JP6468437B2 - Charging system - Google Patents

Description

  The present invention relates to a charging system.

  In the charging system described in Patent Document 1, a first rectifier circuit, a power factor correction circuit, a first inverter, and a voltage regulator circuit are provided on the primary side of the transformer, and a second rectifier circuit and a second inverter are connected to the transformer 2. Provide on the next side. The first rectifier circuit rectifies the commercial AC power supply, the power factor correction circuit boosts the rectified DC voltage, and the first inverter converts the boosted DC voltage into a first high-frequency AC.

  The second rectifier circuit rectifies the high-frequency alternating current induced in the secondary winding based on the first high-frequency alternating current and outputs it to the main battery. The second inverter converts the DC voltage of the main battery into a second high-frequency AC.

Japanese Patent Laid-Open No. 9-9417

  The power factor correction circuit provided in the charging system described in Patent Document 1 has a function of increasing the power factor and a function of not sending a current ripple having a frequency twice that of the power supply system to the high power DC line and the battery. Yes.

  However, in recent years, there has been a demand for a circuit capable of eliminating the power factor correction circuit and realizing a function of not sending a current ripple having a frequency twice that of the power supply system to the high-power DC line and the battery and a function of increasing the power factor. It was.

  An object of the present invention is to provide a charging system capable of realizing a function that eliminates a power factor correction circuit and does not send a current ripple having a frequency twice that of a power supply system to a high-power DC line and a battery.

The ripple cancel controller is connected to the output side of the charger that rectifies the AC voltage of the AC power source to obtain the DC voltage, the battery charged by the charger, and the input side of the inverter, and is based on the DC voltage input to the inverter Generate a ripple cancel signal consisting of a current with a waveform that changes periodically, and add the ripple cancel signal to the D-axis AC current converted by the converter to double the frequency of the commercial AC power generated by the charger To absorb current ripple.

According to the present invention, a ripple cancel signal including a current having a waveform that periodically changes based on a DC voltage input to an inverter is generated, and the ripple cancel signal is added to the D-axis AC current converted by the converter. in so absorbs the current ripple of twice the frequency of the frequency of the commercial AC power source generated by the charger, current ripple of twice the frequency of the power supply system to the battery is no longer delivered.

It is a figure which shows the structure of the charging system which concerns on Example 1 of this invention. It is a timing chart of phase difference (phi) of switch element Q1 and switch element Q5 in DAB of the charging system which concerns on Example 1 of this invention, and each switch element. It is a detailed block diagram of the charger controller of the charging system according to the first embodiment of the present invention. It is a detailed block diagram of the motor controller of the charging system which concerns on Example 1 of this invention. It is a figure which shows the operation | movement waveform of the voltage of each part of the charging system which concerns on Example 1 of this invention, an electric current, and electric power. It is a timing chart of each part when the active ripple cancellation controller in the motor controller of the charging system which concerns on Example 1 of this invention is ON. It is a figure which shows the operation waveform of the electric current and electric power of the motor of the charging system which concerns on Example 2 of this invention. It is a figure which shows the operation waveform of the electric current and electric power of the motor of the charging system which concerns on Example 3 of this invention.

Hereinafter, a charging system according to an embodiment of the present invention will be described in detail with reference to the drawings.
Example 1

  FIG. 1 is a diagram illustrating a configuration of a charging system according to Embodiment 1 of the present invention. This charging system includes a commercial AC power source 1, a terminal 2, a charger 3, a battery 4, an inverter 5, a motor 6, a motor controller 7 including an active ripple cancel controller 8, and a charger controller 10.

  The commercial AC power supply 1 outputs an AC voltage of a commercial system of 50 Hz or 60 Hz to the filter 31 in the charger 3 via the terminal 2 for insertion. The charger 3 rectifies the AC voltage of the commercial AC power supply 1 to obtain a DC voltage, and includes a filter 31, a rectifier 32, and a DAB (Dual Active Bridge) 33. The filter 31 includes capacitors C1 to C3 and a transformer T1, and removes noise included in the AC voltage of the commercial AC power supply 1.

  The capacitor C1 is connected to both ends of the terminal 2. In the transformer T1, the first winding n1 and the second winding n2 are electromagnetically coupled, one end of the first winding n1 is connected to one end of the capacitor C1, and the other end of the first winding n1 is one end of the capacitor C2. It is connected to the. One end of the second winding n2 is connected to the other end of the capacitor C1, and the other end of the second winding n2 is connected to one end of the capacitor C3. The other end of the capacitor C2 and the other end of the capacitor C3 are grounded.

  The rectifier 32 rectifies the AC voltage from the filter 31 and outputs the rectified voltage to the DAB 33. The DAB 33 includes a first bridge circuit 33a, a transformer T2, and a second bridge circuit 33b. The first bridge circuit 33a bridge-connects the first switch element Q1, the second switch element Q2, the third switch element Q3, and the fourth switch element Q4, and converts the rectified voltage of the rectifier 32 into a high frequency voltage. .

  Both ends of the series circuit of the first switch element Q1 and the second switch element Q2 and both ends of the series circuit of the third switch element Q3 and the fourth switch element Q4 are connected to the output terminal of the rectifier 32 and both ends of the capacitor C4. ing.

  In the transformer T2, the primary winding P and the secondary winding S are electromagnetically coupled, and the primary winding P has a connection point between the first switch element Q1 and the second switch element Q2, a third switch element Q3, and a fourth switch element. It is connected to a connection point with the switch element Q4. The secondary winding S is connected to a connection point between the fifth switch element Q5 and the sixth switch element Q6 and a connection point between the seventh switch element Q7 and the eighth switch element Q8.

  The second bridge circuit 33b bridge-connects the fifth switch element Q5, the sixth switch element Q6, the seventh switch element Q7, and the eighth switch element Q8, and converts the high-frequency voltage of the first bridge circuit 33a to DC via the transformer T2. The voltage is converted and supplied to the battery 4.

  By using the DAB 33 including the first bridge circuit 33a, the transformer T2, and the second bridge circuit 33b, the charger 3 can be reduced in size.

  Both ends of the series circuit of the fifth switch element Q5 and the sixth switch element Q6 and both ends of the series circuit of the seventh switch element Q7 and the eighth switch element Q8 are connected to both ends of the capacitor C5 and the input terminal of the inverter 5. ing. The first switch element Q1 to the eighth switch element Q8 are made of MOSFETs. The battery 4 is connected to the output side of the charger 3 and is charged by the charger 3 by turning on the switches SW1 and SW2.

  The inverter 5 is connected to the battery 4 via the output side of the charger 3 and the switches SW1 and SW2, and converts the DC voltage into AC. The inverter 5 is composed of a three-phase inverter, and includes a U-phase ninth switch element Q9 and a tenth switch element Q10, a V-phase eleventh switch element Q11 and a twelfth switch element Q12, a W-phase thirteenth switch element Q13, and a tenth switch element Q13. It has 14 switch elements Q14. The series circuit of the ninth switch element Q9 and the tenth switch element Q10, the series circuit of the eleventh switch element Q11 and the twelfth switch element Q12, and the series circuit of the thirteenth switch element Q13 and the fourteenth switch element Q14 are capacitors C5 and C6. Connected to both ends of the.

  The connection point between the ninth switch element Q9 and the tenth switch element Q10 is connected to the U-phase coil 6a of the motor 6, and the connection point between the eleventh switch element Q11 and the twelfth switch element Q12 is connected to the V-phase coil 6b. It is connected. A connection point between the thirteenth switch element Q13 and the fourteenth switch element Q14 is connected to the W-phase coil 6c. The ninth switch element Q9 to the fourteenth switch element Q14 are formed of insulated gate bipolar transistors (IGBT).

  The motor 6 is a three-phase motor, is connected to the output side of the inverter 5, and is driven to rotate by an alternating current from the inverter 5.

  A motor controller 7 having an active ripple cancel controller 8 is connected to both ends of the input of the inverter 5. The motor controller 7 generates a UVW-phase three-phase modulation rate command based on the motor rotation angle sensor reading from the motor 6, the current sensor readings from the UVW-phase current sensors 7a to 7c, and the voltage values at both ends of the inverter 5. Generate a value. The motor controller 7 controls the motor 6 by outputting the generated three-phase modulation factor command value to the UVW phase of the inverter.

  The active ripple cancel controller 8 is connected to the output side of the charger 3, the input side of the battery 4 and the inverter 5, and absorbs a current ripple having a frequency twice that of the commercial AC power source 1 generated in the charger 3. The charger controller 10 controls the transmission power P of the charger 3.

Next, the operation of the charging system according to the first embodiment configured as described above will be described with reference to the drawings. First, the AC voltage V and the AC current I from the commercial AC power source through the terminal 2 change positively and negatively at a frequency _fGRID of 50 Hz or 60 Hz as shown in FIG. Since the power is obtained by multiplying the AC voltage V and the AC current I, the frequency of the power P is twice the frequency _fGRID .

  Next, the AC voltage V and the AC current I that have passed through the filter 31 are output to the rectifier 32 and the charger controller 10. As shown in FIG. 3, the charger controller 10 includes a switch control unit 11, an LPF 101, an absolute value conversion unit 102, a conductance unit 103, a multiplier 104, a coefficient unit 105, a divider 106, and a coefficient unit 107.

  The switch control unit 11 alternately turns on and off one of the two switch elements Q1 and Q4 and the other two switch elements Q2 and Q3 arranged diagonally with respect to the first bridge circuit 33a with a duty of 50%. The switch control unit 11 alternately turns on and off one of the two switch elements Q5 and Q8 and the other two switch elements Q6 and Q7 arranged diagonally with respect to the second bridge circuit 33b with a duty of 50%.

  The switch control unit 11 controls the phase difference φ between the switch elements Q1 and Q4 and the switch elements Q5 and Q8 and the phase difference φ between the switch elements Q2 and Q3 and the switch elements Q6 and Q7. The electric power P is controlled.

This transmitted power P is expressed by the following formula (1).
P = E ₁ I ₁ = E ₂ I ₂ = E ₁ E ₂ φ (1-φ / π) / ωL (1)

Here, E ₁ is the input voltage of the first bridge circuit 33a, E ₂ is the output voltage of the second bridge circuit 33b, φ is the phase difference, and L is the primary winding P and secondary winding of the transformer T2. This is a leakage inductance with respect to S. ω = 2πf is an angular velocity, and f is a frequency of a voltage applied to the transformer T2.

The phase difference φ is transformed into equation (2) using equation (1). However, the part of (1-φ / π) is regarded as _1, and the control is aimed at such that I ₁ = kE ₁ . k is a certain conductance value.
φ = kE ₁ ωL / E ₂ (2)

  For this reason, the transmitted power P can be varied by adjusting the phase difference φ. FIG. 2 shows an example in which the phase difference φ between the pulse signal of the switch element Q1 and the pulse signal of the switch element Q5 is changed. The phase difference φ is generated by the following process of the charger controller 10.

First, the LPF 101 passes only a low frequency in the frequency of the AC voltage from the filter 31. The absolute value converting unit 102 generates the positive AC voltage E ₁ by ablating the AC voltage from the LPF 101. The conductance unit 103 outputs a reciprocal k of resistance, which is conductance, to the multiplier 104.

Multiplier 104 generates a target value of current I ₁ having the same phase as that of the positive AC voltage by multiplying the positive AC voltage from absolute value unit 102 by the reciprocal of the resistance that is the conductance. That is, as shown in FIG. 5, the phase of the voltage V of the first bridge circuit 33a and the phase of the current I can be made the same phase, and the power factor can be improved. The absolute value conversion unit 102, the conductance k generation unit 103, and the multiplier 104 correspond to the current generation unit of the present invention.

The coefficient unit 105 multiplies the current I from the multiplier 104 by a certain coefficient to generate a voltage E ₁ . Divider 106 corresponds to the divider of the present invention, it divides the signal from the coefficient multiplier 105 at a voltage E ₂ from the second bridge circuit 33b. The coefficient unit 107 multiplies the division output from the divider 106 by ωL to obtain the phase difference φ, and outputs the phase difference φ to the switch control unit 11. The coefficient unit 107 corresponds to the phase difference calculation unit of the present invention.

At the output of the second bridge circuit 33b, the voltage becomes a constant DC voltage V as shown in FIG. Since the power P is constant and the frequency is twice the frequency f _GRID , the frequency of the current I is also twice the commercial frequency _fGRID .

Next, the direct current voltage V and the direct current component of the current I from the second bridge circuit 33 b are input to the battery 4. The DC voltage V and the AC component of the current I from the second bridge circuit 33 b are input to the inverter 5. For this reason, the frequency of the alternating current component of the current I input to the inverter 5 is twice the commercial frequency _fGRID .

  At this time, the active ripple cancel controller 8 controls so that the current ripple from the second bridge circuit 33 b is absorbed and the current ripple is not sent to the battery 4. The active ripple cancel controller 8 and the motor controller 7 will be described with reference to FIG.

  First, in the motor controller 7, the coefficient unit 71 multiplies the motor rotation angle sensor reading value from the motor 6 by a certain coefficient and outputs the result to the UVW / DQ converter 72 and the DQ / UVW converter 80. The UVW / DQ converter 72 converts the three-phase AC current reading value of the inverter 5 detected by the three-phase current sensors 7a to 7c into the D-axis AC current and the Q-axis AC current, and the D-axis AC current. Is output to the adder 77, and the Q-axis AC current is output to the adder 74. The UVW / DQ converter 72 corresponds to the converter of the present invention.

  Next, in the active ripple cancel controller 8, the coefficient unit 84 multiplies the inverter DC voltage sensor reading value from the input terminal of the inverter 5 by a certain coefficient and outputs the result to the adder 87. The inverter DC voltage sensor reading value from the input terminal of the inverter 5 includes a current ripple having a frequency twice that of the commercial AC power supply 1.

  The coefficient unit 86 multiplies the DC voltage 85 that is the target value by a coefficient and outputs the result to the adder 87. The adder 87 subtracts the output from the coefficient unit 84 from the output from the coefficient unit 86 and outputs the result to the multiplier 89. The multiplier 89 multiplies the sine wave signal from the sine wave unit 88 and the output from the adder 87.

  The adder 91 adds the output from the multiplier 89 to the DC voltage 90 and outputs the result to the LPF 93 via the coefficient unit 92. The LPF 93 passes only the low frequency output from the coefficient unit 92. The limiter 94 limits the amplitude of the output from the LPF 93. The square root unit 95 obtains the square root of the output from the limiter 94 and outputs it to the multiplier 96.

  The multiplier 96 multiplies the sine wave signal from the sine wave unit 88 and the output from the square root unit 95 and outputs the multiplication output to the adder 77 as a ripple cancel signal. That is, the active ripple cancel controller 8 generates a ripple cancel signal composed of a current having a waveform that periodically changes based on the DC voltage input to the inverter 5. The ripple cancel signal, that is, the ripple canceling D-axis AC current includes a signal composed of the square root of the addition output obtained by adding the sine wave signal and the DC voltage (second DC voltage of the present invention). .

  The adder 77 absorbs the current ripple by subtracting the D-axis alternating current converted by the UVW / DQ converter 72 from the ripple cancel signal generated by the active ripple cancel controller 8. For this reason, current ripple is not sent to the battery 4 without using a power factor correction circuit, and the heat generation and noise of the battery 4 can be reduced.

  FIG. 6 shows a timing chart of each part when the active ripple cancel controller 8 is on. When the charger 3 is turned on at time t1, a ripple current having a large amplitude having 100 Hz which is twice the commercial frequency 50 Hz is generated. When the active ripple cancel controller 8 is turned on at time t2, the active ripple cancel controller 8 generates a ripple cancel signal. For this reason, since the ripple current having a large amplitude of 100 Hz is canceled by the D-axis AC current formed of the ripple cancel signal, the ripple current of the battery current is reduced.

  Further, since the motor 6 does not generate torque by using the D-axis AC current, vibration and noise are not generated from the motor 6 during the operation of the single-phase charger 3.

The sine wave signal of the D-axis alternating current has a frequency twice the commercial frequency _fGRID . That is, since the current ripple generated by the charger 3 is twice the frequency of the commercial frequency _fGRID , the frequency can be synchronized in order to cancel this current ripple component.

  Next, the PI compensator 78 and the adder 79 subtract the result of the proportional process P and the integral process I from the output of the adder 77 subjected to the proportional process P to obtain the D axis. It outputs to the DQ / UVW converter 80 as an alternating current. This D-axis alternating current is a signal composed of the square root of the added output obtained by adding the sine wave signal and the DC voltage.

  The adder 74 subtracts the Q-axis AC current from the DC voltage 73 that is the target value. The PI compensator 75 and the adder 76 subtract the result of the proportional processing P and the integration processing I from the output of the adder 74 subjected to the proportional processing P to obtain the Q-axis AC current. Output to the DQ / UVW converter 80. The DQ / UVW converter 80 converts the D-axis AC current from the adder 79 and the Q-axis AC current from the adder 76 into a UVW AC current, and outputs it as a three-phase modulation factor command value via the coefficient units 81 to 83. Output to the UVW switch elements Q9 to Q14 of the inverter 5.

  The inverter 5 performs on / off control of each of the UVW switch elements Q9 to Q14 based on the three-phase modulation rate command value from the motor controller 7 to convert direct current into alternating current, and supplies the alternating current to the motor 6. At this time, the D-axis AC current Id is a signal composed of the square root of the addition output obtained by adding the sine wave signal and the DC voltage. That is, since the input power to the motor is a sine wave, the control becomes easy.

Also, when L _D is the D axis inductance, i _{D_MAX} is the maximum value of the D axis AC current, i _{D_MIN} is the minimum value of the D axis AC current, f _GRID is the frequency of the commercial AC power supply 1, and P _{CHARGE_AVE} is the average power The following formula (3) is established.
L _D × (i _{D_MAX} ² −i _{D_MIN} ² ) / 2 × 2π × (2f _GRID ) = P _{CHARGE_AVE} (3)

That is, the amplitude of the current ripple generated by the single-phase charger 3 and the current ripple absorbed by the motor 6 can be matched, and the effect of absorbing the current ripple can be maximized.
(Example 2)

  FIG. 7 is a diagram illustrating operation waveforms of the motor current and power in the charging system according to the second embodiment of the present invention. In FIG. 7, the motor D-axis current Id is a sine wave signal having the same frequency as that of the commercial AC power supply 1.

  Even if the frequency of the D-axis AC current Id is the same as the frequency of the commercial AC power supply 1, the power P is a value obtained by multiplying the squared value of the motor D-axis current Id by a coefficient. The frequency is twice the frequency of the AC power supply 1. By setting the D-axis AC current Id to the same frequency as that of the commercial AC power supply 1, the input power to the motor 6 becomes a sine wave, so that control becomes easy.

  In this case, the frequency of the D-axis AC current Id can be made the same as the frequency of the commercial AC power supply 1 by changing the three-phase modulation rate command value output from the motor controller 7 to the inverter 5.

  Further, as shown in FIG. 7, the phase of the current Id composed of a sine wave signal is delayed by 45 ° + n × 180 ° (n is a natural number) with respect to the phase of the AC signal of the commercial AC power supply 1 shown in FIG. . For example, the phase of the AC signal of the commercial AC power supply 1 where the current is zero is zero, and the phase of the current Id consisting of a sine wave signal where the current is zero is 45 °.

  That is, the amplitude of the current ripple generated by the single-phase charger 3 and the current ripple absorbed by the motor 6 can be matched, and the effect of absorbing the current ripple can be maximized.

Further, when L _D is the D-axis inductance, i _{D_AMP} is the D-axis AC current, f _GRID is the frequency of the commercial AC power supply 1, and P _{CHARGE_AVE} is the average power, the following equation is established.
L _D × (i _{D_AMP} ² ) / 2 × 2π × (2f _GRID ) = P _{CHARGE_AVE} (4)

That is, the amplitude of the current ripple generated by the single-phase charger 3 and the current ripple absorbed by the motor 6 can be matched, and the effect of absorbing the current ripple can be maximized.
(Example 3)

  FIG. 8 is a diagram illustrating operation waveforms of the motor current and power in the charging system according to the third embodiment of the present invention. In FIG. 8, the D-axis AC current Id is a sine wave signal having the same frequency as that of the commercial AC power supply 1. For this reason, the effect similar to the effect of the charging system which concerns on Example 2 is acquired.

  Further, as shown in FIG. 8, the phase of the current Id composed of the sine wave signal is opposite to the phase of the current Id composed of the sine wave signal shown in FIG. For this reason, the phase of the current Id composed of the sine wave signal shown in FIG. 8 is delayed by 45 ° + n × 180 ° (n is a natural number) with respect to the phase of the AC signal of the commercial AC power supply 1. For example, the phase of the rising timing of the AC signal of the commercial AC power supply 1 where the current becomes zero is zero, and the phase of the rising timing of the current Id consisting of a sine wave signal where the current is zero is 225 °.

  Further, since the phase of the current Id consisting of the sine wave signal shown in FIG. 8 is opposite to the phase of the current Id consisting of the sine wave signal shown in FIG. What is necessary is just to input into the inverter 5. Even with such a configuration, the same effect as that of the charging system according to the second embodiment can be obtained.

  In addition, although the Example was described taking the electric vehicle as an example, the application destination of the present invention is not limited to the use of the automobile. For example, the present invention can also be applied to industrial equipment and electric appliances having an inverter and a motor.

DESCRIPTION OF SYMBOLS 1 Commercial AC power supply 2 Terminal 3 Charger 4 Battery 5 Inverter 6 Motor 7 Motor controller 7a-7c Current sensor 8 Active ripple cancellation controller 10 Charger controller 11 Switch control part 31 Filter 32 Rectifier 33a 1st bridge circuit 33b 2nd bridge Circuit 72 UVW / DQ converter 77 Adder 102 Absolute value conversion unit 103 Conductance unit 104 Multiplier 106 Divider 107 Coefficient unit T1, T2 Transformers Q1-Q14 1st switch element-14th switch element SW1, SW2 switch

Claims (7)

A charger that rectifies the AC voltage of the AC power source to obtain a DC voltage;
A battery connected to the output side of the charger and charged by the charger;
An inverter connected to the output side of the charger and the battery, for converting the DC voltage of the battery into AC and supplying AC to the motor;
A converter for converting a three-phase AC current of the U phase, V phase and W phase of the inverter into a D-axis AC current and a Q-axis AC current;
The converter is connected to the output side of the charger, the battery, and the input side of the inverter, and generates a ripple cancel signal comprising a current having a waveform that periodically changes based on the DC voltage input to the inverter, and the converter in example Bei a ripple cancellation controller to absorb the current ripple of twice the frequency of the frequency of the AC power generated in the charger by adding the ripple cancellation signal converted D-axis AC current,
The charger includes a first bridge circuit that bridges the first switch element to the fourth switch element, and converts the rectified voltage obtained by rectifying the AC voltage into a high-frequency voltage by switching, and
A transformer having a primary winding connected to the output side of the first bridge circuit;
A second bridge circuit that bridge-connects the fifth to eighth switch elements, is connected to a secondary winding of the transformer, converts the high-frequency voltage to the DC voltage via the transformer, and supplies the DC voltage to the battery; ,
For each of the first bridge circuit and the second bridge circuit, one two switch elements and the other two switch elements arranged diagonally are alternately turned on and off to switch one of the two switches of the first bridge circuit. The phase difference between the element and one of the two switch elements of the second bridge circuit and the phase difference between the other two switch elements of the first bridge circuit and the other two switch elements of the second bridge circuit are controlled. A switch control unit, a current generation unit that generates a current having the same phase as the phase of the AC voltage, a divider that divides a voltage based on the current generated by the current generation unit by the DC voltage of the second bridge circuit, ; and a charger controller including a phase difference calculator for calculating and outputting the phase difference based on dividing the output of the divider to the switch controller Charging system. The D-axis AC current, the charging system of claim 1, wherein in that it consists sine wave signal and a second DC voltage and the square root of the sum output that is obtained by adding the. The charging system according to claim 2 , wherein the frequency of the sine wave signal is twice the frequency of the AC power supply. L _D is the D-axis inductance, i _{D_MAX} is the maximum value of the D-axis AC current, i _{D_MIN} is the minimum value of the D-axis AC current, f _GRID is the frequency of the AC power supply, and P _{CHARGE_AVE} is the average power Formula L _D × (i _{D_MAX} ² −i _{D_MIN} ² ) / 2 × 2π × (2f _GRID ) = P _{CHARGE_AVE}
The charging system according to claim 2, wherein: Charging system of claim 1, wherein the D-axis AC current, which is characterized in that it consists of a sine wave signal of the same frequency of the AC power source. The charging system according to claim 5 , wherein the phase of the sine wave signal is delayed by 45 ° + n × 180 ° (n is a natural number) with respect to the phase of the AC power supply. When L _D is a D-axis inductance, i _{D_AMP} is a D-axis AC current, f _GRID is the frequency of the AC power supply, and P _{CHARGE_AVE} is an average power, the following formula L _D × (i _{D_AMP} ² ) / 2 × 2π × (2f _GRID ) = P _{CHARGE_AVE}
The charging system according to claim 5, wherein:

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