IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 5, MAY 2013
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Characteristic of a Variable Inductor Using Magnetorheological Fluid for Efficient Power Conversion Dong-Wook Kim, Honnyong Cha, Se-Hee Lee, and Dong-Hun Kim Department of Electrical Engineering, Kyungpook National Univ., Daegu, 702-701, Republic of Korea This paper proposes a new variable inductor for efficient power conversion which consists of the ferrite core and the gap filled with a magnetorheological fluid. Its main feature is to show a large inductance variation versus inductor currents even with a simple inductor structure and so it leads to improving light and intermediate load efficiency of power conversion systems compared with the conventional inductor with an air gap. To predict the characteristics of the variable inductor, the nonlinear magnetic permeability of the magnetorheological fluid used is accurately measured because the inductance value strongly depends on the magnetic nonlinearity of the fluid. With the obtained B-H curve, a 1 kVA variable inductor is designed and analyzed with three-dimensional finite element method taking into account the losses of the core and the fluid. Finally, to prove the feasibility and usefulness of the proposed inductor, a prototype inductor is fabricated and its experimental results are compared with numerical ones. Index Terms—Electromagnetic analysis, inductors, magnetorheological (MR) fluid, power conversion.
I. INTRODUCTION
W
HEN magnetorheological (MR) fluids are exposed to magnetic fields, their mechanical properties, such as viscosity and stress, are easily controllable with the field strength. Owing to the feature, MR fluids have been widely used in mechanical devices such as rotary brakes, clutches, rotary and linear dampers, etc. [1]–[5]. Most of previous works have been restricted to the design and analysis of mechanical applications of the fluids to date. However, it is worth noticing the fluids have another important property that the magnetic permeability is nonlinear to the growth of the field as well. Such the unique field-dependent permeability of the MR fluids may bring significant benefits to the areas of electromagnetic devices. That is the motivation to launch the research on which device is suitable to exploit the magnetic property of the fluids. Meanwhile, inductors are widely used in power electronics to store magnetic energy and to limit electric current for power conversion. In general, most of the inductors have a constant inductance value in a normal condition which operates below the core saturation. A variable inductor, of which the inductance varies with the current flowing through it, has drawn little attention until now. Even though the constant-value inductor is used in most of the power electronic applications, there still exist some applications, such as electronic ballasts, dc-dc converters, etc., where the variable inductor is more beneficial than the constant-value inductor in terms of the efficiency of power conversion. A saturable inductor in [6] was utilized to achieve soft switching and to reduce conduction loss of the converter. Due to the saturable inductor, the converter efficiency can be improved significantly but it cannot be used in high power conversion applications because the core loss of the inductor is very high. In [7], a planar nonlinear inductor was proposed to improve light and intermediate load efficiency of buck converters but its core structure is too complicated for practical use. To tackle the aforementioned defects of the previous variable inductors, this paper presents a new variable inductor consisting of a ferrite core and the gap filled with a MR fluid. Even though
the proposed inductor has a very simple structure only with the MR fluid gap instead of the air gap, it yields a large inductance variation versus inductor currents and so it leads to improving light and intermediate load efficiency of the power converters. To predict the performances of the proposed inductor, the nonlinear magnetic permeability of the MR fluid used is accurately measured because the inductance value is strongly dependent on the magnetic nonlinearity of the fluid. With the B-H nonlinear curve obtained, a 1 kVA variable inductor is designed based on the magnetic circuit theory and analyzed with three-dimensional (3D) finite element method (FEM) taking into account the losses of the core and the fluid. Finally, to prove the feasibility and usefulness of the proposed inductor, a prototype inductor is fabricated and its experimental results are compared with numerical ones. II. MEASUREMENT OF B-H NONLINEAR CURVE MAGNETORHEOLOGICAL FLUID
FOR A
To predict the performances of the variable inductor, the first thing is to obtain the accurate B-H nonlinear curve for the MR fluid because the inductance values strongly depend on the magnetic nonlinearity of the fluid used. For the purpose of doing this, the magnetic property measurement system (MPMS) produced by Quantum Design, Inc. was used as in Fig. 1(a). The MR fluid called MRF-122EG was selected for the variable inductor and the fluid sample with the weight of 438.97 mg and mass density was encapsulated inside a small transparent capsule of 3 which was located at the middle of a straw as shown in Fig. 1(b). Fig. 2 shows the magnetization loop of the fluid for the variation of the magnetic fields of which the values are given in CGS unit. For the nonlinear finite element analysis, the mean values were extracted from the raw data on the M-H loop and then they were transformed into the B-H curve data in SI unit. The nonlinear curve of the MR fluid is compared with the permeability line of air in Fig. 3 where the relative permeability of the fluid is about 2.77 in the linear region of the B-H curve. III. SIMULATION SETUP OF A VARIABLE INDUCTOR
Manuscript received November 10, 2012; revised January 17, 2013; accepted January 17, 2013. Date of current version May 07, 2013. Corresponding author: D.-H. Kim (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2013.2242457
Using the magnetic circuit theory, a 1 kVA prototype inductor was designed. The inductor consists of two U-shaped ferrite 53 cores shown in Fig. 4(a) where the core size is 95 mm mm and each core is wound with 20 coils connected in series as in the overall inductor structure of Fig. 4(b).
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Fig. 5. Loss curve for the Mn-Zn ferrite core at 20 kHz in log scale. Fig. 1. Small capsule containing a MR fluid located at the middle of straw mounted in the magnetic property measurement system (MPMS). (a) MPMS. (b) Capsule and straw.
While the conventional inductor with a constant-value inductance has an air gap between the two cores, the proposed variable inductors includes the MR fluid in the gap (named as a MR fluid gap). To predict the inductor performance, a 3D finite element analysis (FEA) tool, a transient and successive substitution solver of MagNet VII [8], is used taking into account the material nonlinearity and time-dependent voltage source. A. Loss Calculation
Fig. 2. Magnetization curve versus applied magnetic field from the MPMS where initial data were obtained in CGS unit.
According to the materials used, the losses generated by the proposed inductor are classified into three types: the winding loss, core loss and MR fluid loss [9]. The winding loss corresponds to the Joule loss due to the conductivity of the copper coil including the skin effect of the source frequency and it is easily estimated from the FEA results. On the other hand, the assessment of the core loss requires experimental data on the power loss density of the core shown in Fig. 5 where the loss curve is plotted for the operating frequency of 20 kHz. Utilizing the loss data, the ferrite core loss is given by the Steinmetz formula as: (1)
Fig. 3. B-H curves of MR fluid and air in SI unit.
where is the power loss in W/kg, is the operating frequency, is the average value of magnetic flux density, and the rest symbols ( , , , , and used here) are constant coefficients for the loss curve fitting. In the meantime, the hysteresis loss of the MR fluid can be negligible because the residual flux density was almost zero as seen in Fig. 2. Consequently, just like the winding loss, the eddy current loss of the MR fluid is calculated with a bulk model of which the conductivity is set to be the measured value of 300 S/m. B. Calculation of AC Inductance The unique inductance variation feature of the proposed inductor is applied to conventional dc-dc power conversion systems in order to improve light and intermediate load efficiency of the converter. Improving light load efficiency of the converter is very important in such applications as portable electronics, battery charger, and other battery operated electronics [9], [10]. Fig. 6 shows a circuit diagram of the conventional buck (step-down) converter adopting the proposed variable inductor marked in a dotted box. The inductance is calculated by
Fig. 4. Dimensions of ferrite core and cross-section of the inductor. (a) Dimensions. (b) Proposed inductor.
(2)
KIM et al.: CHARACTERISTIC OF A VARIABLE INDUCTOR USING MAGNETORHEOLOGICAL FLUID
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Fig. 9. Prototype of 1 kW variable inductor where two gaps are filled with the MR fluid. Fig. 6. Circuit diagram of a buck converter using the proposed inductor.
Fig. 10. Distributions of magnetic flux density when the inductor current is 7 A and the gap length is 1.4 mm. (a) Air-gap. (b) MR fluid gap. Fig. 7. Comparison of current waveforms. (a) Conventional inductor. (b) Proposed inductor.
the time interval and so (2) can be still applied to the inductance calculation of the proposed variable inductor. IV. RESULTS
Fig. 8. Inductance calculation method used for the proposed inductor.
where and are the incremental linkage flux and the is the voltage current ripple of the inductor, respectively, is the converter duty cycle, and is across the inductor, the switching period. The theoretical inductor current waveforms between the conventional constant-value inductor and the proposed variable inductor are compared in Fig. 7. As to the conventional air-gap inductor, the inductor current slopes in both rising and falling intervals are almost linear because the inductance is constant. However, the inductor current waveform of the proposed inductor becomes nonlinear in both the intervals because the MR fluid has the nonlinear permeability as the load current changes. Therefore, the inductance of the proposed inductor cannot be obtained directly from (2). To tackle this problem, the nonlinear inductor current waveform is divided into narrow subintervals as illustrated in Fig. 8. Since the time duration of the subinterval is very short, the inductor current waveform is assumed to be almost linear during
To verify the feasibility and usefulness of the proposed variable inductor, a 1 kVA prototype inductor with UU shaped ferrite core shown in Fig. 9 was built and two-type (air gap and MR fluid gap) inductors were tested. The fiberglass reinforced plastic (FRP) frame is added to hold the cores and to adjust the gap length. The operating frequency of the pulse voltage is 20 kHz and the gap length is 1.4 mm. in Fig. 6 reaches a peak value of When the load current 7.115 A, the distributions of the magnetic flux density between the two inductors are compared with each other in Fig. 10. Even for the same current, it is observed that the magnetic saturation is proceeding rapidly in the core of the proposed inductor. That is because the magnetic reluctance of the proposed inductor is decreased due to the MR fluid compared with the conventional air-gap inductor. The measured voltage and current waveforms of the proposed inductor is presented in Fig. 11 where the inductor has the nonlinear current ripple. Fig. 12 shows the calculated loss characteristic of the two inductors. The core loss of the proposed inductor is much larger than that of the conventional inductor because the magnetic saturation already starts in the ferrite core of the proposed inductor due to the MR Fluid even with the same load current. The eddy current loss of the MR fluid has a very small portion (about 0.005%) of the total inductor loss. As the inductor current increases, the inductance variations between the two inductors are presented in Fig. 13. It is obvious that the proposed inductor has relatively large range from 600 to 2,500 and also its inductance is inversely proportional
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Fig. 11. Measured waveforms of the inductor voltage and current.
Fig. 14. Efficiency variations of the buck dc-dc converter adopting the conventional and the proposed inductors, respectively.
respectively. It can be concluded that higher efficiency is achieved at light and intermediate load condition in the case of using the proposed inductor. V. CONCLUSION
Fig. 12. Loss comparison between the conventional and the proposed inductors.
This paper proposes a new-type variable inductor for efficient power conversion which consists of the ferrite core and the MR fluid gap. The results show that the proposed inductor has a large inductance variation versus inductor currents but produces a relatively large core loss compared with the conventional air-gap inductor. Nevertheless, the proposed inductor significantly enhances light and intermediate load efficiency of the power converter because it makes possible to reduce the switching frequency which causes the main converter loss. ACKNOWLEDGMENT This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology under Grant 2011-0029721. REFERENCES
Fig. 13. Inductance variations of the conventional and proposed inductors when the inductor current increases.
to the inductor current when compared with the conventional constant-value inductor. in Fig. 6 Meanwhile, the converter output voltage ripple and is directly proportional to inductor current ripple is inversely proportional to the inductance value and the converter switching frequency . From these relations, it is with increasing while a constant value possible to reduce is maintained. The reduced frequency contributes of to improving the converter efficiency because the switching loss falls under a major portion of the total converter loss. In this paper, the variable on-time control shown in Fig. 6 [10] is with the proposed variable inductor. For used to decrease the buck converter using the conventional air-gap inductor, the is always fixed due to the constant inductance frequency value. In the other hand, for the same buck converter adopting can be decreased the proposed inductor, the frequency exploiting the variable inductance property. Fig. 14 compares measured efficiency of the buck dc-dc converter tested with the proposed inductor and conventional constant-value inductor,
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