Method and apparatus for determining battery properties from complex impedance/admittance
First Claim
1. A device for determining values of at least one of 2n elements comprising an equivalent circuit model of an electrochemical cell or battery where n is an integer equal to or greater than two, said device comprising:
- measuring circuitry adapted to couple to said cell or battery and adapted to pass a periodic current through said cell or battery, to sense a periodic voltage across said cell or battery, and to determine a real part and an imaginary part of complex immittance of said cell or battery at a measurement frequency comprising a component frequency of said periodic current and said periodic voltage;
control circuitry coupled to said measuring circuitry and adapted to command said measuring circuitry to select each one of n said measurement frequencies thereby defining n said real parts, n said imaginary parts and n said measurement frequencies; and
,computation circuitry coupled to said measuring circuitry and to said control circuitry and adapted to numerically combine values of said n real parts, said n imaginary parts, and said n measurement frequencies to determine said values of at least one of said 2n elements comprising said equivalent circuit model of said electrochemical cell or battery.
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Abstract
A device includes a microprocessor or microcontroller and measures real and imaginary parts of complex immittance of a cell or battery at n discrete frequencies, where n is an integer number equal to or greater than 2. The device determines cell/battery properties by evaluating components of an equivalent circuit model comprising 2n frequency-independent elements. Equating real and imaginary parts of measured immittance to values appropriate to the model at the n measurement frequencies defines a system of 2n nonlinear equations. Introducing 2n intermediate variables permits solving these equations and leads to values for the 2n model elements. A table of element values contains virtually the same information as the spectrum of complex immittance over a wide frequency range but provides this information in a more concise form that is easier to store, analyze, and manipulate. Thus, the 2n element values may themselves comprise the desired result. If desired, however, a predetermined relationship between one or more of the elements and an additional electrical, chemical, or physical property of the cell/battery may be further invoked to determine the additional property.
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Citations
21 Claims
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1. A device for determining values of at least one of 2n elements comprising an equivalent circuit model of an electrochemical cell or battery where n is an integer equal to or greater than two, said device comprising:
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measuring circuitry adapted to couple to said cell or battery and adapted to pass a periodic current through said cell or battery, to sense a periodic voltage across said cell or battery, and to determine a real part and an imaginary part of complex immittance of said cell or battery at a measurement frequency comprising a component frequency of said periodic current and said periodic voltage; control circuitry coupled to said measuring circuitry and adapted to command said measuring circuitry to select each one of n said measurement frequencies thereby defining n said real parts, n said imaginary parts and n said measurement frequencies; and
,computation circuitry coupled to said measuring circuitry and to said control circuitry and adapted to numerically combine values of said n real parts, said n imaginary parts, and said n measurement frequencies to determine said values of at least one of said 2n elements comprising said equivalent circuit model of said electrochemical cell or battery. - View Dependent Claims (2, 3, 4)
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5. A device for determining an electrical, chemical, or physical property of an electrochemical cell or battery comprising:
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measuring circuitry adapted to couple to said cell or battery and adapted to pass a periodic current through said cell or battery, to sense a periodic voltage across said cell or battery, and to determine a real part and an imaginary part of complex immittance of said cell or battery at a measurement frequency comprising a component frequency of said periodic current and said periodic voltage; control circuitry coupled to said measuring circuitry and adapted to command said measuring circuitry to select each one of n said measurement frequencies thereby defining n said real parts, n said imaginary parts and n said measurement frequencies where n is an integer number equal to or greater than two; and
,computation circuitry coupled to said measuring circuitry and to said control circuitry and adapted to numerically combine values of said n real parts, said n imaginary parts, and said n measurement frequencies to determine said electrical, chemical, or physical property of said electrochemical cell or battery. - View Dependent Claims (6, 7, 8, 9)
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10. A method for determining an electrical, chemical, or physical property of an electrochemical cell or battery comprising the steps of:
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measuring real and imaginary parts of complex immittance of said electrochemical cell or battery at n discrete frequencies where n is an integer number equal to or greater than two; evaluating 2n intermediate variables by numerically combining values of said n discrete frequencies and values of said real and imaginary parts of said complex immittance at said n discrete frequencies; evaluating n-1 capacitive time constants by numerically combining values of n-1 of said 2n intermediate variables; evaluating an inductive time constant by numerically combining values of said n-1 capacitive time constants and values of two of said 2n intermediate variables; evaluating n resistive elements by numerically combining values of said n-1 capacitive time constants, the value of said inductive time constant, and values of n of said 2n intermediate variables; evaluating n reactive elements by numerically combining each value of said n resistive elements with a corresponding value of one of said n-1 capacitive time constants and said inductive time constant; and relating values of one or more of said resistive elements and said reactive elements to said electrical, chemical, or physical property of said electrochemical cell or battery. - View Dependent Claims (11, 18)
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12. A method for determining element values of an equivalent circuit model of an electrochemical cell or battery, said model comprising a series interconnection of a single two-element series R-L subcircuit and n-1 two-element parallel R-C subcircuits where n is an integer number equal to or greater than two, said method comprising the steps of:
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measuring real and imaginary parts of complex immittance of said electrochemical cell or battery at n discrete frequencies; evaluating 2n intermediate variables by numerically combining values of said n discrete frequencies and values of said real and imaginary parts of said complex immittance at said n discrete frequencies; evaluating n-1 capacitive time constants by numerically combining values of n-1 of said 2n intermediate variables; evaluating an inductive time constant by numerically combining values of said n-1 capacitive time constants and values of two of said 2n intermediate variables; evaluating a resistance of said single R-L subcircuit and n-1 resistances of said n-1 R-C subcircuits by numerically combining values of said n-1 capacitive time constants, the value of said inductive time constant, and values of n of said 2n intermediate variables; and
,evaluating an inductance of said R-L subcircuit and n-1 capacitances of said n-1 R-C subcircuits by numerically combining a resistance value for each said subcircuit with a corresponding time constant value associated with the same said subcircuit. - View Dependent Claims (13)
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14. A method for determining element values of an equivalent circuit model of an electrochemical cell or battery, said model comprising a series interconnection of a single two-element series R-L subcircuit and n-1 two-element parallel R-C subcircuits where n is an integer equal to or greater than two, said method comprising the steps of:
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measuring real and imaginary parts of complex immittance of said electrochemical cell or battery at n discrete frequencies where one of said n discrete frequencies is a high frequency; evaluating a resistance and an inductance of said R-L subcircuit by numerically combining the value of said high frequency and values of said real and imaginary parts of said complex immittance at said high frequency; evaluating a difference impedance at each of n-1 remaining frequencies by numerically combining values of said resistance, said inductance, and said remaining frequency, with the value of said complex immittance at each said remaining frequency; evaluating 2n-2 intermediate variables by numerically combining values of said n-1 remaining frequencies and values of real and imaginary parts of said difference impedance at said n-1 remaining frequencies; evaluating n-1 capacitive time constants of said n-1 R-C subcircuits by numerically combining values of n-1 of said 2n-2 intermediate variables; evaluating n-1 resistances of said n-1 R-C subcircuits by numerically combining values of said n-1 capacitive time constants and values of n-1 of said 2n-2 intermediate variables; and
,evaluating n-1 capacitances of said n-1 R-C subcircuits by numerically combining a resistance value of each said subcircuit with a corresponding capacitive time constant value of the same said subcircuit. - View Dependent Claims (15)
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16. A method for determining electrical, chemical, or physical properties of an electrochemical cell or battery comprising the steps of:
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measuring real and imaginary parts of complex immittance of said electrochemical cell or battery at n discrete frequencies where n is an integer number equal to or greater than two and one of said discrete frequencies is a high frequency; evaluating a first resistance and an inductance by numerically combining the value of said high frequency and values of said real and imaginary parts of said complex immittance at said high frequency; evaluating a difference impedance at each of n-1 remaining frequencies by numerically combining values of said first resistance, said inductance, and said remaining frequency with the value of said complex immittance at each of said n-1 remaining frequencies; evaluating 2n-2 intermediate variables by numerically combining values of said n-1 remaining frequencies and values of real and imaginary parts of said difference impedance at said n-1 remaining frequencies; evaluating n-1 time constants by numerically combining values of n-1 of said 2n-2 intermediate variables; evaluating n-1 second resistances by numerically combining values of said n-1 time constants and values of n-1 of said 2n-2 intermediate variables; evaluating n-1 capacitances by numerically combining the value of each of said n-1 second resistances with a corresponding value of each of said n-1 time constants; and
,relating values of one or more of said first resistance, said n-1 second resistances, said inductance, and said n-1 capacitances to said electrical, chemical, or physical property of said electrochemical cell or battery. - View Dependent Claims (17)
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19. A device for determining element values of an equivalent circuit model for an electrochemical cell or battery, said model comprising a series interconnection of single two-element series R-L subcircuit and n-1 two-element parallel R-C subcircuits where n is an integer number equal to or greater than two, said device adapted to perform the steps of:
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measuring real and imaginary parts of complex immittance of said electrochemical cell or battery at n discrete frequencies; evaluating 2n intermediate variables by numerically combining values of said n discrete frequencies and values of said real and imaginary parts of said complex immittance at said n discrete frequencies; evaluating n-1 capacitive time constants by numerically combining values of n-1 of said 2n intermediate variables; evaluating an inductive time constant by numerically combining values of said n-1 capacitive time constants and values of two of said 2n intermediate variables; evaluating a resistance of said single R-L subcircuit and n-1 resistances of said n-1 R-C subcircuits by numerically combining values of said n-1 capacitive time constants, the value of said inductive time constant, and values of n of said 2n intermediate variables; and
,evaluating an inductance of said R-L subcircuit and n-1 capacitances of said n-1 R-C subcircuits by numerically combining a resistance value for each said subcircuit with a corresponding time constant value associated with the same said subcircuit.
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20. A device for determining element values of an equivalent circuit model of an electrochemical cell or battery, said model comprising a series interconnection of single two-element series R-L subcircuit and n-1 two-element parallel R-C subcircuits where n is an integer number equal to or greater than two, said device adapted to perform the steps of:
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measuring real and imaginary parts of complex immittance of said electrochemical cell or battery at n discrete frequencies where one of said n discrete frequencies is a high frequency; evaluating a resistance and an inductance of said R-L subcircuit by numerically combining the value of said high frequency and values of said real and imaginary parts of said complex immittance at said high frequency; evaluating a difference impedance at each of n-1 remaining frequencies by numerically combining values of said resistance, said inductance, and said remaining frequency, with the value of said complex immittance at each said remaining frequency; evaluating 2n-2 intermediate variables by numerically combining values of said n-1 remaining frequencies and values of real and imaginary parts of said difference impedance at said n-1 remaining frequencies; evaluating n-1 capacitive time constants of said n-1 R-C subcircuits by numerically combining values of n-1 of said 2n-2 intermediate variables; evaluating n-1 resistances of said n-1 R-C subcircuits by numerically combining values of said n-1 capacitive time constants and values of n-1 of said 2n-2 intermediate variables; and
,evaluating n-1 capacitances of said n-1 R-C subcircuits by numerically combining a resistance value of each said subcircuit with a corresponding capacitive time constant value of the same said subcircuit.
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21. A device for determining an electrical, chemical, or physical property of an electrochemical cell or battery adapted to perform the steps of:
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measuring real and imaginary parts of complex immittance of said electrochemical cell or battery at n discrete frequencies where n is an integer number equal to or greater than two and one of said discrete frequencies is a high frequency; evaluating a first resistance and an inductance by numerically combining the value of said high frequency and values of said real and imaginary parts of said complex immittance at said high frequency; evaluating a difference impedance at each of n-1 remaining frequencies by numerically combining values of said first resistance, said inductance, and said remaining frequency with the value of said complex immittance at each of said n-1 remaining frequencies; evaluating 2n-2 intermediate variables by numerically combining values of said n-1 remaining frequencies and values of real and imaginary parts of said difference impedance at said n-1 remaining frequencies; evaluating n-1 time constants by numerically combining values of n-1 of said 2n-2 intermediate variables; evaluating n-1 second resistances by numerically combining values of said n-1 time constants and values of n-1 of said 2n-2 intermediate variables; evaluating n-1 capacitances by numerically combining the value of each of said n-1 second resistances with a corresponding value of each of said n-1 time constants; and
,relating values of one or more of said first resistance, said n-1 second resistances, said inductance, and said n-1 capacitances to said electrical, chemical, or physical property of said electrochemical cell or battery.
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Specification