new method to achieve ac harmonic elimination and energy storage integration for 12-pulse diode...

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 7, JULY 2013 2547

New Method to Achieve AC Harmonic Eliminationand Energy Storage Integration for

12-Pulse Diode RectifiersSanzhong Bai, Student Member, IEEE, and Srdjan M. Lukic, Member, IEEE

Abstract—The 12-pulse rectifier is often used to supply high-power industrial loads. Its ability to effectively and cheaply mit-igate the harmonics on the ac side has ensured its dominance inthe industry even as active front ends become cheaper and morereliable. Despite its many benefits, the 12-pulse rectifier is not ableto reduce the ac-side harmonics to a level acceptable by the perti-nent IEEE standards without additional filtering. In this paper, weoutline a novel method to profile the rectifier output current to betriangular which results in low ac-side harmonics. The novelty inthe proposed approach is that we exploit the dc-side filter design tominimize the volt-amperes (VA) rating of the current source usedto profile the dc-side rectifier current. Additional benefits of theproposed method include lower VA rating of the dc filter, simpleintegration of dc energy storage, and effective ac harmonic controleven when the initial rectifier current is discontinuous.

Index Terms—Active power filter, energy storage, harmonics,12-pulse diode rectifier.

I. INTRODUCTION

AVAILABILITY of reliable and inexpensive semiconduc-tor devices has led to numerous power electronics inten-

sive industrial loads requiring dc power supply for operation.When a number of dc-powered loads are in proximity, it be-comes viable for them to share a common dc bus. Many suchsystems benefit from local dc storage to perform the following:1) reduce the power demand from the grid; 2) provide backuppower; and 3) store locally generated renewable power ratherthan feeding it back to the grid. Local dc distribution hasbeen considered for data centers [1], dc-level plug-in vehiclecharging stations [2], more electric ships, and aircrafts [3].

The 12-pulse rectifier is a common, simple, and cost-effective method to provide a stable dc supply while at the sametime minimizing the grid-side harmonics. The 12-pulse rectifieris a good tradeoff between harmonic reduction and subsystemcomplexity and is commonly used in the industry. However,the 12-pulse rectifier alone does not sufficiently reduce the acharmonics to a level prescribed by relevant standards, such asIEEE 519 [4].

A standard way to eliminate ac-side harmonics is to useactive, passive, or hybrid power filters [5]–[7]. Although these

Manuscript received November 14, 2011; revised February 11, 2012;accepted March 15, 2012. Date of publication April 30, 2012; date of currentversion February 28, 2013.

The authors are with North Carolina State University, Raleigh, NC 27606USA (e-mail: [email protected]; [email protected]).

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.2012.2196903

methods are well understood and widely used, passive filtersare bulky, while active filters require complex control andspecialized power electronics. An alternative method controlsthe current draw from the dc side so as to minimize the acharmonics.

Researchers have shown that, for the 12-pulse rectifier, theac-side harmonics are minimized by shaping the two six-pulserectifier output currents to be triangular and out of phase. Theresulting total harmonic distortion (THD) is as low as 1%[8], [9]. In [8]–[13], researchers exploit this property; whileeffective at reducing the harmonics, the circuitry used to shapethe current is placed in path of the load current, resulting insubstantial VA rating. Furthermore, the proposed approaches in[8]–[13] are only effective for continuous rectifier currents andare not capable of dc storage integration.

In this paper, we propose a new method of profiling thedc-side rectifier current by using current sources placed inparallel with each six-pulse rectifier bridge to inject currentand shape the rectifier output current. The method is simple toimplement and makes use of standard series-connected isolatedgate bipolar transistor or metal oxide semiconductor field-effecttransistor (MOSFET) modules. The property of the resultingcurrent sources is that they are able to deliver power to theload, allowing for the integration of an energy storage systemon the dc side. The VA rating required to profile the current issubstantially reduced by a proper choice of the dc-side LC filterparameters.

The remainder of this paper is organized as follows: InSection II, we review the proposed methods for harmonicreduction by shaping the rectifier output current; in Section III,we establish the proposed harmonic reduction topology andcontrol strategy. We present simulation and experimental resultsin Section IV and close with conclusions in Section V.

II. REVIEW OF EXISTING METHODS FOR AC HARMONIC

ELIMINATION BY PROFILING THE DC RECTIFIER

CURRENT FOR THE 12-PULSE RECTIFIER

A. Principle of Harmonic Elimination

In analyzing the operation of 12-pulse rectifier (Fig. 1),some methods are dedicatedly designed to shape the outputcurrent of 12-pulse rectifier (irec1, irec) so as to minimize theac-side harmonics (ia, ib, ic) formed by the operation of therectifier. The exact shape of the rectifier output current thatresults in complete elimination of ac input current harmonics

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2548 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 7, JULY 2013

Fig. 1. Twelve-pulse diode rectifier.

has been derived in [8] and [9]. Authors in [8]–[13] show thatthe triangular waveform, shown in Fig. 2, presents a good ap-proximation of the ideal rectifier output current that completelyeliminates the ac current harmonics. Assuming that the rectifiercurrent is profiled to be triangular, its Fourier series expansiongives

irec1 = IL + 4IL ·∞∑

n=1

1− (−1)n

n2π2· cos(6nωt)

irec2 = IL + 4IL ·∞∑

n=1

1− (−1)n

n2π2· cos

(6(nωt+

π

6

))(1)

where ω is the line frequency, IL is the load current deliveredto the dc load, and irec1 and irec2 are defined in Fig. 1. Basedon the operation of the six-pulse rectifier, the Fourier seriesexpansion of rectifier output voltage is

vrec1=vrec1_dc+vrec1_ac

=3·Vp

π+6·Vp

π·

∞∑n=1

−(−1)n

36n2 − 1·cos(6nωt)

vrec2=vrec2_dc+vrec2_ac

=3·Vp

π+6·Vp

π·

∞∑n=1

−(−1)n

36n2 − 1·cos

(6(nωt+

π

6

))(2)

where Vp is the peak value of the ac input voltage and vrec1 andvrec2 are defined in Fig. 1 as the rectified voltages.

Assuming that the profiled current is triangular as expressedin (1), it is quite simple to calculate the harmonics in theac-side line current, namely, by realizing that the ac-side phase-a current ia can be expressed as

ia = (ia1 − ic1)/√

3 + ia2 (3)

where the currents are defined in Fig. 1. We can express theac-side current ia as the sum of the Fourier expansions of therectified currents irec1 and irec2

ia =irec1 · S∠30◦ − irec1 · S∠150◦√

3+ irec2 · S∠0◦ (4)

Fig. 2. Construction of the input current.

where S is defined as

S =2√3

π

(sin(ωt)− 1

5sin(5ωt)− 1

7sin(7ωt)

+1

11sin(11ωt) +

1

13sin(13ωt) · · ·

)(5)

which is the switching function shown in Fig. 2. By numericallyevaluating (4), the ac-side line current THD is shown to be closeto 1% [8], [9].

Analyzing (1) and (2), both vrec and irec have a strong accomponent at six times the source frequency. The fundamentalac components of the voltage and the current are in phase foreach six-pulse rectifier, while these ac components are out ofphase when comparing the upper and lower rectifiers, as evidentfrom Fig. 2 and (1) and (2). The fact that the fundamental accomponents of the voltage and the current are in phase foreach six-pulse rectifier is exploited in the LC filter design asdiscussed in later sections.

B. Existing Methods for Current Profiling

Numerous topologies have been proposed to shape the recti-fier output current in order to eliminate the ac harmonics.

They generally rely on directly shaping the rectifier current[12], [13] or on inserting a voltage source between the capacitorbank and the rectifier [8]–[11]. In [12], the authors proposeto directly shape the rectifier output current by using activeswitches in the current path. The approach outlined in [13] uses

BAI AND LUKIC: NEW METHOD TO ACHIEVE AC HARMONIC ELIMINATION AND ENERGY STORAGE INTEGRATION 2549

Fig. 3. Proposed method with parallel-connected current sources.

a dedicatedly sized reactor to shape the output current; however,the approach is only effective for a fixed load value.

Other approaches insert a voltage source into the rectifieroutput loop [8]–[11]. The voltage source generates a rectan-gular pulse voltage with controlled amplitude and six times theline frequency, resulting in triangular rectifier output current.Researchers present a rough implementation of this idea in [10]by using the tap changer, while Liu et al. [8] uses a five-levelfixed-amplitude voltage source. The control accuracy of thesesetups is limited. In [9] and [11], authors shape the rectifieroutput current by using pulse width modulated active converterto control the inserted voltage source.

The problem with the approaches in [8]–[11] is that theyrequire continuous rectifier output current to function. In addi-tion, the rectifier output voltage needs to be ripple free to haveexpected results, requiring a large filter capacitor. Moreover,the current through the 360-Hz transformer (for 60-Hz grid)has an amplitude of ±2IL resulting in a large conduction loss.The noise generated by the low-frequency transformer posesanother problem.

III. PROPOSED METHOD FOR HARMONIC REDUCTION AND

ENERGY STORAGE INTEGRATION

A. Proposed Approach

A novel approach proposed in this paper inserts three currentsources into the circuit as shown in Fig. 3. The two currentsources (is1 and is2) in parallel with each rectifier are used toshape the rectifier currents irec1 and irec2 in order to eliminatethe ac-side harmonics. The third current source is3 is used toinject active power from an energy storage system. In additionto providing the ability to inject real power on the dc side,we will show that, with the correct choice of the LC filterparameters, the VA rating of the current source used for filteringcan be substantially reduced compared, for example, to thedirect current profiling case. A direct comparison with otherproposed solutions is more difficult, since the VA ratings of thevoltage source will be a function of the design of the entiresystem.

The hardware implementation of the three current sourcesshown in Fig. 3 is shown in Fig. 4. The current sources areimplemented using two cascaded buck-and-boost converterswhich provide two independent currents is1 and is2. The third

Fig. 4. Configuration of the proposed ac/dc rectifier with current sourcesformed by two buck-and-boost converters.

current is3 results from a combination of is1 and is2 (is3 =is1 − is2). The dc bus of the cascaded buck-and-boost convertercan be supplied by a capacitor bank, much like in active filterdesigns; otherwise, the dc bus can be used to interface energystorage.

In comparison with the existing methods discussed inSection II, the proposed method has the following advantages:

1) The parallel-connected current sources can be used tointerface energy storage system to inject active power.

2) Additional 360-Hz transformer presented in approachesoutlined in [8]–[11] is eliminated.

3) The proposed method works even if the initial rectifiercurrent is discontinuous.

4) Since the current sources only need to compensate thecurrent difference, the VA rating of the current sourceswill be comparable to (or less than) those in [8]–[11].

B. System Analysis and Parameter Optimization

We propose to shape the rectifier current by inserting a cur-rent source in parallel with each six-pulse rectifier. To improvethe efficiency of the proposed approach, we minimize the VArating of these current sources through appropriate choice offiltering components.

The equivalent circuit of the 12-pulse rectifier is shown inFig. 5. Considering the dc and fundamental component, eachsix-pulse rectifier can be represented by a dc and an ac sourcein series (vrec_ac and vrec_dc). Looking at the equivalent circuitof the system, the two dc voltage sources are connected in seriesand will produce a dc current in the load which is also the dccomponent of irec. The dc load current can be calculated as

IL =6

π· Vp

RL. (6)

To attenuate the effect of vrec_ac on the dc load, an LC filteris inserted between the rectifier and the load. The inductor isformed by the leakage inductance of the transformer Lleak, andadditional inductor Lf is inserted on the dc side.


Fig. 5. Equivalent circuit of the 12-pulse rectifier.

Fig. 6. Rectifier output voltage and current.

In our investigations, rather than using the LC filter toattenuate the effect of vrec_ac on the load, we use the LCfilter to shape the rectifier output current irec to be as close aspossible to the desired shape irec_ref , as shown in Fig. 6. Asdescribed by (1) and (2), the fundamental component of vrec_ac

is dominant, and it is in phase with the fundamental componentof the triangular current reference irec_ref , given in (1). TheTHD of irec_ref can be calculated based on (1), as 12.12%,which suggests that the fundamental component of irec_ref isalso dominant.

To ensure that vrec1 and irec1 remain in phase, the LC filtershould be purely resistive (i.e., at resonance) at the frequencyof interest, namely, 6ω. Using the superposition principle andassuming resonance in the two LC filters at 6ω results in acurrent flow only in the respective LC filter. This is the result ofthe infinite impedance presented by the parallel resonance in theother branch, as shown graphically in Fig. 71 for vrec1_ac; theanalysis is similar for vrec2_ac. Therefore, the ac component ofirec will only be determined by vrec_ac and the ESR of the LCfilter (which is not shown in the figure). By only consideringthe fundamental component of vrec_ac and irec and assumingthat irec is continuous, the peak value of the ac component ofirec can be calculated

Irec_ac,peak =6

35π· Vp

ESRLC(7)

where ESRLC is the total ESR of the LC filter. The optimalvalue of ESRLC will depend on the load current, and the

1In reality, the impedance of the LC circuit is determined by the equivalentseries resistance (ESR) of the LC and the resistance of the load. In practice, theresulting current through the branch is negligible.

Fig. 7. Decoupling of the currents produced by the fundamental of vrec1_ac.

Fig. 8. Equivalent circuit for the upper current source using the superpositionprinciple.

ESR can only be optimized for one value of load. To derivethe optimal ratio between ESRLC and RL, we define theparameter M as

m =Irec_ac,peak

IL. (8)

Solving numerically for a value of M that gives the minimumdifference between the fundamental component of irec_ac andthe triangular reference irec_ref , we get

m = 0.77. (9)

The rectifier output current and triangular reference areshown in Fig. 6 for m = 0.77. It is apparent that the twowaveforms are quite close. Combining (6), (7), and (8)results in

ESRLC

RL=

1

35m. (10)

Based on (9) and (10), the optimized ESR can be chosen for acertain load resistance.

C. Injected Current Flow

Next, using the superposition principle, we analyze the cur-rent flow from the inserted current source. Based on the equiv-alent circuit shown in Fig. 8, three paths are possible. Ideally,the current should flow primarily through path I. Assuming theworst case where the initial rectifier output current is purely dc,the current source will need to inject

is = 4IL ·∞∑

n=1

1− (−1)n

n2π2· cos(6nωt). (11)

Therefore, the fundamental of the current source will be at360 Hz. It is apparent that, if Lf is larger than Lleak, the higher


Fig. 9. Equivalent circuit of the 12-pulse rectifier with the current sourcesincluded.

Fig. 10. Control diagram.

order harmonics will take the desired path. At 360 Hz, whenLf and Cf are in resonance, only paths I and II are possible, asshown earlier. To ensure that the current takes the desired path,it is preferable to minimize the transformer leakage inductanceand ESR (which is not shown in Fig. 8) so that most of thecurrent takes path I (Fig. 8).

D. Control Strategy

This section describes the proposed control strategy for thethree current sources shown in Fig. 3. Our approach is to controlthe currents is1 and is2 through the two inductors in Fig. 9.The control diagram of the system is shown in Fig. 10. Similarto active power filter control, a simple proportional controlleris used to act on the error between the references is1_ref andis2_ref and the inductor currents is1 and is2.

The current references for the two inductors is1_ref andis2_ref are made up of three components. The first componentensures the tracking of the triangular reference. The desired tri-angular references irec1_ref and irec2_ref are generated by mul-tiplying the averaged rectifier output current (Irec1 and Irec2)and the triangular reference which is synchronized with theline voltage. The dynamics of the averaging can be fairly slow,since the result of a mismatch between the estimated and actualvalues of IL simply results in real power injection/absorptionby current source into the load during the transient. The second

TABLE IPARAMETERS OF THE AC/DC RECTIFIER FOR SIMULATIONS

Fig. 11. Verification of optimized ESR.

component balances the voltages of the energy storage elements(batteries or capacitors) that supply the current source. Since thevoltage sources (CDC1 and CDC2 in Fig. 4) represent dc signalswith fairly large time constants, a proportional–integral controlis used to ensure zero steady-state error. The third componentis used to inject active power into the dc bus from the energysource. Overall, the control is much simpler than that of the ac-side active power filters [14], [15].

IV. SIMULATION AND EXPERIMENTAL RESULTS

Two systems are presented in this paper: We analyze a largeindustrial 1-MVA system and validate the proposed concepton a smaller experimental setup. The main limitation of theexperimental setup is the high leakage inductance and the highESR of the transformer.

A. Simulation Results

We model the 1-MVA rectifier using Sim-Power-SystemsToolbox in Simulink. The specifications of the setup are givenin Table I. The LC filter ESR is optimized according to (10)to give the minimum current source VA rating at RL = 0.5 Ω(with RL = 0.37 Ω corresponding to full load resistance).

To assess the required current source ratings, we subtractthe actual rectifier current from the ideal triangular waveform.Simulation results summarized in Fig. 11 show that the rmscurrent of current source normalized by the load current reachesa minimum at RL = 0.54 Ω which is close to the designed valueof RL = 0.5 Ω. The small difference comes from the omissionof higher order harmonics in the original analysis and neglectedcross-coupling between LC filters due to finite ESR of the


Fig. 12. Simulation results with the switching model of the proposed system.

LC resonant circuit. At the point when the load resistance is0.7 Ω, there is a mode change from continuous to discontinuousrectifier current.

In order to account for the nonidealities of the control loopand the practical implementation of the current source, wesimulated a switching model of the current source. The resultsare shown in Fig. 12. The VA rating remains low, particularly atoptimized point. The system can be optimized at different loadconditions depending on application requirements. Note that,in all cases, the THD is below 5%. It is also worth noting herethat the rectifier current becomes discontinuous at 0.56 (p.u.),yet the filter is still able to control the harmonics all the waydown to 0.2 (p.u.). This is one of the benefits of the proposedapproach compared to other approaches that shape the 12-pulserectifier output current. Additionally, the LC filter VA rating iskept quite low.

B. Experiment Results

A small-scale experiment setup (Fig. 13) is built to verifythe functionality of the proposed system. The specifications ofthis setup are given in Table II. The three-phase transformerconsists of three single-phase transformers (VPT48-10400),and the secondary windings are rewound to get the desiredvoltage level. The 12-pulse diode rectifier consists of two three-phase diode bridges (SC50VB80). Two inductors are connectedin series to get Lf . The filter inductors were hand wound arounda ferrite E80 core. The MOSFETs used for the buck-and-boost converters are IXFH40N50Q2. We used the TDS5034Boscilloscope from Tektronix and associated measurement andanalysis software to capture the experimental waveforms andperform power quality analysis.

Fig. 13. Experimental setup.

TABLE IIPARAMETERS OF THE AC/DC RECTIFIER FOR EXPERIMENT

The experiment setup has some limitations. First, based onthe analysis in Section III, the setup requires a high currentinjection from the current sources due to the relatively highleakage inductance and ESR of the transformers.

Fig. 14 shows the experimentally obtained waveforms withand without the compensation current when the load currentIL is 4.2 A. Fig. 15 shows the compensation currents is1 andis2 at the same load. The improvement of the line currentharmonic level is apparent: The THD drops from 4.60% to2.41%. The magnitude of each harmonic is plotted in Fig. 16.It is interesting to note that even the initial harmonics are fairlylow and much lower than for the 12-pulse rectifier with LCfilter design for dc ripple minimization. This is due to thechoice of the LC filter that amplifies the 360-Hz harmonic inthe current. In Fig. 14, results show that the rectifier current issuccessfully shaped into the triangular form.

Further comparisons are shown in Fig. 17, with differentload conditions. Fig. 17 shows that the proposed method iseffective at reducing the harmonics in the input line current evenas the rectifier output current is becoming discontinuous. TheVA rating of the current sources at different load conditionsis shown in Fig. 18. It can be seen that the optimized point(where the VA rating is minimized) is when the load currentis 2.6 A (with load resistance as 25 Ω). On the other hand,according to (7) and (8) and Table II, the calculated optimalpoint is when the load resistance is 22 Ω. The VA rating isrelatively high because of the high leakage inductance andESR of the transformer. According to the current flow analysisdescribed in the previous section, we can see that, for thefilter parameters from Table II, only 57.1% and 56.1% of the


Fig. 14. Comparison of line current and rectifier output current. (a) Withoutrectifier current profiling: (Ch1) Line voltage (phase A), 50 V/Div; (Ch2) linecurrent (phase A), 2 A/Div; (Ch3) irec1, 5 A/Div; and (Ch4) irec2, 5 A/Div.(b) With rectifier current profiling: (Ch1) Line voltage (phase A), 50 V/Div;(Ch2) line current (phase A), 2 A/Div; (Ch3) irec1, 5 A/Div; and (Ch4) irec2,5 A/Div.

Fig. 15. Compensation current when the load current IL is 4.2 A. (Ch1) Linevoltage (phase A), 50 V/Div. (Ch2) Line current (phase A), 2 A/Div. (Ch3) is1,2 A/Div. (Ch4) is2, 2 A/Div.

compensation current goes through loop I. Therefore, almosthalf of the compensation current goes toward reducing the LCfilter current rather than toward shaping the rectifier current intothe triangular reference.

The active power injection function of the current source is3is also verified in experiment. A dc source is connected to the

Fig. 16. Harmonic distribution with and without the current profiling whenload current IL is 4.2 A.

Fig. 17. Comparison of THD with and without current profiling.

Fig. 18. VA rating of the current sources is1 + is2.

dc link of the two buck-and-boost converters to provide activepower. Fig. 19 shows the transition to active power injection.When is3 injects active power, is1 has a positive offset, and is2has a negative offset. The input line current decreases becauseof this active power injection. In addition, the lower currentfrom the rectifier results in a smaller compensation current fromthe filter.

V. CONCLUSION

In this paper, we have presented a new method for activeprofiling of the 12-pulse rectifier output current. The chosentopology acts as a current source in parallel with the inputrectifier and is therefore not in the path of the load current. Inaddition, the current source is constructed from a voltage-fedbuck-and-boost converter, allowing for seamless integration ofdc storage into the system. The VA ratings of the current profil-ing circuitry are further minimized by exploiting the resonanceof the dc-side LC filter.


Fig. 19. Active power injection. (Ch2) Line current (phase A), 2 A/Div.(Ch3) is1, 2 A/Div. (Ch4) is2, 2 A/Div.

In comparison with similar approaches, the proposed methodhas apparent advantages of eliminating the use of low-frequency transformers for shaping the rectifier output current,providing energy storage interface to the system and function-ing regardless of the continuality of the initial rectifier outputcurrent. Simulation of a high-power industrial ac/dc rectifierverified the parameter optimization of the system, while exper-imental results show significant reduction of harmonics in theline current. The dc energy storage integration functionality isalso verified experimentally.

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Sanzhong Bai (S’09) received the B.S. and M.S. de-grees in electrical engineering from Sichuan Univer-sity, Chengdu, China, in 2003 and 2006, respectively.He is currently working toward the Ph.D. degree atNorth Carolina State University, Raleigh, NC.

Between 2006 and 2008, he was a Research As-sistant with the Electric and Technology Institute,Sichuan University. In 2008, he joined the FutureRenewable Electric Energy Delivery and Manage-ment Systems Engineering Research Center, NorthCarolina State University, Raleigh. He is currently a

Research Assistant at North Carolina State University. His primary areas ofinterest are electric vehicle charging station, resonant power conversion, andpower quality issues.

Srdjan M. Lukic (S’02–M’07) received the M.S.and Ph.D. degrees in electrical engineering from theIllinois Institute of Technology, Chicago.

From 2002 to 2004, he was with Firefly EnergyInc., where he was responsible for optimizing cer-tain aspects of carbon/graphite foam-based lead acidbatteries for novel automotive applications. He iscurrently an Assistant Professor with the Depart-ment of Electrical and Computer Engineering, NorthCarolina State University, Raleigh, where he servesas the Distributed Energy Storage Devices Subthrust

Leader of the Future Renewable Electric Energy Delivery and ManagementSystems Engineering Research Center. His research interests include designand control of power electronic converters and electromagnetic energy conver-sion with application to wireless power transfer, energy storage systems, andelectric automotive systems.

Dr. Lukic served as a Guest Editor of the IEEE TRANSACTIONS ON

INDUSTRIAL ELECTRONICS and serves as an Associate Editor of the IEEETRANSACTIONS ON INDUSTRY APPLICATIONS.

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