1 Answer
The discharge equation for a lead-acid battery typically follows the general behavior of a battery’s voltage and capacity as it discharges over time. It relates to the battery's terminal voltage, current, and state of charge (SOC). Here's a basic form of the equation:
\[ SOC(t) = SOC_0 - \frac{I \cdot t}{C} \]
Where:
- \( SOC(t) \) is the state of charge at time \( t \).
- \( SOC_0 \) is the initial state of charge (usually 100% when fully charged).
- \( I \) is the discharge current.
- \( C \) is the battery's capacity (in Ah).
- \( t \) is the time (in hours).
Lead-acid batteries' voltage decreases gradually with discharge. The terminal voltage \( V(t) \) can be approximated by the following relation:
\[ V(t) = V_{oc} - I \cdot R \]
Where:
- \( V_{oc} \) is the open-circuit voltage of the battery (which depends on the state of charge).
- \( I \) is the discharge current.
- \( R \) is the internal resistance of the battery.
The open-circuit voltage \( V_{oc} \) is often approximated by:
\[ V_{oc} = 2.1 \cdot (1 - SOC(t)) \]
This means the voltage decreases as the state of charge decreases, typically starting from about 2.1V per cell when fully charged.
As the battery discharges, the available capacity decreases, and the battery experiences an increase in internal resistance. This behavior can be modeled as:
\[ C(t) = C_0 \cdot (1 - \alpha \cdot t) \]
Where:
- \( C(t) \) is the available capacity at time \( t \).
- \( C_0 \) is the initial capacity at full charge.
- \( \alpha \) is a factor that represents the degradation over time (depends on battery age, usage, temperature, etc.).
In practice, battery discharge is affected by many variables, including temperature, rate of discharge, and battery aging, which makes the discharge process more complex. But the above relations provide a simplified way of understanding battery discharge behavior.
- State of Charge (SOC):
\[ SOC(t) = SOC_0 - \frac{I \cdot t}{C} \]
Where:
- \( SOC(t) \) is the state of charge at time \( t \).
- \( SOC_0 \) is the initial state of charge (usually 100% when fully charged).
- \( I \) is the discharge current.
- \( C \) is the battery's capacity (in Ah).
- \( t \) is the time (in hours).
- Voltage (V) as the battery discharges:
Lead-acid batteries' voltage decreases gradually with discharge. The terminal voltage \( V(t) \) can be approximated by the following relation:
\[ V(t) = V_{oc} - I \cdot R \]
Where:
- \( V_{oc} \) is the open-circuit voltage of the battery (which depends on the state of charge).
- \( I \) is the discharge current.
- \( R \) is the internal resistance of the battery.
The open-circuit voltage \( V_{oc} \) is often approximated by:
\[ V_{oc} = 2.1 \cdot (1 - SOC(t)) \]
This means the voltage decreases as the state of charge decreases, typically starting from about 2.1V per cell when fully charged.
- Capacity loss over time:
As the battery discharges, the available capacity decreases, and the battery experiences an increase in internal resistance. This behavior can be modeled as:
\[ C(t) = C_0 \cdot (1 - \alpha \cdot t) \]
Where:
- \( C(t) \) is the available capacity at time \( t \).
- \( C_0 \) is the initial capacity at full charge.
- \( \alpha \) is a factor that represents the degradation over time (depends on battery age, usage, temperature, etc.).
In practice, battery discharge is affected by many variables, including temperature, rate of discharge, and battery aging, which makes the discharge process more complex. But the above relations provide a simplified way of understanding battery discharge behavior.