Modeling the PV production is quite challenging due to the variability caused by low-level cumulus or stratocumulus clouds passing over the panels. Characterizing the ramps and variability in terms of plant size and aerial coverage is important to understand the impacts of variability on the power grid. Recently there has been increasing interest in high-frequency irradiance and power production as utilities move towards integrating more solar power into the grids. However, since little observational data are available, production and ramp estimates must be modeled for desired locations.
The cloud model follows the evolution of clouds (growth and decay) and their advection using a time step on the order of 1-second. It is forced by the NWP model through a one-way nesting. Since the NWP model provides a picture of the atmospheric conditions at ~1-km grid spacing, the cloud model ingests NWP model data such as the cloud cover fraction, cloud-base wind vector (speed and direction) and surface temperature. The cloud model then develops its own representation of the cloud field based on a stochastic-kinematic approach by creating thousands of clouds of different sizes and densities in the simulation domain. The initialization of the cloud field relies on a stochastic approach because each cloud size is chosen randomly following a lognormal distribution with the constraint that the cloud cover fraction within the cloud model must match the NWP modeled data. The kinematic part of the model consists of advecting the clouds across the simulation domain according to the NWP model wind vectors. Within the cloud model, clouds are allowed to grow or shrink as the cloud cover fraction estimated by the NWP model changes. Clouds are created at the lateral boundary of the simulation domain or in areas of voids and decayed/destroyed in areas of surplus following the same stochastic approach used in the initialization step. Several additional cloud characteristics and atmospheric processes such as cloud reflection/refraction/diffraction, cloud thickness, and opacity were implemented in the cloud model based on detailed analyses of the global, direct and diffuse irradiance patterns in 1-second irradiance measurements. The model then employs a power conversion algorithm to convert the irradiance components to PV output.
The stochastic-kinematic cloud model coupled to the NWP model was applied to synthesize solar irradiance and power production data at more than 20 locations on Oahu, Hawaii where high-frequency irradiance measurements were available. The measurement network included 17 pyranometers within a 1-km area and 7 other pyranometers across the island (measuring 1-second global horizontal irradiance), a rotating shadowband radiometer (measuring 3-second solar irradiance components), and 6 schools across Oahu recording 15-minute irradiance and PV at 2-kW rooftop systems. The model was extensively tuned and validated against the various measurements and found to display average diurnal cycles of global horizontal, direct horizontal, direct normal, and diffuse horizontal irradiance similar to observed data.
An important component of the model is its ability to accurately predict the variability expected across the spatial extent of a PV plant. By modeling PV at up to several hundred points in a utility-scale plant or several thousand points across a group of distributed PV systems, the impact of aggregating values over a geographic area can be examined. By comparing the ramp frequency distribution of GHI aggregated across several points on Oahu, it was found that the model is slightly more variable than measurements, providing a conservative estimate of ramping potential on the PV grid. Results were deemed suitable for use to simulate 2 years of PV output at hypothetical solar plants in Hawaii. The simulated output would subsequently be used to study various development scenarios on the Oahu electrical grid.