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Peukert’s Law

1897

Wilhelm Peukert

(generated image for illustration only)

An empirical formula that describes how the available capacity of a battery decreases as the rate of discharge increases. The law is stated as \(C_p = I^k t\), where \(C_p\) is the capacity at a one-ampere discharge rate, \(I\) is the discharge current, \(t\) is the discharge time, and \(k\) is the Peukert constant, specific to the battery type. It quantifies the inefficiency at high loads.

Peukert’s law provides a more accurate picture of battery capacity than the simple amp-hour rating, which is typically specified at a low, constant discharge rate. The law accounts for the fact that at high discharge rates, the battery becomes less efficient. This inefficiency stems from several factors. Firstly, the internal resistance of the battery causes energy to be lost as heat, a loss that increases with the square of the current (\(P_{loss} = I^2R\)). This wasted energy is unavailable to the load.

Secondly, the electrochemical processes within the battery have finite speeds. At high discharge rates, the chemical reactions cannot keep pace, and the diffusion of ions within the electrolyte becomes a bottleneck. This leads to a depletion of reactants near the electrodes’ surfaces, causing the voltage to drop prematurely and cutting off the discharge before all the active material has been utilized. The unused material means the effective capacity delivered is lower.

The Peukert constant, \(k\), is determined empirically and reflects how much a battery is affected by high discharge rates. A value of \(k\) close to 1 indicates an ideal battery that is not significantly affected by the discharge rate. Lead-acid batteries have a relatively high \(k\) (typically 1.1 to 1.3), while modern lithium-ion batteries have a \(k\) much closer to 1 (e.g., 1.05), indicating their superior performance under heavy loads.

Battery, Electrical Engineering, Electrical Resistance, Energy, Lithium, Process Optimization, Quality Management, Renewable Energy

UNESCO Nomenclature: 3305

– Electrical engineering

Type

Abstract System

Disruption

Substantial

Usage

Widespread Use

Precursors

Ohm’s Law and the concept of internal resistance
Development of practical, high-capacity batteries like the lead-acid cell
The need for predictable performance in industrial applications like electric traction and lighting
Experimental work on battery discharge curves

Applications

battery management systems (BMS) for accurate state-of-charge estimation
designing and sizing battery banks for off-grid solar systems
predicting the range of electric vehicles under different driving conditions
modeling battery performance in uninterruptible power supplies (UPS)

Patents:

Potential Innovations Ideas

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Related to: Peukert’s law, battery capacity, discharge rate, state of charge, battery management system, empirical formula, C-rate, internal resistance.

Historical Context

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Peukert’s Law

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Tsiolkovsky Rocket Equation

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Chloralkali Process

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Exothermic Welding

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