Investigation of local load effect on damping characteristics of synchronous generator using transfer-function block-diagram model

Transcription

1 ORIGINAL ARTICLE Investigation of local loa effect on amping characteristics of synchronous generator using transfer-function block-iagram moel Pichai Aree Abstract of synchronous generator using transfer-function block-iagram moel Songklanakarin J. Sci. Technol., 2005, 27(4) : The transfer-function block-iagram moel of single-machine infinite-bus power system has been a popular analytical tool amongst power engineers for explaining an assessing synchronous generator ynamic behaviors. In previous stuies, the effects of local loa together with amper circuit on generator amping have not yet been aresse because neither of them was integrate into this moel. Since the moel only accounts for the generator main fiel circuit, it may not always yiel a realistic amping assessment ue to lack of amper circuit representation. This paper presents an extene transfer-function block-iagram moel, which inclues one of the q-axis amper circuits as well as local loa. This allows a more realistic investigation of the local loa effect on the generator amping. The extene moel is applie to assess the generator ynamic performance. The results show that the amping power components mostly erive from the q-axis amper an the fiel circuits can be improve accoring to the local loa. The frequency response metho is employe to carry out the funamental analysis. Key wors : power system stability, amping, local loa Ph.D.(Electrical Engineering), Asst. Prof., Department of Electrical Engineering, Faculty of Engineering Thammasat, University, Klong Luang, Pathum Thani, Thailan. apichai@engr.tu.ac.th Receive, 26 July 2004 Accepte, 8 November 2004

2 Vol.27 No.4 Jul. - Aug àõ æ Õ å» º Õß Õ À µàõ ÿ «Àπà«ß Õß ËÕß π øøñ ß π â Õß ºπ æ àõßøíß å Ëπ à Õπ «. ß π π å « (4) : Õß Õß øøñ ß π Ÿª Õß Õß ºπ æ àõßøíß å π à Õπ (transfer-function block-iagram moel) ªìπ Ëπ π Õ «Àå惵 ßæ «µ Õß ËÕß π øøñ ß π (synchronous generator) µà» Õß Ëºà π âæ ÿ «π (fiel wining) Õß ËÕß π øøñ à π Èπ âæ ÿ «Àπà«ß (amper wining) Õ À (local loa) à«π π «Àå «Àπà«ß Õß ËÕß π øøñ ß Àâ à «Àåº Õß Õ À µàõ ÿ «Àπà«ß Õß ËÕß π øøñ âõ à ß Ÿ µâõß ßπ Èπ» π È ß âª ª ÿß Õß Õß øøñ æ ÿ «Àπà«ß π π «ß (q-axis amper wining) Ëß Õßπ È Àâ «Àåº Õß Õ À µàõ à «Àπà«ß Õß ËÕß π øøñ ªìπ ª âõ à ß Ÿ å» â«µõ πõß ß «Ë (frequency response metho) æ «à Õ À æ Ë «Àπà«ß Àâ ËÕß π øøñ ºà π ß «Àπà«ß π «ß «π ««øøñ µ å À µ å Õ Õ ÕßÀ «ß ßÀ«ª ÿ π The transfer-function block iagram moel of single-machine infinite-bus power system (Demello et al., 1969; Anerson, 1993; Saiy et al., 1994; Paiyar, 1995) has provie the basis for excellent explanation of funamental ynamic characteristics of synchronous generator. It has been use amongst power engineers for many years to esign the control equipments such as automatic voltage regulator (AVR) an power system stabilizer (PSS). The moel yiels a great physical insight into how AVR an PSS enhance power system stability. The transfer-function block-iagram moels were avance to incorporate an electric local loa (El-Sherbiny et al., 1973; Yu, 1983; Saccomanno, 2003). The constant impeance loa moel was conventionally use to represent the local loa. These block-iagram moels help to emonstrate the effect of the local loa on stability of synchronous generator. However, reliability of the moels has been brought into question because they only take into account the generator fiel circuit. Hence, use of a higher-orer block-iagram moel (Saiy et al., 1994) has been realize by incluing the an q-axis amper circuits to obtain the realistic amping assessment of synchronous generator (Saiy et al., 1994). However, in this moel, the effect of the local loa has not yet been taken into consieration. In this paper, the transfer-function blockiagram moel (Saiy et al., 1994) has been extene to incorporate the constant impeance local loa an the amper circuit representation. Accoring to the previous stuies (Saiy et al., 1994; Aree et al., 1999), one of the q-axis amper circuits is essentially ae, in aition to the fiel wining, to provie the system realistic amping. The block-iagram moel provies an insightful analysis of how the local loa affects the amping characteristics of synchronous generator through the fiel an q-axis amper circuits. Moreover, this moel is applie to emonstrate the local loa effect on ynamic performance of the generator uner voltage regulator. The analysis is carrie out using the frequency response metho.

3 Vol.27 No.4 Jul. - Aug System an transfer-function block-iagram representation In orer to investigate the funamental effect of local loa on amping of the synchronous generator, the stuy system use by Yu (1983) is moifie to inclue the representation of the q- axis amper circuit. This system is shown in Figure 1. It consists of one synchronous generator in connection with an infinite bus through the tie line system. It shoul be note that since the main objective of this paper is to gain a funamental knowlege of interaction between the generator an the local loa, this system is suitable for this stuy. The small-signal moel that represents the system uner stuy is erive using the non-linear ifferential an algebraic equations (Arrilaga et al., 1990), given by (A-1)-(A-8) in Appenix A. After completing the erivation process presente in Appenix A, the small-signal linearize transfer functions in s omain are expresse as, s δ ω s ω r (1) 2Hs ω r P m P e K D ω r (2) (1 + K 3q τ o s) E q K 3q E f K 4q δ + K 7q E (1 + K 3 τ qo s) E K 4 δ K 7 E q P e K 1 δ + K 2 E + K 2q E q E t K 5 δ + K 6 E + K 6q E q (3) (4) (5) (6) The system K-coefficients are liste by (A-13)-(A-27) in Appenix A. Equations (1)-(6) comprehensively escribe the small-signal ynamics of the stuy system. By suitably combining (1)-(6), the linearize transfer function in the form of block iagram is isplaye insie the otte-line block of Figure 2. The local loa affects the generator ynamic characteristics through all the K-coefficients, which are a function of loa conuctance (G) an susceptance (B). Furthermore, the local loa gives rise to the aitional coefficients K 7 an K 7q, which exist in aition to the K-coefficients presente in the block-iagram moel evelope by Demello (1969), Yu (1983), Saiy et al., (1994). The ynamic interactions between the generator flux linkages ( E q an E ) in the an q-axes take place through the K 7q an K 7 branches. Accoring to (A-15) an (A-19), the coefficients K 7q an K 7 will not appear in the block-iagram moel, if the local loa is not incorporate. Because the local loa influences the ynamic characteristics of the generator flux linkages E q an E with regar to its conuctance an susceptance, the amping power components of the electrical powers P f an P q, mainly erive from the fiel an q-axis amper circuits, respectively, are affecte. The investigations into effect of the local loa on the generator amping characteristics are carrie out in the next section. 2. Effect of local loa on amping characteristics of fiel an amper circuits In this section, the effects of the local loa on generator amping over the relevant frequency range of 1-12 ra/s are investigate. The active power output of the generator is kept at 0.8 per unit (on 100MVA base), whether or not the local loa is inclue into the system. The generator is equippe with AVR (K a 200, τ a 1 sec) an with Figure 1. Synchronous generator with gri an local loa.

4 Vol.27 No.4 Jul. - Aug no PSS. The generator initially has low amping ue to its making use of the high tie-line reactance (0.6 pu) between the generator an infinite bus. It shoul be note that the high value of the interconnecte tie causes egraing in the generator amping (Saiy et al., 1994). The generator an infinite-bus voltages are kept at 1.0 per unit. The generator an AVR parameters are given in Appenix B. To gain an insight into the effect of the local loa on generator amping characteristics through the q-axis amper an fiel circuits, the ynamic responses of electrical power P q an P f ue to the oscillation of rotor angle δ are entirely explore. A measure of contributions of both rotor circuits to synchronizing an amping powers is etermine from the frequency responses of P q / δ an P f / δ (Saiy et al., 1995), shown in Figure 3 an 4. These responses are plotte in the Nyquist form with an ai of the transfer-function block-iagram moel in Figure 2. It shoul be note from the Nyquist plots that the coorinate of P q / δ an P f / δ in the δ irection (real axis) gives the synchronizing power component, an the coorinate in the ω irection (imaginary axis) gives the amping power component. The investigation is firstly carrie out with no incorporation of the local loa. In Figure 3, the response of P q / δ covers the secon quarant along the positive ω irection in the δ- ω plane. This result inicates that the amping contribution erive from the q-axis amper circuit is naturally positive over an entire oscillation frequency. On the other han, the response of P f / δ in Figure 4 covers the thir an fourth quarants along the negative ω irection between ra/s. Thus, the fiel circuit in connection with the high-gain AVR injects negative amping into the system throughout this frequency range. The combine responses of P f / δ an P q / δ, plotte in Figure 5, are use to explore the overall amping characteristics of the system, which are erive from both fiel an amper circuits. From these responses, the capability of the q-axis amper circuit to enhance the system amping can be seen. For example, as compare with the response of P f / δ (otte line in Figure 4), the combine response (otte line in Figure 5) has smaller magnitue an narrower range of the oscillation frequencies that covers the thir an fourth quarants. This result is ue to the q-axis amper circuit, which ais alleviation of the fiel negative amping effect Figure 2. Transfer-function block-iagram moel of the stuy system.

5 Vol.27 No.4 Jul. - Aug Figure 3. Frequency response of P q / δ Figure 4. Frequency response of P f / δ Figure 5. Combine frequency responses of P f / δ an P q / δ accoring to the AVR. Next, when the local loa of 0.5 pu active power eman at typical 0.85 lagging conition is incorporate, the response of P f / δ that expans into the thir an fourth quarants is significantly roppe, as isplaye in Figure 4. This consequence inicates a great reuction of the negative amping contribution from the fiel wining. In aition, the amping contribution from the q-axis amper circuit is greatly increase through a significant increase of the P q / δ response, shown in Figure 3. The q-axis amper counteracts the fiel negative amping effect. Therefore, the overall amping is positive. This stable phenomenon can be observe through the total shifting of the combine response (soli line in Figure 5) into the first an secon

6 Vol.27 No.4 Jul. - Aug quarants. The effects of the local loa in relation to the changes in its active power consumption an power factor are further investigate. When the active power consumption of the local loa is increase from 0.5 to 1.0 pu, the P q / δ response is expane along the positive ω irection into the secon quarant, as shown in Figure 3. Thus, more amping power contribution from the q-axis amper circuit is obtaine. The amping contribution of the fiel circuit is also substantially increase over the entire oscillation frequencies since the response of P f / δ is shifte further into the first an secon quarants, as inicate in Figure 4. The combine response in Figure 5 also confirms a great amping improvement. On the other han, when the power factor of the local loa at 0.5 pu active power eman is change from 0.85 lagging to 0.85 leaing conitions, the frequency response of P q / δ is ramatically contracte, as isplaye in Figure 3. The amping erive from the q-axis amper circuit, thus, significantly eclines over an entire oscillation frequency range. Moreover, the changing in the power factor causes the fiel wining to inject an unesire negative amping into the system at the frequency range between 5.0 an 8.6 ra/s, as shown in Figure 4. Hence, the generator becomes unstable ue to lack of amping. The combine response in Figure 5 also confirms this unstable phenomenon. 3. Local loa effect on generator close-loop voltage control performance In this section, the ynamic performances of the generator are assesse in the context of the close-loop terminal voltage control using the open-loop frequency an time response, which are obtaine with an ai of the transfer-function blockiagram moel. The frequency responses, relating to the terminal voltage ( E t ) an the error signal ( E err ), are shown in Figure 6 an the time response Figure 6. Frequency response of E t / E err

7 Vol.27 No.4 Jul. - Aug Figure 7. Time response of generator terminal voltage. of terminal voltage is shown in Figure 7. When the generator has no local loa, the phases an gains versus frequencies of E t / E err reveal the negative phase margin in connection to the highly marke switchback or ip characteristic at the oscillation frequency 5 ra/s. Hence, the generator becomces close-loop unstable as seen through the unampe voltage response in Figure 7. On the other han, when the local loa of 0.5 pu active power eman at 0.85 lagging conition is incorporate, the phase versus frequency in Figure 6 shows consierable increases in the phase avance at the frequency aroun 5 ra/s. This phase avance reuces the switchback characteristic to improve the system phase margin. The generator, therefore, is stable. Moreover, as the level of loa continues to increase from 0.5 to 1.0 pu, a greater phase avance of the frequency response is obtaine. Hence, improving amping. The stable phenomena of the voltage control loop can be also seen through time response in Figure 7. The fact that the amping is enhance ue to an incorporation of the local loa can be explaine from the power transfer point of view. It has shown by Saiy et al., 1994 that the generator amping is epening upon the amount of the active power transfer from the generator to the infinite bus. The amping increases, when the power transfer ecreases. For example, the generator without the local loa elivers 0.8pu active power irectly to the infinite bus. In the situation where the local loa absorbs 0.5 pu active power, the generator power transfer is reuce from 0.8 to 0.3 per unit. Thus, the generator amping can be improve. On the contrary, when the power factor of the local loa is change from 0.85 lagging to 0.85 leaing conitions at the same level of the active power eman (0.5pu), the gain an phase versus frequency in Figure 6 inicate the negative phase margin accoring to the pronounce switchback characteristic at the gaincrossover frequency (5.7 ra/s). Hence, the generator becomes unstable at this frequency ue

8 Vol.27 No.4 Jul. - Aug to lack of amping. This unstable phenomenon with the growth of oscillation through terminal voltage response can be seen in Figure 7. It has been reporte by Saiy et al., (1994) that the stability margin an the ynamic performance of the voltage control loop are eteriorate as the generator operating conition moves towars to leaing conition. Because the changing in the loa power factor from lagging to leaing conitions causes the generator operating conition to become leaing, the unstable close-loop voltage control of the generator can occur. Conclusions A comprehensive transfer-function blockiagram moel is presente in this paper. This moel is far more realistic since the generator q-axis amper circuit is taken into account in aition to the fiel circuit. After the q-axis amper is incorporate, the extene blockiagram moel shows the complete ynamic interaction, which mainly takes place between q-axis amper an the fiel flux linkages. The moel is use to emonstrate a great influence of the local loa on the amping characteristics of the iniviual q-axis amper an fiel circuits. With regar to the constant impeance local loa operate at typical lagging power factor, the amping power contributions, erive from both q-axis amper an fiel circuits, are increase. The ynamic performance of the close-loop voltage control is also improve through a reuction of the switchback characteristic. However, the amping contributions greatly ecline, when the power factor of the local loa is move towars to the leaing conition. In conclusion, an incorporation of the q-axis amper circuit yiels realistic investigation of the local loa effect on the generator amping characteristics. Without the representation of the q-axis amper circuit, the complete amping characteristics of synchronous generator cannot be capture. Acknowlegement The work escribe in this paper was sponsore by the Faculty of Engineering Research Center uner grant number 010/ References Anerson, P.M. an Foua, A.A Power System Control an Stability, IEEE Press, New York. an Acha, E Block iagram moel for funamental stuies of a synchronous generator static var compensator system. IEE Proc. Gener. Transm. Distrib., 146: Arrillaga, J. an Arnol, C.P Computer Analysis of Power System, John Wiley&Sons, New York. Demello, F.P. an Concoria, C Concepts of synchronous machine stability as affecte by excitation control. IEEE Trans. Power Appar. Syst., 88: El-Sherbiny, M. an Mehta, D.M Dynamic system stability. Part 1: Investigation of the effect of ifferent loaing an excitation systems. IEEE Trans. Power Appar. Syst., 92: Paiyar, K.R Power System Dynamics Stability an Control, John Wiley & Sons New York. Saccomanno, F Electric Power System Analysis an Control, Wiley-IEEE Press. Saiy, M. an Hughes, F.M Block iagram transfer function moel of a generator incluing amper wining. IEE Proc. Gener. Transm. Distrib., 141: Saiy, M. an Hughes, F.M Performance improvement of a conventional power system stabilizer. Int. J. of Electr. Power Energy Syst., 17: Yu, Y Electric Power System Dynamic, Acaemic Press, New York.

9 Vol.27 No.4 Jul. - Aug Appenix A System ifferential an algebraic equations: δ t ω r ω s (A-1) 2H ω r t E τ q o t E τ qo t ω s (P m P e K D (ω r ω s )) (A-2) E f E q + (X X )I (A-3) E (X q X q )I q P e E q I q + E I + (X X q )I I q (A-4) (A-5) E 2 t E 2 2 t + E tq Where E t E X q I q (A-6) (A-7) E t E q + X I (A-8) Generator current equation: From Figure 1, the armature current of the generator in - an q-axis frame of reference may be written by, I + ji q (G j(1 / B))(E + je q ) + j(1 / )e jδ V (A-9) Decomposing (A-9) into the - an q-axis components (I an I q ) by making use of (A-7) an (A-8) gives, I G Det E + (1 / X B) t (G2 + (1 / B) 2 )X q Det E + q V ( ) Gsinδ cosδ Det 1 (1 / X B)X t q Det X q (A-10) I Where, G Det E + (1 / X B) + t (G2 + (1 / B) 2 )X q Det E + V sinδ Det 1 (1 / X B)X t ( ) + Gcosδ Det X Det 1 (1 / B)(X + X q ) + (G 2 + (1 / B) 2 )X X q (A-11) (A-12)

10 Vol.27 No.4 Jul. - Aug Q-axis transient e.m.f. equation: Substituting (A-10) into (A-3), then linearizing an expressing (A-3) in s omain, the q-axis transient e.m.f. in (3) is obtaine with the following coefficients, { } K 3q 1+ (1 / X B)(X + X t q ) + (G 2 + (1 / B) 2 )X X q (A-13) q V sinδ (X X K 4q ) (1 + (1 / B)X q ) + V cosδ G(X X q )X q (A-14) Where, K 7q G(X X ) (A-15) q q 1+ (1 / B)(X + X q ) + (G 2 + (1 / B) 2 { )X X q } (A-16) D-axis transient e.m.f. equation: Substituting (A-11) into (A-4), then linearizing an expressing (A-4) in s omain, the -axis transient e.m.f. in (4) is obtaine with the following coefficients, { } K 3 1+ (1 / X B)(X + X t q ) + (G 2 + (1 / B) 2 )X X q (A-17) V cosδ (X X q q K 4 ) (1 + (1 / B)X ) V sinδ G(X q X q )X (A-18) Where, K 7 G(X X ) q q (A-19) 1+ (1 / B)(X q + X ) + (G 2 + (1 / B) 2 { )X q X } (A-20) Electrical power equation: Substituting (A-10) an (A-11) into (A-5), an then linearizing an expressing (A-5) in s omain, the electrical power of the generator in (5) is obtaine with following the coefficients,

11 Vol.27 No.4 Jul. - Aug V (E q + (X X q )I ) K 1 1+ (1 / B)X (E + (X X q )I q cosδ sinδ GX X t q 1+ (1 / B)X q sinδ + cosδ GX X q t (A-21) (E + (X X q )I q ) (1 / X B) + (1 / t B) 2 X q + G 2 X q + G(E + (X q X q )I ) K 2q I q + q (A-22) (E q + (X X q )I ) (1 / X B) + (1 / t B) 2 X + G 2 X + G(E + (X X q )I q ) K 2 I + q (A-23) Where, q {1 + (1 / B)(X q + X ) + (G 2 + (1 / B) 2 X q X } (A-24) Terminal voltage equation: Substituting (A-10) an (A-11) into (A-6), an then linearizing an expressing (A-6) in s omain, the terminal voltage of synchronous generator in (6) is obtaine with the following coefficients, K 5 V E t sinδ X E q GX t X t cosδ 1+ (1 / B)X E tq cosδ X E GX t X q t q + sinδ 1+ (1 / B)X q (A-25) K 6q K 6 E tq { E q t E t { E q t X ((1/ B) + (G 2 + (1 / B) 2 )X q )} GX E q t (A-26) q X q ((1/ B) + (G 2 + (1 / B) 2 )X )} GX E t (A-27) q E t E tq

12 Vol.27 No.4 Jul. - Aug Appenix B 160MVA synchronous generator parameters X pu, X q pu, X pu, X q pu, τ o 5.90 sec, τ qo 0.54 sec, H 5.22 sec, K D 0.0, f 60 Hz (All parameters are base on the generator MVA rating) AVR parameters K a 200, τ a 1.0 sec Tie line system parameter 0.6 pu