**4. Investigation and Comparison of the Characteristics and Converters with and without Energy Dosing Used in the Fast Charging Stations of Electric Vehicles**

Based on the analytical expressions obtained in the analysis of the studied scheme (Figure 1), its characteristics were obtained. For greater objectivity of the formulated conclusions, the characteristics of RI with ED without reverse diodes (RD) of power transistors (PT) and two other competing schemes that are often used in charging stations as high-frequency sources [20–22,26–29]: a half-bridge RI with RD and a full-bridge parallel current fed inverter (PCFI). The use of the same input data for the indicated schemes allows for objective comparisons and definitions of their advantages and disadvantages. In Tables 1–3 and the numerical values from the research are presented, as in the column "Type", the conditions under which the results are obtained are given. In these studies, emphasis was placed on the behavior of the circuits when changing the equivalent load parameters, which was achieved by varying the air gap of the contactless transmitter and/or the load resistance. Specifically for each scheme, they were the following:


The main conclusions that can be drawn were about the reliable operation of the RI with ED, which for these modes, was determined by the conditions for the switching PT. The most favorable were those in which the current and/or voltage were zero (ZCS, ZVS, ZCSZVS). Depending on the equivalent parameters of the AC circuit, the converters operated in one of three modes. If the switching mode at zero current was conditionally accepted as nominal (basic) due to the change of the load or the operating frequency, different changes in the values of the main electrical and phase ratios were observed.


**Table 1.** Characteristics of the RI with ED.


**Table 2.** Characteristics of the RI with an RD.

**Table 3.** Characteristics of the PCFI.


The other conclusions were as follows:

(1) As the load parameters (R) decreased, the load circuit and the equivalent AC circuit gained an inductive misalignment. For this reason, the frequency of the RI's own oscillations decreased. The current of the PT, when it was switched off by the control pulses, was different from zero, and this created conditions for switching on the reverse diode of the inoperative transistor. The described phenomenon is the reason for the partial reduction of the RI power, as the second recharging of the resonant capacitors in the considered half-period began. As the operating frequency increased, the power could be set equal to the nominal one, and at the same time, the effect of reducing the switching current of the PT-*IOFF* was obtained. When the resonance in the load oscillating circuit was reached again, both currents *IOFF* and *ION* became equal to zero. Such a favorable development of the processes was observed when reducing the load parameters to 25–30%. With an even greater reduction in the load, for example, by 50% to achieve *ION = IOFF =* 0, it was necessary to increase the frequency, which led to an increase in power by 30% above the nominal value (Table 1).

(2) When the inverter was unloaded (R increased), the load oscillating circuit was capacitively disrupted. The frequency of the inverter's natural oscillations increased and the current of the PT naturally became equal to zero before the termination of the control pulse. For this reason, conditions were created for the occurrence of a mode with a natural shutdown of the PT until the power drops, as noted above. By reducing the operating frequency until the resonance in the load oscillating circuit was restored, the ZCS mode could be re-established (*ION = IOFF =* 0), but the power, although insignificant, was reduced (by 5–10%) in accordance with Equation (19).

From the point of view of the operational characteristics and reliability of RI with ED, it is important that in all operating modes, it is not possible to exceed the set power determined by Equation (19). In practice, energy dosing protects the PT from overload and ensures the natural adaptation and self-alignment of the RI to the load. This, in turn, determines a major positive quality of an RI with ED that is not possessed by a traditional RI.

In the case of similar changes in the load, the circuit of the RI with ED without an RD of the PT always worked with the nominal power without the need to change the operating frequency. The technical applicability of this circuit variant was determined mainly by the voltage on the PT, which was obviously greater than that in the RI with ED and the OD of the PT.

Another important result of the presented characteristics should be noted, which was that switching the PT currents on and off in both cases (when increasing and decreasing R) could be maintained equal to zero if the operating frequency changes in one direction or another until resonance was obtained in the load circle (Table 1). The fact that the most favorable modes in terms of power and currents of switching on and switching off of the PT were obtained by the resonance of the load circuit, facilitates the synthesis of control of the power electronic converter.

The second group of conclusions was about the qualities of the other two schemes and their comparisons with the RI with ED: (1) In the half-bridge RI with RD, with the change of the load parameters, the power changed more strongly (Table 2), and to return to the nominal value, it was necessary to regulate the frequency more deeply, which significantly increased the voltage on the resonant capacitors *UCRm* and currents on and off (i.e., the PT-*ION* and *IOFF*). Generally speaking, this scheme could not cover a range of variation of the load parameters greater than 15–20% while maintaining a favorable operating mode of the PT. (2) In the full-bridge PCFI, there was an even stronger change in power and the need for deeper regulation of the frequency for its stabilization (Table 3). As R increased, the voltage of the oscillating circuit *UCm* increased and, accordingly, the forward and reverse voltages of the semiconductor devices increased. In some of the modes, the circuit time for PT recovery disappeared. Based on the presented results, it was concluded that both alternative RIs had significantly less coordination (regulatory) capabilities than the RI with ED.

A visual comparison is shown in Figure 6, where the characteristics of the output power changing for the load parameter variations for the full-bridge-current-fed inverter (curve 1), half-bridge RI (curve 2), RI with ED and reverse diodes (curve 3) and RI with ED without reverse diodes (curve 4).

**Figure 6.** Comparison of the output characteristics P/PN = f(R/RN) of the full-bridge-current-fed inverter (1), half-bridge RI (2), RI with ED and reverse diodes (3) and RI with ED without reverse diodes (4).

An important point here is that the last two characteristics (curves 3 and 4 in Figure 6) guaranteed practical adaptively of the inverter to the load and its changes, due to which, it could also operate without regulation when the load changes within the limits stated above, i.e., from 0.5 to 1.5 times relative to the nominal value. This contributes to a significant

improvement in the technical and operational qualities of the high-frequency source and provides the opportunity to work with a wide range of loads, which is typical for contactless charging stations for motorcycles and electric vehicles. Based on these characteristics, it was concluded that energy dosing schemes are advantageous over other types of resonant converters.

On the other hand, according to the characteristics of Figure 6 for the most frequently used topologies based on resonant inverters with reverse diodes (most often LLC), the conclusions made in [30–32] regarding the need to use optimal control in order to realize the charging cycles were confirmed.
