Solar Energy Slides

What is solar energy availability mostly a function of?

Location- including latitude, local climate / altitude. Time of day / year as well.

typical irradiation at 1.5 AM

+1000 W/m^2, 10% is diffuse radiation (scattered light from the rest of the blue sky)

typical irradiation per day

7.6 kWh/m^2/day (w/o tracking, const AM)

air mass (AM, or m in numerical problems)

The ratio of actual length of solar beam through the atmosphere to that at zeinith, at sea level

air mass (AM aka m) equation

m = cb/ab = l/lo = sec(zeta), with cb and l being length sunlight travels when at an angle, and ab and lo being length sunlight travels when its directly overhead. Zeta is angle between these two lines

Zeta

Angle between path of sunlight and vertical direction

Equation for m whn zeta <= 62 degrees

m = p/[(po)cos(zeta)]

Attenuation

Loss of power

Why does air mass depend on pressure p and not height?

Because attenuation depends on amount of air molecules, not height directly

How does light decay as it travels through air?

Exponentially

What happens to solar energy as it travels through more air?

Higher air mass means sunlight travels through more atmosphere, causing increased scattering and absorption, which reduces the direct beam intensity.

What two losses contribute to solar energy decay?

Solar energy is limited by geometry (cosine effect) and atmospheric attenuation (air mass)

Explain the rational behind this equation: Id = So cos(zeta)

Id represent the heat flux received by a surface, So is the solar constant, and zeta is the zenith angle (angle between path of sunlight to earth and vertical direction). An area receives So when the sun is directly overhead, but when the sun is lower in the sky- it's at an angle. The same amount of sunlight is spread out over a larger area, which makes the heat flux (W/m^2) smaller. Its intensity is reduced proportionally to cosine(zeta)

How is Ao = Acos(zeta) found?

Think of it like finding the hypotenuse from a smaller side of a triangle, just the angle between them is the zeta angle. Hypotenuse is Ao and the side you know is A.

Total instantaneous solar irradiation equation

Gs = (Ib,N)cos(zeta) + C(Ib,N), where (Ib,N) = direct beam solar irradiance on a surface perpendicular to the sun's rays, C = diffuse factor

Ib,N aka direct beam solar irradiance on a surface perpendicular to the sun's rays equation

(Ib,N) = (Cn)(So)exp(-k'm). Cn = clearness factor, k' = atmospheric attenuation constant, m: air mass

Albedo

fraction of solar radiation reflected

Albedo according to solar energy community

Fraction of solar energy that is reflected from ground, ground cover, bodies of water, things on the ground. "Ground reflectance" may be a better term.

Albedo according to astronomers / meteorology

Fraction of solar radiation reflected by ground /and/ clouds + atmosphere

What is your optimum angle of tilt?

Your latitude. For example, since Wichita' latitude is 37.7 degrees, it's optimum angle of tilt is 37.7 degrees

Is solar constant a fixed number?

No, it can vary slightly with sunspot cycles and solar activity

Solar thermal options

Flat plate collectors, concentrating collectors (parabolic troughs and parabolic dishes), concentrating arrays, storage. Even more: Solar updraft towers, water desalination, clotheslines

Flat Plate Collectors

Dark absorber plate + glass cover, with water flowing through pipes. They absorb sunlight and transfer it to the water, for domestic hot water and space heating

Concentrating collectors: parabolic trough

Long curved mirrors focus sunlight onto a pipe, heats fluid -> generates steam -> drives turbine

Concentrating collectors: parabolic dishes

Dish-shaped mirrors focus to a single point, can power Stirling engines and cooking systems

Concentrating arrays

Many mirrors work together to focus sunlight onto a central tower, for large-scale electricity

Storage

Thermal energy using molten salt for example stored for night operations

Residential solar water heaters

Active solar heaters (direct and indirect circulation) that need power and passive heaters (integral collector storage and batch heaters) that do not need power

Active Solar Residential water Heaters

Split into two types: direct circulation, where water flows directly through a flat plate solar collector, to send hot water to house. Simple but risks freezing. And indirect: uses antifreeze loop + heat exchange, avoids freezing risks but more complex.

Passive Residential Solar Water Heaters

They use thermosyphon principle: hot water rises naturally and cold water sinks. They are made of integral collector storage where water in stored directly in a collector, and batch heaters where heat water in a tank exposed to sun.

Heat Collector Design Options

Flat plate collectors (cheap) and evacuated tubes (complicated)

Flat plate collectors

Made of a glass cover, absorber plate, tubes carrying fluid and insulation. They are cheap to make with simple (even DIY) materials, and can be improved with "designer coatings"

Evacuated Tube Collectors

Glass tubes with vacuum and an absorber inside, it eliminates convection losses and works well in cold climates. It's more expensive and fragile though.

Capacity factor

actual energy generated over a period of time / maximum possible energy

What's the capacity factor of a PV panel rated at 1 kW, and over a year it generates 1661 kWh (per pvwatts)

First find max possible energy in kWh per year, 1 kW x 24 x 365 = 8760. CF = 1661 / 8760 = 19%

A certain 10 kW PV panel is quoted to be performing at a capacity factor of 19%. Estimate the total energy generated by this panel over a year in MWh, MJ, and Btu.

CF = actual energy / max possible energy = E / (Prated x time). -> E = CF x Prated x time = 0.19 x 10kW x 8760 hours/year = 16644 kWh. Convert to MWh: E = 16.644 MWh. Convert to MJ: 1 kWh = 3.6 MJ. E = 16644 x 3.6 = 59918.4 MJ. Convert to BTU: 1 kWh = 3412 Btu. E = 16644 x 3412 = 5.68 x 10^7 BTU.

Theoretical CF of solar panels

1/pi

Theoeretical efficiency of solar panels

| (300 K - 5800 K ) / 5800 K | x 100% = 95% efficient. Where 300 K is 27 degrees C and 5800 K is temp of sun

CF of solar PV in field

29%

CF of Solar Thermal in field (including CST with storage)

23%

Why is CF of solar energy so low?

One big reason is they can only, at most, work half the day (when there is sunlight)

What are some trends for solar?

+Rapid growth in solar installations

+Increasing share of electricity generation

+Cost decreasing over time

What costs for solar are not decreasing?

"Soft costs" of residential installation, unlike hardware which is

Soft Costs

Labor, permits, marketing, overhead, profit margin

A certain array of solar panels is "rated" to be 10 kW (rated power). If that ratingis based on 1000 W/m^2 of solar irradiation (incoming solar energy, also called"insolation"), and an efficiency of 21%, find the total area of that array of solarpanels in sq meters.

Efficiency = electrical power output / solar power input = rated power / (solar irradiation x area). -> Area = rated power / (Efficiency x solar irradiation) = 10000 / (0.21 x 1000) = 47.6 m^2