Innovative Bidirectional Isolated High-Power Density On-Board Charge for Vehicle-to-Grid

This paper deals with developing and implementing a bidirectional galvanically isolated on-board charger of a high-power density. The power density of the new charger was 4 kW/kg and 2.46 kW/dm3, and the maximum efficiency was 96.4% at 3.4 kW. Due to the requirement to achieve a high-power density, a single-stage inverter topology was used. Regarding switching losses, due to the topology of the circuit with so-called hard switching, the switching frequency was set to 150 kHz. A laboratory prototype was built to verify the properties and operating principles of the described charger topology. The on-board charger has been tested in a microgrid test platform. Due to the parasitic properties of the transformer and other electronic components, overvoltage with subsequent oscillations occurred on the primary side of the transformer and damped resonance on its secondary side. These parasitic properties caused interference and especially voltage stress on the semiconductor elements. These undesirable phenomena have been eliminated by adding an active element to the charger topology and a new transistor control strategy. This new switching control strategy of transistors has been patented.


Introduction
Electromobility has become a growing global phenomenon. Not only it has the potential to contribute to the reduction of CO 2 emissions and improve the environment, especially in large urban agglomerations [1], but it may also provide a solution to the problem of limited fossil fuel reserves. The advances in electromobility concern both passenger cars as well as public transport (electric buses and trolleybuses with battery backup). However, these developments are also accompanied by problematic power engineering and operational character aspects. For the smooth incorporation of electric vehicles, it is necessary to ensure that there is enough electricity and sufficient transmission capacity in the power grid to charge electric vehicles (EVs) when needed or to optimise the charging mode of a significant proportion of EVs so that the electricity sources and distribution grids are able to cover the demand [2].
The battery charging time is significantly longer than the refuelling time of a conventional car [3]. Charging times range from tens of minutes to tens of hours, depending on the specific vehicle type, the battery itself and the charging station [4]. Fast charging is limited, among other things, by the need for high power consumption from the grid and the capacity of the distribution grid at a particular place and time. This problem is solved, for example, by including a battery in the charging station to cover significant power • A description of the implementation of the first prototype and its problems related to the circuit topology and parasitic properties of the elements encountered and their solutions not reported in the literature; • Describe the elimination of voltage spikes using passive disconnectors (RCDs) proved inappropriate due to the significant power losses; • The introduction of an innovative approach that eliminates voltage spikes based on the use of an applied active clamp in this situation; • Proposed and described a switching control method that eliminates unwanted HF oscillations on both the primary and secondary sides of the transformer in the on-board charger; • Description of the development, implementation and testing of a bidirectional charger with galvanic isolation, whose parameters were 4 kW/kg and 2.46 kW/dm 3 and the maximum power of the charger is 7.2 kW, which uses a switching frequency of 150 kHz.
For comparison, comparable power converters reported in the literature achieve power density of 0.65 kW/dm 3 [35], 1.875 kW/dm 3 [36] (gravimetric densities are not specified), 2 kW/dm 3 with 1.2 kW/kg [37] and 2.44 kW/dm 3 (gravimetric density is not specified) [38].  This paper is organised as follows. Section 2 deals with the characteristics of the first charger prototype. The relationships for the design of the storage choke are also derived. Section 3 focuses on solving the overvoltage and oscillation problems in the prototype. Relations for calculating the value of the surge eliminating capacitor are given, including Figure 1. Bidirectional single-stage charger topology [33,39]. This paper is organised as follows. Section 2 deals with the characteristics of the first charger prototype. The relationships for the design of the storage choke are also derived. Section 3 focuses on solving the overvoltage and oscillation problems in the prototype. Relations for calculating the value of the surge eliminating capacitor are given, including the timing of its switching. The simulations were used to check the correctness of the proposed solution set-up. The logic signal waveforms for charging and discharging modes are shown. Section 4 describes the second prototype of the bidirectional charger, including the surge and oscillation suppression circuit. Section 5 described the platform where the on-board charge was laboratory tested. Finally, Section 6 describes the measurements on the second prototype, including the measurement results.

Verification of Selected Topology of Bidirectional Charger
When we compare the characteristics of the different topologies of inverters suitable for implementing on-board bidirectional chargers for electric vehicles, the best option seems to be the topology, as shown in Figure 1 [33,39].

Calculation of Accumulating Inductor Inductance
To derive inductance of accumulating inductor, Figures 1 and 2 are considered. The primary purpose of the inductor is to accumulate energy in charging mode, where together with bridge Q 5 to Q 8 it forms the so-called boost converter. The switching frequency of transistors Q 5 to Q 8 is many times higher than mains frequency. For this reason, the voltage u d might be considered constant during a single switching period of these transistors.  In time interval ton the energy is accumulated in inductor L. Voltage ud is applied to it and inductor current starts to rise. In time toff, inductor supplies energy into the battery through the transformer and its current starts to decrease. In time toff the inductor voltage is equal to the battery voltage multiplied by transformer ratio k and reduced by voltage ud. The inductor shall be designed so that its current ripple is below the limit. The following equations apply: where k = 1.33 is the transformer ratio. Error! Reference source not found. implies the equation for the inductor current period: 1 In time interval t on the energy is accumulated in inductor L. Voltage u d is applied to it and inductor current starts to rise. In time t off , inductor supplies energy into the battery through the transformer and its current starts to decrease. In time t off the inductor voltage is equal to the battery voltage multiplied by transformer ratio k and reduced by voltage u d . The inductor shall be designed so that its current ripple is below the limit. The following equations apply: where k = 1.33 is the transformer ratio. Figure 2 implies the equation for the inductor current period: Combining (1), (2) and (3), the equations below are derived: Combining (1), (3) and (6), the equation below is derived: Equation (7) can be used to derive the equation for inductance: The switching frequency of the charger is 150 kHz. For a ripple current of 10 A, a choke inductance of 45 µH was calculated according to Equation (8). Due to the fact that at this inductance value, the inductor's core was oversaturated, a value of 25 µH was finally chosen experimentally. For this inductance, its ripple current reaches up to 20 A.

Experimental Results Measured on the First Prototype of Bidirectional Charger
To verify the selected topology of the charger and its proposed control principles, a laboratory prototype was built.
The prototype was assembled from three separate printed circuit boards: control, driver and power. The control board contains:  The waveforms in Figure 4 show transient phenomena in the circuit during two switching periods. After the switch-off of the first transistor pair Q 5 , Q 8 , the voltage starts to rise ( Figure 4, point 1) on the primary side of the transformer and at the same time also, its current starts to rise. Transformer TR (see Figure 1) is not able to immediately pass the inductor L current due to its leakage inductance. This causes overvoltage followed by oscillations ( Figure 4, point 2). The energy transfer through the transformer ends when all transistors Q 5 to Q 8 have switched on again.  After the primary voltage of the transformer decreases to zero volts, a decrease in its secondary side voltage follows. A steep decrease in the secondary voltage induces dumped oscillations due to parasitic circuit properties ( Figure 4, point 3). Overvoltage and oscillations are not only the source of EMI noise but cause voltage to overstress to power transistors, which could lead to their destruction. For this reason, we had to find a solution to eliminate the oscillations and reduce the overvoltage.

Selected Topology Troubleshooting
In Figure 5 there is a principal scheme of the bidirectional charger, to which relate all the following descriptions of logic signals of transistor Q1 to Q13 and all experimental measurements. After the primary voltage of the transformer decreases to zero volts, a decrease in its secondary side voltage follows. A steep decrease in the secondary voltage induces dumped oscillations due to parasitic circuit properties ( Figure 4, point 3). Overvoltage and oscillations are not only the source of EMI noise but cause voltage to overstress to power transistors, which could lead to their destruction. For this reason, we had to find a solution to eliminate the oscillations and reduce the overvoltage.

Selected Topology Troubleshooting
In Figure 5 there is a principal scheme of the bidirectional charger, to which relate all the following descriptions of logic signals of transistor Q 1 to Q 13 and all experimental measurements.
After the primary voltage of the transformer decreases to zero volts, a decrease in its secondary side voltage follows. A steep decrease in the secondary voltage induces dumped oscillations due to parasitic circuit properties ( Figure 4, point 3). Overvoltage and oscillations are not only the source of EMI noise but cause voltage to overstress to power transistors, which could lead to their destruction. For this reason, we had to find a solution to eliminate the oscillations and reduce the overvoltage.

Selected Topology Troubleshooting
In Figure 5 there is a principal scheme of the bidirectional charger, to which relate all the following descriptions of logic signals of transistor Q1 to Q13 and all experimental measurements.   As was already described in Section 2, using the bidirectional topology charger from The first problem with voltage u p overshoots was successfully solved by implementing an active circuit element marked "D" in Figure 5 and its exact timing. This active element consists of series connection of transistor Q 13 with capacitor C 13 . Transistor Q 13 switches in the capacitor C 13 at exactly defined time period.
The second problem with damped resonance of parasitic circuit elements on the secondary side of the transformer was eliminated by a different control technique of transistors Q 9 to Q 13 (different to the control shown in Figure 2).

Root Cause Description of Overvoltage on the Primary Side of Transformer and Solution
When the transistor pair Q 5 , Q 8 or Q 6 , Q 8 is switched off, inductor L acts as a source of constant current. In the ideal case, this current would start to flow through the primary winding of transformer, but its leakage inductance prevents that. In case the active element "D" (see Figure 5) is missing, the current will not have a path to flow, and voltage will rise between nodes a and b. This would lead to severe overvoltage.
The moment of switching off the transistor pair Q 5 , Q 8 or Q 6 , Q 7 could be described based on Figure 6, which represents circuit schemes in simulation software Microcap, which was used to verify the circuit behaviour. of constant current. In the ideal case, this current would start to flow through the primary winding of transformer, but its leakage inductance prevents that. In case the active element "D" (see Figure 5) is missing, the current will not have a path to flow, and voltage will rise between nodes a and b. This would lead to severe overvoltage.
The moment of switching off the transistor pair Q5, Q8 or Q6, Q7 could be described based on Figure 6, which represents circuit schemes in simulation software Microcap, which was used to verify the circuit behaviour. Capacitor C13 and leakage inductance Lsigma together form a resonant circuit. Its resonant frequency is given by (9).
During the transient, the energy accumulated in inductance Lsigma is: At the moment of switching off transistor pair Q 5 , Q 8 (Q 6 , Q 7 ), the transistor Q 13 is also switched off. See Figure 2, time t 0 (t 0 + 1 /2T). The inductor current i L flows immediately through internal body diode D13. For the purpose of simplification, its magnitude could be considered constant over the duration of transient. At the same time, the current through leakage inductance L sigma starts to rise. In time t 1 (t 1 + 1 /2T) transistor Q 13 turns on.
Capacitor C 13 and leakage inductance L sigma together form a resonant circuit. Its resonant frequency is given by (9).
During the transient, the energy accumulated in inductance L sigma is: The same amount of energy accumulates in the capacitor C 13 , which is based on the general knowledge about the behaviour of resonant LC circuits: Let us assume that in t 0 the capacitor C 13 is charged to voltage k·u BAT from the previous period, where k is transformer ratio. The following equation is obtained using (10) and (11): Neglecting the voltage drop across the body diode D 13 and transistor Q 13 (see Figure 5), Equation u C13max = u abmax applies. If the maximum u abmax voltage is specified (for example based on breakdown voltage of semiconductors), required C 13 capacity can be calculated as: For the capacitor C 13 to remain charged to a voltage of magnitude k·u BAT during the end of the transient effect, exactly one-half period of resonant effect needs to occur. In time t 0, charging of capacitor occurs through diode D 13 . Discharging occurs through transistor Q 13 , which needs to be turned off at specific time. The total time of current conduction through the capacitor must be half of the period of the resonant frequency. Time t Q13 cannot be longer than the switch-off duration of one of the transistor pairs from bridge "B", further reduced by safety margin time t delay , which corresponds to ( 1 /2T − t ov − t delay ). In that case, the time t Q13 is shorter compared to (14): For time interval when t ov < ( 1 /2T − t delay ), (14) applies. For time interval when t ov ≥ ( 1 /2T − t delay ), (15) applies. It is desirable to design the capacitance of C 13 so that there is no voltage breakdown of semiconductors during the maximum instantaneous current i L magnitude and during maximum battery voltage.
It was decided that the highest voltage amplitude u abmax is in the range 650 V to 700 V. Review of parameters for which C 13 was designed: Leakage inductance L sigma of used transformer is 1 µH, maximum battery voltage is 420 V, transformer ratio is 1.33, maximum inductor current amplitude i L is below 50 A.
For the given voltage u abmax amplitude, the C 13 capacitance was calculated according to (13) in the range from 125 nF to 308 nF. Capacity 270 nF was chosen, for which the duration was calculated as t Q13 = 1632 ns. The calculations were verified by simulations, see Figure 6.
Inductor L is replaced with a constant current source i L in the scheme above. Its value can either be set as a constant value or as a periodic triangular waveform. Transistors were replaced by switches controlled by voltage sources (V5 to V13) with configurable switching diagram. A switch marked as Q 5 to Q 8 substitutes transistors of bridge "B", and diode D5 to D8 represents their body diodes.
The purpose of the first simulation was to verify the amplitude voltage spike during maximum current i L = 50 A and maximum battery voltage u BAT = 420 V. Simulation is performed for 150 kHz inverter switching frequency therefore 300 kHz frequency of inductor current, L sigma = 1 µH, C 13 = 270 nF. Current source i L supplies constant current with magnitude 50 A. Time t Q13 was configured to be 1632 ns.
Simulated waveforms of voltages and currents are shown in Figure 7. Substituting the values into (13) the resultant voltage amplitude of u abmax = 656.2 V. From the simulation results, the value of 654.4 V was obtained. This is almost a full match to the calculated value.  Another simulation was performed in order to confirm the correctness of (9) to (15) and the overall functionality of the proposed solution. Specific values of voltages and currents, which were measured during experimental measurements with bidirectional charger, were simulated.
The following parameters are considered: Periodic waveform iL of triangular shape with values iLmin = 24 A, iLmax = 43 A, uBAT = 371 V. The tov overlap time was 1833 ns. The switch-off time interval of the transistor pair of bridge "B" was 1430 ns, for this reason, according to (15), the time tQ13 was shortened to Another simulation was performed in order to confirm the correctness of (9) to (15) and the overall functionality of the proposed solution. Specific values of voltages and currents, which were measured during experimental measurements with bidirectional charger, were simulated.
The following parameters are considered: Periodic waveform i L of triangular shape with values i Lmin = 24 A, i Lmax = 43 A, u BAT = 371 V. The t ov overlap time was 1833 ns. The switch-off time interval of the transistor pair of bridge "B" was 1430 ns, for this reason, according to (15), the time t Q13 was shortened to 1430 ns.
The simulation result is shown in Figure 8. The experimentally measured values are shown in Section 6. The simulated and experimentally measured waveforms clearly show the agreement. The simulations also verified the correctness of the derived equations.

Principle of the New Strategy of Bidirectional Charger Control in the Charging Mode
In order to achieve higher efficiency, transistors Q1 to Q4 (bridge "A") are actively driven with mains frequency 50 Hz and work as an active rectifier. Transistors Q1 to Q4 always switch in pairs Q1, Q4 and Q2, Q3. Correct switching of those transistor pairs is dependent on the polarity of instantaneous mains voltage and is activated after zero crossing.
Switching period T is in the order of units of μs, which relates to switching frequency in order of hundreds of kHz. Switching period for transistor Q13 is two times shorter (twice the frequency). Transistors Q5 to Q8 (bridge "B") always switch on all together during energy accumulation into inductor L and during the energy transfer the pair Q5, Q8, or Q6, Q7 is switched on. For the following explanations, it is assumed that time t0 starts a new period when the energy transfer from inductor L through transformer TR (see Figure 5) into the battery occurs. The circuit is in a dynamically stabilised state from the previous period. Energy is accumulated in inductors and capacitors.
Specific switching time intervals for transistors Q5 to Q13 for charging and discharging mode are described below. Logic diagrams of these transistors switching are shown in Figure 9 for better clarity. Figure 10 shows experimentally acquired waveforms of voltages and current in specific time intervals. All these waveforms are relevant only for charging mode. Important parameter in charging mode is overlap duration tov. During this time, all four transistors Q5 to Q8 are switched on and energy is being accumulated into inductor L. Duration marked as tdelay is achieved with shifting of microcontroller timers.

Principle of the New Strategy of Bidirectional Charger Control in the Charging Mode
In order to achieve higher efficiency, transistors Q 1 to Q 4 (bridge "A") are actively driven with mains frequency 50 Hz and work as an active rectifier. Transistors Q 1 to Q 4 always switch in pairs Q 1 , Q 4 and Q 2 , Q 3 . Correct switching of those transistor pairs is dependent on the polarity of instantaneous mains voltage and is activated after zero crossing.
Switching period T is in the order of units of µs, which relates to switching frequency in order of hundreds of kHz. Switching period for transistor Q 13 is two times shorter (twice the frequency). Transistors Q 5 to Q 8 (bridge "B") always switch on all together during energy accumulation into inductor L and during the energy transfer the pair Q 5 , Q 8 , or Q 6 , Q 7 is switched on. For the following explanations, it is assumed that time t 0 starts a new period when the energy transfer from inductor L through transformer TR (see Figure 5) into the battery occurs. The circuit is in a dynamically stabilised state from the previous period. Energy is accumulated in inductors and capacitors.
Specific switching time intervals for transistors Q 5 to Q 13 for charging and discharging mode are described below. Logic diagrams of these transistors switching are shown in Figure 9 for better clarity. Figure 10 shows experimentally acquired waveforms of voltages and current in specific time intervals. All these waveforms are relevant only for charging mode. Important parameter in charging mode is overlap duration t ov . During this time, all four transistors Q 5 to Q 8 are switched on and energy is being accumulated into inductor L. Duration marked as t delay is achieved with shifting of microcontroller timers.   This duration needs to be applied when transistors Q9 to Q12 are actively driven due to a delay in energy transfer from the primary to the secondary winding of the transformer. Duration of tdelay needs to be long enough to guarantee that voltage generated on the secondary winding is higher than the battery voltage uBAT. Without tdelay the current would flow from the battery through transistor pair Q9, Q12 or Q10, Q11 first, and later it would be overdriven by current generated in the transformer's secondary winding. Time interval marked as tdead guarantees reliable turn off of all transistors connected in com-    This duration needs to be applied when transistors Q9 to Q12 are actively driven due to a delay in energy transfer from the primary to the secondary winding of the transformer. Duration of tdelay needs to be long enough to guarantee that voltage generated on the secondary winding is higher than the battery voltage uBAT. Without tdelay the current would flow from the battery through transistor pair Q9, Q12 or Q10, Q11 first, and later it would be overdriven by current generated in the transformer's secondary winding. Time interval marked as tdead guarantees reliable turn off of all transistors connected in com- This duration needs to be applied when transistors Q 9 to Q 12 are actively driven due to a delay in energy transfer from the primary to the secondary winding of the transformer. Duration of t delay needs to be long enough to guarantee that voltage generated on the secondary winding is higher than the battery voltage u BAT . Without t delay the current would flow from the battery through transistor pair Q 9 , Q 12 or Q 10 , Q 11 first, and later it would be overdriven by current generated in the transformer's secondary winding. Time interval marked as t dead guarantees reliable turn off of all transistors connected in common part of the circuit. It shall never occur that transistors Q 9 and Q 11 or Q 10 and Q 12 switch on at the same time.
In time t 0 transistor pair Q 5 , Q 8 was turned off while transistors Q 6 , Q 7 remained turned on from the previous period. Transistor Q 13 is turned off. Additionally, transistor Q 12 was turned off. All the transistors in bridge "C" are turned off. The explanation refers to  Sensors 2022, 22, x FOR PEER REVIEW 13 of 32 mon part of the circuit. It shall never occur that transistors Q9 and Q11 or Q10 and Q12 switch on at the same time.
In time t0 transistor pair Q5, Q8 was turned off while transistors Q6, Q7 remained turned on from the previous period. Transistor Q13 is turned off. Additionally, transistor Q12 was turned off. All the transistors in bridge "C" are turned off. The explanation refers to  i Current iL flows through inductor L while the primary winding current ip of transformer TR is zero. In an ideal case, the inductor L current should immediately flow into the primary winding of transformer TR, but this is not possible due to its leakage inductance. Inductor current iL continues through the body diode of transistor Q13 into capacitor C13, which charges up and accumulates energy. In case of C13 absence, the voltage between a and b nodes would rise to dangerous overvoltage, leading to transistor destruction. The active element, composed of a series connection of transistor Q13 and capacitor C13, prevents that. Current is, which is induced by current increase ip, is flowing back through the body diodes of transistors Q10 and Q11. In this time the, bridge "C" works as a passive diode bridge rectifier.
The time t1 (tdelay) is very short, i.e., units of percent of the switching period (150 kHz). In this case, it was 100 ns. The explanation refers to Figures 9, 10 and 12. The primary purpose of this t1 is to add two safety delays:  Between switching off transistor pair Q5, Q8 and switching on Q3, while transistors Q6, Q7 remain switched off. Simultaneous switching on of all transistors in bridge "B" would mean short circuit of capacitor C13.  Guarantees that voltage generated across the secondary winding of the transformer is greater than battery voltage uBAT.
Current i L flows through inductor L while the primary winding current i p of transformer TR is zero. In an ideal case, the inductor L current should immediately flow into the primary winding of transformer TR, but this is not possible due to its leakage inductance. Inductor current i L continues through the body diode of transistor Q 13 into capacitor C 13 , which charges u p and accumulates energy. In case of C 13 absence, the voltage between a and b nodes would rise to dangerous overvoltage, leading to transistor destruction. The active element, composed of a series connection of transistor Q 13 and capacitor C 13 , prevents that. Current i s , which is induced by current increase i p , is flowing back through the body diodes of transistors Q 10 and Q 11 . In this time the, bridge "C" works as a passive diode bridge rectifier.
The time t 1 (t delay ) is very short, i.e., units of percent of the switching period (150 kHz). In this case, it was 100 ns. The explanation refers to Figures 9, 10 and 12. The primary purpose of this t 1 is to add two safety delays:

•
Between switching off transistor pair Q 5 , Q 8 and switching on Q 3 , while transistors Q 6 , Q 7 remain switched off. Simultaneous switching on of all transistors in bridge "B" would mean short circuit of capacitor C 13 .

•
Guarantees that voltage generated across the secondary winding of the transformer is greater than battery voltage u BAT .  In time t1 transistors Q10, Q11 and Q13 turn on. Current ip is rising and is now given by the difference of currents iL and capacitor current iC13. After some time, both currents iL and ip equalise and in this moment direction of current through C13 reverses. The energy which was accumulated in C13 is now being discharged into transformer TR. Current ip is now given by the sum of capacitor iC13 and inductor iL currents. In this time interval, the energy is transferred from the primary to the secondary winding of transformer TR. Transistors Q10 and Q11 were turned on to reduce losses during the secondary current flow.

Time Interval t2 ≤ t < t3
In time t2 transistors Q10 and Q13 were turned off, while the capacitor C13 was disconnected from the bridge "B". The current ip dropped. The leakage inductance of the transformer tries to keep its current magnitude. For this reason, the polarity of up is reversed, but body diodes of transistors Q5 and Q8 clamp the voltage to approximately zero. The explanation refers to Figures 9, 10 and 13.
Considering that in time t2 transistor Q10 is turned off, the energy accumulated in the leakage inductance of transformer keeps up the current is, which flows through Q10 body diode. In time t 1 transistors Q 10 , Q 11 and Q 13 turn on. Current i p is rising and is now given by the difference of currents i L and capacitor current i C13 . After some time, both currents i L and i p equalise and in this moment direction of current through C 13 reverses. The energy which was accumulated in C 13 is now being discharged into transformer TR. Current i p is now given by the sum of capacitor i C13 and inductor i L currents. In this time interval, the energy is transferred from the primary to the secondary winding of transformer TR. Transistors Q 10 and Q 11 were turned on to reduce losses during the secondary current flow.
In time t 2 transistors Q 10 and Q 13 were turned off, while the capacitor C 13 was disconnected from the bridge "B". The current i p dropped. The leakage inductance of the transformer tries to keep its current magnitude. For this reason, the polarity of u p is reversed, but body diodes of transistors Q 5  In time t1 transistors Q10, Q11 and Q13 turn on. Current ip is rising and is now given by the difference of currents iL and capacitor current iC13. After some time, both currents iL and ip equalise and in this moment direction of current through C13 reverses. The energy which was accumulated in C13 is now being discharged into transformer TR. Current ip is now given by the sum of capacitor iC13 and inductor iL currents. In this time interval, the energy is transferred from the primary to the secondary winding of transformer TR. Transistors Q10 and Q11 were turned on to reduce losses during the secondary current flow.

Time Interval t2 ≤ t < t3
In time t2 transistors Q10 and Q13 were turned off, while the capacitor C13 was disconnected from the bridge "B". The current ip dropped. The leakage inductance of the transformer tries to keep its current magnitude. For this reason, the polarity of up is reversed, but body diodes of transistors Q5 and Q8 clamp the voltage to approximately zero. The explanation refers to Figures 9, 10   Considering that in time t2 transistor Q10 is turned off, the energy accumulated in the leakage inductance of transformer keeps up the current is, which flows through Q10 body diode. Considering that in time t 2 transistor Q 10 is turned off, the energy accumulated in the leakage inductance of transformer keeps up the current i s , which flows through Q 10 body diode.

Time Interval t 3 ≤ t < 1 /2T
In t 3 instant, the transistors Q 5 and Q 8 were turned on, while transistors Q 6 , Q 7 and Q 11 remained turned on. Transistors Q 5 , Q 8 are turned on at zero voltage, which was reached during the previous time interval.
The primary winding of transformer TR is shorted out with transistors Q 5 to Q 8 , current i p decreases to zero. The instantaneous voltage of rectified grid voltage u d is now connected to inductor L, its current rises, and energy is being accumulated. The accumulation phase remains till 1 /2T. The time during which the energy is being accumulated into the inductor is marked as t ov .
In order to increase the amount of energy accumulated in inductor L, which is transferred to the secondary winding of transfer, the overlap duration t ov needs to be extended while t 3 and t 2 shortened.
During the accumulation period, the transistor Q 11 from bridge "C" remains turned on and, together with the body diode of transistor Q 12 keeps the secondary voltage u s close to zero till the moment when no more energy is transferred into the battery. The explanation refers to Figures 9, 10 and 14. 3.2.4. Time Interval t3 ≤ t < ½T In t3 instant, the transistors Q5 and Q8 were turned on, while transistors Q6, Q7 and Q11 remained turned on. Transistors Q5, Q8 are turned on at zero voltage, which was reached during the previous time interval.
The primary winding of transformer TR is shorted out with transistors Q5 to Q8, current ip decreases to zero. The instantaneous voltage of rectified grid voltage ud is now connected to inductor L, its current rises, and energy is being accumulated. The accumulation phase remains till ½T. The time during which the energy is being accumulated into the inductor is marked as tov.
In order to increase the amount of energy accumulated in inductor L, which is transferred to the secondary winding of transfer, the overlap duration tov needs to be extended while t3 and t2 shortened.
During the accumulation period, the transistor Q11 from bridge "C" remains turned on and, together with the body diode of transistor Q12 keeps the secondary voltage us close to zero till the moment when no more energy is transferred into the battery. The explanation refers to Figures 9, 10 and 14.  Time ½T is half of the switching period when everything starts to repeat. The main difference is that transistor pairs Q5, Q8 and Q6, Q7 switched their roles.
In time ½T transistor pair Q6, Q7 was turned off, while transistors Q5, Q8 remained turned on from the previous period. Transistor Q13 is turned off. Furthermore, transistor Q11 was turned off. All the transistors from bridge "C" are now turned off. Waveforms of voltages and currents are analogous to what was described in Section 3.2.1.

Time Interval (t1 + ½T) ≤ t < (t2 + ½T)
In time (t1 + ½T), transistors Q9, Q12 and Q13 were turned on. Transistors Q9, and Q12 were turned on in order to reduce conduction losses during the secondary current flow. Waveforms of voltages and currents are analogous to what was described in Section 3.2.2.

Time Interval (t2 + ½T) ≤ t < (t3 + ½T)
In time (t2 + ½T), transistors Q9 and Q13 were turned off. Transistors Q5, Q8 and Q12 remained turned on. Waveforms of voltages and currents are analogous to what was described in Section 3.2.3. In time 1 /2T transistor pair Q 6 , Q 7 was turned off, while transistors Q 5 , Q 8 remained turned on from the previous period. Transistor Q 13 is turned off. Furthermore, transistor Q 11 was turned off. All the transistors from bridge "C" are now turned off. Waveforms of voltages and currents are analogous to what was described in Section 3.2.1.
3.2.6. Time Interval (t 1 + 1 /2T) ≤ t < (t 2 + 1 /2T) In time (t 1 + 1 /2T), transistors Q 9 , Q 12 and Q 13 were turned on. Transistors Q 9 , and Q 12 were turned on in order to reduce conduction losses during the secondary current flow. Waveforms of voltages and currents are analogous to what was described in Section 3.2.2.

Time Interval
In time (t 2 + 1 /2T), transistors Q 9 and Q 13 were turned off. Transistors Q 5 , Q 8 and Q 12 remained turned on. Waveforms of voltages and currents are analogous to what was described in Section 3.2.3.

Time Interval (t 3 + 1 /2T) ≤ t < T
In time (t 3 + 1 /2T), transistors Q 6 and Q 7 were turned on. Transistors Q 5 , Q 8 and Q 12 remained turned on. Waveforms of voltages and currents are analogous to what was described in Section 3.2.4.

Principle of the New Strategy of Bidirectional Charger Control in the Discharging Mode
In discharging mode of a bidirectional charger, transistors Q 1 to Q 4 (bridge "A" in Figure 5) and transistors Q 9 to Q 12 (bridge "C" in Figure 5) work as inverters. Transistors Q 5 to Q 8 (see bridge "B" in Figure 5) work as rectifiers. Transistors Q 9 to Q 12 chop the direct voltage of battery u BAT into AC voltage, which is later transformed by transformer TR and actively rectified by transistors Q 5 to Q 8 .
The voltage u d itself does not have a constant magnitude, but it is modulated with change of t on parameter in such a way that it resembles rectified sine wave. Change of t on is realised by switching on the duration of transistor pairs Q 9 , Q 12 or Q 10 , Q 11 (inverter "C" in Figure 5), while transistors Q 12 and Q 11 are switched on for the whole duration of switching half-period. Only after t delay transistor pairs Q 5 , Q 8 or Q 6 , Q 7 (inverter "B" in Figure 5) are switched on.
The function of inverter "A" is to toggle the polarity of direct pulsing voltage u d so that it reflects the actual polarity in power grid and thus allows the energy to flow from the battery into power grid.
Labelling of transformer windings is kept the same as in charging mode in the Subsection B. Winding of transformer on the battery side is labelled as the secondary winding even though its function in discharging mode is inverted.
Switching period T has µs unit, which reflects the switching frequency in the order of hundreds of kHz. The switching frequency of 150 kHz is used in the example below.
In the following example, it is assumed that time t 0 is the start of a new period and that the circuit is in a dynamically stabilised state from the previous period, inductors and capacitors have accumulated energy. For clarity, Figure 15 shows the logic switching waveforms of transistors. Figures 16 and 17 show experimentally acquired waveforms of voltages and currents in specific time instants. All those waveforms are relevant only for discharging mode. The main parameter for discharging mode is marked as t on . During this time one of the transistor pairs Q 9 , Q 12 or Q 10 , Q 11 is switched on and energy is transferred via transformer TR and inverter "B" and "A" into power grid. Duration marked as t delay for switching of transistor Q 13 is realised by a phase shift of timer of microcontroller and for transistors Q 5 to Q 8 by utilizing t dead in the microcontroller.       Voltage spikes are reduced with capacitor C13, first passively and later after tdelay through switched-on transistor Q13. In the specific moment, the accumulated energy of C13 discharges back into the circuit through switched-on transistor Q13.

Time Interval t0 ≤ t < t1
In moment t0, transistors Q9, Q12 are turned on. Transistors Q5 to Q8, Q10, Q11 remain turned off. The secondary side of the transformer TR is connected to battery voltage uBAT. Due to this, the secondary and later also the primary current starts to flow through the transformer TR, which causes voltage up to rise. Current ip flows back through the body diodes of transistors Q5 and Q8. The explanation refers to Figures 15-18.  Voltage spikes are reduced with capacitor C 13 , first passively and later after t delay through switched-on transistor Q 13 . In the specific moment, the accumulated energy of C 13 discharges back into the circuit through switched-on transistor Q 13 .

Time Interval
In moment t 0, transistors Q 9 , Q 12 are turned on. Transistors Q 5 to Q 8 , Q 10 , Q 11 remain turned off. The secondary side of the transformer TR is connected to battery voltage u BAT . Due to this, the secondary and later also the primary current starts to flow through the transformer TR, which causes voltage u p to rise. Current i p flows back through the body diodes of transistors Q 5 and Q 8 . The explanation refers to Figures 15-18.

Time Interval t0 ≤ t < t1
In moment t0, transistors Q9, Q12 are turned on. Transistors Q5 to Q8, Q10, Q11 remain turned off. The secondary side of the transformer TR is connected to battery voltage uBAT. Due to this, the secondary and later also the primary current starts to flow through the transformer TR, which causes voltage up to rise. Current ip flows back through the body diodes of transistors Q5 and Q8. The explanation refers to     Primary voltage u p reaches the magnitude which corresponds to the product of battery voltage and transformer TR transforming ratio. If the voltage u p exceeds the voltage of capacitor C 13 , the current starts to flow through the body diode of transistor Q 13, and capacitor C 13 is charging. At this moment, energy is transferred into power grid and capacitor C 13 .

Time Interval t 1 ≤ t < t 2
In time instant t 1 transistors Q 5 , Q 8 , Q 13 are turned on to reduce conduction losses across their body diodes. The delay of switching on the transistors t delay is implemented due to the leakage inductance of transformer TR. Voltage u p is greater than instantaneous voltage u d , and inductor current i L is rising. Capacitor C 13 is charging, and its current decreases. In a moment when the currents i p and i L have the same magnitude, the current's direction through C 13 reverses and its accumulated energy starts to discharge. Current i L is now determined by the sum of capacitor current i C13 and current i p . The explanation refers to Figures 15-17

Time Interval t1 ≤ t < t2
In time instant t1 transistors Q5, Q8, Q13 are turned on to reduce conduction losses across their body diodes. The delay of switching on the transistors tdelay is implemented due to the leakage inductance of transformer TR. Voltage up is greater than instantaneous voltage ud, and inductor current iL is rising. Capacitor C13 is charging, and its current decreases. In a moment when the currents ip and iL have the same magnitude, the current's direction through C13 reverses and its accumulated energy starts to discharge. Current iL is now determined by the sum of capacitor current iC13 and current ip. The explanation refers to Figures 15-17 Figure 19. Discharging mode-time interval t1 ≤ t < t2.

Time Interval t2 ≤ t < t3
In time instant t2, transistors Q9 and Q13 are turned off. The secondary current is must maintain its direction and flows through the body diode of transistor Q11. At the same time, the transistor Q13 current is interrupted. Next, the current ip drops. Transformer leakage inductance tries to maintain the current through the transformer ip magnitude. This causes a decrease in up voltage. The explanation refers to Figures 15-17 and 20. Figure 19. Discharging mode-time interval t 1 ≤ t < t 2 .

Time Interval
In time instant t 2 , transistors Q 9 and Q 13 are turned off. The secondary current i s must maintain its direction and flows through the body diode of transistor Q 11 . At the same time, the transistor Q 13 current is interrupted. Next, the current i p drops. Transformer leakage inductance tries to maintain the current through the transformer i p magnitude. This causes a decrease in u p voltage. The explanation refers to Figures 15-17 and 20.

Time Interval t2 ≤ t < t3
In time instant t2, transistors Q9 and Q13 are turned off. The secondary current is must maintain its direction and flows through the body diode of transistor Q11. At the same time, the transistor Q13 current is interrupted. Next, the current ip drops. Transformer leakage inductance tries to maintain the current through the transformer ip magnitude. This causes a decrease in up voltage. The explanation refers to Figures 15-17 and 20.  Figure 20. Discharging mode-time interval t2 ≤ t < t3.

Time Interval t3 ≤ t < t4
In time instant t3 transistors Q5 and Q8 are turned off. Inductor current iL maintains its direction even after the end of energy transfer from the transformer. Current iL flows   Figure 21. Discharging mode-time interval t3; discharging mode-time interval t4 ≤ t < ½T. t < t4.

Time Interval t4 ≤ t < ½T
In time instant t4, the energy accumulated in the leakage inductance of the secondary winding is depleted and, therefore, the transistor Q12 is turned off. Other transistors were already turned off in the previous time interval. This allows zero current switching on during the next time interval. The explanation refers to Figures 15-17

Time Interval t 4 ≤ t < 1 /2T
In time instant t 4 , the energy accumulated in the leakage inductance of the secondary winding is depleted and, therefore, the transistor Q 12 is turned off. Other transistors were already turned off in the previous time interval. This allows zero current switching on during the next time interval. The explanation refers to Figures 15-17 Figure 21. Discharging mode-time interval t3; discharging mode-time interval t4 ≤ t < ½T. t < t4.

Time Interval t4 ≤ t < ½T
In time instant t4, the energy accumulated in the leakage inductance of the secondary winding is depleted and, therefore, the transistor Q12 is turned off. Other transistors were already turned off in the previous time interval. This allows zero current switching on during the next time interval. The explanation refers to Figures 15-17

Time Interval 1 /2T ≤ t < (t 1 + 1 /2T)
In time instant 1 /2T transistors Q 10 , Q 11 are turned on, and transistors Q 5 to Q 8 , Q 10 , Q 11 remain turned on. Current i p flows back through the body diodes of transistors Q 6 and Q 7 . If the voltage u p exceeds the magnitude of capacitor C 13 voltage, the current through the body diode of transistor Q 13 starts to charge the capacitor C 13 . Waveforms of voltages and currents are analogous to what was described in Section 3.3.1.
3.3.7. Time Interval (t 1 + 1 /2T) ≤ t < (t 2 + 1 /2T) In time instant (t 1 + 1 /2T), transistors Q 6 , Q 7 and Q 13 are turned on, and energy from the battery is transferred into power grid. Waveforms of voltages and currents are analogous to what was described in Section 3.3.2.
3.3.8. Time Interval (t 2 + 1 /2T) ≤ t < (t 3 + 1 /2T) In time instant (t 2 + 1 /2T), transistors Q 10 and Q 13 are turned off. The secondary current i s must maintain its direction and flows back through the body diode of transistor Q 12 . At the same time, the transistor Q 13 current is interrupted. Waveforms of voltages and currents are analogous to what was described in Section 3.3.3.

Time Interval (t 3 + 1 /2T) ≤ t < (t 4 + 1 /2T)
In time instant (t 3 + 1 /2T), transistors Q 6 and Q 7 are turned off. Current i L flows back through the body diodes of transistors Q 5 to Q 8 . Waveforms of voltages and currents are analogous to what was described in Section 3.3.4.

Time Interval (t 4 + 1 /2T) ≤ t < T
In time instant (t 4 + 1 /2T), transistor Q 11 is turned off. Other transistors were turned off during the previous time interval. Waveforms of voltages and currents are analogous to what was described in Section 3.3.5.

New Prototype of a Bidirectional Charger Enhanced with Active Element "D"
To verify the modified topology of the bidirectional charger, a new prototype enhanced with an active element "D" was assembled. The new prototype consists of six interconnected PCBs: AC filter, inverter power stage, DC filter, control system, transistor driver circuits 1 and transistor driver circuit 2, as shown in Figure 23. The main parameters of the bidirectional charger are shown in Table 1.  what was described in Section 3.3.5.

New Prototype of a Bidirectional Charger Enhanced with Active Element "D"
To verify the modified topology of the bidirectional charger, a new prototype enhanced with an active element "D" was assembled. The new prototype consists of six interconnected PCBs: AC filter, inverter power stage, DC filter, control system, transistor driver circuits 1 and transistor driver circuit 2, as shown in Figure 23. The main parameters of the bidirectional charger are shown in Table 1   Inverter power stage contains four power transistors Q 1 to Q 4 type IPW60R017C7XKSA1, see bridge "A" in Figure 5 and five power transistors Q 5 to Q 8 and Q 13 type C3M0032120K, see bridge "B" and active element "D", four power transistors Q 9 to Q 12 type C3M0030090K, see bridge "C" in Figure 5.
Transistor driver circuit 2 contains seven drivers of ADUM4135BRWZ type for transistors Q 1 , Q 2 , Q 5 , Q 7 , Q 9 , Q 11 and Q 13 and seven pieces of galvanically isolated DC/DC power supplies.
Control system contains five galvanically isolated power supplies, linear regulators (5, 3.3 V), 3.3 V voltage reference for AD converter and analogue supply for microcontroller, circuit for isolated measurement of voltages and currents, two high-speed CAN transceivers, service communication interface with RS485, temperature measurement and 32-bit microcontroller ARM Cortex M4, STM32F446XC (STMicroelectronics, Geneva, Switzerland).
Microcontroller STM32F446XC works at 180 MHz system clock, and five timers are used to control charging and discharging mode. For every single transistor control, specific timer output was assigned. For example, channel 1 of timer TIM 1 for transistor pair Q 5 , Q 8 . All timers utilise asymmetric PWM. To better understand the control algorithms, logic signals for charging mode are shown in Figure 9 and in Figure 15 for discharging mode. Duration labelled as t delay is in charging mode realised with phase shift of timers. In discharging mode the duration t delay for transistors Q 5 to Q 8 is realised with timer dead time and for transistor Q 13 with phase shift of timer.
Considering the requirements for as small as possible dimensions and weight, fluid cooling was selected for transistor cooling. The simulation focused on thermal transfer, and fluid movement in the heatsink was performed in software COMSOL Multiphysics 5.5 (COMSOL Inc., Stockholm, Sweden). For both charging and discharging modes, the temperature 80 • C without radiation effects was assumed. All the heat is dissipated through the heatsink. This simplification corresponds to real conditions in the charger, whose internal space is heated-up with power dissipation of the remaining components. To prevent overheating damage of power transistors, simulations of the maximal possible temperature of cooling fluid were performed. It showed that it is possible to reach up to 110 • C of cooling fluid without exceeding the absolute maximum temperature rating of the transistor junction.
Two variants of transistor Q 1 to Q 13 control techniques were simulated in charging and discharging modes.
In the first variant, referred to as "Uncontrolled", only transistors Q 5 to Q 8 and Q 13 were driven in charging mode and only transistors Q 1 to Q 4 , Q 9 to Q 12 and Q 13 were driven in discharging mode. In the second variant, referred to as "Controlled", all transistors were actively driven.
The inlet temperature of the coolant is 80 • C at a flow rate of 2 L/min. Figure 24 shows the example of temperature simulation of all transistors placed on the heatsink. This is for maximal power of the charger and active control of all transistors in charging mode. Coolant inlet temperature was 80 • C, and outlet temperature was 82.2 • C at a flow rate of 2 L/min. Considering the requirements for as small as possible dimensions and weight, fluid cooling was selected for transistor cooling. The simulation focused on thermal transfer, and fluid movement in the heatsink was performed in software COMSOL Multiphysics 5.5 (COMSOL Inc., Stockholm, Sweden). For both charging and discharging modes, the temperature 80 °C without radiation effects was assumed. All the heat is dissipated through the heatsink. This simplification corresponds to real conditions in the charger, whose internal space is heated-up with power dissipation of the remaining components. To prevent overheating damage of power transistors, simulations of the maximal possible temperature of cooling fluid were performed. It showed that it is possible to reach up to 110 °C of cooling fluid without exceeding the absolute maximum temperature rating of the transistor junction.
Two variants of transistor Q1 to Q13 control techniques were simulated in charging and discharging modes.
In the first variant, referred to as "Uncontrolled", only transistors Q5 to Q8 and Q13 were driven in charging mode and only transistors Q1 to Q4, Q9 to Q12 and Q13 were driven in discharging mode. In the second variant, referred to as "Controlled", all transistors were actively driven.
The inlet temperature of the coolant is 80 °C at a flow rate of 2 l/min. Figure 24 shows the example of temperature simulation of all transistors placed on the heatsink. This is for maximal power of the charger and active control of all transistors in charging mode. Coolant inlet temperature was 80 °C, and outlet temperature was 82.2 °C at a flow rate of 2 l/min.

The Experimental Microgrid Platform
The experimental microgrid platform for the development of the Vehicle to Grid technologies simulates the electricity consumption of a typical single-family home. The

The Experimental Microgrid Platform
The experimental microgrid platform for the development of the Vehicle to Grid technologies simulates the electricity consumption of a typical single-family home. The microgrid system is based on a hybrid AC/DC architecture. The centre of the experimental platform is a Conext XW+ 8548 E hybrid inverter (Schneider Electric SE, Rueil-Malmaison, France). The testing platform consists of two parts. The first part is based on the main 48 V DC bus, whereas the second is based on the 230 V AC bus. The DC part consists of two Conext 80 600 DC/DC-MPPT PV inverters (Schneider Electric SE, Rueil-Malmaison, France). These PV inverters convert electricity to supply appliances and storage batteries from photovoltaic strings. The batteries are thin plate pure lead Hawker 12XFC115. One battery's nominal voltage and capacity are 12 V and 115 Ah. These batteries are connected in a battery bank, forming four groups, each including four batteries. The 48 V DC bus voltage varies from 40.5 to 64 V DC depending on the battery's state of charge and the charging process. The rated power of each of the two PV strings is 2 kW. The second part of the platform is based on a 230 V AC bus with a frequency of 50 Hz. The AC bus is drawn directly from the hybrid inverter to which the individual household appliances are connected. Figure 26 shows a schematic of the microgrid system used to perform the experiments in this article.

The Experimental Microgrid Platform
The experimental microgrid platform for the development of the Vehicle to Grid technologies simulates the electricity consumption of a typical single-family home. The microgrid system is based on a hybrid AC/DC architecture. The centre of the experimental platform is a Conext XW+ 8548 E hybrid inverter (Schneider Electric SE, Rueil-Malmaison, France). The testing platform consists of two parts. The first part is based on the main 48 V DC bus, whereas the second is based on the 230 V AC bus. The DC part consists of two Conext 80 600 DC/DC-MPPT PV inverters (Schneider Electric SE, Rueil-Malmaison, France). These PV inverters convert electricity to supply appliances and storage batteries from photovoltaic strings. The batteries are thin plate pure lead Hawker 12XFC115. One battery's nominal voltage and capacity are 12 V and 115 Ah. These batteries are connected in a battery bank, forming four groups, each including four batteries. The 48 V DC bus voltage varies from 40.5 to 64 V DC depending on the battery's state of charge and the charging process. The rated power of each of the two PV strings is 2 kW. The second part of the platform is based on a 230 V AC bus with a frequency of 50 Hz. The AC bus is drawn directly from the hybrid inverter to which the individual household appliances are connected. Figure 26 shows a schematic of the microgrid system used to perform the experiments in this article.

Results and Discussion
For experimental verification of the bidirectional charger, a new prototype enhanced with an active element "D" was assembled, and a new control strategy of transistors Q 9 to Q 12 was used. The measurement station mainly consisted of the following instruments: Rigol MSO4054 oscilloscope, Micsig DP 10013 high voltage differential probe, Rigol RP1002C current probe, PEM CWTUM/03/B ultra-miniature HF current probe.
In Section 2.2, waveforms of voltages and currents in charging mode with inductor inductance 25 µH were shown. Those waveforms were acquired while using the new topology according to Figure 1, i.e., without active element "D". Figure 27 shows waveforms of voltages and currents in charging mode with the topology according to Figure 5, i.e., with the active element "D". Comparing Figures 4 and 27, it is obvious that u p and u ab overvoltage problem, caused by transformer leakage inductance, was solved by the active element "D". Voltage u p waveform after modification contains higher frequency oscillations caused by other parasitic properties, which were not present with the topology according to Figure 1. The root cause of these oscillations is mainly the parasitic properties of PCBs and electronic components. These oscillations have much lower amplitude and do not overstress the semiconductors with overvoltage. Voltage u p amplitude is, in this case, equal to 600 V and did not exceed the absolute maximum voltage of 700 V, see Section 3.1. Dumped resonances of voltage u s (Figure 4), caused by circuit parasitic on the secondary side of the transformer, were successfully suppressed with alternative control strategy of transistors Q 9 to Q 12 , different to what was mentioned in Section 2.1.
In Section 2.2, waveforms of voltages and currents in charging mode with inductor inductance 25 μH were shown. Those waveforms were acquired while using the new topology according to Figure 1, i.e., without active element "D". Figure 27 shows waveforms of voltages and currents in charging mode with the topology according to Figure 5, i.e., with the active element "D". Comparing Figure 4 and Figure 27, it is obvious that up and uab overvoltage problem, caused by transformer leakage inductance, was solved by the active element "D". Voltage up waveform after modification contains higher frequency oscillations caused by other parasitic properties, which were not present with the topology according to Figure 1. The root cause of these oscillations is mainly the parasitic properties of PCBs and electronic components. These oscillations have much lower amplitude and do not overstress the semiconductors with overvoltage. Voltage up amplitude is, in this case, equal to 600 V and did not exceed the absolute maximum voltage of 700 V, see Section 3.1. Dumped resonances of voltage us (Figure 4), caused by circuit parasitic on the secondary side of the transformer, were successfully suppressed with alternative control strategy of transistors Q9 to Q12, different to what was mentioned in Section 2.1.  Figure 27 shows waveforms of the different quantities during single switching period. Measurement was taken at nominal power and represented its specific time instant. Figure 28 shows the voltage and current waveforms over a time interval of several periods of the 50 Hz power grid at rated power. The figure implies that waveforms of  Figure 27 shows waveforms of the different quantities during single switching period. Measurement was taken at nominal power and represented its specific time instant. Figure 28 shows the voltage and current waveforms over a time interval of several periods of the 50 Hz power grid at rated power. The figure implies that waveforms of power grid current i g follow the shape of power grid voltage u g with minimal total harmonic distortions and phase shift (unity power factor).  Distortion of battery current iBAT was caused by dynamic properties of the used electronic artificial load connected to the battery. This electronic load substituted insufficient battery capacity as well as dissipated energy during charging mode. This prevented repetitive battery cycling during the experimental measurements.

Experimental Measurement Results Acquired in Charging Mode
The control principle supports very high dynamics of change of power grid current Distortion of battery current i BAT was caused by dynamic properties of the used electronic artificial load connected to the battery. This electronic load substituted insufficient battery capacity as well as dissipated energy during charging mode. This prevented repetitive battery cycling during the experimental measurements.
The control principle supports very high dynamics of change of power grid current i g , but its dynamics is reduced with respect to requirements and usage of the bidirectional charger. Figure 29 shows the voltage and current waveforms during one single switching period. It shows the values corresponding to a specific time interval at rated power. Distortion of battery current iBAT was caused by dynamic properties of the used electronic artificial load connected to the battery. This electronic load substituted insufficient battery capacity as well as dissipated energy during charging mode. This prevented repetitive battery cycling during the experimental measurements.

Experimental Measurement Results Acquired in Discharging Mode
The control principle supports very high dynamics of change of power grid current ig, but its dynamics is reduced with respect to requirements and usage of the bidirectional charger.

Experimental Measurement Results Acquired in Discharging Mode
Error! Reference source not found. shows the voltage and current waveforms during one single switching period. It shows the values corresponding to a specific time interval at rated power.  Figure 30 shows the voltage and current waveforms over a time interval of three periods of the 50 Hz power grid. The waveforms also indicate minimal harmonic distortion, similarly to the charging mode.  Figure 30 shows the voltage and current waveforms over a time interval of three periods of the 50 Hz power grid. The waveforms also indicate minimal harmonic distortion, similarly to the charging mode. Optimal function and maximum efficiency in charging and discharging mode is achieved with active control of all transistors Q1 to Q13. Figure 31 shows the efficiency curve of the bidirectional charger for battery voltages of 300 and 400 V. The maximum efficiency of the bidirectional charger in charging mode for a battery voltage of 300 V was 96.4% at 3.4 kW and for a battery voltage of 400 V was Optimal function and maximum efficiency in charging and discharging mode is achieved with active control of all transistors Q 1 to Q 13 . Figure 31 shows the efficiency curve of the bidirectional charger for battery voltages of 300 and 400 V. The maximum efficiency of the bidirectional charger in charging mode for a battery voltage of 300 V was 96.4% at 3.4 kW and for a battery voltage of 400 V was 95.6% at 4.6 kW. The maximum efficiency in discharge mode for 300 V battery was 96.3% at 3.8 kW and for 400 V battery, voltage was 95.7% at 4.4 kW, see Figure 31.  The results of all these EMC measurements meet the given criteria. Figure 32 shows the emissions testing waveform for the bidirectional charger.   The results of all these EMC measurements meet the given criteria. Figure 32 shows the emissions testing waveform for the bidirectional charger.

Conclusions
This paper describes the research, development and experimental testing of a bidirectional galvanically isolated on-board charger for electric vehicles. The main objective was to meet the requirements of 4 kW/kg and 2 kW/dm 3 , bidirectional power control and galvanic insulation from the power grid. The power density of the realised charger was 4 kW/kg and 2.46 kW/dm 3 , and the maximum efficiency was 96.4% at 3.4 kW. To be able to achieve such low weight and values, specific electronic and mechanical elements had to be addressed. As for the electronic circuits, we mostly addressed the inductor and transformer, and as for the mechanical components, the solution concerned the heatsink. To achieve as low weight and volume as possible, fluid cooling was used to cool down the power transistors. To make the inductor and transformer smaller, high switching frequency of 150 kHz had to be used.
Based on the state-of-the-art research, a circuit scheme of the bidirectional charger was proposed, and a prototype for testing the control algorithms was built. In fact, several prototypes were built, two most prominent being described in this paper. The first prototype of the charger is described in Section 2, where problems and their solutions are also dealt with. Due to the parasitic properties of the transformer and other electronic circuits, overvoltage and oscillations occurred across the primary winding of the transformer. There was also dumped resonance across the secondary winding. Those undesirable effects were eliminated with topology modification by adding an active element "D" into the charger and with new Q 9 to Q 13 control strategy. The feasibility of this solution was verified with a new prototype of the bidirectional charger, which is described in Section 4. The novel switching strategy of Q 9 to Q 13 transistors' control and modified topology with an active element "D" were patented. The realised charger has an output of either 7.2 kW if it uses only single-phase or 21.6 kW if it uses three-phases.
The contribution of this work can be summarised as follows: • The single-stage inverter topology was modified to eliminate undesirable phenomena. • Bidirectional power control and galvanic insulation from the power grid.

•
Owing to the novel switching strategy of Q 9 to Q 12 transistors' control, the charger does not need RCD snubbers in order to limit the voltage spikes caused by leakage inductance of the transformer. This has the effect of reducing losses, increasing efficiency and also reducing weight and volume.

•
The proposed transistor switching control method eliminates unwanted HF oscillations on both the primary and secondary sides of the transformer in the on-board charger.

•
In order to reduce the size and weight of the inductor and transformer, high switching frequency of 150 kHz was used.

•
The charger allows V2G technology.

•
The power density of the new charger was 4 kW/kg and 2.46 kW/dm 3 , and the maximum efficiency was 96.4% at 3.4 kW.

•
The new charger has an output of either 7.2 kW if it uses only single-phase, or 21.6 kW if it uses three-phases.

Patents
The solution presented in the paper has been patented. The name of the patent is "Charger for bidirectional energy flow and controlling it". The patent number is PUV 2020-37617 (308969), CZ2020236A3.

Conflicts of Interest:
The authors declare no conflict of interest.
Patent Annotation: Charger for bidirectional energy flow, which has on the way from the mains voltage source (u g ) to the battery: the first bidirectional converter (A) consisting of switches (S 1 to S 4 ) operating on the mains frequency, the second bidirectional converter (B) consisting of switches (S 5 to S 8 ) operating at a frequency in the order of hundreds of kHz, a transformer (TR) and a third bidirectional converter (C) consisting of switches (S 9 to S 12 ) operating at the same frequency as the second converter. A coil (L) is connected in one of the buses (+, −) connecting the first and second converters (B, C), behind which the buses (+, −) are connected via a separate switch (S 13 ) and a capacitor (C 13 ). The method of controlling the charger by the control unit for the mains battery charging phase consists of a signal from the control unit being switched by a switch (S 13 ) with period T/2 and the second and third converters (B, C) are switched with period T. For safety reasons, the control unit leaves the switch (S 13 ) open for additional time during the safety delays t dead and t delay before the interval t 0 , or after this interval t 0 .