Second harmonic generation for estimating the state of charge of lithium-ion batteries

A system for determining a state of charge in a battery containing a lithium-based electrolyte, the system comprising:

• a potentiostat for performing at least one cycle of charging a calibration battery to a maximum state of charge and discharging a calibration battery to a minimum state of charge;
• an ultrasonic transmitter configured to, for each of a plurality of states of charge, cause an ultrasonic wave to propagate through the calibration battery;
• an ultrasonic receiver configured to, for each of the plurality of states of charge, issue an output signal corresponding to an amplitude of a first harmonic of the ultrasonic wave and an amplitude of a second harmonic of the ultrasonic wave, the calibration battery being disposed between the ultrasonic transmitter and the ultrasonic receiver;
• and
• a processor coupled, directly or indirectly, to each of the ultrasonic transmitter and the ultrasonic receiver, the processor being configured to:
• for each of the plurality of states of charge, calculate a nonlinear parameter based on the amplitude of the first harmonic and the amplitude of the second harmonic;
• calculate a correlation between the nonlinear parameter and the state of charge of the calibration battery and store the correlation in memory;
• instruct the ultrasonic transmitter and the ultrasonic receiver to cause a further ultrasonic wave to propagate through a test battery and generate a further output signal corresponding to an amplitude of a first harmonic of the further ultrasonic wave and an amplitude of a second harmonic of the further ultrasonic wave;
• calculate a nonlinear parameter of the test battery based on the amplitude of the first harmonic of the further ultrasonic wave and the amplitude of the second harmonic of the further ultrasonic wave;
• determine a state of charge of the test battery based on the nonlinear parameter of the test battery and the stored correlation.