Induction heating (IH) technology is nowadays the heating technology of choice in many industrial, domestic, and medical applications due to its advantages regarding efficiency, fast heating, safety, cleanness, and accurate control. Advances in key technologies, i.e., power electronics, control techniques, and magnetic component design, have allowed the development of highly reliable and cost-effective systems, making this technology readily available and ubiquitous. This paper reviews IH technology summarizing the main milestones in its development and analyzing the current state of art of IH systems in industrial, domestic, and medical applications, paying special attention to the key enabling technologies involved. Finally, an overview of future research trends and challenges is given, highlighting the promising future of IH technology.

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Induction Heating Technology and Its Applications: Past Developments, Current Technology, and Future Challenges

Inductive power transfer (IPT) is an emerging technology that may create new possibilities for wireless power charging and transfer applications. However, the rather complex control method and low efficiency remain the key obstructing factors for general deployment. In a regularly compensated IPT circuit, high efficiency and controllability of the voltage transfer function are always conflicting requirements under varying load conditions. In this paper, the relationships among compensation parameters, circuit efficiency, voltage transfer function, and conduction angle of the input current relative to the input voltage are studied. A design and optimization method is proposed to achieve a better overall efficiency as well as good output voltage controllability. An IPT system design procedure is illustrated with design curves to achieve a desirable voltage transfer ratio, optimizing between efficiency enhancement and current rating of the switches. The analysis is supported with experimental results.

Design for Efficiency Optimization and Voltage Controllability of Series–Series Compensated Inductive Power Transfer Systems

Secondary series- and parallel-compensations are widely used in inductive power transfer (IPT) systems for various applications. These compensations are often studied under some isolated constraints of maximum power transfer, optimal efficiency at a particular loading condition, etc. These constraints constitute an insufficient set of requirements for engineers to select appropriate compensation techniques to be used as a voltage converter with optimal efficiency and loading conditions. This paper studies the characteristics of the IPT system at various frequencies of operation utilizing the two compensation techniques to work as a voltage converter. The frequencies that can provide maximum efficiency of operation and load-independent voltage-transfer ratio are analyzed. The optimal frequencies corresponding to the two compensation techniques are found and compared to facilitate the design of voltage converters with efficient power conversion and load-independent frequency of operation. The analysis is supported by experimental measurements.

Analysis and Comparison of Secondary Series- and Parallel-Compensated Inductive Power Transfer Systems Operating for Optimal Efficiency and Load-Independent Voltage-Transfer Ratio

This study presents an approximate model for multi-strand wire winding, including litz-wire winding. The proposed model is evaluated using Dowell's equation. The model takes into account the existence of proximity effect within the litz-wire bundle between the strands and between the bundles, as well the skin effect. The expressions for optimum strand diameter and number of strands at which minimum winding AC resistance is obtained for the litz-wire windings are derived. The boundary frequency between the low-frequency and the medium-frequency ranges are given for both litz-wire and solid-round wire inductors. Hence, the low-frequency ranges of both wire windings are determined. It is shown that litz-wire is better than the solid wire only in specific frequency range. The model has been verified by the measurements, and the theoretical results were in good agreement with those experimentally measured. Comparison of the theoretical predictions of the proposed approximate litz-wire model with models proposed in other publications and with experimental results is given.

Winding resistance of litz-wire and multi-strand inductors

This paper describes a novel, model-based, and design optimization methodology for high-power medium-frequency transformers (MFTs) for medium-voltage high-power electronic applications, namely emerging solid-state transformers. Presented procedure enables the designer to interactively select the most optimal design in a simple and intuitive way, while inherently offering flexibility in terms of various design alternatives, depending on the component availability. The core of the design algorithm is explained in detail together with all of the relevant modeling and technical challenges associated with realization of a prototype. A $\text{100 kW}$ , $\text{10 kHz}$ MFT prototype has been designed, according to the presented algorithm, practically realized and thoroughly tested in order to verify the theoretical design.

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100 kW, 10 kHz Medium-Frequency Transformer Design Optimization and Experimental Verification

In this paper, an analytical optimization of solid-round-wire windings conducting sinusoidal current is performed. New closed-form analytical equations are derived for the normalized solid-round-wire diameter to achieve minimum ac winding losses for sinusoidal current. Approximations of Dowell's equation are used to derive expressions for normalized diameter at the local minimum of winding ac resistance and normalized critical diameter. An equation for the winding ac resistance at the local minimum is derived. Additionally, equations for the normalized diameter at the local maximum of ac resistance and the normalized boundary diameter between low- and medium-frequency ranges are given. The formulas enable inductor and transformer designers to minimize winding loss without utilizing finite-element method analysis. Experimental verification of the presented theory is given.

Analytical Optimization of Solid–Round-Wire Windings

An analytical model based on the one-dimensional Dowell's equation for computing the ac-to-dc winding resistance ratio of the litz-wire windings independent of the porosity factor is derived. The model takes into account proximity effect within the bundle and between bundle layers, as well as the skin effect in each strand. Three frequency ranges for the winding resistance characteristics are considered: low-, medium-, and high-frequency range. In each range, the behavior of the ac-to-dc winding resistance ratio $F_R$ is different. Moreover, an analytical optimization of the litz-wire winding strand diameter for litz-wire windings conducting sinusoidal and multiharmonic currents independent of the porosity factor is performed.

Winding Resistance and Power Loss of Inductors With Litz and Solid-Round Wires

In this study, an analytical optimisation of the foil, strip, square and solid-round-wire winding inductors conducting sinusoidal current is performed. The Ampere law is used to derive analytical equations for the AC-to-DC winding resistance ratio of different shape inductor windings valid at low and medium frequencies. These equations are used to perform optimisation of windings to obtain the global minimum of the winding AC resistance of the foil and strip wire windings and the local minimum of the winding AC resistance for the square and solid-round-wire windings. Derivations of AC-to-DC winding resistance ratio and winding AC resistance based on Ampere's law for the solid-round-wire windings are compared to Dowell's equation. Results of the predicted winding AC resistance based on Ampere's law for the solid-round-wire windings are validated by experimental results.

Analytical winding size optimisation for different conductor shapes using Ampere's law

This study presents a derivation of an expression for the optimum thickness of foil inductors operating under DC and AC non-sinusoidal periodic currents. The exact equation for the DC winding power loss and approximated equations for the AC winding power loss are used to determine the optimum thickness of the foil for the single-layer and multi-layer inductors, operating with multi-harmonic AC currents superimposed on the DC component. The design procedure for inductors with minimum winding power loss is presented for a pulsewidth-modulated DC–DC buck converter operating in discontinuous conduction mode (DCM). The comparison of the total winding power loss of the designed inductor with optimum foil thickness to the total winding power loss of the inductor with non-optimised round conductor is also given. The theoretical predictions have been verified by measurements of inductors with three different foil thicknesses.

Rafal P. Wojda

Papers

Winding resistance of litz-wire and multi-strand inductors

Analytical Optimization of Solid–Round-Wire Windings

Winding Resistance and Power Loss of Inductors With Litz and Solid-Round Wires

Analytical winding size optimisation for different conductor shapes using Ampere's law

Optimum foil thickness of inductors conducting DC and non-sinusoidal periodic currents