A comprehensive study on modeling of photovoltaic arrays and calculation of photovoltaic potential using digital elevation model

ABSTRACT

In solar energy applications, a complete knowledge and detailed analysis of the solar radiation potential is a prerequisite. In this paper, two different photovoltaic (PV) potential analysis approaches are compared. The first approach is based on a simulation of PV array and six different solar radiation estimation models. The outputs of these models are compared with hourly ground measured data by using statistical error methods. The most suitable solar radiation model which gives more accurate results is used to calculate the PV potential of Engineering Faculty of Eskişehir Technical University. The PV panel simulation is implemented in Matlab/Simulink besides that a suitable algorithm is selected to calculate the possible amount of PV panel energy generation based on the hourly measured wind speed (WS), air pressure, global solar radiation (GSR), and temperature values. In the second approach, building roof surface PV potential of the selected area is calculated and the available roof area for PV installation is determined by using Aeronautical Geographical Information System (ArcGIS) software. When the performances of the methods are compared, these methods obtained satisfactory results. Furthermore, it is clear that the algorithms and effective factors of the two methods are different. The results of ArcGIS outperform the PV array simulation based on Badescu model by the reason of its suitability of selecting optimal site for PV installation.

KEYWORDS:

• Solar radiation
• pv potential
• pv array
• estimation
• ArcGIS

Nomenclature

$\beta$ Slope angle $(degree)$

${\beta }_{Vmp}$ Maximum voltage coefficient $(V{/}^{o}C)$

${\beta }_{Voc}$ Open circuit voltage coefficient $(V{/}^{o}C)$

$\delta (T_c)$ Thermal voltage of PV $(unitless)$

${\mathrm{\Delta }}_t$ Temperature difference from data sheet ${(}^{o}C)$

${\mathrm{\Delta }}_T$ Difference between of PV temperatures ${(}^{o}C)$

${\omega }_1$ Sunrise hour angle $(degree)$

${\omega }_2$ Sunset hour angle $(degree)$

${\omega }_s$ Hour angle $(degree)$

$\varphi$ Latitude of the zone $(degree)$

${\rho }_g$ Ground reflectance coefficient $(unitless)$

$\sigma$ Declination angle $(degree)$

$\theta$ Angle of incidence $(degree)$

${\theta }_z$ Zenith angle $(degree)$

$a,b$ Coefficients from PV array data sheet $(unitless)$

$A_i$ Anisotropy index $(degree)$

$a_{0-4}$ Coefficients of air mass factor $(unitless)$

$a_{Imp}$ Maximum current coefficient $(A{/}^{o}C)$

$a_{Isc}$ Short circuit current coefficient $(A{/}^{o}C)$

$AOI$ Angle between the sun and module $(degree)$

$b_{0-5}$ Incident angle coefficients $(unitless)$

$c_0,c_1$ Coefficients regarding $I_{mp}$ $(unitless)$

$c_2,c_3$ Coefficients regarding $V_{mp}$ $(unitless)$

$ET$ Equation of time $(min)$

$f$ Modulating function $(unitless)$

$f_{c-s}$ View factor for diffused radiation $(unitless)$

$G_{sc}$ Planck constant

$H_b$ Direct solar radiation on horizontal surface $(kWh/m^2-hour)$

$H_n$ Nominal solar radiation, generally 1000 $(W/m^2)$

$H_T$ Total GSR on sloped surface $(kWh/m^2-hour)$

$H_t$ Measured solar radiation on PV $(W/m^2)$

$H_{T,b}$ Direct solar radiation on sloped surface $(kWh/m^2-hour)$

$H_{T,d}$ Diffused solar radiation on sloped surface $(kWh/m^2-hour)$

$H_{T,r}$ Reflected solar radiation on sloped surface $(kWh/m^2-hour)$

$I$ Output current of the PV array $(A)$

$I_{mp}$ Current at the maximum-power point $(A)$

$I_o$ Saturation current of the PV array $(A)$

$I_{pv,n}$ Light-generated current at ${25}^{o}C$ $(A)$

$I_{pv}$ PV current of the PV array $(A)$

$I_{sc,n}$ Nominal short-circuit current $(A)$

$I_{sc}$ Short-circuit current $(A)$

$k$ Boltzmann’s constant $(J/K)$

$k_d$ Hourly diffuse fraction $(unitless)$

$K_T$ Hourly clearness index $(unitless)$

$L_L$ Local longitude $(degree)$

$L_s$ Standard time meridian $(degree)$

$LT$ Local standard time $(hour)$

$M$ Air mass depend on ${\theta }_z$ and air pressure $(unitless)$

$m_{\beta Voc}$ Coefficient providing the irradiance dependence for the $V_{oc}$ temperature coefficient, $(V{/}^{o}C)$

$m_{\beta Vmp}$ Coefficient providing the irradiance dependence for the $V_{mp}$ temperature coefficient $(V{/}^{o}C)$

$M_{st}$ Standard air mass $(unitless)$

$N$ Day of the year $(unitless)$

$n$ Ideality factor of the diode $(unitless)$

$N_p$ Number of cells in parallel in PV $(unitless)$

$N_s$ Number of cells in series in PV $(unitless)$

$N_{pp}$ Total number modules in the parallel $(unitless)$

$N_{ss}$ Total number modules in the series $(unitless)$

$P$ Measured air pressure $(mmHg)$

$P_o$ Nominal pressure 760 $(mmHg)$

$P_{max,e}$ Maximum measured peak output power $(W)$

$P_{max,m}$ Calculated maximum power $(W)$

$P_{mp}$ Power at maximum-power point ($W$)

$q$ Electron charge $(coulomb)$

$R_p$ Parallel resistance in PV $(\mathrm{\Omega })$

$R_s$ Series resistance in PV $(\mathrm{\Omega })$

$ST$ Solar time $(hour)$

$T$ Measured temperature for ideal PV simulation ${(}^{o}C)$

$T_a$ Measured ambient air temperature ${(}^{o}C)$

$T_c$ Cell temperature inside module ${(}^{o}C)$

$T_m$ Back-surface module temperature ${(}^{o}C)$

$T_n$ Nominal cell temperature ${(}^{o}C)$

$V$ Output voltage of the PV array $(V)$

$V_t$ Thermal voltage $(V)$

$V_{mp}$ Voltage at maximum-power point ($V$)

$V_{oc,n}$ Nominal open circuit voltage data sheet $(V)$

$V_{oc}$ Open-circuit voltage ($V$)

$WS$ Wind speed measured at 10-m height $(m/s)$

$H_d$ Diffused solar radiation $(kWh/m^2-hour)$

$H_0$ Extraterrestrial solar irradiation $(kWh/m^2)$

$H_m$ Measured solar radiation on horizontal surface $(kWh/m^2-hour)$

$r_b$ Direct radiation conversion coefficient $(unitless)$

$A$ Total PV panel area ($m^2$)

$E$ Solar energy potential ($kWh$)

$H$ Annual solar radiation ($kWh/m^2$)

$n$ Number of hours $(unitless)$

$PR$ Performance ratio coefficient $(unitless)$

$r$ PV panel yield $(unitless)$

$Yi,c$ Calculated solar radiation $(kWh/m^2-hour)$

$Yi,m$ Measured solar radiation $(kWh/m^2-hour)$

Acknowledgments

This study is supported in part by the Scientic Research Projects Commission of Eskişehir Technical University under the general purpose grant 19ADP005.

Thanks to Earth and Space Sciences Institute of Eskişehir Technical University that provided us Digital Elevation Data and Aerial Image of the Campus.

Additional information

Notes on contributors

Kübra Bitirgen

Kübra Bitirgen graduated from Anadolu University in Turkey as an Electrical and Electronics Engineer in 2016. She got MSc from Anadolu University in 2018. She is currently a PhD student in Electrical and Electronics Engineering in Eskişehir Technical University. Her special fields of interest include power systems, electrical machines, energy systems, intelligent systems, and renewable energy.

Ümmühan Başaran Filik

Ümmühan Başaran Filik graduated from Anadolu University in Turkey as an Electrical and Electronics Engineer in 2002. She got MSc and PhD degree from Anadolu University in 2004 and 2010, respectively. She is currently an associate professor on Power System Analysis in Eskişehir Technical University. Her special fields of interest include power system analysis–optimization, renewable energy systems, and smart grids.