All-In-One Induction Heating Using Dual Magnetic Couplings

energies

Article All-In-One Induction Heating Using Dual Magnetic Couplings

Wei Han , Kwok Tong Chau * , Hoi Chun Wong, Chaoqiang Jiang and Wong Hing Lam Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong, China; [email protected] (W.H.); [email protected] (H.C.W.); [email protected] (C.J.); [email protected] (W.H.L.) * Correspondence: [email protected]; Tel.: +852-28578617

Received: 21 March 2019; Accepted: 6 May 2019; Published: 10 May 2019

Abstract: This paper proposes and implements an all-in-one induction heating system, which can accommodate both pan-shaped and wok-shaped utensils. Traditionally, the pan is heated by a planar induction cooktop while the wok is heated by a curved induction cooktop. In this paper, both magnetic inductive coupling and magnetic resonant coupling are utilized to achieve excellent heating performance of the wok based on a planar primary coil. The key is to flexibly employ a detachable frustum coil for heating the wok. Specifically, the theoretical models of the proposed induction heating system with and without using the frustum coil are derived to analyze the proposed system. Computational simulation results of the magnetic and thermal fields of the proposed system are provided to elaborate the heating performance of the wok. A 1500 W prototype is designed and built. The calculated, simulated and experimental results are all in good agreement, which validate the feasibility of the proposed induction heating system well.

Keywords: induction heating; wireless power transfer; magnetic resonant coupling; magnetic inductive coupling

1. Introduction At present, energy crises and global warming have attracted urgent research attentions worldwide. Traditionally, heat energy is produced by burning combustible substances, which unavoidably leads to severe energy wastage and environmental deterioration. These drawbacks stimulate researchers to develop a fresh heating approach. In the past decades, induction heating based on magnetic coupling has been advocated highly and developed rapidly because of the definite advantages of cleanness, safety and high efficiency [1]. In order to expedite the development of induction heating, a considerable number of researchers have explored this technology and obtained abundant achievements [2]. Specifically, an all-surface induction heating system was developed with the capability of detecting the presence of metallic vessels and their material types [3]. The selective operating frequency technique was developed for all-metal domestic induction heating [4]. Meanwhile, the effective six phase matrix converter was designed for induction heating with characteristics of zero voltage switching [5]. There is no doubt that the coils are the most important component in an induction heating system. The modeling, design and optimization of coils utilizing either analytical approaches or finite element methods have been discussed by many researchers. Adaptable-diameter inductors and a movable primary coil system were proposed and implemented to increase the range of suitable pot diameters and achieve uniform heating for different sizes of cookware, respectively [6]. By using the particle swarm optimization to design a concentric multi-coil transverse flux induction heating system, the system could heat strips of different widths [7]. Six concentric spiral coils were arranged in the same plane and controlled by six independent inverters to achieve homogeneous induction

Energies 2019, 12, 1772; doi:10.3390/en12091772 www.mdpi.com/journal/energies Energies 2019, 12, x FOR PEER REVIEW 2 of 18

Energiesin the 2019same, 12 ,plane 1772 and controlled by six independent inverters to achieve homogeneous induction2 of 17 heating [8]. Furthermore, superconducting windings were adopted to produce a strong rotating magnetic field for heating aluminum billets [9]. Additionally, an induction heating system with a heating [8]. Furthermore, superconducting windings were adopted to produce a strong rotating flexible cooking zone was developed by adopting several overlapped coils [10]. A strongly-coupled magnetic field for heating aluminum billets [9]. Additionally, an induction heating system with outer-squircle inner-circular coil with the proper phase control was proposed to enhance the a flexible cooking zone was developed by adopting several overlapped coils [10]. A strongly-coupled efficiency and all-surface heating performance [11]. In addition, multiple coils which are arranged outer-squircle inner-circular coil with the proper phase control was proposed to enhance the efficiency independently or concentrically with proper control from multiple inverters can be used to achieve and all-surface heating performance [11]. In addition, multiple coils which are arranged independently uniform thermal distribution so as to enhance the heating quality [12,13]. All-metal induction heating or concentrically with proper control from multiple inverters can be used to achieve uniform thermal can be achieved by adopting double-layer coils while operating at a constant resonant frequency [14]. distribution so as to enhance the heating quality [12,13]. All-metal induction heating can be achieved Apart from those pan-shaped vessels, wok-shaped vessels can be inductively heated by utilizing by adopting double-layer coils while operating at a constant resonant frequency [14]. Apart from those variable turn pitch coils to boost the heating performance [15]. pan-shaped vessels, wok-shaped vessels can be inductively heated by utilizing variable turn pitch In 2007, by successfully transferring energy to a bulb two meters away, the wireless power coils to boost the heating performance [15]. transfer (WPT) based on magnetic resonance coupling (MRC) was experimentally demonstrated [16]. In 2007, by successfully transferring energy to a bulb two meters away, the wireless power transfer Given the benefits of extending the transfer distance to tens of centimeters, the resulting WPT (WPT) based on magnetic resonance coupling (MRC) was experimentally demonstrated [16]. Given the becomes especially attractive for battery charging of electric vehicles [17] or other electronic devices benefits of extending the transfer distance to tens of centimeters, the resulting WPT becomes especially via a large air gap [18]. Similar to induction heating technology, the coil design and optimization for attractive for battery charging of electric vehicles [17] or other electronic devices via a large air gap [18]. WPT play an important role in transferring the desired power with high efficiency. Moreover, the Similar to induction heating technology, the coil design and optimization for WPT play an important orthogonal receiving coil was implemented to improve the transfer efficiency under coil role in transferring the desired power with high efficiency. Moreover, the orthogonal receiving coil misalignment and achieve homogenous WPT for move-and-charge scenarios [19]. A WPT system was implemented to improve the transfer efficiency under coil misalignment and achieve homogenous with a bowl-shaped transmitting coil to charge small electronics such as hearing aids and an effective WPT for move-and-charge scenarios [19]. A WPT system with a bowl-shaped transmitting coil to method to calculate the magnetic field in the air was proposed in [20]. Meanwhile, by adopting the charge small electronics such as hearing aids and an effective method to calculate the magnetic field in MRC mechanism [21], selective induction heating can be achieved by regulating the operating the air was proposed in [20]. Meanwhile, by adopting the MRC mechanism [21], selective induction frequency at different resonant frequencies [22]. Although the MRC mechanism has been recently heating can be achieved by regulating the operating frequency at different resonant frequencies [22]. applied to induction heating [23,24], the research only dealt with flat-bottom pans. Relevant work on Although the MRC mechanism has been recently applied to induction heating [23,24], the research the convex-bottom wok is absent in the literature. only dealt with flat-bottom pans. Relevant work on the convex-bottom wok is absent in the literature. Currently, as shown in Figures 1a,b, the primary cooktop for induction heating needs to be Currently, as shown in Figure1a,b, the primary cooktop for induction heating needs to be specifically designed as a planar cooktop and a curved cooktop to heat flat-bottom pans and convex- specifically designed as a planar cooktop and a curved cooktop to heat flat-bottom pans and bottom woks, respectively. This specific arrangement significantly limits the utilization of cookware. convex-bottom woks, respectively. This specific arrangement significantly limits the utilization Inevitably, customers are required to install various induction cookers in order to use different of cookware. Inevitably, customers are required to install various induction cookers in order to use cookware for different cooking styles. The purpose of this paper is to propose and implement an all- different cookware for different cooking styles. The purpose of this paper is to propose and implement in-one induction heating system for different utensils, including both flat-bottom pans and convex- an all-in-one induction heating system for different utensils, including both flat-bottom pans and bottom woks. The key is to introduce a detachable frustum cooktop and to adopt dual magnetic convex-bottom woks. The key is to introduce a detachable frustum cooktop and to adopt dual magnetic couplings so as to effectuate the desired heating performance. couplings so as to effectuate the desired heating performance.

(a) (b)

FigureFigure 1. 1.Existing Existing inductioninduction heatingheating systems.systems. ((aa)) PlanarPlanar cooktop.cooktop. ((bb)) CurvedCurved cooktop.cooktop.

InIn SectionSection2 2,, the the proposed proposed induction induction heating heating system system and and its its principle principle of of operation operation is is described. described. Then,Then, thethe theoreticaltheoretical modelingmodeling ofof thethe proposedproposed systemsystem isis derivedderived inin SectionSection3 ,3, with with emphasis emphasis on on the the functionalityfunctionality of of the the frustum frustum coil. coil. SectionSection4 4 is is devoted devoted to to the the computational computational simulation simulation of of the the proposed proposed system,system, includingincluding the the magnetic magnetic ﬂux density,flux density, eddy-current eddy-current density anddensity Joule lossand densityJoule distributions.loss density

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Energies 2019, 12, 1772 3 of 17 distributions. In Section 5, an experimental prototype is constructed and tested so as to further validate the feasibility of the proposed all-in-one induction heating. Finally, a conclusion is drawn in InSection Section 6. 5, an experimental prototype is constructed and tested so as to further validate the feasibility of the proposed all-in-one induction heating. Finally, a conclusion is drawn in Section6. 2. Proposed Induction Heating System 2. Proposed Induction Heating System Figure 2 shows the configuration of the proposed induction system, which consists of a planar cooktopFigure and2 ashows detachable the configuration frustum cooktop, of the both proposed of themthem induction tunedtuned atat thethe system, samesame which resonantresonant consists frequency.frequency. of a planar WhenWhen cooktopheating a and flat-bottom a detachable pan, the frustum frustum cooktop, cooktop both is detached; of them whereas tuned at when the same heating resonant a convex-bottom frequency. Whenwok, the heating frustum a flat-bottom cooktop pan, is employed the frustum to cooktopartfully isheat detached; the outer whereas part whenof the heating wok. Additionally, a convex-bottom the wok,use of the the frustum frustum cooktop shape iscan employed help hold to woks artfully of heatdifferent the outer sizes. part Since of thethe wokprinciple. Additionally, of the induction the use ofheating the frustum for a shapeflat-bottom can help pan hold using woks a planar of diﬀerent cooktop sizes. has Since been the widely principle discussed, of the induction the following heating fordiscussion a ﬂat-bottom will focus pan usingon the a wok planar heating cooktop using has a been planar widely cooktop discussed, together the with following a detachable discussion frustum will focuscooktop. on the wok heating using a planar cooktop together with a detachable frustum cooktop.

FigureFigure 2.2. Proposed induction heating system.system.

TheThe principleprinciple ofof operationoperation ofof thethe proposedproposed inductioninduction heatingheating systemsystem isis basedbased onon dualdual magneticmagnetic couplingcoupling mechanisms,mechanisms, namelynamely magneticmagnetic inductiveinductive couplingcoupling (MIC) andand magneticmagnetic resonantresonant couplingcoupling (MRC).(MRC).(MRC). Firstly,Firstly,Firstly, a high-frequencyaa high-frequencyhigh-frequency power powerpower supply supplysupply or a resonantoror aa resonantresonant inverter inverterinverter [24] with [24][24] an operatingwithwith anan frequencyoperatingoperating rangingfrequencyfrequency from rangingranging 20 to 100fromfrom kHz 2020 serves toto 100100 to kHzkHz energize servesserves the toto primary energize coil. the Then, primary it induces coil. Then, the resonant it induces current the toresonant flow in current the frustum to flow coil in via the MRC, frustum and coil the eddyvia MR currentC, and mainly the eddy flows current in the mainly inner part flows of thein the wok inner via MIC.part of Meanwhile, the wok via the MIC. frustum Meanwhile, coil further the induces frustum the coil eddy further current induces to mainly the eddy flow incurrent the outer to mainly part of theflowflow wok. inin thethe In outerouter order partpart to theoretically ofof thethe wok.wok. InIn analyze orderorder toto the theotheo proposedretically system, analyze an the equivalent proposed circuit system, was an established equivalent ascircuit depicted was inestablished Figure3, where as depictedLp, Lf, inLi Figureand Lo are3, where the self-inductances Lpp,, LLff,, LLii andand L ofoo areare the thethe primary self-inductancesself-inductances coil, frustum ofofcoil, thethe innerprimary part coil, of thefrustum wok andcoil, outer inner partpart ofof thethe wok,wok and respectively; outer partR pof, Rthef, R wok,i and respectively;Ro are the corresponding Rpp,, Rff,, Rii andand internalRoo areare thethe resistances, correspondingcorresponding respectively; internalinternal Cresistances,resistances,p and Cf are respectively;respectively; the compensated Cpp andand capacitors Cff areare thethe connectedcompensatedcompensated in series capacitorscapacitors with theconnected primary in coil series and with frustum the coil,primary respectively. coil and All frustum mutual coil, inductances respectively. through All mutual magnetic inductances couplings, namely,throughthroughM magneticmagneticpf, Mpi, M couplings,couplings,fi, Mpo, Mfo namely,namely,and Mio ,M arepfpf,, consideredMpipi,, Mfifi,, Mpopo in,, M thefofo and model.and Mioio It,, areare should consideredconsidered be noted inin that thethe themodel.model. ferrite ItIt barsshould and be aluminum noted that shield the ferrite are ignored bars and because aluminum they wouldshield are cause ignored unnecessary because complication they would incause the equivalentunnecessary circuit complication while the in corresponding the equivalent eff ectcircuit on improving while the corresponding the magnetic field effect strength on improving is somewhat the compensatedmagnetic field by strength the magnetic is somewhat field leakage. compensated by the magnetic field leakage.

((a)) ((b))

Figure 3. Equivalent circuit represented by (a)) mutualmutual inductance;inductance; ((bb)) decoupleddecoupled circuit.circuit.circuit.

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According to Figure3a, the impedances of the primary coil, frustum coil, inner part of the wok and outer part of the wok are denoted as:   Zp = jωLp + 1/jωCp + Rp   Z = jωL + 1/jωC + R  f f f f . (1)   Zi = jωLi + Ri   Zo = jωLo + Ro

By referring the impedances of the inner and outer parts of the wok to the frustum and primary coils, the equivalent circuit of Figure3a can be depicted as Figure3b so as to derive the decoupled circuit for the sake of easy calculation. Thus, the system equation can be expressed as:       Vp   Zp jωMp f jωMpi jωMpo  Ip        0   jωM Z jωM jωM  I    =  p f f f i f o  f      . (2)  0   jωMpi jωM f i Zi jωMio  Ii       0 jωMpo jωM f o jωMio Zo Io

Accordingly, the currents in the primary coil and frustum coil as well as in the inner and outer parts of the wok can be obtained as:

 C  I = V  p 2 p  AC B  B−  I = V  f 2 p  AC B  −MpiC + M f iB Vp (3)  I = jω( )( )  i 2 2  Z + (ωM ) /Z AC B  i io o −  MpoC + M f oB Vp   Io = jω( )( )  Z + (ωM )2/Z AC B2 o io i − where  2 2  A = Zp + (ωMpi) /Zi + (ωMpo) /Zo   B = jωM . (4)  p f  2 2  C = Z f + (ωM f i) /Zi + (ωM f o) /Zo

Here, Ip and If are currents in the primary coil and frustum coil, respectively; Ii and Io are the induced eddy currents in the inner part and outer part of the wok, respectively. In order to eﬀectively transfer power from the primary coil to the frustum coil through a large air gap, it is necessary to ensure that both the primary and frustum coils work at the same resonant frequency, as given by:

p q fresonant = 1/(2π LPCP) = 1/(2π L f C f ). (5)

According to (1) and (5), the inductances of the primary and frustum coils are fully compensated by their capacitances. Thus, the impedances Zp and Zf can be regarded as the pure resistances Rp and Rf, respectively: ( Z = R p p . (6) Z f = R f Generated by the eddy current, the heating eﬀect is mostly concentrated in a peripheral layer of the skin depth δ, which can be obtained as:

1 δ = p (7) π f µ0µrσ Energies 2019, 12, 1772 5 of 17

where f is the resonant frequency; σ is the electrical conductivity; µr and µ0 are the relative permeability and vacuum permeability, respectively. For easy calculation, the wok can be regarded as a spherical cap, which is a portion of a sphere cut off by a plane. Since the equivalent resistance of a vessel can be determined by the skin effect of the eddy current, then the resistances of the inner and outer parts of the wok can be expressed as:   1  Ri = δ Si  σ × × (8)  1  Ro = δ So  σ × × where Si and So are the surface areas of the inner and outer parts of the wok and are equal to 2πRE0 and 2πR(E E ), respectively; R is the radius of the wok; E and E are the vertical heights of the inner − 0 0 part and outer part of the wok, respectively. Therefore, by substituting (7) into (8), the equivalent resistances of the wok inner and outer parts can be expressed as:  r  π f µ µr  0  Ri = 2πRE0  × σr . (9)   π f µ0µr  Ro = 2πR(E E ) − 0 × σ By measuring the equivalent impedances of the primary and frustum coils under different conditions, the parameters in (2) can be quantitatively calculated and defined. In particular, the equivalent impedances of the primary coil itself, with the wok only and with both the frustum coil and the wok are Zp, Zpw and Zpfw, respectively.   Zp = Rp + jωLp   Z = (R + D2R + E2R ) + jω(L D2L E2L ) (10)  pw p i o p i o  2 2 − 2 − 2 2  Z = (Rp + D R + E Ro) + jω(Lp D L E Lo) + B /C p f w i − i − where  ωMpi Mpi   D = q = (ωLi >> Ri)  2 Li  Ri + (ωLi)  . (11)  ωMpo Mpo   E = q = (ωLo >> Ro)  2 Lo  Ro + (ωLo) Similarly, the equivalent impedances of the frustum coil itself, with the wok only and with both the primary coil and the wok are Zf, Zfw and Zfwp, respectively.   Z f = R f + jωL f   Z = (R + F2R + G2R ) + jω(L F2L G2L ) (12)  f w f i o f i o  2 2 − 2 − 2 2  Z = (R + F R + G Ro) + jω(L F L G Lo) + B /A f wp f i f − i − where   ωM f i M f i   F = q = (ωLi >> Ri)  2 Li  Ri + (ωLi)  . (13)  ωM M  f o f o  G = q = (ωLo >> Ro)  2 Lo  Ro + (ωLo)

Accordingly, the six unknown variables, namely, Li, Lo, Mpi, Mpo, Mﬁ and Mfo, can be calculated based on the six equations listed in (10) and (12). The key terms of the proposed induction heating system are shown in Table1. Energies 2019, 12, 1772 6 of 17

Table 1. Key parameters of the coils and the wok.

Items Symbol Value Unit

Primary coil inductance (without wok) Lp 309.6 µH Primary coil resistance (without wok) Rp 0.24 Ω Primary coil inductance (with wok) Lpw/Lpfw 210.1/164.3 µH Primary coil resistance (with wok) Rpw/Rpfw 16.21/4.53 Ω Primary coil capacitor (with wok) Cp 75.4 nF Frustum coil inductance (without wok) Lf 201.41 µH Frustum coil resistance (without wok) Rf 0.14 Ω Frustum coil inductance (with wok) Lfw/Lfwp 79.1/68.3 µH Frustum coil resistance (with wok) Rfw/Rfwp 19.55/11.46 Ω Frustum coil capacitor (with wok) Cf 200 nF Wok inner part equivalent inductance Li 73.45 µH Wok inner part equivalent resistance Ri 11.77 Ω Wok outer part equivalent inductance Lo 667.86 µH Wok outer part equivalent resistance Ro 105.9 Ω Mutual inductances Mpf/Mpi/Mpo/Mﬁ/Mfo 119.8/119.1/231.1/109.1/267.7 µH Wok electrical conductivity σ 1 107 S/m × Wok relative permeability µr 200 – Vacuum permeability µ 4π 10 7 H/m 0 × − Skin depth δ 5.63 10 5 m × −

Based on (3) and (4), it can be found that the eddy currents Ii and Io are induced via both MIC and MRC mechanisms in the inner and outer parts of the wok, respectively. However, the eddy current Ii is mainly caused by the MIC mechanism because of the large Mpi, which is governed by the short distance between the primary coil and the inner part of the wok. Thus, there is no need to add an intermediate resonant coil to heat the inner part of the wok. On the contrary, the eddy current Io mainly depends on Mpf and Mfo or the MRC mechanism because of the small Mpo, which is determined by the large distance between the primary coil and the outer part of the wok. Mpf denotes the coupling strength between the primary coil and the frustum coil, while Mfo determines the coupling strength between the frustum coil and the outer part of the wok. Moreover, the transmission eﬃciency of the proposed system can be calculated by:

V I cos (I2R + I2R ) P p p ϕ p p f f η = out = − (14)

Pin VpIp cos ϕ where Pout is the dissipated power in the wok; Pin is the input power from the inverter; ϕ is the phase angle between the input voltage Vp and current Ip. Because of the MRC mechanism of the frustum coil, both Mpf and Mfo are signiﬁcantly improved to induce the desired the eddy current. As a result, the proposed all-in-one induction heating system can eﬀectively heat both the inner and outer parts of the wok by using a planar primary coil and a detachable frustum coil.

3. Theoretical Modeling Given that the operating frequency of the induction heating system is around 20–100 kHz, the quasi-static approximation is employed for mathematical modeling. The geometric model of the wok, which can be regarded as a part of the spherical surface with the radius R, can be built in the cylindrical coordinate, and its cross-section along the sphere diameter can be built in the orthogonal coordinate as shown in Figure4. In the ﬁgure, E stands for the vertical height and D the horizontal radius of the wok, while the angle from the wok edge to the bottom center is θ. The wok is virtually divided into two parts, namely the inner part and outer part, which cover one third and two thirds of the horizontal diameter, respectively. The size of the primary coil size is selected by taking into account Energies 2019, 12, 1772 7 of 17

Energies 2019, 12, x FOR PEER REVIEW 7 of 18 the eﬀective heating for all wok areas while avoiding unexpected magnetic leakage. The size of the offrustum the frustum coil is determined coil is determined with the considerationwith the consideration of fully boosting of fully the poorboosting heating the performance poor heating of performancethe outer part of of the the outer wok andpart achievingof the wok a and more achi uniformeving thermala more uniform distribution thermal of the distribution wok. All critical of the wok.parameters All critical of the parameters wok model of are the given wok model in Table are2. given in Table 2.

Figure 4. GeometryGeometry model of the proposed system.

Table 2. Key parameters of the wok geometry model. Table 2. Key parameters of the wok geometry model.

ItemsItems SymbolSymbol ValueValue Unit Unit PrimaryPrimary coil number coil number of turns of turns n n 5050 – -- Primary coil inner/outer radius r /rpo 2/12 cm Primary coil inner/outer radius pi rpi/rpo 2/12 cm Frustum coil number of turns m 40 – Frustum coil number of turns m 40 -- Frustum coil inner/outer radius rﬁ/rfo 5/12 Ω FrustumVertical coil heightinner/outer of wok radius outer part E rfi/rfo 75/12 cm Ω

VerticalVertical height height of wok of wok outer inner part part E0 E 1.67 cm cm Vertical height Wokof wok radius inner part R E’ 17.51.6 cm cm WokWok radius thickness e R 217.5 mm cm Wok horizontal radius D 14 cm Wok thickness e 2 mm Ceramic glass thickness g 7 mm FerriteWok bar horizontal size (length radiuswidth height) -D 8.5 1.5 0.514 cm cm × × × × AluminumCeramic shield glass size thickness (radius thickness) -g 12 27 cm mm × × Ferrite bar size Resonant(length × frequencywidth × height) f - 40 8.5 × 1.5 × kHz0.5 cm Aluminum shield size (radius × thickness) - 12 × 2 cm Consequently, theResonant point on frequency the edge of the wok inner part canf be expressed40 by the correspondingkHz arc angle θ0, horizontal radius D0 and vertical height E0, as given by: Consequently, the point on the edge of the wok inner part can be expressed by the corresponding arc angle Ɵ’, horizontal radius D’ and vertical height E’,1 asD given0 by: θ0 = π 2 tan− (15) ' − − DE0 θπ' =−2tan 1 (15) where e, g and d are the wok and ceramic glass thicknessesE and' the vertical wok thickness, respectively. where e, g and d are the wok and ceramic glass thicknesses and the vertical wok thickness, e respectively. d = (16) cos θ e 0 d = (16) According to the Maxwell equations, the relationshipcosθ ' between the magnetic ﬂux density B and the inducedAccording eddy to currentthe MaxwelljωσA equations,is given by: the relationship between the magnetic flux density B and the induced eddy current jɷσA is given by: = ( ) ∇×B =μμµ0µr()j ωσωσA − Jsource (17) ∇ × BAJ0 rsourcej − (17) where ω and A are the operating frequency and magnetic vector potential in the wok, respectively; Jsourcesource isis the the applied applied current current density density in in the the coil. coil. In In or orderder to to assess assess the the importance importance of of the the frustum frustum coil, coil, the theoretical modeling is separately realized with and withoutwithout thethe useuse ofof thethe frustumfrustum coil.coil.

3.1. Without Frustum Coil

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Energies 2019, 12, x FOR PEER REVIEW 8 of 18 3.1. Without Frustum Coil When the wok is heated directly by a planar pr primaryimary coil without the frustum coil, the geometric model is depicted in Figure 5, where the magnetic flux density B1 at an arbitrary point N (rie, zie) on model is depicted in Figure5, where the magnetic ﬂux density B1 at an arbitrary point N (rie, zie) on the wokthe wok outside outside surface surface (the curved(the curved red line) red isline) the is point the point of interest. of interest. The inner The andinner outer and radiiouter of radii the planarof the planar primary coil are rpi and rpo, respectively. The parameter lie represents the vertical distance primary coil are rpi and rpo, respectively. The parameter lie represents the vertical distance between the between the coil and the wok outside surface at the point of interest, which varies from lmin to lmax as coil and the wok outside surface at the point of interest, which varies from lmin to lmax as follows: follows: ' lielRed==− (1(cos)1 cos θ0)R +−+ e d (18)(18) ie − − ( lg= lminmin= g  =++. .(19) (19) lmaxlEgemax= E + g + e

Figure 5. WokWok heating using magnetic inductive coupling (MIC) without frustum coil.

Accordingly, followingfollowing the the process process of of derivation derivation in [in15 ],[15], the magneticthe magnetic vector vector potential potential at the at point the ofpoint interest of interest in the in cylindrical the cylindrical coordinate coordinate produced produced by a single-turn by a single-turn coil located coil located at P (ri ,0)at P of ( theri,0) planarof the primaryplanar primary coil can coil be expressedcan be expressed as: as: − ∞ +−−kd11 kd Z −kl ()()kke11 kke Ar(, z )=×μμ Ir eie J ()() krJ krk(k + k )ek1d (k k )e k dk1d ie ie011 r p i∞ klie i 221 kd1− kd− (20) A(rie, zie) = µ0µrIpri 0 e− J1(kr)J1(kri)k ()kk+−− e ()− kk− e dk (20) × 112 kd 2 kd 0 (k + k1) e (k k1) e− where Ip is the primary current; k is the integration variable; J1(kr) is a Bessel− − function of the first kind 2 1/2 whereand orderIp is one; the primaryk1 represents current; (k +k jisɷ theμ0μr integrationσ) . Hence, variable; the magneticJ1(kr) isflux a Besseldensity function at the point of the of first interest kind 2 1/2 andproduced order one;by thek1 planarrepresents primary (k + coiljωµ 0havingµrσ) .n Hence,turns can the be magnetic obtained flux as: density at the point of interest produced by the planar primary coil having nturnsn can be obtained as: =∇× Brz1(,) Arz (ie , ie ) . (21) =  n  i 1 X  B (r, z) =  A(r , z ). (21) 1 ∇ ×  ie ie  = 3.2. With Frustum Coil i 1 3.2. WithAs mentioned Frustum Coil above, the proposed induction heating system incorporates a detachable frustum coil toAs help mentioned heat the above,wok. For the the proposed inner part induction of the wok, heating the wireless system incorporatespower is mainly a detachable transferred frustum using coilthe MIC to help mechanism heat the wok. due Forto the the short inner transfer part of the distan wok,ce. the For wireless the outer power part is of mainly the wok, transferred the wireless using thepower MIC is mechanism mainly transferred due to the using short transferthe MRC distance. mechan Forism the in outer the partpresence of the of wok, a large the wireless air gap. power The isgeometric mainly transferredmodel is depicted using the in Figure MRC mechanism6, where the in magnetic the presence flux density of a large B2 airat an gap. arbitrary The geometric point N (rje, zje) on the wok outside surface (the curved red and blue lines) is the point of interest. There are model is depicted in Figure6, where the magnetic flux density B2 at an arbitrary point N (rje, zje) on thetwo wok scenarios: outside The surface point (the of interest curved is red below and bluethe specified lines) is the single-turn point of interest. coil (zj > Therezje), as are shown two scenarios:in Figure 6a, or the point of interest is above the specified single-turn coil (zj ≤ zje), as shown in Figure 6b. For The point of interest is below the specified single-turn coil (zj > zje), as shown in Figure6a, or the the first scenario, zje is a negative value, and the magnetic vector potential at the point of interest point of interest is above the specified single-turn coil (zj zje), as shown in Figure6b. For the first produced by a single-turn coil located at Q (rj, zj) of the frustum≤ coil can be derived as: scenario, zje is a negative value, and the magnetic vector potential at the point of interest produced by −−− ∞ kdz11()je kdz () je a single-turn coil located at Q (rj,−zklj) of the frustum()kke coil+−− can be derived () kke as: =×μμ je 11 Ar(,je z je )011 r I f r j e J ()() krJ krk j − dk (22) 0 +−−22kd kd ()kk11 e () kk e where If denotes the current in the frustum coil that was calculated in Section 2.

Energies 2019, 12, 1772 9 of 17

Z k (d z ) k (d z ) (k + k )e 1 je (k k )e 1 je ∞ klje 1 − 1 − − A(rje, zje) = µ0µrI f rj e− J1(kr)J1(krj)k − − dk (22) × 2 kd 2 kd 0 (k + k1) e (k k1) e− Energies 2019, 12, x FOR PEER REVIEW − − 9 of 18 where If denotes the current in the frustum coil that was calculated in Section2.

(a) (b)

Figure 6.6. Wok heatingheating using using MIC MIC and and magnetic magnetic resonance resonance coupling coupling (MRC) (MRC) with with frustum frustum coil. coil.(a) z(ja>) zzj je>. (zbje). (zb) zzj ≤ .zje. j ≤ je

For the second scenario, zjeje is a positive value, and the magnetic vector potential at the point ofof interest cancan bebe derivedderived as:as: +−+ ∞ kdz11()je kdz () je Z −kl ()kke+−−k1(d+ () kkezje) k1(d+zje) =×μμ ∞ je kl (11k + k1)e (k k1)e− AAr((,rje, z je) ) = µ011µ r II f rr j ee Jje ()()J krJ(kr) krkJ j(kr )k − −− dk. dk.(23) (23) je je 0 r f j0 − 1 1 j +−−22kd2 kd 2 0 ×()kk11(k + ek ) () kkekd (k ek ) e kd 1 − − 1 − Assuming that the number of turns of the primary coil is np and the number of turns of the Assuming that the number of turns of the primary coil is np and the number of turns of the frustum coil is nf, the magnetic flux density at the point of interest along the outer surface of the wok frustumcan be obtained coil is n fas, the magnetic ﬂux density at the point of interest along the outer surface of the wok can be obtained as nf  n  Xf  Brz(,)=∇× Arz ( , )  2 B2(r, z) =  jeA( jerje, z je ) (24)(24) ∇= ×   j 1 j=1

4. Computational Simulation As the the finite finite element element method method (FEM) (FEM) has been has wi beendely widely accepted accepted for numerical for numerical analyses, the analyses, FEM- thebased FEM-based software package software JMAG package was JMAGadopted was to simula adoptedte the to electromagnetic simulate the electromagnetic field and hence field the eddy and hencecurrent the loss. eddy In currentorder to loss. achieve In order the todesired achieve heating the desired performance heating while performance maintaining while high maintaining transfer highefficiency transfer and effi lowciency electromagnetic and low electromagnetic interference, interference, the operating the frequency operating frequencywas set to was40 kHz. set to The 40 kHz. key Theparameters key parameters of the ofproposed the proposed heating heating system system for forboth both theoretical theoretical calculation calculation and and computational simulation are listed in Table2 2.. ItIt shouldshould bebe notednoted thatthat thethe ferriteferrite barsbars andand aluminumaluminum shieldshield werewere taken into accountaccount duringduring simulation.simulation. Firstly, thethe magnetic magnetic flux flux distributions distributions without withou andt and with with the frustumthe frustum coil were coil simulatedwere simulated as shown as inshown Figure in7 Figure. When 7. there When is there no frustum is no frustum coil attached coil attached beneath beneath the wok, the it wok, can beit can observed be observed that a largethat a amountlarge amount of magnetic of magnetic flux does flux not does couple not with couple the outer with partthe ofouter the wokpart owingof the to wok the correspondingowing to the largecorresponding air gap. Such large severe air gap. magnetic Such field severe leakage magn andetic weak field magnetic leakage couplingand weak inevitably magnetic deteriorate coupling theinevitably heating deteriorate performance. the On heating the contrary, performance. when equipped On the contrary, with the frustumwhen equipped coil, the magneticwith the frustum flux can couplecoil, the eff magneticectively with flux both can thecouple inner effectively and outer partswith ofboth the the wok. inner Moreover, and outer it can parts be observed of the fromwok. FigureMoreover,7c,d thatit can the be frustum observed coil from utilizes Figures the MRC7c,d th mechanismat the frustum to significantly coil utilizes strengthen the MRC mechanism the magnetic to couplingsignificantly of the strengthen outer part the of magnetic the wok, coupling while suppressing of the outer the part magnetic of the fieldwok, leakage.while suppressing The potential the magnetic interferencefield leakage. can The be furtherpotential reduced magnetic by properly interference shortening can be the further outer reduced radius of by the properly frustum coilshortening and adding the outer shielding radius around of the thefrustum wok edge.coil and adding shielding around the wok edge.

Energies 20192019,, 1212,, 1772x FOR PEER REVIEW 1010 of of 1718

(a) (b)

Figure 7.7. Magnetic ﬂuxflux distribution. ( a)) Line plot of B without frustum coil. ( b) Line plot of B with frustumfrustum coil.coil. (c) Vector plotplot ofof BB withoutwithout frustumfrustum coil.coil. (d)) VectorVector plotplot ofof BB withwith frustumfrustum coil.coil.

In orderorder toto accuratelyaccurately determinedetermine the parametersparameters of the frustumfrustum coilcoil andand exhibitexhibit thethe enhancedenhanced magnetic coupling eeffect,ffect, the simulated results of the magnetic fluxflux density along the wok surfacesurface withoutwithout andand with the frustum coil were compared with the analytical results from Section3 3,, as as shown shown inin FigureFigure8 8.. Particularly, Particularly, the the calculated calculated lines lines were were obtained obtained by movingby moving points points mentioned mentioned in (20) in and(20) (23)and along(23) along the wok’s the wok’s curved curved bottom. bottom. The slightThe slight discrepancy discrepancy was mainlywas mainly due todue the to inevitable the inevitable magnetic magnetic field leakage,field leakage, as well as as well the effasect the of theeffect ferrite of the bars fe andrrite aluminum bars and shield. aluminum Because shield. of the Because ferromagnetic of the propertyferromagnetic of the property wok, the of magnetic the wok, fluxthe magnetic flowed along flux flowed the wok along surface the towok form surface a closed to form path. a closed Thus, as depicted in Figure8, the magnetic flux density at the center of the wok was almost zero, which can Energiespath. Thus, 2019, 12 as, x depictedFOR PEER REVIEWin Figure 8, the magnetic flux density at the center of the wok was 11almost of 18 alsozero, be which observed can also from be the observed magnetic from flux the distributions magnetic flux shown distributions in Figure 7shown. in Figure 7. Focusing on Figure 8a, it can be observed that the magnetic flux density exhibited two peaks at the two ends of the inner part, but dropped dramatically at the outer part of the wok. Taking the magnetic flux density of 5.9 mT at the two ends of the inner part as the expected value, the number of turns of the frustum coil can be designed to meet this expected magnetic flux density:

n f Brz(,)=∇× Arz ( , )= B (,) rz − Brz (,) (25) 21 je jeexp ected j=1 where Bexpected(r, z), B1(r, z) and B2(r, z) are the expected, original and compensated magnetic flux densities along the wok, respectively.

(a) (b)

Figure 8. Magnetic flux ﬂux density along wok surface. ( a) Without frustum coil. ( b) With frustum coil.

In order to ensure that the magnetic flux density in the outer part of the wok is effectively boosted above the expected line and to prevent uneven thermal distribution caused by too many coil turns, the turn number of the frustum coil should be carefully designed. Thus, the turn number of the frustum coil was calculated to be 40 according to (24) and the key parameters listed in Tables 1 and 2. As a result, after being equipped with the frustum coil, the magnetic flux density in the wok is as shown in Figure 8b. To assess the effectiveness of the heating performance produced by the frustum coil, the average eddy current density in the surface of the wok was numerically computed. As depicted in Figure 9a, without using the frustum coil, the planar primary coil can only produce a lower eddy current density concentrating on a small ring area in the inner part of the wok while the outer part of the wok involves much less eddy current density. In contrast, as depicted in Figure 9b, after utilizing the artfully designed frustum coil, the proposed induction heating effectively enlarges the area of high eddy current density to both the inner and outer parts of the wok. This improvement was attributed to the proposed dual magnetic couplings, namely the MIC and MRC mechanisms. Moreover, the Joule loss density could be readily obtained from the simulation and directly related to the heating performance, which was adopted and analyzed under different operating frequencies as shown in Figure 10. When the operating frequency was 37 kHz, which is lower than the resonant frequency of 40 kHz, it was found that the thermal effect was relatively poor with a maximum value of 5.17 × 107 W/m3 and an average value of 3.78 × 107 W/m3. On the other hand, when the operating frequency was 43 kHz, which is higher than the resonant frequency, the Joule loss density concentrated on the inner part and a small ring area of the outer part of the wok. The corresponding maximum and average Joule loss densities were 7.31 × 107 and 4.41 × 107 W/m3, respectively. As expected, when the system was operated at the resonant frequency, the maximum and average Joule loss densities were 7.94 × 107 and 5.67 × 107 W/m3, respectively, which are higher than those of other operating frequencies. This confirms that the proposed induction heating is capable of enhancing the thermal performance by regulating the operating frequency at the resonant frequency. Moreover, the high uniformity of thermal distribution at the resonant state can avoid the fast aging of the wok and improve its heating quality.

Energies 2019, 12, 1772 11 of 17

Focusing on Figure8a, it can be observed that the magnetic flux density exhibited two peaks at the two ends of the inner part, but dropped dramatically at the outer part of the wok. Taking the magnetic flux density of 5.9 mT at the two ends of the inner part as the expected value, the number of turns of the frustum coil can be designed to meet this expected magnetic flux density:

 n  Xf    B2(r, z) =  A(rje, zje) = Bexp ected(r, z) B1(r, z) (25) ∇ ×   − j=1 where Bexpected(r, z), B1(r, z) and B2(r, z) are the expected, original and compensated magnetic flux densities along the wok, respectively. In order to ensure that the magnetic flux density in the outer part of the wok is effectively boosted above the expected line and to prevent uneven thermal distribution caused by too many coil turns, the turn number of the frustum coil should be carefully designed. Thus, the turn number of the frustum coil was calculated to be 40 according to (24) and the key parameters listed in Tables1 and2. As a result, after being equipped with the frustum coil, the magnetic flux density in the wok is as shown in Figure8b. To assess the effectiveness of the heating performance produced by the frustum coil, the average eddy current density in the surface of the wok was numerically computed. As depicted in Figure9a, without using the frustum coil, the planar primary coil can only produce a lower eddy current density concentrating on a small ring area in the inner part of the wok while the outer part of the wok involves much less eddy current density. In contrast, as depicted in Figure9b, after utilizing the artfully designed frustum coil, the proposed induction heating effectively enlarges the area of high eddy current density to both the inner and outer parts of the wok. This improvement was attributed to the proposed dual magnetic couplings, namely the MIC and MRC mechanisms. Moreover, the Joule loss density could be readily obtained from the simulation and directly related to the heating performance, which was adopted and analyzed under different operating frequencies as shown in Figure 10. When the operating frequency was 37 kHz, which is lower than the resonant frequency of 40 kHz, it was found that the thermal effect was relatively poor with a maximum value of 5.17 107 W/m3 and an average value of × 3.78 107 W/m3. On the other hand, when the operating frequency was 43 kHz, which is higher than × the resonant frequency, the Joule loss density concentrated on the inner part and a small ring area of the outer part of the wok. The corresponding maximum and average Joule loss densities were 7.31 107 and × 4.41 107 W/m3, respectively. As expected, when the system was operated at the resonant frequency, × the maximum and average Joule loss densities were 7.94 107 and 5.67 107 W/m3, respectively, × × which are higher than those of other operating frequencies. This confirms that the proposed induction heating is capable of enhancing the thermal performance by regulating the operating frequency at the resonantEnergies 2019 frequency., 12, x FOR PEER Moreover, REVIEW the high uniformity of thermal distribution at the resonant state12 of can 18 avoid the fast aging of the wok and improve its heating quality.

(a) (b)

Figure 9.9. EddyEddy currentcurrent density density distributions distributions in in the the wok. wok. (a )( Withouta) Without frustum frustum coil. coil. (b) With(b) With frustum frustum coil. coil.

Figure 10. Joule loss density distributions in the wok at different operating frequencies.

5. Experimental Verification In order to verify the proposed induction heating, a prototype was built for experimentation. The testing setup is shown in Figure 11, in which the AC power source was provided by a full-bridge inverter, the DC source of the inverter was provided by a high-power DC supply (Kikusui PWR1600M), the current was measured by current probes (Tektronix TCP A300), the temperature was measured by a thermal probe (NI USB-TC01) and recorded by the LabVIEW, the thermal image was captured by a noncontact thermal scanner (Fluke TiS40), the power factor and power were measured by a power analyzer (Voltech PM300) and all waveforms erre recorded in an oscilloscope (Lecroy 6100A). The resonant frequency was set at 40 kHz and the ambient temperature was 20 °C. For experimentation, the frustum coil was temporarily fixed by sticky tape and adhesive for the sake of experimental convenience. In future, it should be fixed by thermally adhesive coating with a sleeve. The corresponding compensation capacitor can be embedded inside the sleeve during the production stage so that it will become more practical and compact for commercialization.

Energies 2019, 12, x FOR PEER REVIEW 12 of 18

(a) (b)

EnergiesFigure2019, 129., Eddy 1772 current density distributions in the wok. (a) Without frustum coil. (b) With frustum12 of 17 coil.

Figure 10. Joule loss density distributions in the wok at didifferentﬀerent operatingoperating frequencies.frequencies.

5.5. Experimental VerificationVerification InIn orderorder toto verifyverify thethe proposedproposed inductioninduction heating,heating, a prototypeprototype was built for experimentation. TheThe testingtesting setupsetup isis shownshown inin Figure 1111,, in which thethe ACAC power source waswas providedprovided byby aa full-bridge inverter,inverter, thethe DC DC source source of the of inverterthe inverter was provided was provided by a high-power by a high-power DC supply (KikusuiDC supply PWR1600M), (Kikusui thePWR1600M), current was the measured current was by currentmeasured probes by current (Tektronix probes TCP (Tektronix A300), the TCP temperature A300), the was temperature measured bywas a measured thermal by probe a thermal (NI USB-TC01) probe (NI USB-TC01) and recorded and recorded by the LabVIEW, by the LabVIEW, the thermal the thermal image image was capturedwas captured by aby noncontact a noncontact thermal thermal scanner scanner (Fluke (Fluke TiS40), TiS40), the the power power factor factor andand powerpower werewere measuredmeasured byby aa powerpower analyzeranalyzer (Voltech PM300)PM300) andand allall waveformswaveforms erreerre recordedrecorded inin anan oscilloscopeoscilloscope (Lecroy(Lecroy 6100A).6100A). TheThe resonantresonant frequencyfrequency was set at 4040 kHzkHz and thethe ambientambient temperature was 20 ◦°C.C. ForFor experimentation,experimentation, thethe frustumfrustum coilcoil waswas temporarilytemporarily fixedfixed byby stickysticky tapetape andand adhesiveadhesive forfor the sake ofof experimental convenience.convenience. In future,future, it should be fixed fixed by therma thermallylly adhesive coating with a sleeve. sleeve. TheThe correspondingcorresponding compensationcompensation capacitorcapacitor cancan bebe embeddedembedded insideinside thethe sleeve during the production stageEnergiesstage soso 2019 thatthat, 12 itit, x will willFOR becomebecomePEER REVIEW moremore practicalpractical andand compactcompact forfor commercialization.commercialization. 13 of 18

Figure 11. Experimental prototype and testing setup.

InIn addition, Figure Figure 1212 shows shows the the detailed detailed construc constructiontion of ofthe the prototype. prototype. For Forexperimentation, experimentation, the thefrustum frustum coil coil was was simply simply fixed fixed using using heat-resistant heat-resistant tape tape.. In In future, future, it it will will be be coated coated by by heat-resistant heat-resistant resin toto protect protect the the coil coil and and increase increase the structural the structur strength.al strength. Meanwhile, Meanwhile, six ferrite six bars ferrite and anbars aluminum and an shieldaluminum were shield adopted were under adopted the primary under the coil primary so as to coil improve so as theto improve magnetic the field magnetic strength field and strength reduce theand magneticreduce the field magnetic leakage, field respectively. leakage, respective The wokly. was Thepurposely wok was purposely kept empty kept to empty facilitate to accuratefacilitate temperatureaccurate temperature measurement measurem usingent a thermal using a scanner. thermal scanner.

Figure 12. Construction of the prototype.

To analyze the system response when operating at the resonant and non-resonant states, the input phase angle and power factor are shown in Figure 13a, while the calculated and measured root- mean-square (RMS) currents are shown in Figure 13b. When the operating frequency was at the resonant frequency, it was found that the phase angle and power factor reached the minimum value of 8.7° and the maximum value of 0.988, respectively. In addition, the measured results of the primary and frustum coil currents agree well with the calculated results obtained from (3) and (4), as shown in Figure 13b. Namely, the inductor was fully compensated by the capacitor so that the MRC mechanism was achieved to maximize the power factor and currents at the resonant frequency. It should be noted that the measured results are slightly higher than the calculated results because the ferrite bars and aluminum shield were neglected in the calculation.

Energies 2019, 12, x FOR PEER REVIEW 13 of 18

Figure 11. Experimental prototype and testing setup.

In addition, Figure 12 shows the detailed construction of the prototype. For experimentation, the frustum coil was simply fixed using heat-resistant tape. In future, it will be coated by heat-resistant resin to protect the coil and increase the structural strength. Meanwhile, six ferrite bars and an aluminum shield were adopted under the primary coil so as to improve the magnetic field strength andEnergies reduce2019, 12the, 1772 magnetic field leakage, respectively. The wok was purposely kept empty to facilitate13 of 17 accurate temperature measurement using a thermal scanner.

FigureFigure 12. ConstructionConstruction of of the the prototype. prototype.

ToTo analyze analyze the the system system response response when when operating operating at atthe theresonant resonant and andnon-resonant non-resonant states, states, the inputthe input phase phase angle angle and power and power factor factor are shown are shown in Figure in Figure 13a, while 13a, while the calculated the calculated and measured and measured root- mean-squareroot-mean-square (RMS) (RMS) currents currents are areshown shown in Figure in Figure 13b. 13 b.When When the the operating operating frequency frequency was was at at the the resonantresonant frequency, itit waswas foundfound that that the the phase phase angle angle and and power power factor factor reached reached the the minimum minimum value value of of8.7 8.7°◦ and and the the maximum maximum value value of of 0.988, 0.988, respectively. respectively. In In addition,addition, thethe measuredmeasured results of the primary primary andand frustum coil currents agreeagree wellwell withwith thethe calculated calculated results results obtained obtained from from (3) (3) and and (4), (4), as as shown shown in inFigure Figure 13b. 13b. Namely, Namely, the inductorthe inductor was fully was compensated fully compensated by thecapacitor by the capacitor so that the so MRC that mechanism the MRC mechanismwas achieved was to maximizeachieved to the maximize power factor the andpower currents factor at and the currents resonant at frequency. the resonant It should frequency. be noted It shouldEnergiesthat the 2019 be measured noted, 12, x FOR that resultsPEER the REVIEWmeasured are slightly results higher are than slight thely calculatedhigher than results the calculated because theresults ferrite because bars14 of andthe 18 ferritealuminum bars shieldand aluminum were neglected shield inwere the neglected calculation. in the calculation.

(a) (b)

Figure 13. FrequencyFrequency response. response. ( (aa)) Phase Phase angle angle and and power power factor. factor. ( (bb)) RMS RMS value value of of currents. currents.

Meanwhile, the the input input power power as as well well as as the the primary primary and and frustum frustum coil coil currents currents can can be be flexibly flexibly adjusted with a wide range by simply changing the input voltage. Specifically, Specifically, the simulated and calculatedcalculated Ip andand IIf funderunder different different input input voltages voltages are are shown shown in in Figure Figure 14a.14a. The The trend trend of of the the calculated calculated currentcurrent is inin goodgood agreementagreement with with the the simulated simulated current current while while the the values values are are slightly slightly lower lower due due to the to thefact fact that that the the ferrite ferrite bars bars and and aluminum aluminum shielding shielding were were neglected. neglected. As shownAs shown in Figure in Figure 14b, 14b, when when the thevalue value of V ofp wasVp was varied varied from from 20 V20 to V 140to 140 V, theV, the input input power power increased increased from from 20 W20 toW 1500 to 1500 W whileW while the theprimary primary (frustum) (frustum) coil RMScoil RMS current current increased increased from 0.97from A 0.97 (1.26 A A) (1.26 to 10.73 A) to A 10.73 (12.12 A A). (12.12 Thus, A). when Thus,Vp whenwas set Vpat was 20 set V, 60at 20 V, 100V, 60 V V, and 100 140 V and V, the 140 waveforms V, the waveforms of Vp, I pofand Vp, Ipf andat the If at resonant the resonant frequency frequency were weremeasured measured as shown as shown in Figure in Figure 15. The 15. corresponding The corresponding RMS valuesRMS values of Ip (I fof) wereIp (If) 0.97were A 0.97 (1.26 A A), (1.26 3.58 A), A 3.58(4.42 A A), (4.42 7.34 A), A (8.467.34 A A) (8.46 and 10.73A) and A 10.73 (12.12 A A), (12.12 respectively. A), respectively. Also, as shownAlso, as in shown Figure in15 Figured, the V 15d,p and theIp Vwaveformsp and Ip waveforms are almost are in phasealmost due in phase to the due LCresonance, to the LC whichresonance, notonly which caused not only thehigh-power caused the factorhigh- powerof 0.988, factor but alsoof 0.988, helped but toalso reduce helped the to switching reduce the loss. switching Therefore, loss. the Therefor systeme, ethefficiency system at efficiency the rated atpower the rated of 1500 power W was of 1500 calculated W was to ca belculated equal toto 96.75%.be equal to 96.75%.

(a) (b)

Figure 14. Currents and power control by the input voltage. (a) Calculated results. (b) Measured results.

Energies 2019, 12, x FOR PEER REVIEW 14 of 18 Energies 2019, 12, x FOR PEER REVIEW 14 of 18

(a) (b) (a) (b) Figure 13. Frequency response. (a) Phase angle and power factor. (b) RMS value of currents. Figure 13. Frequency response. (a) Phase angle and power factor. (b) RMS value of currents. Meanwhile, the input power as well as the primary and frustum coil currents can be flexibly adjustedMeanwhile, with a wide the input range power by simply as well changing as the primarythe input and voltage. frustum Specifically, coil currents the cansimulated be flexibly and calculatedadjusted with Ip and a wideIf under range different by simply input changingvoltages are the shown input involtage. Figure Specifically,14a. The trend the of simulated the calculated and currentcalculated is inIp andgood If underagreement different with input the simulated voltages are cu rrentshown while in Figure the values 14a. The are trend slightly of the lower calculated due to thecurrent fact thatis in thegood ferrite agreement bars and with aluminum the simulated shielding current were while neglected. the values As shown are slightly in Figure lower 14b, due when to the valuefact that of Vthep was ferrite varied bars from and 20aluminum V to 140 shieldingV, the input were power neglected. increased As shownfrom 20 in W Figure to 1500 14b, W whilewhen the valueprimary of V(frustum)p was varied coil from RMS 20 current V to 140 increased V, the input from power 0.97 A increased (1.26 A) tofrom 10.73 20 WA (12.12to 1500 A). W Thus,while whenthe primary Vp was (frustum)set at 20 V, coil 60 V, RMS 100 currentV and 140 increased V, the waveforms from 0.97 ofA V(1.26p, Ip and A) toIf at 10.73 the resonantA (12.12 frequencyA). Thus, werewhen measured Vp was set asat shown20 V, 60 in V, Figure 100 V and15. The 140 correspondingV, the waveforms RMS of valuesVp, Ip and of IIfp at (I thef) were resonant 0.97 A frequency (1.26 A), 3.58were A measured (4.42 A), 7.34as shown A (8.46 in A) Figure and 10.7315. The A (12.12corresponding A), respectively. RMS values Also, of as I pshown (If) were in 0.97Figure A (1.2615d, theA), V3.58p and A (4.42Ip waveforms A), 7.34 A are (8.46 almost A) and in phase10.73 Adue (12.12 to the A), LC respectively. resonance, Also, which as not shown only in caused Figure the 15d, high- the powerVp and factorIp waveforms of 0.988, are but almost also helped in phase to reducedue to the switchingLC resonance, loss. whichTherefor note, only the systemcaused efficiencythe high- atpower the rated factor power of 0.988, of 1500 but Walso was helped calculated to reduce to be the equal switching to 96.75%. loss. Therefore, the system efficiency Energiesat the rated2019, 12 power, 1772 of 1500 W was calculated to be equal to 96.75%. 14 of 17

(a) (b) (a) (b)

Figure 14.14. CurrentsCurrents and and power power control control by theby inputthe input voltage. voltage. (a) Calculated (a) Calculated results. results. (b) Measured (b) Measured results. results.

Energies 2019, 12, x FOR PEER REVIEW 15 of 18 (a) (b)

Figure 15. WaveformsWaveforms of of voltage voltage and and current current at: ( at:a) V (pa =)V 20p V;= (20b) V V;p = ( b60)V V;p (c=) V60p = V; 100 (c )VV; (pd)= V100p = 140 V; (V.d)V p = 140 V.

In orderorder toto verifyverify thethe eeffectivenessﬀectiveness ofof thethe frustumfrustum coilcoil andand hencehence the MRCMRC mechanismmechanism in the proposed induction heating, heating, the the wok wok was was heated heated fo forr 180 180 s without s without and and with with the thefrustum frustum coil coilat the at thepower power rating rating of 1500 of 1500 W. Then, W. Then, the temperatures the temperatures of nine of nineevenly evenly distributed distributed points points along along the wok the woksurface surface diameter diameter were were measured measured by the by thermal the thermal probe. probe. Throughout Throughout the whole the whole heating heating period, period, the thetemperatures temperatures were were sampled sampled every every 20 20s. s.When When the the wok wok was was heated heated without without the the frustum frustum coil, coil, it was observed (Figure 16a)16a) that that only only a asmall small area area near near th thee center center was was heated heated up upwhile while the the outer outer part part of the of thewok wok was was poorly poorly heated. heated. In particular, In particular, the temperatur the temperaturee of the of wok the wokinner inner part partreached reached over over70 °C 70 with◦C witha maximum a maximum temperature temperature of 85.5 of °C 85.5 at◦ C180 at s. 180 However, s. However, the temperature the temperature of the of wok the wokouter outer part partwas wascomparatively comparatively low lowwith with a minimum a minimum temperature temperature of of35.2 35.2 °C.◦C. When When the the wok wok was was heated heated with the frustum coil, it waswas observedobserved (Figure(Figure 1616b)b) thatthat fastfast heatingheating andand uniformuniform temperaturetemperature distributiondistribution could be achieved both in the inner and outer parts of the wok.wok. In particular, the temperature of the wok inner partpart reached overover 105105 ◦°CC with a maximum temperature of 105.9 ◦°CC at 180 s. What is more, the temperature of the wok outer part was remarkablyremarkably improved and reached above 95 ◦°C.C. Hence, the overall heating performance was significantly increased while the temperature difference was hugely reduced by the proposed system.

(a)

Energies 2019, 12, x FOR PEER REVIEW 15 of 18

Figure 15. Waveforms of voltage and current at: (a) Vp = 20 V; (b) Vp = 60 V; (c) Vp = 100 V; (d) Vp = 140 V.

In order to verify the effectiveness of the frustum coil and hence the MRC mechanism in the proposed induction heating, the wok was heated for 180 s without and with the frustum coil at the power rating of 1500 W. Then, the temperatures of nine evenly distributed points along the wok surface diameter were measured by the thermal probe. Throughout the whole heating period, the temperatures were sampled every 20 s. When the wok was heated without the frustum coil, it was observed (Figure 16a) that only a small area near the center was heated up while the outer part of the wok was poorly heated. In particular, the temperature of the wok inner part reached over 70 °C with a maximum temperature of 85.5 °C at 180 s. However, the temperature of the wok outer part was Energiescomparatively2019, 12, 1772 low with a minimum temperature of 35.2 °C. When the wok was heated with15 ofthe 17 frustum coil, it was observed (Figure 16b) that fast heating and uniform temperature distribution could be achieved both in the inner and outer parts of the wok. In particular, the temperature of the wokthe overall inner part heating reached performance over 105 °C was with signiﬁcantly a maximum increased temperature while of the 105.9 temperature °C at 180 s. di Whatﬀerence is more, was thehugely temperature reduced by the proposed system.

(a)

(b)

Figure 16. Temperature distributions. (a) Without frustum coil. (b) With frustum coil.

Finally, the entire heating effect of the proposed induction heating system equipped with the frustum coil was assessed. Specifically, the dissipated power in the primary coil, frustum coil and the wok were 27.63, 20.56 and 1435.98 W, respectively. The wok inner part is mostly heated by the primary coil with the MIC mechanism and the wok outer part is mainly heated by the frustum coil with the MRC mechanism. Thus, a homogenous power density can be generated to achieve an even temperature distribution. The corresponding thermal images of the wok after heating for 180 s are captured as shown in Figure 17. Specifically, the temperatures of the selected nine evenly distributed points along the wok surface diameter varied between 105.3 ◦C and 93.6 ◦C, as depicted in Figure 17a, which agree well with the data shown in Figure 16b. In addition, as depicted in Figure 17b, the temperatures of five evenly distributed points along the wok vertical height varied between 108.8 ◦C and 93.8 ◦C. This indicates that the heating performance of the wok along the vertical direction was as effective as that along the horizontal direction. Therefore, the experimental results well agree with the theoretical analysis and computational simulation, verifying the heating performance of the proposed induction heating. Energies 2019, 12, x FOR PEER REVIEW 16 of 18

Figure 16. Temperature distributions. (a) Without frustum coil. (b) With frustum coil.

Finally, the entire heating effect of the proposed induction heating system equipped with the frustum coil was assessed. Specifically, the dissipated power in the primary coil, frustum coil and the wok were 27.63, 20.56 and 1435.98 W, respectively. The wok inner part is mostly heated by the primary coil with the MIC mechanism and the wok outer part is mainly heated by the frustum coil with the MRC mechanism. Thus, a homogenous power density can be generated to achieve an even temperature distribution. The corresponding thermal images of the wok after heating for 180 s are captured as shown in Figure 17. Specifically, the temperatures of the selected nine evenly distributed points along the wok surface diameter varied between 105.3 °C and 93.6 °C, as depicted in Figure 17a, which agree well with the data shown in Figure 16b. In addition, as depicted in Figure 17b, the temperatures of five evenly distributed points along the wok vertical height varied between 108.8 °C and 93.8 °C. This indicates that the heating performance of the wok along the vertical direction was as effective as that along the horizontal direction. Therefore, the experimental results well agree with Energiesthe theoretical2019, 12, 1772 analysis and computational simulation, verifying the heating performance of16 ofthe 17 proposed induction heating.

Figure 17. ThermalThermal images images of of the the wok wok from the top view and side view.

6. Conclusions Conclusions In this paper, anan all-in-oneall-in-one induction heating system was proposed and implemented, which is capable of eeffectivelyffectively heating both flat-bottomflat-bottom pans and convex-bottom woks based on a planar cooktop. The The key key is to utilize a detachable frustum cooktop, which is actually a frustum coil coated with heat-resistant resin. Thus, the proposed systemsystem functionally combines the conventional planar cooktop and curved cooktop together while bringing dramatic convenience for cooking utensils with differentdifferent shapes, which isis absentabsent inin thethe literature.literature. Focusing on heating the wok, which is much more demanding than heating the pan, the frustum coil serves to provide the MRC mechanism to boost the magnetic coupling of the outer part of the wok with a a large large air air gap. gap. Meanwhile, Meanwhile, the the inner inner part part of ofthe the wok wok with with a small a small air airgap gap is heated is heated by the by MICthe MIC mechanism. mechanism. The Thenumber number of turns of turns of the of frustu the frustumm coil coilcan canbe properly be properly calculated calculated so that so thatthe systemthe system not notonly only heats heats a curved-bottom a curved-bottom wok wok successf successfully,ully, but but also also achieves achieves a a relatively uniform thermal distribution along the wok. Specifically, Specifically, the theoretical models of the proposed inductioninduction heating system with and without using the the frustum frustum coil coil are are derived derived to to analyze analyze the the proposed proposed system. system. Based onon thethe FEM-based FEM-based software software package package JMAG, JMAG, a computational a computational simulation simulation of the of proposed the proposed system wassystem provided was provided to elaborate to elaborate the heating the heating performance performance of the wok.of the Afterwok. After fabricating fabricating a prototype a prototype with withthe maximum the maximum delivering delivering power power of 1500 of W, 1500 a series W, ofa experimentsseries of experiments was performed. was performed. The calculated, The calculated,simulated andsimulated experimental and experimental results are all results in good ar agreement,e all in good thus agreement, validating thethus feasibility validating of the proposedfeasibility inductionof the proposed heating induction system. heating system.

Author Contributions: W.H. and K.T.C. designed the system, analyzed the results and wrote this paper. H.C.W. and C.J. helped conduct the experiments and analyzed the data. W.H.L. helped made important suggestions. Funding: This work was funded by The University of Hong Kong, Hong Kong, grant number SFBR201711159046. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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