A new efficiency figure of merit for induction heating appliances operating under highly variable operating conditions

Abstract

Induction heating is an efficient and high-performance heating method which already has a significant market penetration and economic impact due to its benefits inherent to contactless energy transfer systems such as quickness, cleanness, and safety. Efficiency is a key design parameter since it determines not only the appliance performance but also its environmental impact, with significant socio-political implications. However, it is not easy to determine and compare the actual power converter efficiency operating under highly variable conditions typical of IH. This paper proposes an averaged efficiency parameter elaborated based on technical and typical IH usage conditions that offers a useful value to compare power converters operating under realistic operation conditions. The proposed parameter has been evaluated in some of the most significant power converter topologies used in reported state-of-the-art induction heating systems.

Keywords

Induction heating power electronics efficiency

1. Introduction

Cooking is one of the main daily activities where engineering plays a key role on providing efficient and sustainable energy sources [1]. Induction heating (IH) cooktops [2–4] (Fig. 1) have become a successful product, with a high market share gain in many countries in the last decade, due to its high performance [5–8]. In order to reach the current technology maturity, several innovations regarding power electronics, magnetic component design, and digital control have been developed. Stimulated by an increasingly electrified environment, the high efficiency [9–11] of the appliance has become the spearhead to achieve a greater market penetration.

Fig. 1.

Advanced domestic IH system.

However, from the electronic design point of view, efficiency calculations do not take into account the singularities of the cooking process [12–14]. Generally, the resonant topologies that implement the converter are designed in order to operate under highly variable conditions. These affect not only the output power, e.g. 100% down to 5% nominal power, but also other aspects, including resonant tank variation up to 50%. Consequently, it is usually difficult to measure and compare efficiency achievements among different topologies.

In this context, the main aim of this paper is to provide a path to define a real-world fair energetic labeling for domestic induction heating appliances. Nowadays, there is no well-established energetic labeling for these appliances (as it exists, for instance, for ovens, dishwashers, or fridges). Since the technology inside these power converters, i.e. resonant power converters, makes them to have efficiency performance highly dependent on the operating point, this analysis is of utmost important to achieve realistic results.

Due to the high relevance of the efficiency figure of merit, with significant socio-economic and industrial implications [14], this paper proposes a new averaged efficiency parameter which serves as a figure of merit to compare power converters under realistic operating conditions [15]. Similar efforts have been carried out for photovoltaic (PV) converters [16]. In this case, the technical constraints specific of domestic IH systems as well as their typical usage are considered.

2. Induction heating efficiency analysis

Induction heating appliances are a paradigmatic example of an indirect ac-ac converter (alternating current to alternating current) applied to domestic applications. These systems are composed of an electromagnetic compatibility filter (EMC), a rectifier unit, a dc (direct current) filtering element, and an inverter stage (Fig. 2). Typically, a low-capacitance filtering capacitor is used to achieve a high power factor without the need for an additional power factor correction stage, which may add additional power losses and cost.

Fig. 2.

Main power conversion blocks in an induciton heating appliance.

Considering this structure, the main power flux in an induction heating appliance is summarized in Fig. 3. The power absorbed from the grid, P_in, suffers from power losses in the rectifier, P_Rect, inverter, P_Inv, and inductor, P_ind, and part of the power transmitted wirelessly to the pot is also lost through conductive, P_Glass, and convective, P_Air, heat conduction to surrounding elements. Finally, a significant portion of the power is also lost in form of vapor in boiling water, P_B, and the heat finally applied to the food is P_h. This paper will focus on part of the power losses that can be controlled and measured by the power electronic designer, i.e., power losses in the power converter.

Fig. 3.

Main power losses in an induction heating appliance.

Figure 4 summarizes the most common inverter stages used nowadays to implement induction heating systems, the half-bridge and full-bridge series resonant converters, which are complemented by the single-switch quasi-resonant inverter for low-end applications. Whereas different implementations are made for specific applications, the general efficiency analysis can be applied to all the existing topologies.

Fig. 4.

Half-bridge (left) and full-bridge (right) series resonant inverters.

Efficiency is defined by the properties of real power devices and voltage and current stress imposed by the selected converter topology. Considering non-ideal switching devices, the losses can be classified into two terms: conduction losses, P_on, and switching losses, P_sw (Fig. 5).

Fig. 5.

Power loss representation in a power device.

According to this model, both the on-state and the switching transitions are non-ideal whereas the off-state resistance effect has been neglected (ideal off-state resistance is considered). As a result, the average conduction losses, P_on, in a switching period, T_sw = 1∕f_sw, results $\begin{eqnarray}P_{on}=\frac{1}{T_{sw}}\int _{t_{on}}v_{t}(t)i_{t}(t)dt,\end{eqnarray}$ (1) where i_t, v_t, denote the current through the switching devices and the device on-state voltage drop, respectively, and t_on is the device conduction time interval. On the other hand, the switching losses can be defined by means of both the turn-on and the turn-off switching losses, P_{sw, ON}, P_{sw, OFF}, respectively, resulting $\begin{eqnarray}P_{sw}=P_{sw,ON}+P_{sw,\mathit{OFF}}=f_{sw}(E_{sw,ON}+E_{sw,\mathit{OFF}}).\end{eqnarray}$ (2) According to this, each switching loss term, E_{sw, ON}, E_{sw, OFF}, results $\begin{eqnarray}\displaystyle E_{sw,ON}=\int _{t_{sw,ON}}v_{t}(t)i_{t}(t)dt, & & \displaystyle\end{eqnarray}$ (3) $\begin{eqnarray}\displaystyle E_{sw,\mathit{OFF}}=\int _{t_{sw,OFF}}v_{t}(t)i_{t}(t)dt, & & \displaystyle\end{eqnarray}$ (4) where t_{sw, ON}, t_{sw, OFF} are the turn-on and turn-off switching intervals, respectively. The simulated normalized loss term i.e. both the conduction, P_{on, n} = P_on∕P_o, and the switching losses, P_{sw, n} = P_sw∕P_o, normalized to the output power, P_o, have been plotted in Fig. 6a. In addition, the losses have been disaggregated depending on the stage, i.e. the rectifier and the inverter. As it can be seen, the main losses are concentrated in the inverter stage, being conduction losses the most important term. Besides, due to the resonant behavior, switching losses are minimized close to the resonant frequency, whereas they are significantly increased when the output power is decreased, i.e., higher switching frequency.

Fig. 6.

Typical power loss curve in a resonant converer for domestic induction heating (a) and power control curve (b).

Finally, it is worth noting that in a resonant inverter the output power is controlled by adapting the switching frequency (frequency control or square wave modulation, SW). Continuing with the previous analysis, decreasing the output power implies increasing the switching frequency and, consequently, incurring in additional switching losses that rapidly degrades the system efficiency. For that reason, pulsed control strategies are applied from a certain point, as it is shown in Fig. 6b.

The main conclusion from this study is that the efficiency of an induction heating appliance severely depends on the operating point and cannot be defined by a single point at maximum power. The operating point will depend on the cooking habits of the user, making very difficult to establish efficiency standards. For that reason, there is no well-established energetic labeling for induction heating appliances today. In this context, this paper proposes an efficiency figure of merit based on an application-oriented averaged efficiency parameter.

3. Averaged induction heating efficiency

In order to provide a simple and useful figure of merit for efficiency comparison, an averaged value is provided by means of the following expression, which averages the efficiency obtained at each output power i, 𝜂(P_{o, i}), by using the averaging coefficients, k_{P
_{o, i}}, as follows: $\begin{eqnarray}\bar{{\eta}}_{IH}=k_{P_{o,1}}{\eta}(P_{o,1})+k_{P_{o,2}}{\eta}(P_{o,1})+\cdots +k_{P_{o,m}}{\eta}(P_{o,m})=\mathop{\sum }_{i}k_{P_{o,i}}{\eta}(P_{o,i}),\quad \text{where }\mathop{\sum }_{i}k_{P_{o,i}}=1.\end{eqnarray}$ (5) This calculation provides a more realistic and useful information about induction heating appliance efficiency, and it is similar to the proposed for PV systems, where the EURO (European efficiency) or CEC (California Energy Commission) efficiency [16] is calculated to take into account operation at different output powers considering different levels of irradiation. For induction heating systems, a specific set of coefficient and measurement points is proposed taking into account the specific technical and usage constraints of the application.

4. Proposed averaging method

In order to calculate the averaged IH efficiency, $\bar{{\eta}}_{IH}$ , several technical and usage constraints must be taken into account. Figure 7(a) shows the typical exponential output power distribution as a function of the selected power level. It is important to note that for low output power, pulse density modulation (PDM) [17] is applied to ensure high efficiency. That level is limited by the IEC 61000 directive [18] that restricts the maximum pulsating powers as a function of the time between pulses. That level will define the first threshold to consider, typically at a 20% of maximum power.

Fig. 7.

Normalized output power, P_{o, n}, as a function of the selected level (a) and the cooking process (b).

Fig. 8.

Probability density for each cooking technique (a) and combined result (b).

In addition to this, different cooking techniques (CT) lead to different output power demands. Figure 7(b) shows the typical normalized output power, P_{o, n}, for some of the most common cooking processes: fry, boil, sauté (cooking technique with high power, fast cooking, and low fat consumption), and stew. These values are measured at thein put of the induction heating appliances, considering that efficiencies above 90% supports this simplification. Note that the time has been normalized for better graphical display. The power applied to the load actually varies due to changes in the resonant tank, e.g. different cookware, geometry, or temperature, the CT applied by the user and user preferences. Thus, the output power at each time for a given CT can be assumed to have a normal distribution, i.e., $\begin{eqnarray}{\varphi}_{{\mu}(CT,t),{\sigma}}=(1/{\sigma}\sqrt{2{\pi}})e^{-0.5\left(\frac{p-{\mu}(CT,t)}{{\sigma}}\right)^{2}},\end{eqnarray}$ (6) where p is the value of the variable, i.e. the output power, the mean, 𝜑_{𝜇(CT, t), 𝜎}, depends on the CT and the time applied, t, as represented in Fig. 7(b), and the standard deviation, 𝜎, has been considered to be 10%, and 𝜇(CT, t) is the mean power for that CT. This defines a probability density function at each time interval and, as a consequence, an averaged probability density function for each CT, 𝜑_CT, can be obtained by integrating in the whole cooking process, i.e. $\begin{eqnarray}{\varphi}_{CT}=\frac{1}{T_{CT}}\int _{0}^{T_{CT}}{\varphi}_{{\mu}(CT,t),{\sigma}}dt,\end{eqnarray}$ (7) where T_CT is the time required for each cooking technique. By performing the proposed statistic average, the probability densities for each cooking process shown in Fig. 8(a) are obtained. As it expected, processes such as frying are more likely to operate at higher output power whereas stewing requires operating in the low output power range. For this study, the probability to use each CT in a typical European home is applied, i.e. P_FRY = 35%, P_BOIL = 20%, P_SAUTÉ = 20%, P_STEW = 25%. As a consequence, the combined probability density $\bar{{\varphi}}$ shown in Fig. 8(a) is obtained as $\begin{eqnarray}\bar{{\varphi}}=\mathop{\sum }_{CT}P_{CT}{\varphi}_{CT}.\end{eqnarray}$ (8)

Finally, once that a combined probability density is obtained, the last step is to divide it in regions so an easy-to-use averaged induction heating efficiency expression is obtained. Figure 8(b) shows the proposed division into 4 regions. R₁ covers the PDM region which implies constant efficiency. R₂ and R₃ covers the low and medium power areas, respectively, including one peak in probability density in each region. Finally, R₄ covers the maximum output power region. In order to calculate each coefficient k_{P
_{o, i}} of expression (5), the combined probability density function, $\bar{{\varphi}}$ , is integrated, obtaining: $\begin{eqnarray}k_{P_{o},i}=\int _{R_{i}}\bar{{\varphi}}dP_{o,n}.\end{eqnarray}$ (9) By applying these expressions, the following average induction heating efficiency expression is obtained: $\begin{eqnarray}\bar{{\eta}}_{IH}=0.1{\eta}(P_{o,n}=20\%)+0.3{\eta}(P_{o,n}=30\%)+0.4{\eta}(P_{o,n}=70\%)+0.2{\eta}(P_{o,n}=100\%).\end{eqnarray}$ (10)

This expression offers an easy to calculate mean efficiency that takes into account real usage of domestic induction heating appliances. By applying this expression, the complex efficiency curves of resonant converters, which depend highly on the operating point, can be translated into a single parameter that can be used for comparing the performance of different systems. This can be used to set improved efficiency performance to improve economic and environmental impact of induction heating cooking appliances.

5. Discussion and future trends

The proposed 𝜂_IH is a figure of merit that allows a fair comparison of power converter efficiency under realistic operating conditions. It is clearly shown that peak efficiency importance is reduced whereas efficiency at low-medium output powers play a key role. In order to evaluate the importance of this expression, the efficiency of power converters proposed in the last years has been evaluated and summarized in Table 1, where it is compared with the maximum efficiency, 𝜂. These results are obtained from the experimental data provided in the references, which include efficiency curves at different power levels.

Table 1
Efficiency comparison

Topology/Modulation $\hat{{\eta}}$ (%) $\bar{{\eta}}_{\mathit{IH}}$ (%) Δ𝜂 (%)

Half-bridge/SW [17] 95.0 94.2 0.9

Half-bridge/ADC [30] 96.0 95.8 0.2

Half-bridge/PWM+PDM [31] 94.5 93.9 0.6

Class D-DE half-bridge/SW [32] 95.3 95.2 0.1

Multi-MOSFET half-bridge /SW [33] 98.3 98.1 0.2

Direct ac-ac boost/ADC [34] 99.0 98.8 0.3

Direct ac-ac full ZCS/HF-PDM [35] 97.2 97.0 0.2

Direct ac-ac class-E/P1N0 [36] 95.0 94.1 0.9

Direct ac-ac class-E/P1N0+P1N1 [36] 96.1 95.9 0.2

Series resonant multiinverter/SW [37] 95.8 93.5 2.4

Series resonant multiinverter/HF-PDM [38] 97.8 95.4 2.4

Twin half-bridge/HF-R [39] 96.5 92.6 4.1

Full-bridge/AVC [40] 96.0 94.2 1.9

Full-bridge/AVCo [41] 96.0 95.4 0.6

PFC+Half-bridge/CCM+DCM [42] 94.5 93.2 1.3

Topology/Modulation	$\hat{{\eta}}$ (%)	$\bar{{\eta}}_{\mathit{IH}}$ (%)	Δ𝜂 (%)
Half-bridge/SW [17]	95.0	94.2	0.9
Half-bridge/ADC [30]	96.0	95.8	0.2
Half-bridge/PWM+PDM [31]	94.5	93.9	0.6
Class D-DE half-bridge/SW [32]	95.3	95.2	0.1
Multi-MOSFET half-bridge /SW [33]	98.3	98.1	0.2
Direct ac-ac boost/ADC [34]	99.0	98.8	0.3
Direct ac-ac full ZCS/HF-PDM [35]	97.2	97.0	0.2
Direct ac-ac class-E/P1N0 [36]	95.0	94.1	0.9
Direct ac-ac class-E/P1N0+P1N1 [36]	96.1	95.9	0.2
Series resonant multiinverter/SW [37]	95.8	93.5	2.4
Series resonant multiinverter/HF-PDM [38]	97.8	95.4	2.4
Twin half-bridge/HF-R [39]	96.5	92.6	4.1
Full-bridge/AVC [40]	96.0	94.2	1.9
Full-bridge/AVCo [41]	96.0	95.4	0.6
PFC+Half-bridge/CCM+DCM [42]	94.5	93.2	1.3

From this table, it is clear that there are significant differences between the values obtained with different topologies due to the effects of real-world usage. Moreover, it is clear that the efficiency cannot be measure at a single point (typically resonant frequency at maximum efficiency), since it will provide unfair values that may lead to technical design decision far from the optimum value to achieve economic and environmental objectives.

Future design trends will make this analysis even more necessary. The use of advanced topologies and wide bandgap semiconductors [19–21] will bring new levels of efficiency and scenarios where switching losses will become less important, enabling new design alternatives for efficiency and control strategies. Also, versatile induction heating appliances, including all-metal implementations [22,23] and multi-load systems [24–26], will define new user experiences with important efficiency implications that must be taken into account when defining energetic labeling. Even more important are the current efforts to combine induction heating with under worktop implementations and inductive power transfer functions [27] under the Ki standard (Ki is a standard for wirelessly delivering up to 2200 watts of power to smart cordless appliances), that will result in completely new usage scenarios. Finally, the use of artificial intelligence (AI) for advanced IH-load detection and power converter control [28,29] will open new area of performance and efficiency optimization.

6. Conclusions

Efficiency is a key figure of merit of induction heating appliances due to its major performance and socio-economic impact. In order to obtain a more accurate comparison parameter under realistic operating conditions, the averaged induction heating efficiency has been defined. The proposed averaging method based on both technical and usage constraints has been explained, and a final expression has been given. This proposed expression has been evaluated for 15 power converters and modulation strategies previously reported, proving the usefulness of this proposal.

Footnotes

Acknowledgement

This work was partly supported by Projects PID2019-103939RB-I00, PDC2021-120898-I00, TED2021-129274B-I00, CPP2021-008938 and ISCIII PI21/00440, co-funded by MCIN/AEI/10.13039/501100011033 and by EU through FEDER and NextGenerationEU/PRTR programs, by the DGA-FSE. This work was partly supported by BSH Home Appliances.

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