Battery models, systems, and methods using robust fail-safe iteration free approach for solving differential algebraic equations

A system for charging a rechargeable battery comprising:

• a computing device in electrical communication with a programmable chip on an electronics board, the computing device configured to:
• generate a model of the rechargeable battery;
• determine one or more initial conditions for one or more algebraic variables of the model using a solver based on perturbations;
• hold differential variables of the model static by a switch function while the one or more initial conditions are being determined for one or more algebraic variables;
• and
• apply the initial conditions to differential equations of the model by the switch function, and determine one or more parameters for the rechargeable battery by solving the algebraic and differential equations of the model with the solver;
• and
• the programmable chip of the electronics board configured to electrically connect a DC power supply to the rechargeable battery,
• wherein the electronics board is configured to adjust charging or discharging of the battery based on the one or more parameters received from the computing device,
• wherein the switch function is a tan h function.

A computer-readable storage device storing computer-executable instructions, the instructions causing charging a rechargeable battery by:

• generating, by a computing device, a model of the rechargeable battery;
• determining one or more initial conditions for one or more algebraic variables of the model using a solver based on perturbations;
• holding differential variables of the model static by a switch function while determining the one or more initial conditions for one or more algebraic variables;
• applying the initial conditions to differential equations of the model by the switch function;
• determining one or more parameters for the rechargeable battery by solving algebraic and differential equations of the model with the solver;
• and
• adjusting a state of the battery based on the one or more parameters,
• wherein the switch function is a tan h function.