Method, system and computer-readable media for measuring impedance of an energy storage device
Real-time battery impedance spectrum is acquired using a one-time record. Fast Summation Transformation (FST) is a parallel method of acquiring a real-time battery impedance spectrum using a one-time record that enables battery diagnostics. An excitation current to a battery is a sum of equal amplitude sine waves of frequencies that are octave harmonics spread over a range of interest. A sample frequency is also octave and harmonically related to all frequencies in the sum. A time profile of this sampled signal has a duration that is a few periods of the lowest frequency. A voltage response of the battery, average deleted, is an impedance of the battery in a time domain. Since the excitation frequencies are known and octave and harmonically related, a simple algorithm, FST, processes the time profile by rectifying relative to sine and cosine of each frequency. Another algorithm yields real and imaginary components for each frequency.
1. A method of measuring impedance of an energy storage device, comprising:
generating an excitation time record comprising a summation of one or more sinusoidal signals with a frequency step factor of octave harmonics therebetween;
stimulating an energy storage device with the excitation time record;
during the stimulating, capturing a response time record at a sampling frequency, the response time record indicative of a response of the energy storage device to the excitation time record; and
rectifying the response time record relative to a sine and a cosine for at least one of the one or more sinusoidal signals to determine at least one of an in-phase component and a quadrature component of an impedance of the energy storage device.
2. The method of claim 1 , wherein capturing the response time record further comprises capturing the response time record at the sampling frequency that is octave related and harmonically related to frequencies of the one or more sinusoidal signals of the excitation time record.
3. The method of claim 2 , wherein capturing the response time record at the sampling frequency further comprises capturing at a frequency that is at least four times a highest frequency of the one or more sinusoidal signals.
4. The method of claim 1 , further comprising:
determining measurement conditions having known magnitude and phase for each frequency to be detected within the excitation time record for excitation current for the act of stimulating the energy storage device; and
conditioning the excitation time record to be compatible with measurement conditions prior to the act of stimulating the energy storage device.
5. The method of claim 4 , wherein the excitation current is a Root Mean Square (RMS) level of current.
6. The method of claim 1 , wherein rectifying the response time record further comprises rectifying the response time record relative to the sine at each frequency of the one or more sinusoidal signals with a sine rectification sum.
7. The method of claim 1 , wherein rectifying the response time record further comprises rectifying the response time record relative to the cosine at each frequency of the one or more sinusoidal signals with a cosine rectification sum.
8. The method of claim 1 , wherein rectifying the response time record further comprises:
rectifying the response time record relative to a sine for each frequency of the one or more sinusoidal signals with a sine rectification sum to obtain a sine-rectified response time record for each frequency of the one or more sinusoidal signals;
summing the sine-rectified response time record for each frequency of the one or more sinusoidal signals to obtain a sine-rectified response time sum;
generating a normalized sine-rectified response by dividing the response time record by a number of periods for the sine for each frequency of the one or more sinusoidal signals;
rectifying the response time record relative to a cosine for each frequency of the one or more sinusoidal signals with a cosine rectification sum to obtain a cosine-rectified response time record for each frequency of the one or more sinusoidal signals;
summing the cosine-rectified response time record for each frequency of the one or more sinusoidal signals to obtain a cosine-rectified response time sum;
generating a normalized cosine-rectified response by dividing the response time record by a number of periods for the cosine for each frequency of the one or more sinusoidal signals; and
using the normalized sine-rectified response time sum and the normalized cosine-rectified response time sum in determining the in-phase component and the quadrature component of the impedance of the energy storage device.
9. The method of claim 1 , wherein rectifying the response time record relative to the sine at each of the one or more sinusoidal signals is performed for sinusoidal signals that pass through zero at a discrete time step, wherein N is a number of samples over a period of time.
10. The method of claim 1 , wherein rectifying the response time record relative to the cosine at each of the one or more sinusoidal signals is performed for sinusoidal signals that pass through zero at a discrete time step, wherein N is a number of samples over a period of time.
11. The method of claim 1 , further comprising the acts of:
repeating, at least once, the original acts of:
generating the excitation time record, stimulating the energy storage device, capturing the response time record at the sampling frequency, and rectifying the response time record, wherein the one or more sinusoidal signals are phase shifted in the repeated acts relative to the original acts; and
interleaving the response time record of the original acts with the response time record of the repeated acts to obtain a higher resolution response time record.
12. A computing system configured for executing instructions for determining impedance of an energy storage device, the instructions configured to cause the computing system to:
generate an excitation time record comprising a summation of one or more sinusoidal signals with a frequency step factor of octave harmonics therebetween;
stimulate an energy storage device with the excitation time record;
during the stimulating, capture a response time record at a sampling frequency, the response time record indicative of a response of the energy storage device to the excitation time record; and
rectify the response time record relative to a sine and a cosine for at least one of the one or more sinusoidal signals to determine at least one of an in-phase component and a quadrature component of an impedance of the energy storage device.
13. The computing system of claim 12 , wherein the instructions are further configured to cause the computing system to capture the response time record at the sampling frequency that is octave related and harmonically related to frequencies of the one or more sinusoidal signals of the excitation time record.
14. The computing system of claim 13 , wherein the instructions are further configured to cause the computing system to capture the response time record at the sampling frequency that is at least four times a highest frequency of the one or more sinusoidal signals.
15. The computing system of claim 12 , wherein the instructions are further configured to cause the computing system to:
determine measurement conditions having known magnitude and phase for each frequency to be detected within the excitation time record for an excitation current for the act of stimulating the energy storage device; and
condition the excitation time record to be compatible with measurement conditions prior to the act of stimulating the energy storage device.
16. The computing system of claim 15 , wherein the excitation current is a Root Mean Square (RMS) level of current.
17. The computing system of claim 12 , wherein the instructions are further configured to cause the computing system to rectify the response time record relative to the sine at each frequency of the one or more sinusoidal signals with a sine rectification sum.
18. The computing system of claim 12 , wherein the instructions are further configured to cause the computing system to rectify the response time record relative to the cosine at each frequency of the one or more sinusoidal signals with a cosine rectification sum.
19. The computing system of claim 12 , wherein the instructions are further configured to:
rectify the response time record relative to a sine for each frequency of the one or more sinusoidal signals with a sine rectification sum to obtain a sine-rectified response time record for each frequency of the one or more sinusoidal signals;
sum the sine-rectified response time record for each frequency of the one or more sinusoidal signals to obtain a sine-rectified response time sum;
generate a normalized sine-rectified response by dividing the response time record by a number of periods for the sine for each frequency of the one or more sinusoidal signals;
rectify the response time record relative to a cosine for each frequency of the one or more sinusoidal signals with a cosine rectification sum to obtain a cosine-rectified response time record for each frequency of the one or more sinusoidal signals;
sum the cosine-rectified response time record for each frequency of the one or more sinusoidal signals to obtain a cosine-rectified response time sum;
generate a normalized cosine-rectified response by dividing the response time record by a number of periods for the cosine for each frequency of the one or more sinusoidal signals; and
use the normalized sine-rectified response time sum and the normalized cosine-rectified response time sum in determining the in-phase component and the quadrature component of the impedance of the energy storage device.
20. The computing system of claim 12 , wherein the instructions are further configured to rectify the response time record relative to the sine at each of the one or more sinusoidal signals that pass through zero at a discrete time step, wherein N is a number of samples over a period of time.
21. The computing system of claim 12 , wherein the instructions are further configured to rectify the response time record relative to the cosine at each of the one or more sinusoidal signals that pass through zero at a discrete time step, wherein N is a number of samples over a period of time.
22. The computing system of claim 12 , wherein the instructions are further configured to:
repeat, at least once, the original acts of:
generating the excitation time record, stimulating the energy storage device, capturing the response time record at the sampling frequency, and rectifying the response time record, wherein the one or more sinusoidal signals are phase shifted in the repeated acts relative to the original acts; and
interleave the response time record of the original acts with the response time record of the repeated acts to obtain a higher resolution response time record.
23. Non-transitory computer-readable media including instructions, which when executed by a computing system cause the computing system to:
capture a response time record at a sampling frequency during stimulation of an energy storage device with an excitation time record, the excitation time record comprising a summation of one or more sinusoidal signals with a frequency step factor of octave harmonics therebetween, and the response time record indicative of a response of the energy storage device to the excitation time record; and
rectify the response time record relative to a sine and a cosine for at least one of the one or more sinusoidal signals to determine at least one of an in-phase component and a quadrature component of an impedance of the energy storage device.
24. The non-transitory computer-readable media of claim 23 , wherein the instructions are further configured to cause the computing system to capture the response time record at the sampling frequency that is octave related and harmonically related to frequencies of the one or more sinusoidal signals of the excitation time record.
25. The non-transitory computer-readable media of claim 24 , wherein the instructions are further configured to cause the computing system to capture the response time record at the sampling frequency that is at least four times a highest frequency of the one or more sinusoidal signals.