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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 Voc.
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
It = Ido*(exp (V/eta*Vt)-1)-Iph = 0
exp (V/eta*Vt) = 1+ (Iph/Io)
Applying anti log on both sides of the equation we get
Voc = η*Vt*ln (1+ (Iph/Io))
Where η is ideality factor 1 for Ge and 2 for Si,
Vt is voltage equivalent of temperature=26 mV at 27 Degrees,
Iph is the short circuit current proportional to light intensity,
Io is reverse saturation current of diode or dark current flow through the cell due to thermal agitation.
Hence Voc depends on following factors
- Temperature of material(Vt=k*t/q where K is Boltzmann constant, t is absolute temperature in kelvin, q is charge of electron)
- magnitude of photo current(Iph)
- 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 (Io)
- 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
It = Ido*(exp (V/eta*Vt)-1)-Iph / V = 0
It = Ido*(exp (0)-1)-Iph
It = -Iph
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 (Isc) a solar cell can provide.
Another material property which effects Isc 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
Ld = (D*τ)1/2
Where D is diffusion constant in m2/s, Ld 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
Where G is the generation rate depends on photon flux (solar intensity)
Q is charge of electron
Ln is the diffuse length for electrons
Lp 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 Voc to zero and current decreases from Isc to zero. The power delivered to load will be zero if the solar cell is operated at two extreme points in IV characteristic (0, Isc) (Voc, 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 = Pele/ (Pinc) = (Iop*Vop)/Pin = FF* (Voc *Isc)/ Pin
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=25o C and Air mass ratio of 1.5, a hypothetical solar cell of 1 m2 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.
Voc is the maximum voltage that can be generated by solar cell; Isc is the maximum current through the solar cell. If the solar cell could simultaneously deliver the Voc and Isc the power delivered will be
Pmax, d = Voc *Isc
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 Voc. Hence the operating point is characterized by (Iop, Vop) where Iop< Isc, Vop< Voc. Therefore the actual power delivered will be
Pop, d = Iop*Vop
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 = Pop, d/ Pmax, d = (Iop*Vop)/ (Voc *Isc)
Efficiency of conversion of solar cell in terms of fill factor
The Efficiency of conversion of solar cell is given as
ξ = Pele / (Pinc) = (Iop*Vop)/Pin = FF* (Voc *Isc)/ Pin
where Pele is the generated electrical power= Iop*Vop
Pinc incident light power which is incident light energy per unit time
Iop is operating point current through solar cell
Vop is operating point voltage across solar cell
FF is solar cell fill factor = (Iop*Vop)/ (Voc *Isc) hence Iop*Vop = FF*(Voc *Isc)
Voc is open circuit voltage of solar cell
Isc is short circuit current of solar cell.
The parameters VOC, ISC are design and environmental dependent parameters of solar cell. Pin 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.