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      Global Energy Interconnection

      Volume 1, Issue 4, Oct 2018, Pages 460-466
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      Impact of solar radiation variation on the optimal tilted angle for fixed grid-connected PV array—case study in Beijing

      Yanbo Shen1,2 ,Jun Zhang3 ,Peng Guo1,2 ,Xinwen Wang1,2
      ( 1.China Meteorological Administration, Public Meteorological Service Center, Beijing100081, P.R.China , 2.Center for Wind and Solar Energy Resources, China Meteorological Administration, Beijing 100081,P.R.China , 3.Nanjing University of Information Science &Technology Library, Nanjing 210000, P.R.China )

      Abstract

      A key design parameter for fixed grid-connected photovoltaic (PV) arrays, the optimal tilt angle, does not only depend on the geographic location but is also directly affected by atmospheric conditions.In this paper, long-term variations of solar radiation (i.e.global solar irradiance, direct horizontal irradiance, diffuse irradiance, and ratios of direct and diffuse irradiance) in Beijing are considered to determine their effect on the optimal tilt angle for a fixed grid-connected PV array.We found that there is a declining trend in global solar irradiance over the past 55 years, mainly caused by the decreased direct horizontal irradiance.In contrast, the decline of diffuse irradiance is not obvious, leading to a considerable decrease in the direct irradiance ratio and consequent increase in the diffuse irradiation ratio.Likewise, the long-term optimal tilt angle shows a downward trend.Compared with the optimum in the 1960s, the optimal tilt angle has decreased by 2° in 2011–2015.These results suggest that the declining trend in the optimal tilt angle is mainly caused by the decrease in direct irradiance ratio, which is highly related to atmospheric conditions.Therefore, the design and construction of PV power stations must consider the variations of atmospheric conditions and solar irradiance to determine the optimal tilt angle.

      1 Introduction

      Currently, the development and utilization of solar energy resources is rapidly increasing in China.Among them, photovoltaic (PV) power generation is the mainstream for solar energy utilization and can be divided into gridconnected and off-grid generation.From the perspective of module installation, PV power stations can be divided into fixed, adjustable, and tracking.China’s PV power stations are mainly fixed and grid-connected and require module installation at an oblique angle to the south.To maximize power generation from the received solar irradiance, the tilt angle should be set to the optimum during design and construction.

      Diurnal and seasonal changes in solar irradiance demand determining the optimal tilt angle based on the latitude and sun’s position.In addition, global solar irradiance can be affected by clouds and other atmospheric conditions, which also influence the optimum.Several studies both in China and other regions worldwide have addressed methods to calculate the optimal tilt angle and slope of global solar irradiance.For instance, [1]calculated the optimal tilt angle of a fixed grid-connected PV array in Yunnan by using the Hay model.[2]used computer-aided design to calculate the optimum, whereas [3]and [4]evaluated several methods to determine the slope of global solar irradiance and the optimal tilt angle.[5]calculated the amount of global solar irradiance and optimal tilt angle on inclined planes with different azimuths, and [6]discussed the optimal tilt angle of solar devices considering the resources.

      The abovementioned research mainly aims to establish,verify, or improve the calculation of the optimal tilt angle and slope of global solar irradiance.These studies mostly considered average values over some period to obtain results, and hence their conclusions are static in the sense that they neglect optimal tilt angle variations over time on a climate scale caused by several conditions.In this paper,the Beijing area in China is taken as example to determine the optimal tilt angle, the long-term changes in global solar irradiance over the past 50 years are analyzed, and its impact on the optimum is unveiled to provide guidelines on the design of PV power stations.

      2 Methods

      2.1 Data

      This study relied on data from monthly and yearly global solar irradiance, direct horizontal irradiance, and diffuse irradiance measured at the Beijing Southern Suburb Observatory from 1961 to 2015.These data are provided by the National Meteorological Information Center that guarantees their high quality and consistent processing.The Beijing Southern Suburb Observatory was established in 1913 and moved to its current location at 116°28'10''E longitude and 39°48'22''N latitude on April 1st, 1997.This location has an altitude of 31.3 m.The observatory began to record global solar irradiance on January 2, 1956,and it is now a reference for irradiance measurements,with observations including global solar irradiance, direct horizontal irradiance (both normal and calculated direct horizontal irradiance), diffuse irradiance, reflected irradiance, and net irradiance.The observatory is equipped with TBQ-2-B sensors to measure global solar, diffuse, and reflective irradiance, FBS-2-B sensors to measure direct horizontal irradiance, and FNP-1 sensors to measure net irradiance.

      2.2 Calculation of optimal tilt angle

      According to the characteristics of fixed grid-connected PV arrays, the optimal tilt angle must maximize the global solar irradiance received by the array surface over a year.Therefore, determining this optimum requires data on the annual global solar irradiance received at any angle between 0° (horizontal placement) and 90° (vertical placement), and selecting the maximum power point.

      Many methods for calculating the annual global solar irradiance at any angle are available.To meet the domestic engineering design habits, this paper adopts the Klein–Hay model recommended by code GB 50797-2012 [7], in which the slope of diffuse irradiance considers anisotropy,including global solar irradiance and isotropic dispersion.The main equations of the model are as follows:

      where QS, DS, SS, and RS are the global, direct horizontal,diffuse, and reflected monthly irradiance on an inclined surface, respectively, and QH, DH, and SH are the global,direct horizontal, and diffuse irradiance on the horizontal plane, respectively, with irradiance being expressed in kilowatts hour per square meter (kWh/m2), and Rb is the monthly average ratio of direct radiation from the inclined surface to the horizontal plane when the azimuth is positive to the south.Variable ϕ is the latitude, β is the angle between the inclined and horizontal plane (tilt angle),δ and ω are the solar declination and sunset angle of a representative day in each month, respectively, and ρ is the monthly average surface albedo (set to 0.2 in this study).Angles δ and ω are calculated according to astronomical formulas[8].

      The above calculation method indicates that the main factor determining the solar irradiance slope is the global solar irradiance, direct irradiance, and diffuse irradiance with respect to the horizontal plane.This amount corresponds to the global solar irradiance of the horizontal plane,and therefore the slope depends on the direct horizontal irradiance and diffuse irradiance, or the proportion of each one to the global solar irradiance on the horizontal plane(hereinafter referred to direct irradiance ratio and diffuse irradiance ratio, respectively).In turn, direct irradiance and diffuse irradiance depend on the degree of cleanliness of the atmosphere, as a very clean atmosphere increases direct irradiance, whereas a turbid atmosphere increases diffuse irradiance.Hence, the ratio of these two irradiances according to atmospheric conditions affects the irradiance slope and optimal tilt angle.

      2.3 Direct horizontal irradiance and diffuse irradiance separation

      Direct horizontal irradiance DH is obtained from normal irradiance DN as

      with

      where cloud type n has empirical coefficient cn, CFn is a threshold determining the cloud type from cloud concentration CF.Both cn and CFn should be fitted by ground-based measurements to the direct irradiance and satellite inversion of the relationship between direct irradiance DN0 and cloud concentration CF.

      Diffuse irradiance SH is calculated as

      where segmentation values 0.35 and 0.75, a1 to a5, and clear sky index kT are empirical values obtained by fitting the statistical relationship between direct horizontal irradiance,diffuse irradiance, global solar irradiance, and external global solar radiation.Finally, global horizontal irradiance QH can be obtained as the sum:

      The component separation presented above allows the calculation of the necessary parameters to determine the optimal tilt angle.

      3 Results and discussion

      3.1 Long-term variation of solar irradiance in Beijing

      Fig.1 shows the evolution of global solar irradiance,direct horizontal irradiance, and diffuse irradiance in Beijing from 1961 to 2015.The global solar irradiance in Beijing has declined over the past 50 years, with the most obvious decline in the late 1960s and 1980s, and relatively stable changes since the 1990s.The main component determining this decline is direct horizontal irradiance, as shown from the slope correlations.Specifically, direct irradiance accounts for 86% (−4.893/−5.676) of the variation in global solar irradiance.In contrast, the variation of diffuse irradiance is relatively stable with no clear downward trend,and its effect on global solar irradiance only accounts for 14% (−0.783/−5.676).The downward trend in global solar irradiance is consistent with a worldwide behavior [9,10],especially around the 1990s, which conforms to research conclusions reporting from a reduced to an increased irradiance trend [9].[11]attribute the change of direct horizontal irradiance mainly to the reduction of aerosol use in recent years, but the increase of haze in Beijing may be the main contributor to the decline in direct horizontal irradiance.The causes of global solar irradiance changes are more difficult to determine, as it may arise by the combination of various factors such as clouds, natural and anthropogenic aerosols, and water vapor [12], but these causes are out of the scope of this study and will not be further analyzed.

      Fig.1 Annual variation of global solar irradiance, direct horizontal irradiance and diffuse irradiance in Beijing

      Fig.2 shows the evolution of the direct irradiance ratio and diffuse irradiance ratio in Beijing from 1961 to 2015, where the former has considerably dropped, from a maximum of 60% in the 1960s to the minimum around 50%in the last decade.Correspondingly, the diffuse irradiance ratio has notably increased in the 21st century, sometimes exceeding the direct irradiance ratio.This variation of the global solar irradiance, direct irradiance ratio, and diffuse irradiance ratio directly affects the optimal tilt angle for fixed grid-connected PV arrays in Beijing.

      Fig.2 Annual variation of direct irradiance ratio and diffuse irradiance ratio in Beijing

      3.2 Optimal tilt angle variation over time in Beijing

      Table 1 lists the optimal tilt angle obtained from the monthly measurements of the Southern Suburb Observatory,and Fig.3 shows its evolution over time.The optimal tilt angle in Beijing lays mostly between 36° and 38°, as this range contains 76% of the optima.The maximum optimal tilt angle is 41° (1995) and the minimum is 34° (1991).Overall, the optimal tilt angle has declined over the last 55 years and fluctuated greatly around the 1990s.These results are consistent with the trend of global solar irradiance discussed above.

      Table 1 Annual optimal tilt angle for fixed grid-connected PV array in Beijing

      Year Optimal tilt angle (°) Year Optimal tilt angle (°) Year Optimal tilt angle (°) Year Optimal tilt angle (°) Year Optimal tilt angle (°) Year Optimal tilt angle (°)1961 39 1971 39 1981 37 1991 34 2001 36 2011 37 1962 38 1972 36 1982 36 1992 35 2002 38 2012 37 1963 38 1973 39 1983 37 1993 36 2003 37 2013 37 1964 36 1974 36 1984 37 1994 36 2004 38 2014 36 1965 37 1975 38 1985 38 1995 41 2005 39 2015 35 1966 37 1976 37 1986 38 1996 39 2006 36 1967 40 1977 37 1987 36 1997 37 2007 37 1968 37 1978 37 1988 39 1998 38 2008 39 1969 38 1979 37 1989 36 1999 38 2009 36 1970 39 1980 38 1990 36 2000 36 2010 38

      Fig.3 Annual variation of optimal tilt angle for fixed grid-connected PV array in Beijing

      According to the requirements of the Design Code for PV Power Stations [7], solar energy resource analysis and calculations must use data from at least 10 years.We averaged the data from the Southern Suburb Observatory over 10-year periods to determine the corresponding optimal tilt angle, as listed in Table 2 for the fixed gridconnected solar PV array in Beijing.Fig.4 shows the optimum variation trend.There is a declining trend in the optimal tilt angle, from 38° in the 1960s, remaining stable at 37° in the following four decades, and falling to 36° in 2011–2015.Combined with the long-term trends of global solar irradiance, direct horizontal irradiance, and diffuse irradiance, this downward trend in the optimal tilt angle is clearly related to the decreasing global solar irradiance and direct irradiance ratio.

      For PV arrays in most parts of China, tilting the modules to the south increases the received direct irradiance and a portion of the reflected irradiance, but reduces the acquired diffuse irradiance (that behind the module).Therefore, if the direct irradiance ratio decreases and diffuse irradiance ratio increases, the direct horizontal irradiance on the module is reduced, and the loss of diffuse irradiance increases, which leads to a reduction in the global solar irradiance slope.If the tilt angle is appropriately reduced, the total irradiance received on each module increases.For Beijing, the optimal tilt angle should decrease by 2° as both the global solar irradiance and direct irradiance ratio decreased.

      Table 2 Optimal tilted angle for fixed grid-connected PV array in Beijing over the decades

      Period 1961–1970 1971–1980 1981–1990 1991–2000 2001–2010 2011–2015 Optimal tilt angle (°) 38 37 37 37 37 36

      Overall, we found that the optimal tilt angle of a PV power station in a region is not fixed.Besides being affected by the latitude and longitude, the optimum is also affected by changes in global solar irradiance and direct irradiance ratio, which are in turn affected by changes in atmospheric conditions.In fact, if atmospheric conditions improve,both the global solar irradiance and direct irradiance ratio increase, and the optimum tilt angle also increases, whereas deteriorated atmospheric conditions would cause the opposite effects.To design PV power stations, the optimal tilt angle elevation can increase the shadow generated by each PV module, thus demanding a longer distance between adjacent rows of modules in the array and increasing the associated costs of area and installation.Therefore, this study can contribute to the proper design of PV arrays in the context of the current dramatic changes in atmospheric conditions.Gaining deeper knowledge on the change of global solar irradiance will allow to properly design the optimal tilt angle based on reliable data.

      Fig.4 Optimal tilt angle at different decades for fixed grid-connected PV array in Beijing

      4 Conclusions

      Taking the Beijing area as an example, this study analyzed the long-term variation of global solar irradiance and its influence on the optimal tilt angle of fixed gridconnected PV power stations based on measured data from meteorological stations and calculations recommended by a Chinese national standard.The main conclusions of the study are as follows:

      Global solar irradiance over the last 55 years in Beijing showed a decreasing trend mainly influenced by the drastic decrease in direct horizontal irradiance, accounting for 86% of the variation, whereas the diffuse irradiance only accounted for 14% of the variation.Correspondingly, as the direct irradiance ratio decreased, the diffuse irradiance ratio increased.

      The decrease in global solar irradiance and direct irradiance ratio also reduces the optimal tilt angle for fixed grid-connected PV power arrays in Beijing.The current optimum obtained from 2011 to 2015 is 36°, which is 2°below the optimum in the 1960s.These changes can be attributed to the variable atmospheric conditions.In recent years, the quality of atmospheric conditions has notably changed in many areas of China, and the impacts of the changing atmospheric conditions should be considered as design and construction parameters for PV power stations.In addition, the design should include an analysis over several years of data to calculate the optimal tilt angle of the PV power array, from which the optimal global solar irradiance and power generation can be obtained.

      The design life of photovoltaic power plants is usually 25 years.In the next 25 years, the optimal tilt angle of the power plants will change with the change of atmospheric environment.The change of atmospheric environment is closely related to the degree of social control of atmospheric pollution.If the control is effective and the atmospheric environment becomes better, the proportion of direct radiation will increase, accordingly, the optimum tilt angle of photovoltaic power station will also increase; otherwise,if the process of control is slow and the atmospheric environment is further deteriorated, the proportion of scattered radiation will increase.In addition, the optimal tilt angle of PV plants will also decrease.

      Acknowledgements

      This work was supported by the Ministry of Science and Technology Special Key Project on “Estimation and Prediction of the Solar Radiation in China” (No.GYHY201306048).

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      Fund Information

      supported by the Ministry of Science and Technology Special Key Project on “Estimation and Prediction of the Solar Radiation in China”(No.GYHY201306048);

      supported by the Ministry of Science and Technology Special Key Project on “Estimation and Prediction of the Solar Radiation in China”(No.GYHY201306048);

      Author

      • Yanbo Shen

        Yanbo Shen received bachelor degree at Lanzhou University, Lanzhou, 2000, and received master and Ph.D.degree at Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou, 2005.He is working in Public Meteorological Service Center, China Meteorological Administration, Beijing.His research interests includes solar energy resource assessment and forecasting, climate change, etc.

      • Jun Zhang

        Jun Zhang received bachelor degree at Nanjing University of Information Science &Technology, Nanjing, 2015.She is working towards master degree at Nanjing University of Information Science & Technology, Nanjing.Her research interests includes variation of solar radiation and Urbanization.

      • Peng Guo

        Peng Guo received master degree at Wuhan University, Wuhan, China, 2012.He received bachelor degree at Wuhan University, Wuhan,China, 2010.He is working in Public Meteorological Service Center, China Meteorological Administration, Beijing.His research interests includes Radiation resource simulation and PV power forecasting.

      • Xinwen Wang

        Xinwen Wang received bachelor degree at Party School of the CPC Central Committee, Beijing,2006.She is working in Public Meteorological Service Center, China Meteorological Administration, Beijing.Her research interests includes Radiation resource simulation and PV power forecasting.

      Publish Info

      Received:2018-08-15

      Accepted:2018-08-27

      Pubulished:2018-10-25

      Reference: Yanbo Shen,Jun Zhang,Peng Guo,et al.(2018) Impact of solar radiation variation on the optimal tilted angle for fixed grid-connected PV array—case study in Beijing.Global Energy Interconnection,1(4):460-466.

      (Editor Ya Gao)
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