IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 6, JUNE 2008 2459
Modified One-Cycle Controlled BidirectionalHigh-Power-Factor AC-to-DC ConverterDharmraj V. Ghodke, Student Member, IEEE, Kishore Chatterjee, and B. G. Fernandes
Abstract—AC-to-DC converters based on one-cycle control ex-hibit instability in current control at light load conditions as wellas when they are operating in the inverting mode. In this paper, amodified one-cycle controller for bidirectional ac-to-dc converteris proposed. A fictitious current component in phase with the util-ity voltage is synthesized. The sum of this current component andthe actual load current is compared with the sawtooth waveform togenerate the gating pulses for the switches. This modification notonly renders stability to the converter at light load conditions andthe inverting mode of operations but also enables the converterto seamlessly transfer its operation from the rectifying mode tothe inverting mode and vice versa. Detailed simulation studies arecarried out to verify the effectiveness of the proposed scheme. Tovalidate the viability of the scheme, detailed experimental studiesare carried out on a 2-kW laboratory prototype.
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIE.2008.921671
RF Fictitious resistance.Reff Parallel equivalent resistance of Rf
and Re.Rs Shunt current sensing gain.VM Modulating voltage.PO Output power.Vin(pk) Single-phase peak voltage.P Positive terminal of the output dc
voltage.N Negative terminal of the output dc
voltage.〈PTotal〉T2L Total averaged power over one-half ac
line period.〈VO〉T2L Averaged dc link output voltage over
one-half ac line period.〈I2〉T2L Average current over one-half ac line
period.r2 Converter output load incremental
resistance.PTotal Total output power.KP Proportional gain.KI Integral gain.fS Converter switching frequency.
I. INTRODUCTION
TRADITIONALLY, diode rectifiers or thyristor bridge con-verters were employed to synthesize dc voltage from the
ac utility. These rectifiers pollute the utility with low-orderharmonics, which are difficult to filter. Pulsewidth modulation(PWM) converters are employed to overcome this problem.These converters shift the frequency of the dominant harmonicsto a higher value, so that they can be easily filtered by em-ploying a small passive filter [1], [2]. The PWM bidirectionalconverter draws a near-sinusoidal input current while providinga regulated output dc voltage and can operate in the first andsecond quadrants of the voltage–current plane [3].
Generally, the control structure of a three-phase six-switchPWM boost converter consists of an inner current controlloop and an outer voltage control loop [4]–[15]. The currentcontroller senses the input current and compares it with asinusoidal current reference. To obtain this current reference,the phase information of the utility voltages or current isrequired. Generally, this information is obtained by employingeither a phase-locked loop (PLL) or a current phase observerdigital technique [9]–[15]. To simplify the control structure ofthese grid-connected systems, one-cycle-control (OCC) basedac-to-dc converters have been proposed [5]–[7], [16]–[20]. This
2460 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 6, JUNE 2008
Fig. 1. Single-phase full bridge converter.
control technique does not require the service of the PLL.Moreover, in these schemes, the switching frequency of thepower semiconductor devices is held constant, which is anadded advantage for medium- and high-power applications.However, the schemes based on OCC exhibit instability inoperation when the magnitude of the load current falls below acertain level or when the converter is operating in the invertingmode of operation [5], [16]–[19], [29].
In this paper, a modified one-cycle controller for ac-to-dcbidirectional boost converter is proposed. This control schemenot only addresses the aforementioned limitation but also canseamlessly transfer the mode of operation from rectifying toinverting and vice versa. This is realized using only dc linkvoltage information. In this technique, three fictitious currentsignals, which are proportional to the respective phase voltagesand in phase with three utility voltages, are synthesized. Thesecurrent signals are added to the actual source current signals,and their sum is compared with the sawtooth waveform togenerate gating pulses for the converter switches. The proposedtechnique requires neither the knowledge of 60◦ angular sectorsof input voltage nor the service of additional multiplexers, gatedistribution logic, and other additional analog and digital logiccircuits, as in [6], [7], and [29]. Moreover, it does not need toselect positive and negative peak voltages as reference currentvectors, as required in [16]. Detailed simulation studies arecarried out to verify the effectiveness of the proposed scheme.The viability of the scheme has been ascertained by per-forming extensive experimental studies on a 2-kW laboratoryprototype.
II. ONE-CYCLE CONTROLLED AC-TO-DC CONVERTER
To understand the principle of operation of the proposedOCC-based ac-to-dc converter, first, the basic one-cycle con-trolled ac-to-dc converter presented in [17] is explained. Theschematic power circuit diagrams of single-phase full-bridgeand three-phase six-switch boost bidirectional converters areshown in Figs. 1 and 2, respectively. The control block diagramof the scheme for the single-phase full-bridge converter isshown in Fig. 3. The dc link capacitor voltage vO is sensed andcompared with the desired value V ∗
O. This error is processed bya proportional–integral (PI) controller to generate a signal VM .Therefore, at steady state, when vO is equal to V ∗
O, the signalVM is proportional to the real component of the source currentof the converter. Using the signal VM , a bipolar sawtoothwaveform of amplitude VM and having a time period of TS is
Fig. 2. Three-phase six-switch boost converter.
Fig. 3. Control block diagram for the single-phase OCC-based converter [17].
synthesized. This is achieved by integrating the signal VM witha time constant Ti so that
Ti =TS
2
where TS is the time period of clock pulses, which resetsthe integrator. The switching frequency of the converter de-vices is the same as that of the frequency of the clockpulses.
At every rising edge of the clock pulse, switches S2 and S4
are turned on, and the source (inductor) current increases. Theexpression for the rising slope K1 of the sensed source currentsignal is given as follows:
K1 = Rs(vS + VO)
L(1)
where vS is the utility voltage, and L is the magnitude of theboost inductor. The output of the comparator, which comparesthe inductor current with the sawtooth waveform, determinesthe turnoff instant of S2 and S4, and the turn-on instant ofS1 and S3. When S1 and S3 are turned on, the sensed boostinductor current signal falls with a slope K2. The value of theslope is given as follows:
K2 = Rs(vS − VO)
L. (2)
Fig. 4 shows the logic used to generate the switching signalsby comparing the sawtooth waveform with the source current,wherein d is the duty ratio of S2 and S4. The control equationfor the converter as given in [17] is presented as follows:
VM (1 − 2d) = RsiS . (3)
GHODKE et al.: ONE-CYCLE CONTROLLED BIDIRECTIONAL HIGH-POWER-FACTOR AC-TO-DC CONVERTER 2461
Fig. 4. Source current along with the sawtooth waveform for the basicone-cycle-controller-based single-phase converter [17].
It is also shown in [17] that the expression for the peak value ofcurrent in each switching cycle is
iS =(VMvS)(VORs)
(4)
where Rs is the gain of the source current sensor. It can beinferred from (4) that the source current is proportional to thesource voltage and, hence, is in phase with it. The approximatevalue of power handled by the converter is given by
PO ≈(VMV 2
S
)(VORs)
(5)
where VS is the rms value of the source voltage. As VM ,VO, and Rs are constants for a given steady-state condition,therefore, iS can be expressed as
iS =vS
Re(6)
wherein
Re =VM
RsVO. (7)
Hence, Re represents the effective or emulated resistance thatthe converter is offering to the utility. The principle of operationof the controller for a three-phase converter shown in Fig. 5 issimilar to that of the single-phase converter [16]. In this case,the phase currents are given by
in ≈ (VMvn)(2VORs)
, n = A,B,C (8)
and the approximate value of the power handled by the three-phase converter is given by
PO ≈ 3VMV 2S
2RsVO(9)
Fig. 5. Control block diagram for a three-phase OCC-based converter [16].
where VS is the rms magnitude of the phase voltage. It canbe concluded from (8) that the respective phase currents andvoltages are in phase. The derivations for (8) and (9) areprovided in Appendix I.
III. CRITERION FOR CURRENT CONTROLLABILITY
It can be inferred from Fig. 4 that if the falling slope K2 >K3, the source current fails to intersect with the carrier sawtoothwaveform in the subsequent cycles, and the system becomesunstable. From Fig. 4
K2(1 − dN )TS + K3dNTS = K1dN+1TS + K3dN+1TS
(10)
where the subscript N represents the N th cycle, N + 1 repre-sents the (N + 1)th cycle, and
K3 =VM
Ti=
2VM
TS=
2VORs
ReTS(11)
where Ti is the time constant of the integrator.Therefore
dN+1 =K2
K1 + K3− K2 − K3
K1 + K3dN . (12)
When |(K2 − K3)/(K1 + K3)| < 1, the control function isconvergent. The combination of (10)–(12) yields the stability
2462 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 6, JUNE 2008
Fig. 6. Control block diagram for the modified one-cycle-controller-basedsingle-phase converter.
criterion as follows:
�vS� <LVM
TiRs(13)
or
VM > −TiRs
LvS(peak). (14)
The signal VM is proportional to the magnitude of powernegotiated by the converter as shown in (5) and (9). Therefore,as the load on the converter falls below the limiting value sothat the inequality of (14) is no longer being satisfied, theoperation becomes unstable. Therefore, combining (5) and (14),the criterion for stable operation can be expressed as
PO >√
2V 3
s Ti
LVO. (15)
The criterion for stability depicted in (14) remains the same forthe three-phase case where vS is the phase voltage [16].
IV. MODIFIED ONE-CYCLE CONTROLLER
A. Single-Phase Case
The schematic control block diagram of the modified one-cycle controller for the single-phase case is shown in Fig. 6.A fictitious current, iF , proportional to the source voltagevS is generated by multiplying the sensed source voltage bya gain 1/RF . The signal iF Rs is then added to the sensedsource current to obtain the signal i0Rs. The signal i0Rs isthen compared with the carrier sawtooth waveform to obtainthe switching instants for the devices S1 to S4. Therefore,in the modified one-cycle controller, instead of the signal iSRs,the signal i0Rs is compared with the carrier sawtooth wave-form, and the rest of the controller structure remains the same asthat of the controller shown in Fig. 3. The logic used to generateswitching signals by comparing the sawtooth waveform withRs(iS + iF ) is shown in Fig. 7. Hence, the control equations(3) and (4) get modified for the proposed controller as follows:
Rs(iS + iF ) = VM (1 − 2d) (16)
iS + iF =(VMvS)(VORs)
(17)
Fig. 7. Sum of the source current and the fictitious current along with thesawtooth waveform for the proposed one-cycle-controller-based single-phaseconverter.
or
vS
Re+
vS
RF=
(VMvS)(VORs)
. (18)
Therefore
VM =Rs
Re(VO) +
Rs
RF(VO). (19)
Combining (14) and (19), the criterion for stable operation canbe derived to be
1RF
>Ti
LVOvS(peak) −
1Re
(20)
and the effective emulated resistance as offered by the con-troller is given by
Reff =RF Re
RF + Re. (21)
Hence, by choosing a suitable value of RF based on (20), thesystem can be made to stably operate even when the converteris operating on no load (Re = ∞) or when the converter isoperating in the inverting mode (Re = −ve).
B. Three-Phase Case
The controller structure for the modified one-cycle-controlled ac-to-dc converter is shown in Fig. 8. Referring toFig. 2 and assuming the average value of the voltage across theboost inductor in a switching period to be zero, it can be shownthat average voltages at nodes A,B, and C with respect to nodeN can be equated to the pertinent sinusoidal functions as [5]
vn = (1 − dn) · VO (n = A,B,C) (22)
GHODKE et al.: ONE-CYCLE CONTROLLED BIDIRECTIONAL HIGH-POWER-FACTOR AC-TO-DC CONVERTER 2463
Fig. 8. Control block diagram for the proposed one-cycle-controller-basedthree-phase converter.
where dA, dB , and dC are the duty ratios for S2, S4, and S6,and vn is the instantaneous ac voltage. The control equation forthe proposed controller is given by
VM (1 − dn) = RsiLn + Rsinf , n = A,B,C (23)
where
VM =VORs
Rel+
VORs
RF. (24)
The emulated resistance Rel represents the effective per-phaseload resistance seen by the ac source, Rs represents the gainof the current controllers employed for sensing the source cur-rents, and iLn (n = A,B,C) is the peak of the boost inductorcurrents. Therefore, the stability criterion remains the same asthat of (20) wherein vS(peak) is to be replaced by vn(peak),and Re is to be replaced by Rel. The logic of generating theswitching pulses for six switches of the converter is shown inFig. 9.
V. INVERTING MODE OF OPERATION
The proposed one-cycle-controller-based converter intro-duced in this paper can also negotiate loads supplying powerback to the source. In this case, the converter would oper-ate as an inverter. The conventional one-cycle-controller-basedconverter fails to operate in the inverting mode as the emu-lated resistance Re assumes a negative value. This also sets a
Fig. 9. Phase currents along with the sawtooth waveform for the proposedthree-phase one-cycle-controller-based converter.
negative value for VM . As a result, the slope of the sawtoothwaveform reverses, which leads to instability in current control-lability. The control structure of earlier schemes on one-cycle-controller-based converter operating in the inverting mode [5],[6], [29] is fairly complicated, as it requires the knowledgeof 60◦ instants of the input voltage and positive and negativecurrent reference vectors for modulation. In the proposed con-troller, the value RF is chosen based on (20) in such a way thatVM assumes a positive magnitude for the minimum expectedvalue of Re or Rel as per (19). The minimum value of Re
or Rel is decided by the maximum power that the converteris expected to feed back to the utility. If the aforementionedcondition is ascertained, then i0 (in the case of single phase)or ieff(n) (n = A,B,C) will be in phase with the respectiveutility voltage(s), although iS (in the case of single phase) oriLn (n = A,B,C) is 180◦ out of phase with respect to thephase voltage(s).
VI. LARGE SIGNAL MODEL AND ANALYSIS OF THE
PROPOSED ONE-CYCLE-CONTROLLER-BASED
CONVERTERS
A. Modified One-Cycle-Controlled Single-Phase Converter
As shown in Fig. 7, the sum of the source current signal(RsiS) and the fictitious current RsiF = (Rs/RF )vS is com-pared with the sawtooth waveform to generate the switchingpulses.
Therefore
RsiO = Rs(iS + iF ) = Rs
(iS +
1RF
vS
). (25)
Referring to Fig. 7, the change in current within a switchingcycle is given by
∆iS = IN+1 − IN = I∗N + K1t1 − (I∗N − K2t2) .
2464 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 6, JUNE 2008
Fig. 10. Phasor circuit model of the modified single-phase one-cycle-controller-based converter.
Substituting K1 and K2 from (1) and (2)
∆iS = K1t1 + K2t2 =(
vS + VO
L
)t1 +
(vS − VO
L
)t2.
(26)
The change in the peak current between two switching cyclescan be expressed as follows:
∆iS =vS
L(t1 + t2) +
VO
L(t1 − t2). (27)
Referring to Fig. 7 and assuming that the change in the on-time(t1) of the switch in two consecutive switching cycles is small,time t1 and t2 can be expressed as
t1 =VM − IN+1
K3, t2 =
VM + IN+1
K3.
Therefore, the difference (t1 − t2) can be expressed as follows:
(t1 − t2) =(VM − IN+1) − (VM + IN+1)
K3= −IN+1
VMTS .
(28)
From (27) and (28)
L∆iSTS
= vS − RsVO
VMiO. (29)
Combining (24) and (29)
∆iSTS
= vS − RsVO
VM
(iS +
1RF
vS
). (30)
Considering the switching time period TS to be small, (30) canbe approximated and is given by (31). Considering vS to be asinusoidal forcing function and neglecting the harmonic contentin iS , the steady-state phasor form of (31) can be represented as(32), i.e.,
RsVO
VMiS + L
diSdt
= vS
(1 − Rs
RF
VO
VM
)(31)
iS =VS
(1 − Rs
RF
VO
VM
)RsVO
VM+ jωL
. (32)
Based on (32), the steady-state phasor model of the systemis depicted in Fig. 10. From this phasor model, it can be in-ferred that if ((Rs/RF )(VO/VM )) < 1, the converter operatesin the rectifying mode, and if ((Rs/RF )(VO/VM )) > 1, theconverter operates in the inverting mode.
Fig. 11. Phasor circuit model of the modified three-phase one-cycle-controller-based converter.
B. Modified One-Cycle-Controlled Three-Phase Converter
The waveforms of the sum of phase currents and fictitiouscurrents inf = Vn/RF (n = A,B,C) along with the sawtoothwaveform are shown in Fig. 9. ieff(n) is given as follows:
ieff(n) =Rs(inf +iLn)=Rs
(Vn
RF+iLn
), n=A,B,C.
(33)
Moreover
t2 =IOA − IOB
K3
t3 =IOB − IOC
K3. (34)
The change in current in phase A is given by
∆IA =vA
LA(TS) − vA
3LA(t3 + 2t2). (35)
Combining (33)–(35) and considering TS to be small, (35) canbe approximated as
RsVO
2VMiA + LA
diAdt
= vA
(1 − Rs
RF
VO
2VM
). (36)
Considering VA to be a sinusoidal forcing function and neglect-ing the harmonic content in iA, the steady-state phasor form of(36) can be represented as follows:
iA =vA
(1 − Rs
RF
VO
2VM
)RsVO
2VM+ jωLA
. (37)
Therefore, the input currents of the three phases are given by
in =vn
(1 − Rs
RF
VO
2VM
)RsVO
2VM+ jωLn
, n = A,B,C. (38)
Based on (38), the steady-state phasor model of the systemis depicted in Fig. 11 from which it can be inferred that if((Rs/RF )(VO/2VM )) < 1, the converter operates in the rec-tifying mode, and if ((Rs/RF )(VO/2VM )) > 1, the converteroperates in the inverting mode.
GHODKE et al.: ONE-CYCLE CONTROLLED BIDIRECTIONAL HIGH-POWER-FACTOR AC-TO-DC CONVERTER 2465
Fig. 12. (a) Large signal line frequency converter model, averaged over oneswitching period TS . (b) Separation of the power source into its constant andtime-varying components. (c) Removal of second-harmonic components byaveraging over one half of the ac line period T2L. (d) Small-signal modelobtained by perturbation and linearization of (c). (e) Simplified small-signalmodel of (d). (f) Simplified small-signal linearized model for a constantpower flow.
TABLE IPARAMETERS USED FOR SIMULATING THE
PROPOSED ONE-CYCLE-CONTROLLER-BASED
BIDIRECTIONAL CONVERTER
VII. SMALL-SIGNAL MODELING OF THE VOLTAGE
CONTROLLER LOOP FOR A MODIFIED
OCC CONTROLLER
A small-signal model of the converter based on the modifiedone-cycle controller is derived to determine the transfer func-tion v0(s)/vM (s) of the system. The treatment followed hereis adapted from [28]. The averaged large signal model of theconverter is shown in Fig. 12. If the ac grid input voltage vS isexpressed as
vS(t) =√
2 · VS sin(ωt) (39)
then the instantaneous output power averaged over a switchingcycle TS〈pTotal〉TS
is given by
〈pTotal(t)〉TS=
〈vS(t)〉2TS
Reff=
V 2S
Reff(1 − cos(2ωt)) . (40)
Now, 〈pTotal〉TS= PLoad + PF , where PF represents the fic-
titious power due to the presence of RF in the controller. Theoutput power consists of a constant term V 2
S /Reff and a termthat varies with twice the frequency of the utility. These twoterms are explicitly shown in Fig. 12(b). As the closed-loopvoltage controller is designed with low bandwidth (< 10 Hz),the second-harmonic component of the output voltage will befiltered out and, hence, is not seen by the controller. By averag-ing the model of Fig. 12(b) over one half of the ac line period,the model shown in Fig. 12(c) is obtained. This step removesthe second-harmonic variation in the power expression [28].
From Fig. 12(c), the power at the input and output ports canbe expressed as
〈i2〉T2L · 〈VO〉T2L = 〈PTotal〉T2L (41)
or
〈i2〉T2L =〈PTotal〉T2L
〈VO(t)〉T2L
(42)
where 〈i2〉T2L is the current, 〈VO(t)〉T2L is the dc linkcapacitor voltage, and 〈PTotal〉T2L is the total power aver-aged over a half-line ac line period, as given in Fig. 12(c).Therefore, 〈PTotal〉T2L = V 2
Srms/Reff . It may be noted that
2466 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 6, JUNE 2008
Fig. 13. Schematic test setup for a three-phase six-switch boost converter in rectifier and inverting modes of operations.
second-harmonic components are absent in the dc link capacitorvoltage. Hence
i2 =V 2
S
Reff · VO(43)
PTotal =V 2
S
Reff. (44)
The circuit model depicted in Fig. 12(c) is time invariant butnonlinear. To linearize the system, small-signal perturbation isapplied around a steady-state operating point so that
VS =V S + vS , VO = V O + vO
VM =V M + vM , i2 = i2 + i2.
The Taylor series expansion of the function
i2(VS , VO, VM ) =V 2
S
Reff · VO
yields
i2 =∂i2∂vS
vS +∂i2∂vO
vO +∂i2∂vM
vM .
Assuming line voltage VS to be constant, i.e., vS = 0, the aboveequation reduces to
i2 =∂i2∂vO
vO +∂i2∂vM
vM = − vO
r2+ j2vM .
Define 1/r2 = −∂i2/∂vO and j2 = ∂i2/∂vM . The coefficientsr2 and j2 are evaluated as follows:
∂i2∂vO
=∂
∂vO
[V 2
S
ReffVO
]=
−V 2S
Reff · V 2O
= − 1r2
or
−r2 =V 2
O
V 2S
Reff =V 2
O
PTotal(45)
where r2 = −V 2O/PTotal, which is the load (output) incremen-
tal resistance, and
j2 =∂i2∂vM
=∂
∂vM
[V 2
S
ReffVO
]
=∂
∂Reff
[V 2
S
ReffVO
]× ∂Reff
∂vM= −
[V 2
S
R2effVO
]× ∂Reff
∂vM.
Since Reff = (Rs/VM )VO, j2 can be rewritten as
j2= −[
V 2S
R2effVO
]× ∂
∂vM
[RsVO
vM
]= −
[V 2
S
R2effVO
]×
[RsVO
−V 2M
]
or
j2 =V 2
S Rs
V 2MR2
eff
=PTotal
V 2M
Reff
Rs
=PTotal
VOVM. (46)
The small-signal linearized model of the system is shown inFig. 12(d), where j2 = PTotal/VOVM and r2 = −VS/ReffV 2
O.If the modified OCC converter is feeding a constant power
load PTotal, then the incremental resistance is given by−V 2
S /PTotal [28]. It can be noted that this incremental re-sistance of a constant power load is equal in magnitude butopposite in polarity to that of a modified OCC converter.This incremental resistance of the modified OCC converteris r2 = −V 2
S /PTotal. The parallel combination of these twoincremental resistances, i.e., V 2
S /PTotal‖ − V 2S /PTotal, tends to
infinity. A small-signal block diagram for a constant power loadis reduced to the equivalent circuit model shown in Fig. 12(e).Therefore, the transfer function of the system is given by
vO(s)vM (s)
=j2
sCF(47)
or
vO(s)vM (s)
=PTotal
VOVMsCF. (48)
GHODKE et al.: ONE-CYCLE CONTROLLED BIDIRECTIONAL HIGH-POWER-FACTOR AC-TO-DC CONVERTER 2467
Fig. 14. (a) Simulated result of a conventional OCC-based three-phase converter when the load is periodically changed from 10 kW to 100 W. (b) Simulatedresult of the modified one-cycle-controller-based three-phase converter when the load is periodically changed from 10 kW to 100 W. (c) Simulated result ofthe modified three-phase one-cycle-controller-based converter operating in inverting and rectifying modes. (d) One of the phase voltages and currents under thedistorted supply voltage condition.
VIII. DESIGN OF PI CONTROLLER
The open-loop transfer function of the system is expressed asfollows:
vO(s)vM (s)
=PTotal
VOVMsCF× KV (49)
where KV is the attenuation factor for the output dc link voltagesensor, or
vO(s)vM (s)
=A1
s
where
A1 =PTotal
VOVMCFKV .
Hence, the plot of the logarithmic gain of the open-loop trans-fer function crosses the zero gain at the frequency A1 rad/s.Assuming a closed-loop crossover frequency of FC rad/s anda phase margin of 45◦, the proportionality constant of the PIcontroller KP can be derived as follows:
KP =2πFC
A1. (50)
2468 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 6, JUNE 2008
A phase margin of 45◦ can now be achieved by placing aninverted zero at Fc. The integral gain KI of the PI controllercan, therefore, be derived as
KI = 2πFCKP . (51)
The PI controller is expected to accomplish the output voltageregulation and to give a zero steady-state error (between theactual voltage and its reference). The size of the inductor inthe boost-converter-based rectifier is small, and its influenceon the low-frequency components of the outer loop converterdynamics is negligible [28]. The inner high bandwidth control(one-cycle controller) system converts the inductor currentinto a current source, i.e., 〈iL〉TS
= VS · sin(ωt)/Reff . Thebandwidth of the inner and outer loops is wide apart (a typicalvalue of 10 kHz/10 Hz, i.e., 1000 : 1), so that the inductorimpedance does not reflect in the outer loop small-signalmodel.
IX. SIMULATED PERFORMANCE
To predict the performance of the modified one-cycle con-troller proposed here, detailed simulation studies are carriedout on the three-phase bidirectional ac-to-dc converter on aMATLAB/Simulink platform. The parameters chosen for thispurpose are provided in Table I. The schematic power circuitdiagram used for the study is depicted in Fig. 13. The single-pole double-throw (SPDT) switch changes the mode of opera-tion of the converter from rectifying to inverting as the switchposition is changed from 2 to 1. When the converter is operatingin the inverting mode, the average power fed back to the utilityis given by
Pinv =(
VG − VO
Rc
)VO (52)
whereas in the rectifying mode, the power drawn from theutility is given by
Prect =V 2
O
RL. (53)
Simulated waveforms of the conventional OCC-based three-phase converter operating in the rectifying mode are provided inFig. 14(a). The dc side load is periodically changed from 10 kWto 100 W while the SPDT switch is in position 2. Trace 1 showsthree-phase currents of the converter. Trace 2 shows phase Autility voltage and current, whereas trace 3 depicts VM . It canbe seen that as the load on the converter reduces to a low value,the current drawn by the converter from the utility becomesuncontrollable, and the dc link voltage becomes unregulated.Fig. 14(b) shows the results of the proposed scheme for thesame condition. It can be observed that the regions of instabilityin current at light load condition are absent, and the dc linkvoltage remains regulated. The operation of the modified one-cycle-controller-based converter is made to swing between theinverting and rectifying modes of operation, and the simulatedwaveforms are shown in Fig. 14(c). In this case, the dc side loadon the converter is changed from −11 to +10 kW and back.
Fig. 15. Photograph of the laboratory prototype.
TABLE IIPARAMETERS USED FOR THE LABORATORY PROTOTYPE
OF THE PROPOSED ONE-CYCLE-CONTROLLER-BASED
BIDIRECTIONAL CONVERTER
From trace 3, it can be seen that the value of VM remains pos-itive during the inverting mode of operation, ensuring stabilityover the whole operating range.
As information regarding instantaneous utility voltages isrequired by the proposed controller, it may appear that distor-tions present in the utility voltage may affect the operation ofthe modified controller. The steady-state performance of theconverter encountering this situation is emulated by deliber-ately introducing switching frequency harmonic distortions inthe utility voltage. The simulated waveforms of one of thephase voltages and currents under this condition are shownin Fig. 14(d). It can be noted that the converter operation isunaffected even in the presence of multiple zero crossings inphase voltages.
X. EXPERIMENTAL STUDIES
A 2-kW laboratory prototype of the proposed three-phasebidirectional one-cycle-controller-based ac-to-dc converter hasbeen developed, the photograph of which is shown in Fig. 15.The schematic power circuit of the experimental setup re-mains essentially the same as that of Fig. 13. The componentsand the parameters chosen for this purpose are provided inTable II. Detailed experimental studies are carried out utilizingthe prototype to confirm the viability of the proposed scheme.The performance comparison of the converter based on theconventional OCC and that based on the proposed scheme
GHODKE et al.: ONE-CYCLE CONTROLLED BIDIRECTIONAL HIGH-POWER-FACTOR AC-TO-DC CONVERTER 2469
Fig. 16. Performance comparison of the converter operating with a con-ventional OCC-based technique and a modified one-cycle-controller-basedtechnique (M-OCC) at light load condition. CH1: Modulating voltage(vm, 5 V/div). CH2: DC link voltage (100 V/div). CH3: Phase A current(iA, 0.4 A/div). CH4: Phase A voltage (vA, 40 V/div). Time scale 40 ms/div.
is depicted in Fig. 16. The converter operates as a rectifiersupplying 250 W at 400 V. Initially, the converter is operatedutilizing the conventional OCC technique by making the signalsvA, vB , and vC to be zero (refer to Fig. 8). At t = 160 ms, thecontrol is transferred to the proposed one-cycle controller (byconnecting the signals vA, vB , and vC). It can be seen that in thecase of the conventional OCC-based converter operation, thecurrent control is lost as VM has become negative. Moreover,the controller is not able to regulate the dc link voltage. The dclink voltage is more than the reference value and is graduallyincreasing, showing that it has become uncontrollable. How-ever, in the case of the proposed one-cycle-controller-basedconverter, VM is positive, and the controllability in the currentand the dc link voltage is restored. The mode of operation of theproposed converter is changed from inverting to rectifying, andthe recorded waveforms are shown in Fig. 17. The active loadon the dc side for the inverting mode of operation is maintainedat −1400 W, whereas for the rectifying mode, it is +1000 W.The results show that the performance of the converter duringthe changeover is satisfactory, and the instability in currentcontrollability is absent. Fig. 18(a) shows one of the utilityvoltages and input currents of the three phases and the harmonicspectrum of phase A current for the rectifying mode of opera-tion. The same quantities for the inverting mode of operationare shown in Fig. 18(b). It can be noted from the harmonicspectrum that all the low-order harmonics are absent in theinput current of the converter, and the total harmonic distortion(THD) of the current is found to be less than 4%, in the rangeof half to full load when the utility voltage is having a THD ofaround 2%.
As the information regarding instantaneous utility voltagesis required by the controller, it may appear that the distortionspresent in the utility voltage may affect the operation of theproposed controller. The steady-state performance of the con-verter encountering this situation is emulated by deliberatelyintroducing harmonic distortions in the utility voltage. This
Fig. 17. Performance of the modified one-cycle-controller-based converterwhen the mode of operation is abruptly changed from inverting to rectifying.CH1: Load current (Io, 2 A/div). CH2: DC link voltage (100 V/div). CH3:Phase current (iA, 5 A/div). CH4: Phase voltage (vA, 100 V/div). Time scale10 ms/div.
is achieved by connecting 50-µH inductors in series with thesource. Due to the presence of switching frequency harmonicsin the current drawn by the converter, the utility voltages getdistorted. These distorted voltages are fed to the proposedcontroller of the converter for generating the fictitious currents.The measured waveforms of three utility voltages and phase Acurrent under this situation for the rectifying mode of operationare shown in Fig. 19(a). It can be noted that, although theutility voltages have multiple zero crossings, the operation ofthe converter is not affected by them.
The efficiency of the proposed converter and the THDof the source current are measured for various load condi-tions by employing Voltech power analyzer, PM3000A. Theplots showing the variation of efficiency and the THD ofthe converter operating in rectifying and inverting modes areshown in Fig. 20(a) and (b), respectively. The full load effi-ciency of the system is found to be 97.85% for the rectifyingmode of operation and 96.58% for the inverting mode ofoperation.
XI. CONCLUSION
A modified one-cycle controller for a bidirectional three-phase boost ac-to-dc converter is proposed. The inherent lim-itations of the conventional OCC-based converter, such asinstability in current controllability at a light load and the invert-ing mode of operation, are overcome in the proposed scheme.This feature is incorporated without requiring the knowledge of60◦ angular sectors and other details of the utility voltage. Inaddition, the service of analog multiplexers and the synthesisof positive and negative reference voltage vectors are alsonot required. The overall control structure is simple. Detailedsimulation studies are carried out to verify the effectiveness ofthe scheme. The viability of the scheme is confirmed throughdetailed experimental studies.
2470 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 6, JUNE 2008
Fig. 18. (a) Phase currents and the harmonic spectrum of phase A currentfor the rectifier mode of operation. CH1–CH3: Phase currents (2 A/div).CH4: Phase voltage (vA, 100 V/div). Ch-M: Harmonic spectrum of phaseA current (iA, 0.5 A/div). Time scale 4 ms/div. (b) Phase currents and theharmonic spectrum of phase A current for the inverter mode of operation.CH1–CH3: Phase currents (2 A/div). CH4: Phase voltage (vA, 100 V/div).Ch-M: Harmonic spectrum of phase A current (iA, 0.5 A/div). Time scale4 ms/div.
APPENDIX
DERIVATION OF THE SOURCE CURRENT AND THE INPUT
POWER FOR THE ONE-CYCLE-CONTROLLED
THREE-PHASE AC-TO-DC CONVERTER
Instants depicting intersections among the sawtooth wave-form with three-phase currents drawn at a particular switchingcycle, wherein iA > iB > iC , are shown in Fig. 21. Consid-ering Rs = 1, the duration for which iA, iB , and iC are lessthan the sawtooth waveform is t1, whereas t4 is the duration forwhich iA, iB , and iC are greater than the sawtooth waveform.The duration for which only iA is greater than the sawtooth ist2, whereas t3 is the duration for which only ic is less than thesawtooth waveform. The slopes of the source currents of each
Fig. 19. Phase voltages and current in the rectifier mode of operation underthe distorted supply voltage condition. CH1–CH3: Phase voltages (100 V/div).CH4: Phase A (iA, 5.0 A/div). Time scale 10 ms/div.
Fig. 20. (a) Variation of efficiency and the THD of the converter with load inthe rectifying mode of operation. (b) Variation of efficiency and the THD of theconverter with load in the inverting mode of operation.
phase n (where n is A, B, or C) for the time durations t1, t2,t3, and t4 are K1n, K2n, K3n, and K4n, respectively, and arelisted in Table III.
GHODKE et al.: ONE-CYCLE CONTROLLED BIDIRECTIONAL HIGH-POWER-FACTOR AC-TO-DC CONVERTER 2471
Fig. 21. Phase currents along with the sawtooth waveforms for the three-phase OCC-based converter.
TABLE IIISLOPES OF PHASE CURRENTS AT VARIOUS SWITCHING INSTANTS
Since the utility considered is a three-phase three-wiresystem
iA + iB + iC = 0. (54)
Therefore
t3 =IB − IC
K3, t2 =
IA − IB
K3(55)
where IA, IB , and IC denote the magnitude of iA, iB , and iCat the instants where they intersect with the falling slope of thesawtooth waveform. The change in the phase A current, i.e.,∆iA, during a switching cycle (∆t = TS) is given by
∆iA =vA
LATS − VO
3LA(2t2 + t3). (56)
Combining (55) and (56), and using (54)
vA = LA∆iATS
+iAVO
K3TS. (57)
Substituting K3 from (11) and considering the switching timeperiod to be small, (57) can be approximated as
vA = LAdiAdt
+iAVO
2VM. (58)
Considering vA to be a sinusoidal forcing function and neglect-ing the harmonic content of iA, the steady-state phasor form of(58) can be approximated for phase A as follows:
iA =vA
VO
2VM+ jωLA
. (59)
Therefore, three-phase source currents can be represented as
in =vn
VO
2VM+ jωLn
, n = A,B,C. (60)
As ωLn is considerably small compared to the ratio of VO andVM , (60) can be approximated as follows:
in ≈ VM vn
2VO, n = A,B,C. (61)
Considering the gain of current sensors utilized for measuringsource currents to be Rs, (61) can be expressed as
in ≈ VM vn
2RsVO, n = A,B,C. (62)
The power drawn by the three-phase one-cycle-controlledac-to-dc converter can, therefore, be expressed as follows:
PO ≈ 3VMv2S
2RsVO. (63)
ACKNOWLEDGMENT
D. V. Ghodke would like to thank A. Sharma andE. S. Shreeraj for their help in discussions at various stages.The authors would also like to thank K. Muralikrishan andB. Aray for their help in hardware, assembly, and testing.
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Dharmraj V. Ghodke (M’01–S’03) was born inSolapur, Maharashtra, India, on October 20, 1968.He received the B.E. degree in electrical engineeringfrom the Shivaji University, Kolhapur, India, in 1991.He is currently working toward the Ph.D. degree inpower electronics at Indian Institute of TechnologyBombay, Mumbai, India.
He joined the 35th batch of training school inBhabha Atomic Research Centre, Department ofAtomic Energy, Mumbai. After the training, in 1992,he joined Raja Ramanna Centre for Advanced Tech-
nology, Indore, India, as a Scientific Officer. There, he demonstrated firstindigenous solid-state pulsed modulator for copper vapor laser to replace thethyratron-based pulsed modulator. He also designed and developed variouscircuits for low-voltage and high-voltage isolated switch mode power supplies,capacitor charging power supply of 1 W to 11 kW, and trigger and driver unitsfor IGBT-based and thyratron-based pulsed modulators. These developmentswere made for different kinds of lasers. He is specialized in the area ofhigh-frequency high-power switch mode and solid-state pulse power supply,auxiliary controllers, and circuits for laser applications. His current researchinterests include simulation and digital controller of PWM active UPF rectifiers,active filters, and ac-to-dc and dc-to-dc converters for high-power applications.
Kishore Chatterjee was born in Calcutta, India, in1967. He received the B.E. degree from the MaulanaAzad College of Technology, Bhopal, India, in 1990,the M.E. degree from Bengal Engineering Col-lege, Calcutta, in 1992, and the Ph.D. degree fromthe Indian Institute of Technology, Kanpur, India,in 1998.
From 1997 to 1998, he was a Senior ResearchAssociate with Indian Institute of Technology, wherehe was involved with a project on power factor cor-rection and active power filtering, which was being
sponsored by the Central Board of Irrigation and Power, India. In 1998, hewas an Assistant Professor with the Department of Electrical Engineering,Indian Institute of Technology Bombay, Mumbai, India, where he has been anAssociate Professor since 2005. His current research interests include modernvar compensators, active power filters, utility-friendly converter topologies, andinduction motor drives.
B. G. Fernandes received the B.Tech. degree fromMysore University, Mysore, India, in 1984, theM.Tech. degree from Indian Institute of Technology,Kharagpur, India, in 1989, and the Ph.D. degree fromIndian Institute of Technology Bombay, Mumbai,India, in 1993.
He was an Assistant Professor with the Depart-ment of Electrical Engineering, Indian Institute ofTechnology, Kanpur, India. In 1997, he joined theDepartment of Electrical Engineering, Indian Insti-tute of Technology Bombay, where he is currently a
Professor. His current research interests include permanent magnet machines,high-performance ac drives, quasi-resonant link converter topologies, andpower electronic interfaces for nonconventional energy sources.
