In this paper, we present the winning solution to the ECMLPKDD Discovery Challenge 2017 on Multi-Plant Photovoltaic (PV) Energy Forecasting. The goal of the challenge is to utilize the historic data of three di erent PV plants in Italy regarding meteorological conditions and production in order to forecast their energy production. A major problem is that the data contains many missing value for most sensors and especially for the period of the year for which predictions shall be made in the subsequent year. We investigate two approaches: a regression tree ensemble whose hyperparameters where tuned via Bayesian optimization and a simple rule that just predicts the hourly averages that were observed during the previous year. The latter approach is the winning solution of the challenge.
1 Paderborn University 2 IBM Research Ireland
Due to the urgent need to reduce pollution emission, clean and renewable energy sources have become a strategic European Union and international sector. In particular, photovoltaic (PV) power plants, which are already widely distributed in Europe, are becoming a major source of renewable energy. The main challenges faced by the renewable energy market are grid integration, load balancing and energy trading. In order to face these challenges, we need reliable tools for the prediction of the energy production.
Challenge. In the ECML PKDD 2017 Multi-Plant Photovoltaic Energy Forecasting Challenge, we are given multiple time series regarding meteorological conditions and production collected by sensors on three closely located PV plants in Italy. Given the data for the period from January to December 2012, the goal is to forecast the energy production of each plant for the period from January to March 2013.
Related Work. [
For detailed information on the given data, we refer to [
Time Series. The given data set consists of time series data regarding weather conditions and production collected by sensors on three closely located PV plants in Italy. The elements of these time series are hourly aggregations obtained as the average of all the measures available during a speci c hour at a speci c day of the year. That is, for each plant, day, and sensor, we are given a time series of 19 values representing hourly aggregated observations (plants are active from 2am to 8pm).
The data was gathered locally, from sensors available on plants and from the closest meteorological stations. There are three time series that describe the plant: irradiance, temperature, and the power production. There are seven time series that describe the weather: temperature, cloudcover, dewpoint, humidity, pressure, windbearing, and windspeed.
Train and Test. The given training data spans over a period of 12 months (year 2012) and includes the target time series, i.e. the power production observed for each plant. The testing data consists of 3 months (January to March 2013) for which the target time series is not provided. According to the challenge website, min-max scaling (between 0 and 1) on power variables needs to be performed on the training and testing data before applying the prediction model. Additional Information. According to the challenge website, the data can contain reasonable missing values or outliers. Missing values are indicated by zero measurements. Besides that, the PV plants have a maximal power rate of 1 000 kW/h. 3
Some of the power measurements are much higher than the maximal power rate of 1 000 kW/h (e.g. 885 124 kW/h). Therefore, in the following gures, we clean the power measurements by setting all power values larger than 1 000 kW/h to exactly 1 000 kW/h. 3.1
In Fig. 1 we consider the impact of the single variables with respect to the power production and, additionally, the average monthly and hourly power production. The results con rm our expectation: First and foremost, we expect that the power production is higher during summer, during the middle of a day, and while the plant irradiance is higher. We expect that, if the weather is sunny, then the plant irradiance is higher. We expect sunny weather if the weather temperature is higher, the pressure is rather high, there are few clouds, and the humidity is low.
Most notably, there is a strong correlation between the plant irradiance and the power production. The correlation of the power production with the weather temperature, pressure, cloud cover, and humidity is less striking. Besides that, in Fig. 2, we see that these variables also correlate with the plant irradiance.
The dewpoint, the wind speed, and wind bearing do not seem to be correlated to the power production, respectively. One might suspect that the informativeness of the wind speed and bearing might depend on the location. However, except for the wind bearing measured at the plant with index 1 (see Fig. 1), these location dependent gures are similar to the averages (over all plants) depicted in Fig. 1.
Last but not least, apparently, there is a signi cant number of missing values, which have been set to zero by default (see Sec. 2). 3.2
We considered the plant irradiance and the plant temperature the most promising variables. Fig. 3 depicts the daily averages values of these variables during the year 2012.
For plant 1, a lot of the plant irradiance and plant temperature measurements are probably missing between day 30 and day 58. During this interval, both measurements are constantly 0, respectively. Besides that, we observe that the plant power of plant 1 drops signi cantly during the very same time. That is, in comparison to the other plants, we would expect roughly 150 kW/h, but observe about 100 kW/h.
Regarding plant 2, there seem to be even more missing values in the rst 90 days of the year 2012. During the rst 90 days, the plant irradiance and plant temperature measurements are constantly 0. Besides that, the plant power measurements behave as expected. Still, there seems to be a slight drop of the power production between day 25 and 50.
Finally, consider the measurements regarding plant 3. Here, there seem to be no missing measurements. However, we observe a strange behavior of the plant irradiance measurements: Approximately between day 50 and day 150, the plant irradiance increases much faster compared to the irradiance measurements for plant 1 and 2, respectively. At day 150, the measurements decrease to values which are similar to the values measured for plant 1 and 2, respectively. Again, there seems to be a slight drop of the power production between day 25 and 50.
To sum up, the time series of all three plants exhibit an unusual behavior in the rst 90 days of the year 2012. Unfortunately, the test data consists of measurements for the rst 90 days of the subsequent year. On a side note, the test data does not seem to contain missing plant irradiance or plant temperature measurements.
From Sec. 3, we know that the data set most probably contains a lot of missing values, which are indicated by zero measurements, and outliers. Missing Data. Recall that missing values are indicated by zero measurements. However, a zero measurements does not necessarily indicate a missing value. Therefore, we did not mark all zero measurements as missing: In the plant irradiance time series, we marked a zero measurement as missing if, at the same time point, the plant temperature was also zero (i.e. we marked 2577 of 7921 zero measurements as missing) (cf. exploration of data regarding plant 2 in Sec. 3.2). After that, we marked all zero measurements in the plant temperature, weather pressure, and weather pressure time series as missing.
Outlier Removal. First, we removed unusual values. In the given training data, the minimum plant temperature is -3 C, while in the test data we observe plant temperature measurements of up to -202 C. This is why we decided to remove (i.e. mark as missing) all plant temperature measurements of less than -3 C from the test data.
Second, we used the outlier removal proposed by [
Normalization of Power Measurements. After our outlier removal there were still some power measurements larger than the maximal power value of 1 000 kW/h. We simply replaced these measurements with the maximal power value (i.e. 1 000 kW/h).
Additional Date Features. We created one training and test data set that contains the plant ids, the plant sensor features, weather features, and additionally, three date features. The date features indicate the hour of the day (by values 1; : : : ; 19), the day of the year (by values 1; : : : ; 366), and the month (by values 1; : : : ; 12). 5
In the following, we rst describe two approaches: a regression tree ensemble and an evaluation of hourly averages. The latter has turned out to be the winning solution of the challenge. 5.1
In order to estimate the performance of our approaches, we split the training data in two splits: The rst split T1 23 contains all data from the training data set concerning the rst 23 days of each month in 2012. The second split T24+ contains the remaining data, i.e. all training data containing the 24th day through the last day of each month in 2012. In the following, we train our models using the larger split T1 23, and evaluate the resulting models with respect to T24+.
Our motivation for these splits is twofold: First of all, we want to ensure that there is enough information about each month contained in each split. Second, we want the splits to correspond to rather independent time series. In other words, we want that the number of measurements vt for which the subsequent measurement vt+1 is contained in a di erent split than vt is as small as possible. This property would be violated if, for example, we would choose the assignment of a measurement to one of the splits uniformly at random. 5.2
Our rst approach is to use gradient boosted regression trees (GBRT) [
Our second approach is to predict hourly average values: For each plant p, hour of the day h, and for each month m, we computed the average power production of plant p during the month p at this speci c hour h of the day. For instance, our prediction of the power production of plant 1 for February 1st between 1pm and 2pm is the average power production of plant 1 between 1pm and 2pm in February 2012. 5.3
First, let us consider the performance of our models with respect to the validation split T24+: Our resulting regression tree ensemble yields a root mean squared error (RSME) of 0.0685. In comparison, our hourly average approach performs poorly and only achieves an RSME of 0.1297. However, our models perform di erently with respect to the testing data.
Regarding the testing data, our simple hourly average approach turned out to be the winning approach. Tab. 1 depicts the temporary and the nal leaderboard, which have been published on the challenge website. Our simple hourly average approach already achieved the second best score on the temporary leaderboard, which contains 10% of the testing data. Regarding the complete testing data, the hourly approach outperformed all the other competing solutions. position As already explained, the given training data contained many missing values, especially, during the time of the year, for which we have to predict the power production in the subsequent year (see Sec. 3.2). We expect that, given more reasonable data, a machine learning approach will outperform our simple hourly average approach.