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As the share of solar energy in the energy mix increases, accurate solar power forecasting becomes more important than ever before. The amount of solar energy being traded in energy markets is increasing rapidly. In many regions, where previously there were no cost implications for inaccurate forecasts, imbalance penalties are now being introduced.
In this article we discuss the most commonly used metrics to evaluate forecast errors, and what Solargis is doing to improve accuracy of solar power forecasts.
The most commonly used statistical error metrics for evaluating performance of solar power forecasts are summarised below.
Mean Absolute Error (MAE) - MAE provides a good overview of average error. This is a useful metric to understand cost of inaccurate forecast when the penalty for forecast error is linear. This metric is popular amongst energy traders.
Root Mean Square Error (RMSE) - RMSE gives a higher weightage to large forecast errors and is thus a suitable metric when the penalty for larger forecast errors is higher.
Mean Bias Error (MBE) - MBE indicates whether a forecasting model in general tends to overestimate or underestimate in comparison to actual values. It should be noted that systematic deviations are easier to correct.
In addition to these metrics, there exist several other error metrics that are often used by forecasting experts to compare performance of different forecast models - however these metrics may not always be relevant for understanding cost implications of inaccurate forecasts.
When reporting forecast accuracy metrics, they are often normalised against total capacity of the power plant or average power output. This is useful for comparing forecast performance for power plants of different size and/or locations across different climatic conditions.
Forecasting of PV power production is as a 2-step process. In the first one, both solar radiation and air temperature (possibly also other meteorological variables such as wind speed and relative humidity) are predicted. In the second step, the predicted variables are converted to power output taking into consideration the technical specifications of the power plant.
The level of detail and accuracy at which a PV system can be defined is much higher than what can be achieved for the weather system. Indeed, the uncertainty of solar radiation forecast is nearly one order of magnitude higher than the uncertainty associated with the conversion of solar radiation to PV power output. Therefore the accuracy of the solar radiation forecast is a key factor that determines the accuracy of the PV power forecast. With this in mind, we discuss below approaches taken by Solargis to improve accuracy of solar radiation forecasts.
Just as there are horses for courses, different forecasting techniques are more suitable depending on the intended forecast lead time. Figure 1 shows a comparison of expected forecast skills as a function of forecast lead time for the most important families of forecasting methods: (i) Ground-based methods, (ii) satellite-based methods, and (iii) Numerical weather prediction (NWP) models.The maximum forecast skill (one) is for a perfect forecast.
Figure 1. Conceptual plot of forecast skill vis-á-vis forecast lead time for ground-, satellite- and NWP-based forecast methods. The forecast skill values, shown for illustration purposes, are only approximated. The pyranometer and sky camera photos are courtesy of the University of Jaén, Spain
At sub-hourly forecast lead times, methods based on on-site ground observations provide the highest skill (see Fig. 1) because, at this time scale, changes in weather patterns are relatively small. Forecasts based on the combination of solar radiation measurements and statistical methods such as auto-regressive or state-space models, do a great job at casting the current observed conditions into near future times. A trivial model is the so-called smart persistence, which assumes clouds do not change throughout forecast lead time and only the changes due to the deterministic course of the sun are modelled. Another approach is based on the observation of the cloud field over the location of interest using on-site cloud sky cameras. By comparing two or more consecutive images, the overall speed and trajectory of cloud structures can be inferred and used to cast the cloud locations into the future.
As the forecast lead time moves from sub-hourly to several hours ahead, the relative importance of remote weather features prevails over local features. In essence, clouds far from the site of interest will be affecting local weather in a matter of tens of minutes to few hours. As a consequence, local observations are not enough to account for future events and the observation area needs to be expanded. The satellite-based methods then come naturally to the playing field. Figure 1 shows that the forecast skill of ground-based methods is eventually surpassed by the forecast skill of satellite-based methods for horizon forecasts about half an hour.
At Solargis, we are processing satellite imagery in near real-time basis from 5 geostationary satellites. Imagery from these satellites extend over thousands of kilometres and describe clouds with a spatial resolution in the order of 2 to 5 km and a refresh rate between 10 and 30 minutes depending on the satellite. As with sky cameras, the forecasting principle consists of a similarity analysis of two or more consecutive cloud images. From it, the positions of matching cloud structures in the two images are used to determine the speed and trajectory of clouds, which are represented by a spatial field of vectors customarily referred to as cloud motion vectors (CMV). Then, assuming CMV stay the same for the next hours, the future position of clouds is inferred, from which solar radiation is computed.
Figure 2. (Left) solar radiation modeled based on satellite observations. (Right) Solar radiation for same period but modeled using cloud motion vector model - cloud position for next hours is extrapolated based on analysis of consecutive satellite images.
Contrarily to sky cameras, satellite-based forecasting method implemented by Solargis does not require costly on-site equipment and maintenance. Moreover, the new and forthcoming satellite systems promise spatial and temporal resolutions never seen so far, being soon eventually capable of reaching spatial resolutions comparable to large PV power plants.
As shown in Fig. 1, the skill of satellite-based forecasts decreases with increasing forecast lead time. This happens because the spatio-temporal correlation of current and future weather patterns drops off. NWP-based forecasting methods tend to provide higher forecast skill than satellite-based methods beyond typically 5 or 6 hours ahead.
Global NWP models—which are run virtually only by public weather services and research centres due to their huge computational demands—provide worldwide coverage at the expense of limited spatial resolution (currently in the approximated range from 9 to 25 km) and temporal resolution (currently hourly or 3-hourly). The typical refresh rate is once every 6 or 12 hours, with each new forecast normally providing values up to about 10 days ahead.
Although all NWP models are physically-based and are mostly founded on the same major physical assumptions, they do have different capabilities depending on the weather conditions. For this reason, the best approach is to use a consensus forecast that optimally integrates forecasts from various NWP models.
At Solargis, we are processing forecasts from 3 global NWP models:
A key advantage we have over other providers of solar forecast service is that we maintain a historical archive of solar radiation time series, modeled based on satellite observations.This enables us to evaluate the performance of different NWP models by comparing historical forecasts with solar radiation that has been modeled based on satellite observations. Forecasts from different NWP models can then be optimally combined to achieve improved accuracy.
This data processing is customarily referred to as model output statistics (MOS) and spans a wide spectrum of methods to combine observations and forecasts, from the simple and ubiquitous linear regression to the recent rise of a comprehensive family of skilful methods jointly referred to as Machine Learning.
An example is given below to demonstrate the potential improvement in forecast accuracy by combining forecasts from three different NWP models. Figure 3 shows the normalised RMSE for different forecast models for Tokyo, Japan. For calculation of RMSE, irradiance data modeled based on satellite observations are used as reference.
Figure 3. Improvement of solar radiation forecast by combining forecasts from multiple NWP models for Tokyo, Japan
The validation of models is shown for models with both no MOS (thin dashed lines) and MOS (thin solid lines) post-processing, respectively. The benefits of the MOS post-processing and the combination of models is quite clear. The MOS post-processing and models blending considerably improve the initial performance, by about 10% on average.
It can thus be concluded that combination of models systematically provides better forecast than any individual forecast model.
If you are a PV power plant owner/operator, and inaccurate forecasts of solar power have cost implications for you, we can provide a free evaluation of forecast accuracy that can be achieved for your project. Get in touch to discuss how we can help you.
Note: This blog is a shortened and modified version of an article that was originally published in the Sep 2017 issue of PV-Tech Power magazine.
