The purpose of this paper is to study on a novel maximum power point tracking (MPPT) method for photovoltaic (PV) systems. First, the simulation environment for PV systems is constructed by using PSIM software package. A 516 W PV system established with Kyocera KC40T photovoltaic modules is used as an example to finish the simulation of the proposed MPPT method. When using incremental conductance (INC) MPPT method, it usually should consider the tradeoff between the dynamic response and the steady-state oscillation, whereas the proposed modified incremental conductance method based on extension theory can automatically adjust the step size to track the maximum power point (MPP) of PV array and effectively improve the dynamic response and steady-state performance of the PV systems, simultaneously. Some simulation and experimental results are made to verify that the proposed extension maximum power point tracking method can provide a good dynamic response and steady-state performance for a photovoltaic power generation system.

The characteristic curves representing the output current-voltage

One of the existing MPPT methods is the Perturb and Observe (P & O) method [

A number of studies on MPPT have concentrated on the application of artificial neural network (ANN) [

In this paper, a novel intelligent technique based on extension theory is proposed and used together with INC based MPPT controller in a PV system. The proposed MPPT controller can adaptively tune the tracking step size of tradition INC MPPT method to obtain superior dynamic response and steady-state performance, simultaneously. The less constructed data utilized, no learning procedures needed, and easy implementation are the good features of the proposed MPPT method.

In 1983 Professor Cai, a scholar from China, first proposed the concept of extension theory, which was designed to study things in terms of their extensity. This theory explores qualitative and quantitative solutions for contradictions among things [

Extension theory expresses information about things through the matter-element model, using the matter-element transformation to represent the changing correlation between the quality and quantity of the characteristics of matter. Then, the results from this correlation function are used to better understand the effects that these qualities and quantities have on the matter, so as to clearly express the level of impact from the characteristics of the matter.

Extension theory handles problems through the use of the matter-element model. If such a model is represented by a mathematical function, it can be expressed asfollows:

In extension matter-element theory, when a characteristic of matter element is one of many, it is expressed as the

The vector form of this characteristic value is expressed as

If the characteristic magnitude is an interval, then it is called a classical domain and is contained within a neighborhood domain. Assuming that an interval is set to between

Classical mathematics measures the distance relationship between two points. Extension theory measures the distance relationship between any point on the actual domain and the interval, which is expressed as a function in (

In addition to considering the correlation between points and intervals, there is also the need to consider the correlation between points and two intervals, or between intervals. Therefore, if we let

The correlation function is a function formed by dividing the rank value by distance, such as in the following:

Schematic diagram of elementary correlation function.

In addition, when

This study proposed an extension theory-based MPPT method designed to analyze the

Figure

Schematic diagram of

From (

In this paper, to let the MPPT method possess adaptive capability, the step size of the INC MPPT method of the PV arrays is adaptively tuned by extension error tuning scheme. The tuning scheme is driven by a sum of static conductance

Change diagram of

Distribution of 12 interval categories as divided by the

Figure

Slope error

Category number | Slope error category | Slope error change category | Duty cycle step size |
---|---|---|---|

1 | −0.01 | ||

2 | −0.02 | ||

3 | −0.05 | ||

4 | −0.01 | ||

5 | −0.02 | ||

6 | −0.05 | ||

7 | 0.02 | ||

8 | 0.03 | ||

9 | 0.05 | ||

10 | 0.02 | ||

11 | 0.03 | ||

12 | 0.05 |

Dynamic slope analysis diagram of

Based on matter-element extension theory, the results from the matter-element model for a 12-category classical domain are shown in Table

The classical domains of categories.

Category | Classical domain | Category | Classical domain |
---|---|---|---|

1 | 7 | ||

2 | 8 | ||

3 | 9 | ||

4 | 10 | ||

5 | 11 | ||

6 | 12 |

The following is the tracking control procedure using the proposed extension MPPT method.

From slope error

Entering the to-be-classified slope error

Based on the slope error

Select weights

Calculate the degree of correlation with each category:

Select the maximum value from the calculated degree of correlation to identify the classified slope error

Figure

Component parameters of the implemented MPPT circuit.

Part name | Inductor | Output capacitor | Input capacitor |
---|---|---|---|

Value | 2.4 mH | 46 | 460 |

Structural diagram of the proposed extension MPPT system.

This study carried out simulations under two different linear variations in irradiation conditions: one with an irradiation that dropped from 1,000 W/m^{2} to 700 W/m^{2}, then increased back to 1,000 W/m^{2}; and another with a irradiation that increased from 450 W/m^{2} to 750 W/m^{2} and then dropped back to 450 W/m^{2}. These linear variations in irradiation are shown in Figures

Simulation waveform of irradiation that dropped from 1,000 W/m^{2} to 700 W /m^{2} and then increased back up to 1,000 W/m^{2}.

Simulation waveform of irradiation that increased from 450 W/m^{2} to 750 W/m^{2} and then dropped back to 450 W/m^{2}.

Figures

Simulated output power, dynamic conductance, static conductance, and duty cycle waveforms of a PV module array using the traditional INC method under irradiation that dropped from 1,000 W/m^{2} to 700 W/m^{2}, and then increased back up to 1,000 W/m^{2}.

Simulated output power, dynamic conductance, static conductance, and duty cycle waveforms of a PV module array using the variable step size INC method under irradiation that dropped from 1,000 W/m^{2} to 700 W/m^{2} and then increased back up to 1,000 W/m^{2}.

Simulated output power, dynamic conductance, static conductance, and duty cycle waveforms of a PV module array using the proposed extension method under irradiation that dropped from 1,000 W/m^{2} to 700 W/m^{2} and then increased back up to 1,000 W/m^{2}.

In addition, to display excellence in maximum power tracking performance of the proposed extension MPPT method under various conditions of irradiation, this study followed a linear change in irradiation that increased from 450 W/m^{2} to 750 W/m^{2} and then dropped back down to 450 W/m^{2} (irradiation changes as shown in Figure

Simulated output power, dynamic conductance, static conductance, and sduty cycle waveforms of a PV module array using the traditional INC method under irradiation that increased from 450 W/m^{2} to 750 W/m^{2} and then dropped back to 450 W/m^{2}.

Simulated output power, dynamic conductance, static conductance, and duty cycle waveforms of a PV module array using the variable step size INC method under irradiation that increased from 450 W/m^{2} to 750 W/m^{2} and then dropped back to 450 W/m^{2}.

Simulated output power, dynamic conductance, static conductance, and duty cycle waveforms of a PV module array using the proposed extension method under irradiation that increased from 450 W/m^{2} to 750 W/m^{2} and then dropped back to 450 W/m^{2}.

The PV module array used during the measurement was a solar simulator [

Figures ^{2} to 700 W/m^{2}, then rises again to 1,000 W/m^{2}, as simulated by the solar simulator. As can be seen in Figures

Measured output power, dynamic conductance, static conductance, and duty cycle waveforms of a PV module array using the traditional INC method under irradiation that dropped from 1,000 W/m^{2} to 700 W/m^{2} and then increased back up to 1,000 W/m^{2}.

Measured output power, dynamic conductance, static conductance, and duty cycle waveforms of a PV module array using the variable step size INC method under irradiation that dropped from 1,000 W/m^{2} to 700 W/m^{2} and then increased back up to 1,000 W/m^{2}.

Measured output power, dynamic conductance, static conductance, and duty cycle waveforms of a PV module array using the proposed extension method under irradiation that dropped from 1,000 W/m^{2} to 700 W/m^{2} and then increased back up to 1,000 W/m^{2}.

In addition, to verify that the proposed extension MPPT method conforms with the simulated results, such that it still has good tracking performance for maximum power under various conditions of irradiation, the developed maximum power tracking circuit was used to carry out experimental testing under levels of irradiation that rose linearly from 450 W/m^{2} to 750 W/m^{2} and then dropped back down to 450 W/m^{2}. As can be seen in Figures ^{2}, 800 W/m^{2}, and 450 W/m^{2} at sunshine times of 2 hrs, 3 hrs, and 4 hrs, respectively, for a comparison of the output power values from the three MPPT methods; the results of which are shown in Table

Average value of steady-state power output under three types of irradiation using various MPPT methods.

Irradiation | Method | ||
---|---|---|---|

Traditional INC method | Variable step size INC method | Extension INC method | |

1,000 W/m^{2} | 512 W | 514 W | 516 W |

800 W/m^{2} | 411 W | 412 W | 413 W |

450 W/m^{2} | 229 W | 230 W | 231 W |

Output energy during different hours of operation using various MPPT methods under three types of single day irradiation.

Irradiation (Operation hours) | Method | ||
---|---|---|---|

Traditional INC method | Variable step size INC method | Extension INC method | |

1,000 W/m^{2 } (2 hrs) | 1024 Wh | 1028 Wh | 1032 Wh |

800 W/m^{2 } (4 hrs) | 1644 Wh | 1648 Wh | 1652 Wh |

450 W/m^{2 } (6 hrs) | 1374 Wh | 1380 Wh | 1386 Wh |

Measured output power, dynamic conductance, static conductance, and duty cycle waveforms of a PV module array using the traditional INC method under irradiation that increased from 450 W/m^{2} to 750 W/m^{2} and then dropped back to 450 W/m^{2}.

Measured output power, dynamic conductance, static conductance, and duty cycle waveforms of a PV module array using the variable step size INC method under irradiation that increased from 450 W/m^{2} to 750 W/m^{2} and then dropped back to 450 W/m^{2}.

Measured output power, dynamic conductance, static conductance, and duty cycle waveforms of a PV module array using the proposed extension method under irradiation that increased from 450 W/m^{2} to 750 W/m^{2} and then dropped back to 450 W/m^{2}.

This paper proposed an intelligent extension theory-based maximum power point tracking method for a 516 W PV power generation system. This study carried out simulation and measurement of maximum power tracking performance under variable irradiation conditions to verify the effectiveness of the proposed method. The simulated and measured results show that the proposed extension MPPT method possesses quick dynamic response to rapidly changing irradiation conditions. Its steady-state response at the MPP also has better performance than the traditional INC and variable step size INC MPPT methods. Meanwhile, the power loss of the proposed extension MPPT method at the MPP is far less than the traditional INC and variable step size INC MPPT methods. Thus, it can improve the overall power generation efficiency of the PV power generation system.

This study is grateful for the support provided by the research grants from the Bureau of Energy of the Ministry of Economic Affairs and for the technical assistance received from the Green Energy and Environment Research Laboratories, Industrial Technology Research Institute, Taiwan.