[doi 10.1109%2ftpel.2014.2310731] j. galvez; m. ordonez -- swinging bus operation of inverters for...

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI10.1109/TPEL.2014.2310731, IEEE Transactions on Power Electronics

1

Swinging Bus Operation of Inverters for Fuel CellApplications with Small DC-Link Capacitance

Juan M. Galvez, Student Member, IEEE, and Martin Ordonez, Member, IEEE

Abstract—For reliability reasons, the employment of smallfilm capacitors instead of electrolytic ones is an interestingalternative for the dc-link in single-phase inverters for fuelcell applications. Due to the low capacitance that can beaccomplished at an acceptable cost using this technology, thereare large low-frequency voltage fluctuations (100Hz/120Hz andharmonics) in the dc-link caused by the double-frequencypower transfer. By allowing these variations in the bus, thecapacitor bank absorbs the current ripple from the inverter toavoid detrimental oscillations in the fuel cell. Traditional con-trol strategies for inverters are usually designed to operate withnearly constant input voltage and are not able to effectivelyhandle large (e.g., > 10%) low-frequency input voltage fluctua-tions. This manuscript introduces the analysis of a swinging busin the context of fuel cell standalone applications (i.e., voltage-source inverters) and proposes a non-linear control approachto operate inverters with very large input voltage swing:the Natural Switching Surface (NSS). Under the proposedscheme, the inverter presents excellent dynamic and steady-state characteristics, even at moderate switching frequency(e.g., 3.6kHz). In order to illustrate the superior performanceof the NSS, a comparison to a proportional-resonant controlleris performed. Unlike the linear compensator, the NSS is able toreject the large bus voltage oscillations and achieve high-qualityoutput voltage with low total harmonic distortion (THD).Simulation and experimental results are provided to illustratethe behavior of the swinging bus and to validate the NSS controlscheme under the proposed demanding operating conditions.

Index Terms - Boundary control, dc-link, Film capacitors,Fuel Cell Applications, Natural Switching Surface,Normalization, Swinging Bus, Voltage-Source Inverter.

I. INTRODUCTION

Fuel Cells (FCs) are a type of power source that has been gaininga lot of attention in the last decade due to their high efficiency undera wide range of operating conditions and a projected reductionin their cost [1]. Power extraction from these devices is a topicof critical importance and many research efforts have been madein order to enhance the performance and extend life expectancy.Three-phase inverters with unbalanced load and single-phase in-verters present a characteristic low-frequency current ripple on thedc power source that is inherent to these systems and is producedby the double-frequency power transfer from the output of thesystem. In order to maximize power extraction, this 100Hz/120Hz(and harmonics) current ripple reflection into the fuel cell must

J. M. Galvez and M. Ordonez are with the Department of Electrical andComputer Engineering, The University of British Columbia, Vancouver,BC, V6T 1Z4, Canada (e-mail: [email protected], [email protected]).

be minimized or eliminated since it generates undesired effects onthe source, such as a significant reduction in power delivery [2,3], a decrease in hydrogen utilization [4] leading to a decreasein efficiency [5], the degradation of materials and the consequentdiminution in performance [6] and the shortening of lifetime [7].

Many schemes requiring extra hardware have been proposed tomitigate the aforementioned ripple by using an active filter [8, 9],auxiliary energy storage systems (batteries and super-capacitors)[10–12] or auxiliary power conditioning modules [13–15], whichincrease the size and cost of the system. In recent literature, awaveform control has been proposed for current ripple eliminationin a single-stage differential inverter [16]. Under this scheme,the low-frequency current component is absorbed by the outputcapacitors and the dc component is supplied by the fuel cell.

In two-stage converters, traditional controllers for inverters typ-ically operate with nearly constant bus voltage, requiring large andunreliable electrolytic capacitors to minimize the low-frequencyripple. If a smaller capacitance is used and the dc-link is controlledto minimize the double-frequency fluctuations, the low-frequencycurrent ripple is reflected to the fuel cell. This undesirable effectcan be mitigated if a swinging dc-link is used instead in such away that the bus absorbs the current oscillations, and without theneed for extra components, as proposed by recent literature [17–20]. However, the double-frequency fluctuations (100Hz/120Hz andharmonics) at the input terminals of inverters present a challengeto the control scheme, injecting significant harmonic content to theoutput [21]. A solution for grid tie inverters has been proposed[22], in which a second-order notch filter is used to eliminate thelow-frequency ripple from the current reference and obtain a high-quality output current. However, a solution for standalone voltage-source inverters for fuel cell applications is lacking in the literature.

The power conversion system that interfaces the fuel cell andthe load should have a minimum lifespan, greater that the lifeexpectancy of the source. The requirements for the lifetime offuel cell can vary significantly for different applications, rangingfrom approximately 4,000 for intermittent operation to 40,000hours when running continuously in stationary applications [23,24]. The electrolytic capacitors employed for the dc bus are theweak link in the system since they are prone to failures andhave a reduced life span [25, 26]. A small film capacitor can beconnected across the electrolytic capacitor bank to increase thelifetime of the dc-link since part of the current ripple is handledby the film capacitor and the electrolytic capacitors dissipate lesspower. However, as can be seen in Fig. 2 of [27], the magnitudeof the low-frequency current ripple (especially significant in thisapplication) is scarcely reduced, while the high-frequency contentis considerably attenuated. Therefore, the electrolytic capacitorsstill have to deal with the double-frequency ripple, which isthe limiting factor in this case. Another alternative is replacingelectrolytic capacitors and employing small film capacitors insteadto increase the system reliability [9, 28–34]. Due to the elevated



2

THD = 4.5%

Load step

glitches

THD = 2.1%

No load step

glitches

vo

vo

(a)

(b)

vo

+

-

Q1

Q2

Q3

Q4

+

-

Q1Q2Q3Q4

PR + feedforward

Control

Swinging bus voltage

(20% V )bus

vbus

200V

240V

vo

+

-

Q1

Q2

Q3

Q4

+

-

Q1Q2Q3Q4

NSS

Control

Swinging bus voltage

(20% V )bus

vbus

200V

240V

Fig. 1. Swinging bus operation of an inverter using (a) a traditional linear controller and (a) the proposed control scheme.

cost of this technology, the capacitance in the dc-link should beminimized, which is in contrast with the requirement of traditionalcontrollers of having small low-frequency voltage ripple at theinput terminals of the inverter. A control scheme for invertersable to handle these fluctuations can combine the advantages ofextended lifetime of the system (a more reliable technology as filmcapacitors can replace electrolytic capacitors), higher efficiencyin the power extraction from the fuel cell (the current ripple iseliminated), and high-quality sinusoidal synthesis for a wide rangeof input voltages.

This paper presents a thorough characterization of the swingingbus to provide insight into its behavior and establish the require-ments for inverters with varying dc-link in fuel cell standaloneapplications. A technical solution based on boundary control isproposed using the Natural Switching Surface (NSS), a non-linearcontrol scheme that provides high-quality sinusoidal synthesis fora wide range of input voltages and loading conditions. This isillustrated in Fig. 1, in which the performance of the proposedcontrol technique is conceptually contrasted to that of a traditionallinear controller, highlighting the enhanced behavior of the NSS.A full set of experimental results, including different loading andoperating conditions, is provided in Section IV. The control ofinverters with nearly constant dc-link using non-linear controlbased on switching surfaces (SSs) has been gaining attention [35–38] although there is no indication of their ability to handle largelow-frequency ripple on the dc-link. The boundaries or SSs splitthe state-plane in regions, and depending on whether the operatingpoint is on one side of the SS or the other, the state of theswitches is determined. Inverters can benefit from this type ofcontrollers if the boundaries are properly selected, since preciseand predictable behavior can be achieved, with high-performancedynamic and steady-state characteristics. This paper introduces the

concept of boundary control for swinging bus inverters, employingthe normalized natural trajectories of the converter in the state-plane as the analytical framework for the study. The behaviors ofthe inverter and the dc-link are analyzed geometrically and thecontrol laws are derived based on the insight gained. Simulationand experimental results are presented to confirm the theoreticalpredictions and the properties of the proposed control strategy.The results are compared to those of a linear PR controller withinput voltage feedforward, verifying the superior performance ofthe NSS.

II. SWINGING BUS OPERATION AND THE NATURALSWITCHING SURFACE

A simplified schematic diagram of the power conversion systemconsidered in this manuscript is presented in Fig. 2. This two-stagesystem is composed of a fuel cell, a front-end dc-dc converter,the dc-link, and a single-phase inverter. For illustrative purposes,this figure shows some characteristic waveforms. The first powerconversion stage supplies the current ibus to the bus capacitor,which is discharged by the inverter input current iinv . The front-end dc-dc converter is controlled employing a linear dual-loopcompensator with the addition of a filter on the voltage loop.The filter removes the 100Hz/120Hz components and harmonics.Hence, the double-frequency ripple that naturally appears on thebus generated by the single-phase 50Hz/60Hz inverter is eliminatedfrom the feedback, allowing the dc-link to swing at twice the outputfrequency. In this way, the bus absorbs the current oscillations andthe input power is kept constant, therefore, the low-frequency rippledoes not propagate to the fuel cell, maximizing the power extractedfrom the source. Any attempt to minimize the double-frequencyfluctuations in the bus voltage will reflect the 100Hz/120Hz rippleinto the fuel cell, producing detrimental effects on the source. If the



3

vfc vbus

vo

ioC

iC

L

iL

+

-

Q1

Q2

Q3

Q4

Cbus

+

-

Q1

Q2

Q3

Q4

σ( , , , , )iC

vbusvo vr iCr

ifc

Tlinet

io Tline

dc-dc

converter

ibus

Tline

vbus v∆ bus

t

iinv Tline

tt

Swinging strategy

Conventional control

Fig. 2. Fuel cell two-stage power extraction simplified schematic.

reactive current is neglected and a constant dc bus is considered,the current supplied to the inverter iinv is a scaled version of thewaveform of the instantaneous output power (vo×io). For example,for a linear resistive load, iinv is an average sine wave mounted ona DC component. On the other hand, when the dc-link is assumedto have low-frequency ripple components, the current waveformhas some distortion that allows for compensation for a reduced orincreased bus voltage in such a way that the instantaneous inputpower (vbus × iinv) matches the output power.

The full-bridge inverter can be represented mathematically usingnormalized equations to obtain a general expression independentfrom the parameters of the converter. Based on the simplifiedcircuit in Fig. 2, this normalization is performed by using the peakoutput voltage reference Vr = Vop, the characteristic impedanceof the LC output filter Zo =

√L/C, and the natural frequency of

the filter fo = 1/To = 1/(2π√LC) as base quantities for

vxn =vxVr

(1)

ixn =ixVr

Zo (2)

tn = t · fo (3)

where vx and ix represent generic voltages and currents, trepresents time, and vxn, ixn, and tn represent their respectivenormalized values. The behavior of the buck-derived inverter canbe represented by the following normalized differential equations:

diLn

dtn= 2π(vbusnu− von) (4)

dvondtn

= 2π(iLn − ion). (5)

The voltage applied to the inverter output filter can take two activelevels (Fig. 3(a) and (b)), vbus and −vbus depending on the stateof the switches and the direction of the current. This is representedin (4) by u = 1 and u = −1 for vbus and −vbus respectively. Ashort circuit or zero state can also be applied to the output filterwhen u = 0 (Fig. 3(c)). vbusn is highlighted in the equations toindicate this variable is the focus of the study. Based on (4) and(5), a detailed derivation of the normalized natural trajectories of

the converter in the phase plane (λx), which are determined bythe evolution of the instantaneous values of the capacitor currentand voltage in this domain, is given in the Appendix. As well, theswitching surfaces (σx) that rule the behavior of the swinging busthe inverter can be written as follows:

σ1 = λ1 : i2Cn +(von −vbusn)2 = i2Crn +(vrn − vbusn)

2 (6)

σ2 = λ2 : i2Cn + (von)2 = i2Crn + (vrn)

2 (7)

σ3 = λ3 : i2Cn +(von +vbusn)2 = i2Crn +(vrn + vbusn)

2 (8)

where iCn is the normalized output filter capacitor current, iCrn isthe normalized output filter capacitor current reference, von is thenormalized output voltage, vrn is the normalized output voltagereference, and vbusn is the normalized dc-link voltage. Equations(6) to (8) are simple circles that model the geometrical behaviorof the converter (natural trajectories in the phase plane). Theobjective of the control strategy is to select the best combinationof natural trajectories to achieve the target. Note that the center ofthe of the circle is located on vbusnu. Swinging bus operationresults in fluctuations of vbusn, and, therefore, has an impacton the natural trajectories and on the geometrical location of theproposed switching surfaces (6) and (8). The sinusoidal outputvoltage reference of the inverter and the output capacitor currentreference (with normalized peak value equal to the normalizedline frequency fLn) describe an elliptical target trajectory in thenormalized phase plane (red trace in Fig. 4). It is important tonote that the natural trajectories are valid for any possible inverterregardless of the filter values L and C, output voltage reference,and switching frequency. Note that the control laws σx and thenatural trajectory λx are interchangeable. The NSS control laws inmonopolar operation are formally defined by quadrant as:

Quadrant I: if σ2 > 0 then u = 0, else u = 1

Quadrant II: if σ3 > 0 then u = −1, else u = 0

Quadrant III: if σ2 > 0 then u = 0, else u = −1

Quadrant IV: if σ1 > 0 then u = 1, else u = 0.

Fig. 4 shows the conceptual evolution of the natural trajectoriesof the inverter with varying dc-link voltage in monopolar operation.



4

vo

+

-

vcc

+

-

vo

+

-

vcc

+

-

vo

+

-

(a) (c)(b)

Fig. 3. Equivalent circuits for states (a) u = 1, (b) u = −1, and (c) u = 0.

σ2

σ2

iCn

ta

tb

tf

tg

von

te

tc

td

1σ

σ3

th∆vbusn

Vbusn∆vbusn

-Vbusn

Fig. 4. Swinging bus operation using the natural SS (monopolar operation):conceptual evolution of the natural trajectories with swinging dc bus.

The curves σ1, σ2 ,and σ3 depicted in Fig. 4 represent the evolutionof the switching surface as the discrete references (small circleson the elliptical target trajectory) dynamically change (Just a fewpoints are considered to facilitate the visualization of the curves).In each quadrant, there are two circular natural trajectories thatdirect the operating point towards the outside of the ellipticaltarget trajectory (red trace) and one that brings the point insidethe reference trajectory again. Under the proposed scheme, theswitching surface that coincides with the latter natural trajectory ischosen in each sector, guaranteeing that the output will not growunbounded. For example, in Quadrant I, the blue trace representsthe evolution of the operating point in the normalized state plane.As can be seen, this trace moves according to the natural trajectoryλ1 (u = 1) until the corresponding switching surface σ2 isintersected and the structure of the inverter changes (u = 0).At that moment, the operating point is forced to move along thenatural trajectory λ2, and since the perimeter of this circle matchesthe target (small circles on the elliptical trajectory), the controlobjective is accomplished. The references change dynamically indiscrete steps as well as the bus voltage, and the radius of the circleσ2 is adjusted to match the new target (see (7)), and, therefore,the operating point is maintained around the target at all times.A similar analysis can be performed for the other sectors. ForQuadrants II and IV, in addition to the radius, the center of thecircles σ1 and σ3 respectively is adjusted as the bus voltage swings(refer to (6) and (8)).

In addition to the monopolar operation, the NSS control lawsfor bipolar mode (i.e., the zero state is not allowed) are defined byquadrant as:

Quadrants I and II: if σ3 > 0 then u = −1, else u = 1

Quadrants III and IV: if σ1 > 0 then u = 1, else u = −1.

For the case of the swinging bus inverter, a mixed modeoperation will be considered, i.e., a combination of monopolarand bipolar operation that merges the advantages of monopolarmode (reduced voltage and current ripples in the output filter)and bipolar mode (distortion elimination in the region of outputvoltage zero-crossing, especially under heavy loading conditions).When low-frequency ripple is considered in the dc-link instead of anearly constant bus (the main focus of this paper), the bus voltageevolution (vbusn) results in a dynamic evolution of the naturaltrajectories. This is conceptually represented in Fig. 5 and can beexplained as follows:

The variations on the bus voltage happen in a periodic fashionand reflect the current charge from the fuel cell and the pulsatingcurrent discharge of the bus capacitor Cbus, which depends onthe nature of the inverter load. The current fed to the inverteriinv is subtracted from the constant input current supplied bythe first power stage (dc-dc converter), which is equal to theaverage inverter input current, yielding the bus capacitor current.For illustrative purposes, the behavior of the system under linearresistive load is analyzed. The phase-plane representation of thedc-link capacitor Cbus is shown in Fig. 5(a), where the buscapacitor current is filtered in order to eliminate the ripple at theinverter switching frequency and to recover the fundamental. Fivedistinctive points can be observed in the periodic behavior:

• t1 represents the start of a cycle (where vbus is nominal).• t2 corresponds to the instant in which the inverter input

current equals the current injection into Cbus (maximum busvoltage occurs).

• t3 denotes the instant of negative peak current in the capacitorat nominal bus voltage.

• t4 corresponds to the instant in which the inverter inputcurrent matches the current injection into Cbus (minimumbus voltage).

• t5 represents the end of the cycle and the start of a new one(vbus is nominal).

These five distinctive points are mapped into Quadrants I andIV of the inverter phase plane (normalized output voltage versusnormalized output capacitor current) depicted in Fig. 5(b) to gaininsight into the dynamic evolution of the NSS. The referencesvalues at instants t1 to t5 are indicated in the elliptical targettrajectory as circles. In addition, the evolution of the bus voltage(which corresponds to the center of the circular SS σ1 (6)) isindicated with t1 to t5 marked as dots on the horizontal axis. Hence,the switching surfaces at the distinctive moments mentioned beforeare obtained by evaluating (6) and (7) with the current bus voltageand references values at the respective instants.

When the inverter is operated in Quadrant I, the behavior isgoverned by σ2 (7), which is a circle whose center is in 0 and isindependent of vbusn. Therefore, the fluctuations in the dc-link donot affect the SS. For instance, the dc-link reaches its maximumvoltage at instant t2. However, the SS that intersects the targetoperating trajectory at that instant (σ2b) remains unaltered with its



5

(a) (b)

t4 t2t1t3t5

t2

t3

t4t5

t1

∆vbusn

Vbusn

von

iCn

σ1a

σ1bσ1c

σ2c

σ2b

σ2a

t4 t2

t1

t3

t5

∆vbus

L

iCbus

Vbus

2ω

vbus

bus Lω

PoC

=busV

Fig. 5. Swinging bus operation using the natural trajectories analysis: a) bus capacitor evolution and b) natural trajectories with swinging bus.

center in 0. It can be deduced that, during operation in Quadrant I,the fluctuations in the bus voltage only affect the natural trajectoriesfor u = 1 (λ1). When the operating point crosses the boundaryσ2b, the control law makes the converter to change its structure(u = 0) and the control objective is successfully accomplishedirrespective of the bus voltage. This interesting property (rejectionof any variations in the dc-link voltage) also applies to operationin Quadrant III.

During operation in Quadrant IV, the behavior is reversed byσ1, which depends on the dc-link voltage vbusn. In this case, thecircumference that acts as SS (6) has its center in the normalizedbus voltage. The starting point for the analysis is the instant t3,which corresponds to the boundary between Quadrants I and IV(maximum output voltage and current). As shown in Fig. 5(b), thebus voltage is nominal at t3, and, therefore, the NSS control law atthis instant is exactly the same for both varying and constant dc-link operation. Furthermore, since the synthesis of the crest of theoutput voltage happens for nominal bus voltage, operation underswinging bus does not affect the bus voltage availability duringthat critical interval.

It can be concluded that the geometrical location of the NSScontrol laws is not affected by the low-frequency ripple in the dc-link either in Quadrant I or the boundary between Quadrants Iand IV. Now, the behavior of the NSS σ1 at instant t4 shouldbe analyzed, which corresponds to minimum bus voltage. Thedisplacement of the center of the circumference (6) is consistentwith the reduction in vbusn, as depicted in Fig. 5(b). Althoughthe geometrical location of the SS for swinging bus operationis different compared to the one under constant dc-link voltage,and since the inverter switching frequency is higher than the100Hz/120Hz component present in the bus, it can be consideredthat the system operates in a fixed voltage fashion with a reducedvalue. In this case, it is necessary to measure the dc-link voltage toaccurately compute the σ1 and obtain all the benefits of the NSSperformance.

To summarize, between instants t3 and t4, the dc-link voltageexperiences a progressive reduction until the minimum is achievedat t4. Thereafter, the bus voltage increases to reach its nominal

0 0.5 1 1.5

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

von

i Cn

σ2

σ1σ1a

σ1b

∆vbusn

t2

t4t5

t3

t5t3 t2t4 /

Fig. 6. Swinging bus operation with 20% voltage variation: Quadrants Iand IV.

value at t5, which corresponds to the intersection between Quad-rants IV and III. A similar analysis can be performed in QuadrantII, in which σ3 rules the behavior of the converter. For simplicityand clarity, the reactive current that circulates through the filter hasbeen neglected and will be explored in the following section.

III. DYNAMIC ANALYSIS AND SIMULATIONS

The dynamic analysis of the converter in a phase plane is firstpresented, and then extended to the time domain to illustrate someparticular aspects that result from operation under the proposedscheme. The effect of the filter reactive current on the bus voltageis also discussed in this section.

A case example is employed for illustrative purposes with anormalized line frequency fLn = 0.195, normalized switchingfrequency fswn = 11.7, and normalized bus voltage Vbusn = 1.3



6

(nominal), where fLn = 2πfL/ωo and fswn = 2πfsw/ωo. Therest of the specifications are shown in Table II. Due to the constantcurrent injection from the first power stage (dc-dc converter), thepulsating current fed to the inverter, and most importantly, thevalue of the dc-link capacitor, vbusn presents voltage swings of20% (peak-to-peak) for the analyzed example. Fig. 6 depicts thebehavior of the system in Quadrants I and IV under swingingbus operation. The SS σ2 is highlighted in Quadrant I for twodistinctive moments to indicate the instants in which the bus voltagehas its nominal value (t3) and when it reaches its maximum (t2). Asindicated before, σ2 has its center in 0, and, hence, it is not affectedby the variations in the dc-link voltage. When Fig. 6 is comparedto the analysis performed on Fig. 5 in the previous section, a slightshift in the instants of maximum and nominal dc-link voltage canbe observed due to the presence of the reactive current that flowsthrough the LC output filter. It can also be noticed in this figure thatthe normalized peak capacitor current is fLn = 0.195. Therefore,in order to minimize the aforementioned shifting effect, the reactivecurrent should be reduced, which can be accomplished by selectinga higher natural frequency of the LC output filter.

The analysis is extended to Quadrant IV, where another twoSSs are shown. The first one (σ1a) corresponds to the instant inwhich the dc-link voltage is minimum (t4). The center of this circleis located on the normalized bus voltage vbusn (green dot onthe horizontal axis). In this region of Quadrant IV, the inverteris operating in monopolar mode and the behavior of the converterunder the proposed control scheme is as explained in Section II.Following t4, the dc-link voltage reverts again to its nominal valueafter 7 switching cycles in the case example considered (t5). TheSS corresponding to this instant σ1b has its center on vbusn (yellowdot on the horizontal axis) and is located in the region of bipolaroperation. It is interesting to note that the NSS control law inQuadrant IV is identical for monopolar and bipolar operation:

σ1 : i2Cn + (von − vbusn)2 = i2Crn + (vrn − vbusn)

2.

Therefore, in the mixed mode operation in Quadrant IV, theonly difference between monopolar and bipolar mode is that thestructure u = 0 is not allowed in the region of bipolar operationand the structure u = −1 is enforced instead. As the bus voltageincreases, the system continues to operate with σ1 as SS in bipolarmode and transitions to Quadrant III.

So far, the analysis of the inverter under swinging bus operationusing the NSS control strategy has been performed in the phaseplane. While this representation provides valuable geometricalinsight into the behavior of the converter, more understandingof the system can be obtained from the traditional time domainrepresentation.

The analysis of the behavior in the time domain is done usingthe same case example that has been employed throughout thissection. The system presents a cyclic behavior in steady-stateoperation, and, therefore, only one semicycle is examined in detail.Fig. 7 presents the positive semicycle of the normalized outputvoltage (von) that is obtained using the proposed control strategy.Furthermore, in the same figure, the detailed switching sequence(vswn) that is applied to the LC output filter to generate thesinusoidal output voltage can be observed. As can be seen, theamplitude of the PWM pulse train is also modulated as a resultof the low-frequency oscillations in the dc-link. As long as theenvelope of vswn is greater than the normalized output voltagereference vrn, the inverter will be able to effectively synthesize theoutput voltage. The ability of the NSS to successfully reject the

16 18 20 22 24 26−1.5

−1

−0.5

0

0.5

1

1.5

v on

16 18 20 22 24 26−1.5

−1

−0.5

0

0.5

1

1.5

time [ms]

v swn

Fig. 7. Swinging bus operation with 20% voltage variation: normalizedoutput voltage (von) and normalized switching sequence applied to the LCfilter (vswn).

16 18 20 22 24 26

1.2

1.3

1.4v busn

16 18 20 22 24 26−1

−0.5

0

0.5

1

time [ms]

i Cbusn

Fig. 8. Swinging bus operation with 20% voltage variation: effect ofthe inverter switching frequency on normalized bus voltage (vbusn) andnormalized bus capacitor current (iCbusn).

significant variations in the bus voltage and produce high-qualitysinusoidal synthesis is remarkable. Fig. 8 depicts the effect of theinverter switching frequency on different waveforms of the system.It shows a closer representation of the behavior the normalized busvoltage (vbusn) and the normalized bus capacitor current (iCbusn).In both of them, in addition to the large low-frequency ripple,some high-frequency components are present. In particular, this isimportant in the case of the current since both components are tobe considered when estimating the lifetime of the bus capacitorbank. The capacitor current is the difference between the constantcurrent supplied by the first power stage and the pulsating currentfed to the inverter. In steady-state operation, the average capacitorcurrent is zero to guarantee a constant average dc-link voltage.The behavior of the bus during the negative semicycle presentsexactly the same waveforms shown Fig. 8. In the following section,experimental validation of the proposed technique under swingingbus is provided.



7

TABLE IPROPOSED FILM DC-LINK WITH 20% RIPPLE VS ELECTROLYTIC CAPACITOR BANK WITH 1% RIPPLE

Film ElectrolyticValue 7× 100µF (EZPE50107MTA) 4× 1,500µF (PEH200VO415AQB2)

Rated voltage UR 450V 400VDimensions 57.5mm× 35mm 66.6mm

Height 56mm 109.2mmTotal volume 788,900mm3 1,521,672mm3

Mass 7× 139g = 973g 4× 415g = 1,660gESR 4.7mΩ/7 53mΩ/4

RMS ripple current IRAC 18A 9.1ALifetime @ 85C 200,000hs 12,500hs

Price (qty. 50) (2014) $19.67 each $56.39 each

Vol.=788.9cm3 Vol.=1,521.7cm 3

Fig. 9. Rendering of proposed Film dc-link vs Electrolytic capacitor bank(Scale 1:5)

i inv

i fc

vbus

8.33ms

220V

26A

41V

iCbus

Fig. 10. Swinging bus operation under linear loading condition: inputcurrent ifc (Ch1), bus capacitor current (Ch2), bus voltage (Ch3), andcurrent fed to the inverter (Ch4).

IV. EXPERIMENTAL RESULTS

This section presents the experimental results of a 2.1kW in-verter operating under swinging bus condition at fixed switchingfrequency (3.6kHz). Although inverters usually work at higherswitching frequencies (around 20kHz), a moderate value waschosen in order to facilitate the visualization of the results. Theevolution of the natural trajectories of the inverter on the stateplane is distinctly perceived at such a frequency. In order to

TABLE IIDESIGN SPECIFICATIONS

Value Norm. valuevo = 120V von = vo/Vop = 0.707

Vop = 120√2V Vopn = Vop/Vop = 1

vbus = 220V ± 10% Vbusn = Vbus/Vop = 1.3Cbus = 700µFPo = 2.1kWfL = 60Hz fLn = fL/fo = 0.195

fsw = 3.6kHz fswn = fsw/fo = 11.7C = 50µF

L = 5.33mH

TABLE IIITOTAL HARMONIC DISTORTION

NSS LinearPo = 525W −→ ∆vbus = 5%Vbus 1.0% 2.4%Po = 1050W −→ ∆vbus = 10%Vbus 1.1% 2.9%Po = 1575W −→ ∆vbus = 15%Vbus 1.4% 3.5%Po = 2100W −→ ∆vbus = 20%Vbus 2.1% 4.5%

verify the behavior of the proposed control scheme, the results arecontrasted to those obtained using a Proportional-Resonant (PR)controller with an input voltage feedforward to compensate forthe fluctuations in the dc-link. The NSS control laws were im-plemented using a floating-point DSP, and the measured variableswere sampled at 216kHz (i.e., 60 times per switching period). Inorder to avoid errors (e.g., dc offset in the output voltage), thesignal conditioning circuitry and the A/D conversion were preciselycalibrated. The digitized variables are normalized (refer to (1)and (2)) and then plugged into the NSS equations ((6) to (8))to determine the state of the switches in order to produce high-quality sinusoidal synthesis while successfully rejecting the low-frequency voltage oscillations in the dc-link. The DSP was alsoemployed for the generation of the discrete references vrn and



8

TABLE IVOUTPUT VOLTAGE VARIATION WITH LOAD

Full load % vo Regulation %0% 120.6V −0.50%25% 120.3V −0.25%50% 120.0V 0.00%75% 119.8V 0.17%100% 119.1V 0.75%

iCrn. The experimental validations were carried out under heavyloading condition and the dc-link capacitor (700µF ) was selectedto produce a 20% voltage swing (peak-to-peak) with constantpower injection from the first power stage. It is important to notethat if the bus is allowed to swing, capacitors of higher voltageratings will be required. The capacitance of the dc-link can berealized using different technologies, namely electrolytic and film.Table I presents a comparison between the proposed film capacitordc-link and an electrolytic capacitor bank that would produce 1%voltage ripple. A state-of-the-art electrolytic capacitor has beenselected in order to provide a fair comparison. As can be concluded,the film alternative is superior in every aspect, providing a long-lasting, smaller, lighter, more efficient, and cheaper solution asstorage elements for the proposed fuel cell application. Moreover,a render is presented in Fig. 9 to provide a graphical contrast ofthe proposed film capacitor bank against the electrolytic capacitorbank, in which it can be easily observed that the latter is almosttwice as large as the former (1,521.7cm3 vs 778.9cm3). Therefore,a control strategy for inverters like the NSS that can handle largelow-frequency oscillations in the dc-link is suitable for long-lastingfilm-based systems. The design specifications for the inverter areshown in Table II with their equivalent normalized quantities. Forcomparative purposes, these values are the same as the ones usedin the simulations in the previous section.

First, the low-frequency voltage fluctuations of the dc-link forresistive full-load operation (2.1kW) are analyzed and depicted inFig. 10. As can be observed, the dc-link voltage has a 120Hzoscillation, i.e., twice the output frequency of the inverter. Thisfigure also illustrates the current supplied to the inverter iinv ,whose envelope is approximately a rectified version of the inverteroutput current, and the dc-link capacitor current iCbus, which isthe difference between the constant current injected from the firstpower stage (dc-dc converter) and the current fed to the inverter.For both currents, the ripple at the inverter switching frequency canbe seen. In order to further illustrate the implications of maintainingthe dc-link at a constant value, Fig. 11 is provided. It is interestingto note that the efficiency of the inverter slightly decreases whenconsidering swinging bus operation (a drop of less than 0.4%compared to the nearly constant bus case). However, it shouldbe taken into account that operation with constant dc-link wouldreflect the large double-frequency oscillations into the fuel cell, ascan be seen in Fig. 11, resulting in a significant reduction in powerdelivery, the efficiency of the total system and the shortening oflifetime.

Fig. 12 illustrates the effect of the swinging bus on the mod-ulation of the pulses. As can be observed, the envelope of theswitching sequence reflects the low-frequency variations of thedc-link voltage, resulting in a combined amplitude and PWMmodulation of the pulses. An important remark: as can be seen

i inv

i fc

vbus 220V

26A

iCbus

Fig. 11. Nearly constant bus operation under linear loading condition:input current ifc (Ch1), bus capacitor current (Ch2), bus voltage (Ch3),and current fed to the inverter (Ch4).

vsw

vbus220V

41V

Fig. 12. Effect of the swinging bus on the pulse modulation: switch state(Ch2), and bus voltage (Ch3).

in (6) to (8), the control laws consider the normalized capacitorcurrent iCn as a variable. This current is the difference betweenthe normalized inductor current iLn and the normalized outputcurrent ion, i.e., the loading condition is implicit in these equations.However, iCn is proportional to the derivative of the normalizedoutput voltage von, and thus its shape and amplitude are inde-pendent from the load. Therefore, the proposed control strategyis able to successfully generate low-distortion sinusoidal outputvoltage, even for loads with capacitive, inductive, or non-linearcharacteristics. As predicted by the theory, the proposed controlscheme was able to accommodate the swinging bus effect andsuccessfully synthesize high-quality output voltage (< 2.1% THD)under linear resistive load (Fig. 13) and non-linear high-crest-factor(CF = 2.3) loading condition (Fig. 14). In order to provide furtherinsight into the geometrical evolution of the trajectories of theinverter, the experimental phase-planes for the loading conditionsoutlined above are presented in Fig. 15 and Fig. 16. The monopolarand bipolar operating regions can be easily identified in thesefigures, as well as the elliptical target trajectory defined by thesinusoidal output voltage and capacitor current references.

The dynamic response of the system was tested under a severedrop in the dc-link voltage, as depicted in Fig. 17. The bus voltageexperiences a progressive reduction from 240V (maximum peakvalue) to 160V (minimum bus voltage). Despite this demand-ing transient under full loading condition, the NSS was able tocompensate for the voltage drop and continued to supply theload highlighting the input voltage flexibility of the swinging bus



9

vo

vsw

io50A

339.4V

Fig. 13. Swinging bus inverter operation under heavy resistive loadingcondition (time domain): output voltage (Ch1), switch state (Ch2), andoutput current (Ch4).

vo

vsw

io18A

16.66ms

Fig. 14. Swinging bus inverter operation under high-crest-factor loadingcondition (CF = 2.3) (time domain): output voltage (Ch1), switch state(Ch2), and output current (Ch4).

inverter controlled with the NSS. In a traditional stiff bus inverter,the crest of the output voltage would be saturated if the dc-linkvoltage is less than 170V . However, in the swinging bus inverter,a close examination of the waveforms shows that the bus voltage is175V when the crest of the sinusoid happens. Therefore, althoughthe average value of the bus voltage after the voltage drop in Fig.17 is 180V with a ±10% ripple (i.e., the minimum dc-link voltageis approximately 160V , which is less than the peak of the outputvoltage), the envelope of the switching sequence is still greater thanthe peak of the reference output voltage at all times, and the NSSis able to successfully synthesize the sinusoidal waveform withoutsaturating it.

The behavior of the inverter operating under resistive load wasevaluated both for the linear controller and the NSS, and thedistortion results for different loading conditions are reported inTable III. A considerable improvement in the THD is obtainedwhen the proposed technique is employed, especially for heavyloads (2.1% for the NSS against 4.5% using the PR+FF controller)for which the fluctuations of the bus increase significantly andthe linear compensator cannot handle them effectively. Unlikethe linear controller, the NSS scheme is able to synthesize high-quality output voltage for a wide range of input voltages andloading conditions. An important remark is that although a THDof 4.5% is less than the 5% acceptable distortion according toIEEE standards, it is close to the limit. Some factors like aging,temperature, some non-linear loads, etc., could make the THD toincrease, surpassing the maximum allowed. The proposed control

Fig. 15. Swinging bus inverter operation under heavy resistive loadingcondition (phase plane): output voltage (X-axis) and output capacitorcurrent (Y-axis).

Fig. 16. Swinging bus inverter operation under high-crest-factor loadingcondition (CF = 2.3) (phase plane): output voltage (X-axis) and outputcapacitor current (Y-axis).

technique provides a 2.1% THD, less than half the one obtainedwith the linear controller. Therefore, it can be almost guaranteedthat the distortion will be below 5% for any operating condition.Furthermore, the LC output filter could be designed using smallercomponents and still comply with the standards, giving the NSSan important competitive advantage. The dynamic response of thesystem was also benchmarked against the linear controller as shownin the loading transients in Fig. 18 and Fig. 19. While the PR+FFcontroller produces sags and swells after the step-up and step-downdisturbances respectively, the NSS achieves steady state almostinstantaneously and the transients are imperceptible, demonstratingthe remarkable ability of the NSS to revert to the new operating



10

vo

io

vbus 180V

220V

41V

Fig. 17. Swinging bus inverter operation using the natural SS: outputvoltage (Ch1), bus voltage transient (Ch2), and output current (Ch4) underheavy loading condition.

vo

io

vsw

50A

25A

Fig. 18. Swinging bus inverter operation using the natural SS: outputvoltage (Ch1), switch state (Ch2), and output current transient (Ch4).

condition in a few switching cycles.The load regulation is presented in Table IV. The NSS is able

to maintain its value well below 0.75%, even for a demandingoperating condition such as full-load operation (2.1kW). Finally,in order to test the robustness of the proposed technique, somesimulations were carried out and the THD of the output voltagewas calculated for different scenarios. The objective was to test thesensitivity of the NSS to the mismatch between the converter modeland the actual parameters of the converter. These discrepanciescould be due to temperature or aging. The actual component valueswere modified above and below the nominal ones (±20%). As aresult, the switching surfaces are slightly modified such that thecircles σ1 to σ3 turn into ellipses. Nevertheless, the THD valuesobtained are, in the worst case scenario, 0.4% higher compared tothe ideal-components scenario. Another case was also evaluated,in which the values of the current and voltage measurements areaffected by a scaling factor (±20%), resulting in THD values atmost 0.2% higher compared to the ideal case.

V. CONCLUSIONS

This manuscript introduced an effective control scheme forinverters to deal with low-frequency voltage variations in the dc-link. In order to eliminate the detrimental effect of the current rippleinto the fuel cell, the bus voltage is allowed to swing to absorb thepulsating current fed to the inverter and avoid propagation into thesource. Moreover, the reliability of the system can be enhanced byreplacing electrolytic capacitors with small-value film capacitorsand allowing larger fluctuations in the bus. Swinging bus operationhas proven to be a challenge and a necessary requirement for fuel

vo

io

vsw

50A

25A

Fig. 19. Swinging bus inverter operation using a linear controller: outputvoltage (Ch1), switch state (Ch2), and output current step-down transient(Ch4).

cell inverters. The behaviors of the swinging bus and the inverter inthis operating mode were characterized in a normalized geometricaldomain, and based on this analysis, a solution in the form ofboundary control was proposed: the natural switching surface. Thisstudy provided significant insight into the switching sequences andnatural trajectories of the inverter while taking into account the busfluctuations. As predicted by the theory and unlike traditional linearcontrollers, the NSS was able to comply with stringent standardsfor transient and steady-state performance and compensate for thelow-frequency ripple in the dc-link while successfully synthesizinghigh-quality sinusoidal output voltage (< 2.1% THD) even atmoderate switching frequencies.

ACKNOWLEDGMENT

The authors would like to thank Mr. Peter Ksiazek for hisassistance in the execution of the experimental work and Dr. RafaelPena Alzola for the comments provided.

APPENDIXA. NORMALIZED DERIVATION

By combining (4) and (5), a second order differential equationis obtained whose solution is:

iLn = [iLn(0)− ion] cos(2πtn)

+ [vbusnu− von(0)] sin(2πtn) + ion. (A-1)

By using the following trigonometric identity

A cosx+B sinx =√

A2 +B2 sin

[x+ tan−1

(A

B

)]the normalized inductor current can be arranged as

iLn =√

(iLn(0)− ion)2 + (vbusnu− von(0))2

sin

[2πtn + arctan

(iLn(0)− ion

vbusnu− von(0)

)]+ ion. (A-2)

By isolating the argument of the trigonometric function andreplacing it on the derivative of (A-2), the normalized time tnis eliminated using cos[sin−1(x)] =

√1− x2, yielding the nor-

malized natural trajectories of the inverter

λi : i2Cn + (von − vbusnu)2

= iCn(0)2 + (von(0)− vbusnu)

2. (A-3)



11

Finally, the initial conditions for steady state operation are

iCn(0) = iCrn (A-4)

von(0) = vrn (A-5)

Replacing these values in (A-3) results in the NSS switchingsurfaces (6) to (8).

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[doi 10.1109%2ftpel.2014.2310731] j. galvez; m. ordonez -- swinging bus operation of inverters for...

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