Method for estimating the current and the state of charge of a battery pack or cell, without direct detection of current under operating conditions

A method for estimating an operating current (I) dispensed by a battery pack or cell, comprising the steps of:

• acquiring characterization data of the battery pack or cell, related to measured time trends of a characterization voltage (Vm) and of a characterization current (Im) of the battery pack or cell, each time trend being associated with a respective value of a plurality of characterization temperature values (Tk);
• processing said characterization data to determine a plurality of parameters (P) of an operating model of the battery pack or cell, as a function of temperature and state of charge (SOC) of the battery pack or cell;
• while the battery pack or cell is under operating conditions, measuring an operating voltage (V) of the battery pack or cell and an operating temperature (T);
• estimating the operating current (I) of the battery pack or cell, by using said operating model, based on the measured operating voltage (V), on the measured operating temperature (T) and on said plurality of parameters (P);
• wherein the processing step comprises the following stages, performed for each value of said plurality of characterization temperature values (Tk):
• identifying a plurality of time observation windows (Wi) along the respective time trends of the characterization voltage (Vm) and of the characterization current (Im), associated with the characterization temperature (Tk), and detecting the respective characterization current (Imi) and characterization voltage (Vmi) values;
• at each observation window (Wi), calculating a respective value of the state of charge (SOCi) of the battery pack or cell;
• at each observation window (Wi), calculating a respective estimated voltage (VABi), by using the operating model of the battery pack or cell, as a function of respective nominal values of the parameters (P), and determining a respective error function (Ei) dependent on the difference between the estimated voltage (VABi) and the characterization voltage (Vmi) of the time observation window (Wi);
• at each observation window (Wi), calculating an actual value (Pi) for each of the plurality of parameters (P) of the model of the battery pack or cell, by minimizing said error function (Ei);
• associating the actual values (Pi) of the parameters calculated at the observation windows (Wi) with the respective state of charge (SOCi) and characterization temperature (Tk), to obtain said plurality of parameters (P) as a function of temperature and state of charge of the battery pack or cell;
• defining a thermal model of the battery pack or cell;
• in at least one measurement time interval, estimating the dissipated electric power (Pe) using the operating model of the battery pack or cell, based on the values, measured in said interval, of the voltage (V) and temperature (Te) of the battery pack or battery cell, and based on the parameters (P) corresponding to said temperature (Te) of the battery pack or battery cell;
• at the same at least one measurement time interval, estimating the dissipated thermal power (Pd) using the thermal model of the battery pack or cell, based on said temperature value (Tc) of the battery pack or battery cell and based on an ambient temperature value (Te), both temperature values being measured in said interval, and based on the parameters (P) corresponding to said temperature (Te) of the battery pack or battery cell;
• determining a difference (ΔP) between the dissipated electric power (Pe) and the dissipated thermal power (Pd) estimated;
• and
• correcting the parameters (P) according to said estimated difference (ΔP), so as to obtain corrected values of the parameters (P) which take into account degradation and/or aging phenomena.