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EE535: Renewable Energy: Systems, Technology & Economics. Session 4: Solar (1): Solar Radiation. Annual solar radiation on a horizontal surface at the equator is over 2000kWh/m 2 In Northern Europe this falls to about 1000kWh/m 2 (per annum)

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Ee535 renewable energy systems technology economics

EE535: Renewable Energy: Systems, Technology & Economics

Session 4: Solar (1): Solar Radiation

S Daniels

Solar radiation

Annual solar radiation on a horizontal surface at the equator is over 2000kWh/m2

In Northern Europe this falls to about 1000kWh/m2 (per annum)

The tilt between the sun and the land reduces the intensity of the midday sun

Solar Radiation

Energy from the sun in the form of ultra-violet, visible and infra-red electromagnetic

radiation is known as solar radiation

Ultraviolet 0.20 - 0.39µ

Visible 0.39 - 0.78µ

Near-Infrared 0.78 - 4.00µ

Infrared 4.00 - 100.00µ

S Daniels


Flux of solar radiation incident on a surface placed at the top of the atmosphere, depends on time t, geographical location (latitude φ, longitude λ, and on the orientation of the surface









E(t, Ф, λ) = S(t)cos Ф(t , Ф, λ)

S(t) is known as the solar constant

δ is the declination of the sun

ώ is the hour angle of the sun

Ф is the angle between the incident

solar flux and the normal to the surface

The solar constant is the amount of incoming solar electromagnetic radiation

per unit area that would be incident on a plane perpendicular to the rays,

at a distance of one astronomical unit (AU) (roughly the mean distance from

the Sun to the Earth).

S Daniels

The sun produces light with a distribution similar to what would be expected from a 5525 K (5250 °C) blackbody, which is approximately the sun's surface temperature

Radiation interacts with matter in several ways:





Solar radiation spectrum for direct light at both the top of the Earth’s atmosphere and at sea level

S Daniels

Solar quantities
Solar Quantities would be expected from a 5525 K (5250 °C) blackbody, which is approximately the sun's surface temperature

  • The sun generates approximately 1.1 x 10 E20 kilowatt-hours every second.

  • The earth’s outer atmosphere intercepts about one two-billionth of the energy generated by the sun, 1.5 x 10 E18 kilowatt-hours per year.

  • Because of reflection, scattering, and absorption by gases and aerosols in the atmosphere, only 47% of this, (7 x 10 E17 ) kilowatt-hours, reaches the surface of the earth.

  • In the earth’s atmosphere, solar radiation is received directly (direct radiation) and by diffusion in air, dust, water, etc., contained in the atmosphere (diffuse radiation). The sum of the two is referred to as global radiation.The amount of incident energy per unit area and day depends on a number of factors, e.g.:

    • Latitude

    • local climate

    • season of the year

    • inclination of the collecting surface in the direction of the sun.


  • The solar energy varies because of the relative motion of the sun. This variations depend on the time of day and the season. In general, more solar radiation is present during midday than during either the early morning or late afternoon. At midday, the sun is positioned high in the sky and the path of the sun’s rays through the earth’s atmosphere is shortened. Consequently, less solar radiation is scattered or absorbed, and more solar radiation reaches the earth’s surface.

  • The amounts of solar energy arriving at the earth’s surface vary over the year, from an average of less than 0,8 kWh/m2 per day during winter in the North of Europe to more than 4 kWh/m2 per day during summer in this region. The difference is decreasing for the regions closer to the equator.

  • The availability of solar energy varies with geographical location of site and is the highest in regions closest to the equator.

S Daniels

Solar absorption and reflection
Solar Absorption and Reflection would be expected from a 5525 K (5250 °C) blackbody, which is approximately the sun's surface temperature

  • When a photon is absorbed, its energy is changed into a different form: electrical or heat

  • A fraction of the incoming solar radiation is reflected back into space – this is known as the albedo (a0) of the earth-atmosphere system

  • Annual average of a0 is 0.35

    • Reflection from clouds – 0.2

    • Reflection on cloudless atmosphere (particles, gases) - 0.1

    • Reflection on the earths surface – 0.05

  • Radiation absorbed by the Earth’s atmosphere

    • A0 = E (1-a0)

S Daniels

Solar corrections
Solar Corrections would be expected from a 5525 K (5250 °C) blackbody, which is approximately the sun's surface temperature

  • Direct normal solar radiation

    • is the part of sunlight that comes directly from the sun. This would exclude diffuse radiation, such as that which would through on a cloudy day. Iindication of the clearness of the sky.

  • Diffuse sky radiation

    • is solar radiation reaching the Earth's surface after having been scattered from the direct solar beam by molecules or suspensoids in the atmosphere.

    • It is also called skylight, diffuse skylight, or sky radiation and is the reason for changes in the colour of the sky.

    • Of the total light removed from the direct solar beam by scattering in the atmosphere (approximately 25% of the incident radiation when the sun is high in the sky, depending on the amount of dust and haze in the atmosphere), about two-thirds ultimately reaches the earth as diffuse sky radiation.

  • Global Horizontal Radiation

    • total solar radiation; the sum of direct, diffuse, and ground-reflected radiation;

    • however, because ground reflected radiation is usually insignificant compared to direct and diffuse, for all practical purposes global radiation is said to be the sum of direct and diffuse radiation only.

[Insolation is a measure of solar radiation energy received on a given surface area in a given time.

It is commonly expressed as average irradiance in watts per square meter (W/m2) per day.

In the case of photovoltaics it is commonly measured as kWh/(kWp·y) (kilowatt hours per year per kilowatt peak rating). ]

S Daniels

Direct normal radiation
Direct Normal Radiation would be expected from a 5525 K (5250 °C) blackbody, which is approximately the sun's surface temperature

  • E┴ = EscτRaτO3τGaτWaτAEτrmCi

    • Ra : Rayleigh scattering by molecules in the air

    • O3 : absorption by ozone

    • Ga : absorption by uniformly mixed gasses (CO2 & O2)

    • Wa : absorption by water vapour

    • Ae : extinction by aerosol particles

    • Ci : extinction by high clouds of cirrus types

  • Scattering and absorption are strongly wavelength dependent - (consequence?)

S Daniels

Clouds would be expected from a 5525 K (5250 °C) blackbody, which is approximately the sun's surface temperature

  • Cloudfree (direct beam insolation) and cloudy periods (prevailing diffuse radiation) average to a mean irradiance

  • For the assessment of solar power plant sites, short interval recordings of sunshine, direct and diffuse radiation are required

  • Clouds can be classified by their optical depth

    • 2 > dci (1) > 0.2 > dci (2) > 0.02 > dci (3) > 0

  • Cloud Free Line Of Sight Probabilities (CFLOS) are available (World Atlas)

    • indicates for a given time and location to what percentage the sky is cloudfree

S Daniels

European irradiation
European Irradiation would be expected from a 5525 K (5250 °C) blackbody, which is approximately the sun's surface temperature

S Daniels

The European Commission's Joint Research Centre, Institute for Environment and Sustainability

Quotation from met ie
Quotation from would be expected from a 5525 K (5250 °C) blackbody, which is approximately the sun's surface temperature

  • Ireland normally gets between 1400 and 1700 hours of sunshine each year.

  • The eastern Sahara Desert, however, which is the sunniest place in the world, gets an average of 4300 hours per year.

  • Irish skies are completely covered by cloud for well over fifty percent of the time. This is due to our geographical position off the northwest of Europe, close to the path of Atlantic low pressure systems which tend to keep us in humid, cloudy airflows for much of the time.

  • 1887 was the sunniest summer in the 100 years from 1881 to 1980, according to measurements made at the Phoenix Park in Dublin. A more recent summer, 1980, was the dullest. The difference was considerable, with the summer of 1887 being twice as sunny as that of 1980.

S Daniels

Typical figures
Typical Figures would be expected from a 5525 K (5250 °C) blackbody, which is approximately the sun's surface temperature

  • The intensity of the sunlight that reaches the earth varies with time of the day and year, location, and the weather conditions. The total energy on a daily or annual basis is called irradiation and indicates the strength of the sunshine. Irradiation is expressed in Wh/m² per day or for instance kWh/m² per day.

  • To simplify calculations with irradiation data solar energy is expressed in equivalents of hour's bright sun light. Bright sun light corresponds with a power of about 1,000 W/m² so one hour of bright sunlight corresponds with an amount of energy of 1 kWh/m².

  • This is approximately the solar energy when the sun shines on a cloudless day in the summer on a surface of one square meter perpendicular to the sun.

  • The optimum orientation and inclination angle will vary from site – to – site

  • On-site measurements essential

  • Ideally you want the cell oriented at 90 to the sun at all times

S Daniels

Solar panels
Solar Panels would be expected from a 5525 K (5250 °C) blackbody, which is approximately the sun's surface temperature

  • A solar panel produces electricity even when there is no direct sunlight. So even with cloudy skies a solar energy system will produce electricity (see How does it work). The best conditions, however, are bright sunlight and the solar panel facing towards the sun. To benefit most of the direct sunlight a solar panel has to be oriented as best as possible towards the sun. For places on the Northern Hemisphere this is south, for countries on the Southern Hemisphere this is north. 

  • In practice, the solar panels should therefore be positioned at an angle to the horizontal plane (tilted). Near the equator the solar panel should be placed slightly tilted (almost horizontal) to allow rain to wash away the dust.

  • A small deviation of these orientations has not a significant influence on the electricity production because during the day the sun moves along the sky from east to west.

  • Panels are often set to latitude tilt, an angle equal to the latitude, but performance can be improved by adjusting the angle for summer and winter.

S Daniels

Important geometrical parameters which describe earth sun relations
Important geometrical parameters, which describe Earth-Sun relations

Declination Angle

n – day of year (days since Jan 1st )

Sun Height

h = hour angle

L = Latitude

The optimal solar device tilt

Can be estimated from:

Solar Azimuth

S Daniels


Declination angle
Declination Angle relations


The declination angle, denoted by d, varies seasonally due to the tilt of the Earth on its axis of rotation and the rotation of the Earth around

the sun. If the Earth were not tilted on its axis of rotation, the declination would always be 0°.

However, the Earth is tilted by 23.45° and the declination angle varies plus or minus this amount.

Only at the spring and autumn equinoxes is the declination angle equal to 0°.

S Daniels

Solar panel tilt angle
Solar Panel Tilt Angle relations

  • The sun moves across the sky from east to west. Solar panels are most effective when they are positioned facing the sun at a perpendicular angle at noon.

  • Solar panels are usually placed on a roof or a frame and have a fixed position and cannot follow the movement of the sun along the sky. Therefore they will not face the sun with an optimal (90 degrees) angle all day. The angle between the horizontal plane and the solar panel is called the tilt angle. 

  • Due to motion of the earth round the sun there are also seasonal variations. In the winter the sun will not reach the same angle as in summer. Ideally, in the summer solar panels should be placed somewhat more horizontal, to benefit most from the sun high in the sky. However these panels will then not be placed optimally for the winter sun.

  • To achieve the best year round performance solar panels should be installed at a fixed angle, which lies somewhere between the optimum angle for summer and for winter. For each latitude there is an optimum tilt angle. Only near to the equator the solar panels should be placed horizontally.

S Daniels

Tilt and azimuth angle of photovoltaic modules
Tilt and azimuth angle of photovoltaic modules relations

  • The proper tilt and azimuth angle choice is by far more important for photovoltaic systems design than solar thermal system design.

    • Manual or automatic tilt angle adjustment can increase the total light-electricity conversion up to 30 % and more in locations with high values of solar radiation.

    • Incidence angle should be as close to 90° as possible.

    • Shaded locations, including partially shaded, are not suitable for photovoltaic module fixation.

    • Modules should be south oriented.

  • The following general recommendations should be considered, if you design a photovoltaic system:Yearly average maximum output power - the photovoltaic modules tilt angle should equal local latitude.Maximum output power in winter - the photovoltaic modules tilt angle should equal local latitude + 15° (max +20°). Such a tilt angle is a good solution in areas, where the winter load is greater than the summer load. The electricity consumption for lighting is greater during winter than summer.Manual photovoltaic module tilt angle adjustment - in small systems modules should be fixed in a way, which allows manual adjustment of the module tilt angle. In March the tilt angle should be adjusted to equal latitude, in May the tilt angle equals latitude minus 10 degrees, in September the tilt angle equals latitude and in December the tilt angle equals latitude plus 10 degrees. With such an adjustment the maximal efficiency could be obtained throughout the year. Accurate and maximum energy output of larger systems should be based on exact calculations, because energy output is influenced by different factors, such as local climatic conditions (solar radiation availability in different seasons, local cloudiness or fogginess in winter, temperature and so on). You will need a long-term solar radiation data for the chosen location.

S Daniels

Watt peak
Watt Peak relations

  • A solar cell produces electricity when it is exposed to light. Depending on the intensity of the light (the irradiance in W/m²) a solar cell produces more or less electricity: bright sunlight is preferable to shade and shade is better than electric light. To compare solar cells and panels it is necessary to know the so-called nominal power of such a cell or panel. The rated power, expressed in Watt peak or Wp, is a measure of how much energy such a solar panel can produce under optimal conditions.

  • To determine and compare the nominal power of solar panels, the output is measured under standard test conditions (STC). These conditions are: - An irradiance of 1,000 W/m² - Solar reference spectrum AM 1.5 (this defines the type and colour of the light)- Cell temperature of 25 °C (Importantly, the efficiency of a solar panel drops when the cell temperature rises).

S Daniels

Site analysis
Site Analysis relations

  • The choice of a proper location is the first and the very essential step in solar system design procedure.

  • It is critical that the modules are exposed to sunlight without shadowing at least from 9 am to 3 pm; therefore, the properties and values of solar insolation should be studied. The modules have to be fixed with proper tilt angle allowing the system efficient operation.

  • When planning a solar array installation one of the first things you'll need to determine is the design month, which is the month with the lowest insolation. - this assumes power consumption is more or less constant throughout the year. If not the case then the design month becomes the month with the highest average daily power use. In systems tied to an electric grid this isn't as important because your utility can pick up the slack but when dealing with off the grid systems it becomes imperative in order to keep the battery charged

S Daniels

Useful solar power
Useful Solar Power relations

  • Solar Thermal – direct heating of buildings and water

  • Solar Photovoltaic – direct generation of electricity

  • Solar Biomass – using trees, bacteria, algae, corn, soy beans, or oilseed to make energy fuels, chemicals, or building materials

  • Food – feeding plants, humans, and other animals

S Daniels

Global averages
Global Averages relations

  • The average annual global radiation impinging on a horizontal surface which amounts to approx.

    • 1000 kWh/m2 in Central Europe, Central Asia, and Canada reach approx.

    • 1700 kWh/m2 in the Mediterannian.

    • 2200 kWh/m2 in most equatorial regions in African, Oriental, and Australian desert areas.

  • In general, seasonal and geographical differences in irradiation are considerable and must be taken into account for all solar energy applications.

S Daniels

Calculation relations

  • From European Irradiation Data (slide 10), Ireland has on average 1000kWhrs / m2 / year of sunlight

  • = 2.7 kWhrs / m2 / day

  • = ~ 108 watts / m2

  • Assume average (total) energy consumption in Ireland is 120kWh / day / person (

S Daniels

Calculation relations

  • Population of Ireland – 4010000

  • Assume panels are 10% efficient

  • This works out at 440 ~ 1m2 panels per person

  • Assume approx 4 times this area per panel needed for infrastructure – 1777 m2

  • Required area for the population of Ireland???

    • 7182 km2

    • > area of Mayo (5589km2)

    • = area of Cork (7459km2)

S Daniels

Moral of the story
Moral of the Story relations

  • Country scale problem needs country scale solution

  • (economically) Harvestable power limited

  • Storage needed due to fluctuating nature (scale?)

  • Infrastructure requirements substantial

  • Impact of efficiency substantial

  • What about seasonal variations?

S Daniels

S Daniels relations