New Control Strategies for a Two-Leg Four-Switch STATCOM

New Control Strategies for a wo-leg Four-Switch SACOM sao-sung Ma, Meber, IEEE Abstract oltage control and fast reactive power copensation are two iportant functions concerning FACS application in the odern power systes. It has been well accepted that the static synchronous copensator (SACOM) is the ost versatile and powerful FACS device that can provide effective eans for controlling reactive power flow and iproving the voltage stability of power networks. However, the SACOM circuitry has coplex and coupled syste dynaics which reuire advanced controllers to achieve satisfactory perforances. his paper presents the design of a space vector pulse width odulated (SPWM) two-leg four-switch SACOM to provide satisfactory perforances in perforing various reactive power flow control functions during steady-state and transient operations of power systes. For coparative purposes, two topologies, i.e., -leg 4-switch (L-4S) and -leg 6-switch (L-6S) based SACOM are investigated in this study. Siulation studies carried out in the Matlab/Siulink environent are firstly described. ypical results are then presented to verify the feasibility of the L-4S SACOM and the effectiveness of the proposed controllers. Index ers power syste voltage control, flexible ac transission systes (FACS), static synchronous copensator (SACOM), space vector pulse width odulation W I. INRODUCION IH the trend of deregulating power industry and installing ore distributed generators, the future power syste needs to provide sufficient, stable, secure, econoic, and high-uality electric power to various load centers. It is envisaged that flexible ac transission systes (FACS) devices or controllers are going to play a critical role in operating the new type of power systes under such a coplex operating environent []-[]. he basic concept drawn fro the Flexible AC ransission Systes (FACS) terinology eerges as a reedy to release the extreely transission syste tension. It needs the aid of odern power electronics and advanced control techniues to successfully replace the conventional echanical controlled apparatuses in systes. By doing so, FACS technology has been expected to offer two ain advantages: () to bring the transfer capability of transission line approaching its theral liit without violating the stability criteria and () to re-assign power flows at will and on a real-tie basis so as to facilitate an ideal electricity arket. Besides, FACS can also enhance the stability of the power syste with its fast control characteristics Manuscript received Deceber 8, ; revised January,. his work was supported in part by the National Science Council of aiwan, R.O.C. through: NSC 99--E-9-8. sao-sung Ma is with the Dept. of Electrical Engineering, CEECS, National United University, aiwan, R.O.C. (phone: +886-7-869; fax: +886-7-7887; e-ail: tonya@nuu.edu.tw; tonya@ieee.org). and continuous copensating capability. Of the known FACS devices, the static synchronous copensator (SACOM) being a new generation of reactive power copensating devices has been widely used in various power syste control []-[]. he hardware of a SACOM is siilar to the shunt branch of the Unified Power Flow Controller (UPFC) and can be controlled to provide concurrent real and reactive copensations with an external electric energy source adding to the bus. In the literature, a nuber of feasible hardware configurations have been proposed for the SACOM to perfor various reactive power and voltage control functions in power systes ebedded with distributed generators; however, ost of the are designed on a -leg 6-switch (L-6S) structure operated either by SPWM or ulti-odule and ulti-level techniues []-[5]. o achieve a cost-effective design without sacrificing the control perforances soe possible topologies with advanced controllers with fast-response features are still call for investigations. his paper presents the design of a space vector pulse width odulated (SPWM) two-leg four-switch (L-4S) SACOM to provide satisfactory perforances in perforing various reactive power flow control functions during steady-state and transient operations of power systes. Coprehensive siulation studies carried out in the Matlab/Siulink environent and results of various power flow control exaples are presented to show the successful design of the L-4S SACOM and the effectiveness of the proposed control strategy. II. SACOM PRINCIPLES AND IS CONROLLERS A. SACOM Review In a conventional SACOM syste, the internal phase inverter norally constructed by a -leg and 6-switch configuration provides the ain control functions via connecting its output voltage with a controllable agnitude and phase angle in shunt with the copensated power syste through a transforer. In this paper, a siple three-phase converter constituted by -leg and 4-switch is adopted to perfor both the reactive power and voltage copensation tasks [6]-[8]. his arrangeent can provide an alternative topology for SACOM with lower syste cost; however, the related controllers ust be properly designed to achieve a satisfactory perforance. Fig. shows a siple test power syste with the proposed -leg and 4-switch SACOM configuration. As shown in Fig., the SACOM is connected to a utility distribution syste at the load terinal. he utility syste is represented by a three-phase voltage source behind series RL eleents in each phase. he load is a three-phase, passive RL load. In a SACOM syste, the voltage acts essentially as a controllable synchronous ac voltage source. In addition to the voltage regulator, the

three-phase inverter can independently generate or absorb controllable reactive power as desired and thereby provides independent shunt reactive copensation for the syste. It is iportant to note that if a source can be added to the SACOM the control of real and reactive power on the connected point of transission line can be achieved by adjusting the voltage with an appropriate agnitude and angle of the inverter. In this study, the output reactive power of a SACOM is controlled by the agnitude of -axis current coponent of the proposed two-leg four-switch (L-4S) SACOM. Fig.. Scheatic representation of the test power syste with a -leg and 4-switch SACOM. B. SACOM Matheatical Model Fro Fig., the ac-side voltage euations of the SACOM can be expressed as: v = R i + L p( i ) + v () abcs S abcs s abcs abcl he P in the above euation is a derivative operator. In (), RS = diag{ Rs, Rs, Rs} L = diag{ L, L, L }, S s s s, and [ ] [ ] [ ] = () abcs as bs cs i i i i = () abcs as bs cs abcl al bl cl = (4) Considering only the fundaental coponents of the switching functions of the converter switches, the SACOM terinal voltages can be expressed as follows: sin θ( t) vas() t vbs() t π = Av sin( θ () t ) (5) vcs() t π sin( θ () t + ) where, θ ()= t ωt +. A and are respectively the aplitude and angle odulation indices. ω is the syste freuency, and v is the bus voltage. Since the dynaic odel of an electrical power syste is traditionally developed in a d- frae, it is desirable to obtain the odel of SACOM in the utility d- frae. o transfer the abc variables to a d- frae, a transforation atrix is selected such that the voltage and current coponents of SACOM are proportional to its real and reactive power coponents respectively. hus, the control of each current coponent regulating the corresponding power coponents as desired. he SACOM variables in the abc frae can be transferred to the d- frae by Clark transforation. f dos = Kf (6) abcs he transforation atrix K is defined as π π cos θs cos θs cos θs + π π K = sin θs sin θs sin θs + Substituting abc variables fro () to (5) into (6), the voltage euations (8) of the SACOM in the d- frae are obtained using (7): ( ) ( ) sin Av cos = Ri S dos + Lsp( idos ) + ω - Li s dos + v l he l is the aplitude of load terinal voltage. For the-side circuit of the SACOM, we have v p = C ( i ) and the -side current can be atheatically expressed as π ias sin ( θ ) + ibs sin θ i = A () π + ics sin θ + Using abc variables fro () and the transforation euation (6), the d- odel of the circuit can be obtained as (). v sin ( ) A i s p = () C + ids cos( ) Under steady-state and balanced three phase conditions, the three phase active power and reactive power of the SACOM ay be expressed in ters of d- uantities as () and (), where the v and i are the peak values of phase voltage and phase current respectively, and θv and θi are the phase angles for phase voltage va and phase current ia respectively. (7) (8) (9) P = v i cos ( θv θi) = ( vi + vdid) () = v i sin ( θv θi) = ( vi vdid) ()

C. oltage SPWM Controllers for the oltage Source Inverter he odeling steps of a space vector pulse width odulation (SPWM) algorith are described in this subsection. According to the syste setup shown in Fig. the switching status is represented by binary variables to 4, which are set to when the switch is closed and when it is open. In addition, the switches in one inverter branch are controlled copleentary, therefore: 4 + = (4) + = (5) Cobinations of switching S-S4 result in 4 general space vectors - 4 as shown in Fig.4. he coponents β of the voltage vectors are gained fro abc voltages by using Clark s transforation. Let ref represents the reference voltage being synthesized by the L-4S inverter within a switching period of length. According to the space vector techniue, the desired voltage can be atheatically expressed as: = + + + (8) ref β β 4 4 Fig. 4. oltage vectors of the SPWM in first section. Fro Fig.4, and ref ref in first section can be expressed as ref = + = + ββ (9) D. Modelling of SPWM Control Patterns Calculating the Section Data of ref : Fig.. opology structure of three-phase voltage source inverter he cobinations of the states of the switches originate four different vectors and the related paraeters in the β plane are given in able and. hese vectors are phase shifted of π/ fro each other. Using the above vector definitions one ay split the β plane into four (I to I) sectors as shown in Fig.. (,) Using and β, the angle and the corresponding section data of the desired voltage signal can be obtained. β θ = tan () Calculating X, Y : X, Y can be calculated as follows. Section(): 7~ degrees. Fro (6), (7) and (9), and β can be calculated as expressed in (). (,) (,) =- β, = a () 4 (,) Fig.. Basic voltage space vectors for L-4S inverter =, β = () Also, the and can be obtained as follows. Fro Fig., the following relations can be derived. =, = =, = 4 Conseuently, the voltage coponents are given by = ( - ) ( ) (6) = β + (7) =, = () β X = β, Y = (4) With the siilar ethod, the and in other sections can be readily derived.

Switch Seuence: In noral operations, a triangle wave with proper freuency is used to copare with aon, bon and con. he aplitude of the triangle wave represents odulated period while the freuency of the triangle wave can be chosen based on the capability of IGB used. able. he and in all sections S 7 - S - 9 S 9-8 S4 8-7 -X -X y -y -Y Y x x o ake an easier representation of the PWM operations, two variables CMPR and CMPR can be used in section I to I as shown in able. through a transission lines. he SACOM is placed at the load bus to support the voltage. his siple syste is chosen in order to evaluate the power flow control perforances of the proposed new SACOM configurations with two basic control strategies, i.e. reactive power and voltage regulations. he detailed control structure for the proposed SACOM and the related syste paraeters are shown in Fig. 6. In Fig. 6, the control schee shown in Fig. 5 (PI and decoupled controllers) is used to perfor the P& power flow control functions. Fig. 7 to 9 show a set of typical siulation results, in which the control results concerning () reactive power regulations and () PCC voltage regulations under load disturbances (two-steps in load changes) with the proposed SPWM ethods are presented. able. he coparator values in various sections Sections S S S S4 alues 7 - - 9 9-8 8-7 CMPR con bon aon bon CMPR bon con bon aon III. IMPLEMENAION OF SACOM P- CONROLLERS As entioned previously, in a noral operation two sets of separate controllers are used for controlling the SACOM, one for the real power (or euivalently the voltage) and the other for reactive power regulation. As well known, control of the SACOM active and reactive currents can be achieved by respectively varying the active and reactive coponents of the internal inverter voltage. Fig. 5 shows the control syste block diagra of the proposed P- controllers and the SACOM circuits. Fig. 6. he overall control syste and paraeters.5 x 7 e i ds v ds.5 D ωl s AR -.5 - D ωl s PCC PCC e i s v s -.5....4.5.6.7.8.9 Fig. 7. (a) Reactive power regulations (two-steps in coand changes) with the proposed SPWM controller. Fig. 5. he control syste block diagra of the proposed P- controllers.5 x 7 P I. ES POWER SYSEMS AND RESULS For identifying and controlling the dynaics of the power syste and the -leg 4-switch SACOM, the single-achine infinite-bus (SMIB) power syste as shown in Fig. is siulated in a Matlab/Siulink environent. Siulink odel tool is a coercial grade transient siulator of electric networks with the capability of odeling coplex power electronics, controls and the nonlinear power network. he power syste shown in Fig. coprises a voltage source (a synchronous generator with an autoatic voltage regulator (AR) is used), which is connected to a load bus W, AR.5.5 -.5 - -.5 - -.5....4.5.6.7.8.9 Fig. 7. (b) he effects of reactive power regulations (two-steps in coand changes) on the real power (the blue line) with the proposed SPWM controller.

.5 x 4.5 (A).5 ( I ) ( II ) -Phase oltage.5 -.5 (pu) - -.5 - -.5....4.5.6.7.8.9.95..4.6.8 Fig. 7. (c) he terinal voltages of the SACOM in reactive power regulations (two-steps in coand changes) with the proposed SPWM controller..5 (B).5..5 DC() 9.95 9.9 9.85 DC oltage on the two capacitors 9.8....4.5.6.7.8.9 Fig. 7. (d) he voltage of the SACOM in reactive power regulations (two-steps in coand changes) with the proposed SPWM controller. (pu) ( I ) ( II ).95....4.5.6.7.8.9 Fig. 9. (a) he PCC oltage regulation results (two-steps in load changes) with SPWM controller: (A) PCC oltage uncontrolled; (B) PCC oltage with the L-4S SACOM in operation..5 x 7.5 P.5.5 P (A) W, AR.5 -.5 AR(pu) -.5 - -.5 - - -.5....4.5.6.7.8.9 Fig. 8. (a) he P- regulation results (two-steps in P- coand changes) with the proposed SPWM controller..5 x 4.5 -.5....4.5.6.7.8.9 Fig. 9. (b) he corresponding P- results in PCC voltage regulations (two-steps in load changes..5.5 ( I ) ( II ) (A) -Phase oltage.5 -.5 - (pu) -.5 - -.5 - -.5....4.5.6.7.8.9 Fig. 8. (b) he terinal voltages of the SACOM in P- regulations (two-steps in P- coand changes) with the proposed SPWM controller. -.5 -..4.6.8 Fig. 9. (c) he corresponding terinal voltages of the SACOM in PCC voltage regulations (two-steps in load changes).

Mag (% of Fundaental) 5 5 Fundaental (6Hz) =.798, HD= 4.% 4 6 8 Freuency (Hz) Fig. 9. (d) he easured haronic spectra of the SACOM phase-a current. Pu Pu.5.5 -.5 - -.5 ( I ) -.5..5.4.5.5 -.5 - -.5 ( II ) (B) I-SACOM -Grid -SACOM I-SACOM -Grid -SACOM -.65.7.75.8 Fig. 9. (e) he terinal voltages and currents of the SACOM. (I) Inductive operation and (II) Capacitive operation.. CONCLUSION his paper has presented a new control ethod based on SM switching strategy for the proposed hardware siplified L-4S SACOM. he ain feature of the proposed circuit and switching strategy is that it can fast odify the switching patterns of the internal power electronic switches of the proposed SACOM to achieve the desired voltage with only thirds of the nuber of power devices reuired in the conventional design. he paper has also developed a detailed dynaic odel of the proposed L-4S SACOM. he odel has been verified with a practical design case in which the basic P- power flow control functions in a SACOM are tested. Feasibility and overall perforance of the new SACOM syste, including the siplified power circuitry and control subsystes have been verified via coprehensive digital tie-doain siulations. REFERENCES [] X. gping and S. Bhattacharya, Perforance iproved during syste fault of angle controlled SACOM by current control, IEEE Power and Energy Society General Meeting, pp. 8, -4 July 8. [] K. Li, J. Liu, Z. Wang and B. Wei, Strategies and Operating Point Optiization of SACOM Control for oltage Unbalance Mitigation in hree-phase hree-wire Systes, IEEE rans. PD, ol., Issue, pp. 4 4, Jan. 7. [] X. Zhengping and S. Bhattacharya, SACOM Control and Operation with Series Connected ransforer Based 48-pulse SC, IEEE Industrial Electronics Conference, pp. 74 79, Nov. 7. [4] S. iang, L. Wenhua, Y. Zhichang, Multilevel Optial Modulation and Dynaic Control Strategies for SACOMs Using Cascaded Multilevel Inverters, IEEE ransactions on Power Delivery, vol, no, pp.97 946, July 7. [5] H. Xie, L. Anguist, H.-P. Nee, Coparison of oltage and Flux Modulation Schees of StatCo Regarding ransforer Saturation During Fault Recovery, IEEE ransactions on Power Systes, vol, no 4, pp.65 66, Nov. 8. [6] R. Sternberger, D. Jovcic, heoretical Fraework for Miniizing Converter Losses and Haronics in a Multilevel SACOM, IEEE ransactions on Power Delivery, vol, no 4, pp.76 84, Oct. 8. [7] G. Zhao, J. Liu and Z. Wang, An analysis on the influence of interface inductor to SACOM syste with phase-shift control and corresponding design considerations, IEEE Conference on Power Electronics and Motion Control, pp.9 44, May 9. [8] S. Mohagheghi, G.K. enayagaoorthy, S. Rajagopalan, R.G. Harley, Hardware Ipleentation of a Madani Fuzzy Logic Controller for a Static Copensator in a Multiachine Power Syste, IEEE ransactions on Industry Applications, vol 45, no 4, pp.55 544, July-aug. 9. [9] N. oraphonpiput and S. Chatratana, SACOM Analysis and Controller Design for Power Syste oltage Regulation, IEEE/PES 5 ransission and Distribution Conference and Exhibition, pp. 6, July 5. []. Spitsa, A. Alexandrovitz, E. Zeheb, Design of a Robust State Feedback Controller for a SACOM Using a Zero Set Concept, IEEE ransactions on Power Delivery, vol 5, no, pp.456 467, Jan.. [] B. Singh, S.S. Murthy, S. Gupta, SACOM-Based oltage Regulator for Self-Excited Induction Generator Feeding Nonlinear Loads, IEEE ransactions on Industrial Electronics, vol 5, no 5, pp.47 45, Oct. 6. [] B. Singh, S.S. Murthy, S. Gupta, Analysis and design of SACOM-based voltage regulator for self-excited induction generators, IEEE ransaction on Energy Conversion, vol 9, no 4, pp.78 79, Dec. 4. []. Wei, R.G. Harley, G.K. enayagaoorthy, Coordinated Reactive Power Control of a Large Wind Far and a SACOM Using Heuristic Dynaic Prograing, IEEE ransactions on Energy Conversion, vol 4, no, pp.49 5, June 9. [4] H. Xie, L. Anguist, H.-P. Nee, Design and Analysis of a Controller for a Converter Interface Interconnecting an Energy Storage With the Dc Link of a SC, IEEE ransactions on Power Systes, accepted for future publication, pp. 9, 9. [5] H. Gaztanaga, I. Etxeberria-Otadui, D. Ocnasu, S. Bacha, Real-ie Analysis of the ransient Response Iproveent of Fixed-Speed Wind Fars by Using a Reduced-Scale SACOM Prototype, IEEE ransactions on Power Systes, vol, no, pp.658 666, May 7. [6] C.-H. Liu, Y.-Y. Hsu, Design of a Self-uning PI Controller for a SACOM Using Particle Swar Optiization, IEEE ransactions on Industrial Electronics, accepted for future publication, pp., 9. [7] S. Rahizadeh, M. avakoli Bina, A. Houshand iki, Steady State Model of SACOM and SSSC Using Averaging echniue, IREE, Part-B, vol. 4. n. 6, pp. 9-4, 9. [8] G. Shahgholian, Developent of State Space Model and Control of the SACOM for Iproveent of Daping in a Single-Machine Infinite-Bus, IREE, Part-B, vol. 4. n. 6, pp. 67-75, 9.