The use of computational techniques in time series forecasting is one of the most active fields in academic research. With the advent of machine learning techniques, new algorithms have been developed and often made available through libraries for large-scale use.

This study discusses some characteristics of electricity price formation for the spot electricity market in Brazil, also known as by the initials SPD (Settlement Price for the Differences), and its applications through a new methodology for time series forecasting, using Machine Learning techniques, more specifically the XGBoost algorithm.

When XGBoost is compared to ARIMA [1], it is observed that XGBoost has advantages, such as the lack of a need to preprocess the data, a fast operation speed, complete feature extraction, a good fitting effect, and high prediction accuracy. When XGBoost is compared to Deep Learning techniques [2], the main conclusion points out that boosting methods demand fewer data and features. Other studies [3], beyond time series scope, also point out that XGBoost is more suitable for tabular data, in the case of this study. The main reasons are specific features of tabular structure: irregular patterns in the target function, uninformative features, and non-rotationally-invariant data where linear combinations of features misrepresent the information.

In this study, the time series features will be passed to the model as input variables, allowing the representation of seasonality and time cycles. A variable representing the characteristics of the Brazilian Interconnected Electricity System (BSIN), from the official models NEWAVE, DECOMP, and DESSEM, is also inserted in the model. Different forecast horizons will be provided, and especially for the very short and short term, the forecast performance will be measured [4] and presented.

The BSIN is characterized by the interconnection, through the Basic Power Transmission Network, of four of the country’s subsystems: Northeast, North, South, and Southeast, the latter together with the Center-West. The interconnected system is operated centrally by the National Electric System Operator (ONS) and is integrated by different electricity generation and transmission companies, which may be public or privately owned.

The Brazilian electricity generation profile makes the system predominantly hydrothermal; that is; most of the energy consumed is generated in hydroelectric powerplants, in addition to thermal plants (nuclear, natural gas, biomass, coal, and fuel oil) and renewables such as wind and solar plants.

Data from ANEEL, published in January 2022, indicate that 60.12% of the electric energy demand is met by hydroelectric powerplants (HPP), 8.95% by thermal power plants (TPP) operating on natural gas, 5.02% by TPPs operating on liquid petroleum-derived fuels, and 1.97% by coal-fired TPPs. These Hydro and Thermal sources meet about 76% of the energy demand [5].

Renewable sources, such as wind, small hydro, and solar power plants, play an important role in the composition of the electricity generation matrix, but in the operational optimization process, the expected renewable generation from these plants is deducted directly from the expected Gross Demand for electricity and is not explicitly considered in the centralized operation optimization process.

Due to the stochastic nature of the Gross Demand and the renewable generation, this operation allows a single parcel to be presented to the hydrothermal optimization model, and this parcel is known as the Net Energy Demand, adopted as deterministic (single scenario) in the SPD calculation process.

The system’s hydrothermal characteristic impacts the electricity generation’s price since the cost of generating electricity is a function of the optimal dispatch of the hydraulic and thermal sources to minimize the cost over an operation horizon.

In pricing the SPD, the computer models used by ONS to operate the BSIN optimize the operation and calculate the Marginal Cost of Operation (MCO). These models take into account the constant changes in the operating condition of the system, especially related to meteorological issues—favorable or not of the Affluent Natural Energy (ANE) and Energy Stored (ES) in the reservoirs of the hydroelectric power plants—as well as the Unit Generation Costs (UGC) of each thermal power plant.

Decision Trees are branching structures with three types of nodes used in data classification. The root node represents the entire data set. After it, there are internal nodes, which represent the variables in the data set and the decision criteria for further branching. In summary, each internal node will contain a comparison of a given variable x_i ∈ X—also called the independent or input variable of the model—against a specific value and criterion, such as: “is x_i ≥ 23.7?” [7]. From the answer to this comparison presented at this inner node, which can assume “TRUE” or “FALSE” values, there will be a new branch to the left or right. This branching will continue until there is no more possibility to proceed, either because all variables have been entered into the model or because all samples have been correctly classified. The last node of the tree is called the leaf and consists of the target variable of the prediction commonly called the dependent variable and notated as y_i.

The most common and used structures are called CART (Classification and Regression Trees) because of their applicability in several classes of problems, which involve classification and regression.

As advantages of using this type of structure, one can list, as presented by [7]:

• Non-linearity, due to the possibility of representing complex data classification boundaries through logical branching;

• Support for categorical variables, which result in binary outcomes, TRUE or FALSE, for example;

• Interpretability, due to the easily built of a self-explanatory structure;

• Robustness, due to the possibility of exponential growth of new variables and possible tests;

• Application in regression problems, in addition to the traditional classification applications in the Data Science universe. This advantage is crucial to obtain a prediction of a numerical value, the target of this study.

The XGBoost stands for Extreme Gradient Boosting and is a scalable and distributed gradient-boosted decision tree (GBDT) machine learning library. It is built upon distributed computing and parallel tree boosting, and the model uses the following concepts: supervised machine learning, decision trees, ensemble learning, and gradient boosting.

In this study, two XGBoost model metrics will be assessed. The first is called Weight and represents the frequency of use of which variable to generate new branches. A higher value of Weight for a variable also indicates its greater importance in the definition of the forecast model. A higher value of Weight for a variable indicates its greater importance in the definition of the forecast model.

The second is called Gain split, based on Equation (1) and indicates the average Gain value of a variable used in the creation of new branches. A higher Gain value for a variable, relative to the others also means its greater importance in generating forecasts.

L s p l i t = L E + L D − L R − γ = 1 2 [ ( ∑ i ∈ I E g i ) 2 ∑ i ∈ I E h i + λ + ( ∑ i ∈ I D g i ) 2 ∑ i ∈ I D h i + λ − ( ∑ i ∈ I R g i ) 2 ∑ i ∈ I R h i + λ ] − γ (1)

To facilitate the presentation of graphs and results, only the Southeast submarket will be addressed, but the machine learning model can also be applied to other electrical submarkets, with very similar results. The main metropolitan regions of Brazil are part of the Southeast submarket, making this chosen scenario a good example to discuss the proposed methodology.

Additionally, the performances of the very short-term and short-term forecasts were evaluated with two metrics commonly used in linear regression assessment, which are MAPE and RMSE (Mean Absolute Percentage Error and Root Mean Square Error, respectively).

A third metric was specially created by the authors and was named TAI (Trend Accuracy Index), defined according to Equation (2). This index represents the adherence between the actual hourly SPD variation, verified between subsequent hours, with the forecasted variation in these same periods. To exemplify, consider that between 00:00 and 01:00 on a given day, an increase in the SPD was predicted, and when verifying the actual SPD for the same period, it was found that the actual SPD also showed an increase. In this example, a score of 1 will be assigned for this hit, and if it is not similar, a score of 0 will be assigned.

This metric aims to provide the decision-maker with the sensibility on what to expect from the price behavior in the analysis horizon, answering with certain accuracy the question: In this horizon will the SPD go up or down?

After the analysis of all intervals, all scores are added up and the result is divided by the maximum possible score, which is 24 (number of hours in a day). The result, multiplied by 100, will represent a percentage score of the adherence between the Forecast and the Realized, in the variation of the SPD.

s c o r e i = { 1 ,   if   F o r i > F o r i + 1   and   R e a l i > R e a l i + 1 ,     or   F o r i < F o r i + 1   and   R e a l i < R e a l i + 1 0 , otherwise .

T A I = ∑ i = 1 24 s c o r e i 24 × 100 (2)

where:

F o r i = Variable of the predicted hourly SPD increase or decrease, for period i.

R e a l i = Variable of the real hourly SPD increase or decrease, for period i.

s c o r e i = grade assigned for the forecast accuracy, for period i.

This study presented the XGBoost model as an interesting tool in the projection of multivariate time series, with a relevant application in the hourly projection of the SPD for the Brazilian electricity market.

This projection encompassed different forecast horizons and proved to be flexible when incorporating temporal and BSIN variables, dealing satisfactorily with tabular-type information.

As shown in this study, the official models have an optimistic bias in the medium and long term, so there is much to evolve in the strategy presented of basing the creation of scenarios on a group of series of the SPD Week Level. Potential new studies can be developed to anticipate this bias more consistently by including other variables that can translate potential water crises ahead, such as ANE and ES. Although the official models include these indicators in the SPD Week Level, the inclusion of specific variables for this purpose may be a promising field for further studies.

From a model robustness point of view, with the increase of samples inserted into the Learning Base, the XGBoost model will gradually become more comprehensive, serving as an important decision-making support tool.

The authors declare no conflicts of interest regarding the publication of this paper.

dos Santos, C.R.R., Castro, R., Marques, R. and da Silva, L.C.P. (2022) An Application of Decision Trees Algorithm to Project Hourly Electricity Spot Price as Support for Decision Making on Electricity Trading in Brazil. Energy and Power Engineering, 14, 327-342. https://doi.org/10.4236/epe.2022.148018