Basic Math behind solar calculations

Due to today’s tour of several teachers of the University of Texas RGV campus, the following are math terms to remember:

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Pictures taken at Los Fresnos Texas in a 900 Panel Installation. The installation is receiving the 5th year maintenance.

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The inverters are PVPowered 50kw.

Basic Solar Energy Math Concepts

 

The basic unit of power or electricity is Watt. It is actually a measure of rate of energy. Larger units of power are measured in multiples of 1000. For example,

1000 watts     =       1 kilowatt (kW)

1000 kW        =       1 megawatt (MW)

1000 MW       =       1 Gigawatt (GW)

1000 GW       =       1 Terawatt (TW)

If an electrical appliance consumes 1000 watts for one hour, it has consumed 1 kWh of energy or 1 unit of electricity. So, 1000 watt hours = 1 kilowatt hour (kWh). If you run a 100 watt bulb for 10 hours, it again consumes 1 kWh.

Solar panels are characterized by number of watts (Wp) they can produce under Standard Test Conditions (STC) of 1000 W/m2 irradiation, cell temperature of 25 degree Celsius and air mass of 1.5. This is their peak performance. However, the amount of power they actually produce in outdoor conditions depends upon the amount of sunshine.

Air Mass

Air mass is a measure of the distance traveled by sunlight through the Earth’s atmosphere. Since light intensity is attenuated by scattering and absorption, the more distance it passes through the atmosphere, the greater is the attenuation. Consequently, the sun appears less bright at the horizon (morning and late afternoon) than when at the zenith (noon). An air mass of 1 means the sun is looking straight down on the sea surface when it is directly overhead. At any location with latitude greater than 23.5 degrees, the sun is never directly overhead and so air mass will be always greater than 1. The number 1.5 has been agreed upon for the STC (Standard Test Condition) for testing solar panels.

Solar Irradiance and Solar Constant

Solar irradiance is the amount of sunshine incident on a unit area and is typically expressed in watts per square meter (W/m2) or kilowatts per square meter (kW/m2). Irradiance is measured through an instrument called ‘pyranometer,’ which displays the instantaneous power available from the Sun.

Solar constant is the solar irradiance outside the earth’s atmosphere on a 1 square meter surface oriented normal to the sun’s rays. It is about 1367 W/m2. This is attenuated by the atmosphere and the peak solar insolation on a earth’s surface oriented normal to the sun on a clear day is of the order of 1000 W/m2.

This irradiance of 1000 W/m2 corresponds to Standard Testing Conditions (STC) and is called “peak sun” or “1 sun”. If the incident radiation is concentrated 10 times using a lens or a mirror assembly and the incident power increases to 10,000 W/m2, then the irradiance is called “10 Suns.”

Solar Insolation

Insolation is the amount of solar irradiance that is incident on a fixed area over a period of time, and hence is a unit of energy. It is typically expressed in watt-hours per square meter per day (Wh/m2/day) or kilowatt-hours per square meter per day (kWh/m2/day) or even (kWh/m2/year) for a particular location, orientation and tilt of a surface.

Since 1000 W/m2 is “1 sun”, one hour of this ideal irradiance produces 1,000 watt-hours per square meter (1 kWh/m2). This is also known as “1 sun hour.” Colorful maps of solar potential display solar energy in kWh/m2/day, which is equivalent to the number of full sun hours per day. This is a useful parameter for sizing solar panels in the PV systems. More “sun hours” means more potential for solar power.

Global Horizontal Insolation (GHI): It is the solar insolation received by a fixed flat horizontal surface.

Global Tilt Insolation (GTI): The fixed solar panel or collector is generally inclined at an angle roughly equal to the latitude of its location (facing south in India or any place in the northern hemisphere) to maximize the annual insolation received. The insolation received by such an oriented surface is called the Global Tilt Insolation (GTI).

How much energy does one panel produces?

The unit of electrical energy consumed is generally measured in kilowatt-hours (kWh). If an array of solar panels rated at 1000 Wp produce electricity for 1 hour under good sunshine, they have produced 1 kWh or 1 unit of electricity. The total amount of energy they produce during the day is governed by things like solar latitude which is associated with latitude and season, and atmospheric conditions such as cloud coverage, temperature and degree of pollution apart from panel orientation and shading.

For same sunshine, panels produce more power in cooler climates than under hot temperatures. In India, ideal orientation for solar panels is slight tilt towards true south; in South India placing panels flat (horizontal) will also do.

How much space is required to install 1 kW solar panels?

Under clear skies and good sunshine each square meter is receiving about 1000 watts of solar energy. At typical 15% panel efficiency, a 1 sq m area will generate 150 watts of power. For 1 kW power output about 7 sq m area will be required. After leaving some free space, about 10-12 sq m clear roof area will be required.

How much power a 1 kW solar PV system will annually produce in Delhi?

New Delhi has average daily sunshine of 5.5 hours. If we assume loss of 30 days due to rains and clouds every year, then total annual sun hours are 5.5 x 335 = 1843. Ideally 1843 kWh of energy can be produced. But the actual performance will be less than 100 percent because the outdoor conditions are different from standard test conditions of the panels. So, for a 80 percent system performance the annual power production will be 1474 kWh (ie 1843*0.8). In locations where there are shadows and panel tilt is not towards true south, it is often advisable to consider loss of another 10-15%.

How to calculate the annual solar energy output of a photo voltaic system

The global formula to estimate the electricity generated in output of a photo voltaic system is :

          E = A * r * H * PR 

E = Energy (kWh) 
A = Total solar panel Area (m²) 
r = solar panel yield (%) 
H = Annual average solar radiation on tilted panels (shadings not included)
PR = Performance ratio, coefficient for losses (range between 0.5 and 0.9, default value = 0.75)



r is the yield of the solar panel given by the ratio : electrical power (in kWp) of one solar panel divided by the area of one panel.
Example : the solar panel yield of a PV module of 250 Wp with an area of 1.6 m² is 15.6%. 
Be aware that this nominal ratio is given for standard test conditions (STC) : radiation=1000 W/m², cell temperature=25 °C, Wind speed=1 m/s, AM=1.5 The unit of the nominal power of the photovoltaic panel in these conditions is called “Watt-peak” (Wp or kWp=1000 Wp or MWp=1000000 Wp). 

H  is the annual average solar radiation on tilted panels. Between 200 kWh/m².y (Norway) and 2600 kWh/m².y (Saudi Arabia). You can find this global radiation value here : Solar radiation data 
You have to find the global annual irradiation incident on your PV panels with your specific inclination (slope, tilt) and orientation (azimut). 

PR : PR (Performance Ratio) is a very important value to evaluate the quality of a photovoltaic installation because it gives the performance of the installation independently of the orientation, inclination of the panel. It includes all losses.

Example of detailed losses may be

 PR value (depend on the site, the technology, and sizing of the system) : 
– Inverter losses (4% to 10 %) 
– Temperature losses (5% to 18%) 
– DC cables losses (1 to 3 %) 
– AC cables losses (1 to 3 %) 
– Shadings 0 % to 80% !!! (specific to each site) 
– Losses at weak radiation 3% to 7% 
– Losses due to dust, snow… (2%) 

 

All this data

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