Generation of spatially dispersed irradiance time-series based on real cloud patterns

Clouds, being complex components of the atmosphere, have significant effects on power generation by photovoltaic (PV) systems. For example, shadows caused by the cloud coverage over a geographically distributed PV power plant may cause significant fluctuations in power generation by leaving a number of PV panels unable to generate power and contribute to power generation by the plant at each time instant. Thus, investigation of the mentioned effects on PV power generation requires realistic spatial irradiance information. Such information should be evaluated based on the existing real cloud coverage and its light transmission characteristics. This also provides the opportunity to select appropriate coping strategies against the mentioned negative effects of partial shading on PV plant's power output. This paper presents a modeling approach which generates Spatially Dispersed Irradiance Profiles (SDIPs) for PV arrays based on existing cloud patterns derived from local sky images taken at the application sites. The model gets the direct, diffuse and global irradiance values incident on a horizontal surface, which are primarily obtained utilizing a solar irradiance model (the Morf (2013) model), along with local sky images captured at the application sites and cloud transmittance values, as input data and yields site-specific Spatially Dispersed Irradiance Profiles (SDIPs) incident on the surface of inclined PV panels within PV application areas, as a result of process of the inputs. Utilization of local sky images and cloud transmittance values for different cloud types creates the opportunity for precise analysis of interactions of sunlight with the existing cloud type and hence, obtaining unique and site-specific irradiance profiles according to the existing cloud type and distribution in the sky. The model firstly detects the cloudy and clear-sky parts in the sky image and then instantly utilizes the most appropriate ellipse on the cloud layer associated with each solar panel through which the beam irradiance is received by the panel. The model also considers the light transmission characteristics of different cloud types as the parameter affecting the beam irradiance. The diffuse and ground-reflected irradiance components are assumed to be spatially constant and thus identical for all solar panels. Cloud base heights, as provided in the International Cloud Atlas (1987), are also utilized to calculate the ground area covered by each sky image. Daily irradiance sequences for different observation points in a PV array are simulated under partly cloudy sky conditions using a set of sky images and utilized for validation purpose of the proposed algorithm. It is demonstrated that instantaneous irradiance values, as well as daily irradiance sequences, differ from point to point in a geographically distributed PV application site depending on the distribution of clouds in the sky. The mentioned variable characteristic of the irradiance sequences received at different observation points, as well as the model's capability to reflect the mentioned variabilities, is verified using irradiance data derived from satellite observations. The performance of the proposed model is validated using variability index (VI) metric as a measure of irradiance variability during a day. The modeled VI values are validated against the measured VI values for a reference point located at the center point of the generated irradiance profiles. Daily VI values calculated for both measured and simulated 1-min global horizontal irradiance (GHI) data are compared for a population of totally 117 days during April - August time period. The results of comparison show statistics of mean bias error (MBE) of 0.16, root mean square error (RMSE) of 2.394, correlation coefficient of 0.94 and mean absolute error (MAE) of 1.91. The validation results demonstrate capability and accuracy of the proposed model for estimation of irradiance values under cloudy sky conditions.