Peukert's law

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Peukert's Law , presented by German scientist Wilhelm Peukert in 1897, reveals approximately the change in the capacity of rechargeable lead-acid batteries at different discharge rates. As the discharge rate increases, the available battery capacity decreases, approximately according to Peukert's law.

Video Peukert's law

Battery

The manufacturer determines the battery capacity at the specified discharge rate. For example, a battery may be rated at 100 A ° when it runs out at a rate that will completely discharge the battery within 20 hours (at 5 amperes for this example). If removed at a faster rate, the capacity is sent less. Peukert's law describes the power relationships between discharge currents (normalized to some base rated current) and the capacity transmitted (normalized to rated capacity) over some range of discharge currents. If Peukert is constant ${\ displaystyle k}$ , exponent, same as unity, capacity sent will be out of stream. For real batteries, exponents are larger than a single unit, and capacity decreases as the rate of discharge increases. For lead-acid batteries ${\ displaystyle k}$ is usually between 1.1 and 1.3. For different lead acid rechargeable battery technology usually ranges from 1.05 to 1.15 for AGM VRSLAB batteries, from 1.1 to 1.25 for the gel, and 1.2-2.6 for the batteries being flooded. Peukert's constant varies with battery age, generally increasing (getting worse) with age. Applications at low discharge levels should take into account the battery self-discharge current. At very high currents, a practical battery will give less capacity than predicted with fixed exponents. The equation does not take into account the effect of temperature on battery capacity.

Maps Peukert's law

Formula

Untuk tingkat debit satu ampere, hukum Peukert sering dinyatakan sebagai

${\ displaystyle C_ {p} = I ^ {k} t,}  ÂÂ$

dimana:

${\ displaystyle C_ {p}}  ÂÂ$ adalah kapasitas pada tingkat debit satu-ampere, yang harus dinyatakan dalam jam ampere,

${\ displaystyle I}  ÂÂ$ adalah arus keluar aktual (yaitu saat ini diambil dari beban) di ampere,

${\ displaystyle t}  ÂÂ$ adalah waktu aktual untuk mengeluarkan baterai, yang harus dinyatakan dalam jam.

${\ displaystyle k}  ÂÂ$ adalah konstanta Peukert (tanpa dimensi),

Kapasitas pada tingkat debit satu ampere biasanya tidak diberikan untuk sel praktis. Dengan demikian, dapat bermanfaat untuk merumuskan ulang undang-undang ke kapasitas dan tingkat debit yang diketahui:

${\ displaystyle t = H \ kiri ({\ frac {C} {IH}} \ right) ^ {k}}  ÂÂ$

dimana:

$            {\displaystyle         H      }        \{\backslash \; displaystyle\; H\}\;  ÂÂ$ adalah waktu pengosongan yang ditentukan (dalam jam),

${\ displaystyle C}  ÂÂ$ adalah kapasitas pengenal pada tingkat debit tersebut (dalam jam ampere),

${\ displaystyle I}  ÂÂ$ adalah arus keluar aktual (dalam ampere),

${\ displaystyle k}  ÂÂ$ adalah konstanta Peukert (tanpa dimensi),

${\ displaystyle t}  ÂÂ$ adalah waktu aktual untuk mengeluarkan baterai (dalam jam).

Dengan menggunakan contoh di atas, jika baterai memiliki konstanta Peukert 1,2 dan dibuang pada laju 10 ampere, baterai akan habis dalam waktu ${\ displaystyle 20 {\ left ({\ frac {100} {10 \ cdot 20}} \ right) ^ {1.2}}}  ÂÂ$ , yang kira-kira 8,7 jam. Oleh karena itu akan memberikan hanya 87 ampere-jam daripada 100.

Hukum Peukert dapat ditulis sebagai

${\ displaystyle Ini = C \ kiri ({\ frac {C} {IH}} \ right) ^ {k-1},}  ÂÂ$

memberikan ${\ displaystyle It}  ÂÂ$ , yang merupakan kapasitas efektif pada tingkat pelepasan ${\ displaystyle I}  ÂÂ$ .

Peukert's law, literally, would imply that the total charge sent by the battery ( ${\ displaystyle It}$ ) go to infinity as the debit level goes to zero. This is of course impossible, since there is a limited amount of reactants from the electrochemical reaction on which the battery is based.

Jika kapasitas terdaftar untuk dua tingkat debit, eksponen Peukert dapat ditentukan secara aljabar:

${\ displaystyle {\ frac {Q} {Q_ {0}}} = \ kiri ({\ frac {T} {T_ {0}}} \ right) ^ { \ frac {k-1} {k}}}  ÂÂ$

Bentuk lain dari hukum Peukert adalah:

${\ displaystyle {\ frac {Q} {Q_ {0}}} = \ kiri ({\ frac {I} {I_ {0}}} \ right) ^ { \ alpha},}  ÂÂ$

dimana:

${\ displaystyle \ alpha = {\ frac {k-1} {2-k}}}  ÂÂ$

Some representative examples are different? and the corresponding k is tabulated below:

Peukert's law becomes a key issue in battery electric vehicles, where batteries are rated, for example, at a discharge time of 20 hours used at a much shorter discharge time of about 1 hour. At high load currents, the internal resistance of the real battery eliminates significant power, reducing the available (wattage) power for the load in addition to the Peukert reduction, providing a smaller capacity than the predicted simple power equation equations.

A critical study in 2006 concluded that the Peukert equation can not be used to accurately predict the state of battery charge unless it is discharged at constant and constant current temperatures.

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Chemical Battery Effect

Peukert's Law was developed for Lead-Acid batteries, and works well in that application.

That does not always apply to other battery chemicals, especially Lithium-Ion batteries. Lithium-Ion batteries tend to heat themselves during rapid discharge, and Nernst Equation predicts the battery voltage will increase with temperature. Thus, the effect of increased resistance is offset by its own heating effect. Excess Lithium-Ion battery is a well-known advertised feature, see [1]. In a research paper, the tested 50Ah lithium-ion battery was found to provide the same capacity at 5A and 50A; This is due to the possibility of Peukert losses in capacity being offset by an increase in capacity due to a temperature rise of 30 ° C due to self-heating, with the conclusion that the Peukert Equation does not apply.

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Fire Safety

Peukert Law brings certain fire security levels to many battery designs. This limits the maximum output power of the battery. A good example of this is the lead-acid battery, which will not burn through excessive discharges. Thus, starting a car is safe even if the lead-acid battery dies. The danger of fire with lead-acid batteries occurs during overcharging when hydrogen gas is produced. This hazard is easily controlled by limiting the available load voltage, and ensuring the ventilation is present during charging to vent the excess hydrogen gas.

On the other hand, Lithium-Ion batteries self-heat, do not follow the law Peukert, and has a flammable electrolyte. Combination results in catching their fire when it runs out at a fast rate. Specifically, if cells develop internal shorts, they tend to overheat, release electrolytes, and burn. Fire generates additional heat, which can melt the adjacent cells and generate additional leakage of flammable electrolyte. In addition, fire can also increase the temperature of the cells in the adjacent cell, and this further increases the available fault current (and heat). The resulting runaway reaction can be spectacular.

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References

General

• W. Peukert, ÃÆ'â "dead air AbhÃÆ'¤ngigkeit KapazitÃÆ'¤t von der bei der EntladestromstÃÆ'¤rke Bleiakkumulatoren , Elektrotechnische Zeitschrift 20 (1897)

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External links

• A detailed description of the legal effects of Peukert
• Peukert legal calculation sheets in Microsoft Excel format
• Explanations and examples
• The online Peukert legal calculator

Source of the article : Wikipedia