DEVELOPMENT OF A STOCHASTIC-KINEMATIC CLOUD MODEL TO GENERATE HIGH-FREQUENCY SOLAR IRRADIANCE AND POWER DATA

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1 DEVELOPMENT OF A STOCHASTIC-KINEMATIC CLOUD MODEL TO GENERATE HIGH-FREQUENCY SOLAR IRRADIANCE AND POWER DATA Philippe Beaucage, Michael C. Brower, Jaclyn D. Frank, Jeffrey D. Freedman AWS Truepower LLC 463 New Karner Rd. Albany, NY pbeaucage@awstruepower.com ABSTRACT In the absence of sufficient direct observations of surface irradiance, a novel approach to generate high-frequency synthetic irradiance and power data for proposed solar photovoltaic (PV) systems is presented. This method utilizes low-frequency outputs from a mesoscale Numerical Weather Prediction (NWP) model coupled to a newly developed stochastic-kinematic cloud model to account for the rapid ramps caused by passing clouds. The cloud model simulates the movement and evolution of clouds (advection, growth, and decay). It is forced by the NWP model through a one-way nesting scheme. The coupled model is being applied to create two years of two-second solar irradiance and power production data for more than 100 proposed utility-scale (centralized) and rooftop (distributed) PV sites in Hawaii. The output is being validated with observations from over 25 stations. Results so far show good agreement with observed irradiance ramp rates for a wide range of temporal and spatial scales. 1. INTRODUCTION A characteristic of solar photovoltaic (PV) power output is its tendency to fluctuate very rapidly due to the passage of cloud shadows (see Fig. 1). Fast-moving low-level clouds cause the most rapid ramps. Understanding the ramping behavior of large amounts of fluctuating PV capacity - while taking into account their geographic distribution - is a priority for grid operators anticipating future growth in PV generation [1-5]. Their time scale of interest ranges from seconds (the domain of frequency regulation) to hours (load following). An extreme down (up) ramp occurs at a PV system when the sun is completely blocked (unblocked) by a cloud. The rate at which this occurs depends on the speed and height of the cloud, the angular width of the sun, and the size of the PV array. In a simple model, the time Δt it takes for a cloud edge to pass across a PV system plane of array equals the array width (d) plus the effective width of the sun at the cloud height (h) divided by the cloud speed (v): / (1) For example, assuming a cloud base height of 1500 m and a cloud base wind speed of 10 m/s, the minimum ramp duration for a small residential PV system with d ~ 1-2 m would be Δt ~ 1.4 s. For a 25 megawatt (MW) PV power plant, d ~ 1000 m and Δt ~100 s. Finally for all rooftop PV systems in a city 10 km across, Δt ~ 15 minutes. Given the scarcity of high-frequency observational data, production estimates and ramps need to be modeled for desired locations. In this study, we developed a method combining a mesoscale numerical weather prediction (NWP) model and a stochastic-kinematic ("microscale") cloud model. Low-level cumulus clouds are not well resolved by most NWP models as these features are typically of the same scale or finer than the models grid spacing. In particular, the cloud edges responsible for the most rapid ramps are not sharply defined in NWP models. The stochastic-kinematic cloud model is able to resolve those edges. The coupled system is being applied to simulate the behavior of several hundred megawatts (MW) of PV capacity on the Oahu and Maui (Hawaii) grids. The Hawaii Solar Integration Study is a cooperative project funded by 1

2 the US Department of Energy, Hawaii Natural Energy Institute, Hawaii Electric Company (HECO), and the Hawaii Department of Business, Economic Development and Tourism, and being carried out by AWS Truepower and GE Energy Consulting. The data are a critical input for understanding the potential impact of solar plants on system reserves, extreme ramps, frequency stability, and other issues. in 2009 [7]. Finally, HECO s Sun Power for Schools program provides publicly available irradiance and power production data for 9 2-kW rooftop systems on Oahu for the study period ( ) [8]. This paper presents an overview of PV variability as a function of time and space, describes the new approach to simulating this behavior, and provides preliminary results from the Hawaii study (Oahu and Maui). Fig. 2: Location of the 18 solar radiation instruments near the Kalaeloa airport, Oahu (HI). This figure was taken from [6]. 3. CLOUD MODELING Fig. 1: A typical pattern of direct and diffuse horizontal irradiance (cyan and red lines, respectively) measured by a rotating shadowband radiometer over a single day (19 May 2010) at a station near Kalaeloa airport, Oahu. Since PV systems respond almost instantly to changes in irradiance, similar patterns are seen in PV output. 2. MEASUREMENTS The island of Oahu is particularly well equipped with irradiance monitoring stations. A network of 18 solar radiation sensors, including 17 pyranometers and one rotating shadowband radiometer, were installed within a 1- km area near the Kalaeloa airport (see Fig.2) to capture the transient cloud shadows experienced by large central PV plants. The National Renewable Energy Laboratory (NREL) has been collecting solar irradiance data from this network since March In addition to the NREL network, which is located in the southwest region of Oahu, HECO and NREL installed several pyranometers throughout the island Clouds and aerosols play a major role in the Earth s annual energy balance. On average, approximately 51% of the incoming solar radiation reaches the earth's surface while the rest is either reflected or absorbed by the atmosphere and clouds [9]. While aerosols scatter and absorb solar radiation, much of the variability in solar irradiance at the ground is due to the passage of clouds. Satellites such as the Geostationary Operational Environmental Satellites (GOES), Multifunctional Transport Satellites (MTSAT), and Meteosat can track clouds in real time at spatial resolutions of 1-10 km and temporal resolutions of 30 minutes, respectively. However, NWP models can be used to achieve finer temporal and spatial resolutions and to fill data gaps. These physics-based models simulate the cloud formation processes and lifecycle dynamics in varying atmospheric conditions. NWP models are equipped with a full suite of physics parameterization schemes including radiation, cloud microphysics, planetary boundary layer (PBL) turbulence, and a land surface-atmosphere interaction scheme, to simulate all atmospheric processes up to the model's grid resolution. Although the NWP cloud field captures the general spatial and temporal distribution of the cloud fraction, the clouds are fuzzy, as they cannot be fully 2

3 resolved by the model due to the grid spacing, typically no finer than 1 km. Therefore NWP models do not capture the sharp cloud edges responsible for rapid irradiance ramps. The system we developed is a combination of a mesoscale NWP model and a stochastic-kinematic cloud model. In the first step of our approach, the Mesoscale Atmospheric Simulation System (MASS) [10] establishes a baseline simulation of cloud cover fraction and irradiance as well as cloud-base and near-surface wind speed and temperature fields over the region of interest at a particular spatial and time resolution, such as 1 km and 10 minutes (see Fig. 3). lateral boundary of the simulation domain and also in areas of flow divergence (which would otherwise leave cloud voids); they are destroyed in areas of flow convergence (cloud excess). Fig. 3: Global horizontal irradiance (GHI) in W/m 2 over Hawaii modeled by MASS for a particular moment in time. Low values of GHI indicate high cloud cover. The second step consists of coupling a stochastic-kinematic cloud model with the NWP model in a one-way nesting to follow the evolution of clouds on the order of 1-second time resolution. The stochastic-kinematic cloud model is initialized from the NWP cloud cover fraction, cloud-base wind speed and direction, and temperature. The cloud model develops its own representation of the cloud field by creating multiple clouds of different sizes and densities in the simulation domain. Figure 4 shows an example of the cloud field created by the cloud model over Oahu. The initialization of the cloud field relies on a stochastic approach. Each cloud's size is chosen randomly using a lognormal distribution with the constraint that the spatiallyaveraged cloud cover fraction must match the NWP modeled data. The kinematic aspect of the cloud model consists in advecting the clouds across the simulation domain and growing and shrinking them following the variations in space and time of the cloud cover fraction estimated by the NWP model. Clouds are created at the Fig. 4: A sample distribution of clouds in the stochastickinematic cloud model for a particular moment in time. The background colors represent the NWP cloudiness fraction. The clouds move through the domain with the speed and direction predicted by the NWP model. Several additional cloud characteristics and atmospheric processes were parameterized, such as the cloud thickness (and hence transmittance), reflection (including refraction and diffraction), and maximum growth and decay rates, as well as the sun width, empirical clear-sky diurnal cycle of direct horizontal irradiance, and small random fluctuations in direct and diffuse irradiance representing the effects of non-homogeneous cloud shape and opacity as well as highlevel clouds. These parameters were adjusted to achieve realistic irradiance diurnal cycles and ramp statistics, as determined by analyses of the observed global, direct, and diffuse irradiance patterns, as well as some findings in the literature [11-12]. For instance, a slight overshoot in GHI caused by reflections is often observed when clouds approach or leave an area. An empirical model was developed to parameterize the reflection on the side of clouds as well as the refraction near the edge of a cloud and the diffraction between closely spaced clouds. Increases in diffuse irradiance due to cloud reflections (including refraction and diffraction) can lead to GHI measurements in partly cloudy conditions exceeding the clear sky value. 3

4 4. METHODOLOGY The coupled mesoscale NWP model and stochastickinematic cloud model described in the previous section is being used to simulate the ramping behavior of several hundred MW of centralized and distributed PV systems that might be deployed in the future on the islands of Oahu and Maui. Lastly, the modeled irradiance and power outputs were quality controlled and compared to available observations. The first set of checks consisted of visual inspection of the average annual, monthly and diurnal profiles of irradiance and power at individual sites and island aggregates. Statistical checks were also performed by calculating the minimum, maximum and mean irradiance and power at each individual site. The first step in the Hawaii solar integration study consisted of selecting sites for possible centralized and distributed PV systems. AWS Truepower identified sites for several hundred MW of centralized and distributed PV on both islands. The second step involved fine tuning the coupled NWP and stochastic-kinematic cloud model to remove most diurnal, monthly and annual biases on an island-wide basis. It is important to anchor the NWP modeled data in high-quality observations from the project area to achieve the standards of accuracy required for solar integration studies. The adjustments to the NWP model outputs were done using all available observations described in section 2. (It is likely that the model will require similar tuning in other regions where it is applied because of differing model biases and cloud characteristics.) For the third step, the coupled NWP and stochastickinematic cloud model was run to generate two years ( ) of irradiance data at a 2-sec time step over the islands of Oahu and Maui. The modeled solar irradiance was then extracted for each of up to several thousand grid points spanning each PV site. This approach allows the model to simulate the effects of cloud passages for individual PV systems of arbitrary size, shape, and module density, as well as scattered rooftop PV systems in urban areas. Next, the irradiance at each grid point was converted to power and aggregated across each PV site using a program which calculates the direct and diffuse components on the plane of array as well as the various solar angles and geometry between the sun and solar panels [13]. Both single-axis tracking and fixed-tilt systems were modeled. In addition, the program takes into account losses such as temperature, soiling, shading, module mismatch and quality, inverter efficiency, availability, wiring, transformer, and non-standard operations. A DC to AC ratio of 1.15 was assumed. Fig. 6: Worst 2-s, 1-min and 1-hour down ramps occurring at a single site on Oahu over as modeled by the coupled NWP and stochastic-kinematic cloud model. In the next set of checks, the ramp frequency distributions at 6 s, 1 min and 10 min at individual sites and island aggregates were screened for outlying values. The last check involved calculating the 95th, 99th and 99.9th percentiles of up and down ramps as well as the worst up and down ramps for These ramps statistics were calculated at several time intervals from 2 s to 1 hour. Figure 6 shows the worst 2-s, 1-min. and 1-hour down ramps occurring in the 2- year period at a single site on Oahu. The worst ramps increase in size as the time interval increases. In the case shown in Fig. 6, the worst 2-s, 1-min. and 1-hour down ramps were 9.1%, 79.4% and 91.2% of the total capacity, 4

5 respectively. This hypothetical centralized PV plant had a total capacity of 4 MW. 5. RESULTS The mean diurnal profiles, distributions and ramp statistics were validated against all available measurements described in section 2. Those plots and statistics were generated for individual sites and site aggregates. The mean diurnal profiles of global, direct and diffuse irradiance fit well with the observed profiles. Figure 7 shows an example at one site near Kalaeloa airport on Oahu. Although the modeled data reproduces the mean diurnal profiles of irradiance, a deviation in the mid-day cloud cover fraction derived from the NWP model remains at some sites. It was also found that the model has a small positive bias in the warmer months and a negative bias in the cooler months. The mean bias on GHI is -2% compared to all available high-quality observations for The modeled solar irradiance data was then converted to power using the program described in section 4, and compared to the Oahu schools data. The data recovery and quality of the measured irradiance and power at the nine schools were uneven, with an average data recovery of 85%. The mean GHI and capacity factor modeled were 10% low in irradiance and 7% high in power compared to the schools data. It is hypothesized that module maintenance and degradation may be responsible for the relatively low PV output measured at the schools. The frequency distribution of GHI at one site near the Kalaeloa airport indicates that the coupled NWP and stochastic-kinematic cloud model captured relatively well the distribution of partly cloudy conditions, which peak around 300 W/m 2. Fig. 7: Diurnal mean global horizontal (top), direct normal (middle), and diffuse horizontal (bottom) irradiance from the cloud model (red dots) compared to measurements (black dots) for May 2010 at Kalaeloa airport, Oahu. The cyan dots are the maximum modeled values and the blue the maximum observed, while the green correspond to 80% of the solar irradiance at the top of the atmosphere. The X-axis corresponds to the time of day (in decimal units) and the Y- axis to the irradiance (W/m 2 ). 5

6 Fig. 8: Histogram of observed (top) and modeled (bottom) 2-second GHI for May 2010 between 5 am and 8 pm at Kalaeloa airport, Oahu. Apart from the annual, monthly, and daily averages, rapid fluctuations are particularly important to grid operators. The 6-s, 1-min and 10-min ramp distributions for an aggregate site (combination of surface stations) are shown in Figure 9. Overall, the modeled ramp distributions agree well with the observed. The slightly more variable modeled data are conservative from the perspective of assessing impacts on grid reliability. We found similar agreement with the observed ramp distributions at point measurements. As expected, larger ramps are more frequent over longer time intervals. As an example of the behavior of PV output, Figure 10 shows the ramp distributions for a hypothetical 12 MW plant. The fluctuations are larger over longer time intervals in a similar way to the irradiance fluctuations. The 30-s ramps in Fig. 10 agree qualitatively with the 20-s ramps obtained by Marcos et al. [3] for a 9-MW solar plant located in Spain. Fig. 9: 2-s, 1-min. and 10-min. modeled (red) and observed (black) global horizontal irradiance ramp distributions for October 2010 for an aggregation of five stations across Oahu. The X-axis corresponds to the ramps (W/m 2 ) and the Y-axis to the frequency (%, log scale). 6

7 irradiance was converted to power and compared to 2-kW rooftop PV systems on Oahu schools, a mean bias of 7% in power production was found. However, PV system performance issues may be partly responsible. Most importantly, the modeled ramp distributions agreed well with the observed distributions, both for individual sites and site aggregates, on time intervals ranging from 2 seconds to 1 hour. The modeled PSD also had a shape and features similar to the observed PSD, with the exception of the flattening of the modeled spectrum in the 5-min to 1-hour range. Both the ramp distributions and PSD agreed in a qualitative sense with findings from previous studies in different areas [3,1]. Fig. 10: 2-s to 1-hour ramp distributions of modeled power as a fraction of the total capacity at a hypothetical 12-MW centralized PV plant for Lastly, the power spectral density (PSD) was calculated from the 2-sec global horizontal irradiance in May 2010 at Kalaeloa airport and compared with observations. Figure 11 demonstrates that the modeled and observed PSD have similar shape and features such as the peaks at 24 and 12 hour, and follow a -1/3 exponent trend at low frequencies, confirming findings of Curtright and Apt [1] based on 10- sec net power data from a 4.59-MW PV plant in Arizona. However, the modeled PSD differs from the observed in some ways, such as a flattening of the spectrum in the 5-min to 1-hour range and an increase in periodicity at 4-s. 6. CONCLUSIONS A novel approach for generating high-frequency irradiance and power production data for proposed photovoltaic plants used in grid integration studies was developed. It combines a mesoscale NWP model and a newly developed stochastickinematic cloud model. The coupled model was used to create two years of two-second solar irradiance and power production data for the islands of Oahu and Maui, and the results were validated with high-frequency observations from over 25 locations. We've shown that the coupled model is able to simulate the mean behavior of the solar radiation resource as well its high-frequency fluctuations or ramps with acceptable accuracy. The mean diurnal profiles fit relatively well with available high-quality observations and the mean bias on GHI is -2%. When the modeled Fig. 11: Power spectrum distribution of modeled (red) and observed (blue) global horizontal irradiance from 2-s data in May 2010 at a site near the Kalaeloa airport on Oahu. Validation of the synthetic irradiance and plant output data is continuing, but the results so far indicate that the method provides a data set of acceptable fidelity for grid integration studies. Aside from capturing the ramping behavior of individual systems, a major advantage of the coupled model is that it preserves the spatial and time correlation in solar irradiance and power between sites. This allows the realistic simulation of the behavior of PV output over a very wide range of spatial and temporal scales. 7

8 ACKNOWLEDGMENTS We would like to thank HECO and NREL for their support of this work and for providing access to the data used in the validation, and GE Energy Consulting for useful ideas concerning the validation of large ramps. Many thanks to Dr. R. Perez at SUNY Albany for kindly providing some Fortran subroutines used in the solar angle calculations. REFERENCES (1) Curtright, A., and Apt, J.. The character of power output from utility-scale photovoltaic systems. Progress in Photovoltaics: Research and Applications, vol. 16, pp (2) Hoff, T. E., and R. Perez. Quantifying PV output variability. Solar Energy, vol. 84, pp (3) Marcos, J., L. Marroyo, E. Lorenzo, D. Alvira, and E. Izco. Power output fluctuations in large scale PV plants: one year observations with one second resolution and derived analytic model. Progress in Photovoltaics: Research and Applications, vol. 16, pp da9010VgnVCM bacRCRD&vgnextfmt=d efau&vgnextrefresh=1&level=0&ct=article. (9) Ahrens, C.D. Meteorology Today - an introduction to weather, climate and the environment. Thomson Learning. 544 pp (10) Manobianco, J., J. W. Zack and G.E. Taylor. Workstation-based real-time mesoscale modeling designed for weather support to operations at the Kennedy Space Center and Cape Canaveral Air Station. Bull. Amer. Meteor. Soc., vol. 77, pp (11) Rodts, S. M. A., P. G. Duynkerke, and H. J. J. Jonker. Size distributions and dynamical properties of shallow cumulus clouds from aircraft observations and satellite data, J. of Atmos. Science, vol. 60, pp (12) Ghate, V. P., M. A. Miller, L. DiPretore. Vertical velocity structure of marine boundary layer trade wind cumulus clouds, J. Geophys. Res., vol. 116, D16206, doi: /2010jd (13) Luque, A. and S. Hegedus. Handbook of photovoltaic science and engineering. John Wiley and sons, 2 nd edition, 1132 p (4) Freedman, J., J. Frank, and J. Manobianco. Generating high-frequency irradiance data on Oahu. Technical report from AWS Truepower, Albany, NY.12 pp (5) Mills, A., and R. Wiser. Implications of Wide-Area Geographic Diversity for Short-Term Variability of Solar Power. Technical report from Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley (CA). 45 pp (6) Wilcox, S., R. George, D. Lew, A. Andreas, P. Gotseff, and K. Kelly. Hawaii/Oahu Solar Variability Grid Project Instrument Installation and Validation. Report from the National Renewable Energy Laboratory.11 pp (7) National Renewable Energy Laboratory. Measurement and Instrumentation Data Center (MIDC). [Online]. Available at (8) The Hawaiian Electric Company. Sun Power for Schools. [Online]. Available at baa14340b4c0610c510b1ca/?vgnextoid=64e95e658e0fc010 VgnVCM fea9RCRD&vgnextchannel=529bf2b 8