solar spectrum and effect of azimuth angle

Photo electric effect

Solar to electrical

Solar cell

Solar cell Characteristics

Off Grid Solar power plant

Charge Contorllers

## Efficiency and Theoretical performance of solar cell

## Open circuit voltage

The maximum voltage that can be generated by a solar cell. It is denoted by **V _{oc}**.

If light falls on the surface of an open circuited PN junction, photo generation takes place. Since minority carrier fall down the junction barrier the minority carrier current increases. Under open circuited junction the total current through the junction should be zero. So the majority current should also increase in line with the minority carrier current so that the net current through the junction is zero. The rise in majority carrier current is possible only because of a retarding field which lower the barrier height. Hence the barrier height is automatically lowered due to radiation. Across the diode terminals there appears a voltage equal to the amount by which the barrier height is reduced. This voltage is called **photo voltaic EMF**. The maximum photo voltaic voltage across an open circuited diode is found out by equating the total current through the diode to zero

I_{t} = I_{do}*(exp (V/eta*V_{t})-1)-I_{ph} = 0

exp (V/eta*V_{t}) = 1+ (I_{ph}/I_{o})

Applying anti log on both sides of the equation we get

**V _{oc }= η*V_{t}*ln (1+ (I_{ph}/I_{o}))**

Where η is **ideality factor** 1 for Ge and 2 for Si,

V_{t} is voltage equivalent of temperature=26 mV at 27 Degrees,

I_{ph} is the short circuit current proportional to light intensity,

I_{o} is reverse saturation current of diode or dark current flow through the cell due to thermal agitation.

Hence V_{oc} depends on following factors

- Temperature of material(V
_{t}=k*t/q where K is Boltzmann constant, t is absolute temperature in kelvin, q is charge of electron) - magnitude of photo current(I
_{ph}) - Amount of doping in semiconductors(conductivity, life time e.t.c depends on doping levels and affects Reverse saturation current)
- Material properties such as conductivity, mobility, diffusion constant e.t.c (I
_{o}) - Band gap of absorber material

**Short circuit current**

Short circuit current is the maximum current that can be delivered by a solar cell. The short circuit current of a solar cell can be found out by equating the voltage across the diode to zero in equation for total current

I_{t} = I_{do}*(exp (V/eta*V_{t})-1)-I_{ph} / V = 0

I_{t} = I_{do}*(exp (0)-1)-I_{ph}

** I _{t} = -I_{ph} **

When connected to a load, in a real solar cell the short circuit current will be less than photo current due to nonzero series resistance and finite shunt resistance.

Short circuit current depends on number of parameters such as

**Area of solar cell**

Higher the area of solar cells higher the collection area for light energy and higher will be the current.

**Solar spectral properties**

The spectrum of light emitted by sun plays a crucial role in limiting the efficiency of the solar cell. Each semiconductor material is characterised by band gap specific to that material. The photons having energy less than this energy gap are not capable of exciting electrons from valence band to conduction band. The frequency of photon whose energy is just sufficient to excite an electron valence band to conduction band is termed as **critical energy** and the frequency associated with this energy is known as **critical frequency**. The spectrum of frequencies below the critical frequency is not a usable form of sun energy as far as photo voltaics are considered.

**Solar light intensity**

The solar light intensity(solar energy per unit time per unit area of solar cell) available to detector (PV cell) depends on so many factors such as effect of azimuth angle, orientation of solar cell with respect to sun e.t.c. All these effects can be taken into consideration by Air mass ratio.

**Properties of material used in the construction of solar cell**

The material properties greatly influence the short circuit current of PV cell. When light falls on a material, the photons striking on the material can be

**Absorbed**by the material**Reflected**by the material**Refracted**by the material i.e it freely passes through the material

The reflection and refraction leads to **Optical losses** as they are the fraction of light incident in the material that is unused. Also the **band gap** of the material is the property of material which plays a role in determining the maximum current (I_{sc}) a solar cell can provide.

Another material property which effects I_{sc} is **Life times** of electrons and holes. **Life time** of carriers is defined as the average time interval a free electron in conduction band or hole in valence band survives before it recombines. The average distance a carrier travels in **life time** is defined as **diffusion length**. The relation between **diffusion length** and **life time** of a carrier is defined as

**L _{d} = (D*τ)^{1/2}**

Where D is diffusion constant in m^{2}/s, L_{d }is carrier diffusion length in meters, τ is carrier life time in seconds.

The **carrier life time** and **diffusion lengths** will depend on the number of defects present in the material, so that as **doping** the semiconductor increases the **defects** in the solar cell increases. The diffusion lengths also depends on the fabrication techniques used to manufacture solar cells.

The short circuit current equation of a solar cell can be approximated as

**I _{sc}=q*A*G*(L_{n}+L_{p})**

Where G is the generation rate depends on photon flux (solar intensity)

Q is charge of electron

L_{n} is the diffuse length for electrons

L_{p} is the diffusion length for holes.

## Maximum power that can be generated

In solar cell as the load is increased from open circuit to short circuit the voltage generated will decrease from V_{oc} to zero and current decreases from I_{sc} to zero. The power delivered to load will be zero if the solar cell is operated at two extreme points in IV characteristic (0, I_{sc}) (V_{oc}, 0). There exists an optimum point at which the power delivers to load will be maximum. By using controllers the solar cell can be operated at **maximum power generation point** at all times.

## Efficiency of conversion of solar cell

**Efficiency of conversion** **of solar cell** denotes the percentage of incident optical (light) power converted into electrical power.

**ξ = P _{ele}/ (P_{inc}) = (I_{op}*V_{op})/P_{in }= FF* (V_{oc} *I_{sc})/ P_{in}**

The **efficiency of conversion** **of solar cell** depends mainly on internal quantum efficiency of solar cell and on parasitic resistances. Under standard test conditions with solar irradiance = 1000 w/m2, T=25^{o }C and Air mass ratio of 1.5, a hypothetical solar cell of 1 m^{2} with **efficiency of conversion** equal to 0.4 will be able to produce power of 400 watts.

## Fill factor of solar cell

**Fill factor of solar cell** is one of the important characteristic parameter which determines efficiency of conversion of solar cell. The fill factor of solar cell always should be as high as possible to extract maximum power from solar cell.

V_{oc} is the maximum voltage that can be generated by solar cell; I_{sc} is the maximum current through the solar cell. If the solar cell could simultaneously deliver the V_{oc }and I_{sc} the power delivered will be

**P _{max, d }= V_{oc} *I_{sc}**

In practice in PV systems we will not operate the solar cell in either open circuit or short circuit condition as it leads to no power delivered to load. From the characteristics of solar cell is obvious that if the current through the solar cell increases the voltage it can generate decreases and the voltage generated at that particular current will be less than V_{oc}. Hence the operating point is characterized by (I_{op}, V_{op}) where **I _{op}< I_{sc}, V_{op}< V_{oc}**. Therefore the actual power delivered will be

** P _{op, d} = I_{op}*V_{op}**

The **fill factor** is defined as ratio of actual power delivered at operating point of solar cell to the product of open circuit voltage and short circuit current (maximum fictious power that it can deliver).

Solar cell **Fill factor = P _{op, d}/ P_{max, d} = (I_{op}*V_{op})/ (V_{oc} *I_{sc})**

**Efficiency of conversion of solar cell in terms of fill factor **

The Efficiency of conversion of solar cell is given as

**ξ = P _{ele }/ (P_{inc}) = (I_{op}*V_{op})/P_{in} = FF* (V_{oc} *I_{sc})/ P_{in}**

where P_{ele} is the generated electrical power= I_{op}*V_{op}

P_{inc} incident light power which is incident light energy per unit time

I_{op} is operating point current through solar cell

V_{op} is operating point voltage across solar cell

FF is solar cell fill factor = (I_{op}*V_{op})/ (V_{oc }*I_{sc}) hence I_{op}*V_{op} = FF*(V_{oc} *I_{sc})

V_{oc} is open circuit voltage of solar cell

I_{sc} is short circuit current of solar cell.

The parameters V_{OC}, I_{SC} are design and environmental dependent parameters of solar cell. P_{in} is incident solar cell which is not in our control, at most we can track the sun at all times during day to collect more energy from sun. Therefore the efficiency of conversion depends only on **fill factor of solar cell** which is dependent on operating pint current and voltage. Hence care must be taken to operate the solar cell at **maximum power point** to obtain better **efficiency of conversion of solar cell**.