A Design Procedure for Control Systems of Inverterbased DG in Microgrids

Transcription

1 A Design Procedre for Systes of Inverterbased DG in Microgrids Toshihisa Fnabashi, Shota Igarashi, Yske Manabe, Mneaki Krioto, Takeyoshi Kato Abstract-- In constrcting icrogrids with only inverter-based DGs, fast transient response and robst stability are reqired in inverter control syste. However, it is difficlt to design a control syste of the inverter with those abilities becase of non-linearity of inverter control syste and loads in icrogrids. This paper stdies a design ethod for an inverter control syste of a icrogrid at an isolated ode. Keywords: icrogrid, isolated operation, inverter, PI controller, stability. I. INTRODUCTION n electrification of a reote area sch as reote islands and Irral villages, it is necessary to constrct atonoos systes. In sch places, ipleentation of an isolated icrogrid, a network of generators and loads, is assed. Conventionally, the atonoos syste was constrcted sing rotary achines sch as diesel generators. In recent years, de to the high penetration of renewable energy sorces into power systes, icrogrids can be constrcted with only inverterbased distribted generations (DGs). However, becase icrogrids are sall systes, it is difficlt to aintain voltage and freqency within a proper range and to sppress haronics in icrogrids at isolated operation, when a distrbance occrs [], [2]. Frtherore, in icrogrids coposed with only inverter-based DGs, these probles becoe ore serios since there are no rotating achines with inertia. In constrcting icrogrids, fast transient response, reference following characteristic and robst stability are reqired in inverter control systes to solve these probles. Silation and verification tests of icrogrids with only inverter-based DGs at isolated operation have been perfored [3], [4]. Paraeters of control systes in previos approaches have been deterined by trial and error sing silation tool. Otherwise, inverter otpt crrent has been regarded as distrbance and paraeters have been designed to sppress the inflence of the distrbance in individal inverters [5], [6]. However, control systes are designed withot considering whole icrogrids inclding controller perforance in isolated operation. Therefore, they ight have been nderestiated. Frtherore, to design control systes considering whole icrogrids, it is necessary to represent nonlinear plant odels sch as DGs and nonlinear loads in icrogrids by a transfer fnction or a state-space fnction. By linearization of these coponents, controllers can be designed to have a perforance of fast response and robst stability near an operating point. However, in above ethod, it is difficlt to linearize all control targets properly. In this paper, syste identification of the plant odel for a icrogrid inclding only inverter-based DGs was perfored sing pertrbation signals. An inverter control syste was designed considering the whole icrogrid. Concrete design procedres are as follows. () The icrogrid was odeled sing XTAP (expandable Transient Analysis Progra) [7]. (2) A Bode diagra of the non-linear plant odel was calclated by adding a pertrbation signal to a voltage reference of the inverter control syste. (3) The plant odel was identified fro the Bode diagra and a controller in the inverter control syste was designed sing MATLAB. (4) ler perforance was confired by silation sing XTAP. The validity of this design ethod is confired by transient silations with both designed control systes by the proposed ethod and by the conventional ethod. II. MICROGRID MODEL The icrogrid odel in this paper incldes an Energy Storage Syste (ESS) rated 5kA, a Photovoltaic Syste (PS) rated kw and an RL load rated 5kW (PF=.8). Fig. shows a single-line layot of the icrogrid syste and Table shows ain paraeters vales of icrogrid coponents. The ESS is a voltage-control-type storage syste and it controls voltage and freqency in the icrogrid. The PS is a crrentcontrol-type generation syste and it generates active/reactive power otpt. RMS(Rated Mean Sqare) voltage and freqency in the icrogrid are 66 and 6Hz respectively. Details of each coponent in the icrogrid are as follows. A. ESS A Battery energy storage syste is presented by the DC voltage sorce. It is interconnected to the PCC (Point of Coon Copling) throgh an inverter, a transforer, and a filter. Fig. 2 shows the control syste of the ESS. Where, ref is voltage reference ( p..), is inverter otpt RMS line voltage which is calclated by () sing dq transforation and is odlation signal. Freqency is fixed at 6Hz. We wold like to thank grant for Environental Research Projects fro The Sitoo Fondation. Toshihisa Fnabashi, Shota Igarashi, Yske Manabe, Mneaki Krioto, and Takeyoshi Kato are with Nagoya University, Chiksa-k, Nagoya city, Japan (e-ail: fnabashi@iass.nagoya-.ac.jp). Paper sbitted to the International Conference on Power Systes Transients (IPST27) in Seol, Repblic of Korea Jne 26-29, 27

2 E P ESS Inverter Boost converter & Inverter PS t Trans 46/6.6k % Trans 46/6.6k % Filter R f C f Filter R f C f Fig.. Microgrid odel. L f L f Breaker Breaker PCC R l L l Load crrent control, and a control. Instantaneos active/reactive power is calclated by (2) and (3) sing dq transforation. A PI controller is sed in the active/reactive control and the crrent control. In addition, a non-interacting control st be adopted in the crrent control. v a,b,c p p ref q q ref PLL i a,b,c θ Active Power Reactive Power abc dq i dref i qref i d,q Crrent Fig. 3. Block diagra of PS s controller. TABLE I PARAMETERS OF THE MICROGRID COMPONENTS Paraeter Freqency E Inverter rated power of ESS P rated power Inverter rated power of PS carrier freqency Indctance of trans Rf Lf Cf Rl Ll ale 66 6Hz 9 5kA kw 5kA 3kHz 77H oh 4.94H.548 υf 89 oh 3.85H p= vi + vi d d d q q q q= vi vi q d ( 2) ( 3) III. SYSTEM IDENTIFICATION In this paper, paraeters of the PI controller in the ESS shown in Fig. 2 are deterined to eet desired design indexes. Fig. 4 shows a topology of the feedback control syste. Where, E is voltage of the battery energy storage syste and G( s ) is the plant odel coposed of the transforer and the filter of the ESS, the PS and the load shown in Fig. in dotted lines. In addition, RMS voltage is fed back throgh a priary delay in order to reove the short-period coponent of voltage. To design this voltage control, G( s) is obtained by syste identification. At this tie, PS otpts 6kW with nity power factor. The voltage aplitde signal is deterined fro the deviation of and throgh the voltage control. In ref addition, a PI controller is sed in the voltage control block. cos(2π6t) ref = v + v 2 2 d q B. PS oltage Fig. 2. Block diagra of ESS s controller. ( ) A P is represented sing an eqivalent circit. This P is interconnected to the PCC throgh a boost converter, an inverter, a transforer and a filter. Fig. 3 shows the control syste of PS. Where, v abc,, is inverter otpt phase voltage, iabc,, is inverter otpt phase crrent, p is instantaneos active power, and q is instantaneos reactive power. The control syste consists of an active/reactive power control, a ref oltage Fig. 4. cos(2π6t) Feedback control syste of the ESS. A. Method of syste identification Procedres for syste identification are following. () The feedback loop in the control syste of the ESS shown in Fig. 4 was disconnected and the signal expressed as (4) was inptted to the control. Where, f is any freqency. Sig =.75 cos(2π6 t) +.5 cos(2 π ft) ( 4) (2) RMS voltage of the PCC point in Fig. was calclated several ties by changing freqency f. (3) For the inpt signal Sig and the otpt signal, Forier series expansion were perfored respectively and a Bode diagra was plotted fro aplitde and phase change in freqency f. (4) A transfer fnction was calclated fro the Bode diagra sing identification toolbox in MATLAB. E t G(s)

3 B. Identification reslts The plant odel G( s) was identified as the third-order transfer fnction fro silation reslts and expressed as (5). Fig. 5 shows the Bode diagra of the identified odel of (5) and silation reslts of above step (3). Fit rate expressed as (6) was 68%. Where, yk is the Bode diagra of silation reslts, y is its average and y ( k ) is the Bode diagra of ave G( s ). However, those were consistent in edi-freqency fro w = rad/s to 6rad/s. Therefore, the controller can be designed sing this plant odel G( s ) s s+ 6.5 Gs () = s s +.76 s Magnitde[dB] Phase[deg] Silation reslt a. Gain diagra. b. Phase diagra. Fig. 5. Bode diagra of the plant odel. N 2 [ y ( k) yk ] Fit = k = 6 N 2 [ yk yave ] k = Silation reslt Identified odel G(s) Identified odel G(s) They are design indexes. Robst stability is to keep stability even if paraeters of the plant odel G( s ) change by PS otpt flctation or load flctation. In addition, the controller is designed sing SISO design tool in MATLAB. A. Sensitivity analysis for robst stability design A plant odel is represented by a set of odels expressed in (7). Where, ( s) is a stable transfer fnction which represents the ncertainty of the odel and Gn ( s ) is noinal odel and it is assed as (5) in this paper. A weighting fnction W( s ), which satisfies (8), is decided by perforing a sensitivity analysis to represent the noinal odel as a set of odels. Frtherore, a control syste has a robst stability if it satisfied (9). Where, C( s ) is a controller. ~ Gs () = + () s G () s 7 ( jω) 8 n W jω W( jω) C( jω) Gn ( jω) + C( jω) G ( jω) n <, ω 9 The plant odel G( s ) changes according to load and PS otpt state in the icrogrid. Therefore, the variation of the Bode diagra is exained by perforing sensitivity analysis shown in Table II. The Bode diagras are calclated in the sae way as section Ⅲ. TABLE II SENSITIITY ANALYSIS CONDITIONS FOR CALCULATING THE WEIGHTING FUNCTION Case Magnitde of load[ka] PS otpt[kw] 2 5 Fig. 6 shows the Bode diagra of sensitivity analysis reslts. Fro Fig. 6, it can be seen that an ipact, that PS otpt gave to the noinal odel, was sall. However, an ipact, which load flctation gave to the noinal odel, was large. Especially, flctation of the Bode diagra becae large when s PS was disconnected. Fig. 7 shows Bode diagra of which plotted the axi vale of the ncertainty of the sensitivity analysis reslts of each case and W( s ). In addition, W( s ) is deterined as () fro sensitivity analysis. 3 (PS disconnection) (PS disconnection) I. CONTROLLER DESIGN The controller of ESS s inverter is designed sing the plant odel G( s ) so that the control syste has qick response tie reference following characteristic and robst stability.

4 Magnitde[dB] Magnitde[dB] Plant odel Case Case2 Case3 Case4 Case5 Case Fig. 6. Bode diagra of sensitivity analysis reslts. Δ(s) Fig. 7. Bode diagra of W( s ) and ( s).25s + W( s) =.25s +. B. Design reslts PI controller was designed as () considering design indexes. Fig. 8 shows a step response of closed loop. Settling tie was.97s. Fig. 9 shows Bode diagra of the left side of (9). Fro these figres, it was confired that all design indexes are et. Cs =.74( + ).73s Aplitde W(s) Fig. 8. Step response of the closed loop Fig. 9. Bode diagra of the left side of (9).. SIMULATION RESULTS The designed controller perforance is confired by the silation. The PI controller of () is ipleented in ESS s control syste as shown in Fig. 2. Frtherore, it is copared to the design by sing ltiate sensitivity ethod. A. Ultiate sensitivity ethod Paraeters of the PI controller is deterined sing ltiate sensitivity ethod expressed as in (2). Where, K is the critical gain sing only proportional control, P is the oscillation period, K p is proportional gain, T I is integral tie. K and P were calclated by the XTAP silation. As a reslt, the controller was obtained with (3) ( K =5, P =2.8s). Kp =.45 K ; TI =.83P 2 ( s) = 5.75( + ).8s 3 C Magnitde[dB] B. Silation Reslts The silation odel is sae as that of Fig. and the PS otpts is 6kW (PF=.). The Load decreases fro 5kA to ka at t=.s fro the start of silation and the PS is disconnected at t=.5s. Fig. shows the active power, the reactive power, and the freqency in the icrogrid, the instantaneos voltage and RMS voltage at the PCC, respectively sing the controller of (). Fig. shows RMS voltage at the PCC point sing the controller of (3). Fro Fig., it was confired that silation was perfored correctly. In addition, fro Fig. (d), the designed control syste had feedback stability and reference following characteristic. In addition, it had a fast response since the settle tie is within.2s. Frtherore, voltage contined to be stable even if load flctation and PS disconnection had occrred. Ths, this control syste has a robst stability. On the other hand, when sing a controller of (3), the voltage was nstable fro t=.5s as in Fig.. When sing the ltiate sensitivity ethod, the gain argin was 8.55dB. However, the axi vale of ncertainty ax ( s) is 36dB. The circit configration was changed largely by PS disconnection and ncertainty increased. As a reslt, voltage becae nstable

5 since robst stability was not considered in the ltiate sensitive ethod. Active power [P.U.] (Base:kW) Reactive power [P.U.] (Base:kvar) PS Load ESS (a) Active power Load ESS PS (b) Reactive power oltage [P.U.] (Base:66) Fig.. Silation reslt sing the conventional ethod. I. CONCLUSION In this paper, assing the icrogrid coposed only inverter-based DGs in isolated operation, a syste identification of the plant odel was perfored sing the pertrbation signals. The inverter control syste of the ESS was designed in order to have feedback stability, reference following characteristic, fast response, and robst stability considering the whole icrogrid. The perforance of the designed controller was confired by silation. oltage in the icrogrid contined to be stable even if load flctation and PS disconnection occrred. It was validated that the control syste has desired perforance. Ths, this design ethod is feasible. Freqency [Hz] oltage[] (c) Freqency (d) Instantaneos voltage at PCC II. REFERENCES [] F. Li and J. Haodong, "Coprehensive Stdy abot Stability Isses of Mlti-odle Distribted Syste," IPEC24, Hiroshia, Japan, 24. [2] M. Tachibana, M. Paler, A. Yona, T. Senjy, and T. Fnabashi, "oltage Stability Analysis and (P, Q)- Characteristics of Mlti-bs Syste," CIGRE AORC Technical Meeting, Tokyo, Japan, 24. [3] J. Sita, K. Nishioka, Y. Noro, Y. Ito, M. Yabki, and N. Kawakai, "A erification Test Reslt of Isolated Operation of a Microgrid Configred with New Energy Generators and a Stdy of Iproveent of oltage," IEEJ Trans.PE, vol. 29, no., pp.57-65, 29. [4] J. Arai, "New inverter control in an isolated icrogrid coposed of inverter power sorces withot synchronos generator," IEEJ-IEEE PES Thailand Joint Syposi, 25. [5] Y. W. Li, D. M. ilathgawa, and P. C. Loh, "Design, analysis and realtie testing of controllers for lti-bs icro-grid syste," IEEE Trans. Power Electron., vol. 9, no. 5, pp.95-24, 24. [6] asqez, J. M. Gerrero, M. Savaghebi, J. Eloy-Garcia, and R. Teodoresc, "Modeling, Analysis, and Design of Stationary Reference Frae Droop led Parallel Three-Phase oltage Sorce Inverters," IEEE Trans. Ind. Electron., vol.6, no.4, pp.27-28, 23. [7] T. Noda and A. Aetani, "XTAP, chapter 5 of the book Nerical Analysis of Power Syste Transients and Dynaics," IET, oltage [P.U.] (Base:66) Fig.. (e) RMS voltage at PCC Silation reslts sing the proposed ethod.