Controller Design Using Coefficient Diagram Methods for Matrix Converter Based Unified Power Flow Controllers

Transcription

1 APSAEM Journal of the Japan Socety of Appled Electromagnetcs and Mechancs Vol., No.3 (03) Regular Paper Controller Desgn Usng Coeffcent Dagram Methods for Matrx Converter Based Unfed Power Flow Controllers Tsuyosh HANAMOTO *, Hroak YAMADA *, Farzalah Malah NASHIREN * and Msron NORHISAM * Ths paper presents a new controller desgn method usng the coeffcent dagram method (CDM) for matrx converters (MCs). MCs are able to convert AC to AC power drectly wthout DC lnk capactors. In ths paper MCs are used n unfed power flow controllers (UPFCs), whch s one of the flexble AC transmsson system (FACTS) devces located n the transmsson lne. The CDM s an effectve method for desgnng adequate gans n a PID controller but s not convenent for solvng the complex characterstc polynomals of non-standard systems such as the multplcaton of controller gans or mult-nput-mult-output systems. We propose to combne CDMs wth Partcle Swarm Optmzaton (PSO). PSO s employed for searchng the near optmal dagram. Our proposed method s appled to a smple transmsson lne and the valdty of the proposed method s shown usng MATLAB/Smulnk smulaton. eywords: matrx converter, unfed power factor controller, partcle swarm optmzaton (PSO), coeffcent dagram method (CDM). (Receved: 3 May 0, Revsed: June 03). Introducton Recently, Matrx Converters (MCs) and ther applcatons have been wdely researched and developed because they are able to convert AC to AC power drectly wthout DC lnk capactors, and reverse electrcal energy flow from loads to sources []-[3]. They can realze small szed systems wth mproved relablty. One of the well-known applcatons of MCs s n AC motor drve controls and another s n statc power converson systems. In ths study we apply MCs to Unfed Power Flow Controllers (UPFCs), whch enable the operaton of power transmsson lnes. A UPFC s one of the Flexble AC Transmsson System (FACTS) devces, well known for ts ablty to smultaneously control transmsson system s lne mpedance, voltage magntude and phase angle [4][5]. To obtan a fast response and robustness n a UPFC system, the pq nstantaneous power model s effectve n the desgn of control systems such as for three phase systems, but the axes are coupled to each other so t s not so easy to desgn the controller gans of a UPFC. The Coeffcent Dagram Method (CDM) s one of the effectve methods for desgnng controller gans [6]. The coeffcent dagram, whch s a sngle logarthmc dagram that shows the coeffcents of the characterstc polynomal of the feedback control system on a logarthmc scale, s used for controller desgn. The coeffcent dagram ndcates the stablty, robustness, and Correspondence: T. HANAMOTO, yushu Insttute of Technology. -4 Hbkno, Wakamatsu, takyushu , Japan emal: hanamoto@lfe.kyutech.ac.jp * yushu Insttute of Technology, * Unverst Putra Malaysa Fg.. Model of a matrx converter. control response of the feedback control system. Generally examples of CDMs are proposed for resonant control but there are a few examples that apply to other systems. We propose combnng CDMs and Partcle Swarm Optmzaton (PSO) [7][8] for the controller desgn of a MC based UPFC. PSO s employed to search the property gans of the closed loop controllers because the UPFC control model n ths study contans the multplcaton factors of controller gans and t s dffcult to obtan the dagram usng an algebrac method. Smulaton results usng MATLAB/Smulnk show the effectveness of the proposed method.. System Descrpton. Matrx Converter Based UPFC Fg. shows a confguraton of a matrx converter (MC) system. MC has nne bdrectonal swtches, each consstng of two semconductor devces connected n ant-seres as shown n the fgure. A MC drectly converts the AC nput nto another frequency and magntude output. In general ths converson s acheved 369

2 日本 AEM 学会誌 Vol., No.3 (03) combnng a rectfer and DC-lnk capactor wth an nverter system. It means the DC-lnk capactor has neglgble effect when usng the MC converter. The absence of a DC lnk capactor s one of the man advantages of the MC. To realze the MC system an adequate swtchng pattern needs to be generated as follows. Each swtch forms a swtchng functon k, j,,3, whch can only have two possble s kj kj states: s f the swtch s closed (the devce s turned on) or skj 0 f the swtch s open (the devce s turned off). The nne swtches of the MC can be represented by a 3 x 3 matrx []: s s s3 S s s s3. () s3 s3 s33 The matrx converter topologcal constrants mply that: 3 kj j s for all k,,3. Accordng to Eq. () and ts transpose matrx, the output voltage and nput current can be expressed as follows: T v v Sv v v T v, () A B C T T S T a b c a. (3) Here, the swtchng pattern of the MC has generated a vrtual AC/DC/AC converson process []. In ths study a MC based UPFC [] s adopted for the FACTS devce. FACTS s a system composed of A B b C c statc equpment based on power electroncs technology and controls one or more AC transmsson systems to enhance controllablty and ncrease power transfer capablty [4]. The UPFC s one of the FACTS devces, well known for ts ablty to smultaneously control a transmsson system s lne mpedance, voltage magntude and phase angle [5]. A conventonal UPFC conssts of a statc synchronous compensator (STATCOM) and a statc synchronous seres compensator (SSSC) connected back-to-back at ther DC sdes va a common DC lnk capactor [4]. Here a MC based UPFC s employed to avod the capactor. Fg. (a) shows a smple transmsson lne wth a MC based UPFC, where v S and v R are the sendng-end and recevng-end voltages.. Closed Loop Model of UPFC To analyze the MC based UPFC model, the UPFC s consdered to be an deal controllable voltage source that s connected n seres wth the transmsson lne as shown n Fg. (b). Consderng a symmetrcal and balanced three-phase system, and assumng vs vr, the followng voltage equaton s obtaned usng pq nstantaneous power theory: d p R L p v dt q R L q L v Cp Cq, (4) sn sn( 3) sn( 3) C, (5) 3 cos cos( 3) cos( 3) (a) Transmsson lne wth matrx converter based UPFC (b) Sngle phase model of the deal UPFC Fg.. Confguraton of the matrx converter based UPFC. 370

3 日本 AEM 学会誌 Vol., No.3 (03) p q C a b c vca vcp, CvCb, (6) vcq vcc where, C s the rotatng coordnate transformaton matrx, p, and q are the pq reference frame currents correspondng to the lne current T, v Cp and v Cq are the pq reference frame voltages generated by the UPFC, and s the angle from the v Sa phase. Instantaneous actve power p and reactve power q are defned as follows: p v q v sp p sq p v v. (7) sq q sp q A rotatng reference frame s synchronzed to the v s so that v sp const. and v 0, consequently p and q are sq proportonal to p and q. Ths means that the desred actve power and reactve power are controlled by the pq axes current. Fg. 3 shows the block dagram of the closed loop UPFC system usng PI controllers, where pp, p, pq and q are the proportonal and ntegral controller gans for each axs. From ths dagram the followng equatons are obtaned: * * p v p ( p p ) pp s * p ( v p Lq ) sl R. (8) * * q vq ( q q ) pq s * q ( vq L p ) sl R The control system s a two-nput-two-output system. In ths study we assume q * 0 because * q s related to the power factor whch s generally set to zero. The relatonshp of p to * p s then consdered to be a 4th order sngle-nput-sngle-output (SISO) system as shown n Fg. 4, and the characterstc polynomal D(s), ncludng the controller gans, s as follows: D( s) L s R( pq 4 L(R pp pq ) L( pp p R ( p q ) ppq pqqs pq pq pp q ) s 3 ) R L s. (9) We consder the desgn of the controller gans usng CDM n the followng subsecton..3 Coeffcent Dagram Method CDM s employed to desgn the controller gans for feed-back control systems [6][8]. The coeffcent dagram s a sngle logarthmc dagram that shows the Fg.3 Block dagram of the controller Fg. 4. Block dagram of the controller converted to SISO model. coeffcents for the characterstc polynomal of the feedback control system on a logarthmc scale (as shown n Fg. 5). The coeffcent dagram ndcates the stablty, robustness, and control response of the feedback control system. In general form Eq. (9) s rewrtten as follows: n n 0 D( s) a s a s a a s, (0) n where s the order of the characterstc polynomal and a s the -th coeffcent of the characterstc polynomal. In our case n = 4. To desgn the shape of the dagram, the stablty ndex and equvalent tme constant are ntroduced: a ( n ), () a a a. () a0 Usng these parameters, the coeffcent a s calculated as follows: a 0 a 0,, (3) In CDM, the followng stablty ndces are strongly recommended: n 3,.5. (4) 37

4 日本 AEM 学会誌 Vol., No.3 (03) CDM s effectve for determnng the controller gans of resonance systems, and effectve desgn methods have been proposed for the two-mass resonant systems of the motor drve. In ths study we employ CDM for the UPFC. From Fg. 4 and Eq. (9), the 4th order characterstc equaton s obtaned. It s not easy to fnd the adequate gans because the characterstc polynomal ncludes the multplcaton factor of the gans..4 Partcle Swarm Optmzaton and Evaluaton Method In ths study, we propose to apply PSO to search for the approprate gans of the MC based UPFC system. The PSO s one of the optmzaton technques and a type of evolutonary computaton technque [7][8]. All solutons n the PSO can be represented as a partcle n a swarm. Each partcle (agent) has a poston and velocty vector and each poston coordnate represents a parameter value. The PSO whch uses the concept of velocty descrbed n Eqs. (5) and (6) can easly accommodate the range of ntal parameters: v k v k c rand() pbest x k k c rand() gbest x k k k x v, (5) x, (6) where, x s the -th partcle, v s the velocty for partcle, pbest means the prevous best poston of the -th partcle, gbest s the best partcle n the populaton, c and c are the acceleraton constants, rand() s a random functon and s the nerta weght factor descrbed n Eq. (7) where k s the generaton. Selectng approprate values for, c and c enables the partcle to move toward the optmum poston: max k. (7) max k max mn Table Parameters of PSO Parameters Specfcaton Number of teraton 000 Swarm sze 30 Dmenson 4 c,c.0 max, mn 0.9, 0.4 Table Smulaton parameters rated power 3000VA rated voltage 00Vrms (phase-to-ground) rated current 0Arms frequency 60Hz lne resstance 0.(0.0p.u.) lne nductance 0mH (0.37p.u.) Table 3 Controller gans searched by PSO pp pq p q Table 4 Load condton tme Actve Power (p.u.) Reactve power(p.u.) In ths study we defne an evaluaton functon F ev n Eq. (8) whch s employed to obtan the suffcent controller gans estmated by PSO: F ev, (8) W f W f where W and W are the weght factor for each fttng functon. Here we decde W s 0 tmes as large as W to obtan the adequate dagram by tral and error. The fttng functons f to f are estmated usng the theory of CDM as follows: (a) The fttng functon to obtan the desred tme constant: f, (9) ref est where ref s the reference of the equvalent tme constant and est s a search result of the PSO. Fg. 5. Search results of CDM usng PSO. (b) The fttng functon to obtan the standard stablty ndex: f 3, (0) _ ref _ est where _ref s the standard stablty ndex and _est s a search result of the stablty ndex. The parameters of the PSO are shown n Table, where dmenson = 4 means the searchng controller gans are pp, pq, p and q. Intally random numbers 37

5 日本 AEM 学会誌 Vol., No.3 (03) are set to the gans and the coeffcents calculated usng Eq. (9), and the PSO algorthm then starts to search for the property gan. After several hundred teratons, the evaluaton functon becomes F ev > n every calculaton, so we set the number of teratons to 000. Fg. 5 shows the coeffcent dagram usng the search result of the PSO when ref = In ths fgure, the x-axs ndcates the order of the coeffcent, the y- axs shows the coeffcent on a logarthmc scale (left scale), and the stablty ndex (rght scale). Shown n the fgure, t s obvous that recommended stablty ndex defned n Eq. (4) s obtaned. 3. Smulaton Results Smulaton parameters are shown n Table. In the system the swtchng frequency s set to khz. The wndng rato of the shunt transformer and the seres transformer are smply set to :. Table 3 shows the controller gans for dfferent equvalent tme constants ref. As shown n the table the controller gans ncrease when a short ref s selected, whch means the system response can be desgned by ref. We select large gans n the smulaton to avod the nterference of the other axs because the proposed controller does not have a de-couplng controller. Fg. 6 shows the smulaton results when = usng MATLAB/Smulnk wth the SmPowerSys tool box. To confrm the valdty of the proposed method no load s connected to the transmsson lne and the power of Bus s controlled. In ths fgure the reference of nstantaneous actve power p * s changed from 0. p.u. to 0.5 p.u. at t = 0. s and the reference of nstantaneous reactve power q * s changed from 0 p.u. to -0. p.u. at t = 0.5 s. The upper fgure shows the nstantaneous power and lower fgure shows the phase current T of the transmsson lne. From these results a fast response wthout steady state error s acheved and the effect of cross-term s hardly evdent even when only smple PI controllers are employed. The step response of p * and q * are shown n Fg. 7, where p * s changed from 0. p.u to 0.5 p.u at t = 0.0 s and 0.5 p.u to 0.3 p.u at t = 0.0 s. Correspondngly, q * s changed from 0.0 p.u to 0. p.u at t = 0.03 s and 0.3 p.u to -0. p.u at t = 0.04 s. Although the voltage references v p * and v q * reach ther lmts n the transent state, fast and smooth responses are acheved for both nstantaneous powers p and q. Fg. 8 shows the phase current when the load s changed to demonstrate the robustness of the system. Here p * and q * are kept at constant values, p * = 0. p.u. and q * = 0.0 p.u.. The load s connected to the transmsson lne as shown n Fg. and the load condton changed as descrbed n Table 3. Here the nstantaneous power of Bus 3 s controlled and L s then kept n a steady state, on the other sde the ampltude and phase of R changes as affected by the load. 4. Conclusons Fg. 6. Step response. Fg. 7. Step response of the system. Fg. 8. Current waveform when the load s changed. 373

6 日本 AEM 学会誌 Vol., No.3 (03) In ths study, we proposed a control desgn method usng the matrx converter based UPFC. The proposed control system s modeled by a SISO system because we assume the reference for nstantaneous reactve power s zero. To combne the CDM and PSO, adequate gans can be obtaned for a 4th order system. The smulaton results showed the valdty of the proposed method. Acknowledgment Ths work was supported by JSPS AENHI Grant Number References [] J. Itoh, I. Sato, A. Odaka et al, A Control Method for the Matrx Converter Based on Vrtual AC/DC/AC Converson Usng Carrer Comparson Method, Electrcal Engneerng n Japan, Vol. 5, No. 3, pp , 005. [] J. Montero, J. F. Slva, S. F. Pnto and J. Palma, Matrx Converter-Based Unfed Power-Flow Controllers: Advanced Drect Power Control Method, IEEE Trans. Power Delvery, Vol. 6, No., pp , 0. [3] A. Aras, C. A. Slva, G. M. Asher et al, Use of a Matrx Converter to Enhance the Sensorless Control of a Surface-Mount Permanent-Magnet AC Motor at Zero and Low Frequency, IEEE Trans. Ind. Elec., Vol. 53, No., pp , 006. [4] A-A. Edrs et al., Proposed Terms and Defntons for Flexble AC Transmsson System(FACTS), IEEE Trans. Power Delvery, Vol., No. 4, pp , 997. [5] N. F. Malah, S. M. Bash, I. Ars and N. Marun, Effect of UPFC s Seres Converter Phase Shft on Output Voltage and Current s Total Harmoncs Dstorton, Proc. APSAEM00, pp , 00. [6] S. Manabe, Coeffcent Dagram Method, Proc. the 4 th IFAC Symposum on Automatc Control n Aerospace, pp. 99-0, 998. [7] J. enney and R. Eberhart, Partcle Swarm Optmzaton, Proc. 995 IEEE Int. Conf. Neural Networks, pp , 995. [8] T. Hanamoto, M. Takenouch, H. Ikeda, Vbraton Suppresson Control of 3-mass Resonance System Usng Partcle Swarm Optmzaton for Desgn of Coeffcent Dagram Method, J. Jpn. Soc. Appl. Electromag. and Mech., Vol. 9 Supplement, pp. S6-S0,