Practical_design_considerations_for_coup.pdf

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Practical Design Considerations for Coupled Inductor

Based Bi-directional Converters of High Voltage Ratio

Saad Ul Hasan, Liu Jinjun, Liu Fangcheng, Zhang Haodong

Power Electronics and Renewable Energy Research Center

School of Electrical Engineering, Xi’an Jiaotong UniversityXi’an, Shaanxi, China

[email protected]

Abstract — This work presents a study on the theoretical and

practical design of Coupled Inductor based Non-Isolated bi-

directional converters of high voltage ratio. Coupled Inductor

can be regarded as a tapped Inductor having windings with

different individual characteristics and it can be modeled in

terms of an ideal transformer. Usually transformer based DC-DC

topologies are utilized in conventional bi-directional DC-DC

converters because of the natural property of a transformer to

provide the benefit of isolation. Moreover soft switchingtechniques such as Zero-voltage switching (ZVS) and Zero-

current switching (ZCS) are achieved to increase efficiency by

decreasing the switching losses. Unfortunately the use of more

than 4 switches along with several passive components in

transformer based topologies increases the costs and makes the

topology more complex in terms of working and control. In this

work a coupled inductor based bi-directional DC-DC target

converter is studied emphasizing the basics of Coupled Inductor

including its physics, it modeling in terms of an ideal transformer

and its operation in the transformer mode to get a high Voltage

ratio. Simulation results of a Coupled Inductor based boost

converter are also given for basic understanding of the

characteristic waveforms of a Coupled Inductor. Experiment

results of an 80 Watt prototype of the target converter are given

to verify the successful Coupled Inductor operation in the

transformer mode to achieve the required high voltage ratio.

Keywords— Coupled Inductor design, Bi-directional converter,

high voltage ratio, step-up

I. I NTRODUCTION

The renewable energy sources are required everywhere as

secondary sources of energy. Batteries are a major part in the

“Renewable Energy Systems”. In many automatic energy

supply systems, batteries act as an intermediate storage device

along with one or more power converters to be used in the

step-up or step-down mode in accordance with the

requirements of the system. In the recent years many

researchers have proposed their ideas how to make the system

more compact and efficient i.e. Introduction of a bi-directional

converter instead of many converters in addition to many

advantages such as low cost, high efficiency and compact size.

The main requirement of a bi-directional DC-DC converter is

that when the utility is working properly the battery is being

charged, hence the converter acts in the step-down mode

(Buck) and when there is some failure in the utility, then the

converter shifts to the step-up mode (Boost) and during these

transitions there should be no losses ideally in addition to acompact design and high efficiency. The block diagramshowing the basic structure of a bi-directional DC-DC

Converter based renewable energy system is shown below:

Fig. 1. Block diagram of a bi-directional DC-DC converter

Transformer (XFMR) based topologies for bi-directional power flow are most commonly used topologies [1][2] because of their tendency to provide isolation in addition tothe achieving of soft switching phenomenon such as ZeroVoltage Switching (ZVS) or Zero Current Switching (ZCS)

for making the system more efficient. Unfortunately the use ofmore than 4 switches makes the system complex and degradesthe system efficiency. Therefore the concept of using CoupledInductor (CL) in the bi-directional DC-DC converters has

been put forward in the recent years making the system morecompact and efficient along with the major requirement ofachieving high voltage gain in the boost mode. The CL based

boost converters can be classified into many categories such asCL with voltage doubler [3], CL with active clamp [4], CLwith passive clamp [5], CL with passive snubber [6], switchedCL [7] and CL with switched capacitor [8].

The problems associated with a traditional inductor based boost converter are discussed and some theoretical and

simulation results are presented to depict the benefit of usingCL. The magnetic and electric model of CL is discussed andits modeling in terms of an ideal transformer is also presented.Finally some experiment results based on an 80 Watt

prototype of a target converter [4] are included to depict thehigh step-up achievement in addition to some conclusions inthe end.

II. THEORETICAL DESIGN AND MODELLING OF CL

Consider the magnetic and the corresponding electricmodel of CL [9] shown below:

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Fig. 2. (a) Magnetic Model of CL, (b) Electric Model of CL

Although CL and XFMR look superficially similar but theyhave many differences in terms of power flow, currentdirections, leakage inductance effects etc. Both the magneticand electric models of CL are corresponding to each other.Both ends of the CL are terminated by voltage sources asshown in the magnetic model and correspondingly by MMFsources in the electric model. The logical reasoning of this isthat both primary and secondary currents flow inside the CL,hence the polarity of Magneto-motive forces (MMF) in electricmodel can be understood relatively. Moreover while theconstruction of CL, one of the primary side terminals is alwaysconnected to one of the secondary terminals, therefore the

primary and secondary currents always flow into the CLstructure. There is an “air gap” (l g) always present in CLstructure which ensures a large leakage inductance which is the

characteristic property of a CL, hence a reluctance R g can be

seen in the electric model of CL. The reluctance in the electricmodel has the same behavior as a resistance but instead ofdissipating energy, it stores the magnetic energy which is

produced by the MMF, hence CL can be called as an energystorage device. The inherited leakage inductance property can

be utilized both in beneficial and detrimental way e.g. thisleakage inductance results in leakage current which can beused for the soft switching operation in a power converter buton the other hand this leakage current if not properly dealt can

cause serious problems such EMI or resonance phenomenonacross different operating switches, therefore CL can beconsidered as a two-side sword [10] which must be handledcarefully.

The model of a CL in terms of an ideal XFMR is shown inFig. 6.

Fig. 3. Model of CL in terms of an Ideal Transformer

It can be noted that there is an additional 3rd winding alongwith the ideal XFMR. This model can be understood on the

basis of simple faraday laws along with some othermathematical rules. Since according to faraday laws, thevoltage scaling law can be derived, hence the model is just likean ideal transformer. The additional 3rd winding is also shownon the primary side of the transformer which is also called as“magnetizing inductor”, the reason of which is that there is nocurrent scaling law as the transformer but the derivation of

current relationship leads to the 3rd additional winding [9]. Le1 and Le2 present the primary and secondary leakage inductancesrespectively which are always present in case of finite core

permeability of magnetic materials. The magnetizinginductance has the same properties as an ordinary inductorsuch as “saturation” and “hysteresis”.

Mathematically LM for CL is calculated as:

g

M R

N L

21

≈ (1)

Where N1 is the number of primary turns and Rg is thereluctance of “air gap”. The primary side inductance (LP) isalways the sum of the magnetizing inductance (LM) andleakage inductance (LK1). The reluctance of air gap is alwaysgreater than that of the core and it is mathematically shown as:

C

g

g A

l R

µ ≈ (2)

Where l g is the length of air gap, μ is the permeability offree space and AC is the cross-section area of the core used. Note that the reluctance in case of CL is dependent upon the airgap but the reluctance in case of an XFMR depends upon thecore parameters.

III. COUPLED I NDUCTOR BASED DC-DC CONVERTERBENEFITS

There are many issues associated with the XFMR or simpleinductor based traditional DC-DC converters. In case of atransformer based topology, the control algorithm is quitecomplex which becomes more difficult at high frequencyconsidering the dead time. Moreover several numbers of

switches are required to operate the transformer for DC-DCconversion along with the unfavorable characteristics such aslarge size and leakage inductance. For the case of simpleinductor based topologies, the extreme duty cycle may causesevere switch stress along with the saturation problems of theinductor for high voltage ratio achievement.

Consider a simple CL based boost converter shown below:

( )attery LVS

S L

p L

0 D

0C

S ( ) Load HVS

Fig. 4. A simple CL based boost converter

LVS stands for “Low Voltage Side” at which the battery isconnected whereas HVS is the “High Voltage Side” on whichthe DC bus or the load is connected. According to the voltsecond balance, the voltage gain can be calculated as:


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D

nD

V

V

LVS

HVS

−

+=

1

1 (3)

Where D is the duty cycle of switch S and n is the turns

ratio S

P

L

L. Hence it is theoretically proved that the voltage gain

in case of a CL based boost DC-DC converter is larger than

that of having ordinary inductor.

The simulation results also depict the high voltagerealization shown in Fig. 3. The design parameters used are:Switching Frequency (f S) = 100 KHz, Turns Ratio = 1:2, DutyCycle (D) = 50%, Magnetizing Inductance (LM) = 20 µH. Theequivalent model of Fig. 2 is shown below:

Fig. 5. Equivalent Model of CL based boost converter

23.8

23.9

24

24.1

24.2

Input Voltage

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

80

100

120

Output Voltage

Fig. 6. High voltage ratio for a CL based boost converter

IV. EXPERIMENTAL RESULTS

An 80 Watt prototype of a target converter [4] has been built and operated in the boost mode to ensure the successfulXFMR-mode operation of a CL based DC-DC powerconverter. The target topology is shown in Fig. 7. The

simulation model has been built in MATLAB simulink asshown in Fig. 8. The simulation model has implemented asmuch closer to the practical prototype by considering theleakage inductances and parasitic capacitors. Same parametersare used in simulation and experiment. The parameters used aref s=50 KHz, LP:LS = 26μH:104μH, Coupling coefficient=k =0.97, EE-55 core, C1= 47μF/100V, C2= 10μF/200V. S1:IRFP2907 (75V/209A, R DS(on) = 4.5mΩ ; TO-247; S2:HUF75545P (80V/75A, R DS(on)=10mΩ; TO-220; S3,S4:IRFP264N (250V/44A, R DS(on)= 60mΩ; TO-247;

Fig. 7. Target converter topology

Fig. 8. Simulation model of target topology (Boost Mode)

The CL has been utilized in the target topology for theachievement of high voltage gain. The characteristic leakageinductance of the CL is utilized to achieve soft switching toimprove the efficiency, adding the stray energy towards theHVS. The soft switching across the switches is depicted in thesimulation and experiment results as follows:

Voltage

Current

Voltage

Current

Voltage

Current

Voltage

Current

Switch S1

Switch S3

Switch S2

Switch S4

a b

Fig. 9. (a) Simulation results (b) Experiment Results for soft switching


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[4] Duan, Rou-Yong, and Jeng-Dao Lee. "Soft switching bidirectional DC-DC converter with coupled inductor." In Industrial Electronics andApplications (ICIEA), 2011 6th IEEE Conference on, pp. 2797-2802.IEEE, 2011.

[5] Wai, R. J., and R. Y. Duan. "High-efficiency DC/DC converter withhigh voltage gain." IEE Proceedings-Electric Power Applications 152,no. 4 (2005): 793-802.

[6] Wai, Rong-Jong, and Rou-Yong Duan. "High step-up converter withcoupled-inductor." Power Electronics, IEEE Transactions on 20, no. 5

(2005): 1025-1035.[7] Laird, Ian, DD-C. Lu, and Vassilios G. Agelidis. "High-gain switched-

coupled-inductor boost converter." In Power Electronics and DriveSystems, 2009. PEDS 2009. International Conference on, pp. 423-428.IEEE, 2009.

[8] Liang, Tsorng-Juu, Shih-Ming Chen, Lung-Sheng Yang, Jiann-FuhChen, and Adrian Ioinovici. "Ultra-Large Gain Step-Up Switched-Capacitor DC-DC Converter With Coupled Inductor for AlternativeSources of Energy." Circuits and Systems I: Regular Papers, IEEETransactions on 59, no. 4 (2012): 864-874.

[9] Witulski, Arthur F. "Introduction to modeling of transformers andcoupled inductors." Power Electronics, IEEE Transactions on 10, no. 3(1995): 349-357.

[10] Li, Wuhua, Jianguo Xiao, Jiande Wu, Jun Liu, and Xiangning He."Application summarization of coupled inductors in DC/DC converters."In Applied Power Electronics Conference and Exposition, 2009. APEC2009. Twenty-Fourth Annual IEEE, pp. 1487-1491. IEEE, 2009.

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