A novel method for the determination of dynamic resistance for photovoltaic modules

doi:10.1016/j.energy.2011.08.019

Energy

Volume 36, Issue 10, October 2011, Pages 5968-5974

https://doi.org/10.1016/j.energy.2011.08.019 Get rights and content

Abstract

Obtaining the maximum power output in real time is indispensable to the operation of grid connected photovoltaic (PV) power systems under given atmospheric conditions. Focusing on the resistance effect of the solar cells, we propose a new and simple method to directly determine the dynamic resistance of the PV modules from an irradiated current–voltage characteristic curve. In our method, we develop the ability to determine the dynamic resistance with a combination of finite series- and shunt-connected resistance. A series of experiments, including numerical simulations and field data tests, are conducted to examine the dynamic behavior of the PV modules during power tracking. Experimental results show that the proposed direct resistance-estimation method allows the PV modules to achieve their maximum power and impedance matching under various operation conditions.

Highlights

► A novel method to directly determine the dynamic resistance of PV modules from an irradiated I–V curve is proposed. ► The dynamic resistance and MPP of the PV modules can be simply and accurately estimated under different operation conditions. ► A series of experiments, including numerical simulations and field data tests, were conducted to examine the effectiveness of the method. ► The proposed direct resistance-estimation method can be also applied to the MPPT problem and PV stability.

Introduction

Many researches on photovoltaic (PV) energy for various applications have been conducted in recent years, as a consequence of the unique properties of PV arrays [1], [2], [3], [4]. There have also been extensive studies on improving the characteristics of renewable energy for such PV arrays, which are potentially very important for the reduction of certain carbon dioxide emissions [5], [6], [7]. The need for energy-efficient electrical power sources in remote locations is a driving force for the investigation of integrated energy systems. In particular, advancement in wind and PV generation technologies has been applied to wind-alone [8], PV-alone [9], [10], and hybrid wind/PV configurations [11], [12], [13]. PV arrays have also become a reliable energy source that it is hoped can efficiently mitigate some of the worst effects of global warming [14], [15], [16]. Studies related to renewable energy sources, including PV arrays, are especially important for many developing countries around the world.

The PV modules exhibit an extremely nonlinear current–voltage (I–V) characteristic that varies continuously with module temperature and solar irradiation. The main electrical parameters of the solar cell — such as the short-circuit current I_sc, the open-circuit voltage V_oc, the maximum power P_mp, the fill factor FF, and the maximum conversion efficiency η_m — are functions of the resistance of solar cells, i.e., the series resistance R_s and the shunt resistance R_sh [17]. This is what causes low energy-conversion efficiency in the PV modules. Hence, it is worth paying more attention to how to efficiently control the operation of PV modules at maximum power output to the extent possible. A series resistance can be caused either by excessive contact resistance or by the resistance of the neutral regions. The series resistance R_s accounts for all voltages that drop across the transport resistances of the solar cell. Usually, R_s connects to a load or an inverter. The series resistance (R_s) can be determined by different methods under various illumination conditions, such as in the dark, constant illumination, and varying illumination, yielding different results [18]. In the standardized measurement method for solar cells, R_s is normally determined by two different illumination levels, the so-called two-curve method [19]. On the other hand, the shunt resistance (R_sh) usually results from any channel that bypasses the p-n junction. This bypass can be brought about by damaged regions in the p-n junction or surface imperfections. Shunt resistance R_sh occurs in the shunt paths with the diodes of the modeled solar cells. Shunt paths can occur across the surface of real solar cells, at pin holes in the p-n junction, or at grain boundaries. The shunt resistance (R_sh) can be obtained using the so-called two points-single curve method from two points on one illuminated I–V curve [19], [20]. However, when we consider two operation points on one illuminated I–V curve or two illuminated I–V curves, it is found that both methods can lead to large errors because of different operating conditions and complicated mathematical operations. Hence, it is difficult to obtain the dynamic resistances of the PV modules (with low calculation burden), simply by using the two-curve method or two points-single curve method [19]. A less complicated way to find the dynamic resistances of the PV modules through a simpler and more convenient estimation technique is required.

Impedance matching is the practice of designing the input impedance of an electrical load or the output impedance of its corresponding signal source in electrical circuits so as to maximize the power transfer and minimize the reflections from the load. In order to gain the maximum power from a PV module at the current solar irradiance level and temperature, it is mandatory to match the PV source with the load by means of switching from a direct current (DC) to direct current converter (DC–to–DC converter). To ensure the source-load matching, the PV generation system should properly change the operating voltage at the terminals of the PV module according to the actual weather conditions. Due to the nonlinear I–V characteristic curve of PV modules, it is generally difficult to analyze and determine their output impedance, i.e., dynamic resistance. Hence, it is necessary to develop an efficient method for the determination of the dynamic resistance. Such a method should be able to estimate the voltage value corresponding to the maximum power delivered by the PV source and further achieve impedance matching for any kind of PV module.

The dynamic resistance of solar cells and modules can be determined by an I–V characteristic curve. Being a dynamic quantity, the dynamic resistance is normally taken to be the slope or the derivative of the I–V characteristic of a cell or a module and is defined as the change in voltage divided by the change in current as ΔV_pv/ΔI_pv or dV_pv/dI_pv. Furthermore, the dynamic resistance is composed of the series resistance and shunt resistance. However, the effect of the series resistance and shunt resistance is often ignored in the practical quantification of dynamic resistances. Such inaccuracies of the dynamic resistance will lead to the improper PV control operations and to the tracking of incorrect maximum power point (MPP).

As mentioned above, it is still very complicated to obtain the value of the series resistance and shunt resistance which can be done using the two-curve method and the two points-single curve method. This makes it difficult to determine the dynamic resistance using the electrical parameters of a solar cell, i.e., series resistance and shunt resistance. In most cases, electrical circuits are used as interfaces between the PV generators and the loads, or between inverters and the energy accumulators, and operated in off-line mode. A relatively powerful microcontroller is required to implement the above-mentioned methods due to the complexity of the mathematical operations involved.

Focusing on the resistance effect of the solar cells, we propose a new and simple method to directly determine the dynamic resistance of the PV modules from one point on an irradiated current–voltage characteristic curve. This method is developed based on the p-n junction semiconductor theory of solar cells. Through the direct resistance-estimation method, we elucidate the effects of dynamic resistance on the characteristics of PV modules even if the irradiation intensity or ambient temperature is changed. The model of dynamic resistance with a combination of finite series resistance and shunt resistance is also taken into consideration in this study. The correlation between the dynamic resistance and the ambient factors will be discussed in detail in the following sections.

Section snippets

Theoretical basis of the proposed method

The p-n junction recombination mechanism of semiconductors successfully describes the nonlinear characteristics of PV modules [17]. The PV modules exhibit extremely nonlinear voltage–ampere characteristics, which vary continually with module temperature and solar illumination. This fact often causes a great deal trouble leading to a lack of control for the proper operation of the PV modules and the tracking of incorrect MPP. To overcome such problems, we propose a novel and simple method to

Experimental procedures

To evaluate the performance of the proposed direct resistance-estimation method, a variety of experiments including both numerical simulation and field tests with respect to PV modules composed of different cell numbers, various irradiation intensities and temperatures were conducted in this work. In order to efficiently determine the dynamic resistance and achieve the impedance matching for any type or combination of PV modules, we used four PV modules composed of different cell numbers and

Results and discussion

We used four PV modules with different cell numbers to examine the feasibility of applying the proposed direct resistance-estimation method to any type or combination of PV modules. Fig. 3 (a) shows the I–V (current–voltage) curves of the PV modules with different combinations and different numbers of solar cells under an irradiation intensity of 1000 W/m²; AM 1.5G; and an ambient temperature of 25 °C. The cell numbers were 36, 48, 60, and 72 and they were connected in a series to form the four

Conclusions

In this study, we investigated the effectiveness of the proposed direct resistance-estimation method for PV modules functioning under different irradiation intensities and temperatures. With the p-n junction recombination mechanism and the estimation method, the dynamic resistance and MPP of the PV modules are able to be simply and accurately estimated. The dynamic resistances of the PV modules are compared with the experimentally predicted values. Our method provides more accurate results

Acknowledgments

This work was financially supported in part by the President of National Taiwan University and the National Science Council of the Executive Yuan, Taiwan, under grant numbers: 98R0529-2, 99R50019-2, NSC 98-2218-E-002-039, NSC 98-2218-E-002-012, NSC 98-3114-E-002-010, and NSC 100-3113-E-002-005. The authors are deeply grateful to Mrs. Debbie Nester for her great help in English editing. We are also grateful to the Editor and the anonymous referees for their invaluable suggestions to improve the

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¹: Equal contribution, co-first authors.

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A novel method for the determination of dynamic resistance for photovoltaic modules

Abstract

Highlights

Introduction

Section snippets

Theoretical basis of the proposed method

Experimental procedures

Results and discussion

Conclusions

Acknowledgments

Sol Energy Mater Sol Cells

Sol Energy Mater Sol Cells

Renew Energy

Energy

Energy Conv Manag

Energy Conv Manag

Energy

Appl Energy

Renew Energy

Energy

Renew Energy

Energy

Energy

Renew Sust Energ Rev