Chapter 9: Energy Storage

In Chapter 5 I mentioned that electric power is one of the true miracles of modern technology: Energy is delivered, on demand, over huge distances, right to your home or office whenever you want it for as long as you need it. Electric power can be generated in a great variety of ways, from coal or nuclear, oil or gas, hydro or wind or solar. Because your demand is shared with millions of other people, energy storage isn’t essential, and when total demand varies throughout the day and the seasons, power plants can be brought on line or banked down to meet the changing needs, so that the system nearly always operates at high efficiency. The grid, like the net, connects us to our neighbors, allowing us to share the costs of expensive capital facilities. Furthermore, supplies of coal (and nuclear fuel) are abundant, so electrical shortages are not likely to be part of our future unless, for environmental reasons, we decide to shut down our coal- and nuclear-fired power plants.

My summer home is on an island that is not connected to the grid. We generate our own electricity, in earlier days with gasoline-powered generators, and nowadays with solar. The sun doesn’t shine at night or on cloudy days, so we store the energy in batteries and hope that it isn’t cloudy for more than a few days in a row. We keep the generators for backup and for the vacuum cleaner. Our system can handle small power tools and lights and radios and even a high-efficiency refrigerator, but we don’t have toasters or hair driers or a microwave oven. Off-grid uses like ours are uncommon, but there is a sufficiently large market in homes and lighthouses and offshore platforms to support a growing solar power industry.

The largest off-grid market is transportation: Cars, trucks, planes and ships. In each case fossil fuels are the preferred medium of energy-storage. Unfortunately, technology has not found a way to make fossil fuels from electricity, so we take what we need from deep underground and refine it into different products: Kerosene, gasoline, or diesel fuel. As energy storage media, these fuels are spectacular. A liter of gasoline weighs only 0.74 kilograms (compared to one kilogram for water) but releases 36 million joules when burned in air. That’s about 10 kilowatt-hours! Of course only a small fraction of this energy, about a fifth, can be turned into useful work, but that’s still 2 kilowatt-hours in a liter. There is an environmental cost, of course, 2.3 kilograms of carbon dioxide (CO₂) released to the atmosphere per liter of gas, not to mention the pollution due to nitrogen oxides and unburned hydrocarbons. But most energy consumption has an environmental cost.

What are the alternatives for energy storage? What we are really looking for is a way to store electrical energy, although using electricity does not necessarily solve all the environmental problems. The possibilities include batteries, supercapacitors, fuel cells and hydrogen. Each one has its own set of limitations.

Here are some definitions, units and conversion factors you will need to understand the material presented in this chapter. Some of this information was presented in Chapter 0. 1. A joule is a unit of energy, while a watt is a unit of power. A watt delivered for one second – a watt-second – is equal to a joule, or, to put it the other way around, a watt is a joule of energy per second. A watt is also the power delivered by an ampere of current at one volt. A watt-hour is 60 x 60 (3600) joules. 2. A coulomb is a unit of electrical charge equal to an ampere of electrical current delivered for one second. An ampere-hour is 3600 coulombs. 3. A faraday is a mole (6.02 x 10²³) of electrons. It is equal to 96,500 coulombs. Thus 6.94 grams of lithium (a mole), which delivers a mole of electrons when ionized, produces 96,500 coulombs, or 96,500 ampere-seconds, or 26.8 ampere-hours. At three volts, this is about 80 watt-hours. 4. A farad (not to confused with a faraday!) is a unit of electrical capacity. Its units are coulombs per volt. The energy that can be stored in a capacitor is ½ CV², where C is the capacitance in farads and V the maximum voltage.

Batteries are a good place to start. The familiar car battery, used for starting (and lights, radio, etc.) weighs about 30 kilograms and stores about one kilowatt hour of useful energy. (A car battery is rated at 12 volts, and can deliver about a hundred ampere-hours if discharged slowly. That’s 1200 watt-hours.) So two car batteries can deliver about the same energy as a liter of gasoline while weighing 80 times as much. Ouch!

Lead-acid batteries, the type used in cars, are a pretty good choice for stationary applications, such as my island house, where weight is unimportant. Their main drawback is that they age, and the more they are used the faster they age. Lead-acid batteries die quickly if they are repeatedly discharged by more than 50% of capacity, a circumstance that is hard to avoid when the sun doesn’t shine for days on end. Discharging a lead-acid battery by more than 80% (80% depth-of-discharge or 80% DOD) will ruin it even more quickly. In solar applications, it is hard to keep a lead-acid battery in service for more than five years.

There are better batteries, both from the point of view of energy density (stored energy per weight) or cycle life. Nickel-cadmium (NiCad), nickel-metal hydride (NiMH) and lithium ion (LiON) are all better than lead-acid. But nothing comes close to lead-acid in terms of cost. Not that lead-acid batteries are cheap: A car battery only stores about a dime’s worth of electricity, although this isn’t quite a fair measure since the dime can be put in and taken out repeatedly. But you’d need 1000 cycles from the battery at 50% DOD to amortize the cost even if you didn’t have to pay anything to recharge it.

What are the prospects for better batteries? In terms of energy density, lithium ion batteries are close to the theoretical limit, at least in principle. The chemical reaction is Li⁺ + e^-  Li, where e^- represents an electron. The voltage for this reaction is about 3.5V, and the atomic weight of lithium is only 6.94, from which it can be shown that a kilogram of lithium can store nearly 14 kilowatt hours. That’s even better than gasoline! If only it were possible in practice. Lithium atoms (Li) generally require a storage medium, typically graphite, six atoms of carbon¹ per lithium atom. That bumps up the molecular weight from 6.94 to 6 x 12 +6.94, or 78.9. We just lost a factor of eleven! Positive lithium ions (Li⁺) also require a medium, typically manganese dioxide, MnO₂, two molecules per lithium atom. That adds another 174 to the molecular weight, for a total of 253. Now we’re down by a factor of 36. And of course the packaging materials add still more weight. In practice the energy density of LiON batteries is about 0.15 kilowatt hours per kilogram, down by a factor of 100 from the theoretical, and down by a factor of 18 from gasoline.

This is not so terrible as it sounds. A car needs perhaps 100 kilowatt-hours of storage to go 300 miles between refuelings. Lithium batteries could provide this much energy in a 600-kilogram package. That’s comparable to the weight of a car engine. So a battery-powered car is technically feasible provided that LiON batteries can withstand thousands of repeated charge and discharge cycles. This appears to be a real possibility, and in fact prototype cars have been built by the AC Propulsion Company, and their web site is worth visiting. Cost, however, is another matter. Safety is another potential problem.

I think two conclusions can be drawn from the information just presented. First, battery-powered cars are technically feasible. There is already a real market in vehicles that travel only a few miles a day, such as postal vans and fork lifts. Second, there is ample room for technical improvement and cost reduction, although I caution the reader that progress in battery development has always been painfully slow despite what seem to me to have been ample levels of funds. The market for good batteries is not small; the space program has poured money into research. (Communication satellites also need batteries.) No obvious solutions are on the horizon, but I think progress will continue.

What about the other major possibilities for energy storage, ultracapacitors, fuel cells and hydrogen? Unlike a battery, a capacitor stores electrons in a thin film of conductive material, rather than by converting electrical energy to chemical energy. Typical capacitors, the kind found in all electronic devices (radios, television sets, cell phones) store only a miniscule amount of energy. Capacitance is usually measured in microfarads, and a big TV capacitor might reach 10,000 microfarads, or 0.01 farads. At (say) 100 volts, this is only 50 joules of energy. It would take 72,000 such capacitors to store a kilowatt hour. This is not encouraging. A modern “ultracapacitor” the size of a D-cell battery can store about 1000 joules, but that figure still implies 3,600 cells per kilowatt-hour. (By comparison, a D-cell nickel-metal hydride battery can store about 6 ampere-hours, or roughly 28000 joules.)

Traditional capacitors can be charged and discharged endlessly, without degradation. Furthermore, they can be charged or discharged at very high rates, which means that “refueling” times can be very short. This is their attractive side. The negatives are cost, weight and volume. Nevertheless, new types of capacitors have been developed with much higher energy densities, evidently solving the weight and volume problems while preserving the promise of very high rates of charge and discharge. The questions that remain pertain to cycle life and cost. It is too early to know whether these difficulties can be overcome, but prototype cars have been built using ultracapacitors. As with cars powered by lithium batteries, they are sold primarily on their ability to accelerate like a rocket: They can deliver their stored energy over very short periods of time. But it is too soon to evaluate their commercial potential. It does seem likely that a mixed system of batteries and ultracapacitors can provide longer-term energy storage (batteries) with short-term high-power discharge rates (ultracapacitors) in a way that is optimal for both rapid acceleration and highway cruising.

As for fuel cells, they are really not much different from batteries. In a battery, the chemical materials that store energy are usually solids that can be ionized. The ions move only in response to the flow of electricity. In a fuel cell, the reactive chemicals are liquids or gases, which can be moved into position as required. In principle this reduces the areas and volumes required to place the chemicals near a reactive surface. This is an attractive idea. Fuel cells using methanol and air (oxygen) are nearing commercial feasibility. While attractive for small applications, such as laptop computers and cell phones, their benefit in transportation applications is limited, since they still produce carbon dioxide, and the fuels cannot be generated from electricity.

Fuel cells based on hydrogen (H₂) seem, at first glance, to be much more attractive. The energy that is released when hydrogen reacts with oxygen in the air is comparable, on a weight basis, to the energy stored in lithium; hydrogen can be generated, quite easily, from electricity; when consumed in a fuel cell, the only product is water; and fuel cells using hydrogen have been used in spacecraft for many decades. There is absolutely no question as to technical feasibility. Why then are so many scientists skeptical about the future of hydrogen as a transportation fuel, as an energy storage medium? The prime answer, quite simply, is that hydrogen is not readily compressed. It is not the weight per unit of energy storage that is worrisome, but the volume. Hydrogen cannot be liquefied unless it is chilled to extremely low temperatures, and refrigeration is expensive and inefficient. Hydrogen can be compressed without liquefaction, but the steel tanks needed are themselves heavy or bulky, so much so that the perceived advantages of hydrogen on the basis of weight are lost. There is a third way to store hydrogen, via reversible reaction with certain metal powders to produce a metal hydride, in the same way that hydrogen is stored in nickel-metal hydride batteries. But the battery market for laptops and cell phones has shown that the energy storage density in lithium-ion batteries is better than in nickel-metal hydrides, which are already yesterday’s technology. True, the hydrogen storage problem may be solved by newer techniques not yet ready for commercialization. But the storage problem has been around for decades and progress has been almost non-existent. And there are other problems with respect to hydrogen (generation, storage, transportation, safety) that make me think that lithium batteries are a better bet. Ultracapacitors have a serious chance, but for the time being I’ll put my money on lithium.

It would be wonderful if we could make liquid fuels from electricity. That’s another bet I refuse to take. The difficulties are way beyond hard. But there are alternatives. The starch and sugars in plants can be converted to alcohol, and nature makes liquid fuels directly, in the form of vegetable oils: Palm oil, corn oil, safflower oil, olive oil, peanut oil, rapeseed oil, and so on. All of these oils can be converted, quite easily, to diesel fuel, or used (with a little heating) as is. Worldwide production is only a few percent of what is needed to replace petroleum fuels, but in principle we could simply plant more palm trees. Vegetable oil at your local supermarket is only about three times² as expensive as diesel fuel (five times as expensive if we subtract the fuel taxes). Biodiesel fuels hold real promise as an energy storage medium, and their use releases no more carbon dioxide to the atmosphere than the plants remove. We don’t even need electricity: Sunlight³ is the energy source.

Does this sound too good to be true? Perhaps it is. The imbalance between the demand for transportation fuels and the supply of vegetable oils is huge. Biotechnology may offer an alternative. Perhaps oils can be produced by bacteria or other simple organisms. But increased production is not the only way to solve the transportation fuel problem. Reducing demand by increasing efficiency of use is a very reasonable alternative. Volkswagen has produced an experimental car that gets 200 miles to the gallon; hybrid cars and turbo diesels on the market today get over 40. China has announced fuel efficiency standards that far exceed the U.S. standards. I don’t think the world will produce cars that routinely exceed 200 mpg in my lifetime, but if that happened the world could run on biodiesel. There is, I think, ample reason to be hopeful that the transportation fuel problem will be solved before the world “runs out of oil,” by which I mean the time when fossil oil becomes more expensive than vegetable oil.

Conservation, by which I mean improved efficiency, is typically expensive in the short run and cheap in the long run. Hybrid cars cost more in the short run, and some day perhaps less over their lifetime: Capital costs are higher, annual costs are lower. It’s a tradeoff that is hard for a consumer to make. Government regulation can help; so can common sense. My summer house in Maine uses about two or three kilowatt-hours of electricity per day, while my winter house in Massachusetts uses thirty. Why do we use so little in Maine? Because electricity is expensive, a dollar a kilowatt-hour (I estimate) compared to a dime in Massachusetts. So we use compact fluorescent lights in Maine, which have three times the efficiency of the incandescents we use in Massachusetts. Because we dry our wet clothes on a sunlit line, not in a dryer. Because our refrigerator in Maine is three times as efficient as the one in Massachusetts. Because we turn off lights in Maine when we leave a room. Because lugging gasoline to a generator is a time-consuming nuisance. Solar power makes great sense when you’re off the grid, but only when you’re off the grid. As we shall show in the next chapter, off-grid uses may be the only places where solar makes sense, at least at present prices. The technical and economic inadequacies of energy storage are severe. In the very long term it might be cheaper to electrify our roads and streets, as we do with trolley cars, than to try to carry the stored energy with us in our cars and trucks. Maybe only airplanes and ships will run on fossil fuels. We’ll see. There are alternatives, choices to be made, and with luck and intelligence and time we’ll choose well.

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Exercise #1: Find out what is meant by the “self-discharge rate” of a battery. Compare self-discharge rates for the four principal rechargeable batteries on the market today, i.e., lead-acid, nickel cadmium, nickel-metal hydride and LiON. For comparison, what is the self-discharge rate of an ordinary alkaline (non-rechargeable) flashlight battery?

Exercise #2: If a car gets 30 miles to the gallon, which it converts to useful work at 20% efficiency, what energy (in kilowatt-hours) is required to drive 300 miles?

Exercise #3: The “cycle life” of a battery is generally defined as the number of 100% DOD cycles the battery can undergo before losing 20% of its capacity. (For some batteries that cannot withstand a full discharge, it is defined as half the number of 50% DOD cycles.) Compare cycle lives of the four types of batteries mentioned above.

Exercise #4: The “C-rate” of a battery is defined as the time required to charge or discharge it without damage. For example, if a 200 ampere-hour battery can be charged safely at 10 amperes, this a 20-hour rate, often expressed as “C/20”, capacity divided by 20 hours. Compare manufacturers’ recommended maximum C-rates for the batteries mentioned above for both charge and discharge.

Exercise #5: Compare the oil production rates for different types of plants. Which plant produces the most oil per acre? How does this compare to the production rate for corn oil?

Exercise #6: Compare the energy density of a commercially available methanol fuel cell with a LiON battery.

Exercise #7: The Toyota Prius, a hybrid car, uses a small (50 kg) battery pack consisting of about 225 1.2-volt nickel-metal hydride cells. The maximum power output of the battery pack is about 20 kilowatts. If the “energy density” of the battery is about 60 watt-hours per kilogram, what is the discharge C-rate at peak power output?

Exercise #8: Compare the wholesale (commodity) prices of vegetable oil and crude oil.

© 2007 by Peter O’D. Offenhartz