Conductivity distribution derivation method and conductivity distribution derivation device

Patent metadata

Field	Value
Publication number	US-10254352-B2
Application number	US-201515124874-A
Country	US
Kind code	B2
Filing date	Mar 11, 2015
Priority date	Mar 12, 2014
Publication date	Apr 9, 2019
Grant date	Apr 9, 2019

Abstract

A conductivity distribution derivation method for deriving a conductivity distribution within a battery having an electrode plate that is flat includes: obtaining magnetic field information indicating a magnetic field; and deriving, based on a plurality of relational expressions which (i) an x component of a magnetic field vector in an x direction parallel to the electrode plate, (ii) a y component of the magnetic field vector in a y direction parallel to the electrode plate and perpendicular to the x direction, (iii) the conductivity distribution on a two-dimensional plane parallel to the electrode plate, and (iv) an electric potential distribution on a two-dimensional plane parallel to the electrode plate satisfy, the conductivity distribution that satisfies the plurality of relational expressions with respect to the magnetic field information.

First claim

The invention claimed is:

1. A conductivity distribution derivation method for deriving a conductivity distribution within a battery having an electrode plate that is flat, the method comprising:
causing an electric current to flow through a pair of electrode terminals of the battery;
while the electric current flows through the pair of electrode terminals of the battery, obtaining magnetic field information indicating a magnetic field around the battery;
based on a plurality of relational expressions representing a relationship of (i) an x component of a magnetic field vector in an x direction parallel to the electrode plate, (ii) a y component of the magnetic field vector in a y direction parallel to the electrode plate and perpendicular to the x direction, (iii) the conductivity distribution on a two-dimensional plane parallel to the electrode plate, and (iv) an electric potential distribution on a two-dimensional plane parallel to the electrode plate, deriving the conductivity distribution that satisfies the plurality of relational expressions with respect to the magnetic field information; and
displaying an image representing the conductivity distribution, the image representing the conductivity distribution indicating an electrical abnormality of the battery,
wherein the plurality of relational expressions include a first relational expression, a second relational expression, and a third relational expression, and
in the deriving, the conductivity distribution that is represented using σ is derived based on the first relational expression that is represented by [Math. 2], the second relational expression that is represented by [Math. 3], and the third relational expression that is represented by [Math. 4],
φ  [Math. 1]

Δ H x =h T −1 h∂ y {σ( x,y )φ( x,y )}δ( z−z 0 )−σ 0 h{∂ y φ( x,y )}δ′( z−z 0 )  [Math. 2]

Δ H y =−h T −1 h∂ x {σ( x,y )φ( x,y )}δ( z−z 0 )−σ 0 h{∂ y φ( x,y )}δ′( z−z 0 )  [Math. 3]

∂ x 2 φ+∂ y 2 φ=(σ 0 hh T ) −1 σ( x,y )φ( x,y )  [Math. 4]

where x denotes a coordinate in the x direction, y denotes a coordinate in the y direction, z denotes a coordinate in a z direction perpendicular to the x direction and the y direction, z 0 denotes a coordinate of the electrode plate in the z direction, H x denotes the x component of the magnetic field vector, H y denotes the y component of the magnetic field vector, h denotes a thickness of the electrode plate in the z direction, h T denotes a distance between one pair of electrode plates including the electrode plate, σ 0 denotes conductivity of the electrode plate, σ denotes the conductivity distribution, [Math. 1] denotes the electric potential distribution, δ denotes a delta function, δ′ denotes a differential of the delta function, ∂ x denotes a partial differential with respect to x, and ∂ y denotes a partial differential with respect to y.

2. The conductivity distribution derivation method according to claim 1 ,
wherein in the deriving, the conductivity distribution is derived based on a fourth relational expression represented by [Math. 7] and a fifth relational expression represented by [Math. 8], the fourth relational expression being based on the first relational expression, the second relational expression, and the third relational expression, the fifth relational expression being based on the third relational expression,

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Assignees

• Univ Kobe Nat Univ Corp
• Integral Geometry Science Inc

Inventors

• Kimura Kenjiro
• Kimura Noriaki

Classifications

• G01R31/3662 Primary

  Physics · mapped topic

• G01N27/72

  by investigating magnetic variables · CPC title

• G01R31/3651

  Physics · mapped topic

• G01R31/389 Primary

  Measuring internal impedance, internal conductance or related variables · CPC title

• G01R31/385

  Arrangements for measuring battery or accumulator variables (for monitoring G01R31/382) · CPC title