Carrier-based Discontinuous PWM Modulation for Current Source Converters

Transcription

1 Carrier-base Discontinuous PWM Moulation for Current Source Converters Olorunfemi Ojo, Sravan Vanaparthy Department of Electrical an Computer Engineering Tennessee Electric Machines an Power Electronics Laboratory/Center for Electric Power Tennessee Technological University, Cookeville, TN 8505, U.S.A. Phone : (91) , Fax : (91)-72-46, jojo@tntech.eu Abstract- Two generalize iscontinuous carrier-base pulsewith moulation (GDPWM) methoologies for three-phase current source converters (CSC) are evelope base on the classical space vector metho an the carrier-base generalize iscontinuous moulation scheme for voltage source converters (VSC). With feasible operation in both the linear an overmoulation regions, they provie the known avantages of the iscontinuous carrier-base moulation in voltage source converters reuce switching loss an reuce effective switching frequency especially in the over-moulation region. These moulation schemes are implemente for a current source inverter from which experimental results are presente to verify concepts an theory. nex Terms- Current source converters, generalize iscontinuous pulse-with moulation, irect igital space vector, triangle intersection metho.. NTRODUCTON Ajustable-spee motor rives an interfacing converters for utility applications traitionally use three-phase voltage source converters moulate by pulse-with moulation schemes to achieve high system response, reuce current an voltage harmonics an unity or leaing power factor of operation. The popularity of this topology is ue to the simplicity of c supply obtaine from either controlle or uncontrolle rectifiers, stable open loop an minimum-phase ynamic characteristics an its well unerstoo carrier-base an space vector moulation techniques. Unfortunately, voltage source converters require bi-irectional input rectifier for regenerative operation. The switching gives rise to relatively high v/t transitions on the phase leg output voltages which leas to increase motor losses in rives, voltage surges an unacceptable electromagnetic interference (EM) effects. The ual of this converter the current source converter - is known for their simplicity of structure, reliable short circuit protection, four quarant regenerative operation an nearly sinusoial current outputs. The low output rate of change of the voltage resulting from the filtering effect of output capacitors an the irect control of currents make it a premium converter in high power applications such as large synchronous motor rives. There is however the isavantages of the relatively huge input smoothening inuctor an its inherent non-minimum phase characteristics which generally egraes its ynamic performance leaing to possible openloop converter instability. Unlike the voltage source converters where there are well evelope an unerstoo carrier-base triangle intersection pulse-with moulation an irect igital space vector moulation schemes, moulation strategies for current converters are relatively less evelope an less transparent [1-5. Utilizing some of the commonalities an ualities of the voltage an current source converters, space vector moulation strategies optimize for voltage source converters are shown to be applicable with minimal moifications to the current source converters. For close-loop control, space vector algorithms use for current regulate voltage source converters can be slightly moifie for the control of voltage regulate current source converters using the concept of uality [6-8. Current source converters using thyristors with the avantages of ruggeness, lower cost an high power have been realize using a carrier-base triangle intersection PWM moulation scheme. A controlle switching evice place on the c bus acts as the freewheeling path ensuring active SCR commutation [9-10. An integrator-base linearizing pulse-with moulator (LPWM) has also been propose an implemente ensuring linear output AC voltage magnitue to the input DC voltage [11. t will be shown in the sequel that the moulation signals use to realize LPWM is one of the possibilities obtaine from the propose irect generalize iscontinuous carrier-base PWM scheme for the current source converters set forth in this paper. This paper makes new contributions an gives more clarity to the unerstaning an evelopment of carrier-base generalize iscontinuous triangle intersection an the irect igital pulse programming space vector base moulation methos of the current source converters. The moulation schemes provie the known avantages obtaine in the iscontinuous carrier-base an space vector PWM moulation schemes for voltage source inverters especially at high an over-moulation regions. n the first proposal given in Section 2 of this paper, the generalize iscontinuous PWM strategy for the voltage source inverters is extene for use in the current source converters; which with the variation of a control phase angle an implementation of shorting routines effectively synthesizes the reference three-phase currents. n the irect carrier-base iscontinuous triangle intersection PWM scheme base on the classical space vector methoology set forth in Section, the expressions for the generalize iscontinuous moulation signals are etermine which with a unique triangle intersection comparison scheme 2224

2 generate appropriate PWM pulses for the current synthesis. The propose moulation schemes are experimentally implemente in Section 4 for a three-phase converter operating in the linear an over-moulation region to valiate theory.. MODULATON OF CSC USNG VSC GDPWM MODULATON SCHEME Figure 1 below schematically shows a three-phase current source converter (CSC) an a voltage source converter (VSC). n the current source inverter, ioes are connecte in series with the switching evices to ensure uni-irectional input current flow an a three-phase capacitor arrangement is connecte at the output to impress a voltage source on the loa. This converter must satisfy both the current an voltage Kirchoff s laws. The Kirchoff s voltage law imposes the constraint that no two or three top (or bottom) switching evices can be turne on at the same time to avoi shortcircuiting the output capacitors. Consequently, only a switching evice in the top set of evices an another evice in the bottom set of evices must be turne on at all times to ensure current continuity. Also, the two switching evices on only one leg can be turne on at the same time in which case the inuctor current free-wheels through the switching evices. Concretely expresse, given the switching functions of the evices shown in Figure 1(b) for the current source converters, then : are turne on. From Tables an, the switching moes of the VSC is to be mappe into those of the CSC. After manipulation of these Tables using Karnaugh mapping technique, the two switching moes are relate as : T ap = ScnS ap + SbnSbp, T bp SbpS an + ScnScp T cp = ScpSbn + S ans ap, T cn ScnSbp + S ans ap T an = ScpS an + SbnSbp, T bn = SbnS ap + ScnScp 0.5V 0.5V o S ap S an L T ap A =, =, () S bp S bn (a) as T bp B T cp S cp S cn C T ap + T bp + T cp = 1, T ap T bp = 0, T ap T cp = 0, T bp T cp = 0 V bs cs T ap T bp T cp = 0, T an T bn T cn = 0, T an T bn = 0, T bn T cn = 0 T an + T bn + T cn = 1, T an T cn = 0 When a evice is turne on, T ij = 1 an it is equal to zero, if turne off for i = a,b,c an j = p, n, where p,n enote top an bottom evices; respectively. The truth table showing the acceptable switching possibilities for the CSC are shown in Table. There are six active states an three null states. Active states impress currents to the loa while null states free-wheel the source inuctor current through the shorting of the top an bottom evices in a converter leg an ecouples the input sie from the output without current transfer to the loa. For the VSC shown in Figure 1(a), Kirchoff s voltage law imposes the conition that the top an bottom evices on a converter leg cannot be turne on at the same time they must switch on complementarily. To ensure active control of the loa provie paths for the loa currents at all instances - a evice on each leg (three switching evices in all) must be turne all the time. These constraints are expresse mathematically as : S ap + S an = 1, S bp + S bn = 1, S cp + S cn = 1 (2) Switching moes of operation satisfying equation (2) are lai out in Table. There are six active states an two null states when either the three top or bottom switching evices (1) T an T bn (b) Figure 1. (a) Three-phase voltage source converter, (b) threephase current source converter From (), only one evice in the top an bottom are turne ON at any given time. However, accoring to conitions given by (2), the null states of the VSC cannot be mappe into that of the CSC because the output of this prouct term will always be zero. The algorithm of () on its own can be use for generating the gating signals for a CSC but it won t allow the utilization of the available three null states S ap S an, S bp S bn, an S cp S cn which are require for freewheeling. The require freewheeling can be achieve by connecting another switching evice after the input inuctor; increasing the count of the switching evices [9-10. However, the freewheeling can be one without aing an extra switching evice by using the null states. Thus, aitional conitions- minimization of the number of switch transitions, balancing switch utilization, symmetry in the output switche currents in orer to have minimum harmonic istortion an reuction of losses can be impose. To satisfy the above requirements a logic circuit is evelope to etect the conition when the null state in () has T cn 2225

3 to be applie. Once the conition for null state is etecte, one of the three legs of the CSC has to be shorte. This is one by gating the evices in the same leg by a common signal, which will be terme as a shorting pulse. The optimize sequence of leg shorting is achieve using the absolute maximum of the line-line of the reference moulation signals so that when line-line current ab is maximum, leg a is shorte, if bc is maximum leg b is shorte, an when ca is maximum we short leg c. This algorithm is proven by computer simulation to achieve minimum switching transition, switching symmetry an balance switch utilization. A C T V E N U L L TABLE. SWTCHNG STATES FOR CSC State T ap T an T bp T bn T cp T cn T T T T T T T T T TABLE. SWTCHNG STATES FOR VSC State S ap S bp S cp S an S bn S cn On Switches Null, T an T bn T cn S 7 S 0 S T cp T an T bn S T bp T an T cn S T bp T cp T an S T ap T bn T cn S T ap T cp T bn S T ap T bp T cn Null, T ap T bp T cp A. Layout an gating pattern signals The gating pulse generate using the GDPWM for three phase voltage source converters (S ap S cn ) are obtaine by comparing the moulation signals (M ip ) [given in (4) for the three top evices with a high frequency carrier triangular signals. The expressions for the moulation signals are aopte from that of the VSC in which the voltage quantities in the original expressions have been replace with currents an the phase shift between VSC an CSC space vector accounte for. n (4), ω is the angular frequency of the reference current an δ is the moulation phase angle, is ( as, bs, cs ) are the reference phase currents. These generalize iscontinuous carrier-base moulation signals clamp the evices for some perio of the funamental frequency to either the positive or negative rail in the process of which the moulator performance may be improve. By varying the moulation phase angle δ, various types of carrier-base generalize iscontinuous PWM moulation signals [GDPWM are obtaine [ M ip = 2 ip / + (1-2 σ) 2 σ max / + 2 min (σ -1)/, ξ ap = as - bs, ξ bp = bs cs, ξ cp = cs as, ξ = max = Max ( ap, bp, cp ), min = Min ( ap, bp, cp ) σ = 0.5[1 + Sgn(Cos (ωt + δ)), i = a,b,c (4) The pulses obtaine from this moulation scheme are entere into () to obtain corresponing pulses for the CSC. Then when the null states are etecte, the shorting logic escribe above an shown schematically in Figure 2 is implemente to short a leg of the CSC.. DSCONTNUOUS PWM MODULATON n this section the irect generalize iscontinuous moulation signals for the six switching evices of the current source converter are etermine using the classical space vector approach. The q stationary reference frame currents for all the feasible active an null states are graphically shown in Figure given that the input current is. A reference three-phase current expresse in the stationary reference frame q * locate in a sector in Figure is synthesize by timeaveraging the two ajacent non-zero state an one of the three null states : q * = qa t a + qb t b + q7 t 7 + q8 t 8 + q9 t 9 (5) t a + t b + t 7 + t 8 + t 9 = 1, t 7 = α (1- t a - t b ), t 8 = β (1- t a - t b ) t 9 = γ (1- t a - t b ), α + β + γ = 1, α β = 0, α γ = 0, β γ = 0 The normalize times t a, t b, t 7, t 8, t 9 are respectively the turnon times of the evices constituting the ajacent states borering the current reference an the three null states while α, β, γ are the weighting factors for which the null states are use. The equations for the times t a an t b from (5) are expresse in terms of the phase reference currents in Table. Figure 4 shows the switching functions (unit magnitue) of the switching evices when operating in sector expresse in terms of the normalize times. The expression for the moulation signal require to generate the PWM pulses to turn on each evice is the sum of the times the respective evices are turne on. The expressions of the total turn-on times of each evice (τ ij ) an the corresponing moulation signals (M ij, i = a,b,c, j = p, n) expresse in terms of the reference three-phase currents ( as, bs, cs ) using Table, are given in Table V. t is the basis for the implementation of the generalize irect igital space vector PWM moulation 2226

4 Sap S bp Scp San Sbn Scn S 1 h1 T ap S 2 h2 T bp S h T cp S 4 h4 T an S 5 S 6 h5 h6 T bn T cn Phase VS Switching States +Shorting Pulse Winow generator From DSP S pa S pb S S pc Figure 2. Generation of current source GDPWM moulation signals from voltage source converter moulation TABLE V. GENERALZED DSCONTNUOUS MODULATON SGNALS ( M ij ) AND TOTAL TURN-ON TMES (τ ij ) FOR THE CSC M ap (τ ap ) M an (τ an ) M bp (τ bp ) M bn (τ bn ) M cp (τ cp ) M cn (τ cn ) as + α (1+ bs ) t a + α (1+ bs ) β (1+ bs ) - bs + β (1+ bs ) t a + t b + βt c cs + γ (1+ bs ) t b + γ (1+ bs ) α (1- cs ) - as + α (1- cs ) t b + β (1- cs ) - bs + β (1- cs ) t a + βt c cs + γ (1- cs ) t a + t b + γ (1- cs ) α (1+ as ) - as + α (1+ as ) t a + t b + bs + β(1+ as ) t b + βt c β (1+ as ) cs + γ (1+ as ) t a + γ (1+ as ) V α (1- bs ) - as + α (1- bs ) t a + bs + β (1- bs ) t a + t b + βt c β (1- bs ) γ (1- bs ) - cs + γ (1- bs ) t b + V as + α (1+ cs ) t b + α (1+ cs ) bs +β (1+ cs ) t a + β (1+ cs ) γ (1+ cs ) - cs + γ (1+ cs ) t a + t b + V as + α (1- as ) t a + t b + α (1- as ) β (1- as ) - bs + β (1- as ) t b + γ (1- as ) - cs + γ (1- as ) t a

5 [, [ S S cp, an S S bp [, [, an 2 [ 0, [ S S cp, bn 2 4 q 5 1 [ S S bp, cn 2 [ 0, 6 S S ap [, [, bn [ S S ap, cn [, Figure. Stationary reference frame space vector current in CSC TABLE. EXPRESSONS FOR TME t a AND t b Time V V V t a as - bs cs - as bs - cs t b cs - as bs - cs as - bs reference three-phase currents are ientifie. For the top evices, the moulation signal in Table V of the phase for which one of the reference currents has a maximum value (M ip where i is the phase with the maximum instantaneous value of the reference currents) is compare with the high frequency triangle to give S ip = 1.0 if the moulation signal is greater than the triangle. Otherwise, the top evice connecte to the phase which has the instantaneous meium value of the three-phase reference currents is turne on. n the case of the bottom evice, the moulation signal (M in ) of the phase for which one of the reference currents is minimum is compare to the triangle an S in = 1.0 if the moulation signal is greater than the triangle. Otherwise, the bottom evice connecte to the phase for which one of the reference currents is the meium value is turne on. V. CONTNUOUS PWM MODULATON For completeness, the expressions for the moulation signals require for continuous PWM are also erive. The efining equations for the CSC from Figure 1(b) are given as : as = (T ap T an ), bs = (T bp T bn ) cs = (T cp T cn ), T ij = 0.5 (2/ + M ij ) (6) S ap S S S bp cp an S bn S cn t a t b γt c Equations (1) an (6) which are uner-etermine are solve to etermine the expressions for the six unknown moulation signals (M ij ). There is an infinite number of solutions which are obtaine by various optimizing performance functions efine in terms of the moulation signals. For a set of linear ineterminate equations expresse as AX =Y, a solution which minimizes the sum of squares of the variable X is obtaine using the Moore-Penrose inverse [15. The solution given as X = A T [AA T -1 Y is for the minimization of the sum of the squares of the six moulation signal. Figure 4. Existence function for the three-phase current source converter operating in sector. schemes which are realizable by various selections of the null state variables α, β γ. The DSP/FPGA realization of this scheme is beyon the scope of this paper. t turns out that the linearizing pulse-with moulation (LPWM) realize in harware in [11 is one of the possibilities in Table V when α = 1 in sectors, 6, β =1 in sectors 2, 5 an γ = 1 in sectors 1,4. The generalize iscontinuous moulation signal expressions shown in Table V are use for the triangle intersection implementation in which they are compare with a high frequency triangle to generate the switching pulses for the six evices. Unfortunately, if the comparison is one as it is usual especially for VSC, the constraint equations in (1) will be violate. Hence, another metho for the switching pulse generation is utilize in this work. The phases with the instantaneous maximum, minimum an meium values of the M ip = - M in = 0.5 is /, i = a,b,c (7) The algorithm escribe in Section for the synthesis of the switching pulses using the generalize iscontinuous carrier-base triangle intersection PWM also applies for the continuous PWM. V. EXPERMENTAL RESULTS The generalize iscontinuous triangle intersection PWM moulation schemes set forth in the proceeing sections were implemente with a TMS 20LF2407 DSP an use for the synthesis of waveforms for a current source inverter feeing a passive loa. The three-phase capacitors shunte across the loa has a per-phase value of 60µF. Figure 5 give experimental waveforms for the inverter operating in the linear an over-moulation regions. t is evient in these waveforms that the continuous moulation scheme gives a loa voltage waveform with the highest purity while the generalize iscontinuous moulation schemes make the 2228

6 (a) (b) (c) Moulation magnitue inex = 0.85 Moulation magnitue inex = 1.2 Figure 5: Experimental results for generalize iscontinuous PWM moulation. nput c current = A. From top : (1) evice a switching function, (2) phase a current flowing into the loa, () input c current, (4) phase a loa voltage. (a) Continuous moulation signals, (b) α = 1 in sectors an 6, β = 1 in sectors 2 an 5, γ = 1 in sectors 1 an 4, (c) α = 1 in sectors an 6, β = 1 in sectors 2 an 5, γ = 1 in sectors 1 an

7 (a) (b) (c) Moulation magnitue inex = 0.85 Moulation magnitue inex = 1.2. Figure 6: Experimental results using voltage source converter generalize iscontinuous PWM moulation. nput c current = A. From top : (1) top evice a moulation signal, (2) phase a current flowing into the loa, () top evice a switching function, (4) phase a loa voltage. (a) Continuous moulation signals, (b) classical space vector σ = 0.5, (c) moulation control angle δ = 0.0º. 220

8 switching evices to switch less, ensuring lower switching loss an effective switching frequency. n figure 6, waveforms for the inverter using the generalize iscontinuous moulation for voltage source converters are shown. Comparatively, the waveforms of Figure 6 are better than those of Figure 5 where the irect generalize iscontinuous moulation scheme is use. Thus the only ifference woul lie in the amount of evice switching loss an the output waveform quality. t is observe from experimental results (not shown in this paper) that space vector PWM with σ = 0.5 has more switching transitions than its iscontinuous counterparts to generate the same output voltages. V. CONCLUDNG REMARKS This paper presents two ifferent schemes for the moulation of the three-phase current source converters. The irect generalize iscontinuous moulation scheme is obtaine using an approach similar to the classical space vector an can be implemente either by irect igital space vector implementation or as a carrier-base triangle intersection methos. Also, starting from the equations for the generalize iscontinuous moulation signals for the threephase voltage source converter, the corresponing moulation metho for the current source converters was etermine an generalizes some of the implementations reporte in [ The triangle intersection versions of the moulation techniques have been experimentally implemente an converter waveforms shown in Figures 5-8, confirm the efficacy of the schemes. The known avantages of iscontinuous moulation schemes in voltage source converters reuce switching loss, reuce effective switching frequency, extene linear region uring overmoulation are carrie over to the three-phase current source converters. Hence the propose generalize iscontinuous moulation schemes shoul fin utility in applications where loss minimization is esire. t woul appear that for the moulation scheme given in Section, the iscontinuous moulation scheme can be use in the over-moulation region an complemente with the continuous moulation when the converter operates in the linear region. n similar fashion, the metho set forth in Section 2, it will be useful to use the moulation signals for the classical space vector when operating in the linear moulation region an transit to the iscontinuous moulation scheme (selecting appropriate δ that meets a require performance objective) when operation in the over-moulation region is require. REFERENCES [1 J. R. Espinoza an G. Joos, Current source converter online pattern generator switching frequency minimization, EEE Trans. on nustrial Electronics, vol. 44, no. 2, pp , April [2 C. Namuuri an P. 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