8.2.1 Components of a Typical Nuclear Reactor

A nuclear reactor consists of a vessel with fuel rods, control rods, the moderator and a coolant.

Reactor fuel rods are commonly made of uranium oxide.

Control rods are made from a material (for example, boron, cadmium, hafnium) with good neutron‐absorbing capabilities, useful in regulating or shutting down the reaction.

The moderator is a material (for example, graphite or water) surrounding the fuel rods that is used to slow down generated neutrons to a speed or energy conducive to capture by uranium nuclei.

The coolant is a fluid (for example, water, CO₂, liquid sodium) used to collect the thermal energy generated by the reactor.

A containment structure prevents radioactivity from escaping to the environment.

8.2.2 Types of Nuclear Reactor

Water reactors can be of the pressurized‐water or boiling‐water variety.

In a pressurized‐water reactor, the thermal energy of the nuclear reaction is used to heat a primary coolant circuit that produces steam in a secondary circuit via an indirect heat exchanger (see Figure 8.2). The steam is then routed to the turbine set for power production.

In a boiling‐water reactor, the indirect heat exchanger and secondary circuit are dispensed with and power is generated by sending steam directly to a turbine.

8.2.3 Environmental Impact of Nuclear Reactors

Although proponents of nuclear power often emphasize the carbon‐free aspect of the technology, all forms of radiation, whether man‐made or naturally occurring, are potentially dangerous, and therefore nuclear power is not without its own radioactive waste issues.

Nuclear power waste is commonly classified into:

• High level – spent reactor fuel, reprocessing material.
• Intermediate level – reactor ancillary equipment, e.g. control rods, instrumentation etc.
• Low level – contaminated laboratory material, operator clothing, miscellaneous rubbish.

During its passage through matter, radiation knocks electrons out of atoms or molecules (ionization). There is no known lower limit of radiation below which no damage is done to living tissue, and the human species is more sensitive than most to radioactivity. Some forms of radioactivity are persistent, having a high mobility in the environment and a tendency to concentrate in biological systems.

Radiation damage takes three forms: immediate physical damage to tissues (‘radiation burns’); delayed damage (cancer); and genetic abnormalities (mutations) including cancer in successive generations.

There are three common SI units describing the effects of radioactive emission/absorption:

• Becquerel – Quantifies the emission rate or activity of a radioactive source.
• Gray – An absorbed dose of radioactive energy (J/kg of tissue).
• Sievert – An absorbed dose modified by a factor to account for the relative susceptibility of the irradiated tissue to a particular type of ionizing radiation, e.g. alpha particles, beta particles, gamma rays etc.

8.3.1 Photovoltaic Power Plants

In 1839, French scientist Henri Becquerel discovered the photo effect; that is, that in some substances, electrons can be separated from their atoms by exposure to discrete packets of light or photons.

The phenomenon can be understood by considering electron orbits. The outermost band (or orbit) that an electron can occupy and still be closely associated with its atom is called the valence band.

An electron receiving energy can jump to a higher conduction band (or orbit), where it may roam through a substance.

The gap between these bands is called the forbidden band, and the amount of energy required to jump the gap is material‐dependent.

Materials can be classified by their valence bands and band gaps thus:

• Insulators are materials with (electron) full valence bands and high band‐gap energies (>3 eV or > 4.8 × 10⁻¹⁶ J).
• Conductors are materials with relatively empty valence bands and low band‐gap energies.
• Semiconductors are materials with relatively full valence bands and lower band‐gap energies (< 3 eV or < 4.8 × 10⁻¹⁶ J).

Examples of semiconductors and their band‐gap energies include copper indium diselenide (1.01 eV), silicon (1.11 eV), cadmium telluride (1.44 eV), cadmium sulphide (2.42 eV) and gallium arsenide (1.4 eV).

In PVs, photons of solar radiation are used to raise an electron from the valence band to the conduction band, making themselves available for current flow.

Photonic energy (W_photon, Joules) is calculated from:

(8.1)

where h is Planck's constant , f is the photon frequency (Hz), λ is the photon wavelength (m) and c is the speed of light in a vacuum.

Photons having less energy than the material band‐gap energy will not raise any electrons, and photons with more energy will dislodge electrons but expend their surplus energy in heat.

Photovoltaic technology exploits this discovery to convert sunlight directly into DC electricity. Suitable power conditioning facilitates a conversion to AC electricity.

Four main types of PVs are currently available:

• Mono‐crystalline silicon – These forms are blue/black and homogenous in appearance. They are sliced from a single silicon crystal. Cell conversion efficiencies are in the range 13–17%, with slightly lower module efficiencies of 12–15%. Typically, a single cell with dimensions of 100 mm × 100 mm can generate 3 amps at 0.5 volts, i.e. 1.5 watts in bright sun.
• Polycrystalline silicon – Polycrystalline forms are blue and multi‐faceted in appearance. They are made from a silicon cast in a mould and consequently can be larger than monocrystalline forms. Cell conversion efficiencies are in the range 12–15%, again with slightly lower module efficiencies of 11–14%. They are cheaper than monocrystalline forms.
• Thin film – These are matt black, grey or brown in appearance. They are made by depositing an amorphous silicon, cadmium telluride or copper indium diselenide coating onto a glass front substrate. The substrate is laminated or polymer coated to provide climatic protection. Cell conversion efficiencies are in the range 5–10%, with lower module efficiencies of 4–7.5%. They are cheaper than polycrystalline forms.
• Dye‐sensitive polymers – Their operation is unlike the PV forms described above, and it more closely resembles photosynthesis. They are manufactured from semiconductor titanium dioxide (TiO₂) and a conducting saline solution, printed onto film.

Although their conversion efficiency is much lower (< 5%), their construction materials are non‐toxic and cheap to produce. Furthermore, they are relatively tilt and shading‐insensitive and their efficiency increases with increasing ambient temperature.

For a single cell, the current is a maximum and the voltage zero under short circuit conditions. Under open circuit conditions, the current is zero and the voltage is a maximum. Between these two conditions, the current–voltage relationship varies, as shown in Figure 8.4.

To obtain useful voltages and currents, PVs are operated in a series/parallel, modular arrangement. For PVs in series, the voltages are additive at a given current and for PVs in parallel, the currents are additive at a single voltage, as shown in Figure 8.5.

The electrical DC power (W) generated by a single cell can be calculated from:

The annual energy output (kWh/m²) of a PV module can be estimated from:

(8.2)

where:

• 
• 
• 
• 
• .

8.3.2 Solar Thermal Power Plants

Many people associate solar electricity generation solely with photovoltaics and not with solar thermal power. Yet, large, commercial, concentrating solar thermal power plants have been generating electricity at a reasonable cost for a number of years.

Solar thermal power plants are designed to maximize the collection of thermal radiation from the sun by focusing and directing solar rays in order to concentrate thermal energy density.

Most techniques for generating electricity from heat need high temperatures to achieve reasonable efficiencies. The output temperatures of non‐concentrating solar collectors are limited to below 200 °C. Concentrating systems are able to do much better. Due to their high costs, lenses are not usually used for large‐scale power plants, and more cost‐effective alternatives are used, including reflecting concentrators. The four most common reflecting arrangements are shown in Figure 8.6.

The reflector, which concentrates the sunlight to a focal line or focal point, has a parabolic shape; reflectors usually track the sun. In general terms, a distinction can be made between one‐axis and two‐axis tracking: one‐axis tracking systems concentrate the sunlight onto an absorber tube in the focal line, while two‐axis tracking systems do so onto a relatively small absorber surface near the focal point of the system.

8.4.1 Forestry, Agricultural and Municipal Biomass for Direct Combustion

Commercially available woody biomass fuels include pellets, logs and chips.

From a practical perspective, the four most important wood biomass fuel characteristics to consider are bulk density, ash content, moisture content and calorific value.

8.4.1.4 Calorific Value (kJ/kg) and Combustion

Wood combustion processes are quite complex due to the nature of the fuel and its non‐uniformity. For dry wood (zero moisture content), the following simplified stoichiometric combustion equation (with oxygen) can be used to estimate product/reactant quantities:

(8.3)

The ultimate (i.e. elemental weight fraction) analysis of dry wood varies slightly from one species of plant to another, but a typical composition for a woody biomass is shown in Table 8.2.

Composition	% by weight
Hydrogen	6.0
Carbon	51.4
Nitrogen	0.4
Oxygen	41.3
Sulphur	0.0
Chlorine	0.0
Ash	0.9
Total	100.0

In order to estimate calorific value, the reactions and energy releases of three elements, i.e. carbon, hydrogen and sulphur, with oxygen must be considered:

• Combustion of carbon:
  
  Carbon has an energy content of 32 793 kJ/kg.
• Combustion of hydrogen:
  
  Hydrogen has an energy content of 142 920 kJ/kg.
• Combustion of sulphur:
  
  Sulphur has an energy content of 9300 kJ/kg.

For example, the resulting calorific value of the fuel detailed in Table 8.2 can be determined by using the weighted mass fraction and component calorific values, thus:

During the combustion process, hydrogen reacts with oxygen to produce water. This will have a negative impact on the resultant calorific value.

Energy used in product water content

Therefore

Typically, in practice, the combustion of dry wood releases about 10–20 MJ per kg.

The following empirical equation may be used to evaluate the higher heating value (HHV, kJ/kg) of biomass:

(8.4)

where C is the weight fraction of carbon; H of hydrogen; O of oxygen; A of ash; S of sulphur and N of nitrogen appearing in the ultimate analysis.

8.4.2 Anaerobic Digestion

Responsible gardeners do not dispose of non‐woody plant and vegetation waste in their waste‐disposal bins. They collect and store or ‘compost’ it in a container so that the products of the natural decomposition of the materials can be used as a fertilizer. Waste plant material used in this way is, quite often, just heaped in a corner of the garden. On the surface of the store, air‐loving or aerobic bacteria break down the material into carbon dioxide, water and residue. However, deep inside the heap or store, there is little air and the bacteria carrying out the breakdown are said to be doing their work under anaerobic (air‐absent) conditions.

(Incidentally, the anaerobic process also goes on in landfill sites, marshland and the guts of ruminants, for example, cows, sheep etc.)

When containers are used for compost storage, they are not usually air‐tight. An anaerobic digester is a scaled‐up storage container with the air deliberately excluded and seeded with bacteria that thrive in the absence of air.

As by‐products of their metabolism, the bacteria in an anaerobic digester produce methane and carbon dioxide (biogas) and a solid/liquid fraction (digestate).

The composition of the biogas will vary depending on the biomass feedstock or ‘substrate’ and process conditions. Typically, a biogas might comprise approximately 65% methane and 35% carbon dioxide, with nitrogen, hydrogen, ammonia and hydrogen sulphide having trace (< 1%) presences.

The energy content of biogas is in the range 17–25 MJ/m³. This compares with 34 MJ/m³ for natural gas.

The digestate is rich in nutrients (nitrates, phosphates, potassium) and can be used as a fertilizer.

Many different biomass waste sources or substrates can be used in anaerobic digestion, including animal slurries, silage, sewage sludge, food processing waste and household/kitchen waste. Woody wastes are, however, less suitable, as the bacteria find them difficult to metabolize. Important substrate properties include the proportion of substrate that is non‐liquid, the proportion that is organic, i.e. composed of carbon and hydrogen compounds and will decompose to form a fuel, and the biogas yield. Energy output can be estimated from:

Annual biogas energy production (MJ/annum) = Biogas production (m³/annum) × Biogas energy content (MJ/m³)

• where Biogas production (m³/annum) = Mass of substrate (tonnes/annum) × [Volatile solid content (%)/100] × Biogas yield (m³/tonne of volatile solid)
• and Biogas energy content (MJ/annum) = 0.34 × [Biogas methane content (%)/100].

The biogas generation process takes place in three stages:

• The addition of water (termed hydrolysis) to break down the waste matter (cellulose and proteins) into amino acids, fatty acids and glucose.
• The conversion (acidification) of these products into organic acids, hydrogen and carbon dioxide by acid and acetate‐forming bacteria.
• The digestion of the organic acids and hydrogen by other bacteria, converting them to methane, carbon dioxide and water (this is termed methanogenesis).

Anaerobic bacteria at the centre of the process require specific conditions to thrive. Typical desirable conditions include:

• The absence of oxygen.
• A substrate with a minimum 50% moisture content.
• An appropriate temperature depending on the strain of bacteria (supplementary heating is usually essential at northern European latitudes).
• Sufficient retention time prior to production (25–40 days for temperatures of 30–40 °C).
• A digester pH value of ∼ 7.5.
• Sufficient substrate surface area – may need chopping/grinding.
• Good mixing in the digester to provide even conditions and avoid pressure build‐up.
• The absence of disinfectants and antibiotics in the substrate.

Distinct environments or zones develop within the reactor over time, as shown in Figure 8.8, resulting in liquid and solid outputs in addition to biogas.

Digester capacities in the range of 5–100 m³ are regarded as small scale, having typical annual substrate supplies in the region of 100–1000 tonnes.

Digester capacities over 100 m³ are classified as farm or large scale, having typical annual substrate supplies in the region of 1000–15 000 tonnes.

After cleaning and gas separation (i.e. CO₂, H₂S, O₂ etc.), biogas can have a range of uses, for example, electricity and heat production in a gas engine. Alternatively, if its calorific value is boosted by the addition of propane, cleaned and pressurized, the resulting biogas (or biomethane) can be injected into the local gas distribution network.

8.4.3 Biofuels

Fuels like gasoline and diesel are based on the distillation and reforming of fossil fuels. The energy they release depends on the breaking of carbon and hydrogen molecular bonds that once constituted ancient life.

Current life on the planet is, of course, still based on the chemistry of carbon and hydrogen, with the important difference that these bonds are being continually re‐made through naturally occurring biochemical cycles.

With a little knowledge of organic chemistry, contemporary carbon and hydrogen can be manipulated to produce renewable liquid fuels or biofuels (principally biodiesel and bioethanol) to be blended with non‐renewable transport fuels.

8.4.3.1 Biodiesel

Around the turn of the 19th century, Rudolf Diesel demonstrated his new compression‐ignition internal combustion engine in Paris. The fuel used by the engine was peanut oil. However, the fast‐developing petrochemical industry soon produced a fossil‐fuel‐based alternative that was cheaper and more readily available.

Diesel's ‘vegetable oil’ fuel has merit and, in the 21st century, this idea is being revisited. In the last 100 years, our understanding of combustion and gas dynamics has improved greatly. It is now understood that reacting a basic vegetable oil with either ethanol (grain alcohol) or methanol (wood alcohol) results in a much‐improved, diesel‐like fuel, i.e. biodiesel. (A chemist or chemical engineer would describe the resulting fuel as an ester and the process as transesterfication.)

The process also results in a useful glycerol by‐product.

Sources of vegetable oils (e.g. rapeseed, sunflower, palm, soya etc.) are commonly used in food processing and are readily and cheaply available. Even waste cooking oil and animal fats have potential as a feedstock for biodiesel.

How does the biodiesel compare with its fossil fuel competitor? For a given volume, the energy content of biodiesel at approximately 34 MJ/m³ is typically 10–20% less than fossil‐fuel diesel. However, compared to normal diesel, biodiesel produces fewer particulates, unburnt hydrocarbons and less carbon monoxide. Typically, 20% of biodiesel can be added to normal diesel as a blend in an unmodified engine.

Blends are usually signified by the use of B followed by the percentage of biodiesel in the blend, for example, B5, B10 and B20.

In Europe, most biodiesel uses rapeseed as a feedstock, with a typical biodiesel annual yield of 1.3 tonnes per hectare.

8.4.3.2 Bioethanol

Bioethanol is the renewable analogue to fossil‐fuel gasoline. Unlike biodiesel it is commonly produced from glucose‐rich plants like corn, sugar cane, beet or sorghum by fermentation in the presence of micro‐organisms. In its simplest form:

It is also possible to produce simple sugars and ethanol from starch‐rich (grain and root) crops and cellulose (woody) plants. Cellulose feedstock, in particular, requires a little more processing (acid or enzyme hydrolysis); however, it is easier to grow and does not place the same demands on the soil as sugar‐rich plants, making it suitable for marginal land, and therefore avoiding conflict with food crop production.

Micro‐organisms are sensitive to their living environment and so the ethanol must be produced at low concentrations and distilled later.

How does the bioethanol compare with its fossil fuel competitor? For a given volume, the energy content of bioethanol at approximately 25 MJ/m³ is typically 25–33% less than fossil‐fuel gasoline. However, power loss is limited due to the better combustion efficiency of the biofuel.

Typically, 20% of bioethanol can be added to normal gasoline as a blend in an unmodified engine. With engine modification, use of up to 85–95% bioethanol is possible.

In Europe, typical bioethanol annual yields of 5 tonnes per hectare for sugar beet and approximately 2 tonnes per hectare for wheat are possible.

On the face of it, the use of liquid biofuels seems to provide a possible answer to carbon dioxide emissions associated with transport.

Some countries have a ‘set‐aside’ policy for agricultural land, and bringing this land back into production for liquid biofuels would again appear logical.

Additionally, the large‐scale take up of liquid biofuels could help reduce a country or region's dependence on imported oil.

However, the ‘food vs. fuel’ issue has to be considered, especially for countries that do not have a food surplus. To alleviate this dilemma, research and development of crops that are able to thrive on marginal land is required.

Furthermore, fossil‐fuel‐based fertilizer is often used to help produce the biofuel crop, and so the ratio of energy produced to fossil fuel consumed is relevant. The magnitude of this ratio varies with crop and land quality. This factor has given rise to ‘second generation’ biofuels based on agricultural and forestry waste.

8.4.4 Gasification and Pyrolysis of Biomass

Compared to gaseous fuels, the combustion of biomass is quite complex. For the combustion of methane with an oxidant, the process concerns the breaking of the gaseous reactant molecules and the formation of the gaseous product molecules, e.g. CO₂, H₂O. However, for the combustion of biomass, it is more accurate to describe the process as being a thermal decomposition of the fuel that boils off the fuel's water content and volatilizes its constituents to produce gases, condensable vapours and a char.

• The process is sequential and temperature‐dependent.
• Some steps require little or no oxidant.
• At 100–150 °C, the water content of a biomass fuel boils off.

At 200–500 °C and in an oxygen‐starved environment, the wood is volatilized to form gases, a bio‐char and a bio‐tar. This low‐temperature anaerobic process is termed pyrolysis. (Roasting between 200–320 °C is termed torrefaction. This produces a superior solid biomass fuel in terms of transport, storage and suitability for further processing.)

At 500–800 °C, the gases would normally combust; however, if the biomass is denied an oxidant at 650–800 °C, the bio‐char is further converted into complex flammable gases (‘producer gas’), and above 800 °C, any remaining tar residues are broken down into simpler components (H₂, CO) which can be reformed into complex fuels. This high‐temperature reduction process is termed gasification.

If the combustion phase is retarded by supplying insufficient oxidizer, it is possible to control the process to maximize the output of condensable vapours and flammable gases (CH₄, H₂ and CO). The control of oxidant (whether oxygen, air or steam), heat supply rate and residence time is at the heart of the pyrolysis and gasification of biomass. The processes are not new and the chemistry for other solid fuels such as coal has been practised for around 100 years. A typical biomass gasifier is illustrated in Figure 8.9.

8.6.1 Theory of Wind Energy

A wind turbine extracts power from the wind by slowing it down. At stand still, the rotor obviously produces no power; at very high rotational speeds, the air is more or less blocked by the rotor, and again no power is produced.

The power produced () by the wind turbine is determined from the net kinetic energy change across it (i.e. from the initial air velocity of at inlet to a turbine exit air velocity of , see Figure 8.13) and is described by:

(8.5)

The mass flow rate of wind is given by the continuity equation as the product of density, area swept by the turbine rotor and the approach air velocity:

(8.6)

Hence, the power becomes:

(8.7)

where is the average speed between inlet and outlet:

(8.8)

Substituting, the power becomes:

(8.9)

To find the maximum power extracted by the rotor, differentiate Equation (8.9) with respect to and equate it to zero:

(8.10)

Since the area of the rotor (A) and the density of the air (ρ) cannot be zero, the expression in the bracket has to be zero. Hence, factorizing the quadratic equation:

Since is unrealistic in this situation, there is only one solution:

(8.11)

Substitution of Equation (8.11) into Equation (8.8) results in:

(8.12)

Equation (8.12) clearly shows that the power:

• Is proportional to the density (ρ) of the air, which varies slightly with altitude and temperature.
• Is proportional to the area (A) swept by the blades and thus to the square of the radius (R) of the rotor.
• Varies with the cube of the wind speed . This means that the power increases eightfold if the wind speed is doubled. Hence, one has to pay particular attention with respect to site selection.

The value in brackets in Equation (8.12) (0.5925) is termed the Betz limit and indicates the theoretical maximum fraction of the power in the wind that could be extracted by an ideal wind turbine. Maximum efficiency depends on optimal wind velocity ratio conditions.

Away from optimal conditions, the theoretical output of the wind rotor is adjusted by the application of a power coefficient, C_p. The variation in power coefficient with wind velocity ratio is shown in Figure 8.14.

8.6.1.1 Actual Power Output of the Turbine

Equation (8.12) does not take into account the mechanical and electrical losses incurred in the production of electricity from a wind turbine. Allowing for non‐optimal aerodynamic conditions and gearbox/electrical generator efficiencies ( and ), the following can be used to predict the shaft power of a wind rotor:

(8.13)

The effect of these factors can be examined by considering the world's largest wind turbine generator which has a rotor blade diameter of 126 metres (rotor swept area 12 470 m²) and is located offshore at sea level where the air density is approximately 1.2 kg/m³.

At its rated wind speed of 14 m/s, the theoretical wind power produced is given by Equation (8.12) and is approximately 12 MW. However, the turbine is rated at 5 MW.

The difference in values indicates the influence of the power coefficient C_p and inefficiencies in the electrical and mechanical power transmission.

Care must be taken when selecting a turbine and assessing the likely energy generation, as the ‘rated power’ is only available when the wind turbine speed reaches a certain level, known as the rated speed. Wind turbine speed performance is split into four different stages:

1. Start‐up speed – The speed at which the rotor and blade assembly begin to rotate.
2. Cut‐in speed – The minimum wind speed at which the wind turbine will generate any usable power. This wind speed is typically between 3 and 4.5 m/s for most turbines.
3. Rated speed – The minimum wind speed at which the wind turbine will generate its designated rated power.
4. Cut‐out speed – The wind speed at which the turbine is intentionally shut down. This is a safety feature to protect the wind turbine from damage. It is facilitated using an automatic brake or ‘spoilers’, which are drag flaps mounted on the blades or the hub, activated by excessive rotor revolutions. Alternatively, the entire machine may be turned sideways to the wind stream at high wind speeds.

8.6.2 Wind Turbine Types and Components

There are two types of wind turbine, distinguished by the axis of rotation of the rotor shafts:

1. Horizontal‐axis wind turbines, also known as HAWT types, have a horizontal rotor shaft and an electrical generator, both of which are located at the top of a tower. The gearbox/generator housing is termed the nacelle.
2. Vertical‐axis wind turbines (VAWT types) are designed with a vertical rotor shaft and a generator and gearbox placed at the base of the turbine. The turbine has a uniquely shaped rotor blade that is orientated to harvest the power of the wind no matter in which direction it is blowing.

Examples are shown in Figure 8.15.

8.7.1 Types of Hydraulic Power Plant

There are two types of hydropower plant in use: run‐of‐river schemes and storage systems.

8.7.1.1 Run‐of‐river Hydropower

Run‐of river hydropower schemes (see Figure 8.17) require a bifurcation or separation of a proportion of the flow via a weir impoundment system (1).

The take‐off canal (2) is commonly called the headrace or leat.

At the end of the headrace is a settling tank (3), often called the forebay.

The forebay/headrace may contain spillways (4) to return excess flow to the river. From the forebay, the water enters a pipe (5), commonly called the penstock, to commence the final leg of its journey down to the hydro‐turbine. If a site has difficult topography or is environmentally sensitive, the canal is sometimes omitted and an extended penstock carries water from the river bifurcation direct to the powerhouse.

The hydro‐turbine and electrical generator are sited in the powerhouse (6).

After passage through the turbine, the water is returned to the river or stream via a calming channel (7), known as the tailrace.

In a barrage scheme arrangement, the headrace and penstock are dispensed with and the powerhouse is effectively in‐line with the river or stream.

Whether considering an impoundment or a barrage scheme, the fraction of flow diverted for energy generation must not leave the depleted region (reach) of the river ecologically damaged, and consequently, extensive local hydrological and biological studies are carried out prior to scheme sizing.

8.7.1.2 Storage Hydropower

Typically, these are large systems that use a dam to store water in a reservoir (see Figure 8.18). Electricity is produced by releasing water from the reservoir through a turbine, which activates a generator.

Storage hydropower provides base load as well as the ability to be shut ‐down and started up at short notice according to the demands of the system (peak load). It can offer enough storage capacity to operate independently of the natural hydrological inflow for many weeks or even months.

8.7.2 Estimation of Hydropower

In a storage hydropower system, the amount of power produced from water is proportional to the potential energy available, due to the difference of head between the surface levels of the upper and lower reservoirs and the mass flow rate of water going through the turbine.

For a reservoir head difference of h (m), the general equation for fluid power (W) is:

(8.14)

However, the actual power produced by the turbine unit is less than is indicated by Equation (8.14) because of frictional losses (Δh_f, m) in the transmission pipework and the turbine's efficiency (η_t, %). If the efficiency of the electrical generator is (η_gen, %), the power output () of the system is:

(8.15)

Run‐of‐river schemes are also evaluated in terms of flow rate (m³/s) and head difference or river fall (m).

8.7.3 Types of Hydraulic Turbine

Traditionally, there are three different types of turbine used in hydropower generation: the Pelton wheel, the Francis turbine and the Kaplan turbine, each of which has different characteristics to suit the available head (m) and discharge or flow rate (m³/s) (see Figure 8.19).

For low‐head, run‐of‐river schemes, technology with a long history is being employed – the Archimedean screw. This technology was first used over 2000 years ago as a pump for lifting water from a river to its bank. However, in power‐generation schemes, a portion of the flow is diverted and the head variation or fall along the river (perhaps via a weir) is used to drive the screw. The screw shaft is connected to a generator, as shown in Figure 8.20.

8.8.1 Characteristics of Waves

The motions of real water waves are complex. Simple analyses assume they have a regular repeating pattern of crests and troughs, as shown in Figure 8.21.

The distance between any two repeating points on the wave is called the wavelength (metres). The time taken for a wave to travel a distance of 1 wavelength, that is to complete a cycle, is called the period (T, seconds). Typical values of ocean wave periods are in the range 1–30 seconds. Storm and earthquake waves can have periods ranging from minutes to hours.

This factor is important, as the power (watts) available in a water wave increases directly with period, so, for example, a wave with a period of 10 seconds will, potentially, have two times more power than a wave with a period of 5 seconds.

The maximum vertical disturbance distance from wave crest to wave trough is called the wave height (H, metres) and depends on the prevailing wind regime.

The term amplitude (a, metres) is used to describe ½ the wave height.

This factor is important, as the power (watts) available in a water wave increases with the square of the amplitude, so, for example, a wave with an amplitude of 2 m will, potentially, have four times more power than a wave with an amplitude of 1 m.

8.8.2 Estimation of Wave Energy

The energy per metre of wave crest and unit of surface is given as:

(8.16)

where ρ (kg/m³) is the density of water.

It can be shown that the wave power available is given by:

(8.17)

8.8.3 Types of Wave Power Device

There are several varieties of wave energy converter (WEC).

If deep water is available close to the shoreline, waves may be directed up a focusing ramp arrangement over a sea wall into a collection tank or reservoir in a so‐called wave capture system. At the base of the reservoir is a low‐head water turbine through which water is returned to the sea.

Essentially, this arrangement is recreating a typical hydroelectric scheme with seawater (see Figure 8.22).

In oscillating‐column devices, the up and down motion of the water wave is used to create a mirrored motion in a volume of enclosed air (see Figure 8.23). The air can only exit its enclosure by passing through an air turbine connected to an electrical generator. The air direction will, of course, change as the water wave rises and falls, but this is overcome by use of a machine called a Wells turbine whose rotational direction is insensitive to the flow direction of the air. Shoreline and floating varieties of this kind of device have been demonstrated to have potential for significant energy generation.

Point absorber wave energy devices usually employ a float to utilize the reciprocating aspect of a wave. Energy conversion and take‐off can take a range of forms, as shown in Figure 8.24. For example, the resulting motion can be used to drive a simple hydraulic pump to transfer a fluid to a reservoir and generator set.

Alternatively, the reciprocating motion can be used directly to drive a permanent magnet linear generator (a set of coils and magnet stack) mounted on the seabed.

These devices have the advantage of being insensitive to wave direction (see Figure 8.24).

Point absorbers may also be completely submerged static‐pressure devices. In this case, as a wave with its peaks and troughs passes above the device, a gas‐filled chamber, tethered to the seabed, will experience changes in pressure (due to the height of water above it), which cause it to move up and down relative to a fixed power take‐off point (see Figure 8.25). Again, the motion can be used to drive a pumping system or to generate electricity directly. This arrangement has the advantage of not exposing the system to the most damaging aspects of oceanic existence in the wave zone.

Floating and semi‐submerged wave profile or line absorber devices typically rock back and forth and side to side in response to incident waves, i.e. they ride the waves instead of responding solely to the vertical motion. They often comprise replicated, articulated units (see Figure 8.26). The motion experienced at the universal joints is transferred to hydraulic rams that create pressure in a hydraulic system connected to electrical generators.

Wave surge devices comprise hinged‐flap structures that oscillate back and forth in a horizontal plane (like a pendulum) with the passage of a wave (see Figure 8.27). The motion is converted into fluid pressure by, for example, a piston arrangement attached to the flap. The piston motion can be used to pump a fluid to a reservoir and electrical generator set.

8.8.4 Tidal Power

The moon and earth are locked together, with a mutual force of gravitational attraction keeping them wedded. The effect is complicated by the planet's oceans, since the liquid and solid parts of the planet feel the pull of the moon to a different extent. The oceans feel it more and, in fact, bulge out towards it in its orbit (and a second bulge is generated on the other side of the planet). This effect is further enhanced, but to a lesser extent, by the proximity of the sun.

As the earth rotates under the bulges, the oceans ebb and flow at the coastline. These are the tides. The difference in height between the highest and lowest level of the tide is termed the tidal range. Out in the deep ocean, the height of the swelling is of the order of 1 m; however, at the ocean's edge, the reducing depth and shape of the coastline can modify the phenomenon, producing much larger tidal ranges. The greatest tidal range in the world is found in the Bay of Fundy (∼ 16 m) in Canada. The second highest tidal range (∼ 15 m) is found in the Severn estuary in the UK.

The time between bulges crossing a point on the planet is approximately 12 hours 25 minutes and is entirely predictable, unlike other forms of renewable energy like wind and solar, making this source very attractive from a power supply management point of view.

This effect can be harvested in two different ways.

8.8.4.1 Tidal Barrage Energy

In tidal barrage schemes, a sea dam is constructed between two adjacent points on a coastline, for example, an estuary, forming a man‐made basin. The basin water volume and difference between water levels across the dam can be controlled via sluice gates. The dam also contains a series of turbo‐generators, making this arrangement, in essence, very similar to a hydroelectric system, in that the energy is produced as a result of a difference in head (h) across the turbine. At its simplest, the greater the tidal range, the greater the potential for energy production. With the utilization of turbines that are insensitive to flow direction, the sluice/turbine arrangement has a good degree of flexibility for ebb/flow generation and/or making the basin available for storage considerations.

Depending on maritime traffic, barrage schemes may require a navigation lock. However, barrages can also double as bridges, providing new road links across the chosen estuaries.

The general characteristics of a tidal barrage scheme are shown in Figure 8.28.

The average fluid power generated by a scheme can be estimated from Equation (8.14), i.e. .

In the case of a tidal scheme, the basin volume is the product of basin area (A) and the tidal range (h). The tidal flow rate will be the basin volume divided by the time between tides, i.e. 4.47 × 10⁴ seconds.

Finally, the power is calculated using the tidal range mid‐point (h/2) thus:

(8.18)

8.9.1 Direct Thermal Energy to Electrical Energy Conversion

The discovery of direct thermal to electrical energy conversion is not recent. In early‐1830s Berlin, Thomas Johann Seebeck heated the junction of a circuit comprising two different metals. He detected a magnetic field close to the circuit but failed to make the link with the presence of a voltage in the circuit. Nevertheless, his work is celebrated by the term Seebeck effect.

Consider the open circuit in Figure 8.29 comprising two different material electrical conductors forming a junction. With a suitable electron intensity difference between the two materials at the heated junction, the application of a little heat input is sufficient to allow electron flow, realizing a potential difference detectable across the circuit.

The magnitude of the voltage is proportional to the temperature of the junction and the chosen materials.

The slope of the voltage–junction temperature relationship is termed the Seebeck coefficient (α_ab, V/K) for the combination of materials a and b.

Mathematically:

(8.19)

where .

The absolute Seebeck coefficient of an individual material (α_i) can be determined by connecting it in a circuit with a superconductor. A comparison of some material Seebeck coefficients at 100 °C is shown in Table 8.3.

Notice that some material coefficients are quoted as positive and some negative. This convention is determined by the resulting flow direction in the circuit.

In 1834, French physicist Jean Peltier applied an electric current to a circuit comprising two dissimilar metals. He discovered that one of the circuit junctions increased in temperature while the other was cooled. He also found that the temperature change depended on the magnitude of the current and that if the current flow was reversed, the junction conditions reversed.

Consider the circuit in Figure 8.30 comprising two different material electrical conductors forming two junctions and a voltage source.

With a current flowing in the circuit, it is found that heat is absorbed at one of the junctions (cold junction) and released at the other (hot junction).

The magnitude of the effect is expressed by the Peltier coefficient (π_ab, volts), which is a function of current (I) and is defined thus:

(8.20)

where Q is the heating (or cooling) effect.

This is essentially a phenomenon coupled with the Seebeck effect and the two are linked by:

(8.21)

where T is the absolute junction temperature in Kelvin.

8.9.2 Thermoelectric Generators (TEGs)

In energy‐harvesting terms, a Peltier device consists of a circuit comprising two dissimilar materials, two junctions, a heat source, a heat sink and a connected external load. A current can be generated in the bi‐material circuit when one junction is heated and the other cooled.

Potentially (p and n type) semiconductors make better thermoelectric generators than metals because of their higher Seebeck coefficients.

A schematic of a semiconductor, single junction thermoelectric generator is shown in Figure 8.31.

For useful power production, such units are usually connected in a series/parallel arrangement where a number of p‐type and n‐type semiconductor materials are sandwiched between electrically insulated ceramic plates joined together by interconnected copper pads.

The power generated in the thermoelectric circuit is given by:

(8.22)

From Ohm's Law and the Seebeck voltage–temperature relationship:

(8.23)

The resistance of the generator is given by:

(8.24)

where A (m²) is the cross‐sectional area of the TEG circuit, L (m) its length and ρ its resistivity (Ω/m).

Substituting into the above, the total power generated by a thermoelectric device is given by:

(8.25)

The thermoelectric generator will be connected in series with the external load. The power expended at an external load will depend on its resistance and resulting current.

For the device described, the efficiency will be the power available across a connected load divided by the power input to the hot junction or heat source.

(8.26)

In general, efficiency values for thermoelectric generators tend to be low, with values below 10% being commonly reported.

However, they have no moving parts, are compact and can use almost any source of thermal energy as the hot source.

8.10.1 Principles of Simple Fuel Cell Operation

• At the anode, hydrogen undergoes a catalytic reaction, splitting into ions (2H⁺) and electrons (2e⁻).
• Ions traverse the electrolyte; electrons flow through the external circuit.
• At the cathode, hydrogen ions, oxygen and electrons from the external circuit form water in a catalyst‐assisted reaction.

A simple arrangement such as this might generate up to 1 volt DC.

Practical fuel cells comprise repeating units of the above in series, forming a stack to produce a more useful level of power. The number of repeating units determines the voltage and the ionic transfer (or transverse) area determines the current.

Electronic conditioning is required to produce AC power with grid‐compatible parameters.

With hydrogen as the fuel, the technology is carbon‐free at the point of generation. Questions remain over the source of hydrogen for use in such cells. Current potential sources include separation from hydrocarbons (e.g. methane can be reformed into H₂ and CO₂) or the splitting of water. Both are potentially energy‐intensive.

8.10.2 Fuel Cell Efficiency

Care must be taken when quoting the efficiency of a fuel cell. In thermodynamic terms, the reversible cell reaction efficiency (η_reaction) is defined by considerations of molar gas flows (, moles), Gibbs energies (, kJ/mol) and enthalpies (, kJ/mol) at a given temperature and pressure:

(8.27)

This provides an estimate of the maximum efficiency attained in the absence of irreversibilities. The equation is often quoted in terms of the molar‐based higher heating value (HHV) of the fuel thus:

(8.28)

At room temperatures and pressures, and .

Therefore, for a pure hydrogen–oxygen fuel cell operating at standard temperature and pressure, this equation returns an impressive 83% efficiency. The reaction efficiency decreases with increasing temperature. At 1000 °C, the reaction efficiency drops to around 65%.

This is not the full story, however. Fuel cells rely on physical and chemical processes, for example, reaction and concentration kinetics, mixing, migration, absorption and dissolution, for their operation. These are neither instantaneous nor perfect.

From work considerations, the reversible electrical potential (E, volts) of the fuel cell is given by:

(8.29)

where is the number of kilomoles of valence electrons flowing in the external circuit and F is Faraday's constant (96.487 kJ/kmol V). For hydrogen, .

The voltage efficiency (η_voltage) of the fuel cell is expressed as the ratio of the actual voltage (V) appearing across the cell compared to the theoretical potential:

(8.30)

The voltage efficiency is inversely proportional to the load current.

Furthermore, an amount of fuel in excess of stoichiometric is usually supplied to the cell to compensate for poor fuel usage, and a third term, the fuel utilization efficiency (η_fuel), is used to describe its impact. It is expressed as the reciprocal of the ratio of actual fuel input (n_fuel,act) divided by the stoichiometric amount of fuel (n_fuel,_act/n_fuel,sto). Then:

(8.31)

8.10.3 Fuel Cell Types

The specifications of some of the more common fuel types are detailed in Table 8.4. The cell names usually reflect the electrolyte used. In all cases, the fuel is assumed to be hydrogen.

8.11.1 Energy Storage Characteristics

The salient operating parameters when considering which form of energy store to employ are:

• Energy density (J/m³) – the energy stored per unit volume of store.
• Specific energy content (J/kg) – the energy stored per unit mass of store.
• Storage efficiency (%) – the fraction of the input energy that is usefully recovered.
• Retrieval rate and depletion time (W, hrs) – how quickly and for how long the energy exchange can be maintained.
• Capital and operating costs (£).

8.11.2 Energy Storage Technologies

There are a number of storage technologies which may suit a particular application. Final selection should be based on the criteria previously described.

8.11.2.1 Hydraulic Energy

Electrical energy can be stored by using it to increase the potential energy of water in a pumped storage scheme (see Figure 8.33). This requires a mountainous terrain, as excess electricity is used to pump water from a low‐level lake or reservoir to another lake or reservoir at high elevation. At times of increased electricity demand, water is run back down to the lower reservoir via a turbine connected to an electrical generator. The pumping and generating functions are usually combined into one hydraulic machine (i.e. a pump/turbine).

The specific energy content is approximately 10 J/kg per metre elevation.

Potential energy, i.e. the energy associated with a mass (m) at a vertical distance (h, metres) above ground level in the earth's gravitational force field, is given by:

(8.32)

Typical efficiencies are around 80%, with outputs in excess of 100 MW being brought on line and up to full power in seconds. Output can be maintained for hours, making the technology very useful for supply management purposes and smoothing out variations in renewable energy grid input.

The deployment of these systems is facilitated by using surplus energy from the grid at times of low power demand (usually at night) and cheap‐tariff electricity.

The ratio of energy supplied to the network and the energy consumed during the pumping cycle must be considered to evaluate the overall viability of the scheme.

8.11.2.2 Pneumatic Energy

Energy can be stored by forcing the molecules of a gas into close proximity with each other, i.e. by compressing the gas and increasing its density in a compressed‐air energy storage scheme (CAES).

When the pressure of the gas (typically 50–70 bar at 50 °C) is later reduced, the molecules will spring apart, releasing the stored energy.

In practical terms, excess electrical energy is used to compress air by forcing it into a closed pressure vessel. Large‐scale pressure vessels are very expensive, and so natural cavities, like disused salt mines, have been used as containers. When electrical demand increases, the compressed air is released to a turbine generating electricity (see Figure 8.34).

If the compression is carried out isothermally, the energy of compression is given by:

(8.33)

where P₂ is the storage pressure and V₂ the storage volume.

Expanding the air directly during generation will result in a large temperature reduction. In order to protect the turbine, natural gas is used to reheat the air. Alternatively, the heat of compression may be used for this function if a thermal store is provided to operate in parallel with the pneumatic store.

Power outputs are of the order of 1–100's MW, with energy‐depletion times in hours. Care must be taken with definitions of efficiency to include air cooling, drying, reheating of the air etc. Recent developments include cooling the air to its liquefaction point to reduce storage volume.

Again, the technology is very suitable for supply management.

8.11.2.3 Ionic Energy

On a small scale, electrical energy can be stored in rechargeable (or secondary) batteries.

Here, excess electrical energy is converted to electrochemical energy during charging and the reverse during discharge. Performance depends on the rate of charge/discharge.

Lead–acid batteries (specific energy content ∼ 0.14 MJ/kg) have been used for many years for applications of < 10 MW and depletion times of around an hour.

Other materials are available, like nickel–iron and nickel–cadmium (specific energy content ∼ 0.09 MJ/kg). Silica oxide‐based batteries have energy storage capacities of up to 0.4 MJ/kg.

Newer systems like flow (pumped electrolyte) batteries (specific energy content ∼ 1–3 MJ/kg) have better performance, and, with power outputs in the Megawatt range and energy depletion times of up to 10 hours, are being considered for supply management and renewable energy smoothing (see Figure 8.35).

8.11.2.4 Rotational Energy

Electrical energy can be stored by converting it to rotational kinetic energy in a flywheel. The amount of energy that can be stored depends on the mass of the flywheel, the square of its radius and the square of its rotational speed. So, a small change in speed will produce better returns than a small increase in mass. The kinetic energy associated with rotational motion (W_rotate, Joules) about an axis can be evaluated from:

(8.34)

where I_m is the moment of inertia (kgm²) that depends on the dimensions (radius, r; mass, m) and the position of the axis of rotation of the body in the relationship:

(8.35)

The factor k for some simple geometries is given in Table 8.5.

Geometric shape	k
Rim‐loaded thin ring	1
Uniform disc	1/2
Thin rectangular rod	1/2
Sphere	2/5
Spherical shell	2/3

The angular velocity of the body, ω (rad/s) can be determined with either knowledge of the time taken for one complete revolution of the body, t (seconds) or its rotational speed in revolutions per minute (N), thus:

(8.36)

Typical wheel peripheral speeds are 1500–2000 m/s or rotational speeds of 100 000 rpm. The maximum amount of energy that can be stored depends on the ratio of the strength of the flywheel material and its density. The best type of material would have high strength and low density, so, for example, carbon fibre (specific energy content ∼ 0.77 MJ/kg) would make a better flywheel than steel (specific energy content ∼ 0.17 MJ/kg). Storage efficiency (typically in the range 95–98%) is affected by friction losses, so flywheels often operate on magnetic bearings in a vacuum. Power outputs are limited to less than 1 MW and energy‐depletion times are measured in minutes, putting them on the boundary for supply management.

8.11.2.5 Electrostatic Energy

A device capable of storing electrical energy in the form of an electric field is termed a capacitor. A capacitor comprises a material separating two plates capable of accumulating and maintaining an electric charge potential between them.

For a given voltage, V, the energy storage (W_cap, Joules) of a capacitor is given by:

(8.37)

where C (Farad) is the device capacitance.

The capacitance is a characteristic dependent on the material properties and dimensions of the device.

Super‐capacitors and ultra‐capacitors (specific energy content up to 0.03 MJ/kg) are electrical devices that charge much like a battery but discharge electrostatically. Storage efficiencies are high (98%) but power outputs of less than 100 kW are only possible for a few seconds, and so use is confined to maintaining the quality of a power supply.

8.11.2.6 Magnetic Energy

A device capable of storing electrical energy in the form of a magnetic field is termed an inductor. An inductor can be as simple as a current‐carrying coil of wire.

For a given current, I (amps) the energy storage (W_ind, Joules) of an inductor is given by:

(8.38)

where L is the device self‐inductance in Henrys.

For a simple inductor comprising a coil of wire wound around a structure or core, the inductance is dependent on the core dimensions and material as well as the number of turns of wire in the coil.

At very low temperatures (5–20 K), some metals become superconducting, i.e. they have no electrical resistance. Any current passed through a superconductor will produce a magnetic field capable of energy storage. Superconducting magnetic energy storage systems (SMESs) have energy densities of the order of 6.5 MJ/m³. Power outputs in excess of capacitors are possible, but again their energy depletion timeframe is in seconds.