Stability Analysis of Inverter for Renewable Energy

Transcription

1 vance n Power an Energy Sytem Stablty naly of nverter for Renewable Energy TOORU MOR, JUNCH R Electrcal Engneerng an Electronc ogakun Unverty Nh-hnjuku, Shnjuku-ku, Tokyo JPN cm1134@n.kogakun.ac.jp TSUMENG MSHRO Tohba Corporaton Shbaura, Mnato-ku, Tokyo, JPN btract : Dc power ource uch a photovoltac cell an fuel cell nee nverter to connect nto an extng electrc ytem. The performance of the nverter etermne by the control, then the nverter control mportant. The utable gan n the control mut be etermne ytematcally. Th paper propoe a Boe analy approach for etermnaton of nverter control parameter for renewable energy. The reult of frequency repone analy compare wth TPDraw mulaton. ey-wor : nverter, Control, Stablty, Lnearzaton, Frequency Repone naly, TP Draw 1 ntroucton Dtrbute Generator uch a photovoltac power generaton have been aopte n all over the worl, an recently large capacty calle a a mega-olar ha been contructe. Power of the photovoltac power generaton prouce n a rect current, o t mut be change to an alternatng current through an nverter to upply electrcty to a loa. f the nverter capacty large compare wth hort crcut power level of ac ytem, there poblty of ntablty n the nverter operaton. The tablty of the nverter epen on control charactertc alo [1]. Th paper propoe a evaluaton metho for tablty check bae on conventonal Boe analy of frequency repone technology. We aume a full brge nverter an lnearzaton apple for equaton repreentng the nverter an ac ytem. We have been evelopng th tool [2][3][4], we report here that frequency repone compare wth TPDraw mulaton an goo agreement n vewpont tablty obtane. The capacty of nverter an hort crcut power level aume 1MW an 5 MW repectvely n the tuy. Lnearzaton of equaton ecrbe fully n the paper. Frequency repone between Boe analy an TPDraw are compare each other n cale of gan an phae angle. n th paper, analy reult of not only actve power control but alo reactve power control are reporte. 2 nverter Crcut The nverter of oltage Source Converter (SC) wth Pule Wth Moulaton (PWM) treate for the tuy [5]. The nverter connecte to a trbuton network aume. However, there are many type of c power ource, photovoltac cell, fuel cell, an battery, a contant c voltage ource aume here for mplcty. SCR 5M 6.6k 5Hz Tranformer 1M 5%z ON/OFF Pule Control crcut 1MW SC Fg.1 nverter moel 4 c The nverter moel for the applcaton hown n Fg.1 whch cont of a voltage ource of 4 c, an nverter of SC wth 1 MW capacty, a 6.6k/2 tranformer of 1 M ratng wth 5 % SBN:

2 vance n Power an Energy Sytem mpeance, an a et of control. The nverter connecte to 6.6 k ac network whch ha a hort crcut capacty of 5 M. The nverter 6-arm full brge confguraton an a pule wth moulaton wth 2 khz carrer wave apple. t aume that the control conte of a contant actve power control an a contant reactve power control. The Eq.(6) ve nto a real part an an magnary part. v v R X p X p (7) v q v B Bq q R X p X p (8 ) Lnearzaton applyng a +Δ a at an operaton pont carre out an relatonhp wth mall perturbe value, Δ, are obtane a hown n Fg. 3. Where p=/ω apple. q 3 Lnearzaton 3.1 c-ytem mple ac-ytem moel conte by a reter an a reactor hown n Fg.2. Δ R X X Δ B R Fg.2 c-ytem The equaton of relaton n th moel Eq.(1). n Eq.(1), the voltage an the current are repreente a follow wth rotatng angle θ. B ( v ( R j jv q X q ) e rotatng on t,. Eq.(2) an Eq.(3) are ubttute nto Eq.(1). The equaton can be j rewrtten on the ax plane by elmnatng e. R jq X jq t X jq j (4 ) t Followng expreon ubttute nto Eq.(4) p t Eq.(1) become Eq.(5), an Eq.(5) can be erve nto a -q ax flame a follow. ) e t j j X v jv v jv q B (1) (2) (3) Bq B R X v jvq v B jvbq R jq X jq p jp R jr X p j p j R R jr X q q j X p X p p jx ( p jp ) (5) p jx p R X p X p (6) q q q q q q p p X q p The noe B aume a an nfnte bu an the noe a bu that the nverter tranformer connecte. 3.2 nverter The nverter moel hown n Fg. 4. The voltage generate by the nverter Eq.(9), where C a control factor an actual value of the econary e lne voltage of the tranformer. [ k ] [ PU ].612 E C (9) The complex voltage of the nverter Eq.(1),(11) Δ q q Fg.3 Lnearze moel of ac-ytem j [ PU ] [ PU ] q co n R (1) (11) X X Fg.4 nverter moel Δ q E SBN:

3 vance n Power an Energy Sytem Where a phae angle of an a phae angle of. Lnearzaton applyng +Δ at an operaton pont carre out a follow. co co co co The perturbe value From Eq.(9) Eq.(13) ubttute for Eq.(12), The perturbe value apple. co n n n n n n n a mlar manner lnearze relatonhp of the nverter obtane a hown n Fg.5, where E a c voltage evaton, an C are control gnal evaton. an ac voltage phae evaton. E Fg.5 Lnearze moel of nverter n n (12) co E E C C E C.612 E C.612E C.612E C.612 E C.612 E C.612 E C.612 E co.612 E C n q.612 E n.612 E C co q C co.612 E C n C q.612c n E (13).612 E C co C.612C n( ) E.612EC co( ).612E n( ).612EC co( ).612C co( ).612EC n( ).612E co( ).612EC n( ) (14) (15) C 4 Confguraton of control The confguraton of the control hown n Fg.6. t ha an actve power (P) control, a reactve power (Q) control, a PQ etector, an a voltage phae etector. Output of P an Q control are change to a phae angle gnal an an ampltue gnal of the nverter voltage through a gnal converon. Three phae voltage gnal are generate by the gnal converon output an the phae gnal β of the ac voltage. Three phae voltage gnal are fe to the PWM logc to get on/off pule gnal for wtche. P control Q control oltage phae etecton P,Q etecton P Q Sgnal conver on amp 3 phae voltage gnal Fg.6 Control block The P an Q control are hown n Fg.7. gnal P correpon to an angle an a gnal Q correpon to an ampltue of the nverter output voltage. PP an QP are proportonal gan, an P an Q are ntegral gan. Thee control block except contant reference value are combne wth lnearze moel of ac ytem an nverter. P et Q et P ref Q ref PP QP Fg.7 P an Q control Carrer wave The lnearze moel of Fg.1 analyze by comparng Boe analy tool an TPDraw mulaton to confrm equvalency [6][7]. 5 Frequency Repone naly The Frequency repone analy tool for lnearze moel evelope by author repreentng on a preaheet program nclung a power flow calculaton to get the operaton pont an a complex P Q P W M P Q SBN:

4 vance n Power an Energy Sytem matrx calculaton for each frequency. n open loop an a cloe loop repone can be calculate n th tool. Two cae are hown n th tuy. 5.1 P control loop The open loop charactertc on the actve power control loop calculate. The control gan are lte n Table1. Gan an phae agram of the open loop are hown n Fg.8 an margn are lte n Table2. Table 1. Gan PP.1 P 1 QP.1 Q 1 Table 2. Reult of frequency repone analy Gan croover 1.75 Phae croover 5.37 Gan margn [B] Phae margn [eg] -1.9 G [B] Fg.8 (a) Gan agram of the open loop Phae [eg] Fg.8 (b) Phae agram of the open loop G [B] Fg.9 (a) Gan agram of the cloe loop Phae [eg] Fg.9 (b) Phae agram of the cloe loop 5.2 Q control loop Parameter of Q control are et to hgher value than the gan of P control. The reaon why to get relatvely rap repone of reactve power control. Calculaton reult of the open loop are hown n Fg.1. n aton, the calculaton reult of the cloe loop are hown n Fg.11. Table 3. Gan PP.1 P 1 QP 17 Q 5 Table 4. Reult of frequency repone analy Gan croover 26.4 Phae croover 4.41 Gan margn [B] Phae margn [eg] G [B] From Table2, th cae table becaue the gan croover frequency le than the phae croover frequency, an gan margn negatve value. The actve power control cloe loop calculate by the ame evelope program hown n Fg.9. Fg.1 (a) Gan agram of the open loop SBN:

5 vance n Power an Energy Sytem Phae [eg] The obtane gan an phae are cloe to the marke pont n Fg.11. Q[pu] Fg.1 (b) Phae agram of the open loop G [B] [] 1. (fle nverter-1mw-moel-qcloe.pl4; x-var t) t: QREF t: QPU Q[pu] (a) Repone t[] Reference value Fg. 11 (a) Gan agram of the cloe loop Phae [eg] [].82 (fle nverter-1mw-moel-qcloe.pl4; x-var t) t: QREF t: QPU (b) Fg.12 TPDraw mulaton The comparon of cloe-loop of the actve power controller hown n Fg.13. G [B] TP t[] Fg.11 (b) Phae agram of the cloe loop From Table4, th cae table becaue the gan croover frequency le than the phae croover frequency, an gan margn negatve value. 6 Confrmaton of Frequency Repone naly Reult The TPDraw mulaton are carre out an are compare wth the frequency repone analy. n example calculaton by TPDraw electe n marke conton n Fg.11 that correpon to 3Hz. n the TPDraw calculaton, reactve power reference value of pu apple an atonally a nuoal gnal of.5 pu ampltue of 3 Hz upermpoe. Fg.12(a) how the reactve power reference value an the repone of the nverter, an enlarge reult are hown n Fg.12(b). Fourer analy apple for thee curve an gan an phae correponng to a cloe loop are calculate. Phae [eg] TP TP Boe Boe (a)gan TP TP Boe (b)phae Fg. 13 Comparon of actve power control The comparon of cloe-loop reactve power control hown n Fg.14. From Fg.13 an Fg.14 the reult of TPDraw an the evelope program are motly agree wth each other. Therefore, t can be a that the SBN:

6 vance n Power an Energy Sytem calculaton reult of frequency repone analy reaonable. G [B] Boe Renewable Energy, The nternatonal Conference of Electrcal Engneerng, anazawa, Japan, PE2-1, 212. [5] Muhamma H. Rah, POWER ELECTRONCS Hanbook, P367, 211. [6] Wllam S. LENE The Control Hanbook, P173, [7] TP RULE BOO, 1992 TP TP Phae [eg] (a)gan Boe TP TP (b)phae Fg. 14 Comparon of reactve power control 7 Concluon Th paper propoe a lnearze moel of the nverter an the frequency repone analy apple for t. The frequency repone analy compare wth TPDraw mulaton an valty of analy emontrate. Th metho wll be ueful an effectve for control egn of renewable energy nverter. Reference: [1] J. ra an F. Funabah : Power electronc technologe for relable operaton of power ytem n Japan, DPRT,28 [2] R. Tanaka an J. ra : Smulaton of an nverter on TPraw5.3, EEJ-T 29, Bangkok, Thalan. [3] R. Tanaka an J. ra : tablty analy of nverter operaton for renewable energy, The nternatonal Conference of Electrcal Engneerng 21, Buan, orea. [4] T. Mor an J. ra : Development of Stablty naly of nverter Control for SBN: