Improvement of Transient Stability of Power System by Thyristor Controlled Phase Shifter Transformer

Transcription

1 American Journal of Applied Science 7 (11): , 010 ISSN Science Publication Improvement of Tranient Stability of Power Sytem by Thyritor Controlled Phae Shifter Tranformer Prechanon Kumkratug Diviion of Electrical Engineering, Faculty of Engineering at Si Racha, Kaetart Univerity, 199 M.6, Tungukhla, Si Racha, Chonburi, 030, Thailand Abtract: Problem tatement: The improvement of tranient tability of the power ytem wa one of the mot challenging reearch area in power engineer. Approach: Thi tudy preent the method to improve tranient tability of power ytem by Thyritor Controlled Phae Shifter Tranformer (TCPST). The mathematical model of power ytem equipped with a TCPST wa ytematically derived. The parameter of TCPST are modeled into power flow equation and thu it wa ued to determine control trategy. The wing curve of the three phae faulted power ytem without and with a TCPST are teted and compared in variou cae. Reult: The wing curve of ytem without a TCPST get increae monotonically and thu the ytem can be conidered a untable wherea the wing curve of ytem with a TCPST can return to table equilibrium point. Concluion: From the imulation reult, the TCPST can increae tranient tability of power ytem. Key word: Power ytem, tranient tability, FACTS device, hunt tranformer, ected current, Unified Power Flow Controller (UPFC), TCPST, erie tranformer, voltage ource, leakage reactance, control trategy, complex power INTRODUCTION mathematical model i applied to deign control trategy of a TCPST. The imulation reult are teted Tranient tability improvement i one of the important apect in modern power ytem. The on a Single Machine Infinite bu ytem. innovative Flexible AC Tranmiion Sytem (FACTS) device have been propoed during the lat three MATERIALS AND METHODS decade for improving tranient tability of power Mathematical model: Figure 1a how the chematic ytem (Barbuy et al., 009). There are variou form of FACTS device uch a Static Synchronou Serie diagram of the Thyritor Controlled Phae Shifter Compenator (SSSC), Static Synchronou Compenator (TCPS). The erie tranformer ect the voltage in (STATCOM), Unified Power Flow Controller (UPFC) erie in the ytem. The active and reactive power and Inter line Power Flow Controller (Bhownick et al., ected by the erie tranformer i taken from the 009; Hannan et al., 009; Magaji and Mutafa, 009; hunt tranformer. For ake implicity of analyi, the Zhang, 003; Leon and Zanetta, 008; Parimi et al., inignificant loe from tranformer and converter i 008; Azbe and Mihalic, 008). neglected. Thu the net complex power (real and A Thyritor Controlled Phae Shifter Tranformer reactive power) exchange between the TCPS and the (TCPST) conit of a hunt tranformer, a erie ytem i zero. The ection of thi complex power tranformer and a converter. The claification of depend on the ection of a erie voltage controlled TCPPS depend on the type of converter ued. The by a converter. converter can be of ac-ac bridge type, Pule-Width Figure 1b how the equivalent circuit of Fig. 1a. Modulation (PWM) type, ac controller type (Badran V and V h are repreented by the ynchronou voltage et al., 008; Daut et al., 006). To verify the capability ource in erie and hunt, repectively. X h i the of TCPST on tranient tability improvement, it leakage reactance of the hunt tranformer. X i the uitable mathematical model and control trategy are leakage reactance een from primary ide of erie needed to be preented. tranformer i given by X = X + n Xh where n i the Thi tudy preent the mathematical model of turn ratio number of the hunt tranformer and X i the power ytem equipped with a TCPST. The preented leakage reactance of the erie tranformer. 1495

2 Am. J. Applied Sci., 7 (11): , 010 Fig. : A imple ingle machine infinite bu ytem with a TCPST; ingle line diagram; equivalent circuit The active (P ) and reactive (Q ) power ected by the erie tranformer are given by: P = R[S ] = bv V in( θ θ ) bv E in( θ ) m m (3) (c) Fig. 1: A ytem equipped with TCPST; Schematic diagram of a TCPST; a erie and hunt ynchronou voltage ource equivalent; (c) a erie ected voltage ource and a hunt ected current ource The hunt ynchronou voltage ource with leakage reactance can be repreented by a hunt ected current model (I h ) a hown in Fig. 1c. A hunt ected current i compoed of in phae current (I p ) and in quadrature current (I q ) which repect to the V m. Thu I h i given by: I (I ji )e θ j m h = p q (1) Conider the ingle machine infinite bu ytem equipped with a TCPS at bu m a hown in Fig. a and b how the equivalent circuit of Fig. a. Note that X 1 i the um of generator tranient reactance, tranformer leakage reactance and equivalent reactance of line 1 and ; X i the equivalent reactance of X, line 3 and 4. The complex power ected by the erie tranformer can be written a: Q = I[S ] = bv V co( θ θ ) + bv + bv E co( θ ) m m (4) Here b = 1/X. The active (P h ) and reactive (Q h ) power drawn by the hunt tranformer are given by: [ ] P = R S = V I (5) h h m p [ ] Q = I S = V I (6) h h m q A mentioned earlier that the net complex power exchange between a TCPST and the ytem i zero. The equality of real power balance between erie and hunt tranformer i given by: P = P (7) h The in phae current (I p ) of a hunt current ection can be written a: bv E I = bv in( θ θ ) + in( θ ) (8) p m Vm Let: Vm + V + E S = V ( I) = V jx () 1496 V = ae V m jα

3 Am. J. Applied Sci., 7 (11): , 010 Fig. 3: Phaor of erie ected voltage and hunt ected current of the TCPST The ize of a i related to the rating of a TCPS (0<a<a max ). The range of α depend on the type of TCPST. Now let the rage of α i π α π. Figure 3 how the phaor diagram of a erie ected voltage and hunt ected current. Thu in phae current a given Eq. 8 i written a: I = abv in( α) + abe in( θ + α) (9) p m m Similarly, the balancing of reactive power exchange i given by: Q = Q (10) h Thu the in quadrature current of a hunt current ection (I q ) can be written a: I = abv coα a bv abe co( θ + α) (11) q m m m The erie ected voltage V with X of Fig. b can be tranformed into the current I a hown in Fig. 4a. The value of I i given by: V j( θm + α 90) = = avm be (1) jx I The current ource connected between bu m and the infinite bu can be replaced by two hunt current ource a hown in Fig. 4b. The net ected current (I ) at bu m can be written a: (c) Fig. 4: Succeive repreentation of erie voltage ource of the TCPST: a erie voltage ource converted to a current ource; a net ected current model; (c) fictitiou load model The ected current I can further be replaced by a fictitiou load S a how in Fig. 4c. The value of the fictitiou load i given by: S = P + Q = V ( I ) (14) m The complex power of fictitiou load power are given by: P = R [S ] = abe V in( θ + α) (15) m m Q = I[S ] = abv coα + a bv + abe V co( θ + α) m m m m (16) The active power balance equation at bu m of Fig. 4c i given by: I = Ih + I (13) 1497 PR1 = P + P (17)

4 Am. J. Applied Sci., 7 (11): , 010 E1Vm VmE where, P1 = in( δ1 θm) and P = in( θm) X1 X After ome mathematical manipulation of Eq. 17, the θm of voltage at bu m can be expreed a: θ X E inδ + ax E in( α) m = tan XE1 coδ1 ax1e co( α) + X1E (18) Similarly, the reactive power balance at bu m of Fig. 4c i: QR1 = Q + Q (19) E1Vm Vm where, QR1 = co( δ1 θm) and X X Vm Vm E Q = co( θm) X X 1 1 After ome mathematical manipulation, the voltage magnitude at bu m i given by: Vm = 1 / [X1 + X + a X1 X1a co( α)] [X E co( δ θ ) ax E co( θ + α) + (0) 1 1 m 1 m X E co( θ )] m It can be een from the Eq. 18 and 0 that the TCPST placed at bu m impact on both the voltage magnitude and the angle. It indicate that the voltage and the angle at bu m can be controlled by a erie ected voltage. The electrical output power of generator (P e ) i given by: E V P = in( δ θ ) (1) 1 m e 1 m X1 The generator dynamic, in claical model of ytem, can be repreented by following two firt order differential equation: power (P e ) of the generator i the main factor that dictate the dynamic behavior of the generator becaue both P m and H are uually conidered a contant. The propoed model of the TCPST indicate clearly that the V m can be controlled by a erie ected voltage. Thu thi propoed model of the TCPST i very eay to implement it to tudy it behavior on tranient tability improvement of the imple ytem. However, the TCPST can help the ytem improve tranient tability of the ytem when a erie ected voltage i properly controlled. Thu the control trategy of a TCPST hould be carefully deigned. Control trategy: Thi tudy ue the machine peed control parameter on a TCPST. When the peed deviation i poitive (ω>0), the P e i raied by controlling parameter on TCPST; When the peed deviation i negative (ω<0), the P e i raied by controlling parameter on TCPST. RESULTS The preented mathematical model and control trategy i ued to tudy the effect of TCPST on tranient tability improvement of the ytem of Fig. 3. In all cae, it i conidered that a three phae elf clearing fault appear at bu m and the fault i cleared without changing the network configuration. Figure 5 how the wing curve of the ytem without a TCPST for clearing time (t cl ) = 144 mec. Figure 6 how the wing curve of the ytem with and without an TCPST for t cl = 145 m ec. DISCUSSION From the reult in Fig. 5 and 6, we found that the critical clearing time of the ytem without a TCPST i mec. It can be een from the Fig. 5 that with fault clearing time (t cl ) = 144, the ytem i conidered a table and the ytem i conidered a untable with t cl = 145 mec a can been in Fig. 6. δɺ = ω () ω ɺ = 1 [ P P m e ] (3) M Here δ, ω, P m, P e and M are the rotor angle, peed, input mechanical power, output electrical power and inertia, repectively, of the generator. Solving the Eq. and 3 yield the variation of δ and ω that can be ued to tudy the dynamic behavior of the generator. Fig. 5: Rotor angle of the ytem without TCPST for Equation 3 clearly indicate that the output electrical t cl = 144 mec 1498

5 Am. J. Applied Sci., 7 (11): , 010 Fig. 6: Rotor angle of the ytem without and with an TCPST for t cl = 145 mec However, the ytem with a TCPST control can tabilize the ytem with t cl = 145 mec. The imulation reult indicate that a TCPST can improve tability of the ytem. CONCLUSION Thi tudy invetigate the capability of the Thyritor Controlled Phae Shifter Tranformer (TCPST) on tranient tability improvement of the ytem. The mathematical model i ytematically derived. The preented mathematical model ha hown that power flow and tability of ytem can be regulated by TCPST. Thi tudy ue machine peed to control parameter on TCPST. The peed deviation i the main factor to decreae and increae power flow of the ytem. The imulation reult are teted on Single Machine Infinite Bu (SMIB) ytem. From the imulation reult, it indicate that a TCPST can improve tranient tability of the ytem. REFERENCES Bhownick, S., B. Da and N. Kumar, 009. An advanced IPFC model to reue newton power flow code. IEEE Tran. Power Syt., 4: DOI: /TPWRS Daut, I., D.M.M. Ahmad, S. Zakaria, S. Uthman and S. Taib, 006. comparion of loe and flux ditribution in 3 phae 100 kva ditribution tranformer aembled from variou type of t-joint geometry. Am. J. Applied Sci., 3: DOI: /ajap Hannan, M.A., A. Mohamed, A. Huian and Majid al Aabby, 009. Development of the unified erie hunt compenator for power quality mitigation. Am. J. Applied Sci., ISSN: Leon, R.V.A. and L.C. Zanetta, 008. A novel approach for modeling the teady tate VSC baed multiline FACTS controller and their contrain. IEEE Tran. Power Syt., 3: DOI: /TPWRD Magaji, N. and M.W. Mutafa, 009. Optimal thyritor control erie neuro-controller for damping ocillation. J. Comput. Sci., 5: ISSN: Parimi, A.M., I. Elamwazuthi and N. Saad, 008. Interline Power Flow Controller (IPFC) baed damping controller for damping low frequency ocillation in a power ytem. Proceeding of the IEEE International Conference on Suitable Energy, Nov. 008, Singapore, pp: DOI: /ICSET Zhang, X.P., 003. Modeling of the interline power flow controller and the generalized unified power flow controller in Newton power flow. IEE Proc. Gener. Tran. Ditrib., 150: DOI: /ip-gtd: Azbe, V. and R. Mihalic, 008. The control trategy for an IPFC baed on the energy function. IEEE Tran. Power Syt., 3: DOI: /TPWRS Badran, I., A.L. Mahmood and M.T. Lazim, 008. Harmonic phae hifter for a three-phae ytem with voltage control by integral-cycle triggering mode of thyritor. Am. J. Applied Sci., 5: ISSN: Barbuy, H.S., A. Rocco, L.A.P. Fernande and G.C. Guimarae, 009. Voltage collape rik aociated to under voltage capacitive compenation in electric power ytem operation. Am. J. Applied Sci., 6: ISSN: