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. In consequence, there is 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] and hybrid systems that combine neural networks with other techniques are also common ^{[8][9][10][11]}.

2. Main Problem

TSOs require fast and frequent forecasts to read manage the actions that adjust 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.

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.

3. Solution

Previously, it was generally assumed that as researchers 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 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 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.

Alfredo Candela et al. ^[12] described, for the first time, an algorithm that makes the optimal schedule of forecasts, so that the system only computes new forecasts when an accuracy improvement is expected. Therefore, the work presents a systematic method to optimize schedules according to accuracy and computational burden. The mentioned work also presents a formula that numerically defines the value of predictions, in order to decide the best calculations to execute at every moment of the day.

4. Literature Review of Scheduling for Short-Term Load Forecasting

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. ^[13], Hippert et al. ^[14], or Hong et al. ^[15].

Other researchers ^{[16][17][18][19][20][21][22]} 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. ^[23] 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. ^[24], 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. ^[25] 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 idea of optimizing the execution schedule could complement automatic forecasting systems, since it offers an extra step at the end of the modeling process, in order to reduce computational burden and increase accuracy. An example of automatically modeled systems is the work conducted by L. Shufen et al. ^[26], 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. ^[27] or the work by D. Shuai ^[28].

Jiang et al. ^[29] 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. ^[30]. 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. ^[31] 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.

Apart from the researches ^[12], there is not previous work about scheduling for forecasting systems. The mentioned research ^{[16][17][18][19][20][21][22][23][29][30][31]} are the most similar works which tackle the prediction evaluation or the computational burden, which is required to decide the most useful predictions and then schedule the forecast execution.   

5. Computational Burden

The time a computer needs to forecast a set of future intervals depends on three variables: the time required to load new input data (I), the number of future intervals to forecast (n), and the time required to compute each prediction (P). So, the run time (t) can be obtained with the Equation (1）

$$\mathrm{t}=\mathrm{I}+\mathrm{P}·\mathrm{n}$$

An example applied to this equation is the Spanish electricity system operator REE. It requires future load of 19 electrical regions, nowadays the entire forecasting horizon spans up to 240 hours, thus the total of future loads that can be predicted extends to 4,560, 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 3,140. 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 maximum number of forecasts.

6. Conclusions

This research presented the need for a method to organize the calculation schedule of a STLF system along the day. The schedule must be adapted to the computational capacity of the computer while increasing the system accuracy. The main idea could 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 the Spanish TSO ^[12].

In addition, solving the computational burden problem will allow a transition to the quarter-hour system with an optimal execution schedule. This research shows 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.