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^{2}

^{3}

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This work, based on the junction recombination velocity (
*Sf*
_{u}) concept, is used to study the solar cell’s electric power at any real operating point. Using
*Sf*
_{u} and the back side recombination velocity (
*Sb*
_{u}) in a 3D modelling study, the continuity equation is resolved. We determined the photocurrent density, the photovoltage and the solar cell’s electric power which is a calibrated function of the junction recombination velocity (
*Sf*
_{u}). Plots of solar cell’s electric power with the junction recombination velocity give the maximum solar cell’s electric power,
*P*
_{m. } Influence of various parameters such as grain size (
*g*), grain boundaries recombination velocity (
*Sgb*), wavelength (
*λ*) and for different illumination modes on the solar cell’s electric power is studied.

Our work is grounded on the junction recombination velocity (Sf_{u}) [_{u}) [

Thus, one-dimensional (1D) studies which used the steady and transient states of the solar cell have determined with great precision, the lifetime of excess minority carriers, their diffusion length, the effective recombination velocity at the backside of the solar cell, the intrinsic junction recombination velocity (Sf_{0,u}), the characteristic I-V and shunt and series resistances [

However for polycrystalline silicon solar cells that provide the best efficiencies [

The efficiency of the solar cell is calculated as the ratio between the maximum power, P_{m}, generated by the solar cell and the power of the incident light’s flux, P_{in}; subscript m refers here to the maximum power point in the module’s I-V curve [

Calculation of the solar cell’s maximum electric power is then fundamental for photovoltaic devices characterization. That is why, the maximum powerpoint tracking (MPPT) control [

In this paper, we used the junction recombination velocity (Sf_{u}) to determine the generated power of the solar for any operating point. Within the first section, the basic theory is presented while the junction recombination velocity’s role and the results related to the influence of grain size (g), grain boundary recombination velocity (Sgb), the wavelength (λ) and the illumination modes are presented in the second part of this paper.

A bifacial solar cell is a device which generates electricity directly from visible light. When light quanta are absorbed, electron hole pairs are generated as it can be seen in

An n^{+}p-p^{+} poly crystalline solar cell, made of many small individual grains, is considered.

Taking into account of the physical process simulation, the 2D representation of the solar cell is illustrated in

The following three illumination modes are considered: front illumination, rear side illumination and simultaneous front and back side illumination. Hence, the electron-hole pairs generation rate G_{u}(z), related to each illumination mode is expressed as [

Coefficient α(l) denotes the absorption of the monochromatic illumination [_{0} is the incident photon flux and R(l) is the reflection at the wavelength, l [

At the junction, N^{+}-P interface (z = 0)), Sf_{u} quantifies how the excess carriers flow through the junction in actual operating conditions and then Sf_{u} characterizes how electrons cross to the junction [

At the back side of the solar cell, (Sb_{u}) is used to translate the losses in this zone. It quantifies hence, the rate at which excess minority carriers are lost at the back side of the cell [

The solar cell’s emitter is considered as a dead zone. So, the excess minority carriers density is determined taking account into only the contribution of the solar cell’s base.

Illumination mode | ||
---|---|---|

Front side illumination (u = fr) | 1 | 0 |

Rear side illumination (u = r) | 0 | 1 |

Simultaneous illumination (u = s) | 1 | 1 |

The excess minority carriers density is derived from the continuity equation [

where D is excess minority carriers diffusion constant while t is the lifetime of the excess minority carriers in the base of the solar cell.

The general solution of this equation is:

The factors c_{k} and c_{j} are eigen values and depend on grain size (g) and grain boundary recombination velocity (Sgb) only. Parameter Z_{kj}(z) express the z-dependence of

Inserting the Equation (3) into (2) and replacing the expression of generation by its value and taking into account of the fact that cos(c_{k}x) and cos(c_{j}x) are orthogonal functions, we obtain:

where

The solution of Equation (4) named Z_{kj}(z) can be written as follows:

The constants ^{+}-P boundary z = 0 [

and (b) at the back side of the bifacial solar cell, z = H [

Using boundary conditions at the contact of two grains respectively in the x-direction at x = ±g/2, and y- direction at y = ±g/2, transcendal Equations (8) and (9) are obtained:

and

The photocurrent density can be calculated by the following equation [

Using the Boltzmann’s relation, the photo voltage V_{ph} can be expressed as [

Here, V_{T} is the thermal voltage, _{i} the intrinsic carriers density.

The power generated by the cell is given by [

The solar cell’s generated power depends on Sf_{u} and then is function of the solar cell’s real operating point varying from the short-circuit operating point to the open one.

In Figures 2-5 we show curves of solar cell’s electric power versus junction recombination velocity which varies from 10^{0} to 10^{12} cm/s when the grain recombination velocity (Sgb), the grain size (g), the wavelength (l) and the illumination mode varies, respectively. In Figures 2-5, the solar cell is illuminated by its front side.

We noted in each plot, as already shown by [_{u} < 10^{2} m/s and Sf_{u} > 10^{10} m/s corresponding to the open-circuit operating and short-circuit operating points, respectively. The open circuit operating point is characterized by the open circuit photovoltage V_{oc} and where the photocurrent is null. The short-circuit operating point is characterised by the short-circuit photocurrent I_{sc}. In our previous studies [_{oc}) and short-circuit photocurrent (I_{sc}) as the grain size (g) increases, conversely, V_{oc} and I_{sc} decrease with the increase of grain boundary recombination velocity (Sgb) [

We also remarked that the solar cell’s electric power increases as the junction recombination velocity is high and goes through a maximum, named maximum power point, P_{m}. There is, for each P_{m}, a related junction recombination velocity Sf_{u}_{,m} corresponding to the real operating point of the solar cell.

P_{m} which is equal to the product of maximum power point photocurrent (I_{m}) and photo voltage (V_{m}), corre- sponds to the “knee” of the I-V curve [

_{m}, increases for high values of grain size (g) and decreases for high values of grain boundary recombination velocity (Sgb). It means that, increasing the grain size leads to fewer recombination in the bulk of the solar cell and hence high electrons’ flow rate crossing the junction, corresponding to an increase of the photocurrent and the efficiency of the solar cell as it can be seen in [

We also noted, for all plots, that the solar cell’s electric power decreases from the junction recombination velocity (Sf_{u}_{,m}) corresponding to the solar cell’s maximum electric power (P_{m}).

The effects of grain size (g) and grain boundary recombination velocity (Sgb) upon the junction recombina- tion velocity (Sf_{u}_{,m}) corresponding to the solar cell’s maximum electricpower (P_{m}) is shown in _{u}_{,m} are obtained with high grain size (g) and low grain boundary recombination velocity (Sgb), respectively.

We deduced that, the increase of the grain size (g) leads to the decrease of the grain boundary recombination velocity (Sgb). We can also conclude that, junction recombination velocity is, effectively, the sum of two terms as applied and demonstrated in some works [

- Sf_{0,u}, the intrinsic junction recombination velocity imposed by the shunt resistance [

- Sf_{j} which is related to current flow passed through the junction is imposed by the external load [

For a fixed external load, corresponding to a specific value of Sf_{j}, Sf_{0,u} increases with the grain boundary recombination (Sgb). This leads to the lower shunt resistance (R_{sh}) and to the initiating short-circuit condition quickly reached [_{0,u} and the shunt resistance decreases and increases, respectively. This situation corresponds to less recombination and the real operating point of the solar cell roll away of the initiating operating short-circuit condition studied in [

Evolution of the solar cell’s electric power in relation to the junction recombination velocity when the wavelength is ranging from 680 nm to 900 nm, corresponding at the domain of high wavelength is plotted on

It is shown, in

Effect of the illumination mode on the solar cell’s electric power is plotted in ^{+}-p-p^{+} bifacial solar cell has the advantage of receiving a light by its rear side. The bifacial solar cell thus receives a simultaneous illumination due the albedo [_{u} < 10^{4} m/s. The back side illumination mode’s contribution can be neglected when compared to solar cell’s electric power that are obtained by front side and both front and back sides. This is consistent with results found by [

Using the junction recombination velocity concept permits us to determine solar cell’s electric power for any operating point of the solar cell contrarily to others studies which used the maximal power point tracking (MPPT) control technic characterized by one operating point corresponding to the maximum output power delivered by solar cell.

It is shown that, for any real operating point, the solar cell’s electric power increases with grain size (g) corresponding then to the best solar cell. It decreases with high gain boundary recombination velocity (Sgb) and with high wavelength (l).

We noted that using an n^{+}-p-p^{+} solar cell which could be illuminated by both front and back sides of the solar cell simultaneously had the advantage of giving a high electric power.

Mayoro Dieye,Senghane Mbodji,Martial Zoungrana,Issa Zerbo,Biram Dieng,Gregoire Sissoko, (2015) A 3D Modelling of Solar Cell’s Electric Power under Real Operating Point. World Journal of Condensed Matter Physics,05,275-283. doi: 10.4236/wjcmp.2015.54028