Understanding the Drivers of Negative Electricity Price Using Decision Tree

Transcription

1 2017 Ninth Annual IEEE Green Technologies Conference Understanding the Drivers of Negative Electricity Price Using Decision Tree José Carlos Reston Filho Ashutosh Tiwari, SMIEEE Chesta Dwivedi IDAAM Educação Superior Houston, TX, USA Houston, TX, USA Manaus, Brazil Abstract This paper proposes a hybrid approach, integrating Decision Trees (DT) and Artificial Neural Networks (ANN) for energy price classification in deregulated electricity market. The proposed model does not aim to predict future values of energy prices, but classify and explain the negative Locational Marginal Price (LMP) that are observed in the grid. The negative LMPs are grouped by the K-means technique and then taken as a target. Starting from a large set of potential variables that influence the price of energy, a feature selection technique is applied to identify the most relevant attributes in pricing. The C5.0 and ANN algorithms are used for classification. The California ISO market is used as a test system to demonstrate the proposed approach. The results show that an ensemble model of C5.0 and ANN produced high accuracy, and can be an interesting tool to explain the occurrence of negative prices. Index Terms-- classification, decision tree, electricity price, feature selection, LMP, multilayer perceptron. I. INTRODUCTION With the increased penetration of renewable energy in the electric grid, the occurrence of negative LMPs in the electric grid has increased. The impact of that is not only limited to individual price nodes, but even the prices at Zonal and Hub level get affected. Thus, it become ever more important to understand what system conditions lead to negative LMPs. This will help power plant operators to better manage the operation of their generating plant. It will also enable the system operator to economically and reliably operate the grid. The future prediction of electric power system operating conditions such as load and related energy prices is an important activity for risk management in energy markets. There are many studies done on the subject in [1]-[4] literature. However, the focus of this paper is to classify power prices and not predict future prices. The most common techniques found in the literature for the energy price feature classification are data mining [5], Support Vector Machines [6], regression and classification trees [7] and neural networks [8]. In this context, this paper proposes a LMP price classification method using decision tree. Predictions are made with respect to whether the LMP is below a threshold level for given system conditions. The decision tree algorithm used is C5.0. These results are compared with artificial neural networks (ANN), another classification technique commonly used. Also, ensemble models combining C5.0 and ANN are analyzed. The main contributions of this paper is to create a model which can be used to determine the occurrence of negative LMP. The model can be used by independent power producers to mitigate the risk of negative prices and curtailment of plant output. The rest of the paper is organized as follows. In Section II, a review of decision tree classification methods is presented. Details of the proposed price classification method are discussed in Section III. Section IV presents the numerical results and the classifications rules obtained. Finally, the conclusions are addressed in Section V. II. CLASSIFICATION ALGORITHMS The classification, prediction, clustering, and feature selection tasks can be performed by a Decision Tree (DT) [9]. Its structure are transparent, intuitive and easy to interpret. Its representation enables users to see the impact of different features on target variables. The DT is constructed by repeated splits of subsets into descendant subsets. In each split an inquiry about the input variables is made, and the answers lead to each descendant subset. The subsets are called nodes. A leaf node is a node without further splits, and has an output value and a rule, which can be expressed in the form of if-then. The DT acts as a classification model applied to existing data. Once DT is applied to new data, with unknown classes, it gives a prediction of the class. In this sense, a DT tree is used in this paper to build a classification model for LMP price classes. Various DT algorithms are based on a greedy top-down recursive partitioning strategy. Those methods uses different variants of impurity measures, like, information gain [10], gain ratio [11], Gini-index [12] and distance-based measures [13], to select an input attribute to be associated with an internal node /17 $ IEEE DOI /GreenTech

2 The most used DT induction algorithms are ID3 (Interactive Dichotomiser 3), C4.5 and CART (classification and regression tree) [10], [11], [12]. The algorithm C5.0 is the current commercial successor of C4.5 and is implemented in this paper. III. PROPOSED METHODOLOY The proposed methodology consists of 5 stages. In the first stage; the dependent and independent variables are selected. Locational Marginal Price (LMP) is considered as the dependent variable. Under the independent variables; system load, power generation (hydro, thermal, nuclear and renewable), and as well as energy imports are considered. Figure 1 presents the five-stage classification process. rules are presented which show the boundary conditions for which the independent variables generate negative LMPs. IV. RESULTS The effectiveness of the proposed methodology is demonstrated by using the California Independent System Operator [14]. All information was taken from CAISO Market data, such as LMP, load, imports and generation data (such as wind, solar, hydro, thermal). The LMP and the independent variables range from 1/1/2013 to 09/30/2016. The LMP location is chosen as Hub SP-15, which is a liquid and major trading hub. Figure 1. 5 stage classification process. In the second stage; LMP prices are grouped into classes by clustering k-means technique. Group formations are tested in different amounts. The configuration that presents better results are grouped into different clusters. Details such as the cluster center, number of samples and cluster percentage on the set of samples are recorded in this stage. In the third stage; feature selection is performed for the independent variables. The aim with this action is to reduce the amount of input vectors of classifiers, eliminating redundant variables and those that are not relevant. In this work, two types of classifiers were applied. The most important predictors were identified using the C5.0 decision tree and ANN. In the fourth stage of this methodology classifiers are modeled. For each of the proposed classifier (C5.0 and ANN) a model is developed to avoid over-training by partitioning the input space in 80% of samples for training and 20% of samples for test. The target price is LMP, and the input space are the selected predictors in the previous step. Finally, in the fifth stage; a hybrid classifier model is created that combines the forces of C5.0 model with ANN. Both for individual models, and for the ensemble model, classifying capabilities are evaluated. At the end, the relevant Figure 2. Histogram of negative LMP. Figure 2, shows the histogram of negative LMP observed over the period of roughly 4 years from 1/1/2013 to 09/30/2016. From the histogram it can be observed that it has a significant left tail. Further, it also shows that there are many hours during which the LMP is in the range of $-25 to $0. In Figure 3, the frequency of negative LMPs occurring at SP-15 Hub can be observed. The occurrence of negative LMPs have increased over the years. Infact, from year 2013 to year 2016, the frequency of occurrence of negative LMP has become little more than double. This definitely means that there is some structural change happening in the CAISO system which is leading to increase in occurrence of negative LMP. The frequency of negative LMPs is generally higher during the months of March-May as shown in Figure 4. On looking more granularly on hourly basis in Figure 5, it can be observed that there s more frequency of negative LMPs between the hours 09hr-14hr. Further it can be observed that frequency has increased over years. 152

3 Figure 5. Frequency of negative LMP by hour for different years. Figure 3. Frequency of negative LMP by year. Year TABLE I. YEARLY SUMMARY OF LMPS AT SP-15 HUB Hub Sum of Negative LMP ($/MW) Average of Negative LMP ($/MWh) Min of Negative LMP ($/MWh) 2013 SP15-3, SP15-6, SP15-15, SP15-6, Figure 4. Frequency of negative LMP by month for different years. TABLE I, shows that statistical summary of negative LMPs at SP-15 hub. It can be observed that not only the frequency of negative LMPs is high, their magnitude is also significant. During the year 2015, the sum of negative LMPs was $/MW(-15,143). This is a significant impact, especially to power plant producers whose revenues get impacted by this. The most negative LMP that was observed in that year for an hour was (-305) $/MWh. These numbers are hard to be overlooked. Therefore, a Decision Tree model is developed to understand system conditions that most likely have the probability of causing negative LMPs. For the investigation for this large dataset, the data mining workbench IBM SPSS Modeler 18 was used. This software was used to develop all the techniques to plan, develop and test the proposed models. At first feature selection process is utilized, which lead to important independent variables. The important variables are solar generation, wind generation, hydro generation, and load. Next, the decision tree model is built by using 80% of the randomly chosen dataset to train the model. Then the remaining 20% of the dataset is used the test the accuracy of the model. To check the accuracy of the model, percentage classification accuracy (PCA) is used. The PCA works as the overall measure of classification error and can be defined in (1). N tot N mis PCA = 100 (1) N tot Where N tot are the total number of samples and N mis are the number of misclassified samples. TABLE II, shows the PCA results arising from the application of equation (1) obtained with the individual models and with the ensemble model. 153

4 PCA (%) TABLE II. PCA RESULTS C5.0 ANN Ensemble Model Training Test Training Test Training Test TABLE III, shows the rules obtained from using decision tree that explains how various system conditions of the input variables lead to negative LMP prices. Rule No Classification Rule TABLE III. CLASSIFICATION RULES If TotalLoad<=25,425 HydroGen>1,523 HydroGen<=1,636 SolarGen>1,544 SolarGen<=5,206 WindGen>2,380 WindGen<=3,541 If TotalLoad<=24,329 HydroGen>829 HydroGen<=1,212 SolarGen<=4,411 WindGen>2,100 WindGen<=2,321 If TotalLoad>22,972 TotalLoad<=23,302 HydroGen>829 SolarGen>585 WindGen>1,678 WindGen<=2,710 Rule No Classification Rule If TotalLoad>23,302 TotalLoad<=25,480 HydroGen>863 HydroGen<=890 SolarGen>585 SolarGen<=4,022 WindGen>1,144 WindGen<=3,653 If TotalLoad>22,066 TotalLoad<=27,353 HydroGen>1,274 HydroGen<=1,636 SolarGen<=6,197 WindGen>2,324 WindGen<=2,380 If TotalLoad<=23,082 HydroGen>2,981 SolarGen>3,305 SolarGen<=5,111 WindGen>1,869 WindGen<=3,181 Solar Load (%) = Solar Generation/Load (2) Wind Load (%) = Wind Generation/Load (3) The higher the Solar Load (%) and Wind Load (%), the more downward pressure on LMP is observed. TABLE IV, shows the solar generation as percentage of load. It can be observed that during months April- May solar load percentage is high and has been increasing over the years. TABLE IV. TOTAL SOLAR % OF LOAD BY MONTH Total Solar Load % by Month Month Jan 1.0% 2.9% 4.0% 4.6% Feb 1.6% 3.7% 6.0% 8.3% Mar 2.0% 5.1% 7.2% 8.6% Apr 2.2% 5.8% 8.5% 10.1% May 2.3% 6.0% 8.3% 11.4% Jun 2.6% 6.3% 7.7% 10.0% Jul 2.3% 5.1% 7.4% 10.1% Aug 2.7% 5.3% 7.2% 9.8% Sep 3.0% 5.2% 6.7% 10.1% Oct 3.1% 5.1% 6.1% NA Nov 2.7% 4.9% 6.4% NA Dec 2.7% 3.2% 5.0% NA TABLE V. TOTAL WIND % OF LOAD BY MONTH Total Wind Load % by Month Month Jan 2.5% 2.9% 1.0% 4.0% Feb 4.4% 5.2% 3.9% 3.4% Mar 5.8% 5.9% 4.5% 7.8% Apr 8.7% 7.4% 7.1% 7.9% May 8.6% 8.7% 9.2% 8.7% Jun 7.8% 9.1% 7.8% 7.9% Figure 6. Total CAISO load by month for different years. Figure 6, shows the CAISO system load by month for different years. It can be observed that there has not been a significant increase in load over the years. Further, the spring season, which is March-May period, can be considered as a low load demand season compared to other seasons. To understand the impact of solar and wind generation on the LMP, it s important to understand how much load is served by solar and wind generation. This can be given by: Jul 5.9% 6.0% 6.4% 7.5% Aug 5.5% 5.6% 6.5% 6.5% Sep 5.4% 4.4% 4.0% 5.0% Oct 3.9% 3.9% 3.4% NA Nov 3.2% 4.0% 3.7% NA Dec 2.3% 3.0% 5.1% NA Similarly, TABLE V, shows the wind generation as percentage of load. It can be observed that during months April-May wind load percentage is high. Thus there is 154

5 significant Load% of solar and wind combined during the April-May period. This explains the cause of high frequency of negative LMPs during these months. TABLE VI, shows solar load % at a more granular hourly level. It can be observed that during the hours of 10hr-14hr is relatively high compared to other hours. This explains the influence of solar generation on lower and negative LMPs during these hours. Further as the solar load percentage has increased over the years, so has the frequency of negative LMP. In TABLE VII, wind load % is shown at an hourly level. It can be observed that during the hours of 2hr-4hr is relatively high compared to other hours. Also, the percentage has increased over the years. This explains the impact of wind generation on negative LMPs in the early morning hours of 3hr-4hr. TABLE VI. TOTAL SOLAR % OF LOAD BY HOUR Total Solar Load % by Hour Time % 0.0% 0.0% 0.0% 2 0.0% 0.0% 0.0% 0.0% 3 0.0% 0.0% 0.0% 0.0% 4 0.0% 0.0% 0.0% 0.0% 5 0.0% 0.0% 0.0% 0.0% 6 0.0% 0.0% 0.0% 0.0% 7 0.1% 0.4% 0.6% 1.3% 8 1.4% 3.2% 4.9% 8.0% 9 3.7% 8.2% 11.9% 16.8% % 11.7% 16.2% 21.4% % 13.2% 17.9% 23.3% % 13.5% 18.2% 23.8% % 13.3% 18.0% 23.6% % 12.7% 17.3% 22.8% % 11.8% 16.1% 21.5% % 9.9% 13.6% 19.1% % 7.0% 9.6% 15.2% % 4.3% 6.1% 10.3% % 1.6% 2.4% 4.5% % 0.2% 0.3% 0.5% % 0.0% 0.0% 0.0% % 0.0% 0.0% 0.0% % 0.0% 0.0% 0.0% % 0.0% 0.0% 0.0% TABLE VII. TOTAL WIND % OF LOAD BY HOUR Total Wind Load % by Hour Time % 7.8% 6.8% 8.7% 2 7.6% 8.0% 7.4% 9.7% 3 7.5% 7.9% 7.3% 9.5% 4 7.2% 7.6% 7.0% 9.2% 5 6.8% 7.1% 6.6% 8.6% 6 6.3% 6.5% 6.0% 7.7% 7 5.5% 5.7% 5.2% 6.7% 8 4.7% 5.0% 4.5% 5.8% 9 4.2% 4.4% 4.0% 5.0% % 3.9% 3.7% 4.5% % 3.7% 3.5% 4.2% % 3.6% 3.5% 4.0% % 3.7% 3.7% 4.2% % 3.9% 3.9% 4.5% % 4.3% 4.2% 5.0% % 4.7% 4.5% 5.6% % 5.1% 4.9% 6.1% % 5.3% 5.2% 6.4% % 5.6% 5.4% 6.8% % 5.8% 5.6% 7.0% % 6.0% 5.8% 7.2% % 6.3% 6.1% 7.6% % 6.8% 6.5% 8.2% % 7.4% 7.0% 8.8% V. CONCLUSIONS Occurrence of negative power prices is a reality now. To understand the drivers of negative LMP, this paper presents a classification model. This immensely helps in establishing a boundary of system conditions that lead to negative prices. To achieve this decision tree algorithm C5.0 and ANN are investigated. In addition, an ensemble model combining C5.0 and ANN is also analyzed. The results show that the ensemble model which combines C5.0 and ANN produced high accuracy, and smaller mean percentage classification error, compared with individual method. However, C5.0 used alone also performs very well. The classification rules automatically extracted from the decision tree are very important to exploratory knowledge discovery. The proposed approach provides a powerful technique for understanding of negative prices and their consequences in the energy marketing process. This methodology can help independent power producers to 155

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