Chapter 4
Prediction of photovoltaic power generation output and network operation
Takeyoshi Kato Institute of Materials and Systems for Sustainability (IMaSS), Nagoya University, Nagoya, Japan
Abstract
The high penetration photovoltaic power systems need to increase the power supply and demand balancing capability in electric power system. For the best use of balancing capability, highly accurate and reliable forecasting methods play a very important role in various time horizons from several hours-ahead to several days-ahead. An accurate and reliable forecasting method should be employed not only in power system but also in individual energy management system. According to the needs of forecasting in power system operations or individual system operations, various forecasting methods and resources such as numerical weather prediction (NWP) models, satellite images, all-sky images, and measured PV power output data, are available. The field of irradiance forecasting is rapidly evolving. This chapter describes a fluctuation characteristics of irradiance, a review of various forecasting methods for various time horizons ranging from a few minutes ahead to a day ahead, and application of forecasting method in power system and individual energy management system.
Keywords
electric power system
energy management system
forecast
irradiance
numerical weather prediction
4.1. Needs for forecasting photovoltaic (PV) power output in electric power systems
The installation of photovoltaic power generation system (PV system) is increasing rapidly in many countries, because the electricity production cost of PV system is becoming competitive to the other power generation resources. As shown in Fig. 4.1, the world cumulative installed capacity of PV system was 140 GW in 2014 [1]. In some European countries such as Germany and Italy, the annual power supply by PV system has already reached 7% of overall electricity supply. In the last few years, the newly installation was large in Asian countries such as China and Japan. The installed capacity in these two countries accounted for 60% of the world installation of 40 GW in 2014.
The high penetration of PV systems would negatively affect the stability of electric power system due to the intermittent and uncertain nature of PV power outputs. Then, power system operators are facing increased levels of variability and uncertainty of residual electricity load, which is the electricity demand minus the aggregated PV power outputs. When the power supply is larger than the electricity demand, the power system frequency rises. Therefore, the power supply and demand balancing capability must be increased in order to avoid the unstable operation of electric power system due to the high penetration PV system. The balancing capability on supply side includes conventional thermal power plants and natural gas combined cycle power plants. However, the start-up times of these power plants takes a few hours depending on fuel types. Therefore, the needs of balancing capability of quicker response such as pumped hydro power plants and storage batteries will be increased as the installation of PV systems increases.
For the best use of balancing capability, highly accurate and reliable forecasting methods play a very important role in various time horizons from several hours ahead to several days ahead. A day-ahead forecast is the most important and influential for the power-demand balancing. On the basis of day-ahead forecast of electricity demand, power system operators usually determine unit commitment scheduling of required generation resources to meet the electricity demand for each hour of the next day. The scheduling is determined at around the noon of the day before the operating day. Depending on the timing of the unit commitment scheduling or electricity markets, at least 36 h-ahead forecasting must be utilized. An hour-ahead and several hours ahead forecasting of the electricity demand are also important for the economic load dispatching control of the power system. The passage of clouds through a project area can cause sudden increases or decreases in irradiance, which are called ramp events. In order to mitigate the impact of ramp events, several-hours-ahead forecasting of the ramp rate and width is important.
An accurate and reliable forecasting method should be employed not only in power system but also in individual energy management system in a microgrid, industrial facilities, commercial buildings, and residential buildings. Based on the forecasted PV system power output as well as forecasted electricity demand, the operation scheduling of conventional generators and storage batteries is optimized so that PV power output is effectively utilized and the fuel consumption of conventional generators is minimized.
According to the needs of forecasting in power system operations or individual system operations, various forecasting methods and resources are utilized as shown in Fig. 4.2. Available resources are numerical weather prediction (NWP) models, satellite images, all-sky images, and measured PV power output data. The usefulness of these resources depends on the forecast time-horizon as described in the Section 4.3.
Figure 4.2 Various forecasting methods according to needs in power system operations.
4.2. Power output fluctuation characteristics
To improve the forecast accuracy, proper understanding of the power output fluctuation characteristics of PV system is essential. This section briefly describes the fluctuation characteristics of single point power output and aggregated power output of high penetration PV systems. The fluctuation characteristics of global horizontal irradiance (GHI) are sometimes discussed instead of PV power outputs, because the irradiance is primary factor which determines PV power outputs. In fact, the performance ratio (PR), which is a metric commonly used to measure how effectively PV system converts the irradiance into the alternating current (AC) electricity relative to what would be expected from the panel nameplate rating, is defined based on the irradiance in IEC 61724 as follows [2].
(4.1)Where ENAC is the measured AC electrical generation (kW), PSTC is the summation of installed modules’ power rating from flash test data (kW), GPOA is the measured plane of array irradiance (kW/m2), GSTC is the irradiance at standard test conditions (=1000 W/m2), and is i: a given point in time. Note that the performance ratio given in Eq. (4.1) is the traditional expression. The current expression is corrected so that the temperature effect is taken into account.
4.2.1. Fluctuation characteristics of irradiance at single point
The power outputs of PV systems have a 24-h fluctuation cycle given by the entirely predictable sun motion. Therefore, PV power outputs essentially increase in the morning hours and decrease in the afternoon. In addition to a 24-h fluctuation cycle, PV power outputs have shorter fluctuation cycles due to the clouds motion over PV systems. The fluctuation cycle depends on the types of cloud passing over PV systems. The clouds are typically classified into 10 types as described in Table 4.1.
Table 4.1
Classification of Cloud Types
| Clouds | Type |
| High | Cirrus |
| Cirrostratus | |
| Cirrocumulus | |
| Mid | Altostratus |
| Altocumulus | |
| Nimbostratus | |
| Low | Cumulus |
| Stratus | |
| Cumulonimbus | |
| Stratocumulus |
Fig. 4.3 shows an example of GHI change in a day at single point. Fig. 4.4 shows the visible satellite image on the same day in Fig. 4.3. As shown in the magnified image on the left, the Chubu area is covered by a number of broken clouds. Therefore, a single point GHI largely fluctuates on second-to-second basis because of the clouds movement over GHI observation point.
Figure 4.3 An example of observed global horizontal irradiance at single point (4/28/2011).
Figure 4.4 An example of visible satellite image (4/28/2011).
Temperature is also a key factor which affects PV power outputs. The PR described above quantifies the overall effect of losses due to various factors such as inverter inefficiency, module temperature, reflection from the module front surface, shading, etc. Some of these factors, especially module temperature, are weather-dependent. The strong dependence of PR on temperature causes a large seasonal variation in PR, which can be as large as ±10%. PV power outputs can be different in along seasons even if the irradiance is the same. Therefore, the performance ratio shown in Eq. (4.1) is corrected so that the temperature effect is taken into account [2].
4.2.1.1. Smoothing effect
When the high penetration of PV systems is realized, a number of PV systems are widely dispersed in electric power utility service area. Because a cloud moves over different PV systems at a different time, the power output fluctuation can be different among PV systems. In such a situation, depending on the distribution of PV systems and the characteristics of clouds, the aggregated PV power outputs can be relatively small compared with those expected for individual PV system. This is referred to as spatial smoothing effect. The proper evaluation of aggregated power output characteristics by properly taking the smoothing effect into account is essential for preparing the practical and economically feasible measures against the negative impacts of high penetration PV systems.
In Fig. 4.3, the ensemble average of GHI at 61 points in the Chubu region in Japan is also shown. A second-to-second basis fluctuation of GHI at single point is significantly mitigated by the smoothing effect. Therefore, for estimating the aggregated power fluctuation of high penetration PV systems dispersed in large coverage area, multipoint observations of PV system power output or irradiance is necessary. Besides, in the real situation, a number of PV systems can be installed even between GHI observation points. As a result, because of larger smoothing effect, the aggregated power output of PV systems can be further smoothed.
From a practical point of view, however, the available number of observation points is limited because the service area of electric power utility is so large. Therefore, upscaling techniques should be employed so that the aggregated power output of all PV systems installed in a given area can be calculated by using the data from a subset representative of those systems. Upscaling techniques have been extensively used in forecasts of wind power output, because the forecasts for each wind turbine in a given area can be a time-consuming task.
In the case of aggregated power output of PV systems or spatial average irradiance, different upscaling techniques from wind power output should be employed because of the difference in fluctuation characteristics. Based on a “Transfer Hypothesis” to describe spatial smoothing effect, a method to calculate fluctuation spectrum of spatial average irradiance Save(f) in a certain area is proposed [3]. The principle of the proposed method is as follows. In Fig. 4.5, Smea.15 shows the fluctuation profiles of ensemble average GHI of 15 points in the Hokuriku region in Japan [4]. Because very long-cycle fluctuations can be coherent among different locations, the spectrum is the same as the simple sums of individual spectrum of 15 points as indicated by Scoh.15 in Fig. 4.5. On the other hand, because very short-cycle fluctuations can be random each other, the spectrum is the same as the Pythagoras sums of individual spectrum of 15 points as indicated by Sran.15 in Fig. 4.5.
Because very long-cycle fluctuations of irradiance can be coherent among different locations, the very long-cycle spectrum of spatial average irradiance can be the same as the spectrum S1(f) at representative single point in a certain area. On the other hand, because very short-cycle fluctuations can be random among different locations, the very short-cycle spectrum of spatial average irradiance can be given by S1(f)/
. As a result, based on a Transfer Hypothesis, Save(f) is given by the following equation:
. As a result, based on a Transfer Hypothesis, Save(f) is given by the following equation:
(4.2)Tx is the cycle below which the long cycle fluctuations among different points are not independent any more, and is determined so that the calculated spectrum fits the observed spectrum of spatial average irradiance fluctuations. N is the number of dummy observation points, and is determined to be as large as possible in a certain area while the short-cycle fluctuations can be seen independent between neighboring two points. In other words, the distance between neighboring two points is set as long as possible while the short-cycle fluctuations can be seen independent. Depending on the fluctuation cycles which should be dealt as independent, the minimum length between neighboring two points can be different. For example, the fluctuation cycle of around 30 min should be dealt as independent, the length of two points should be around 5 km. Because Tx and N is determined as a function of the size of area concerned, Eq. (4.1) works as low-path filter to calculate Save(f) based on S1(f).
4.2.2. Fluctuation characteristics of spatial average irradiance in utility service area
As an example, the fluctuation characteristics of spatial average irradiance in the Chubu region in Japan are shown in this section. The geographical size of the Chubu region is about 200 × 250 km, which corresponds to average size of electric power utility service area in Japan. The spatial average irradiance is calculated as a weighted ensemble average of filtered irradiance observed at 61 points in the Chubu region, in which the weight value is determined based on the distribution of detached houses over the area.
Fig. 4.6 shows examples of change in the observed insolation and the low-path filter applied insolation [5]. In these examples, the fluctuation of spatial average insolation shorter than about 30 min is estimated to be only 20% of observed insolation by applying the low-path filter. On the other hand, the GHI shown in Figure 4.6 includes the large change even though it is the change in spatial average GHI in the electric power utility service area. Such a change is called as ramp events. Ramp events occur when the sudden and large change in GHI almost simultaneously occurs in a certain area by the passage of clouds over the area.
Ramp events are one of the major issues to be addressed for the stable operation of electric power system. In the case of the spatial average irradiance in the Chubu region, where ramp events occur 42 days (12 %) per year, the ramp event is defined as follows: the ramp rate is larger than 160 W/m2 per h, the ramp duration is longer than 1 h, and such a change is caused by clouds movement. Fig. 4.7 shows the relation between duration time and fluctuation width of ramp events. The duration of ramp event varies mainly between 30–120 min. The ramp width increases linearly as the duration increases. In the case of downward ramp of relatively large width, the short-cycle fluctuations before and during the ramp event are as large as that in quasifine day. On the other hand, the short-cycle fluctuations after the downward ramp event are small enough as in a cloudy day [6].
4.3. Forecasting methods
4.3.1. Overview
Forecasts may apply to the power output of single PV system or the aggregated power output of a number of PV systems dispersed over an extended geographic area. According to the applications of forecasting in power system operations or individual system operations and the required forecasting time-horizon, various forecasting methods are utilized as shown in Fig. 4.2. Forecasting methods are characterized by methodologies and available information, and useful methods depend on the time-horizon of forecasting. Fig. 4.8 shows an example of comparison of annual root mean square errors (RMSEs) over a year as a function of time horizon among different forecasting methods [7]. The satellite reference means the satellite nowcasting, that is, the satellite forecast for the time when the satellite image was taken. For longer time-horizons (from several hours ahead to a few days ahead), NWP models are an essential. For the time-horizon up to several hours, satellite image analysis methods perform better than NWP models. For very short time-horizon or nowcasting, the persistence forecast model based on the online data of PV system power outputs or irradiance is preferable. The all-sky images (not included in Fig. 4.8) can be used for short time-horizon up to a few tens of minutes ahead.
Figure 4.8 Comparison of annual RMSEs over a year as a function of time horizon among different forecasting methods [7].
Forecasting methods can be broadly characterized as physical or statistical. The forecasting based on NWP models is physical approach, which forecasts the irradiance based on the computation of an atmospheric motion in space and time and translates it to PV system power outputs as the end product as a function of relevant weather variables and PV system characteristics (manufacturer specifications).
The forecasting based on the persistence models is the statistical approach which relies primarily on past data to “train” models, with little or no reliance on physical models. In that sense, a statistical approach is closely related to and often overlaps with machine learning techniques. Various training techniques such as conventional regression models, pattern recognition models can be applied. Statistical approaches are also useful as a post processing to improve the accuracy of physical approach or to directly forecast the PV power output based on various weather elements forecasted in NWP models. Such approaches are called model output statistics (MOS). Fig. 4.9 shows basic steps of a typical physical approach. The primary influential variables to PV output power are the irradiance in the PV array plane and the temperature at the back of the PV modules.
Figure 4.9 Basic steps of a typical physical approach of PV power output forecasting.
The field of irradiance forecasting is rapidly evolving. This section describes a review of various forecasting methods for various time horizons ranging from a few minutes ahead to a day ahead.
4.3.2. Accuracy measures
Common metrics to evaluate the forecast accuracy include mean bias error (MBE, or bias), mean absolute error (MAE), and RMSE. These are defined as follows:
(4.3)
(4.4)
(4.5)where xf,i and xo,i are the ith forecast and observation, respectively.
The bias or MBE is the average forecast error representing the systematic error of a forecast model to under or overforecast. As described below, a postprocessing of model output is useful to significantly reduce the bias. MAE gives the average magnitude of forecast errors, while RMSE (and MSE) give more weight to the largest errors. RMSE without systematic error (SD) captures the part of the RMSE that is not due to systematic error. The relation between MBE, RMSE, and SD is as follows:
(4.6)Therefore, SD provides an indication of the RMSE that can be achieved when MBE is zero.
The normalized value by dividing with a reference value may be used for all these metrics to facilitate comparisons. In the case of PV system power output, the normalized value by the rated capacity is commonly used. Meanwhile, in the case of irradiance, the normalized value by the average irradiance over the certain period is often used.
4.3.3. NWP models
NWP models are the computer program that simulates an atmospheric motion in space and time. Fig. 4.10 shows an example of forecast results by the global NWP model of the Japan Meteorological Agency (JMA) [8]. NWP models are essentially required to the forecasting of longer time-horizon from several hours ahead to a few days ahead. NWP models can also be applied to several hours ahead forecasting.
Figure 4.10 An example of forecast result of global NWP model by the JMA.
In NWP models, the atmosphere is assumed to be composed of a number of lumps in which corner points are called as the grid points. Simulation using NWP model generates the future state of the model atmosphere at all grid points from its initial state. Fig. 4.11 shows an example of a latitude–longitude grid used in the global NWP model operated by JMA [8]. The model equations and inputs are discretized on a three-dimensional (3D) grid extending vertically from the surface of the Earth. The higher the number of lumps indicates the more elaborate simulation.
Figure 4.11 An example of latitude–longitude grid used in global NWP model by the JMA.
A variety of weather phenomena can be analyzed and predicted by the different types of NWP models. Global models are fundamental NWP models covering the whole Earth. The initial conditions of global models are derived from satellite, radar, radiosonde, and ground station measurements that are processed and interpolated to the 3D grid. Global models are used to provide the boundary conditions of a mesoscale NWP model is described below.
Various global NWP models are run in different countries. The European Center for Medium range Weather Forecasting (ECMWF) forecast model is one of the most famous and accurate global NWP model. Global Forecast System (GFS) produced by the National Centers for Environmental Prediction (NCEP) of the US National Oceanic and Atmospheric Administration (NOAA) is also famous. Because GFS data is freely available at the GFS homepage, GFS is mostly used by research institutes and private companies. NCEP runs GFS four times per day at 0, 6, 12, and 18 Universal Time Coordinated (UTC). The horizontal resolution of GFS is 13 km for the first 10 days and 27 km from 240–384 h (16 days).
Mesoscale or limited area models are NWP models that cover a limited geographical area with higher resolution, and that attempt to account for local terrain and weather phenomena in more detail than global models. Initial conditions for these models are extracted from the global models. The Weather Research and Forecasting (WRF) Model developed at the National Center for Atmospheric Research is used extensively for research and real-time forecasting throughout the world [9]. WRF is a next-generation mesoscale numerical weather prediction system designed for both atmospheric research and operational forecasting needs. In the United States, WRF is currently in operational use at NCEP, Air Force Weather Agency, and other centers. On the other hand, because WRF is an open source model, it has a large community of more than 30,000 registered users in more than 150 countries. WRF serves a wide range of meteorological applications across scales from tens of meters to thousands of kilometers. The setup of Advanced Research WRF (Version 3.5.1) consists of a main grid with horizontal grid spacing of 30 km and one nested domain with 10-km grid spacing. Because WRF is an open source model, the calculation conditions such as initial condition, lateral boundary condition, horizontal resolution, etc. can be adjusted flexibly according to the purpose.
In Japan, the JMA currently operates several NWP models to cover various types of prediction, including very-short-range forecasts, short/medium-range forecasts, typhoon track forecasts, and aviation forecasts. Table 4.2 shows the specifications of NWP models utilized by the JMA [8]. Because the time horizon of the MSM model is 39 h, the MSM model is useful for a day-ahead forecasting. Since the outputs of JMA NWP models do not include the irradiance forecast outputs as of July 2015, postprocessing techniques are applied to generate irradiance forecasts. Possible inputs to generate irradiance are cloud cover, temperature, probability of precipitation, relative humidity, wind speed, and direction, etc.
Table 4.2
Specifications of the JMA’s NWP models
| Specification | Global Spectral Model (GSM) | Mesoscale Model (MSM) | Local Forecast Model (LFM) |
| Forecast range | 84 h (00, 06, 18 UTC), 264 h (12 UTC) | 39 h (00, 03, —, 18, 21 UTC) | 9 h (hourly) |
| Number of horizontal grid points and/or grid spacing (no. of truncation wave) | 0.1875˚ [TL959] | 817 × 661 (5 km at 60˚N and 30˚N) | 1581 × 1301 (2 km at 60˚N and 30˚N) |
| Model domain | Globe | Japan and its surrounding areas | |
| Vertical levels | 100 levels up to 0.01 hPa | 50 levels up to 21.8 km | 60 levels up to 20.2 km |
Because of deficiencies and nonlinearities of NWP models, the forecast results may deviate from their true trajectories as the time-horizon increases, resulting in the large error in the end. Therefore, several techniques described below are applied to improve the forecast results of NWP models.
4.3.3.1. Ensemble forecast of NWP models
One way to improve the forecast accuracy and reliability of NWP models is an ensemble forecast. Most NWP models and most forecast results reflect a deterministic approach. In the actual situation, however, depending on uncertainties in the model, initial conditions, or atmospheric conditions, forecast results also have the uncertainties. In an ensemble forecast, initial conditions or physical parameterizations are varied within a single NWP model. The ensemble mean is more accurate on average than any individual forecast results. In addition, the distribution level of forecast results by the ensemble forecast means the confidence level of forecasting. If the distribution is small, the forecast results do not depend on the initial conditions and can be seen to be very reliable. On the other hand, if the distribution is large, the forecast results depend highly on the initial conditions and are not so reliable. Because the information on uncertainty of forecast results can be practically very useful, the uncertainty is also provided as a confidence interval of forecast results.
4.3.3.2. Spatiotemporal interpolation and smoothing
NWP models provide the forecast results at discrete grid points. Therefore, spatiotemporal interpolation is practically important when NWP models are utilized for forecasting irradiance at a specific single point. The simplest method is to use the forecast results at the nearest grid point to the location of interest, though the spatial resolution is 5 km even in mesoscale NWP model. Other approaches involve interpolating forecasts from grid points surrounding the point of interest. In addition to spatial interpolation, temporal interpolation must be used when available NWP model outputs have a lower temporal resolution than desired.
4.3.3.3. Postprocessing by statistical model
Forecast results of NWP models may include systematic errors or bias errors. Therefore, if measured irradiance data is available, postprocessing contributes to improve the accuracy of forecast results of NWP models. The simplest postprocessing model is a linear function given as follows:
where Ic is the corrected forecast results and Io is the original forecast results of NWP model. Coefficients a and b are estimated by using measured irradiance data and original irradiance forecasts of NWP model during the training period in the past. The simplest way to estimate the coefficients is the least squares method. The Kalman filter is practically useful method to obtain suitable coefficients day by day. Fig. 4.12 shows an example of time series of coefficients obtained from the Kalman filter [10].
Because forecast errors often depend on the time of the day and of the year, on sky conditions, etc., the training should be done separately over individual time in a day, different conditions or regimes. In order to reduce the training process, the sky clearness index is often used together with the information on the position of the sun (cosine of the solar zenith angle).
MOS is applied to correct the original irradiance forecasts of NWP models as a postprocessing technique, when the ground observations of irradiance are available. MOS relates observed weather elements to appropriate variables (predictors) by a statistical approach such as multiple regression. For example, in Ref. [11], a genetic algorithm and artificial neural networks are applied for regression and the National Digital Forecast Database (NDFD) by the US National Weather Service and used as training data.
As of July 2015, because direct outputs of the JMA NWP models did not include the irradiance forecast outputs, the irradiance was forecast by MOS approach using the forecasts of the other weather elements. Possible inputs to generate irradiance are cloud cover, temperature, probability of precipitation, relative humidity, wind speed, and direction, etc. For instance, in Ref. [12], the special average irradiance is forecasted by using a simple linear function of cloud cover forecasts at three levels of GPV (MSM) data and extraterrestrial irradiance. In Ref. [13], the support vector machine is applied.
4.3.3.4. Combination of different forecast models
The combination of different forecast models is a practically feasible way to improve the forecasting accuracy. Various combination is available, that is, the combination of different NWP models such WRF and MSM/JMA, the combination of different boundary condition data for mesoscale NWP models such as GFS and global spectral model (GSM)/JMA, the combination of different postprocessing approaches, etc.
Fig. 4.13a shows the spatial average irradiance forecasts in the Chubu region in Japan by nine different day-ahead forecast models [14]. The forecasts by three models, that is, models B, H, and K are not included in Fig. 4.13a. Some models calculate the irradiance forecasts by using WRF with postprocessing, in which the boundary conditions are given by MSM/JMA. Some models are statistical approach using the forecasts of various weather elements by MSM/JMA. As shown in Fig. 4.13a, the irradiance forecasts are different among models. The RMSE for a month (May 2012) is ranging from 100–133 W/m2. In Fig. 4.13b, the thin line shows the simple average of irradiance forecasts of nine models, and the dashed line shows the best forecasts among nine models in each hour. The RMSE of simple average reduces to 90 W/m2. If the best forecast can be chosen as an ideal situation, RMSE is only 27 W/m2. The result suggests that further significant improvement of forecast accuracy is expected.
4.3.4. Satellite cloud motion vector approach
Irradiance forecasting based on cloud motion vectors from satellite images shows good performance for the time-horizon ranging from 30 min up to several hours. Earlier contributions have shown that satellite-derived cloud motion tends to outperform NWP models for forecast horizons up to 4–5 h ahead depending on location [7]. High quality satellite images are available from various weather satellites such as Multifunctional Transport Satellite (MTSAT) in Japan, the Geostationary Operational Environmental Satellites (GOES) in the United States, etc., and have been used extensively in solar resource mapping. Because the irradiance at the earth surface highly depends on the cloud optical depth, the clearness index, which is defined as the ratio of the horizontal global irradiance to the corresponding irradiance available out of the atmosphere, can be calculated accurately based on the reflectance measured for each pixel in the visible satellite images. Fig. 4.14 shows an example of estimated irradiance calculated based on a radiative transfer model [15].
Figure 4.14 An example of irradiance estimation based on satellite image.
The spatial resolution of geostationary satellite images is 1 km for example in MTSAT-2. Therefore, satellite images are useful to detect large and thick clouds such as stratocumulus and cumulonimbus. On the other hand, detection of cirrus or cirrostratus at the high altitude may be difficult. The sampling interval of full disk images is 30 min in MTSAT-2 and GOES-14. The sampling interval of latest MTSAT in Japan, which was launched in Sep 2014, is improved to 10 min for full disk images and 2.5 min for Japanese local images.
Based on these features, one of the advantages of satellite image-based forecasting compared with NWP models is higher accuracy in a several hours-ahead forecasting. In many methods, the irradiance is forecasted by estimating cloud motion vectors as follows. First, the same feature points are detected in successive images in the last few hours. Then, based on the spatial and temporal difference of feature points in successive images, cloud motion vectors can be estimated. Finally, by assuming that cloud feature points and their motion vectors do not change for next few hours, irradiance is forecast based on the motion vectors of the clouds getting closer to the target location.
4.3.5. All Sky images
Ground-based all-sky images have much higher spatial and temporal resolution compared with the satellite images, though the field-of-view is much smaller than that of satellite images. Therefore, irradiance forecasting based on all sky image analysis is suitable measures for a single point irradiance forecasting of shorter time-horizon shorter than several 10 min [16]. All sky image based forecasting is also useful for the irradiance distribution forecasting and nowcasting within a supply territory of power distribution network. All sky-image-based forecasting is performed by estimating cloud motion vectors by using successive images. With the significant improvement of charge coupled device (CCD) devices, all sky images are available using low cost fish-eye camera [17]. Due to the limited field-of-view of sky imager, the forecast horizon would be shorter than about 15 min. Fig. 4.15 shows an example of forecast output by Sky Imager developed at the University of California San Diego San Diego (UCSD) [18]. Top left is raw HDR image, cropped to remove static objects near horizon. Top center shows the red–blue ratio image. Top right is the cloud decision image (blue: clear sky, light gray: thin cloud, dark gray: thick cloud). Bottom left shows a shadow map over the UCSD domain, showing predicted cloud shadows from images taken 10 min ago. Ground stations are marked by solid black squares. The cloud field mean velocity vector is indicated by the solid black arrow extending from the center, with magnitude indicating predicted distance traveled in 30 s. Bottom right shows the universal sky image (USI) GHI forecast issued at current time for a 15 min horizon (dashed red), USI GHI forecast time series for constant 10 min forecast horizon (solid black), and corresponding measured GHI (solid green). In the bottom right graph, the first vertical dashed line indicates forecast issue time, while the second vertical dashed line shows the 10 min forecast horizon (solid black line must equal red dashed line at that point).
Figure 4.15 An example of USI forecast output using all-sky image.
4.3.6. Statistical models
For an irradiance forecast of very short time horizon (up to a few hours), statistical models based on regression analysis using online irradiance measurement data are accurate and practical approach. The simplest model utilizes the irradiance measurements data only. If relevant exogenous data such as all sky images, satellite images, various weather forecasts of NWP models, and other meteorological observations are available, the accuracy and reliability can be significantly improved. Because the irradiance strongly depends on the solar zenith angle, it may be favorable to treat the nondeterministic atmospheric extinction by excluding the influences of the deterministic solar geometry when using statistical models. For this purpose, clearness index, which is the ratio of measured irradiance at ground level to extraterrestrial irradiance is utilized. The clear sky index, which is the ratio of measured irradiance at ground level to estimated irradiance in clear sky conditions at ground level, is also utilized if a clear sky model and information on atmospheric input parameters are available.
Autoregressive moving average (ARMA) model is one of the most popular statistical tools for time series data analysis and is very useful to predict the future value of a specified time series. ARMA consists of two parts, that is, lagged past values (autoregression) and error terms (moving average). One major requirement for ARMA model is that the time series must be stationary. The autoregressive integrated moving average (ARIMA) model can be applied when the time series are nonstationary but their differences are stationary. In addition to the conventional regression models such as ARMA and ARIMA, an autoregressive model coupled with dynamical system model is proposed for one hour ahead forecasting of irradiance. The combination of dynamical system model contributes to improve the forecast accuracy especially in mostly cloudy days [19].
4.4. Examples of forecasted results
As described above, various research organizations have developed different methods to forecast irradiance or PV system power output. The performance comparison of different models in a standardized evaluation methodology is important for researchers to further improve their models. The comparison is also important for users to assist them in choosing suitable models for their purpose.
One of the performance comparison was made in the framework of The Solar Heating and Cooling Programme of the International Energy Agency (SHC IEA) Task 36 “Solar resource knowledge management” (http://archive.iea-shc.org/task36/), in which three independent validations of GHI multiday forecast models performed in the United States, Canada, and Europe were compared [20]. The focus of the comparison was on the end-use accuracy of the different models including global, multiscale, and mesoscale NWP models as a basis. In addition, different postprocessing techniques to derive site-specific every hour forecasts such as very simple interpolation and advanced statistical method were compared. The models considered for this evaluation are listed below:
1. Satellite image as a reference.
2. Persistence model.
3. The Global Environmental Multiscale (GEM) model from Environment Canada in its regional deterministic configuration.
4. An application of the ECMWF model.
5. A model based on cloud cover predictions from the US NDFD proposed.
6. Several versions of WRF model initialized with GFS forecasts from the US NOAA/NCEP (NCEP).
7. The advanced multiscale regional prediction system model.
8. The mesoscale atmospheric simulation system model.
9. The regional weather forecasting system Skiron operated and combined with statistical post-processing based on learning machines at Spain’s National Renewable Energy Center (CENER).
10. The high resolution limited area model operational model from the Spanish weather service (AEMet) combined with a statistical post-processing at Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT).
11. BLUE FORECAST: statistical forecast tool of Bluesky based on the GFS predictions from NCEP.
12. Forecasts based on meteorologists’ cloud cover forecasts by Bluesky.
GEM and ECMWF are directly based on global NWP systems. Some models are tested in two operational modes: with and without MOS postprocessing. The MOS process consists of integrating ongoing local irradiance measurements, when available, to correct localized errors from the numerical weather prediction process. The last four models are not used in the US case.
The main results are as follows. RMSE composite values of seven sites in the US show a considerable spread for the different models ranging between 32 and 47% for day 1 forecasts as shown in Fig. 4.16. Lowest MAE and RMSE values (or highest accuracy) are found for the global model ECMWF and GEM irradiance forecasts. All considered mesoscale model forecasts as well as the NDFD based forecasts show larger forecast errors. This indicates some drawbacks of irradiance and/or cloud schemes in the selected mesoscale models. On the other hand, the GFS model irradiance forecasts were found to have a similar performance to those of the ECMWF model when applying a simple postprocessing. There is a considerable variation of accuracy in terms of RMSE and MAE for the different sites and climates in the United States. For an arid climate (Desert Rock, United States) with many sunny days, relative RMSEs in the range of 20–25% for day 1 forecasts are considerably smaller than for the other sites for all investigated models, where the RSME values exceed 30%. Largest day 1 RMSE values between 38 and 48% are found for Penn state with the lowest mean irradiance. Extending the model comparison from the United States to Canada and Europe, the finding that ECMWF based irradiance forecasts show a higher accuracy than irradiance forecasts with WRF and the other investigated mesoscale models is confirmed. For Canada, like for the United States, the performance of the Canadian GEM model is similar to the performance of the ECMWF model.
Figure 4.16 Composite RMSE of different forecast models (US case).
Focusing on the difference in machine learning techniques, the irradiance forecasting methods were compared [21]. Popular nonlinear techniques such as neural networks and some rather new methods such as Gaussian Processes and support vector machines were evaluated against simple methods like the autoregressive linear model and reference models like scaled persistence. The performances of the following models were compared in terms of several hours-ahead forecasting of historical GHI data measured on three French islands.
1. Climatological mean (mean historical value of clearness index, which is independent of the forecast horizon).
2. Clear sky index persistence model (SC-pers).
3. Autoregressive process (AR) model.
4. Neural network (NN) model.
5. Gaussian process (GP) model.
6. Support vector machine (SVM) model.
The first two models are called the native model. AR model is a linear model. The last three models are nonlinear models. Fig. 4.17 shows relative RMSE of the different methods for each forecasting time horizon for the case of Reunion Island. The nonlinear methods such as NN, GP, and SVM perform better than the scaled-persistence and the linear model. The advantage increases with the forecasting horizon. For hours ahead forecasting, the picture is less clear and seems to depend on the sky conditions. For stable clear sky conditions (clear skies for instance), the nonlinear methods slightly improve the scaled-persistence. For unstable sky conditions, the discrepancy between the machine learning methods and the simple models is more pronounced with a 2% rRMSE difference in average. Similar results are obtained for the other sites. Because the performance of the three nonlinear methods is practically the same, the choice of the method will depend on the skill and experience of the modeler.
Figure 4.17 RMSE of different forecast models as a function of prediction time horizon.
4.5. Smoothing effect on forecast accuracy
Because of a so-called smoothing effect of irradiance forecast errors at different locations, the forecast accuracy would be higher for the spatial average irradiance than the single point irradiance. Higher impact of smoothing effect is expected for mesoscale model with hourly values and a finer grid resolution. Quantifying the accuracy improvement by smoothing effect seems difficult because it depends on various factors such as climate diversity within the region, PV system distribution, capacities, etc. Nevertheless, some case studies regarding the forecast accuracy improvement by smoothing effect are available in the technical literature.
For example, in the case of ECMWF forecasts, RMSE of a day-ahead forecasting is 13% for the ensemble average irradiance of more than 200 stations in the complete German region with a size of 9 × 10o, while overall RMSE is 37% for single sites [22]. The best results are achieved for average values of 4 × 4 grid points corresponding to a region of 100 × 100 km. An analysis of the GFS model and NAM model showed that 100 × 100 km as a suitable irradiance forecasts [23]. Similarly, in the case of forecast of the average irradiance of 10 ground stations across Canada and the United States, RMSE is about 67% lower than individual RMSE of the irradiance at individual ground stations [24].
4.6. Power system operation considering PV power output fluctuations
In order to maintain the electric power system reliability, electric power utility or Independent System Operator (ISO) must continuously control the electricity supply to meet the demand on a second-to-second basis. Historically, the ISO has controlled conventional thermal power plant units. With the growing penetration of renewable energy resources, there are higher levels of noncontrollable, variable generation resources in a power system. In some countries, renewable power generations increasingly satisfy the electricity demand in certain times of the year. As a result, the requirements to manage a power system are changing due to the high penetration of intermittent and unstable renewable energy resources.
The time series of residual electricity load, which is the difference between the actual electricity demand and the electricity supply from renewable energy sources, is changing to quite different form from the current load curve. In certain times of the year, the residual load curves produce a “bally” appearance in the mid-afternoon that quickly ramps up to produce an “arch” similar to the neck of a duck as shown in Fig. 4.18 [25]. Such a residual load curve is called as “duck curve.” The first ramp in the downward direction occurs in the morning starting around 7:00 am as the power output of PV systems increases steeply. As a result, online conventional generation is replaced by supply from PV power output, producing the belly of the duck. As the PV power output starts to decrease around 4:00 pm, the ISO must dispatch resources that can meet the second significant upward ramp (the arch of the duck’s neck). Immediately following this steep ramp up, as demand on the system decreases into the evening hours, the ISO must reduce or shut down that generation to meet the final downward ramp. Moreover, as shown in Fig. 4.18, surplus electricity supply or overgeneration happens in the daytime when more electricity is supplied by PV systems than is needed. Similarly, overgeneration may happen during night when the electricity supply from wind power generations is large but the demand is small.
Figure 4.18 An example of change in residual electricity load called Duck curve.
The residual load curves represent the variable portion that the ISO must meet in real time. Important parts of power system operations affected by duck curve include regulation reserves requirements and subhourly dispatch. How the system operations can be changed to more economically integrate large amounts of PV power is an open question currently being considered by many utilities and ISO. To understand changing grid conditions, the CAISO, the independent system operator in California performed detailed analysis for every day of the year from 2012–2020 as follows [25]. The analysis shows that the ISO requires a resource mix that can react quickly to adjust electricity production to overcome several emerging conditions due to the high penetration of renewable resources, that is, the ramp up/down of residual electricity load, the surplus power supply exceeding the demand, insufficient capacity to maintain the system frequency. To ensure reliability under changing grid conditions, the ISO needs resources with ramping flexibility and the ability to start and stop multiple times per day and the flexibility to change output levels as dictated by real-time grid conditions. At the same time, the ISO needs to increase interconnection capabilities to neighboring system, and require the curtailment of renewable generation.
For the best use of these flexibilities, an accurate and reliable forecasting of renewable generation is essential. Because forecasting of PV system power output is a cutting edge research area, it has only recently been introduced into the electricity system operation in some countries such as the United States, Germany, and Spain. Probabilistic or ensemble forecasting methods are used for probabilistic unit commitment of electric power system with high penetration PV system.
For example, the CAISO uses a day-ahead forecast and several hours ahead forecast as follows [26]. A day-ahead forecast is submitted at 5:30 prior to the operating day, which begins at midnight on the day of submission and covers (on an hourly basis) each of the 24 h of that operating day. Therefore, a day-ahead forecast is provided 18.5–42.5 h prior to the forecasted operating day. An hour-ahead forecast is submitted 105 min prior to each operating hour. It also provides an advisory forecast for the 7 h after the operating hour. CAISO is considering the implementation of intra-hour forecasts at 5 min intervals.
4.7. Energy management examples of smart house with PV
The concept of the “Smart house” is an intelligent house that incorporates advanced automation systems to provide the inhabitants with sophisticated monitoring and controlling of building’s functions such as lighting, room temperature, security, and etc. Thanks to the cost reduction of PV system and storage battery, a recent smart house often has a home energy management system (HEMS). In the last decade, a number of demonstration projects of smart house have been conducted throughout the world.
4.7.1. United States/Japan demonstration smart grid project in Los Alamos [27]
The New Energy and Industrial Technology Development Organization, Japan, undertakes the United States/Japan demonstration smart grid project in Los Alamos. A smart house equipped with 2 MW PV system, 8.3 MWh storage batteries, and a micro energy management system was demonstrated together with regional microgrid. The HEMS applied in this project controls them that allow for electric demand in the house to be responsive to smart grid signals, minimizing electricity costs and preserving the comfort of residential usage patterns. Based on time of use (ToU) electricity price, PV power output forecast, load power performance, and hot water usage results, the applied optimization method runs a linear programming to minimize the electricity cost of next three days by optimizing the battery charge/discharge and hot water storage of every 15 min.
Fig. 4.19 shows a configuration of PV power output forecasting system. The forecasting method is a combination NWP model, PV power output estimation model, and statistical model. The time-horizons are both short, up to 24 h, and long, up to 1 week. At first, NWP model forecast irradiance, wind speed, and temperature. The grid point data of mesoscale calculated by the JMA is used as the initial conditions of NWP model. Then, PV power output model translates the forecasted weather elements to the PV power output based on the PV system parameters such as installation conditions, specifications of PV module and power conditioner, etc. Finally, the statistical model, which was developed in advance based on the observed values of PV power output and local weather observation data, corrects the statistical bias error of calculated values of PV power output. In addition to the bias correction, the statistical model calculates the forecasting error range (confidence interval).
Figure 4.19 A configuration of PV power output forecasting system.
Fig. 4.20 shows an example of HEMS operation in a day. HEMS controls the storage battery so as to charge with grid power when the TOU price is low during mid night. As a result, the SOC reaches 90% before 5:00 am. Because the daytime electricity demand is small, the excess PV power output is reversed to the grid. Then, after the noon when the ToU price is the highest, HEMS controls the storage battery so as to discharge the electricity and sell it to the grid.
Figure 4.20 An example of HEMS operation in a day.
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