Modeling and Control of VSI type FACTS controllers for Power System Dynamic Stability using the current injection method

Transcription

1 nternational Modeling Journal and Control o Control, o V Automation, type FACT and controllers ystems, or vol. ower 6, no. ystem 4, pp. Dynamic , tability August 2008 using the current 495 Modeling and Control o V type FACT controllers or ower ystem Dynamic tability using the current injection method Jungsoo ark, Gilsoo Jang*, and Kwang M. on Abstract: This paper describes modeling Voltage ourced nverter (V) type Fleible AC Transmission ystem (FACT) controllers and control methods or power system dynamic stability studies. The considered FACT controllers are the tatic Compensator (TATCOM), the tatic ynchronous eries Compensator (C), and the Uniied ower Flow Controller (UFC). n this paper, these FACT controllers are derived in the current injection model, and it is applied to the linear and nonlinear analysis algorithm or power system dynamics studies. The parameters o the FACT controllers are set to damp the inter-area oscillations, and the supplementary damping controllers and its control schemes are proposed to increase damping abilities o the FACT controllers. For these works, the linear analysis or each FACT controller with or without damping controller is eecuted, and the dynamic characteristics o each FACT controller are analyzed. The results are veriied by the nonlinear analysis using the time-domain simulation. Keywords: FACT, FACT control, power system dynamic stability, C, TATCOM, UFC.. NTRODUCTON Fleible AC transmission system (FACT) controllers are power electronics based devices. Among these power electronics controllers, the most advanced type is the controller that employs voltage sourced inverters (V) as synchronous voltage sources []. Representative V type FACT controllers are the static compensator (TATCOM), which is a shunt type controller, the static synchronous series compensator (C), which is a series type controller, and which is the uniied power low controller (UFC), a combined series-shunt type controller [2]. The concepts and the perormances o FACT controllers are described in [3-5]. ubsequently, the studies or dynamic modeling and control methods have been conducted [6-8]. However, since the Manuscript received February 29, 2008; accepted May 28, Recommended by Guest Editor eung Ki ul. This work was supported by a Korea University grant, and by the Korea cience and Engineering Foundation (KOEF) NRL rogram grant unded by the Korea government (MET) (No. R0A ). Jungsoo ark and Gilsoo Jang are with the chool o Electrical Engineering, Korea University, 5- Anam-dong, eongbuk-gu, eoul 36-73, Korea ( s: {jspark98, gjang}@korea.ac.kr). Kwang M. on is with the department o Electrical Engineering, Dong-eui University, 995 Eomgwang-no, Busanjin-gu, Busan 64-74, Korea ( kmson@deu. ac.kr). * Corresponding author. controllers have the nonlinear and comple characteristics, it is hard to model and analyze the power system in which FACT controllers are installed. For that reason, most researches are ocused on the modeling and the simulation o switch unctions o FACT controllers using EMT, and current researches are interested in the steady-state analysis and the stability evaluation or FACT installations [9,0]. n order to solve the diiculties, a uniied model o series connected FACT controllers is presented in [6]. The Jacobian o the power low is modiied to satisy the node power relations or the node where the FACT controllers are installed. ts modeling is based on the power equivalence at the FACT node. n [7] and [8], a uniied model o FACT controllers, which uses the linearized hillips-heron model or a power system, is proposed. The model is useul or control system design or various FACT controllers. However, the methods are diicult to it the algorithms into a conventional power system program. n [], the voltage that is injected by inverters o the UFC and the energy echange between the inverters are converted into the equivalent currents injected to the eternal nodes, and then they are solved by Newton iteration method similar to nonlinear loads in every time step. n this paper, the current injection model is adopted or studying dynamic stability o power system in which FACT controllers are installed. All o V type FACT controllers, which are TATCOM, C, and UFC, are considered, and the supplementary controller is

2 496 Jungsoo ark, Gilsoo Jang, and Kwang M. on designed to damp low-requency inter-area oscillations. All parameters o FACT controller and damping controller are set to increase the damping o inter-area oscillations using the linear analysis. The results are veriied by time-domain simulations. 2. FACT MODELNG The V type FACT controller can internally generate both capacitive and inductive reactive power or transmission line compensation. The inverter, which is supported by a DC capacitor, can also echange active power with the AC system in addition to the independently controllable reactive power []. The active power echange can make the voltage luctuation on DC capacitor during transient. However, the DC voltage perturbation is less than.5% o the rated voltage [2], and compared with the transient phenomena, the major requency o power system dynamics is very low. Additionally, the considered oscillations in this paper have a low-requency the range, within 0.~2Hz. o, it is assumed that the DC capacitor voltage is sti or the mentioned requency range []. 2.. TATCOM As shown in Fig. (a), the TATCOM has one inverter which is connected to the eternal node with a shunt transormer. E in is the magnitude o voltage generated by the shunt inverter, and t is the impedance o shunt transormer. The TATCOM supplies the reactive power to the eternal node or the voltage regulation. Thus, it is assumed that the inverter is the ideal voltage source having the same phase angle with the eternal node. The reactive power can be derived in the equivalent current source,, having 90 phase angle dierence with the eternal voltage, as shown in Fig. (b). t can be derived as ollows, where the V and the θ indicate the voltage magnitude and the phase angle o the eternal node. The compensation eect on the eternal node voltage is illustrated in Fig. (c) C The schematic representation o C is shown in Fig. 2(a). The C is composed o one inverter and a series transormer. Unlike the TATCOM, the transormer is connected in series with transmission line. t is assumed that the C is an ideal reactive power source that generates voltage having the same phase with the voltage on the series transormer,. As shown in Fig. 2(c), the C can control the voltage dierence between the nodes and 2. Consequently, it can regulate the phase angle dierence between the voltages on the nodes and 2, 2, θ in order to control the active power low in transmission line. The phase angle, θ q, o the series injected voltage, V q, is the same as the phase angle o voltage vector, V 2 (= V - V 2 ). t can be derived as ollows, V = V ep jθ, (3) θ q q q V cosθ V2 cosθ2 q = V sinθ V2 sinθ2 tan, (4) where the subscripts and 2 correspond to the nodes and 2 in Fig. 2(a). As described in equation (4), the injected voltage by C depends on the eternal node voltages. The relation is implicit and nonlinear. To solve the compleities, the injected voltage, V q, is converted to a pair o the equivalent current sources, ± q, using π = ep j θ () 2 t Ein V = (2) (a) (b) (a) (b) (c) Fig.. (a) TATCOM model, (b) its equivalent current model, (c) the voltage phase diagram. (c) Fig. 2. (a) C model, (b) its equivalent current model, (c) the voltage phase diagram.

3 Modeling and Control o V type FACT controllers or ower ystem Dynamic tability using the current 497 Thevnin equivalent method as shown in Fig. 2(b). t can be derived as ollows, Vq Vq π q = = ep j θq. (5) j UFC The UFC is the series-shunt combined type FACT controller. As shown in the Fig. 3, it is composed o the series and the shunt inverters and the series and the shunt connected transormers. Thereore, it can be controlled the eternal node voltage and the active and reactive power lows in the transmission line. Unlike the other FACT controllers, the series inverter o UFC can inject the active power into the transmission line. The active power injected by series inverter is drawn, via DC capacitor, rom the eternal node on the shunt inverter side. The injected voltage, V, by the series inverter is superimposed on the voltage o the shunt inverter side node, which is the node in Fig. 3. Thereore, the resulting voltage can be derived as ollows, ( ) V = V ep jθ = V ep j θ + θ. (6) where θ indicates the phase angle o the voltage on the shunt inverter side node, and the subscript implies that the series injected voltage, V, is superimposed on the shunt inverter side voltage, V. n [], the series injected voltage by the UFC is converted into a pair o Thevnin equivalent current sources, ±. t can be derived as ollows, V V π = = ep j θ + θ. (7) j 2 (a) (c) (b) Fig. 3. (a) UFC model, (b) its equivalent current model, (c) the voltage phase diagram. Another current, sh, on the shunt inverter side node is the injected current by the shunt inverter. t is the same current source as TATCOM in (), with the eception o the subscript, sh. π sh = sh ep j θ. (8) 2 The other current source,, is the equivalent current o the active power injected by the series inverter to the transmission line. The active power supplied by the series inverter can be calculated as ollows, Re = V, 2 V (9) V V V2 V = sinθ + sinθ cos( θ θ2 ) 2 ( 2 ) V V + cosθ sin θ θ. (0) As mentioned above, the active power is drawn by the shunt inverter rom the eternal circuit. Thereore, it can be derived as ollows, V =, () = ep jθ. (2) V 3. OWER YTEM MODELNG The power system dynamic model can be written as a set o dierential equations and a set o algebraic equations as ollows, = (,V), (3) (, V) = YV, (4) where is a m dimensional state variable vector, and and V are n dimensional comple injection currents and voltage vectors, respectively. The number m depends on the number and the type o the dynamic models, and the number n is equal to the number o buses in power system. The dierential and the algebraic equations o each FACT controller may be derived as ollows. 3.. Dynamic model Fig. 4(a) shows the structure o the control system o the TATCOM and the shunt inverter o UFC. The integral type regulator controls the internal voltage magnitude, E in, in (2). The dierential equation o E in can be derived as ollows, Droop E = K E K (5) in in U t

4 498 Jungsoo ark, Gilsoo Jang, and Kwang M. on Droop + KV REF K V. t Fig. 4(b) shows the structure o the control system o the C. The ampliier type controller regulates the voltage magnitude, V q, in (3). The dierential equation can be derived as ollows, ( + ) K K V (6) F REF U F q = Vq + τ F V τ τ F F in (6) can be derived rom the current through the series impedance,, in Fig. 2(a). t indicates the real component o the current measured rom the reerence located at the phase angle o the voltage on the node in Fig. 2(a). Thus, the measured current has the same phase angle with the comple power low, and implies the current component which contributes to the active and the reactive power lows, respectively. t can be derived as ollows, V2 ( θq θ ) ( θ θ2 ) Vq = sin + sin. (7) Fig. 4(c) is the structure o the control system o the series inverter o UFC. t is assumed that the series injected voltage, V, is composed o the component, V, which controls the active power low and (a) (b) (c) Fig. 4. The control system o (a) TATCOM, (b) C, and (c) the series part o UFC. quadrature-phase component, V, which control the reactive power low in transmission line. Their dierential equations can be derived as ollows, ( ) K K V V, (8) F REF U F = + τf V τ τ F F ( ) K K V V. (9) F REF U2 F = + τf V τ τ F F and in (8) and (9) can be derived rom the current through the series impedance,, in Fig. 3(a). They indicate the real and the imaginary components o the current measured rom the reerence located at the phase angle o the voltage on the shunt inverter side node, which is the node in Fig. 3(a). Thus, the measured current has the same phase angle with the comple power low, and and imply the current components which contribute to the active and the reactive power lows, respectively. They can be derived as ollows, ( 2 ) V V2 sinθ sin θ θ, V V V2 θ θ θ2 = + (20) ( ) = + cos cos. (2) n (20) and (2), V sinθ and V cosθ are the components o the series injected voltage, V. ince V sinθ and V cosθ contribute to the active and the reactive power low components, they imply V and V in Fig 4(c), respectively. Thereore, the series injected voltage, V, is derived as ollows, ( θ θ ) V = V cos + jsin = V + jv, (22) V θ = tan. (23) V According to (22), the equations (20), (2), and the active power supplied by the series inverter in (0) can be re-written as ollows, ( θ θ2 ) V V2 sin, V V V2 θ θ2 = + (24) ( ) = + cos, (25) V2 V cos 2 ( θ θ2 ) V V + sin. ( θ θ2 ) V V = + (26)

5 Modeling and Control o V type FACT controllers or ower ystem Dynamic tability using the current 499 As mentioned in (8), it is assumed that the shunt inverter o UFC is the same as TATCOM. Thus, the control system o TATCOM is used or the shunt inverter o UFC, ecept that the subscript sh is being used instead o in Fig. 4(a) Damping controller modeling A lead-lag type compensator is considered as a damping controller. As a supplementary input signal, the active power low on the eternal node o FACT is considered as in [2]. sτ + sτ K W U = W low + sτw + sτ2. (27) The dierential equations o the state variables in (27) can be derived as ollows, K, (28) W U = U+ low τw τw τ KW τ + low, τ2 τ2 U2 = U U2 τ2 τ2 τ2 (29) where U and U2 are the state variables o the wash-out and the lead-lag in (27), respectively. Equation (27) can be re-written using the state variables, U and U2, as ollows, K = τ + τ +. (30) W U U U2 low τ2 τ2 ubstituting (33) into (5), (6), (8), and (9) gives the dierential equation o FACT controllers equipped with the damping controller Algebraic equations By the installation o FACT controller, (3) and (4) can be re-written as ollows, = (,V ), (3) F A A A A (V) m Y Y V = (V) n Y Y V = (V ) Y V = 0, A A A A A (32) where the subscript A implies the augmented quantities due to the FACT controller and superscript indicates the variables related to FACT controller. Y m, Y n, and Y are the admittance matrices augmented by FACT installation. The detail epressions are described in []. The equation (32) can be decomposed into two parts as ollows, m F = (V) YV Y V = 0, (33) n F = (V ) Y V Y V = 0. (34) The equivalent currents injected by FACT controllers, (V ) in equations (34), can be epressed in - or 2-dimensional comple matrices as ollows, TATCOM (,V ) =, (35) q C(,V ) =, (36) q sh + UFC(,V ) =, (37) where the st and 2nd rows in (36) and (37) correspond to the node and 2 in Fig 2(b) and 3(b), respectively. The detailed epressions o the current elements in (35), (36), and (37) are described in ()~(2). 4. LNEAR ANALY The linear analysis or small-signal stability studies is the most general method to estimate the dynamic stability o power system quantitatively. n this paper, the method is considered to get the parameters o FACT controllers and damping controllers or dynamic stability enhancement. Taking partial derivatives o (3) and (32) gives the linearized dynamic system equations as ollows, A A A = A + VA, A VA (38) FA FA A + VA = 0. V (39) A A ubstituting (39) into (38), the state space matri or eigen-value analysis can be derived as ollows, A A FA FA = A A = A A. A VA VA A (40) A set o linearized dierential equations or each FACT controller in equation (38) can be derived rom the equations (5)-(9), and (24)-(25). ince TATCOM has one state variable, E in, taking partial derivatives o equation (5) gives the -dimensional linearied dierential equation. C has one state variable, V q. ubstituting equation (7) into equation (6) and then taking partial derivatives o equation (6), the -dimensional linearized dierential equation is derived. UFC has three state variables, V, V, and E in. ubstituting equations (24) and (25) into (8) and (9) and taking partial derivatives o

6 500 Jungsoo ark, Gilsoo Jang, and Kwang M. on (6), (8), and (9), the 3-dimensional linearized dierential equation is derived. the damping controller in (27) is equipped on FACT controller, the 2 dierential equations o damping controller are added to the linearized dierential equations o each FACT controller. n order to get the linearized algebraic equations or each FACT controller, (32) may be decomposed into the real and the imaginary parts. n the case o TATCOM, it becomes a 2-dimensional algebraic equation as ollow, n n Y V cos( φ + θ ) Y V cos( φ θ ) ( φ θ ) ( φ θ ) 0. F n R i i i i R = + F n n i= i i i + i n YV cos + + = n YV sin + (4) n the case o C and UFC, it becomes 4- dimensional algebraic equations as ollows, F F α β 0 (42) F F F F + = + α + βk = 0, F F R qr n 2 q = +, i + k = R2 qr i= k= q 2 R shr + R R n 2 sh R2 R i i= k= 2 n n YiVicos φi + θ i n YiVisin i + i i = n Y2iVicos 2i + i n Y2iVisin 2i + i α β k ( ) n ( φ θ ), n ( φ θ ) n ( φ θ ) ( φ θ ) ( φ θ ) ( φ θ ) ( φ θ ) Y kvk cos k + k Y kvk sin k + k =, Y2kVk cos 2k + k Y2kVk sin 2k + k (43) where R and indicate real and imaginary parts, respectively, and Ys and Φs correspond to the magnitudes and the phase angles o the elements o admittance matrices having the same super- and subscripts in (32). Then, taking partial derivatives o (4), (42), and (43) gives sets o linearized algebraic equations or each FACT controller in (39). 5. NONLNEAR ANALY The partial derivatives with respects to the voltage magnitudes and the phase angles, F A / V A, can be used as Jacobian matri, J A, or the Newton iteration method in time-domain simulations as described in []. FR V F m J J θ = F n R J J V F θ (44) n the time-domain simulation algorithm, (3) is used to update the state variable,, and then the algebraic variables in (32) are solved by the Newton ormula at every time step. The detail epressions are described in []. 6. CAE TUDE 6.. A sample power system model A sample system used in the case study is a twoarea power system model shown in Fig. 5 [3]. t is assumed that all generators are the 4th order 2-ais models equipped with the st order ast eciters. The equations o 2-ais model and the ast eciters are described in [4] and [3], respectively. All loads are assumed to be the constant impedance type. All machine and system parameters are listed in Appendi. t is assumed that the FACT controllers which have the rating o 00MVA are installed in the middle o the tie lines. The system has one inter-area mode with very poor damping. The parameters o each FACT controller in Fig. 4 and the damping controller in (27) are estimated to increase the damping ratio o inter-area oscillations using the linear analysis and its eect is then veriied by the time-domain simulation. The linear analysis and time-domain simulations algorithms are programmed by MATLAB m-ile code in 60Hz requency base. ince the inverters have very ast operating speed in several tens o milliseconds, the time constant, τ F, is considered within 0.0 τ F 0.05 Fig. 5. A sample 2-area power system.

7 Modeling and Control o V type FACT controllers or ower ystem Dynamic tability using the current 50 seconds. t is assumed that all o the voltage and currents injected by FACT controllers are zero in initial condition Linear analysis 6.2. Without damping controller Fig. 6 show the eigen-value locus o the inter-area oscillations in the case o C installed within 0.0 K F.0. As K F is increased, the requency o the mode is decreased. The damping ratios are reached to the maimum values, and then decreased or a higher value. n Fig. 6, the denoted point on each curve indicates the point having the maimum damping ratio or each time constant. They are listed in Table. ince TATCOM is the reactive power compensator or voltage regulation, it has little eect on the inter-area oscillation. Thereore, the linear analysis or TATCOM without damping controller is omitted. ts integrated parameter, K in Fig. 4(a), is assumed to be 20.0 which is enough high to regulate the voltage. The value is also applied to the shunt inverter o UFC. n the case o UFC being installed, the eigen-value locus o inter-area oscillations is shown in Fig. 7. The gains, K F and K F, have the range, 0.0 K F, K F.0. As K F and K F are increased, the damping ratios Fig. 7. Eigen-value locus o the inter-area oscillation mode controlled by UFC. Table 2. The linear analysis results or UFC. Eigen-Values (λ) K F, Damp. τ K F Real mag. Freq. (Hz) F ratio (ζ) (σ) (ω) K F,K F = o inter-area oscillations are increased. However, since the incremental ratio o damping is decreased and the requency is ecessively low in the high values o gains, they are set on the point having the minimum real part o eigen-values. The denoted point on each curve has the minimum real part o eigen-values. They are summarized in Table 2. Fig. 6. Eigen-value locus o the inter-area oscillation mode controlled by C. Table. The linear analysis results or C. K F τ F Eigen-Value (λ) Damp. Freq. Real mag. ratio (ζ) (Hz) (σ) (ω) K F = With damping controller As described above, the TATCOM has little eect on the inter-area oscillation. The C and UFC have a limit to increase the damping ratio. Thereore, the supplementary controller in (35) is considered to enhance the perormance o FACT controllers. ince the FACT controller is assumed to be installed in the middle o tie lines in Fig. 5, the input, low, is set to the active power low in the tie lines. The time constants in (27) are computed rom the phase leadlag angle based on the ormula described in [3]. The phase lead angle is considered in every 5 within ±30. The wash-out time constant is set to 5.0 second. Fig. 8 shows the locus o inter-area oscillations mode controlled by TATCOM and C with damping controller. The gain, K W, has the range, 0.0 K W.0. n the case o the damping controller equipped in C, the higher K W makes the higher

8 502 Jungsoo ark, Gilsoo Jang, and Kwang M. on damping ratio. However, the damping controller equipped in TATCOM has a limit to increase damping ratio. Each eigen-value having the maimum damping ratio is listed in Tables 3 and 4, and the time constants, τ and τ 2, or each compensation angle are listed in Table 5. As described in Tables 3 and 4, the most eective compensation angles or TATCOM and C are 30 lag and 5 lead, respectively. Those show the dierence o dynamic characteristics between TATCOM and C. Comparing TATCOM and C, it can be conirmed that C is more eective than TATCOM. The result indicates that the series type FACT controller is more proitable to damp inter-area low requency oscillations. Dierent rom TATCOM and C, UFC is composed o the series and the shunt inverters. Additionally, since the series inverter control system is modeled with the real and the reactive parts, as shown in Fig. 4, the three supplementary controllers can be equipped in UFC. Fig. 9 shows the locus o inter-area modes controlled by UFC with damping controllers on each inverter control system. n Table 8, the results are described in detail. As shown in Fig. 9 and Table 6, the positive gain with 5 lead-angle o the damping controller is the most eective or the active power low control system in the series inverter o UFC. On the other hand, the negative grain in 30 lead-angle is the most eective in the reactive power low control system and the shunt inverter control systems. The time constants or each compensation angle and each controlled part are listed in Table 7. Comparing the UFC with the C, the eect o damping controller equipped in the active power control system o the series inverter o UFC is much more eective than the controller equipped in the C. t is because the C can control the active Table 4. The linear analysis results or C with damping controller. Lead angle K W Eigen-Value (λ) Real (σ) mag. (ω) Damp. Ratio (ζ) Freq. (Hz) K W = Table 5. The time constants or lead-lag blocks. Lead TATCOM C angle τ τ 2 τ τ Fig. 8. Eigen-value locus controlled by TATCOM and C with damping controller. Table 3. The linear analysis results or TATCOM with damping controller. Lead angle K W Eigen-Value (λ) Real (σ) mag. (ω) Damp. ratio (ζ) Freq. (Hz) K W = Fig. 9. Eigen-value locus controlled by UFC with damping controller.

9 Modeling and Control o V type FACT controllers or ower ystem Dynamic tability using the current 503 Table 6. The linear analysis results or UFC with damping controller. Eigen-Value (λ) U Lead angle Damp. (ζ) Freq. (Hz) Real (σ) mag. (ω) K W = V V E in Table 7. The parameters or the damping controller in UFC. U Lead angle K W τ τ 2 V V E in power low indirectly, by compensating the reactive power, but the series inverter o UFC can supply the active power and control the active power low directly. Contrarily, the damping controller equipped in the reactive power control system o the series part o UFC is less eective than the C. t is because the C is designed to control the active power low, but the reactive power low control system is modeled to control the reactive power. Comparing with the TATCOM, the eect o damping controller equipped in the shunt inverter control system is more eective than the controller equipped in the TATCOM. Additionally, the phase angles or compensation and the gain are also dierent. t shows that the dynamic characteristic dierence between the TATCOM and UFC Time-domain simulations To veriy the results described above, the timedomain simulations are perormed or each system having dierent FACT controllers with or without damping controllers. The 3 phase ault is applied to the load bus in area shown in Fig. 5 at 0.5 second, and then it is cleared ater 6 cycles. The simulations are continued or 0 seconds. The modiied Euler method is used or numerical integration, and the integration time step is 0.5 cycle TATCOM Fig. 0 shows the time domain simulation results or the TATCOM. The limits in Fig. 4(a) are 0.8 E in.2, in p.u. on 00MVA base. The parameters o TATCOM and damping controller correspond to the row or 30 lag compensation in Tables 3 and 5. The dotted, the dashed, and the solid lines indicate no FACT, the without-, and the withdamping controller cases, respectively. As mentioned above, the TATCOM without damping controller has little eect on the inter-area oscillations. However, the Fig. 0. (a) nter-area oscillations, (b) active power lows on tie-lines, (c) internal voltage o TATCOM, E in, (d) eternal node voltage, V. TATCOM with damping controller can damp the inter-area oscillations and regulate the active power low on tie-lines. They are evident in Fig. 0(a) and 0(b). However, since the inverter with damping controller disturbs the terminal voltage in order to control the active power low in the tie lines, the TATCOM with damping controller has a negative eect on the eternal voltage, V. They are well shown in Figs. 0(c) and 0(d) C Fig. shows the time domain simulation results or C. The limit in Fig. 4(a) is V q 0.05 in p.u. on 00MVA base. The parameters o C are listed in the row or τ F = 0.05 in Table, and the parameters o damping controller are employed rom the row or 5 lead compensation in Tables 4 and 5. The dotted, the dashed, and the solid lines indicate no FACT, the without-, and the with-damping controller cases, respectively. As shown in Table, the C Fig.. (a) nter-area oscillations, (b) Active power lows on tie-lines, (c) series injected voltage magnitudes, V q, (d) damping controller output, U.

10 504 Jungsoo ark, Gilsoo Jang, and Kwang M. on without damping controller can increase the damping ratio rom to , and the damping controller can additionally increase the damping ratio up to The eects are shown on the inter-area oscillations and the active power lows in Fig. (a) and (b). The injected voltage magnitudes, V q, by C are shown in Fig. (c), and the supplementary signal o damping controller is shown in Fig. (d). t is conirmed that the damping controller prevents the C oscillate ecessively and help the compensation actions o C UFC Figs. 2 and 3 show the time-domain simulation results or UFC. The limits in Figs. 4(a) and 4(c) are 0.8 E in.2, -.25 sh.25, V, V 0.05 in p.u. in 00MVA base. The parameters o the row or τ F = 0.05 in Table 2 are used or the simulation, and the parameters o damping controller are listed on the row or V control in Table 7. n Figs. 2 and 3, the dotted, the dashed, and the solid lines indicate the no FACT controller, the without-, and the withdamping controller cases, respectively. As shown in Fig. 2(a), the UFC has a positive eect on the inter-area oscillation, and then the damping is increased by the damping controller and the oscillation is damped out. The active power lows in Fig. 2(b) shows the active power low control eect o UFC. Figs. 3(a) and 3(b) show the injected voltages by the series inverter o UFC. The damping controller helps the series inverter to control the active power low. Fig. 3(c) shows the voltage magnitude, E in, generated by the shunt inverter o UFC. t shows the voltage regulation actions o the shunt inverter in Fig. 3(d). The series injected voltage can make the voltage oscillations on the eternal nodes. However, as shown in Fig. 3(d), the eternal node voltage, V, in the shunt inverter side node is regulated by the shunt inverter. Figs. 3(b) and 3(d) show the simultaneous controllability. Comparing the simulation results or each FACT controller in linear analysis and time-domain simulation, the most eective controller or damping o inter-area oscillations is UFC. The eect o C is less than UFC, and TATCOM has the least eects on the inter-area oscillations. Among these FACT controllers, the popular controllers are TATCOM and UFC. Because TATCOM has the advantage o reactive power compensation, and UFC has controllability or active and reactive power low and voltage regulation. Consequently, many research results have been presented or TATCOM and UFC. C is relatively unnoticed, and there are not many research reports or C. However, since it is more eective than Thyristor Controlled eries Compensator (TCC) which is widely used, it may be able to substitute TCC where the series compensation is needed without the voltage regulation. 7. CONCLUON Fig. 2. (a) nter-area oscillations, (b) active power lows on tie-lines. Fig. 3. The series injected voltages, (a) V and (b) V, (c) internal voltage, E in, and (d) shunt inverter side voltage, V. This paper proposed a current injection model o FACT controllers or power system dynamic stability studies. The method can be easily applied to the linear and the nonlinear analysis, and adopt any kind o FACT controllers regardless o model types. As described above, it can be applied to the linear and nonlinear analysis algorithm or power system dynamics studies. Using the linear analysis, the parameters o each FACT controller are estimated in order to have a positive eect on the inter-area oscillation mode. And, the supplementary controller or damping control is designed to increase the damping ratio o power system. The results are veriied by nonlinear analysis using time-domain simulations. The results accomplished by the proposed methods show the dierences among FACT controllers and their control schemes or the inter-area oscillations in power system. According to the results, UFC is the most eective FACT controller or damping interarea oscillations. And, C is more eective than TATCOM. The analysis results show the

11 Modeling and Control o V type FACT controllers or ower ystem Dynamic tability using the current 505 characteristics o each FACT controller. t shows the eectiveness and actuality o the proposed model. AENDX Each step-up transormer has an impedance o j0.5 p.u. on 900MVA and a 20/230kV base. The nominal transmission system voltage was 230kV. The line length is as shown in Fig. 5. The parameters o the lines in p.u. on 00MVA and a 230kV bases are r = p.u./km, L = 0.00 p.u./km, and b C = p.u./km. Each generator has a rating o 00MVA and 20kV and the parameters in p.u. is as ollows, H = 58.5(G, G2), 55.58(G3, G4), D = 0.0, τ d0 = 8.0, τ q0 = 0.4, d = 0.2, d = 0.033, q = 0.8, and q = The FACT controllers have a rating o 00MVA and the parameters in p.u. are as ollows, = 0.05, t = 0., and Droop = 0.0. REFERENCE [] Y. H. ong and A. T. Johns, Fleible AC Transmission ystems (FACT), The nstitution o Electrical Engineers, London, 999. [2] N. G. Hingorani and L. Gyugyi, Understanding FACT, The nstitute o Electrical and Electronics Engineers, New York, [3] L. Gyugyi, Dynamic compensation o AC transmission lines by solid-state synchronous voltage sources, EEE Trans. on ower Delivery, vol. 9, no. 2, pp , April 994. [4] L. Gyugyi, C. D. chauder,. L. Williams, T. R. Rietman, D. R. Torgerson, and A. Edris, The uniied power low controller: A net approach to power transmission control, EEE Trans. on ower Delivery, vol. 0, no. 2, pp , April 995. [5] L. Gyugyi, tatic synchronous series compensator: A solid-state approach to the series compensation o transmission lines, EEE Trans. on ower Delivery, vol. 2, no., pp , January 997. [6] M. Noroozian, L. Angquist, M. Ghandhari, and G. Andersson, mproving power system dynamics by series-connected FACT devices, EEE Trans. on ower Delivery, vol. 2, no. 4, pp , October 997. [7] H. F. Wang, hillips-heron model o power system installed with TATCOM and applications, EE roc. o Generation, Transmission, Distribution, vol. 46, no. 5, pp , eptember 999. [8] H. F. Wang, A uniied model or the analysis o FACT devices in damping power system oscillations - art : Uniied power low controller, EEE Trans. on ower Delivery, vol. 5, no. 3, pp , July [9] H. Kim and. Kwon, The study o FACT impacts or probabilistic transient stability, J. o Electr. Eng. Technol., vol., no. 2, pp , June [0]. Kim, H. ong, B. Lee, and. Kwon, Enhancement o interace low limit using static synchronous series compensators, J. o Electr. Eng. Technol., vol., no. 3, pp , eptember [] K. M. on and R. H. Lasseter, A Newton-type current injection model o UFC or studying low-requency oscillations, EEE Trans. on ower Delivery, vol. 9, no. 2, pp , April [2] Z. Huang, Y. Ni, C. M. Chen, F. F. Wu,. Chen, and B. Zhang, Application o uniied power low controller in interconnected power systems - modeling, interace, control strategy and case study, EEE Trans. on ower ystems, vol. 5, no. 2, pp , May [3]. Kundur, ower ystem tability and Control, McGraw-Hill, New York, 994. [4]. M. Anderson and A. A. Fouad, ower ystem Control and tability, nstitute o Electrical and Electronics Engineers, U..A., FACT controllers. Jungsoo ark received the B.. and M.. degrees in Electrical Engineering rom Korea University in 2002 and 2004, respectively. Currently, he is a h.d. candidate student with the chool o Electrical Engineering at Korea University. His research interests include power system dynamic stability and control, and Gilsoo Jang received the B.. and M.. degrees in Electrical Engineering rom Korea University in 99 and 994, and the h.d. degree in Electrical Engineering rom owa tate University in 997. Currently, he is a roessor with the chool o Electrical Engineering at Korea University. His research interests include power quality and power system control. Kwang M. on received the B.., M.., and h.d. degrees in Electrical Engineering rom eoul National University in 989, 99, and 996, respectively. Currently, he is a roessor with the Department o Electrical Engineering at Dong-Eui University. His research interests include leible AC transmission systems (FACT) and distributed resources.