Introduction to Battery Behavior and Simulations
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Batteries are electrochemical energy storage devices that convert stored chemical energy into electrical energy (and
vice versa during charging) through reversible redox reactions at the electrodes. From an electrical engineering
perspective, they are not ideal voltage sources: their behavior is governed by several interdependent parameters that
determine performance under real-world operating conditions.

Core Electrical Parameters
==========================

* **U (Terminal Voltage)**: The voltage measurable at the battery terminals. It equals the open-circuit voltage
  (OCV or U_ocv) minus voltage drops caused by internal effects.
* **I (Current)**: The flow of charge (positive convention for discharge). High currents (high C-rates) increase
  losses and heat generation.
* **Ri (Internal / Ohmic Resistance)**: The immediate resistive component inside the cell (electrodes, electrolyte,
  separators). It causes an instantaneous voltage drop ``ΔU = I × Ri`` and Joule heating ``P_loss = I² × Ri``. ``Ri``
  depends strongly on state-of-charge (SOC), temperature, current direction, and aging.
* **OCV**: The equilibrium voltage when no current flows; it is a nonlinear function of SOC (and temperature/chemistry).
  Typical Li-ion OCV curves range from ~3.0 V (empty) to ~4.2 V (full) per cell.
* **SOC (State of Charge)**: Remaining capacity as a percentage (0–100 %). Updated dynamically via coulomb
  counting: ``textSOC(t) = SOC(0) – (1 / Capacity) × ∫ I(τ) dτ`` where Capacity is in ampere-hours (``Ah``).

Additional dynamic effects include polarization (activation and concentration overpotentials) that cause delayed
voltage responses, self-discharge, capacity fade (State of Health, SOH), and strong temperature dependence
(performance improves with moderate heat but degrades or becomes unsafe at extremes).

Functionality of Battery Simulations
====================================

Battery simulations solve the model equations (usually ordinary differential equations for SOC and RC voltages) over
time for arbitrary current/power/temperature profiles. Typical outputs:

* Voltage and current response
* SOC/SOH evolution
* Heat generation and temperature rise (coupled electro-thermal models)
* Lifetime prediction under cycling or calendar aging

.. note::
    At the moment, this BalderHub project does not implement all of that in detail. If you are interested in
    contributing, feel free to reach out. Every contribution is warmely welcomed!

They are indispensable for:

* Virtual prototyping of battery packs and Battery Management Systems (BMS)
* Hardware-in-the-Loop (HIL) testing
* System-level optimization (e.g., in electric vehicles, grid storage, portable devices)
* Safety analysis (over-charge, thermal runaway)

In software (Python with SciPy/NumPy, MATLAB/Simulink, PyBaMM, etc.) these models run orders of magnitude faster than
physical tests and allow parameter sweeps that would be impractical experimentally.

This BalderHub package provides reusable test objects and fixtures to integrate such battery models into your Balder
test suites - enabling deterministic, repeatable simulation of battery behavior for device-under-test validation.