## 4 Power Electronics Converter and Power Control  
The developed and tested inductive charging infrastructure contains four successively placed primary coils. Only one transmitting coil is used in static charging tests and four coils in dynamic tests. The power electronics circuit contains full bridge AI with ED and four electronic switches--Figure 7. Each electronic switch has only one transistor (\(VT_{11}\)-\(VT_{13}\); \(VT_{21}\)-\(VT_{23}\); \(VT_{31}\)-\(VT_{33}\); \(VT_{41}\)-\(VT_{43}\)) and one series capacitor (\(C_{11}\)-\(C_{13}\); \(C_{21}\)-\(C_{23}\); \(C_{31}\)-\(C_{33}\); \(C_{41}\)-\(C_{43}\)). This capacitor is part of the matching circuit of the transmitting coil. Every capacitor from the electronic switches is charged up to \(U_{MAX}\) by reverse diode of the transistor, when the transistor is switched off. Later, when the transistor is switched on, a corresponding capacitor will be added to the AC circuit by the transistor and its reverse diode [8]. When changing any of the IPT parameters (depending on the current coil's position) or battery (in charge), the optimal matching and consequently the value of the output power and efficiency are disrupting. An essential point here is the type of matching circuit and output characteristics of the used AI with ED. For most of the ideas, schemes, design, and mathematical interpretation of electromagnetic processes, there are different author claims. Figure 7: Proposed autonomous inverter with energy dosing (AI with ED) and dynamic matching circuit. Figure 8 presents the time charts characterizing the operation of the AI with ED. There are two intervals --(0:\(\div\varphi_{d}\)) of energy consumption from the DC power supply through capacitors \(C_{d1\text{-}3}\), and (\(\varphi\div\pi_{d}\)-\(t_{0}\)) of the short-circuit of the AC circuit over one of the supply lines (positive or negative). Maintenance of constant\(\varphi\) power in the inverter is due to the fact that the energy of the power supply is always consumed through the dosing capacitor. The voltage over the capacitor \(C_{d}\) is fixed up to the value of the DC supply voltage (\(E\)) through diodes \(V_{D6}\) and \(V_{D7}\). Then, the power P, transmitted by the power supply, through IPT to the EV, is equal to  
\[P=4E^{2}fC_{d}=EI_{in}=U_{out}I_{out}=const \tag{23}\]  
i.e., when the operating frequency \(f\), the supply voltage \(E\) and the value of the dosing capacitor are constant, the power given to the load does not depend on its parameters. This internal automatism makes AI with ED very flexible as a source of HF energy in charging stations and is a prerequisite for the successful solution of many problems in matching its output parameters with the battery. Basic analytical dependences of AI with ED have been derived on the grounds of the relationships from the harmonic analysis and the postulates of the general theory of autonomous inverters [18]. The design methods with parallel and series tank circuit have the following sequence:  
1. The pause between control pulses \(t_{0}\) is assigned, e.g., \(t_{0}=0.1\pi\) (Figure 8). 2. Ratio \(\omega_{po}/\omega=1.2-1.4\) value is determined (\(\omega_{po}\) is the natural frequency of the AC equivalent circuit, and \(\omega\) is the control frequency). 3. Phase angle \(\delta\)between AC output voltage and current is determined by \[\delta>(1.2\div 1.4)\omega_{po}/\omega.\]
4. Calculation of the quality factor of the series equivalent circuit is done by \[Q=\omega L_{E}/R_{E}=1/2\Big{(}\omega/\omega_{po}\Big{)}^{2}\Bigg{[}tg\delta +\sqrt{tg^{2}\delta-\Big{(}\omega/\omega_{po}\Big{)}^{2}}\Bigg{]}\] (24)
5. The dosing capacitor is calculated having in mind the power and frequency assigned. \[C_{d}=P/\Big{(}4E^{2}f\Big{)} \tag{25}\]  
Figure 8: Basic time charts of AI with ED at 35 kW output power and battery as a load: the current in inverter AC diagonal; the voltage of the dosing capacitor Cd; the voltage of the transmitting coil.