Charging

• Charging current lower than discharging (e.g. 10x, 20x, etc.).
• Lithium ions Li + must intercalate into the graphite layers → it limits the charging speed.
• By charging, we transfer the cell to an unstable state.
• 
  
• The total charging current $I_{nab}$ is given by
• difference between the charging voltage and internal voltage,
• the size of the internal resistance $R_0$.

• Charging increases the battery voltage.
• By simultaneously increasing of $U_{nab}$, we maintain a constant charging current = constant current charging (1st charging step).
• However, the maximum cell voltage must not be exceeded.
• If $U_{nab}$ reaches the maximum level ($U_{nab} = U_{max}$ ), the voltage does not increase further and is constant = charging with constant voltage (2nd charging step, so-called saturation part).
• The charging current decreases exponentially => this charging is time consuming.
• Manufacturers often publish charging time needed to reach 70-80% capacity.
• Maximum cell voltage depends on technology:
  
  • usually 4.2 V for Co, Ni, Mn, Al.

                                  Step 1: constant current                                   Step 2: constant voltage

Li-ion battery charging

• The cell charging current is usually recommended to be 0.5-1C.
• To increase the battery service life, small charging currents are recommended.
• In parallel, do not charge to full SoC (e.g. do not start the saturation part) → reduced voltage stress.
• High charging currenta speed up the first part, but prolongs the saturation part.
  

Driving mode

• Rated power of the machine in motor and generator mode is practically the same.
• However, the rated charging current of the cell is about 10 times smaller than the rated discharging current!
• => Charging power is less than power of the generator or the battery must be oversized in terms of discharge current.
• Remaining braking torque must be provided by mechanical brakes.
• Often, recharging power is limited by battery management (BMS), depending on set limits or battery condition (cell disbalancing, temperature, etc.).
  

• Charging from standard household sockets or charging stands
• Paremeters in ČR: 230 V, 50 Hz, 16 A
• Power: $P = U I \cos\phi = 230 \cdot 16 \cdot 0.9 = 3.3 \space kW$ (estimated power factor)
• The current can be increased using the wallbox.
  
• The on-board charger converts the AC voltage and current from the household power grid to the DC voltage and current of the battery needs.
• At the same time, the BMS communicates with the charger.
• Be aware of long extension cables; on-board charging systems usually monitor the connection impedance.

• However, the hosehold socket voltage varies in different parts of the world.
• In case of 110 V is the power 1600 W only (at the same current of 16 A).

• Charging from standard household sockets or charging stands
• Parameters in ČR: 3x 400 V, 50 Hz, 16 A, alternatively 32 A in industrial plants
  
• Power:
• a) $P = 3 U I \cos\phi = 3 \cdot 230 \cdot 16 \cdot 0.9 = 10 \space kW$
  
• b) $P = 3 U I \cos\phi = 3 \cdot 230 \cdot 32 \cdot 0.9 = 20 \space kW$

• The on-board charger converts ac voltage and current of the household socket to the dc voltage and current of the battery.
  
• At the same time, the BMS communicates with the charger.