11.4.1.2: Lead-Acid Batteries
- Page ID
- 84611
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Lead-acid battery, the very first type of a rechargeable cell, was invented in France in 1859 by Gaston Plan´e. The positive electrode in such cell is lead dioxide PbO22, and the negative one is metallic lead. The electrolyte is water solution of sulfuric acid H2SO4. When the cell is discharging, the PbO2 in the “+” electrode is gradually converted to lead sulfide, PbSO4, and the same compound forms on the lead “-” plate. In the process, most H2SO4 is removed from the electrolyte, so in a discharged battery the water/acid solution is much more diluted. But a discharged cell can be recharged by sending electric current through it in the “opposite direction”. Now, the PbSO4 in the “+” plate changes back to PbO2, and the PbSO4 in the “-” plate back to metallic Pb. In both reactions H2SO4 is “returned” to the electrolyte, so that at the end of charging it has the same concentration as at the beginning of the discharging process. More details concerning the chemical reactions occurring in the electrodes and the electrolyte can be found in the article linked above.
Even though the lead-acid technology is over 160 years old, such batteries are widely used today and they continue to be “respected members of the family of rechargeable current sources”. This technology is mature and one knows exactly what can be expected from a lead-acid batteries. They tolerate harsh conditions well, such as, e.g., high temperature under the hood of a car or salty moisture on small ocean-going ships. Their electrolyte is nonflammable, in contrast to that in lithium-ion batteries. Also unlike the latter they tolerate well overcharging and do not require sophisticated electronic chargers. Their disadvantages include heavy weight and and relatively short lifespan (measured in the number of charge-recharge cycles).
As energy-storage devices, they may be a good least-expensive option for a single-home “off-grid” solar power installation. An “off-grid” system is designed to meet the needs of one home with no connection to the utility grid (the opposite is a “grid-tied” solar installation, which, in principle, does not require batteries).
There are two main types of lead-acid batteries: “automotive” and “deep cycle” ones. The former (also known as “cranking batteries”) are designed to provide very strong currents, hundreds or even over one thousand of Amps, for a relatively short time – such currents are typically needed for starting a car engine.
The capacity of batteries (lead-acid, as well many other types) is usually given in in the Ah units, i.e., Amp/hours. For instance, if the capacity is given as 50 Ah, it means that the battery can supply the current of 1 A for 50 hours – or, say of 5 A for 10 hours. But since the advent of solar power and of electric cars another unit that expresses more directly the performance of a given battery began to be used: namely, the kilowatt-hour (kWh), a unit of energy. If we remember that 1 Volt multiplied by 1 Ampere gives 1 Watt, and we know the battery’s voltage, then the conversion from Ah to kWh is very simple – e.g., a 12 V and 50 Ah cranking battery has the capacity of:
\[ \text{12 V × 1 A × 50 hours = 12 W × 50 h = 600 Wh = 0.6 kWh} \]
Can we therefore use it as a battery for storing 0.6 kWh of energy? Now, it’s time to to make important warning: if this is an automotive battery, then the answer is no. Charging the battery repeatedly with 0.6 kWh and then and then extracting from it the same energy portion would ruin it after a small number of such charge/discharge cycles! Automotive batteries are not designed for “deep cycling”. If intended to be used for storage, it should be a deep cycle battery.
Because lead-acid batteries have been used for years, almost everyone is familiar with them – therefore, they play one more important role – as a convenient “reference standard” helpful for assessing other types of rechargeable batteries. The two most important parameters of such batteries from the point of view of practical applications are:
- Gravimetric energy density – i.e., the amount of energy that can be stored per mass unit.
- The number of charge/discharge deep cycles the battery guarantees. The energy density of practical lead-acid batteries is 25-40 Wh/kg, and the manufacturers usually guarantee a “lifetime” of 300-500 charge/discharge cycles.
For comparison: the popular nickel-metal hydride rechargeable batteries (widely available in AA and AAA sizes) have the energy density more than twice that of the lead-acid. The lithium-ion batteries of the 18650 type made by Panasonic and used in the Tesla cars have a record-high energy density of 265 Wh/kg. A table listing essential parameters of different rechargeable battery types can be found, e.g., in this Wiki page, or in this Electropaedia chart. Note that in most such tables the lead-acid battery is listed at the top as a familiar reference standard.
Due to the important role that lead-acid batteries have played in the “technosphere” for over 100 years, and the fact that there is a huge industry around the world involved in their production, the US Department of Energy and Argonne National Laboratory have recently launched an initiative to open a new chapter in research on these batteries , with the goal of significantly increasing their capacity and lifetime.
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2It should be noted that most oxides of metals are insulators – PbO2 is one of the few exceptions from that rule. It does conduct electricity, yes, although its conductivity, a parameter used to describe the “goodness” of electric conductors – is over 1000 times worse than that of copper, but is still good enough for an electrode material.