Energy is defined as the capacity to do work Or is defined as ability to do work.

Energy is measured in Joules (symbol J)

Types of energy according to their usefulness

(i)   High grade energy

(ii)    Low grade energy

i. High grade energy is the energy that is easily transformed into other forms of energy and is more suitable for doing works.

Examples are chemical and electrical energy.

ii. Low grade energy is the one that is not easily transformed into anything else.

Examples are the kinetic energy of molecules due to their randomness and the potential energy due to the forces between molecules.


There are two types of energy sources, namely:

(i)    Primary energy sources,

(ii)   Secondary energy sources.

i. Primary energy sources

Primary energy sources are sources of energy that are used in the form in which they occur naturally.

Primary energy sources fall into two groups:

(a)   Finite energy sources,

(b)   Renewable sources.

a. Finite energy sources are those energy sources that last after a number of years when exploited.

Examples are coal, oil, natural gas, and nuclear fuels.

b. Renewable energy sources:  these cannot be exhausted.  Examples are solar energy, biofuels, hydroelectric power, wind power, wave power, tidal and geothermal power, wind power, wave power, tidal and geothermal power.

ii. Secondary energy sources

Secondary energy sources are used in the non – natural form.


Nature of solar energy

The sun’s energy is produced by thermonuclear fusion.

Not all of the solar radiation arriving at the edge of the Earth’s atmosphere reaches the Earth’s surface.

About 30% is reflected back into space by atmospheric dusts and by the polar ice caps.

About 47% is absorbed during the day by the land and sea and becomes internal energy (i.e. heats the Earth).  At night this is radiated back into space as infrared.

23% causes evaporation from the oceans and sea to form water vapour.  This results into rain and hence hydroelectric power.

-0.2% causes convection currents in the air, creating wind power which in turn causes wave power.

-0.02% is absorbed by plants during photosynthesis and is stored in them as chemical energy.  Plants are sources of biofuels

Solar constant

Solar constant is defined as the solar energy falling per second on a square meter placed normal to the sun’s rays at the edge of the Earth’s atmosphere, when the Earth is at mean distance from the sun.

Its value is about 1.35 kWm2

The amount of solar radiation received at any point on the earth’s surface depends on:

(i)  The geographical location,

(ii)   The season, (summer or winter)

(iii)   The time of the day, the lower the sun is in the sky the greater is the atmospheric absorption.

(iv)   The altitude; the greater the height above sea level the less is the absorption by the atmosphere, clouds and pollution


A solar cell (PV, cells) is a PN junction device which converts solar energy directly into electrical energy.

How it Works

PV cells are made of at least two layers of semiconductor material.  One layer has a positive charge (p – type material), the other negative (n-type material).  When light enters the cell, some of the photons from the light are absorbed by the semiconductor atoms, freeing electrons from the cell’s negative layer to flow through an external circuit and back into the positive layer.  This flow of electrons produces electric current.

Uses of the solar cell

1.       (i)Are used to power electronics in satellite and space vehicles.

2.      (ii)Are used as power supply to some calculators.

3.      (iii)Are used to generate electricity for home, office and industrial uses.

Series arrangement of solar cells

Solar panel (module) is a sealed, weatherproof package containing a number of interconnected solar cells so as to increase utility of a solar cell.

When two modules are wired together in series, their voltage is doubled while the current stays constant.

When two modules are wired in parallel, their current is doubled while the voltage stays constant.

To achieve the desired voltage and current, modules are wired in series and parallel into what is called a PV array.
The flexibility of the modular PV system allows designers to create solar power systems that can meet a wide variety of electrical needs, no matter how large or small.

Efficiency of a photovoltaic system

The output power of a solar cell depends on:

(i)    The amount of light energy from the sun falling on a solar panel (the intensity of light).

(ii)   The orientation of the solar panel.  More electricity is produced if light falls perpendicular to panels.

(iii)   The surface area of the panel.  Large area collects more solar energy and hence greater electricity.

The best designed solar cell can generate 240 Wm-2 in bright sun light at an efficiency of about 24%.

Advantages of photovoltaic systems

1.   Solar cells can produce electricity without noise or air pollution.

2.   A photovoltaic system requires no fuels to purchase.

3.    Panels of photovoltaic cells are used for small – scale electricity generation in remote areas where there is sufficient sun.

4.    Net metering:  This has the potential to help shave peak loads, which generally coincide with maximum PV power production.

5.    The electricity from a PV system is controllable.

Disadvantages of photovoltaic systems

1.   They require an inverter to convert the d.c output into a. c for transmission.

2.   They produce electricity only when there is sunlight.  Hence they need backup batteries to provide energy storage.

3.   Suitable in areas which receives enough sunlight.

4.   Photovoltaic large scale power generation is cost effective.  This is due to large surface area of cells required for generating high power outputs and the need to convert d.c to a.c for transmission.

5.   Compared to other energy sources, PV systems are an expensive way to generate electricity.

6.   The available solar resource depends on two variables: The latitude at which the array is located and the average cloud cover.


Winds are due to conventional currents in the air caused by uneven heating in the earth’s surface by the sun.

Wind energy is extracted by a device called wind turbine.

Wind speed increases with the height; it is greatest in hilly areas.  It is also greater over the sea and coastal areas where there is less surface drag.

Wind turbines are also called aerogenerator or wind mills (old name)

Types of wind turbines

There are two types of wind turbines;

(i)    Horizontal axis wind turbines (HAWT)

(ii)  Vertical axis wind turbines (VAWT)

Horizontal axis wind turbine (HAWT)

HAWT has two or more long vertical blades rotating about a horizontal axis.  Modern HAWTs usually feature rotors that resemble aircraft propellers, which operate on similar aerodynamic principles, i.e. the air flow over the airfoil shaped blades creates a lifting force that turns the rotor.  The nacelle of a HAWT houses a gearbox and generator (alternator).

Advantage of HAWT

1.   HAWTS can be placed on towers to take advantage of higher winds farther from the ground.

Disadvantages of HAWT

1.  The alternator (generator) is paced at the top of the supporting tower.

2.  Can produce power in a particular wind direction.

Vertical axis wind turbine (VAWT)

In vertical axis, the blades are long and vertical and can accept wind in any direction.  The blades are propelled by the drag force on the blades as the wind flows.

Advantages of VAWT

1.      It can harness wind from any direction

2.      Typically operate closer to the ground, which has the advantage of allowing placement of heavy equipment, like the generator and gearbox, near ground level rather than in the nacelle.

Disadvantages of VAWT

1.      Winds are lower near ground level, so for the same wind and capture area, less power will be produced compared to HAWT.

2.      Time varying power output due to variation of power during a single rotation of the blade.

3.     The need for guy wires to support the tower.

4.       Darrieus VAWTS are not self starting like HAWTS. (More colorful picture and videos during lecture)

Power of a Wind Turbine

Consider a wind turbine with blades of length, r (area A), the wind speed is v and the air density is ρ.  Assuming that the air speed is reduced to zero by the blades.

Kinetic energy of the wind, K.E =

Kinetic energy per unit volume

K.E per volume = ÷ volume =

The blades sweeps out an area A in one turn, so the volume of air passing in one second is Av.

Kinetic energy per second

= K.E per unit volume x volume per second

K.E per second =  =

The available wind power is P =

Extractable power

The power extracted by the rotating blades is much less than the available wind power. This is because:

(i)   The velocity of the wind is not reduced to  zero at the blades

(ii)    Losses due to friction at the turbine and alternator

(iii)    Due to losses in both the gear train and generator.


The power actually captured by the wind turbine rotor, PR, is some fraction of the available power, defined by the coefficient of performance, Cp, which is essentially a type of power conversion efficiency:


The extractable power (electrical power output) is given by

Where ns and nb are efficiencies (power output over power input) for the generator and the gearbox.

Variations of power with wind speed

The power curve for a wind turbine shows this net power output as a function of wind speed.

i. Cut in wind speed:  This is the lowest speed at which the wind turbine will start generating power.

Typical cut – in wind speeds are 3 to 5 m/s.

ii. Nominal wind speed:  This is the lowest speed at which the wind turbine reaches its nominal power output.

Above this speed, higher power outputs are possible, but the rotor is controlled to maintain a constant power to limit loads and stresses on the blades.

iii. Cut – out wind speed:  This is the highest wind speed which the turbine will operate at.

Above this speed, the turbine is stopped to prevent damage to the blades.

Advantages of Wind Energy

1.  Wind Energy is an inexhaustible source of energy and is virtually a limitless resource.

2.   Energy is generated without polluting environment

3.   This source of energy has tremendous potential to generate energy on large scale.

4.    Like solar energy and hydropower, wind power taps a natural physical resource,

5.    Windmill generators don’t emit any emissions that can lead to acid rain or greenhouse effect.

6.    Wind Energy can be used directly as mechanical energy

7.    In remote areas, wind turbines can be used as great resource to generate energy

8.    In combination with Solar Energy they can be used to provide reliable as well as steady supply of electricity.

9.    Land around wind turbines can be used for other uses, e.g. Farming.

Disadvantages of Wind Energy

1.    Wind energy requires expensive storage during peak production time.

2.    It is unreliable energy source as winds are uncertain and unpredictable.

3.    There is visual and aesthetic impact on region

4.    Requires large open areas for setting up wind farms.

5.    Noise pollution problem is usually associated with wind mills.

6.   Wind energy can be harnessed only in those areas where wind is strong enough and weather is windy for most parts of the year.

7.   Usually places, where wind power set-up is situated, are away from the places where demand of electricity is there.  Transmission from such places increases cost of electricity.

8.  The average efficiency of wind turbine is very less as compared to fossil fuel power plants.  We might require many wind turbines to produce similar impact.

9.   It can be a threat to wildlife.  Birds do get killed or injured when they fly into turbines.

10. Maintenance cost of wind turbines is high as they have mechanical parts which undergo wear and tear over the time.

NB: Even though there are advantages of wind energy, the limitations make it extremely difficult for it to be harnessed and prove to be a setback


Geothermal energy is the energy from nuclear energy changes deep in the earth, which produces hot dry rock.

Geothermal energy originates from the heat retained within the Earth since the original formation of the planet, from radioactive decay of minerals, and from solar energy absorbed at the surface.

Harnessing Geothermal Energy

Most high temperature geothermal heat is harvested in regions close to tectonic plate boundaries where volcanic activity rises close to the surface of the Earth.  In these areas, ground and groundwater can be found with temperatures higher than the target temperature of the application.

Geothermal energy is extracted by using two methods:

(i)   A heat pump system

(ii)   Hot dry rock conversion

The heat pump system

Hot aquifers are layers of permeable (porous) rock such as sandstone or limestone at a depth of 2 – 3 km which contains hot water at temperatures of 60 – 1000C.

A shaft is drilled to aquifer and the hot water pumped up it to the surface where it is used for district space and water heating schemes or to generate electricity.  A second shaft may be drilled to return the cool water to the rock.

The hot dry rock conversion

These are impermeable hot dry rocks found at depth of 5 – 6 km, have temperature of 2000C or more.

Two shafts are drilled and terminate at different levels in the hot rock about 300 m apart.  The rocks near the end are fractured by explosion or by methods to reduce the resistance
to the flow of cold water which is pumped under very high pressure (300 atm) down the injection shaft and emerges as steam from the top of the shallower shaft.

Uses of geothermal energy

Geothermal energy can be used for electricity production, for direct use purposes, and for home heating efficiency (through geothermal heat pumps).

Advantages of geothermal energy

1.   Geothermal power plants provide steady and predictable base load power.

2.   New geothermal power plants currently generate electricity at low cost.

3.    Responsibly managed geothermal resources can deliver energy and provide power for decades.

4.    Geothermal power plants are reliable, capable of operating about 98 percent of the time.

5.    Power plants are small, require no fuel purchase and are compatible with agricultural land uses.

6.    Geothermal plants produce a small amount of pollutant emissions compared to traditional fossil fuel power plants.

Disadvantages of geothermal energy

1.   Many of the best potential resources are located in remote or rural areas, often of  federal or state lands

2.   Although costs have decreased in recent years, exploration and drilling for power production remain expensive

3.    Using the best geothermal resources for electricity production may require an expansion or upgrade of the transmission system.

4.   The productivity of geothermal wells may decline over time. As a result, it is crucial that

developers manage the geothermal resources efficiently.


Wave energy is the energy extracted from the ocean surface wave. Energy that comes from the waves in the ocean sounds like a boundless, harmless supply.

Machinery able to exploit wave power is generally known as a wave energy converter (WEC)

Wave power

Waves in the sea have kinetic energy and gravitational potential energy as the rise and fall.

Consider a sine wave of wave length λ spread over a width d the amplitude of the wave is a and the time period is T.

The power in a wave come from the change in potential energy of the water as it rotates on the circuit paths beneath the surface. It can be shown that the power carried forward by a wave is given by:

Wave Energy Flux

The mean transport rate of the wave energy through a vertical plane of unit width , parallel to a wave crest, is called wave energy flux.

From above,

Harvesting wave energy

There are two type of system:

1.      i. Offshore systems in deep water more than 141 feet deep. The Salter duck method.

(a)  Pumps that use bobbing motion of waves.

(b)  Hoses connected to floats on surface of waves. As float rises and falls , the hose stretches and relaxes, pressurizing the water which then rotates a turbine

2.      ii. Onshore systems are built along shorelines and harvest energy from braking waves.

(a)Oscillating water columns are of concrete or steel and have an opening to the sea below the waterline. It uses the water to pressurize an air column that is drawn through the turbine as waves recede.

(b)A Tapchan is a tapered water system in sea cliffs that forces waves through narrow channels and the water that spills over the walls is fed through a turbine.

(c)A Pendulor device is a rectangular box with a hinged flap over one side that is open to the sea .Waves cause the flap to swing back and forth and this powers a hydraulic pump and generator.

Advantages of Wave energy

1. Renewable: It will never run out.

2. Environment friendly: Creating power from waves creates no harmful byproducts such as gas, waste, and pollution.

3. Abundant and widely available: Another benefit to using this energy is its nearest to places that can use it.

4. Variety of ways to harness: Current gathering method range from installed power plant with hydro turbine to seafaring vessels equipped with massive structures that are laid into the sea to gather the wave energy.

5. Easily predictable: The biggest advantage of wave power as against most of the other alternative energy source is that it is easily predictable and can be used to calculate the amount that it can produce.

6. Less dependency on foreign oil cost.

7. Non damage to land.

Disadvantages of wave energy

1. Suitable to certain locations: The biggest disadvantage to getting your energy from the wave is location. Only power plants and town near the ocean will benefit direct from it.

2. Effect on marine ecosystem: Large machine have to be put near and in the water gather energy from waves .These machines disturb the seafloor, changes the habitat of near-shore creatures (like crabs and starfish) and create noise that disturb the sea life around them.

3. Wavelength: Wave power is highly dependent on wavelength i.e. wave speed, wave length, and wavelength and water density.

4.   Weak performance in Rough Weather:  The performance of wave power drops significantly during rough weather.

5.   Noise and Visual pollution:  Wave energy generators may be unpleasant for some who live close to coastal regions.  They look like large machines working in the middle of the ocean and destroy the beauty of the ocean.  They also generate noise pollution but the noise is often covered by the noise of waves which is much more than that of wave generators.

6.    Difficult to convert wave motion into electricity efficiently.

7.    Difficult to design equipment that can withstand storm damage and saltwater corrosion.

8.   Total cost of electricity is not competitive with other energy sources.

9.    Pollution from hydraulic fluids and oils from electrical components.

Tidal Power is the power of electricity generation achieved by capturing the energy contained in moving water mass due to tides.

Two types of tidal energy can be extracted: Kinetic energy of currents between ebbing and surging tides and potential energy from the difference in height between high and low tides.

Causes of Tides

Tides are caused by the gravitational pull of the moon, and to a lesser extent the sun, on the oceans.  There is a high tide places near the moon and also opposite on the far side.

i. High (spring) tide:  Occurs when there is full moon.  The moon, sun and earth are in line the moon being between earth and sun.  The pulls of the moon and sun reinforce to have extra high tides.

ii. Lowest (neap) tide:  Occurs when there is half moon and the sun and moon pulls are at right angles to each other.

iii. Harnessing Tidal Energy

Tidal energy can be harnessed by building a barrage (barrier), containing water turbines and sluice gates, across the mouth of river.  Large gates are opened during the incoming (flood) tide, allowing the water to pass until high tides, when they are closed.

On the outgoing tide, when a sufficient head of water has built up, small gates are opened, letting the potential energy of the trapped water drive the turbines and generate electricity.

Advantages of Tidal Energy

1.  Decrease reliance on coal driven electricity so less CO2 emissions.

2.   Changing technology allowing quicker construction of turbines, which in turn increases likelihood of investment with a shorter return.

3.   Once constructed very little cost to run and maintain.

4.  Tidal energy is renewable and sustainable.

Disadvantages of Tidal Energy

1.   Intermittent energy production based around tides creates unreliable energy source.

2.   High construction costs

3.   Barrages can disrupt natural migratory routes for marine animals.

4.   Barrages can disrupt normal boating pathways.

5.   Turbines can kill up to 15% of fish in area, although technology has advanced to the point that the turbines are moving slow enough not to kill as many.

Tidal Power
If the tidal height (level) is h and the estuary area is A, then the mass of water trapped being the barrier is and the centre of gravity is h/2 above the low tide level.

The maximum energy per tide is therefore

Potential Energy of tide =

Averaged over a tidal period of T (approx. 12 hours a day), this gives a mean power available of.

Average tidal power =

Note that the efficiency of the turbines (generator) will determine how much of this tidal power will be harnessed.



Example 01

The power output p of a windmill can be expressed as where A is the area swept out by the windmill blades (sails), is the density of air, v is the wind speed and k is a dimensionless constant

(a)  Show that the units on both sides of this expression are the same

(b)  Sketch a graph to show how the power increases with wind speed as v rises from zero to 15ms-1


(a)   Units on L.H.S = Nms-1

Unit on R.H.S. = m2 (kgm-3) x (ms-1)3

= (kgms-2) ms-1=Nms-1

(b)   Variation of power with speed


Example 02

The radiation received from the sun at the earth’s surface in a certain country is about 600 Wm-2 averaged over 8 hours in the absence of cloud.

(a)  What area of solar panel would be needed to replace a power station of 2.0 GW output, if the solar panels used could convert solar radiation to electrical energy at an efficiency of 20%

(b)  What percentage is this area of the total of the country (which is about 3 x 1011m2)?

(c)  If the total power station capacity is about 140 GW, what percentage of the surface of the country would be covered by solar panels if all the power stations were replaced?


(a)   Output of a solar panel


(b)   Percentage area to the country

(c)   Area of solar panels required


Percentage area to the country

Example 03

(a)   What are aerogenerators?

(b)  Estimate the maximum power available from 10m2 of solar panels and calculate the volume of water per second which must pass through if the inlet and outlet temperatures are 200C and 700C.  Assume the water carries away energy at the same rate as the maximum power available.  The specific heat capacity of water is 4200 Jkg-1 and solar constant is 1.4 kWm-2.


(a)   Aerogenerators are devices that convert the kinetic energy of wind into electrical energy.  E.g. windmill.

(b)  Maximum power available from solar panel

Volume of water per second used is given by

1400 =

 Example 04

A coal – fired power station has an output of 100mW. Given that its efficiency is 45%, how much coal must be supplied each day?  Assume 1 tonne of coal gives 3 x 1010 of energy.


Input power of the station is given by


Total input energy in a day is


The amount of coal required is


 Example 05

Calculate the energy required transport1000 tones of oil along a 100km pipeline; given that 0.05 kW hours of energy is used to shift each tone of oil along each km of pipeline.  Given that 1 tonne of oil releases 4.2 x 1010 J if burned, what percentage of the total energy available from 1000 tonnes of oil is used to shift the oil along the pipeline? (Ans: 18GJ, 0.043%)

Example 06

A hydroelectric power station has efficiency of 25%.  The water driving the turbines falls through a height of 300m before reaching the turbines.  Calculate the volume of water that must pass through the turbines each second to give a power output of 2mW.  Assume the density of water is 1000kg-3.


Power of the falling water



 Example 07

The solar energy flux near the Earth is 1.4W m-2. A solar power station consists of concave mirrors that focus sunlight onto a steam boiler.  What must be the minimum mirror area to given an output 1 mW, assuming 100% efficiency? Why in practice, should the mirror area be greater?


Minimum mirror area is given by

The mirror area should be greater to achieve such a power output because part of the incident energy is absorbed by the mirror.

Example 08

A solar panel attached to the roof of a house is used to heat water from 50C to 400C.  If the water flows through the panel at a rate of 0.012kgs-1 Calculate the heat gained per second by the water.  Assume the specific heat capacity of water is 4200Jkg-1K-1.         (Ans. 1764 Q)

Example 09

An aerogenerator has a power output that is proportional to (wind speed) 2 and its efficiency varies with wind speed.  On a day when there is a steady wind of speed 9 ms-1, the power output is 40kW operating at an efficiency of 20%.  If the wind speed on next day is 13.5 ms-1 and the efficiency increases to 25% what is the new power output?


Power output α efficiency × (wind speed)2


Example 10

Estimate the energy released from a tidal power station if 100 km3 of water raised to height of 1.5m by the tide behind a tidal barrier.  What would be the mean power output of such a station if its efficiency is 25% and there are two tides per day?


The tidal power is given by

Note that the centre of gravity of water mass is at the half height up.


Mean power output is


Example 11

An open boat of width 1.0 m has a total weight of 3000N.Used near a beach, it bobs up and down through 0.5 m once every 5s.  Calculate the losses of P.E. every time it drops from a crest to a through.  Hence estimate the mean power available per meter of beach waves.


Loss in P.E. is given by

The mean power available per meter is 300 W

Example 12

(a)   If energy is conserved, why is there energy crisis?

(b)  Explain the terms high grade and low grade energy and give examples.

(c)  Draw an energy flow diagram for a hydroelectric power station.  Why does such a station have a much greater efficiency than a thermal power station?

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