Circuit model of photovoltaic (PV) module is presented in this paper that can be used as a common platform by material scientists and power electronic circuit designers to develop better PV power plant. Detailed modeling procedure for the circuit model with numerical dimensions is presented using power system blockset of MATLAB/Simulink. The developed model is integrated with DC-DC boost converter with closed-loop control of maximum power point tracking (MPPT) algorithm. Simulation results are validated with the experimental setup.

The field of photovoltaics (PV) has experienced a remarkable growth for past two decades in its widespread use from standalone to utility interactive PV systems. The best way to utilize the electric energy produced by the PV array is to deliver it to the AC mains directly, without using battery banks [

A recent study in Germany, of 21 PV systems in operation for 10 years, revealed that inverters contributed for 63% of failures, modules 15%, and other components 23%, with a failure occurring, on an average, every 4.5 years [

At present, PV BOS research uses mathematical functional models for the performance analysis of newly developed systems. These developed systems could not be readily adopted by the field professionals and hence the above failure rate. Hence the need for simplified Simulink modeling of PV module has been long felt.

Simple circuit-based PV models have been proposed in the literature [

In this paper, the design of PV system using simple circuit model with detailed circuit modeling of PV module is presented. In Section

A PV module consists of a number of solar cells connected in series and parallel to obtain the desired voltage and current output levels. Each solar cell is basically a p-n diode. As sunlight strikes a solar cell, the incident energy is converted directly into electrical energy without any mechanical effort.

Transmitted light is absorbed within the semiconductor, by using this light energy to excite free electrons from a low energy status to an unoccupied higher energy level. When a solar cell is illuminated, excess electron-hole pairs are generated throughout the material, hence the p-n junction is electrically shorted and current flows.

For simplicity, the single-diode model of Figure

PV cell modeled as diode circuit.

PV cells are grouped in larger units called PV modules, which are further interconnected in a series-parallel configuration to form PV arrays.

The following are the basic equations from the theory of semiconductors and photovoltaics [

In Figure ^{2}), ^{2}), and the nominal irradiation is 1000 W/m^{2}.

Detailed Simulink model of (

Photocurrent.

S. no. | Insol W/m^{2} | Value of | ||||
---|---|---|---|---|---|---|

25°C | 30°C | 40°C | 50°C | 90°C | ||

1 | 1000 | 2.55 | 2.559 | 2.575 | 2.592 | 2.66 |

2 | 700 | 1.785 | 1.791 | 1.803 | 1.815 | 1.862 |

3 | 500 | 1.275 | 1.279 | 1.288 | 1.296 | 1.33 |

4 | 250 | 0.6375 | 0.6396 | 0.6489 | 0.6481 | 0.6651 |

5 | 100 | 0.255 | 0.2559 | 0.2576 | 0.2592 | 0.2661 |

Solkar make 36 W PV module is taken as the reference module for simulation and the datasheet details are given in Table

Electrical characteristic data of solkar 36 W PV module.

Description | Rating |
---|---|

Rated power | 37.08 Wp |

Voltage at maximum power ( | 16.56 V |

Current at maximum power ( | 2.25 A |

Open circuit voltage ( | 21.24 V |

Short circuit current ( | 2.55 A |

Total number of cells in series ( | 36 |

Total number of cells in parallel ( | 1 |

^{2} with an AM1.5 spectrum at 25°C.

Module reverse saturation current, ^{-19 }C),^{−23} J/K), and

Detailed Simulink model of (

Module reverse saturation current.

Module reverse saturation current varies with temperature as shown in Table

S. no. | Temperature °C | Module reverse saturation current (A) |
---|---|---|

1 | 25 | 1.182 ^{(−006)} |

2 | 30 | 1.503 ^{(−006)} |

3 | 40 | 2.377 ^{(−006)} |

4 | 50 | 3.654 ^{(−006)} |

5 | 90 | 1.609 ^{(−005)} |

The module saturation current

This equation is simulated and shown in Figure

Module saturation current.

The module saturation current

S. no. | Temperature °C | Module saturation current (A) |
---|---|---|

1 | 25 | 1.182 ^{(−006)} |

2 | 30 | 2.456 ^{(−006)} |

3 | 40 | 9.92 ^{(−006)} |

4 | 50 | 3.686 ^{(−005)} |

5 | 90 | 0.003491 |

The basic equation that describes the current output of PV module

The current leakages, the tunnel effect, breakdown by micro plasmas, leaks along surface channels, and so forth, are modeled as a parallel resistance. The parallel resistance has its greatest effect when the voltage is lowest, that is, when the current passing through the diode of the equivalent circuit is very small. The effect of parallel resistance, when it is sufficiently small, is to reduce the open-circuit voltage and the fill factor [

The graph between the relative efficiency of PV modules and isolation for various values

When

The use of simplified circuit model in this paper makes this model suitable for power electronics designers who are looking for an easy and effective model for simulation of photovoltaic devices with power converters. The value of parallel resistance

The series resistance

Equation (

Solving algebraic loop is an iterative process. A successful solution results only if the algebraic loop solver converges to a definite answer. Proper care is to be taken of the feedback loop to get quicker convergence. In this paper simplification of equation is done by excluding

The iterative MATLAB/Simulink model of output current

Module output current _{.}

Relative efficiency versus irradiation.

All the above four blocks are interconnected to get Simulink model of

Simulation of

Detailed discussion of simulation steps of

The hardware for validating the results obtained in developed Simulink model is given in Figure

The description of experimental circuit given in Figure

The Op-Amp, the MOSFET, and the resistor

A linear MOSFET (IRF 150/IRF 460) is used. Gate-Source port of the MOSFET is driven by a low-frequency triangular wave signal.

DSO has been used and therefore repetitive trigger signal is not required and only a slow changing ramp signal is required to change the current from zero to the short-circuit value.

The experimental characteristics smoothened by curve fitting along with characteristics of Simulink model are shown in Figures

Circuit for obtaining the experimental characteristics of PV module.

Hardware setup of an electronic load with sample snapshot of DSO screen for

Simulation and experimental

Simulation and experimental

It can be seen from Figure ^{2 } and

The simulated values of current using the developed model are higher than the experimental values of current by about 2% at higher values of insolation and hence the circuit model has reasonable accuracy.

The above graph also shows that useful voltage output varies from 12 V to 19 V. The maximum power point for all these temperatures lies between these voltages.

In the equivalent circuit of a PV cell, as shown in Figure

Simulink model of

The voltage at the output terminal of the model is fed back as the voltage input

The detailed circuit model of PV module is shown in Figure

Detailed circuit model of PV module.

Circuit model block of PV module.

Further, the forward bias voltage of the diode shown in Figure

Here, a voltage value is chosen initially and the iteration of power equation is carried out as done in normal functional PV model as it involves the algebraic loop problem.

With the variation of irradiation and temperature, the power output of PV module varies continuously. The maximum power point tracking (MPPT) algorithm is used for extracting the maximum power from the solar PV module and transferring that power to the load [

DC-DC converter for operation at the MPP.

By changing the duty cycle of the PWM control signal, the load impedance as seen by the source varies and matches the point of the peak power of the source so as to transfer the maximum power.

The PV modules are always used with DC-to-DC converters to obtain the maximum power point operation. The types of converters used are buck, boost, and buck-boost. For battery charging applications buck-boost configuration is preferred where as boost converters are used for grid-connected applications. DC-DC boost converters are used often in PV systems to step up the low module voltage to higher load voltages. Hence, DC-DC boost converter is used for the design of MPPT controller.

The boost converter configuration, as shown in Figure

Configuration of DC to DC boost converter.

If the switch operates with a duty ratio

The boost converter operates in the continuous conduction mode for value of inductance

The current supplied to the output RC circuit is discontinuous. Thus, a larger filter capacitor is required to limit the output voltage ripple. The minimum value of filter capacitor that provides the output DC current to the load when the diode

Designed component values of DC-to-DC boost converter used for simulation are given in Table

Component values of DC-to-DC boost converter.

Description | Rating |
---|---|

Inductor | 120 |

MOSFET | IRF P460 |

Power diode | 1N5408 |

Capacitor | 330 |

Resistive load | 50 Ω, 50 W |

Switching frequency | 20 kHz |

The DC-DC converter (with configuration given in Figure

Boost converter circuit with DC supply.

With DC supply, the converter voltage boost ratio is directly proportional to the duty cycle.

The battery supply in circuit shown in Figure

Boost converter circuit with PV input.

The detailed experimental verification with circuit response of this developed circuit model is available in [

For the design of MPPT, the data is collected through simulation with the developed circuit model and results are tabulated in Table

Duty cycle variation.

Duty cycle | Input voltage ( | Input current ( | Input power ( | Output voltage ( | Output current ( | Output power ( |
---|---|---|---|---|---|---|

Irradiation—1000 W/m^{2} Temp—25°C | ||||||

0.4 | 17.82 | 2.059 | 36.69 | 40.08 | 0.8106 | 32.13 |

0.41 | 16.7 | 2.303 | 38.46 | 40.45 | 0.8089 | 32.72 |

0.5 | 15.05 | 2.44 | 36.72 | 39.06 | 0.7812 | 30.52 |

Irradiation—700 W/m^{2} Temp—25°C | ||||||

0.3 | 17.6 | 1.375 | 24.21 | 32.46 | 0.6492 | 21.08 |

Irradiation—500 W/m^{2 }Temp—25°C | ||||||

0.2 | 17.64 | 0.8661 | 15.28 | 25.76 | 0.515 | 13.27 |

From Table ^{2} to 0.2 for irradiation of 500 W/m^{2}. This variation coincides with the graph shown in Figure

Duty cycle variation with respect to irradiation.

Many MPPT techniques have been proposed in the literature; examples are the Perturb and Observe (P&O), Incremental Conductance (IC), Fuzzy Logic, and so forth. The P&O algorithm is very popular and simple. So it is used in this paper. The power graph for P&O algorithm is shown in Figure

Power graph for P and O algorithm.

In P&O algorithm, a slight perturbation (

Flow chart of P&O MPPT algorithm.

The Simulink model for P & O MPPT algorithm is shown in Figure

Simulink model for P&O MPPT algorithm.

The above MPPT unit is placed as closed-loop control in the simulation circuit, as shown in Figure

MPPT control circuit.

The schematic diagram of the proposed hardware system is shown in Figure

The DC-DC boost converter acts as an interface between the PV module and the load.

The voltage and current output are sensed and an error signal in digital is generated by the software.

The error signal in digital form is given to the DAC (0808) which converts it to the corresponding analog signal.

This signal is then compared with a high-frequency triangular wave of 20 kHz. The pulse generated given is to the gate of the power semiconductor device (MOSFET), thereby changing the duty cycle of the converter.

This generated pulse must be able to trigger the power circuit of the MOSFET.

Thus the source impedance is matched with the load impedance and maximum power is transferred.

Proposed hardware system.

The hardware setup of the proposed system is shown in Figure

Hardware of MPPT.

The experiment is carried out for 1000 W/m^{2} at 25°C. The experimental values of PV module power and current are lower by about 2 to 5 percent compared to the simulation values, as shown in Figure

Variation of current, power for variable irradiation with experimental results.

Thus the performance of the developed circuit model, in closed-loop control, follows the simulation values with reasonable accuracy.

In Section

The next two equations, (

In Section

Circuit model of photovoltaic (PV) module is presented in this paper, which can be used as a common platform by material scientists as well as power electronic circuit designers to develop the better PV power plant.

The authors wish to thank the management of SSN College of Engineering, Chennai for providing experimental and computational facilities to carry out this work at SSNCE EEE Department Solar Photovoltaic Research Laboratory.