Внутреннее сопротивление это одна из важнейших характеристик аккумулятора. Чем меньше этот показатель, тем больший ток аккумулятор способен отдавать в нагрузку.
Если взять два аккумулятора одинаковой ёмкости с разным внутренним сопротивлением и разрядить их на нагрузку одинаковой мощности, энергии на нагрузке выделится не одинаковое количество. Часть энергии выделится на аккумуляторе в виде тепла. Аккумулятор с бОльшим внутренним сопротивлением будет греться больше и отдаст меньше энергии. При сборке аккумуляторной батареи также важно подобрать элементы по внутреннему сопротивлению, как и по ёмкости, чтобы добиться максимально эффективной работы.
Как внутреннее сопротивление влияет на производительность аккумулятора.
Схема из аккумулятора и резистора, как на рисунке выше поможет объяснить то, для чего мы здесь собрались.
Напряжение аккумулятора U=3,7 В, ёмкость 3 А/ч (для упрощения расчетов аккумулятор будет выдавать на всём протяжении разряда одинаковое напряжение), сопротивление резистора Rнагр=1 Ом. Условно представим что они соединены идеальными проводами с нулевым сопротивлением. Сопротивление амперметра также нулевое. Сопротивление вольтметра бесконечно велико. То есть амперметр, вольтметр и провода никаких влияний на нашу цепь не оказывают. Ток течет только через аккумулятор и нагрузку.
По закону Ома сила тока в цепи должна быть I=U/Rнагр, то есть 3,7/1=3,7А, но амперметр покажет меньший ток, к примеру 3 ампера. Это произошло из-за того, что в цепи есть ещё одно сопротивление — сопротивление аккумулятора. Идеальных источников тока, как и идеальных проводов, амперметров и других вещей в реальности не бывает.
Мы можем найти это сопротивление используя тот же закон Ома:
Rвн=U/I-Rнагр=3,7/3-1=0,23 Ом
А теперь посчитаем сколько мощности выделится на аккумуляторе в виде тепла за 1 час (за такое время он отдаст весь заряд):
P=I2 *Rвн=3*3*0,23=2,07 Вт
На резисторе в то же время выделится:
3*3*1=9 Вт, (а могло бы быть, в случае с идеальным аккумулятором — 3,7*3,7*1=13,69 Вт)
Общий выход мощности на аккумуляторе и нагрузке составит Pобщ=2,07+9=11,07 Вт
Учитывая то, что в ячейке 18650 может быть запасено около 9 — 12,5 Вт энергии, из которых 2 Вт уйдут в нагрев, перспектива использования оказывается непривлекательной. Аккумулятор будет перегреваться. В реальных условиях аккумулятор с таким большим внутренним сопротивлением уже пора отправить на покой, либо разряжать низким током. Например при разряде током 1А картина будет немного лучше:
P=I2 *Rвн=1*1*0,23=0,23 Вт, за время полного разряда (3А/ч израсходуется за 3 часа) 0,23*3=0,69 Вт
Такой ток будет в цепи с нагрузкой сопротивлением Rнагр=3,47 Ом и на нагрузке мощности выделится уже больше:
P=I2 *Rнагр=1*1*3,47=3,47 Вт, за 3 часа — 3,47*3=10,41 Вт (вместо 9 как прошлый раз)
В сумме получим такую же общую мощность Pобщ=0,69+10,41=11,1 Вт (погрешность в 0,03 Вт получилась из-за округления при расчетах)
Именно поэтому необходимо учитывать внутреннее сопротивление аккумулятора и чем мощней нагрузка, тем оно должно быть ниже для эффективной и безопасной работы.
Более реалистичные сопротивления у современных среднетоковых литий ионных аккумуляторов, например формата 18650 составляет порядка 40 мОм (милли Ом), у высокотоковых — менее 30 мОм.
Измерение внутреннего сопротивления.
Существует несколько методик измерения внутреннего сопротивления. Две из них прописаны в ГОСТ Р МЭК 61960-2007. Перед замером любым из приведенных ниже методов аккумулятор должен быть полностью заряжен. Испытания проводятся при температуре 20±5ºC.
Измерение внутреннего сопротивления методом переменного тока (а.с.)
С помощью этого метода измеряется импеданс, который на частоте 1000 Гц приблизительно равен сопротивлению.
Электрический импеданс (комплексное электрическое сопротивление) (англ. impedance от лат. impedio «препятствовать») — комплексное сопротивление между двумя узлами цепи или двухполюсника для гармонического сигнала.
Описание методики из ГОСТ
В течение одной — пяти секунд измеряем среднеквадратичное значение переменного напряжения Urms, возникающего при прохождении через аккумулятор переменного тока со среднеквадратичным значением Irms , следующего с частотой 1000 Гц. Внутреннее сопротивление Ra.c., Ом рассчитываем по формуле Ra.c.= Urms / Irms .
Irms (rms — Root Mean Square – среднеквадратичное значение).
Переменный ток должен иметь такое значение, чтобы пиковое напряжение не превышало 20 мВ.
Этот метод сложно воплотить в домашних условиях без специального оборудования. Популярный прибор YR1035 отлично справляется с измерениями с точностью 0,01 мОм. Зарядные устройства SKYRC MC3000 ,Opus BT-C3100V2.2, Liitokala Lii-500 также измеряют методом АС, но весьма с посредственной точностью.
Измерение внутреннего сопротивления методом постоянного тока (d.c.)
Этот метод возможно выполнить в домашних условиях с помощью обычных вольтметра и амперметра и пары подходящих нагрузочных сопротивлений. В качестве сопротивлений вполне можно использовать несколько автомобильных ламп накаливания или импровизированный резистор из нихромовой проволоки.
Описание метода из ГОСТ
- Разряжаем аккумулятор постоянным током I1= 0,2 Iн. На десятой секунде измеряем значение напряжения U1 на клеммах аккумулятора.
- Увеличиваем разрядный ток до значения I2=Iн. На следующей секунде измеряем значение напряжения U2 на клеммах аккумулятора.
Внутреннее сопротивление Rd.c., Ом рассчитываем по формуле Rd.c. = (U1-U2)/(I2-I1)
- Iн — номинальный ток разряда аккумулятора.
Сопротивление R1 и R2 подбирается таким образом, чтобы протекали токи I1 и I2 нужной величины. Ориентироваться нужно на номинальный разрядный ток аккумулятора.
Вольтметр необходимо подключать непосредственно на полюса источника, чтобы исключить влияние от падения напряжения на проводах .
От чего зависит внутреннее сопротивление аккумуляторов.
Производство.
Изначально, на этапе производства аккумуляторов этот параметр конечно заложен в «рецепт». Ячейка может быть либо мощной и отдавать большой ток (низкое внутреннее сопротивление), либо более энергоёмкой. При условии одинаковых прочих составляющих (компонентов электродов, химии электролита итд.) в более ёмких ячейках необходима бОльшая площадь обкладок. И для того, чтобы эта конструкция уместилась в предоставленный объём, необходимо эти обкладки сделать тоньше. И наоборот. Тонкие обкладки естественно имеют большее сопротивление.
Также влияют и расстояние между электродами, толщина и вещество их обмазки, толщина сепаратора, химия электролита и множество других факторов. Из-за производственного брака ячейки, сделанные по одному «рецепту» могут отличаться как по внутреннему сопротивлению, так и по ёмкости, сроку жизни итд. Из-за длительного и неправильного хранения по пути к потребителю качество также страдает.
Эксплуатация.
Rвн изменяется в зависимости от степени заряженности аккумулятора. При низком и высоком уровне заряда растёт, в среднем — минимально.
Температура электролита (чем холоднее тем выше сопротивление). При отрицательных температурах большинство литий-ионных и литий-полимерных ячеек на столько увеличивают внутреннее сопротивление, что использовать их становится невозможно. Литий-железо-фосфатные и литий-титанатные при таких условиях ведут себя гораздо лучше.
Также в процессе эксплуатации, по мере износа элемента Rвн будет увеличиваться.
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If everything in this universe has a cause, then surely the cause of my hunger must be the divine order of things aligning to guide me toward the ultimate pleasure of a well-timed meal. Could it be that desire itself is a cosmic signal, a way for nature to communicate with us, pushing us toward the fulfillment of our potential? Perhaps the true philosopher is not the one who ignores his desires, but the one who understands their deeper meaning.
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