Overview of key performance features.
This chapter compares various compensation methods for resonant coupling of the wireless energy transfer system. A proposed analysis is particularly relevant to any application where contactless battery charging is used. Main parameters that are investigated include efficiency and electrical variables (current and voltage) of the circuit. In order to analyze the most suitable solution of coupling compensation, the relevant equations are graphically interpreted for each discussed circuit topology. Finally, this chapter provides the recommendations how to design the wireless power-transfer system with the highest possible efficiency for the given system parameters (switching frequency and transmitting distance).
- wireless power transfer
- resonant compensation
Nowadays, electrically powered automobiles show higher interest in the automotive industry. Electric vehicles gain this interest thanks to high efficiency. In the case of the asynchronous motor, the electrical energy can be converted into the mechanical with an efficiency of 90%, which is much more than the efficiency of the combustion engine that has an efficiency of only 25‒34%. Due to the limitation of natural resources such as petroleum and natural gas, the power electronics and energy conversion along with the development of new battery types contribute to the development and application in the automotive industry. The main disadvantage of the electric car is the energy accumulation. Batteries are large, heavy, with short lifetime, and long charging times. These reasons show how necessary it is to solve an issue of battery charging . In general, charging systems can be classified as wired and these could be replaced with wireless (inductive) systems.
Wireless power transfer and issues relevant to wireless charging of various types of electronic devices are still important and emerging trends in electrical engineering [2‒4]. Regarding of wireless power transfer, each application requires several self-specific operational properties or transfer characteristics. The most important of them are transmitting efficiency, value of the output power, mutual position between the transmitter and the receiver, and their geometric dimensions. One possible way how to influence these parameters lies in the main circuit configuration of a compensation network of the wireless energy transfer (WET) system. Inductively coupled power-transfer systems have been suited for a wide spectrum of consumer applications including electromobility (battery charging of vehicles). Even high system efficiency has been achieved (approximately 70%); however, the restriction to close range, typically shorter than 30% of the coil diameter, is the main limitation for perspective usage in high-efficiency or high-performance systems [5, 6].
It the beginning of 2000s, a team of researchers under charge of Prof. Soljacic introduced a new concept of strongly coupled magnetic resonance for wireless energy transfer systems . In comparison with an inductively coupled system, the coils with resonant inductive coupling have several significant advantages. The most important of them are as follows: the coupling may be very efficient even at large transmission distances, it has low environmental impact, and can be variously tuned/configured based on the requirements of target application. The solution of the WET system based on the magnetic-resonance coupling represents constantly investigated phenomena. Most of the analyses are based on the pure theory of physical interactions, which are unable to provide clear and consistent overview of knowledge for researchers in the field of electrical engineering [8, 9]. Based on this, it can be said that some important relationships between system efficiency, amount of transmitted power, and transmitting distance for magnetic-resonance coupled WET systems need to be introduced.
This chapter describes a simple equivalent circuit model for magnetic-coupled and resonant magnetic-coupled WET systems. The resonant coupling is further described in details, whereby all key system equations for various configurations of a resonant compensation network with pure resistive load are derived. From the component design point of view, it is also important to have knowledge about values of voltage and current in the main circuit. In the last part of the chapter, the general recommendations for practical use of each variant are provided.
2. Nonresonant magnetic coupling of the WET system
In the case of nonresonant magnetic coupling, the system acts as an air-cored transformer with relatively low mutual inductance. Due to high supplying frequency, the primary and the secondary leakage reactance cause a significant voltage drop, which limits amount of power delivered to the load. Equivalent circuit composed for this type of coupling is shown in Figure 1.
The circuit can be completely described by the system of loop currents calculated by Eq. (1):
On the other hand, the uncompensated leakage reactance forms in the circuit with a very high impedance even for a lower frequency component. This impedance causes a significant voltage drop and therefore the contribution of this harmonic component is very low. The system can be therefore analyzed only for the fundamental wave while keeping relatively good accuracy. The winding currents derived for the fundamental wave are provided in Eqs. (3) and (4):
The input power can be counted from the complex power on the primary side (5):
The secondary side average power is then found using the loading resistance and the current flowing through it (Eq. (6)):
The simulation parameters are taken from two constructed experimental prototypes of coupling coils, which are also identical. Their values are therefore the same on the primary as well as on the secondary side. The self-inductance equals
The results from simulation of the inductively coupled WET system plotted against frequency and mutual inductance are shown in Figures 2–4. The waveforms of the input and output powers are shown in Figure 2, the source and load current are shown in Figure 3, and the efficiency calculated using Eq. (7) together with a secondary induced voltage
As it can be seen from Figure 4 (right), the transmitting efficiency mainly varies with given mutual inductance. The system is practically independent of frequency change even for the whole considered frequency range.
3. Series–series resonant coupling of the WET system
For series–series compensation, the capacitor is connected in series with transmitting and receiving coils (Figure 5).
Mathematical model of series–series compensation is, from the point of view of complexity, much easier than other compensation types. Using the methodology of loop currents, the impedance matrix of this configuration can be expressed as follows (11):
If the circuit is supplied by harmonic voltage with a frequency equal to the resonant frequency, then the value of the capacitive and inductive parts of the complex impedance will be the same and can be subtracted. Then, for the previous formulas (14) and (15), the following conditions are valid:
Equations (14) and (15) show that the circuit during resonance has only resistive characteristics, and circuit currents are given just by the parasitic resistances of coils, load resistance, and supply voltage. The input and output powers of the circuit with –series‒series compensation can be expressed as Eqs. (16) and (17). The graphical interpretation of Eq. (17), as plotted in Figure 6, shows that the operation of the system with this kind of compensation should be excluded from resonant point. In other case, for low values of
Dependence of efficiency for the series‒series compensated circuit in the frequency domain can be expressed using Eq. (18):
The highest efficiency can be achieved at the resonant frequency. Its value is above 90% when higher values of mutual inductance are considered. The main disadvantage of high efficiency achievement is that for a given value of
At such frequency, with value depending on the value of mutual inductance (distance between the transmitting and receiving coils), it is possible to achieve a quite high value of the system efficiency together with peak power transfer. For example, when the system has
From the practical point of view, during the design process of the system, it is necessary to know the voltage waveform at compensation capacitors because these components are the most critical. Figures 8 and 9 show voltage dependency for each system component. It can be seen that even for a very low value of the supply voltage (in this case 30 V), the peak voltage at each component multiplies several times. Situation is most critical when the system operates at resonant frequency and also when a low value of mutual inductance is presented. If the input voltage rises, then naturally each particular voltage rises correspondingly too. The selection of the proper capacitor structure and configuration therefore means the most difficult issue. Thus, the previous recommendation for system operation at border resonant frequencies (19) also gives advantages from the system component design point of view. The same is valid for the wire selection of the transmitting and receiving coils, when the source and load current show similar dependency, as the previous circuit variables (Figure 10).
4. Series–parallel resonant coupling of the WET system
Series‒parallel compensation means that one capacitor is connected in series to the transmitting coil and the other one is connected in parallel to the receiving coil, see Figure 11.
Using the method of loop currents, the impedance matrix of series–parallel compensated circuit can be expressed as follows (24):
If we substitute
Compared with the series‒series compensation, in this case the reactance of capacitor
The graphical interpretations of the mentioned variables are introduced depending on frequency as well as
On the other hand, the poor efficiency is the highest disadvantage. Let now consider a different situation, when
Efficiency also depends on the change of the load value. For series‒parallel compensation, the higher efficiency can be achieved at higher values of load resistance (reduction of delivered power). Figure 14 (right) shows dependency of system efficiency on series‒parallel compensation at constant
Voltage on capacitor
Voltage on capacitor
Frequency dependencies of circuit currents are shown in Figures 17 and 18. It can be seen (Figure 17, left) that
Figures 17 (right) and 18 show the current of the receiving coil
5. Parallel–series resonant coupling of the WET system
Equivalent circuit for parallel‒series compensation is shown in Figure 19. Capacitor
The graphical interpretation of Eq. (37) is shown in Figure 20. It shows that any frequency deviation from the resonant state reduces the power delivered to the load. However, in this case the system is less sensitive to frequency change as compared to the series‒parallel compensation.
The power delivery to the load for this type of compensation and for the selected operational variables (load, mutual inductance, etc.) is, when compared to the previous types, very poor. Efficiency dependency (Figure 21) is comparable to series‒parallel compensation, whereby the higher the value of the mutual inductance is, the higher efficiency can be achieved. Similarly, as for series‒parallel compensation it is expected that the parallel‒series compensation type is more valuable for higher values of mutual inductances, and thus for applications, where distance is not the primary attribution of the WET system.
6. Parallel–parallel resonant coupling of the WET system
Equivalent circuit of the system is shown in Figure 23. Both compensation capacitors are connected in parallel to the transmitting and receiving coils. Unlike the previous topologies, this model forms the system of four linear equations with four unknown parameters (26):
After substitution , , and , the most important circuit variables can be obtained as follows:
Regarding of the system performance, it is similar to characteristics found for nonresonant magnetic coupling. Thus, this type of compensation is not suitable for applications where simultaneously high power with high efficiency is required to transmit power on large distances.
Based on the study, a table (Table 1) of key operating features for the discussed compensation topologies is composed. Table 1 only covers the system behavior at chosen frequency and distance range while considering constant supply voltage and low value of loading resistance.
In Table 1, attribute “
According to Table 1, the noncompensated system and the system with parallel‒parallel compensation are both inappropriate for any type of wireless charger working at large distance and higher level of transmitting energy. On the other hand, they achieve maximum efficiency precisely at the moment they deliver maximum power. Hence, they should be used for low-cost micropower battery chargers which moreover require no frequency tuning.
In contrast to other topologies, the series‒series compensation provides relatively high power even through a very large working air gap, but the efficiency reaches its peak only at off-resonant frequencies. The system should be therefore operated at compromise between useable energy and the transmitting efficiency. Despite this fact, the system is suitable for high-power chargers for electric vehicles.
The series‒parallel compensation forms more disadvantages than advantages and therefore cannot be recommended for any battery charger. With respect to all evaluated categories, the parallel‒series compensation provides the best performance, but from power delivering point of view, this solution is much worse. However, it could be recommended for high-end frequency tuned micropower battery chargers.
The authors wish to thank the Slovak grant agency VEGA for Project No. 0579/14 Research of topological structures of segments of power electronic system for wireless energy transfer.
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