Battery Power Calculation

Part 1. Understanding basic battery terminology

Before diving into power calculations, it's crucial to understand key battery terms that frequently appear in formulas and discussions.

• Voltage (V): The electric potential difference across the battery terminals, measured in volts. It drives the current through a circuit.

• Current (I): The flow rate of electric charge, measured in amperes (amps). It represents how much charge moves through the battery per second.

• Capacity (Ah or mAh): The total charge a battery can store, expressed in ampere-hours (Ah) or milliampere-hours (mAh). It indicates how long a battery can supply current before running out.

• Power (W): The rate at which energy is transferred or used, measured in watts. It is the product of voltage and current (P = V × I).

• Energy (Wh): The total amount of work a battery can do, measured in watt-hours. It equals power multiplied by time.

• State of Charge (SoC): The current charge level of a battery expressed as a percentage of its full capacity.

Understanding these terms allows us to accurately calculate and interpret battery power under different conditions.

Part 2. Battery pack power calculation

1 What is a Battery Pack?

A battery pack consists of multiple cells connected in series, parallel, or a combination of both to meet voltage and capacity requirements.

• Series connection: Increases voltage by adding the voltage of each cell. The capacity (Ah) remains the same.

• Parallel connection: Increases capacity by adding the capacity of each cell. Voltage remains the same.

2 Calculating Battery Pack Voltage and Capacity

• Total voltage in series: Vtotal​=Vcell​×Nseries​

• Total capacity in parallel:Ctotal​=Ccell​×Nparallel​

3 Power Calculation Formula

Power output from a battery pack can be calculated using the fundamental formula:

P=V×I

Where:

• P = power in watts (W)

• V = voltage in volts (V)

• I = current in amperes (A)

Suppose you have a battery pack made of 4 lithium-ion cells in series (each 3.7 V, 2 Ah), and the load draws 5 A current.

• Total voltage: 3.7×4=14.8 V

• Current: 5 A (same for series connection)

• Power: 14.8×5=74 W

Thus, the battery pack delivers 74 watts of power under this load.

Part 3. Battery charging power calculation

Charging power is the amount of electrical power supplied to a battery during the charging process. Accurate charging power calculation helps in designing appropriate chargers and avoiding battery damage.

1 Factors Affecting Charging Power

• Charger voltage: Must be slightly higher than battery voltage to push current.

• Charging current: Determines how fast the battery charges.

• Charging efficiency: Losses due to heat and chemical reactions reduce effective power.

2 Formula for Charging Power

Charging power can be calculated as:

Pcharge=Vcharge×Icharge×η

Where:

• Pcharge​ = charging power (W)

• Vcharge​ = charger voltage (V)

• Icharge​ = charging current (A)

• η = charging efficiency (typically 80-95%)

3 Charging Power for Different Battery Chemistries

Lithium-ion batteries require controlled charging voltage and current for safety, while lead-acid batteries typically use a constant voltage charging method. This influences charging power:

• Lithium-ion: Constant current-constant voltage (CC-CV) charging profile.

• Lead-acid: Bulk, absorption, and float stages affect charging power.

Example:

A lithium-ion battery pack charged at 16.8 V with a 3 A charging current and 90% efficiency:

Pcharge=16.8×3×0.9=45.36 W

This means about 45.36 watts are used to charge the battery.

Part 4. Battery discharge power calculation

Battery discharge power is the power output when the battery supplies energy to a load.

1Importance of Discharge Power

• Determines the load size the battery can support.

• Helps estimate runtime and battery life.

• Critical for applications requiring bursts of high power.

2 How to Calculate Discharge Power

The basic formula is the same as for power in general:

Pdischarge=Vdischarge×Idischarge

Where:

• Vdischarge​ is the battery voltage under load (usually less than nominal voltage due to internal resistance).

• Idischarge​ is the discharge current.

3 Factors Influencing Discharge Power

• Load resistance: Heavier load increases current and power draw.

• Internal resistance: Causes voltage drop, reducing available voltage at the load.

• Discharge rate (C-rate): Higher rates increase power but may reduce efficiency and capacity.

If a battery’s nominal voltage is 12 V, but under a load, the voltage drops to 11.5 V and the current drawn is 10 A:

Pdischarge=11.5×10=115 W

Part 5. Energy vs. power in battery systems

Understanding the distinction between energy and power is crucial for battery applications.

• Power is the rate of energy delivery (W).

• Energy is the total work done over time (Wh).

Calculating Energy Stored and Delivered

Energy stored in a battery is:

E=V×C

Where:

• E = energy in watt-hours (Wh)

• V = nominal voltage (V)

• C = capacity in ampere-hours (Ah)

A 12 V battery with 100 Ah capacity stores:

E=12×100=1200 Wh

If the load draws 100 W, the estimated runtime is:

t=E/P=1200/100=12 hours

Part 6. Impact of temperature and efficiency on battery power

Temperature Effects

Temperature significantly affects battery performance:

• Low temperatures reduce chemical activity, lowering voltage and capacity.

• High temperatures increase internal resistance and risk of damage.

Efficiency Losses

Not all power supplied or delivered is usable:

• Charging and discharging involve losses (heat, internal resistance).

• Typical round-trip efficiency ranges between 80%-95%.

Adjusting Power Calculations

Account for efficiency:

Peffective​=P×η

Where η is efficiency factor.

Part 7. Power calculation for different battery types

Battery chemistry impacts voltage, capacity, charging, and discharging characteristics.

Power calculations must consider nominal voltage and behavior specific to battery chemistry.

Part 8. Tools and software for battery power calculation

Online Calculators

Several websites offer battery power calculators that allow you to input voltage, current, capacity, and configuration to compute power and energy quickly.

Battery Management Systems (BMS)

Modern batteries often come with BMS that monitor voltage, current, temperature, and calculate real-time power and energy for safety and efficiency.

Spreadsheet Templates

Many engineers use Excel or Google Sheets to customize calculations, allowing detailed input of variables such as temperature, efficiency, and load profiles.

Part 9. FAQ