Battery system and method with capacity estimator

An electrochemical battery system, comprising:

• at least one electrochemical cell;
• a first sensor configured to generate a current signal indicative of an amplitude of a current passing into or out of the at least one electrochemical cell;
• a second sensor configured to generate a voltage signal indicative of a voltage across the at least one electrochemical cell;
• a memory in which command instructions and a reduced observer model configured to generate estimates of state of charge (SoC) of the at least one electrochemical cell are stored;
• and
• a processor configured to execute the command instructions to obtain the current signal and the voltage signal, and to generate an estimated cell nominal capacity (Cnom) of the at least one electrochemical cell by
• monitoring the at least one electrochemical cell during a first charging sequence comprising:
• applying a first charging current to the at least one electrochemical cell for a first predetermined time period;
• ceasing the first charging current for a first predetermined rest period following the first predetermined time period during which no charging current is applied to the at least one electrochemical cell;
• measuring a first open circuit voltage level of the at least one electrochemical cell during the first predetermined rest period using the second sensor;
• applying the first charging current at the first current level to the at least one electrochemical cell for a second predetermined time period following the first rest period;
• measuring a first charging voltage level of the at least one electrochemical cell during at least one of the first predetermined time period and the second predetermined time period;
• and
• measuring a first current level (u1) of the first charging current using the first sensor during at least one of the first predetermined time period and the second predetermined time period;
• generating an estimated first leg Cnom1 of the at least one electrochemical cell during the first charging sequence based on:
• a first estimated SoC for the at least one electrochemical cell during the first charging sequence and the first current level (u1), the processor generating the first estimated SoC using the reduced observer model stored in the memory applied to a predetermined initial estimate of the state of charge Cnom, E, the first current level (u1), and a difference between the first open circuit voltage level and the first charging voltage level, the first estimated state of charge Cnom1 including a first error produced by a current measurement offset (δu) of the first sensor;
• monitoring the at least one electrochemical cell during a second charging sequence comprising:
• applying a second charging current to the at least one electrochemical cell for a third predetermined time period, the second charging current being different than the first charging current;
• ceasing the second charging current for a second predetermined rest period following the third predetermined time period during which no charging current is applied to the at least one electrochemical cell;
• measuring a second open circuit voltage level of the at least one electrochemical cell during the second predetermined rest period using the second sensor;
• applying the second charging current at the second current level for a fourth predetermined time period following the second rest period;
• measuring a second charging voltage level of the at least one electrochemical cell during at least one of the third predetermined time period and the fourth predetermined time period;
• and
• measuring a second current level (u2) of the second charging current using the first sensor during at least one of the third predetermined time period and the fourth predetermined time period;
• generating an estimated second leg Cnom2 of the at least one electrochemical cell during the second charging sequence based on:
• a second estimated SoC for the at least one electrochemical cell during the second charging sequence and the second current level (u2), the processor generating the second estimated SoC using the reduced observer model stored in the memory applied to the predetermined initial estimate of the state of charge Cnom,E, the second current level u2, and a difference between the second open circuit voltage level and the second charging voltage level, the second estimated state of charge Cnom2 including a second error produced by the current measurement offset (δu) of the first sensor;
• and
• generating, with the processor, the estimated cell nominal capacity Cnom based upon the estimated first leg Cnom1, the estimated second leg Cnom2, the first current level (u1), and the second current level (u2), the estimated cell nominal capacity Cnom not including an error produced by the current measurement offset (δu) of the first sensor.