1. Introduction

Short-term load forecasting (STLF) is required to manage production, distribution and economic operations of electric energy from the current hour to the following days. Every Transmission System Operator (TSO) needs accurate energy forecasts, otherwise it will suffer extra production costs with corresponding economic losses. In addition, accurate demand forecasts allow for managing electrical energy from renewable energies. Other entities require load forecasts to manage future operations, such as power marketers, independent system operators, or load aggregators.

Forecasting electricity load is a complex problem, which has been approached through various methods and from different points of view over the last few decades, which has led to a great variety of forecasting algorithms implemented in different electricity networks. Many techniques are based on neural networks ^{[1] [2] [3] [4] [5]}. Other algorithms use statistical methods ^{[6] [7]}. Hybrid systems that combine neural networks with other techniques are also common ^{[8] [9] [10] [11]}.

1.1. Main Problem

TSOs require fast and frequent forecasts to read the results and manage the actions that adjust to future load. When operators with hourly intervals change to quarter-hour, they will have to forecast four times more values due to increase of intervals per day, they will also do this four times more often because of the reduced available time. This article addresses the problem of computational burden while increasing accuracy of the STLF systems already implemented.

The Spanish TSO, Red Eléctrica de España (REE), is working on hourly intervals. It needs forecasts for 19 electrical regions, which is 19 times more calculations than a single STLF system. Due to time limits for submitting predictions, it is not always feasible to calculate all future hours. Therefore, there is a schedule that determines which future intervals are predicted during each hour of the day. However, this schedule was not made with a reasoned basis.

The REE forecasting system cannot keep the previous forecasting schedule with quarter-hour intervals, since it is too computationally heavy to work within the new time restriction. Therefore, it needs a new schedule to forecast only the most useful intervals. A numerical criterion is required to define the usefulness of forecasts, in order to design a method which decides the better calculations to execute. As a result of that need, the main motivation of this work is to make a systematic method to optimize schedules.

1.2. Solution Approach

Previously, it was generally assumed that as we approach to the forecast moment in time, the forecast becomes more accurate, since the information available (weather and load) has more correlation with the forecasted load. However, this hypothesis does not always hold true. Sometimes, predictions calculated in the past are more accurate than recent ones. If the accuracy loss can be known in advance, then the unproductive forecasts made at these times can be canceled, saving computational effort and gaining accuracy.

All forecast calculations must be computed within a time limit; therefore, each computer has a number N of maximum predictions to compute. This limit depends on available time and computation speed, which depends on the computer itself and the forecasting algorithm used. In order to select the best N forecasts that can be calculated at each moment, a method to prioritize them needs to be developed. In addition, even if all predictions can be calculated, they may be counterproductive, since some of them have larger error than previous ones. The paper related to this article describes an algorithm that makes the optimal schedule of forecasts, so that the system only computes new forecasts when an accuracy improvement is expected.

2. Literature Review

The STLF field is extensive, since innumerable works have been published for decades; consequently, reviews of the state of the art have been published, such as those made by Mamum et al. ^[12], Hippert et al. ^[13], or Hong et al. ^[14].

Other researchers ^{[15] [16] [17] [18] [19] [20] [21]} built and compared different STLF mathematical models employing error measures as performance indicators. After that, they did not consider how to apply those models in an optimized schedule, to avoid producing larger errors than past predictions that had already been calculated. J. Mohammed et al. ^[22] did something similar, which also included reliability indicators to assess the model’s performance.

Another example is the work carried out by G. Veljanovski et al. ^[23], in which they proposed a forecasting system based on a neural network. They did not consider the best time at which to obtain data and execute the computation. Weyermüller et al. ^[24] built a minimalistic adaptive neuro-fuzzy inference model. It forecasts the load of one hour 24 h before, so this research could be applied to organize the calculation schedule if more forecast hours are added to the model.

The present work could complement automatic forecasting systems, since it offers an automated extra step at the end of the modeling process, in order to obtain an optimized execution schedule. An example of automatically modeled systems is the work conducted by L. Shufen et al. ^[25], in which they proposed an algorithm to automate time series forecasting for nonexperts. The analysis proposed in this work could be applied to future works of theoretical research. For example, the research by T. Panapongpakorn et al. ^[26] or the work by D. Shuai ^[27].

Jiang et al. ^[28] examined their model for different anticipation times; they also compared different STLF models, taking into account error and computation times. However, anticipation times varied just from 5 min to 16 h ahead and they were used to assess models, in the same way that calculation times were employed to compare entire models.

There is research which focuses on reducing computational burden, such as that by A. McIlvenna et al. ^[29]. This research aims to optimize the use of a previously built forecasting system regardless of which one it is. With a different approach, M. Weimar et al. ^[30] evaluated the improvement of a STLF system according to the economic savings with an econometric model. This is an example of how improving accuracy offers benefits that overcome developing costs.

3. Methodology

3.1. Forecasting system employed

The STLF system used in this research, as testing benchmark, is the developed by the University Miguel Hernández (UMH) ^[8], which was implemented in REE. The system has been operating for more than 4 years, and during this time REE and UMH have continued to collaborate in continuous improvement efforts ^{[31] [32]}.

3.2. Computation limit

The time a computer needs to calculate a set of predictions depends on three factors: the time that it takes to load new input data (I), the number of forecasts (n), and the time that it takes to make each prediction (P). So, the run time (t) can be modeled with the linear equation (1).

Variables I and P depend on the computer and code employed. At the beginning of each hour, the forecasting system loads new input data (temperatures and previous measured load). As mentioned before, due to the limitation of accuracy or computational burden, for each execution, there is a maximum number N of predictions that can be performed without exceeding the response time limit. Therefore, for each execution period, up to N predictions with greater value can be selected.

3.3. Algorithm employment

The result obtained by applying the proposed algorithm is a schedule, which defines the forecasts to execute at each hour of the day. The algorithm does not depend on the mathematical model used, but on the errors that it makes regarding historical records. In this way, it can be applied to any system that is organized by time intervals.

The Figure 1 shows how to use and place the algorithm in a forecasting system. First, the maximum number of predictions that can be calculated per interval is obtained, which depends on available time and computing power, as discussed previously at equation (1). At the same time, the previous year can be predicted to calculate historical error records. Finally, the algorithm is applied to obtain a schedule that will serve to forecast load during the next year.

Figure 1. Process summary.

Other scheduling alternatives have been tested to compare the performance of the proposed algorithm. They are summarized in Table 1.

Table 1. Scheduling options.

4. Proposed Algorithm

To measure the value of a prediction, a numerical indicator called accuracy improvement expectation (AIE) is used. As the name suggests, it represents the expectation of improvement in accuracy of a predicted demand if it is recalculated. To calculate this parameter, historical records of predictions calculated under the same conditions are used; that is, forecasts calculated at the same time of day with the same advance period.

The implemented algorithm prioritizes the hourly forecasts according to larger AIE over the results of a full year, so only the best N forecasts will be executed in order to adhere to the time allowed. Before executing the algorithm, it is necessary to determine the number of maximum forecasts, N, that the computer employed can execute. This is determined empirically by its computational speed and the calculation time limit, as explained at equation (1).

5. Accuracy Results

The paper related to this article explains the tests to validate the proposed algorithm. The main test forecasts the year 2019 with every scheduling option, the accuracy average has been calculated for all the advances of all the hours of the year. In most advances, the optimized algorithm performs better than other methods. In addition, the Optimized Algorithm has a global improvement compared to the current schedule of the spanish TSO.

6. Computational burden

Last-day selection and optimized algorithm compute predictions under 7 min and the first one requires less time. However, the optimized algorithm offers better accuracy in most cases.

The Spanish electricity system operator requires future load of 19 electrical regions. Nowadays, the entire forecasting horizon spans up to 240 h, thus the total of future loads that can be predicted extends to 4560, which require 10.16 min. However, if the quarter-hour system is employed, the number of future intervals to forecast will multiply by four. This new system would entail 18,240 numbers to be calculated in 40.62 min, which is unfeasible since REE requires results before 7 min have passed.

According to Equation (1) and quarter-hour intervals, the maximum number of forecasts to compute in 7 min is 3140. So, there is time to forecast 165 intervals in every electrical region. Therefore 165 is the maximum value that can be used on the algorithm as number N of forecasts.

7. Conclusions

The developed research offers an algorithm that organizes the calculation schedule of a STLF system for the entire day. The schedule obtained is adapted to the computational capacity of the computer while increasing the system accuracy. The methodology can be applied to any forecasting technique, even if computational burden is not an issue because it has been proven that limiting the number of forecasts can be beneficial for accuracy, as it has been demonstrated for the case of REE.

On the other hand, according to results, the main contribution of the work is to reduce the computational load of a predictive system without sacrificing accuracy. This will allow a transition to the quarter-hour system with an optimal execution schedule. The study offers a first approach to improve forecasting systems through calculation planning. Applying a similar study to other time series prediction systems could improve them in a similar way. As future work, it is proposed to use the algorithm to plan the new quarter-hour system of the Spanish TSO.

This entry is adapted from the peer-reviewed paper 10.3390/en15103670