# Energy storage

In this course we cover the basic physics behind energy storage, the important characteristics to consider when thinking about or discussing energy storage and then cover all the current technologies. This is followed by an examination and its uses in society including its benefits and leading on into the environmental impacts. The final section covers the use of energy storage in biological systems, demonstrating as always that nature usually gets there first.

## Introduction

Energy storage first became an issue with the introduction of electricity because there was no easy way to store electrical power. Therefore you had to use it when you produced it. By far the most successfull energy storage for electricity in significant quantities is via pumped storage. With this method you pump water up a hill to a lake and relase it when you want. However the number of sites is very limited.

As the era of cheap energy comes to a close due to Peak oil and to be followed by Peak gas, then the real costs in energy escalates and it is becoming more imperative to be able to store energy and cut down on wastage. This is especially the case with electrical power because if it is not used, it simply goes to waste. Up to now the abundant and easily accessible supplies of plentiful fossil fuels have effectively subsidized all other energy sources, thereby under valuing them and providing little incentive to use energy sparingly.

Further research, invention and improvement of energy storage methods and technologies can help make new energy sources such as renewable energy more practical and economical and energetically possible.

Energy storage is not just confined to large scale energy supply but there is also the whole array of battery technologies which are widespread and ubiquitous. These can be found in every single car and truck and in most consumer electronic products. Without battery technology, probably none of these would be possible.

A significant advance in energy storage technologies would most likely represent a significant technological shift and herald in a whole range of possibilities for society at large. Recognition of this fact may explain the massive interest in High Temperature Superconductors which appeared in the late 1980s. However progress has been relatively slow since then proving the point that major break throughs don't really happen overnight and any technology nearly always takes 20 or 30 years to mature.

## Basic Physics

From the Law of the Conservation of Energy in physics, we know that energy can be neither created or destroyed but it can be converted from one form into another. Overall though the energy is becoming more diluted or spread out as the universe expands. This can be best thought of in the way that the light from the sun is spread out into space and the way that heat dissipates into the environment.

The Second Law of Thermodynamics sets a theoretical limit on the amount of useful energy that can be extracted from any heat engine and the figure turns out to be around 66%.

However not all forms of energy conversion are subject to this. For example potential energy and kinetic energy are be converted in theory between each other with no losses.

With energy storage we are interested in what are the basic underlying forms that we can storage energy and given the physics what does this permit us to do and what limitations it imposes on us. The governing principles also affect how energy storage systems are designed and will also determine things like energy quantity, density and even ease of use.

The materials that are used in any energy storage device will also impact on what is possible or achievable. Depending on the method used, this could depend on any one or a combination of desnity, strength, electrical, magnetic and optical properties including numerous other physical parameters.

### Types of Energy Storage

#### Potential Energy

This is the energy of an object due to its position in force field such as a gravity field or electric field. Here, we will only consider a gravitional field as the case of an electric potential is discussed later in the section on electrical energy.

As anyone knows to raise an object higher takes energy and when it is allowed to fall, it release that energy into the form of moment or kinetic energy. A classic example is a marble released from the top of a smooth frictionaless bowl. It will roll that to the bottom increasing its kinetic energy all the way and roll up the other side to almost a step. In a frictionaless environment this activity should continue indefinitely. It is evident that there is a smooth switch over from 100% potential energy to kinetic energy and back.

The equation for the potential energy of an object is actually quite simple. It is

${\displaystyle E_{p}=mgh\,}$

where

Ep is the potential energy stored in the object
m is the mass of the object
g is the standard gravity (approximately 9.8 m/s2 at the earth's surface)
h is the height to which the object is raised, relative to a given reference level (such as the earth's surface).

If we are interested in energy storage, then both the quantity of mass and the height are important. There is nothing we can do about g because it is effectively constant near the surface of the Earth.

#### Kinetic Energy

This is the energy inherent in a moving object and is described by the famous equation:

${\displaystyle E_{k}={\frac {1}{2}}mv^{2}}$

where:

Ek is the kinetic energy of the object
m is the mass of the object
v is the velocity (or speed) of the object

It is immediately obvious as the velocity is increased the embodied energy rises rapidly. Harnessing the kinetic energy of an object travelling in a straight line is difficult. For example think of trying to capture the energy in a bulletin and successfully converting 100% of that energy to say electrical power. Kinetic energy also applies to rotating objects and the governing equation is slightly different. The capture and conversion of that energy though is a lot easier.

##### Rotational Kinetic Energy

The equation for the rotational kinetic energy is of the same form of the above except it is slightly different. It is:

${\displaystyle E_{rotation}={\frac {1}{2}}I\omega ^{2}}$

where

I is the moment of Inertia given by I = mr2 where m is the mass and r is the radius.
ω is the angular velocity given by v/r where v is the rotational velocity and r is the radius about which the object is rotating.

This is just a simplified explanation because for example in reality where you might have a rotating cylinder, to correctly calculate the moment of inertia, you have to effectively sum up the mass times the radius2 over all parts of the radius from the centre out to the edge.

The key point to note though is that the faster your object rotates the more energy it has and since the moment of inertia is dependent on the radius2, then as the mass is moved further away from the axis of rotation, then the quicker the energy rises. Think of a block of concrete rapidly rotating on the end of a long metal arm and it will be clear and this has a lot of kinetic rotational energy

#### Electrical Charge

Energy stored as electric charge is really a form of potential energy, except it's electrical potential energy. The presence of a charge sets up a voltage potential difference which can be used at some point to attract electrons and thereby make current flow. When storing energy in this way, one needs to accumulate charge on a surface and then keep it insulated or isolated so that the charge does not leak away.

A good example of a device for storing energy as electric charge is a capacitor. This is a common circuit component very widely used in circuit designs of all types. Typical capacitors however store tiny amounts of energy. Capacitance is measured in farads and your average capacitor is rated anywhere from a few microFarad (µF) to as low as a few nanoFarads (nF) or even a picoFarad (pF).

A capacitor can be thought of as two parallel plates separated by an insulator. The equation for capacitance is:

${\displaystyle C=\epsilon {\frac {A}{d}}}$

where

C is the capacitance in farads, F
ε is the permittivity of the insulator used (or ε0 for a vacuum)
A is the area of each plate, measured in square metres
d is the separation between the plates, measured in metres

Therefore it is immediately obvious that to increase the capacitance, the area needs to be increased while the distance separating the plates decreased.

The equation for the energy stored in a capacitor is:

${\displaystyle E_{stored}={\frac {1}{2}}CV^{2}={\frac {1}{2}}\epsilon {\frac {A}{d}}V^{2}}$ .

where

E is the energy measured in joules
C is the capacitance, measured in farads
V is the voltage measured in volts

To increase the energy stored, the fastest way to do this is by increasing the voltage. Unfortunately the material properties get in the way of increasing this indefinitely and if raised too high, the device will suffer voltage breakdown. Early capacitors would have used air gaps between the plates, but the dielectric value for many insulators is actually higher than that of air. Therefore modern capacitors uses novel materials with high dielectric constants to enable them to use higher voltages.

In practice high capacitance is achieved by rolling up the plates or sheets into cylindrical and other shapes. More recent designs have tended towards porous type structures which are able to achieve huge surface areas in tiny volumes.

#### Magnetic Energy

Any electric current will always create a magnetic field around it, and an changing magnetic field can induce an electric current in any nearby electrical conductor. Thus a wire carrying electrical current will also have a tiny magnetic field associated with it. By coiling the wire around in a cylindrical shape or like a coiled spring, the strength of this magnetic field can be increased and also made to self induct. This is the basis of electrical inductors which are common electrical components found in many types of circuits particulary those used for radio receivers and transmitters.

The energy stored in a magnetic field is:

${\displaystyle E={\frac {1}{2}}\cdot L\cdot I^{2}}$

Where

E = energy measured in joules
L = inductance measured in henries, which are units of magnetism.
I = current measured in amperes

The problem with magnetic energy and the electro magnets created by passing current through inductors is that current must be continually added in. This is because your typical copper wire is not completely resistance free, although it is very small. If one were to loop back both ends of an inductor after injecting lots of current into the wire, the current would soon die away and all that energy would be wasted.

Superconductors, unlike normal conductors have essentially zero electrical resistance and is of the order of 10-24 ohms (or even lower and in the idealized scenario outlined above, the current would continue to circulate in the loop for millions of years. Clearly then superconductors are the saviours for devising a means to store energy in magnetic fields.

The problem with superconductors is that they have to be cooled to extremely low temperatures, making them expensive and quite impractical. An additional and important problem is that each type of superconductor has a threshold magnetic field in which it can reside. As the magnetic field strength is increased, this serves to increase the temperature until suddenly it is back above the critical threshold between a superconductor and a normal conductor and thereby limiting the capacity of a given superconductor system.

Overall though from the equation above, it can be seen that the most important parameter for raising the amount of energy stored is the strength of the magnetic field.

#### Chemical Energy

Chemical energy is the most diverse of the various energy storage mechanisms and it is the energy stored in setting up certain higher energy chemical bonds. A single atom can actually have one of its orbiting electrons raised temporarily to a higher energy level, but typically it will fall back to the lower energy level very rapidly. In fact this is the basis of flouresence.

In this discussion we only consider the chemical bonds between atoms as these are far more stable and long lasting. For the chemical energy to be released there must be a new state for the molecule to fall energetically down to. For example the methane molecule given by the chemical formula below can combine with oxygen to form carbon dioxide and water. Actually you need two molecules of each to get a perfect burn and for everything to balance.

2 CH4  + 2 O2 → 2CO2 + 2 H2O

Looking at chemical energy from physical first principles it is really a form of electrical potential energy because each of the various electrons in the atoms of the molecule are at a higher potential energy and will release energy by falling to a lower potential energy.

Luckily for us all the molecules around do not fall automatically to these lower states and this is for a variety of reasons, the main one being that in nearly all cases you need to first raise the energy of the molecule to get it to go to the lower state and form different types of molecules. This is known as the energy of activation. If that was not the case then everything flammable would immediately burst into flames. As we know to burn paper or wood, we first must bring it up to the ignition or activation temperature.

Because of the enormous number of possible types of molecules that can be created, this gives rises to a huge range of molecules capable of storing energy due to their inherent chemical properties. For example some typical fuels that store considerable energy are ethanol, methane, butane, ethane, gasoline and hydrogen.

Explosives also store lots of energy except they release it rather quickly.

To create an energy storage system that makes use of chemical energy, you need a mechanism to pump energy into the system and raise the energy content. Splitting water molecules by electrolysis into their consitutent elements of hydrogen and oxygen requires energy. When you recombine them again through burning, you get back that energy again. Since no system is perfect it will always be less than 100% efficient, so you will lose a bit of energy in the process. A good rule of thumb is that the more chemical steps the lower the overall system efficiency.

Note: Natural gas is largely made up of methane. There will be traces amounts of other gases usually present.

#### Thermal Energy

In its simplest form thermal energy is the energy that has been put into an object or liquid to make it warm or hot. In its application to energy storage one is usually heating something and keeping it at that temperature to save the effort of doing it later and use energy at that time that may be unavailable. An example is the thick walls of a building heating up in the sun and releasing that heat later on during the night when that energy is not available.

In terms of physics though, thermal energy represents the vibrational energy of all the molecules of your substance or object. In a liquid and a gas it also includes the convectional flows. These vibrations will damp down and the object will cool if there is somewhere for the energy to escape too. An object can release its thermal energy by transferring to through contact to other objects and by radiating out infrared radiations. The infrared comes about because the electron orbitals and the molecules themselves are vibrating and rotating. They can move to lower energy levels resulting in less vibration by releasing infrared photons -i.e. infrared radiation.

If you can seal off the object and perfectly insulate it, then you can store that thermal energy indefinitely. In practice this is very hard to do. Storing hot tea in a flask for 3 or 4 hours is good enough for most applications involving hot tea because one is unlikely to want to store it for days or weeks. For energy storage applications, the better the insulation and the quantity of thermal energy stored then the more uses and applications can be made.

When performing engineering analysis of heat flows[[Heat_Transfer]b:Heat_Transfer] there are three primary mechanisms typically considered.

• Radiation - All mass radiates heat based upon its internal absolute temperature. This is called Blackbody Radiation and is calculated precisely by a simple mathematical formula. Since heat radiated is proportional to the fourth power of the absolute temperature warmer mass radiates a lot more energy than colder mass and the net flow of energy is always from the warmer mass to colder mass.
• Conduction - Heat flows through continuous solid materials by molecular vibrations being transferred between constituent atoms and molecules in the solid. This can be calculated from the temperature potential difference or range just as in electric circuits. Heat always flows from warmer areas to colder areas.
• Convection - In liquids and gases heat is carried to or from an immersed solid or energy source or sink by the gas or liquid expanding or contracting from the temperature change. The difference in density then results in the liquid or gas moving from original position due to different gravity forces upon differing temperature areas in the fluid. As the gas moves it carries heat with it which is easily calculated from the temperature and the heat capacity of the fluid. An extreme example of convection is boiling where the newly created steam moves from bottom of boiling water pan in contact with heat source to the surface of the fluid ... carrying all the heat from the heat source through the fluid (which remains at constant 212 deg Fahrenheit) to the atmosphere.

## Technologies

In this chapter all of the main energy storage technologies are outlined and explained in terms of the basic physics that they are taking advantage of. For consideration of their usage see the next chapter.

### Compressed Air Storage

This technology, sometimes referred to by the longer title Compressed Air Energy Storage (CAES) uses the difference in pressure to effectively raise the potential energy of air to store energy. Since air is not a very dense substance large quantities of it must be compressed and typically this means storing the compressed air in a sealed underground cavern.

As of 2007, there were in fact only two such installation but with others under construction. The first was the Huntorf plant, located in North Germany built in 1978 and this can produce 300 MW for 2 hours, whilst the second is the McIntosh plant in Alabama, USA. This plant stores Natural Gas with the air and burns this off when it is released to generate additional power over and above that due to the pressure difference allow.

### Dams

A hydroelectric dam is using the exact same physics as a pumped storage hydro scheme to generate power which is by using the high pressure flow of the water to turn the turbines of a large electric motor. The difference of course is that we rely on nature to effectively pump the water back up behind the dam in the form of rain (and snow) in the catchment area of the river. In both cases though the storage of water behind the dam represents stored potential energy

### Batteries

The above new page should cover at least these battery types.

#### Sodium Sulphur (NaS)

For the moment, see *Vanadium_redox_battery (wiktionary | wikipedia | wikibooks)

### Fuels

The above new page should cover at least these sub categories of fuel below

#### Oils and Gasoline

Fossil hydrocarbons are ideal. Though neither clean nor safe nor sustainable, they were previously cheap and possess a very high energy density. Natural gas and hydrogen powered vehicles both suffer from the same weaknesses. Both are very explosive gases that require a great deal of energy to compress into a portable form. While both provide clean energy through a fuel cell, neither are very energy dense even after compression to a liquid. Natural gas is currently cheap but unsustainable and hydrogen is sustainable though not particularly cheap.

Biodiesel is safe, cheap and fairly clean for a combustion fuel, very energy dense and thus quite portable. Unfortunately biodiesel is not sustainable since the fuel actually comes from processed biomass.

A synthetic hydrocarbon is essentially a fuel like ethanol or methane (natural gas), but one that has been chemically synthesized and not mined. Since liquid hydrocarbon fuels are the most energy dense and easy to transport of the new storage ideas and since they have a well established infrastructure already in place, they seem to be the best solution. Unfortunately liquid hydrocarbons like LNG, methanol and ethanol are explosive and toxic.

The ideal energy source would be clean, efficient, portable, sustainable and safe. If we intend to synthesize a high energy density hydrocarbon, why not produce a non-toxic substance. The class of hydrocarbons comprises not only explosive fuels (alkanes), but fats and sugars too. If we synthesize a non-toxic, even edible fuel, then all environmental factors may essentially be waived.

#### Hydrogen

Hydrogen is often touted as the next great energy source. However hydrogen is not a fuel at least on Earth, where it is not found in its free form. Most hydrogen is bound up in the water molecules (H2O) and to free it requires adding energy to break the chemical bonds. It is only then that hydrogen can be burnt with oxygen back into water and thereby release the energy again as it falls to lower energy state again.

Any number of techniques can be used to split water ranging from electrical hydrolysis to illuminating water or steam with ultraviolet light. Heating to very high temperatures can also work. In all cases though it is crucial that the water splitting process is carried out efficiently so that total overall system efficiency is kept high.

The storage of hydrogen itself presents problems because the molecule itself is very small and it can easily diffuse through thin metal structures. Additionally hydrogen remains in the gaseous state down to very low temperatures and to store sufficient quantities, it needs to be both cooled and kept at high pressures. Therefore it is necessary to use fairly dense and thick metal casings.

Lastly when hydrogen burns the flame is invisible making it even more hazardous.

Currently hydrogen's main energy storage usage today is as a liquid fuel for rockets such as the Space Shuttle, but for everyday usage it is still quite impractical and expensive

### Supercapactors

These are often also known as ultracapacitors.

### Thermal Energy

There are a number of technologies, some still experimental that are used for thermal energy storage. In some cases this method can be used as a proxy for storing electricity.

The criteria to consider are sizing, costing and effectiveness and one needs to take these into consideration when selecting a particular technology.

#### Graphite

There was a lot of work done with high purity graphite in the nuclear industry and it is quite a good material especially for high temperatures where it exhibits increasing heat capacity with temperature.

This form of graphite sometimes known as crystalline graphite is relatively expensive but then carbon itself is very abundant. In a renewable energy setting, it would be best used if place at the focus point of high temperature solar concentrating systems such as ones using arrays of mirrors.

#### Hot Rocks

Rocks can be used for storing low grade heat such as solar thermal energy absorbed during the day and for releasing that for heating during the night. A good example of this in action can be witnessed in any of the large cathedrals in Europe which were built out of huge blocks of rock often tens of feet or more thick. During the day these buildings remain cool even in the hot sun, and at night remain relatively warm even though temperatures can have dropped significantly outside.

In recent years there have been numerous buildings, mainly houses, built that have a bed of rocks in the basement which release the heat at night. Some of these system used semi-active or passive means to direct the flow of warm air over these rocks during the day to capture the heat.

The chief advantage of using rocks for thermal energy storage is that they are abundant and cheap.

## Research Areas

This section covers the current research areas in energy storage

## Energy Storage in Biological Systems

This covers energy storage in Glucose, Starch, Fats and ATP.