Automatic method for estimating the cell's state-of-charge of a battery

A method comprising using a battery-management system that comprises a programmable electronic-computer and a memory for automatically estimating a state-of-charge of a cell of a battery that powers an electric motor that causes an electric vehicle to move along a roadway and to do so based at least in part on measurements obtained by an ammeter and a voltmeter that are connected to said battery-management system, wherein said battery comprises cells that are grouped into stages that connect between first and second terminals thereof, wherein each of said stages comprises a plurality of branches that are connected in parallel, each of which comprises either one cell or several cells in series, wherein cell comprises connections that connect said cell to other cells and ultimately to said terminals of said battery, wherein each cell is modeled by a generator in series with a parallel RC circuit and an internal resistance, wherein said parallel RC circuit comprises a capacitor and a resistor, wherein said cell receives electrical energy while being charged and loses electrical energy while being discharged, wherein a complete discharging of a cell followed by a complete recharging constitutes a cycle of said cell, wherein automatically estimating said state-of-charge of said battery comprises implementing a technical improvement that comprises avoiding corruption caused by errors that arises when linearizing a non-linear observation model of a cell of said battery by causing said programmable electronic-computer by

• executing a first step, a second step, and a third step,
• wherein executing said first step comprises,
• at a first instant k from a series of first instants, using said voltmeter to acquire a measured voltage yk and using said ammeter to acquire a measured current ik, wherein said measured voltage is obtained by using said voltmeter to make a voltage measurement across terminals of said cell, and wherein said measured current is a current that at least one of charges and discharges said cell,
• wherein executing said second step comprises
• estimating a capacitance Cn,k3 of said cell at a second instant k3 from a series of second instants, wherein said capacitance Cn,k3 is indicative of a maximum amount of electrical energy that can be stored in said cell at said second instant k3, wherein said second instant k3 is a second instant that is closest to a corresponding first-instant k, wherein said second instants k3 occur less frequently than said first instants k,
• wherein estimating said capacitance comprises
• calculating a prediction of said capacitance Cn,k3 at a second instant using a state model that relates a capacitance Cn,k3 at said second instant to a capacitance Cn,k3−1 at a preceding second-instant k3−1, and
• correcting said prediction based at least in part on a measured current that is measured at a first instant that is closest to said second instant k3, wherein said measured current is a current that charges or discharges said cell,
• wherein executing said third step comprises
• using digital circuitry that implements an estimator, estimating a state-of-charge SOCk of said cell at said first instant k based at least in part on said measured voltage yk at said first instant, said measured current ik at said first instant, and said estimated capacitance Cn,k3 at said second instant,
• wherein calculating said prediction of said capacitance Cn,k3 comprises
• acquiring, at said second instant k3, a measurable physical quantity zk3, wherein said measurable physical quantity is defined by a summation
• z
• k
• ⁢
• ⁢
• 3
• =
• ∑
• m
• =
• k
• -
• N
• m
• =
• k
• -
• l
• ⁢
• i
• m
• wherein, within indices of said summation, k is a first instant that is closest to said second instant k3 and N is a positive integer, and wherein said measurable physical quantity zk3 at said second instant is equal to current at a preceding first-instant that precedes said first instant ik−1 when N is equal to 1,
• calculating a prediction {circumflex over (z)}k3 of said measurable physical quantity zk3 using an observation model that is given by
• z
• ^
• k
• ⁢
• ⁢
• 3
• =
• (
• SOC
• k
• -
• SOC
• k
• -
• N
• )
• NT
• e
• ·
• 3600
• ·
• C
• n
• ,
• k
• ⁢
• ⁢
• 3
• wherein, within said observation model, k is a first instant that is closest to said second instant k3, wherein SOCk−N is a state-of-charge of said cell at a prior first-instant k−N, and wherein Cn,k3 is, in said observation model, a prediction of said cell's capacitance at said second instant k3 prior to correction thereof, and
• correcting said prediction of said capacitance Cn,k3 at said second instant based at least in part on a difference between said acquired physical quantity zk3 and said prediction {circumflex over (z)}k3 of said measurable physical quantity as calculated from said observation model,
• whereby said technical improvement that comprises avoiding corruption caused by errors that arises when linearizing a non-linear observation model of a cell of said battery is realized.