Passivity-based Control of NPC Three-level Inverter

Transcription

1 International Form on Mechanical, Control and Atomation (IFMCA 06) Passivity-based Control of NPC hree-level Inverter Shilan Shen, a, Qi Hong,b and Xiaofan Zh,c Gangzho Power Spply, Gangzho, Gangdong province, China School of Electrical Engineering, Whan University, Whan, Hbei province, China a, c Keywords: NPC; Balance of dc capacitor voltage; SPWM strategy; passivity theory. Abstract. Unbalance of dc capacitor voltage is a key technical problem of NPC inverter. hrogh establishing the dc capacitor voltage balancing mathematical model of NPC three-level inverter, it can be proved that the NPC three-level inverter is a Passivity nonlinear system. By controlling the total charge of point injection is zero in a sampling period, and considering the Passivity dissipation characteristics of the nonlinear system, this paper calclated crrent of middle line and bilt p the passivity-based control model, and then kept the balance between voltages of dc capacitors, realized the low freqency crrent and dried the load transformer based on this. his control algorithm can achieve balance of dc voltages and otpt crrent at the same time, and the validity and feasibility of this control strategy is verified by simlation reslts, and very good effect has been proved by a practical engineering of 750kVA, NPC hree-level inverter. Based on this, a new idea of solving the nbalance of dc capacitor of diode clamped mlti-level inverter is provided by this stdy. Introdction Mltilevel inverters, which cold increase the nmber of otpt voltage level and redce the harmonic content of otpt, were sitable for high voltage and high power applications [-3]. How to ensre the dc capacitor voltage balance was a key problem of the mltilevel inverters controller, it cold rise the harmonic content of otpt, case voltage rise of switch devices and damage the inverters. With NPC (netral-point-clamped) three-level inverter as an example, nbalance of dc capacitors cold be solved from two ways, improving the hardware circit or optimizing control algorithm. Improving the hardware circit is increasing independent dc sorces to dc capacitors, bt it wold case system costs increasing, larger volme and complicated controller. In the centerline of the NPC inverter alternating crrent was prodced becase that load crrent throgh bridge arm of each phase, and when the alternating crrent flowed into dc capacitors, corresponding voltage flctation wold appear in dc capacitors. Besides, instantaneos nbalance crrent cased by distrbance might also make voltage deviation between two dc capacitors in the dynamic process. he passivity control cold be sed to achieve the prpose of the dc capacitors voltage balance by configring the proper energy fnction, injecting sitable nonlinear damping and make two dc capacitors of NPC inverter voltage gradal convergence to half of the total dc voltage [4-6]. his paper changed NPC three-level inverter netral voltage model to netral crrent model, and designed voltage balance passivity control model of NPC three-level inverter capacitors based on the passivity theory. he positive-seqence component and the zero-seqence component of the reference voltage in the passivity control model wold be calclated at the same time, so it wold be easier to implement in engineering. he simlation show that passivity control algorithm can effectively balance control of dc voltage, keep good steady-state performance and fast dynamic response, and has simple algorithm and strong robstness. Effectiveness of the passivity control algorithm had been proved in 690V-750kVA engineering application. Copyright 07, the Athors. Pblished by Atlantis Press. his is an open access article nder the CC BY-NC license ( 80

2 Analysis of NPC three level inverter circit and passivity control model Circit topology of NPC three level as shown in Figre : in this figre, dc is voltage of dc bs, in order to facilitate analysis, it was assmed that the dc is a constant; C and C are capacitance of dc capacitors, and C=C=C; dc and dc are voltages of dc capacitors; ia, ib, ic are otpt crrents of three phases ABC; la, lb, lc are voltages of load, O is the voltage netral point, io is the total crrent of middle line; Q, Q, Q3 and Q4 are for IGBs (Inslated Gate Bipolar ransistor) on bridge arm of phase A; D and D are clamping diodes on bridge arm of phase A; Ra, Rb, Rc are eqivalent series loss resistances of three phases; Lla, Llb, Llc are eqivalent series indctance of three phases. Condction and shtoff of the IGBs are controlled by SPWM(sine plse width modlation). dc D C dc Q Q O i0 ia ib ic Ra La Rb Rc Lb Lc Q3 C dc D U la U lb U lc Q4 Fig. Main circit topology of NPC De to device different parameters, when energy was exchanging in the transient process, voltages of dc capacitors coldn't keep absolte eqilibrim, what was called netral-point offset. Netral-point offset wold case harmonics otpt of NPC three-level inverter, impacting load performance, and if the imbalance was severe, devices of the NPC three-level inverter wold be damaged. If io=0, voltage of NPC dc capacitors will keep balance, however, only when the switch of NPC inverter is netral point clamped, the crrent of middle line is not eqal to zero, io 0, so the crrent of middle line can be expressed as: i0 = [ abs ( Sa )] ia + [ abs ( Sb )] ib + [ abs ( Sc )] ic = abs ( S a ) ia abs ( Sb ) ib abs ( Sc ) ic According to the principle of PWM control, the average otpt effect of the switch state wold be the eqivalent of reference voltage in a control cycle, signm fnction was defined as:,x 0 sgn(x ) = (),x < 0 hen the zero seqence voltage µ0 that was need to stack cold be got, with its constraint condition, in this formla, max=max(a,b,c), min=max(a,b,c) : 0 = max, 0 + max > sgn(a ) a ia + sgn(b ) b ib + sgn(c ) c ic 0 = 0 = min, 0 + min < sgn(a ) ia + sgn(b ) ib + sgn(c ) ic =,? + &? + ) ( 0 min ) 0 ( 0 max 0 he instrction otpt crrent of NPC three level inverter was spposed to X = ia ib ic, the actal otpt crrent was spposed to X = [ia ib ic ], the error otpt crrent was spposed to Xe = [iae ibe ice ], and X = X Xe. A X e + RX e = F ( A X + RX ) (3) In formla (3), A = diag [ La Lb Lc ] is a definite diagonal matrix, R = diag [ Ra Rb Rc ] is a definite symmetric matrix, which reflects the dissipation characteristics of the system, 8

3 F =[a la,?b lb, c lc, 0] is expression of exchanging energy between system and external environment, Z f = diag[ z fi ] (i=,,3) is damping coefficient matrix, the energy storage fnction is: H= La iae + Lbibe + Lc ice ) = X e AX e (4) ( he derivative on both sides of the eqation is: H = X e A X e = X e ( R + Z f ) X e W ( X e ) < 0 (5) In formla (5), W ( X e ) = β X e, β > 0, X e is Eclidean norms of X e. Above all, the error system is a nder-actated system, in an ideal world, ia, ib, ic can be gradal tracking and dc = 0 at the same time. dia + a 0 la La +Ri a a + zfa ( ia ia ) = 0 dt b +0 lb Lb dib +Ri b b + zfb ( ib ib ) = 0 dt (6) dic c +0 lc Lc dt +Ric c + zfc ( ic ic ) =0 sgn(a ) a ia +sgn(b) b ib +sgn(c) c ic 0 = sgn(a ) ia +sgn(b) ib +sgn(c) ic a, b, c are the reference positive voltages of NPC three level inverter and 0 is the zero seqence voltage needed to inject, that can be got by solving formla (6), then the passivity control block diagram of NPC three level inverter can be shown as figre. lx ix ix* + x Comparator z fx Fig. Passivity control block diagram of NPC Simlation and engineering test In order to verify the NPC inverter nder passivity control algorithm of the dynamic tracking performance and voltages of dc capacitors balancing effect, the simlation process is set to: in 0~0.3s, the operation process; in 0.3s~s, instrctions crrent (RMS) is 50A, freqency is Hz; in s~4s, instrctions crrent change to 80A and the freqency redcing to 0.5Hz; In 4s~6s, instrctions crrent increases to 80A and the freqency redcing to 0.Hz. Fig. 3 hree-phase crrents Fig. 4 Line voltage ab Fig. 5 DC voltage dc and dc Figre 3 shows three-phase otpt crrent waveforms of NPC three-level inverter, figre 4 shows the line voltage waveform between phase A and phase B, figre 5 shows two voltage waveforms of dc capacitors dc and dc. From figre 3 to figre 5, the reslts show that when the instrction crrent 8

4 change, the otpt crrent of NPC three-level inverter is able to respond qickly and accrate tracking instrction crrent, and voltage deviation of two dc capacitors is less than 5. Figre 6 shows A phase the otpt crrent waveform and two voltages waveform of dc capacitors from NPC three-level inverters, when instrction crrent is 60A and crrent freqency is 0. Hz, figre 7 shows the line voltage waveform between phase A and phase B, when instrction crrent is 0A and crrent freqency is 0. Hz. Fig. 6 Otpt crrent and voltages of DC capacitors Fig. 7 Line voltage between phase A and B From figre 6 and figre 7, the reslts show that the otpt crrent can follow instrction crrent and keep a good basic sinsoidal crrent waveform nder passivity control, bt becase that dc side of NPC three-level inverter power spply capacity is limited, in, the voltage of dc capacitors prodced a smaller decline when the instrction crrent of NPC three-level inverter increases. Conclsion Establishment of balance voltage of dc capacitors model and designing a passivity-based controller are to solve the problem of netral-point offset in NPC three-level inverter, throgh theoretical derivation and simlation reslts, feasibility of the control algorithm was proved, and it can be achieved that the otpt crrent fast track the instrction crrent of different conditions, maintaining the balance between voltages of dc capacitors, and this passivity-based control algorithm can be applied to the diode clamping mltilevel inverter. Acknowledgements his work was financially spplied by Scientific Fnds for Otstanding Yong Scientists of China (5075). References [] Wang Xiny, He Yingjie, Li Jinjn. Netral-Point Voltage Balancing Principle of NPC Inverter Modlated by SPWM Injected Zero-Seqence Voltage [J]. ransactions of China Electrotechnical Society. 0, 6 (5): [] Li Yongdong, Wang Chenchen, et al. Object oriented optimal control method for three-level PWM rectifier by zero-seqence voltage injection [J]. ransactions of China Electrotechnical Society, 009, 4 (3): 6-(in Chinese). [3] Po J, Zaragoza J, Ceballos S, et al. A carrier-based PWM strategy with zero-seqence voltage injection for a three-level netral-point-clamped converter [J]. IEEE ransactions on Power Electronics, 0, 7 (): [4] Zhang Maosong, Zha Xiaomin, et al. Passivity-based Control of Cascade D-SACOM [J]. Proceedings of the CSEE, 0, 3 (5): 33-39(in Chinese). 83

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