System and methods for battery recharging

A method for charging a rechargeable battery, comprising:

• connecting a first DC voltage source to an input terminal of an H-bridge circuit, wherein the H-bridge circuit comprises four transistor switches, wherein each transistor switch includes a gate contact;
• connecting a microcontroller to the gate contacts of each of the four transistor switches;
• connecting an output terminal of the H-bridge circuit to a positive terminal of the rechargeable battery;
• connecting a second DC voltage source to the positive terminal of the rechargeable battery, wherein the second DC voltage source is a lead battery;
• generating, by the microcontroller, drive signals configured to control the four transistor switches;
• transmitting the drive signals to the gates of each of the four transistor switches, wherein the drive signals cause the H-bridge circuit to form a sinusoidal with ripple current at the output terminal of the H-bridge circuit;
• measuring, by an impedance meter connected to the microcontroller, an internal impedance of the rechargeable battery;
• performing, by the microcontroller, an autosearch algorithm to identify a frequency of the sinusoidal with ripple current at which the rechargeable battery has a minimum internal impedance by iteratively incrementing the frequency by a frequency step size which has an initial large value which is decreased after each iteration by dividing the frequency step size by two;
• after each iteration, measuring, by the impedance meter, the internal impedance of the battery;
• calculating, by the microcontroller, a phase value of the internal impedance after each iteration;
• comparing the phase value at each step of the iteration to a phase error threshold ε;
• when the phase value is less than the phase error threshold ε, identifying, by the microcontroller, the frequency as a minimum frequency at which an imaginary part of the battery impedance is zero;
• measuring, by the impedance meter, a phase of a voltage at the input terminal of the battery and a phase of a current between the output terminal of the H-bridge and the input terminal of the battery at each iteration;
• calculating, by the microcontroller, a phase difference between the phase of the current and the phase of the voltage;
• comparing the phase difference to the phase error threshold ε;
• when the phase difference is greater than the phase error threshold ε, iteratively incrementing the frequency by incrementing a previous frequency fk−1 by an amount given by:
• −α (512/2N), where a is a sign of the phase difference, and N is a number of the sign changes in the phase difference from k equals one to k equals k−1, where k equals an iteration number, where N equals zero at k equals one until the phase difference is less than the phase error threshold ε;
• identifying, by the microcontroller, the frequency as a minimum frequency at which an imaginary part of the battery impedance is zero;
• adjusting, by the microcontroller, the drive signals to generate the sinusoidal with ripple current at the minimum frequency;
• transmitting, by the microcontroller, the adjusted drive signals to the gates of each of the four transistor switches;
• injecting the sinusoidal with ripple current at the minimum frequency into the rechargeable battery;
• and
• recharging the battery with the sinusoidal with ripple current at the minimum frequency.