Evaluation of solar radiation models on vertical surface for building photovoltaic applications in Beijing

IET Renewable Power GenerationVolume 16, Issue 8 p. 1792-1807 ORIGINAL RESEARCHOpen Access Evaluation of solar radiation models on vertical surface for building photovoltaic applications in Beijing Fen Li, Corresponding Author Fen Li lifen2012@shiep.edu.cn orcid.org/0000-0003-2424-1653 School of Electric Engineering, Shanghai University of Electric Power, Shanghai, China Correspondence Dr. Fen Li, School of Electric Engineering, Shanghai University of Electric Power, Shanghai, China. Email: lifen2012@shiep.edu.cnSearch for more papers by this authorRenkui Wang, Renkui Wang School of Electric Engineering, Shanghai University of Electric Power, Shanghai, ChinaSearch for more papers by this authorLing Mao, Ling Mao School of Electric Engineering, Shanghai University of Electric Power, Shanghai, ChinaSearch for more papers by this authorDonghai Zhu, Donghai Zhu orcid.org/0000-0002-0997-2370 State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Hubei, ChinaSearch for more papers by this authorXu She, Xu She Carrier Corporation, 1300 Hall Blvd., Bloomfield, USASearch for more papers by this authorJianping Guo, Jianping Guo State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, ChinaSearch for more papers by this authorShunfu Lin, Shunfu Lin School of Electric Engineering, Shanghai University of Electric Power, Shanghai, ChinaSearch for more papers by this authorYongheng Yang, Yongheng Yang orcid.org/0000-0002-1488-4762 School of Electric Engineering, Zhejiang University, Zhejiang, ChinaSearch for more papers by this author Fen Li, Corresponding Author Fen Li lifen2012@shiep.edu.cn orcid.org/0000-0003-2424-1653 School of Electric Engineering, Shanghai University of Electric Power, Shanghai, China Correspondence Dr. Fen Li, School of Electric Engineering, Shanghai University of Electric Power, Shanghai, China. Email: lifen2012@shiep.edu.cnSearch for more papers by this authorRenkui Wang, Renkui Wang School of Electric Engineering, Shanghai University of Electric Power, Shanghai, ChinaSearch for more papers by this authorLing Mao, Ling Mao School of Electric Engineering, Shanghai University of Electric Power, Shanghai, ChinaSearch for more papers by this authorDonghai Zhu, Donghai Zhu orcid.org/0000-0002-0997-2370 State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Hubei, ChinaSearch for more papers by this authorXu She, Xu She Carrier Corporation, 1300 Hall Blvd., Bloomfield, USASearch for more papers by this authorJianping Guo, Jianping Guo State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, ChinaSearch for more papers by this authorShunfu Lin, Shunfu Lin School of Electric Engineering, Shanghai University of Electric Power, Shanghai, ChinaSearch for more papers by this authorYongheng Yang, Yongheng Yang orcid.org/0000-0002-1488-4762 School of Electric Engineering, Zhejiang University, Zhejiang, ChinaSearch for more papers by this author First published: 23 April 2022 https://doi.org/10.1049/rpg2.12478AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract Building photovoltaic (PV) may provide a growing share of electricity for big cities. However, lack of measured radiation data on vertical surface remains a critical problem for building PV deployment. With the development of urbanization and industrialization, high aerosol load is altering the nature of solar radiation in Beijing. Hence, ten in-plane solar radiation models are reviewed to choose optimal model for calculating solar radiation on vertical surface in such high turbidity area. At the same time, the effect of atmospheric turbidity on the model accuracy is revealed for further understanding on the optimal model. To give general suggestion on model selection, the performance of the ten models for each weather type is tested based on new method of weather type classification. Finally, solar resource on vertical surface and output energy of building PV system are evaluated by the optimal model to guide building PV deployment. The results indicate that Perez model is suitable to calculate solar radiation on vertical surface in high turbidity area. High atmosphere turbidity will cause Perez model inaccurate. Model selection can be made by the status of atmospheric transmittance. It is feasible to apply building PV in Beijing with AC output energy of 630–971 kWh/kWp/year. 1 INTRODUCTION The Paris Agreement on climate change mitigation aims to reduce carbon intensity of energy systems. Solar photovoltaic (PV) is one of the alternative transition pathways to achieve this target [1]. Many countries are striving to increase the share of solar power in their energy mix. In Mainland China, PV installed capacity was 258.5 GWp by the end of the first quarter of 2021, including 177.36 GWp for PV power stations and 81.14 GWp for distributed PV systems [2]. As an effective way to save energy and reduce carbon emission, building PV becomes more economically feasible [3, 4]. Building PV is close to electricity consumption in cities, and power generation of building PV can be achieved at high level of adoption locally. Building PV also has the potential to cover a significant fraction of the electricity needs of cities [5]. As the capital of China, Beijing is the centre of politics, economics and culture in China. Promoting building PV in Beijing can set an example for optimizing energy consumption structure and promoting low-carbon development. When exploring the potential of building PV, the amount of solar radiation is an integral part since it determines energy production of PV systems. Shirazi [6] evaluated global radiation on building facades and determined the power generation increment of building PV with optimum tilt angle. Díez-Mediavilla [7] assessed the amount of solar radiation on horizontal surface and vertical surface facing the four cardinal points of the compass. The potential of building PV was concluded by the assessment. Shankar [8] simulated incident solar radiation on south facade and obtained the energy supply situation of building PV systems. Fluctuations of solar radiation are often ignored in the evaluations. Although the fluctuations of power generation can be mitigated by control strategies, such as cooperative control strategy and adaptive moving average control [9, 10], optimizing building PV deployment can reduce the fluctuations of PV power generation essentially. In addition, the characteristics of solar radiation also cannot be overlooked in improving the efficiency of resource utilization. Measured radiation data is crucial to the evaluation of solar resource for building PV application. Generally speaking, the meteorological stations only provide global radiation on horizontal surface, but the data on inclined surface for building PV are not available. For instance, in Mainland China, there are 99 radiation observational stations measuring solar radiation on horizontal surface, and none of them can provide measurements on inclined surface. Stationary PV systems are usually oriented and tilted to maximize solar energy. The measurements cannot satisfy the demand for PV application and deployment on inclined surface. Thereby, in-plane solar radiation models can be applied to convert solar radiation from horizontal surface to inclined surface of interest. In 1961, Liu and Jordan assumed that diffuse radiation in the sky was isotropic and firstly proposed an isotropic model [11]. Subsequently, many researchers continued to improve and propose various models [12-20]. The performance of in-plane solar radiation models was reviewed in different climate regions. A total of 18 case studies (18 different orientations/locations) were presented in Yang's research. The performance rankings of 26 in-plane solar radiation models in different cases were various [21]. Fan [22] used solar radiation data and power generation data measured in Zhangbei region of China to evaluate 12 in-plane solar radiation models. Reindl model was chosen as the optimal one to study the relationship between solar radiation and power generation. Toledo [23] evaluated the performance of two in-plane solar radiation models to calculate solar irradiance on vertical surfaces. The error rate decreased slightly for clear days. As the process of urbanization and industrialization, aerosol pollution episodes are frequent in China. The scattering and absorption of aerosols have significant effects on solar radiation [24, 25]. Therefore, it is necessary to reevaluate the performance of in-plane solar radiation models in such high turbidity area. Further, the performance of in-plane solar radiation models for different sky conditions need to be tested to give general suggestion on model selection. The primary contributions of this paper are generalized as following: To test the performance of in-plane solar radiation models for different sky conditions, a new method of weather type classification is proposed by diagnostic analysis of solar radiation and meteorological environmental factors. Ten in-plane solar radiation models in high turbidity area are reviewed based on measured data. Meanwhile, the impact of atmospheric turbidity on the model performance is revealed for further understanding on the optimal model. The performance of the ten in-plane solar radiation models for each weather type is tested to give general suggestion on model selection. Based on the fluctuations of solar radiation, a deployment scheme of building PV is determined to smooth power output. The characteristics of solar resources on the vertical surfaces and output energy of PV system are evaluated to provide guidance for the application of building PV system in Beijing. The content is organized as follows. Data and evaluation methods are introduced in Section 2. New method of weather type classification and evaluation of in-plane solar radiation models are given in Section 3. Solar resource on vertical surface and output energy of PV system are evaluated for building PV applications in Section 4. Finally, the conclusions are generalized in Section 5. 2 DATA AND METHODS 2.1 Data source and quality control The hourly radiation data including global, diffuse, and ground reflected radiation on the horizontal surface, and direct normal radiation from 2010 to 2011 were measured at Beijing Observatory. The observatory is located in south suburbs of Beijing (39°48′N; 116°28′E). Hourly meteorological data including total cloud cover (C), horizontal visibility (V), relative humidity ( R H $RH$ ), station pressure (P), wind speed 10 m above ground (W) were also measured at the observatory. Above data were accessed from National Meteorological Information Center (NMIC) of China Meteorological Administration (CMA). In addition, hourly PM2.5 data were accessed from the U.S. Embassy in Beijing. The measurement system for inclined surface was situated in Beijing Observatory since May in 2009. It was the first available one for global radiation on inclined surface in Mainland China. As shown in Figure 1, radiation data on the vertical surface and tilt angles equal to latitude of Beijing (φ) and φ ± 15° were measured by pyranometers and PV modules, respectively. The global radiation data on the vertical surfaces facing south, east and west from 2010 to 2011 were accessed from Meteorological Observation Centre of CMA, and the data from 5th to 12th, 29th to 30th in August and 13th to 26th in September of 2010 were missing. FIGURE 1Open in figure viewerPowerPoint The measurement system for global radiation on inclined surface at Beijing Observatory All the radiation and regular meteorological data were subjected to strict quality control and inspection implemented by NMIC of CMA. Data that violates physical limits and conservation laws were marked as outliers, which has been discarded: (1) global horizontal radiation greater than horizontal extra-terrestrial radiation; (2) diffuse or beam horizontal radiation greater than global horizontal radiation; (3) the sum of beam and diffuse horizontal radiation with absolute error larger than 20% of global horizontal radiation [26, 27]. 2.2 Evaluation indexes 2.2.1 Meteorological environmental factors The factors that affect the solar radiation reaching the ground can be classified into three categories: astronomical factors, geographical factors and meteorological environmental factors. Astronomical factors are related to time and can be calculated explicitly, such as Earth-Sun distance and solar altitude angle. Geographical factors, such as latitude, altitude and topography, are constant in a period. Meteorological environmental factors have strong randomness mainly due to the change of cloud and atmospheric aerosols. The following factors are used to represent the influence of meteorological environmental conditions on the solar radiation reaching the ground and reveal the complex relationship between them. The clearness index is defined as the ratio of the global horizontal radiation to the horizontal extra-terrestrial radiation. It characterises the transmission and attenuation of global radiation through the atmosphere: k T = I I o , \begin{equation}{k_T} = \frac{I}{{{I_o}}}{\rm{\;}},\end{equation} (1)where I $I\;$ is hourly global horizontal radiation and I o $\;{I_o}$ is hourly horizontal extra-terrestrial radiation. The direct radiation ratio is defined as the beam horizontal radiation divided by the global horizontal radiation and varies with different regions: B d = I b I , \begin{equation}{B_d} = \frac{{{I_b}}}{I},\end{equation} (2)where I b ${I_b}$ is hourly beam horizontal radiation. The atmospheric transmissivity is a function of transmittance of the atmosphere to beam radiation. It mathematically equals to the product of clearness index and direct radiation ratio: τ b = I n I o n = I n c o s θ Z I o n c o s θ Z = I b I o = k T B d , \begin{equation}{\tau _b} = \frac{{{I_n}}}{{{I_{on}}}}{\rm{\;}} = \frac{{{I_n}cos{\theta _Z}}}{{{I_{on}}cos{\theta _Z}}}{\rm{\;}} = \frac{{{I_b}}}{{{I_o}}}{\rm{\;}} = {k_T}{\rm{\;}}{B_d},\end{equation} (3)where I n ${I_n}$ and I o n ${I_{on}}$ are hourly direct normal radiation and extra-terrestrial normal radiation, respectively. θ Z $\;{\theta _Z}$ is the solar zenith angle. Link turbidity factor is an indication of overall spectrally integrated radiation attenuation through the real atmosphere compared to the clean dry atmosphere, which includes presence of aerosols (air pollution) and gaseous water vapour for absorption of near infrared and infrared spectrum. Link turbidity factor is given by [28, 29]: T L = δ δ R = 1 δ R m l n G n γ G s c , \begin{equation}{T_L} = \frac{\delta }{{{\delta _R}}}{\rm{\;}} = \frac{1}{{{\delta _R}m}}{\rm{\;}}ln\frac{{{G_n}}}{{\gamma {G_{sc}}}},\end{equation} (4)where G n ${\rm{\;}}{G_n}$ is direct normal irradiance, G s c ${G_{sc}}$ is solar constant, γ $\;\gamma $ is correction coefficient of Earth-sun distance, m is relative air mass, δ $\;\delta $ is integral optical thickness of the real atmosphere and δ R ${\rm{\;}}{\delta _R}$ is integrated optical thickness of the clean dry atmosphere. Taking into account air pressure correction, the turbidity factor can be developed as: T G = 1 δ R m P P 0 l n G n γ G s c , \begin{equation}{T_G} = \frac{1}{{{\delta _R}m\frac{P}{{{P_0}}}}}{\rm{\;}}ln\frac{{{G_n}}}{{\gamma {G_{sc}}}},\end{equation} (5)where P is station pressure and P0 is standard atmospheric pressure. Integrated optical thickness of the clean dry atmosphere is a function of relative atmospheric mass and pressure, and it is given by [30]: δ R = 0.1005 − m P P 0 − 0.5 × 0.0074 0.0798 − m P P 0 − 3.3 × 0.0047 . \begin{equation} {\delta _R} = \left\{ \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {0.1005 - \left( {m\dfrac{P}{{{P_0}}} - 0.5} \right) \times \;0.0074}\\[15pt] {0.0798 - \left( {m\dfrac{P}{{{P_0}}} - 3.3} \right) \times \;0.0047} \end{array} .\right.\end{equation} (6) 2.2.2 Error and correlation index To compare the performance of in-plane solar radiation models, statistical indexes including mean bias error (MBE), mean absolute percentage error (MAPE), normalized root mean square error (NRMSE) and correlation coefficient (CORR) are introduced [31]: M B E = 1 N ∑ i = 1 N X f i − X o i , \begin{equation}MBE{\rm{\;}} = \frac{1}{N}{\rm{\;}}\mathop \sum \limits_{i{\rm{\;}} = {\rm{\;}}1}^N \left( {X_f^i - X_o^i} \right),\end{equation} (7) MAPE = 1 N ∑ i = 1 N X f i − X o i X ¯ o × 100 % , \begin{equation}{\rm{MAPE\;}} = \frac{{\frac{1}{N}\mathop \sum \nolimits_{i = 1}^N \left| {X_f^i - X_o^i} \right|}}{{{{\bar X}_o}}}{\rm{\;}} \times {\rm{\;}}100{\rm{\% }},\end{equation} (8) N R M S E = 1 N ∑ i = 1 N X f i − X o i 2 X ¯ o × 100 % , \begin{equation}NRMSE{\rm{\;}} = \frac{{\sqrt {\frac{1}{N}\mathop \sum \nolimits_{i = 1}^N {{\left( {X_f^i - X_o^i} \right)}^2}} }}{{{{\bar X}_o}}} \times 100{\rm{\% }},\end{equation} (9) C O R R = ∑ i = 1 N X f i − X ¯ f X o i − X ¯ o ∑ i = 1 N X f i − X ¯ f 2 ∑ i = 1 N X o i − X ¯ o 2 , \begin{equation}CORR{\rm{\;}} = \frac{{\mathop \sum \nolimits_{i = 1}^N \left( {X_f^i - {{\bar X}_f}} \right)\left( {X_o^i - {{\bar X}_o}} \right)}}{{\sqrt {\mathop \sum \nolimits_{i = 1}^N {{\left( {X_f^i - {{\bar X}_f}} \right)}^2}} \sqrt {\mathop \sum \nolimits_{i = 1}^N {{\left( {X_o^i - {{\bar X}_o}} \right)}^2}} }},\end{equation} (10)where X f i $X_f^i$ is the forecast value, X o i $X_o^i$ is the measured value, X ¯ f ${\bar X_f}$ is forecast mean value and X ¯ o $\;{\bar X_o}$ is measured mean value. 2.2.3 Dynamic index The coefficient variation ( V σ ${V_\sigma }$ ), mean anomaly percentage ( X d ${X_d}$ ) and stability index (S) are the standardised quantification indexes of the fluctuations of meteorological and other variables [32]. The smaller the values of coefficient variation and mean anomaly percentage are, the smaller the variable fluctuations are. Stability index is the opposite. They are given by: V σ = 1 X ¯ 1 N ∑ i = 1 n x i − X ¯ 2 × 100 % , \begin{equation}{V_\sigma } = \frac{1}{{\bar X}}{\rm{\;}}\sqrt {\frac{1}{N}\mathop \sum \limits_{i{\rm{\;}} = {\rm{\;}}1}^n {{\left( {{x_i} - \bar X} \right)}^2}} \times {\rm{\;}}100{\rm{\% }},\end{equation} (11) X d = 1 X ¯ 1 N ∑ i = 1 n x i − X ¯ × 100 % , \begin{equation}{X_d} = \left( {\frac{1}{{\bar X}}\frac{1}{N}\mathop \sum \limits_{i = 1}^n \left| {{x_i} - \bar X} \right|} \right){\rm{\;}} \times {\rm{\;}}100{\rm{\% }},\end{equation} (12) S = X m i n X m a x , \begin{equation}S = \frac{{{X_{min}}}}{{{X_{max}}}},\end{equation} (13)where N is the number of samples, x i $\;{x_i}$ is a single sample, X ¯ $\;\bar X$ is mean value and X m i n ${X_{min}}$ and X m a x ${X_{max}}$ represent the minimum and maximum value, respectively. 2.3 In-plane solar radiation models The global radiation on inclined surface is composed of three components, namely beam, diffuse and ground reflected radiation, and it can be expressed as: I T = I b R b + I d R d + I r , \begin{equation}{I_T} = {I_b}{\rm{\;}}{R_b} + {I_d}{R_d} + {I_r},\end{equation} (14)where I d ${I_d}$ is hourly diffuse horizontal radiation. I r $\;{I_r}$ is hourly ground reflected radiation. R b ${R_b}$ is beam radiation conversion factor and it is the ratio of beam radiation on inclined surface to that on horizontal surface. R d $\;{R_d}$ is diffuse radiation transformation factor and it is diffuse radiation on inclined surface divided by that on horizontal surface. It is worth noting that vertical surface is special inclined surface with surface tilt angle of 90°. For vertical surface toward south, east and west, surface azimuth angle are 0°, −90° and 90°, respectively. 2.3.1 Beam radiation on inclined surface There is no difference between in-plane solar radiation models in the calculation of beam radiation on inclined surface. Beam radiation conversion factor is based on solar geometry as follows: R b = cos θ T cos θ Z , \begin{equation}{R_b} = \frac{{\cos {\theta _T}}}{{\cos {\theta _Z}}}{\rm{\;}},\end{equation} (15)where θ T ${\theta _T}\;$ is solar incident angle. 2.3.2 Diffuse radiation on inclined surface Since the spatial distribution of diffuse radiation is generally unknown, many researchers have proposed a variety of models based on different assumptions to calculate diffuse radiation on inclined surface. Liu and Jordan firstly gave an isotropic model in 1961 by assuming that the diffuse radiation in the sky is isotropic [11]. R d ${R_d}$ is given by: R d = 1 + cos β 2 , \begin{equation}{R_d} = \frac{{1 + \cos \beta }}{2}{\rm{\;}},\end{equation} (16)where β $\;\beta $ is surface tilt angle. Then, many models were proposed. Temps and Coulson considered the influence of sky brightening near the sun, horizon brightening during clear day and surface reflection enhancement. They presented an anisotropic model providing a good prediction for sunny days [12]: R d = 1 + cos β 2 1 + sin 3 β 2 1 + cos 2 θ T sin 3 θ Z . \begin{equation}{R_d} = \frac{{1 + \cos \beta }}{2}{\rm{\;}}\left( {1 + {{\sin }^3}\frac{\beta }{2}} \right)\left[ {1 + {{\cos }^2}{\theta _T}{{\sin }^3}{\theta _Z}} \right].\end{equation} (17) Klucher introduced a modulating function for general model. Klucher model approximate Temps and Coulson model for clear sky and reduce to Liu and Jordan model under overcast condition [13]: R d = 1 + cos β 2 1 + F sin 3 β 2 1 + F cos 2 θ T sin 3 θ Z , \begin{eqnarray} {R_d} = \frac{{1 + \cos \beta }}{2}{\rm{\;}}\left( {1 + F{{\sin }^3}\frac{\beta }{2}} \right)\left[ {1 + F{{\cos }^2}{\theta _T}{{\sin }^3}{\theta _Z}} \right],\nonumber\\\end{eqnarray} (18)where F ${\rm{\;}}F$ is the correction factor, which is defined as: F = 1 − I d I 2 . \begin{equation}F = 1 - {\left( {\frac{{{I_d}}}{I}} \right)^2}.\end{equation} (19) Hay concluded that the diffuse radiation consisted of two parts, circumsolar and isotropic diffuse radiation, and proposed the “anisotropic index” to weigh the share of them. It is also reduced to Liu and Jordan model for overcast sky [14]: R d = I b I o R b + 1 + cos β 2 1 − I b I o . \begin{equation}{R_d} = \frac{{{I_b}}}{{{I_o}}}{\rm{\;}}{R_b} + \left( {\frac{{1 + \cos \beta }}{2}} \right)\left( {1 - \frac{{{I_b}}}{{{I_o}}}} \right).\end{equation} (20) By introducing Revfeim's integration of the geometry associated with isotropic diffuse irradiance on a sloping surface, Willmott obtained a new anisotropic model on basic of Hay model [15]: R d = G n G s c R b + C β 1 − G n G s c , \begin{equation}{R_d} = \frac{{{G_n}}}{{{G_{sc}}}}{\rm{\;}}{R_b} + {C_\beta }\left( {1 - \frac{{{G_n}}}{{{G_{sc}}}}} \right),\end{equation} (21)where C β = 1.0115 − 0.20293 β − 0.080823 β 2 0.5 ≤ C β ≤ 1 ${C_\beta } = 1.0115 - 0.20293\beta - 0.080823{\beta ^2}\;0.5 \le {C_\beta } \le 1$ . Skartveit added horizon brightening diffuse radiation for Hay model. Skartveit model becomes Hay model under clear sky and approximates Liu and Jordan model under cloudy conditions [16]: R d = I b I o R b + Z cos β + 1 − I b I o − Z 1 + cos β 2 , \begin{equation}{R_d} = \frac{{{I_b}}}{{{I_o}}}{\rm{\;}}{R_b} + Z\cos \beta + \left( {1 - \frac{{{I_b}}}{{{I_o}}} - Z} \right)\left( {\frac{{1 + \cos \beta }}{2}} \right),\end{equation} (22)where Z is defined as: Z = m a x 0 , 0.3 − 2 I b I 0 . \begin{equation}Z = max\left[ {0,\left( {0.3 - 2\frac{{{I_b}}}{{{I_0}}}} \right)} \right].\end{equation} (23) Reindl also suggested a horizontal brightening correction to Hay model [17]: R d = I b I 0 R b + 1 + cos β 2 1 − I b I 0 1 + I b I sin 3 β 2 . \begin{eqnarray}{R_d} = \frac{{{I_b}}}{{{I_0}}}{\rm{\;}}{R_b} + \left( {\frac{{1 + \cos \beta }}{2}} \right)\left( {1 - \frac{{{I_b}}}{{{I_0}}}} \right)\left[ {1 + \sqrt {\frac{{{I_b}}}{I}} {{\sin }^3}\frac{\beta }{2}} \right].\nonumber\\\end{eqnarray} (24) Muneer corrected the isotropic diffuse radiation of Hay model, and proposed a piecewise function model [18]: R d = I b I 0 R b + 1 − I b I 0 cos 2 β 2 + 2 b π 3 + 2 b × sin β − β cos β − π sin 2 β 2 , b = − 0.62 , for I > I d , θ T < π 2 cos 2 β 2 + 2 b π 3 + 2 b × sin β − β cos β − π sin 2 β 2 , b = 1.68 , for I = I d , θ T < π 2 cos 2 β 2 + 2 b π 3 + 2 b × sin β − β cos β − π sin 2 β 2 , b = 5.73 , for θ T ≥ π 2 , \begin{equation}{R_d} = \left\{ { \def\eqcellsep{&}\begin{array}{@{}*{1}{l}@{}} {\dfrac{{{I_b}}}{{{I_0}}}{R_b} + \left( {1 - \dfrac{{{I_b}}}{{{I_0}}}} \right)\left\{ {\cos^2\left( {\dfrac{\beta }{2}} \right) + \dfrac{{2b}}{{\pi \left( {3 + 2b} \right)}} \times \left[ {\sin\beta - \beta \cos\beta - \pi \sin^2\left( {\dfrac{\beta }{2}} \right)} \right]} \right\},\;b = - 0.62,\;{\rm for}\;I > {I_d},{\theta _T} < \dfrac{\pi }{2}}\\[15pt] {\cos^2\left( {\dfrac{\beta }{2}} \right) + \dfrac{{2b}}{{\pi \left( {3 + 2b} \right)}} \times \left[ {\sin\beta - \beta \cos\beta - \pi \sin^2\left( {\dfrac{\beta }{2}} \right)} \right],\;b = 1.68,\;{\rm{for}}\;I = {I_d},{\theta _T} < \dfrac{\pi }{2}}\\[15pt] {\cos^2\left( {\dfrac{\beta }{2}} \right) + \dfrac{{2b}}{{\pi \left( {3 + 2b} \right)}} \times \left[ {\sin\beta - \beta \cos\beta - \pi \sin^2\left( {\dfrac{\beta }{2}} \right)} \right],\;b = 5.73,{\rm{\;}}{\rm for}{\rm{\;}}{\theta _T} \ge \dfrac{\pi }{2}} \end{array} } \right\},\end{equation} (25) Koronakis thought that southern sky seems to be responsible for more diffuse radiation from the northern and the southern halves of the sky. Koronakis model is given by [19]: R d = 2 + cos β 3 . \begin{equation}{R_d} = \frac{{2 + \cos \beta }}{3}{\rm{\;}}.\end{equation} (26) Perez decomposed diffuse radiation into three parts: circumsolar, horizon brightening and isotropic diffuse radiation, and used two empirical coefficients to weigh the share of the three parts. The model is as follows [20]: R d = 1 − F 1 1 + cos β 2 + F 1 a b + F 2 sin β , \begin{equation}{R_d} = \left( {1 - {F_1}} \right){\rm{\;}}\left( {\frac{{1 + \cos \beta }}{2}} \right) + {F_1}\frac{a}{b} + {F_2}\sin \beta ,\end{equation} (27)where a = m a x ( 0 , cos θ T ) $a\; = \;max( {0,\cos {\theta _T}} )$ ; b = m a x ( cos 85 ∘ , cos θ Z ) $b\; = \;max( {\cos {{85}^\circ },\cos {\theta _Z}} )$ ; F1 and F2 are circumsolar brightening coefficient and horizon brightening coefficient, respectively. 2.3.3 Reflected radiation on inclined surface To simplify the calculation of ground reflected radiation, it is generally assumed that the reflected rays are diffuse and the ground reflected process is isotropic. The in-plane solar radiation models share the same formulation for the ground reflected components, which is described below: I r = I ρ 1 − cos β 2 , \begin{equation}{I_r} = {\rm{\;}}I\rho \left( {\frac{{1 - \cos \beta }}{2}} \right),\end{equation} (28)where ρ is ground reflectivity. 2.4 Methods As shown in Figure 2, the major steps of evaluation of solar radiation models on vertical surface for building PV applications go as follows: first, the nature of the solar resource and meteorological environmental factors are analysed to show the impact of meteorological environmental factors on solar radiation. Second, new method of weather type classification is proposed by diagnostic analysis. Then, ten in-plane solar radiation models are reviewed to choose optimal model in high turbidity area. And the impact of atmospheric turbidity on the model performance is revealed by theoretical analysis. The performance of the ten models for each weather type is tested to give general suggestion on model selection. FIGURE 2Open in figure viewerPowerPoint Flow chart to evaluate the performance of solar radiation models on vertical surface for building PV applications Finally, the variation of solar resource on vertical surface is analysed based on measured data of global radiation on vertical surface. T