Benchmarking Power System Stabilizer Controller Performance Using Conventional Lead/Lag, Fuzzy, and Matlab PID

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1 Bencharking Power Syste Stabilizer Controller Perforance Using Conventional Lea/Lag an Matlab PI MOHAMA HALI BILAL HANI BABA lectrical ngineering epartent University of Balaan P. O. Box ripoli LBANON Abstract: - When a Synchronous achine unergoes a isturbance the rotor exhibits electroechanical oscillations. he Power Syste Stabilizer (PSS) is use to help aping these oscillations an thus iproves the stability of the syste. In this paper the Single Machine Infinite Bus (SMIB) oel is escribe an siulate for a unit step input in echanical torque. he conventional Lea/Lag copensator an the PSS (FPSS) are use as PSSs. ifferent ebership functions are teste for the FPSS to yiel the best perforance. he Matlab PI block use as a PSS is tune for optial an robust perforance. he three ifferent techniques were copare an bencharke. ey-wors: - Power Syste Control; Power Syste Stabilizer; Logic; PI; Optial Control; Matlab. Introuction Power systes are constantly subjecte to loa changes planne an unplanne isturbances an topographical oifications. Consequently the stability an perforance ay be affecte. In noral operating conition a power syste elivers quality power by keeping the voltage profile an the frequency within acceptable liits. However when a power syste unergoes a isturbance or loa changes the syste s stable operating conition ay be shifte to. another stable but critical operating conition or. an unstable operating conition. For both of the above entione cases the power syste ust brought back to the noral operating conition otherwise if the fault persist it ay le to voltage collapse. A synchronous generator is equippe with a Power Syste Stabilizer (PSS) to help aping out the oscillations that are cause by a isturbance or loa changes. In [] a oal perforance easure optiization proble is to select a set of PSS paraeters so that the area uner the oscillatory output response will be iniu. Gupta et al. escribe the stability of the syste for ifferent ebership functions for PSS (FPSS) []. hali et al. propose a new akagi-sugeno FPSS technique then teste for ifferent types of efuzzification an echanical inputs []. he conventional lea/lag an ifferent types of ebership function teste by Sabariya et al. their work showe better perforance for a triangular an Gaussian ebership function in FPSS over the conventional PSS. he optial fuzzy PI technique for PSS is propose an applie by Haki et al. []. Syste Moel Any power syste can be oele into a generator in series with a transission line an infinite voltage bus []. he oel of the Single Machine Infinite Bus (SMIB) power syste is presente in Fig.. Fig. : Single Machine Infinite Bus he classical synchronous generator acceleration equations are r e r () H () r where H an are the inertia constant an the aping torque coefficient respectively. An the fiel circuit ynaic equation is e i. () Now cobine the network equations the excitation syste an linearize the syste yiel the th orer State Space Moel (SSM) shown in () ISBN:

2 r a a a r b a () a a a b v a a a v where a H a H L L a a a B sin cos q H L L L q a a ba a a a b b L L H L s B B q sin cos n sin cos q q L L n q L L L L Bq Biq sin cos q q sin cos L q q L L q i q L L q B q sin cos e e q a Ln l Laqsn n a L l L an t t e e L n L n n L L q a l aqs a l t t Ll. () he corresponing block iagra is shown in Fig.. Wr Vs A xciter.s+ Fiel Circuit *Hs+ W s r.s+ Voltage ransucer Fig. : Classical synchronous achine linearize oel with exciter an AV. Power Syste Stabilizer he ain function of a PSS is to iniize the rotor electroechanical oscillations by controlling the excitation syste. herefore its input is the variation of the rotor spee r an its output is a voltage v s. hen this voltage is use as an input for the excitation syste. here are various types of controllers use as PSS such as lea/lag an PI. he block iagra of the achine with the PSS is shown in Fig. where the etail of the block Synchronous Machine is shown in Fig.. he block PSS represent the controller. hree types of PSS controllers will be copare the conventional lea/lag the logic an the propose optial PI. ISBN:

3 Fig. : Synchronous achine with a PSS.. Conventional Lea/Lag PSS he purpose of PSS is to introuce a aping torque coponent. A logical signal to use for controlling generator excitation is the spee eviation r. Since the PSS ust prouce a coponent of electrical torque in phase with the spee eviation we use the phase copensation block which copensate for the phase lag between exciter input an generator electrical torque. hus the conventional lea/lag PSS is ivie into three blocks phase lea/lag copensator washout an a stability gain Fig.. Fig. : Lea/Lag PSS copensator. he signal washout block serves as high pass filter with tie constant high enough to allow signals associate with oscillations in r to pass unchange an reoves the c signals. he stabilizer gain stab eterines the aount of aping introuce by the PSS. he phase copensator acts like a copensator between the exciter input an generator electrical torque.. PSS sets are the basic concept of fuzzy logic. A fuzzy set is an extension of a crisp set which allows only full ebership or non-ebership whereas fuzzy sets allow partial ebership. In a crisp set the bounaries are precise. For exaple consier a classical set A: A { x / x x } if x x A A x () if x x A A x sets represent coon sense linguistic labels like slow fast sall large heavy low eiu etc. hus in fuzzy set the bounaries are not precise A x. Where A x is efine as ebership function. In general a ebership function is a curve that efines how each point in the input space is relate to a ebership value or egree of ebership between an. hree popular ebership functions riangular rapezoial an Gaussian are shown in (7) (8) an (9) respectively. x aan x c A x x a (7) a x b b a A x a x a a xb b a x bxc x c x c x (8) x x A x exp. (9) Inference Systes (FISs) consist of if-then rules that specify a relationship between the input an output fuzzy sets. relations present a egree of presence or absence of association or interaction between the eleents of two or ore sets. If x is A then y is B; his rule has a ebership function x. For ost applications the fuzzy ebership function x for a given relation is obtaine with iniu or prouct iplication represente as AB x in A x B x () A x B x. An FIS consists on apping the input ata vector into a scalar output using fuzzy rules Fig.. he apping process involves input/output ebership functions fuzzy logic operators if-then rules aggregation of output sets an efuzzification. Fig.. Block iagra of fuzzy inference syste. he Fuzzifier: aps input nubers into corresponing fuzzy eberships. his is require in orer to activate rules that are in ters of linguistic variables. he Fuzzifier takes input values an eterines the egree to which they belong to each of fuzzy sets via ebership functions. ISBN:

4 Inference ngine: efines apping fro input fuzzy sets into output fuzzy sets. Aggregation: It is possible that one or ore rules ay fire at the sae tie. Outputs for all rules are then aggregate. uring aggregation the output set of each rule are cobine into a single a single fuzzy set. he efuzzifier: aps output fuzzy sets into nubers. Given a fuzzy set that encopasses a range of output values the efuzzifier returns one nuber thereby oving fro a fuzzy set to a crisp nuber. here are several ethos for efuzzification; center of gravity weighte average an center of areas. rules play a key role in representing expert control/moeling knowlege an experience linking the input variables of fuzzy controllers to output variable(s). here are two ajor types of fuzzy rules; Maani an akagi-sugeno. he secon type of PSS is the PSS (FPSS) where the aping is base on ebership functions an a set of rules. he inputs of the FPSS are the spee eviation r an the eviation of the acceleration r. he syste shown in Fig. is siulate where the controller is a FPSS with three ifferent ebership functions naely the triangular trapezoial an Gaussian eberships. he 9 rules of the FPSS are presente in able. able. ule-base FPSS Controller Spee Acceleration eviation NB NM NS Z PS PM PB NB NB NB NB NB NM NM NS NM NB NM NM NM NS NS N NS NB NM NS NS Z Z PS Z NM NS NS Z PS PS PM PS NS Z Z PS PS PM PM PM Z PS PS PM PM PM PB PB PS PM PM PB PB PB PB. Optial PI PSS A general optiization proble can be classifie as the iniization (or axiization) of a cost function given soe constraints. i.e. iniize J( k) k n k () subject to ck ( ) () an hk ( ). () n Where k J : the cost/objective function or nk perforance inex an k is the iniizer that represents a vector containing n k paraeters of the nk controller. Moreover c : represents the nk equality constraint an h : p represents the inequality constraint. If the functions J c an h are all linear then the optiization proble is classifie as linear. However if at least one of the aforeentione functions is nonlinear then the optiization proble is classifie as nonlinear. he Mathwork PI controller tuning algorith eets the following objectives by tuning the PI gains to achieve a goo balance between perforance an robustness [7]. Close-loop stability he close-loop syste output reains boune for boune input. Aequate perforance he close-loop syste tracks reference changes an suppresses isturbances as rapily as possible. he larger the loop banwith (the frequency of unity open-loop gain) the faster the controller respons to changes in the reference or isturbances in the loop. Aequate robustness he loop esign has enough gain argin an phase argin to allow for oeling errors or variations in syste ynaics. he algorith esigns an initial controller by choosing a banwith to achieve that balance base upon the open-loop frequency response of the linearize oel. he transfer function of the PI controller is shown in (). Ns Gc s PI () s s N Where N eterines the pole location of the filter in the erivative action is the filter coefficient. SIMULAION Siulation shows that the riangular ebership yiels better perforance than the rapazoial an the Gaussian eberships as it is apparent in both the spee eviation Fig. an the power angle eviation Fig. 7. he three ifferent types of PSS naely the conventional Lea/Lag the with the riangular ebership an the Matlab PI block are siulate an teste using Siulink Fig. 8. he achine -paraeters use in the siulation are shown able. able. Synchronous Machine -paraeters use for siulation Paraeter Value ISBN:

5 7 x Fig.. he spee eviation of the synchronous achine FPSS with ifferent ebership functions Spee eviation r Power Angle eviation riangular Gaussian rapazoial riangular Gaussian rapazoial Fig. 7. he power angle eviation of the synchronous achine FPSS with ifferent ebership functions. After tuning the PI the optial values of the coefficients are obtaine an shown in able. able. Optial PI paraeters Paraeter P I N Value 87 8 he Optial PI PSS the PSS an the conventional Lea/Lag PSS were applie to the linearize synchronous achine oel where the spee an power angle eviations were easure an plotte in Fig. 9 an Fig. respectively for a unit step echanical torque input. x Fig. 9. he spee eviation of the synchronous achine with ifferent controllers for the PSS. Fig 9. Clearly shows that the PSS has better perforance that the conventional Lea/Lag PSS. However Optial PI surpasses the FPSS where the spee variation has no electroechanical oscillations an literally equals to zero..9.8 Spee eviation r Power Angle eviation Lea/Lag Optial PI Lea/Lag Optial PI Fig.. he power angle eviation of the synchronous achine with ifferent controllers for the PSS. Fig. 8. Block iagra of the synchronous achine with three ifferent controllers as PSS. he conventional Lea/Lag PSS oes not suppress the power angle electroechanical oscillations in a short tie Fig.. he FPSS quells the oscillations in secons however it settles at.798. he Optial PI on the other han eliinates the ISBN:

6 oscillation an settles at very sall power angle eviation.. Now to test the robustness of the Matlab PI block in coparison with the conventional Lea/Lag PSS an the FPSS the achine -paraeters are copletely change able at the sae tie the Optial PI paraeters are kept the sae as shown in able. able. Synchronous Machine -paraeters use for robustness test Paraeter Value he siulation results shows the superiority of the Matlab PI in coparison with the conventional Lea/Lag an the FPSS as shown in both Fig. an Fig. ; the conventional Lea/Lag an the FPSS le to copletely unstable syste where the Optial PI not only stabilize the syste but also it lea to excellent perforances by keeping both the spee an the power angle eviations sall in fact alost zero Fig.. he power angle eviation of the synchronous achine with ifferent controllers for the PSS testing the robustness of the Optial PI x - Power Angle eviation Spee eviation r Lea/Lag Optial PI Lea/Lag Optial PI Fig.. he spee eviation of the synchronous achine with ifferent controllers for the PSS testing the robustness of the Optial PI. Conclusion When a Synchronous achine unergoes a isturbance the rotor exhibits electroechanical oscillations. he PSS is use to help aping these oscillations. In this paper three ifferent techniques the conventional Lea/Lag the an Matlab PI block were use for the PSS controller. he three techniques were copare an bencharke. Siulation showe that the PSS (FPSS) was better than the conventional Lea/Lag an the Optial PI was superior to the FPSS. In fact the Optial PI showe a great eal of robustness; the achine s -paraeters were change while aintaining the sae PI paraeters. he Lea/Lag an the FPSS were not able to stabilize the syste whereas the Optial PI was not only able to stabilize the syste but also it was able to eliinating the electroechanical oscillations with approxiately zero spee an power angle eviations. eferences: [] M.. hali A.. Sarkar. Y. Lee an Y. M. Park he Moal Perforance Measure for Paraeter Optiization of Power Syste Stabilizers I ransactions on nergy Conversion vol. 8 no. eceber 99 pp. -. [] N. Gutpa an S. Jain Coparative Analysis of Power Syste Stabilizer Using ifferent Mebership Functions International Journal of Coputer an lectrical ngineering vol. () April pp. -7. [] N. hali M. Mustafa an. Iris Analysis of Power Syste Stabilizer using Various efuzzification Interface for akagi-sugeno Logic I International Power ngineering an Optiization Conference Melaka Malaysia June pp. -7. []. Sabariya an. Prasa obust Power Syste Stabilizer esign for Single Machine Infinite Bus Syste with ifferent Mebership Functions for Logic Controller Intelligent Systes an Control (ISCO) January pp. -9. []. Haki A. Suprijanto an M. Heri PSS Base on Optial fuzzy PI with Particle Swar Optiization Power ngineering Conference eceber 7 pp. 9-. [] P. unur Power Syste Stability an Control NewYork: McGraw Hill 99. [7] MathWorks Inc. Siulink Control esign User s Guie. [8] M. ushawaha an. hare ynaic Stability nhenceent of Power Syste using Logic base Power Syste Stabilizer International Journal of ngineering esearch an echnology vol. pp. -9. ISBN: