PSS systems of Synchronous ma- chines’, PhD Thesis, SPBSPU, Saint Petersburg, Rus- sia, 2002 (In Russian). [7] P. KUNDUR, "Definition and Classification of power System Stability", Draft 2, 14 January,2002 [8] P.M. ANDERSON, A. A. FOUAD "Power System con- trol and Stability", IEE Press, 1991. [9] HONG Y.Y. and WU W.C., « A new approach using optimization for tuning parameters of power system sta- bilizers », IEEE Transactions on Energy Conversion, vol. 14, n°. 3, pp. 780–786, Sept. 1999. [10] GHOURAF D.E., “Study and Application of the ad- vanced frequency control techniques in the voltage au- tomatic regulator of Synchronous machines’, Magister Thesis, UDL-SBA, 2010 (In French). [11] KWAKERNAAK H., SIVAN R. Linear Optimal Con- trol Systems, Wiley-Interscience, 1972. [12] G. STEIN and M. ATHANS “The LQG/LTR procedure for multivariable feedback control design” , IEEE Transaction on Automatic Control, vol. 32, No 2, 1987. [13] YURGANOV A.A., SHANBUR I.J. ‘Fuzzy regulator of excitationwith strong action, proceeding of SPbSTU scientific conference“Fundamental Investigation in Technical Universities”, Saint- Petersburg, 1998. (In Russian)Kwakernaak H., Sivan R. Linear Optimal Con- trol Systems, Wiley-Interscience, 1972. GHOURAF Djamel Eddine. Graduated from the Faculty of Elec- trical Engineering, Djillali Liabes University of Sidi Bel-Abbes (UDL-SBA), and Algeria in 2003. He received the B.Sc and M.Sc. degrees from UDL-SBA in 2008 and 2010, respectively. He is now a Ph.D. student in UDL-SBA and member in the IRECOM Labora- tory, Algeria. His research interests include robust and adaptive control of electric power systems and networks, optimization, power system stabilizer (PSS), stability and robustness, modeling and simulation. E-mail: jamelbel22@yahoo.fr (Corresponding author) Abdellatif NACERI. Graduated from the Faculty of Electrical Engineering, Djillali Liabes University of Sidi Bel-Abbes (UDL SBA), and Algeria in 1997. He received the M.Sc. and Ph.D. de- grees from the Saint Petersburg Polytechnic University (SPB- SPU), Russia in 1999 and 2002, respectively. He is currently an mailto:jamelbel22@yahoo.fr A robust PSS Based Advanced H2 Frequency Control to Improve Power System Stability – Implementation under GUI/MATLAB, GHOURAF Djamel Eddine and NACERI Abdellatif (2014) 72 2. The PSS-AVR model associate professor at UDL SBA and researcher at the IRECOM Laboratory, Algeria. His research interests include intelligent con- trol and appl cations, robust and adaptive control of electric power systems and networks, power system stabilizer (PSS) and °exible alternating current transmission system (FACTS), stability and robustness, modelling and simulation. E-mail: abdnaceri@yahoo.fr APPENDIX 1. Parameters of the used Turbo –Alternators 3. Dynamics parameters calculated through GUI-MATLAB Parame- ters TBB 200 TBB 500 BBC 720 TBB 1000 Notations power nominal 200 500 720 1000 MW Factor of power nominal 0.85 0.85 0.85 0.9 p.u. Xd 2.56 1.869 2.67 2.35 Synchronous longitudinal reactance Xq 2.56 1.5 2.535 2.24 Synchronous reactance transverse Xs 0.222 0.194 0.22 0.32 shunt inductive reactance Statoric Xf 2.458 1.79 2.587 2.173 Inductive reactance of the excitation circuit Xsf 0.12 0.115 0.137 0.143 Shunt inductive reactance of the excitation circuit Xsfd 0.0996 0.063 0.1114 0.148 Shunt inductive reactance of the damping circuit on the direct axis Xsf1q 0.131 0.0407 0.944 0.263 Shunt inductive reactance of the first damping circuit on the quadrature axis q Xsf2q 0.9415 0.0407 0.104 0.104 Shunt inductive reactance of the secend damping circuit on the quadrature axis q Ra 0.0055 0.0055 0.0055 0.005 Statoric active resistance Rf 0.000844 0.00084 0.00176 0.00132 Resistance of the excitation circuit (rotor) R1d 0.0481 0.0481 0.003688 0.002 Active resistance of the damping circuit according to the direct axis R1q 0.061 0.061 0.00277 0.023 Active resistance of the damping circuit according to the Quadrature axis R2q 0.115 0.115 0.00277 0.023 active Resistance of the second damping circuit according to the Quadrature axis mailto:abdnaceri@yahoo.fr