The first objective of this work is to determine some of the performance parameters characterizing the behavior of a particular photovoltaic (PV) panels that are not normally provided in the manufacturers’ specifications. These provide the basis for developing a simple model for the electrical behavior of the PV panel. Next, using this model, the effects of varying solar irradiation, temperature, series and shunt resistances, and partial shading on the output of the PV panel are presented. In addition, the PV panel model is used to configure a large photovoltaic array. Next, a boost converter for the PV panel is designed. This converter is put between the panel and the load in order to control it by means of a maximum power point tracking (MPPT) controller. The MPPT used is based on incremental conductance (INC), and it is demonstrated here that this technique does not respond accurately when solar irradiation is increased. To investigate this, a modified incremental conductance technique is presented in this paper. It is shown that this system does respond accurately and reduces the steady-state oscillations when solar irradiation is increased. Finally, simulations of the conventional and modified algorithm are compared, and the results show that the modified algorithm provides an accurate response to a sudden increase in solar irradiation.

The energy generated by the PV systems depends on various parameters, either environmental as temperature and irradiance or internal parameters of the PV panel, namely, the series and shunt resistors [

On the other side, the maximization of the PV power always remains a major challenge. Researchers have proposed different MPPT algorithms to maximize PV power, namely, FSCC, FOCV, fuzzy logic, neural network, P&O, and INC [

This paper is structured as follows. Following the introduction, Section

As shown in Figure

PV panel equivalent circuit.

Hence, the physical behavior of the PV panel depends on the shunt and series resistances, solar irradiation, and temperature. Therefore, in this work, the impact of these parameters on the output of the PV panel is investigated.

The panel used in this work is MSX-60 panel, and as presented in Table

Characteristics of MSX-60 PV panel at STC.

PV panel parameters | Values |
---|---|

Maximum power, _{max} |
60 W |

Maximum power voltage, _{mp} |
17.1 V |

Maximum power current, _{mp} |
3.5 A |

Short-circuit current, _{sc} |
3.8 A |

Open-circuit voltage, _{CO} |
21.1 V |

Voltage/temp. coefficient, _{V} |
−0.38%/°C |

Current/temp. coefficient, _{I} |
0.065%/°C |

The number of cells, _{s} |
36 |

PV array tool.

Equations (

PV panel PSIM model.

Figure

Figure

Model of (

As presented in Figure ^{2} to 1000 W/m^{2}. Therefore, the irradiance change affects heavily the PV panel current.

Figure

Model of (

Generally, as shown in Figure

The series resistor value is very small, and it may be neglected in some cases. Nevertheless, to make the appropriate model for any PV panel, it is recommended to make a variation of this resistor and show its effect on the PV panel output. As shown in Figure

_{s}.

The simulation was made for three values of series resistance (1 mΩ, 4 mΩ, and 8 mΩ). Moreover, as shown in Figure

As presented in Figure _{sh} should be quite large for a good fill factor. In fact, when _{sh} is small, the current collapses more strongly, then the loss of power is high, and the fill factor is low. Therefore, _{sh} of any PV panel should be large enough for a good efficiency.

_{sh}.

Partial shading also presents a major impact on PV output power. When the insolation received by a part of the PV panel (shaded cells) is less than the insolation received by another part (illuminated cells), the current generated by the illuminated cells is greater than the current produced by the shaded cells; this mismatch makes the diode of shaded cells reverse biased; consequently, the power will be lost in the shaded cells and that may cause a hot spot problem which is the reason of permanent damage to the PV panel [

To simulate the effect of shading, a bypass diode is associated with each string of the panel, and it should be mentioned that the panel used includes two strings and each string is a set of 18 cells. Thus, as shown in Figure ^{2} and the second string by 700 W/m^{2}.

PV panel under nonuniform irradiation.

Under uniform irradiation, the bypass diodes have no impact because they are reversely biased. But under shading, the current flows through the bypass diode instead of the shaded string because the bypass diode is directly biased, and as a result, no power will be lost in the shaded cells and only the illuminated cells generate power. Figure

To get benefit from the model developed, a PV array of 18 PV panels has been built in order to supply a solar pumping station, not studied in this paper. Therefore, as shown in Figure

PV array model.

The model of the PV array has been achieved on PSIM, and simulation result obtained is presented in Figure

As presented in Figure

PV panel provides

The impact of load on

Figure

Boost converter.

The operation principle of this converter is described by the following equations [

By using (_{eq}) and the load resistance (

The choice of the inductor can directly influence the performance of the boost converter. Moreover, the selection of the inductance is a trade-off between its cost, its size, and the inductor current ripple. A higher inductance value results in a minor inductance current ripple; however, that results in a higher cost and larger inductor’s size, which means a larger PCB surface.

By the way, the inductance value can be given as follows:

During _{ON} state,
_{L} can be computed as below, and

Therefore, the optimum inductor value can be computed by using

Based on Figure

Current waveforms of the input capacitor and inductor in CCM.

Therefore,

The choice of the output capacitor is made by using output voltage ripple as follows:

During _{ON},

Therefore, the output capacitor value can be calculated as below, where the desired ∆_{O} equals to 2% of output voltage [

An input capacitor is used to decrease the input voltage ripple and to deliver an alternative current to the inductor. The input voltage ripple matches to the charge voltage during the charge phase of the capacitor, and during this phase, _{Cin} is greater than zero, so this phase is illustrated by the blue area in Figure

Current waveforms of the input capacitor in CCM.

Based on Figure

Therefore, the input capacitor can be calculated by (

The design of the used boost is presented in Table

Design of the boost converter.

Parameters | Values |
---|---|

1.2 mH | |

_{in} |
75 |

_{O} |
75 |

10 kHz | |

50 Ω | |

_{MPP} |
0.69 |

A good MPPT algorithm balances between the tracking speed and steady-state performance. In accordance with these requirements, the INC algorithm can be used even if it can fail in some cases [

Since

The flowchart of the INC algorithm is presented in Figure

Flowchart of INC algorithm.

However, the conventional INC algorithm fails to make a good decision when the irradiance is suddenly increased [^{2} and the PV system operates at load_2, the INC technique controls the PV system in order to reach the MPP (point B). When the irradiance is increased to 1000 W/m^{2}, load_2 will lead the system to point G in ^{2} is at point A, and the slope between point A and C is negative, then the PV panel voltage should have been decreased in order to reach point A, instead of increase voltage and recede from point A as made by the conventional INC algorithm. In addition, as presented in Figure

^{2} and 1000 W/m^{2}.

Conversely, this weakness does not happen if the solar irradiation is decreased. Because as shown in Figure

Based on the above analysis, it is noted that when the solar irradiance increases, both the voltage and the current are increased. Therefore, the sudden increase in solar irradiation can be detected, by checking if the MPP was reached and both the voltage and current are increased. Therefore, a permitted error is accepted (

The proposed algorithm is presented in Figure

Flowchart of the proposed INC algorithm.

The test was made for the conventional and the proposed techniques. At first, the solar irradiance is suddenly increased from 500 W/m^{2} to 1000 W/m^{2} at ^{2} to 500 W/m^{2} at

Test result of the INC algorithm.

Test result of the modified INC algorithm.

In addition, as presented in Figure

Table

Comparison of the proposed algorithm with other improved incremental conductance algorithms proposed in scientific literature.

Technique | Oscillation level | Efficiency (%) | Response time during sudden increase in irradiation | Incorrect decision under sudden increase of irradiation |
---|---|---|---|---|

Conventional | 2.5 W | 96 | Slow | Yes |

[ |
1 W | 96.40 | Fast | No |

[ |
1.5 W | 98.5 | Fast | Yes |

[ |
1 W | 97.5 | Medium | Yes |

Proposed | Neglected | 98.8 | Very fast | No |

In this paper, PV panel’s parameters are found using MathWorks tool (PV array); hence, by using these parameters, a PV panel and a PV array are modeled, and the results show that the model is in accordance with experimental data of the used panel (MSX-60). In addition, a modified INC algorithm which can overcome the confusion faced by the conventional INC technique is proposed in this paper. As a result, the tests show that the modified technique detects the fast increase of irradiation and makes a correct decision, contrary to the conventional technique. Moreover, by using the modified algorithm, steady-state oscillations are almost neglected. Hence, the loss of energy is minimized; consequently, the efficiency is equal to 98.8% instead of 96% obtained by the conventional technique.

As a perspective, the modified INC algorithm can be more improved and then implemented in an embedded hardware device.

Diode’s ideality factor

Output current of the panel (A)

_{s}:

Diode saturation current (A)

_{ph}:

Panel photocurrent (A)

Solar irradiation (W/m^{2})

Boltzmann constant (J⋅K^{−1})

Electron charge (C)

The load (

_{eq}:

The resistance seen by the panel (Ω)

_{s}:

Series resistance (Ω)

_{sh}:

Shunt resistance (Ω)

Junction temperature (K)

Output voltage of the panel (V)

_{O}:

Output voltage of the boost converter (V)

_{O}:

Output current of the boost converter (A)

Switching frequency (Hz)

Input voltage ripple of the boost converter (V)

_{O}:

Output voltage ripple of the boost converter (V)

_{L}:

Inductor current ripple (A).

Duty cycle.

Continuous conduction mode

Fractional short-circuit current

Fractional open-circuit voltage

Incremental conductance

Maximum power point

Maximum power point tracking

Perturb and observe

Photovoltaic

Standard test conditions.

The authors declare that they have no conflicts of interest.