Please note this is a comparison between Version 1 by Alfredo Candela Esclapez and Version 5 by Rubing Xu.

At eElectrical power distribution networks, enerenergy is consumed at the same time as it is generated, since its storage is unfeasible on large scale. Therefore, load forecasting is required by Transmission System Operators (TSO) to manage energy grid operations and supplies. Lshort-term load forecastings are required very often everyday, then a lot of prediction calculations are executed during every forecasting interval is needed to manage energy operations. In Europe, owing to directives and new technologies, prediction systems will change from hour to be on a quarter-hour intervalbasis. Therefore, a predictive system may not have enoughdispose of sufficient time to compute all future forecasts. If all future intervals cannot bPrediction systems perform calculations throughout the day, calculating the same forecasts repeatedly as the predicted by atime approaches. However, there are forecasting load system, it will need a daily scheduts that are no more accurate than others that have already been made. If previous forecasts are used preferentially over these, then computational burden will be saved while accuracy increases. In this way, it will be possible to decide which foptimize the schedule of future intervals will be quarter-hour systems and fulfill the execution time limits. A proposed algorithm estimates which forecasted at every moment of the days provide greater accuracy than previous ones, and then it makes a forecasting schedule.

- short-term load forecasting
- computational burden
- forecasting schedule
- forecasting accuracy

Short-term load forecasting (STLF) is requirsed to manage the production, and distribution and economic of electricity, and operations ofe electric energyity markets from the current hour to the following days. Every Transmission System OIf the electricity operator (TSO) needs accurate energy forecasts, otherwise it will sufferoverestimates future electricity load, there will be extra production costs with corresponding economic lossesthat will lead to economic losses. On the other hand, if the electricity demand is underestimated, power plants may not have sufficient reserves for their generators to meet the energy demanded by the grid, compromising its stability and risking the possibility of a blackout. In addition, an accurate demand forecasts allow fort indirectly facilitates the managingement of electrical energy from renewable energies. O In addition to electricity operators, other entities require lbenefit from accurate electricity 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 iswhich 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]}. and hHybrid systems that combine neural networks with other techniques are also common ^{[8]} ^{[9]} ^{[10]} ^{[11]}.

STSOs require fast and frequenLF systems calculate forecasts frequently most likely hourly. The system must obtain fast forecasts to read , so the operator can read the results and manage the actions that adjust to future load. When operatorsThe latest measurement systems tend to use quarter-hour intervals. The STLF systems that currently work with hourly intervals chanwill considerably increase their computational burden, whenever they change to quarter-hour, t intervals. They will have to forecast four times more values due to increase of intervals per day,d granularity and they will also do this four times more often because of the reduced available time, due to an increase in frequency. This paper addresses the problem of computational burden while attempting to increase the accuracy of the STLF systems already implemented.

The Spanish transmission system operator (TSO,) is Red Eléctrica de España (REE), and it is working on hourly intervals. It needs forecasts for 19 electrical regions, which is 19 times more calculations than a single STLF system, with a total of 2.5 s for every hour that is predicted nationwide. 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 needsthere is need for a new schedule to forecast only the most useful intervals.

P Furtheviously, it was generally assumed that as researchers approach to the forecast moment in time, the forecast becomes more accurate, since the informrmore, the new schedule must be based on a criterion that numerically determines which predictions are most useful. Satisfying the need for a systematic method to optimize schedules is the main motivation available (weaof this work.

Ither and load) has more correlation withwas assumed that as we approach the forecast moment, the forecasted load becomes more accurate. However, this hypothesis does not always hold true. Sometimes, predictions calculated in the past are more accurate than recent ones. If the There is an obvious trend in which accuracy increases as more recent information (weather and load) becomes available. Nevertheless, sometimes, there seem to be some periods in which new forecasts are actually less accurate. If accuracy loss periods can be known in advance, then the unproductive forecasts made at these times can be cancelespared, saving computational effort and gaining accuracywhile achieving a more accurate forecast.

A This work aims to determine the optimal schedul fe of forecast calculations mus so that the system only computes new forecasts when an accuracy improvement is expected.

The forecast needs to be computed within a time limit; therefore, each computer has a number of maximum predictions to compulimit of N hourly values, beyond which the forecast would arrive late. This limit depends on availablthe time and computllowed and the calculation speed, which again depends on the computer itself and on 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 ea greater predictive error than some of the previous ones.

Alfredo Candela et al. ^{[12]} d

Thescr STLF fibed, for the first time, an algorithm that makes the optimal schedule of forecasts, so that the system only computes new forecasts when an accuracyeld 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]}, Himprovement isppert et al. ^{[13]}, or Hong expectedt al. ^{[14]}.

The prefore, the work presents avious work on the STLF systematic method to optimize used in this paper schedules^{[15]} according to accuracy and computational burdenompared the autoregressive and neural models used. 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.

Thresearch defined which one performs better in different contexts, being determined by the model configuration, availability of data and the use STLF ofield 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. exogenous variables. On the other hand, the proposed research took into account the performance of the same model ^{[13]},for Hdippert et al. ^{[14]}, or Hong fferent time lapset als. ^{[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 idpresea of optimizing the execution schedule cnt work could complement automatic forecasting systems, since it offers an automated extra step at the end of the modeling process, in order to reduce computational burden and increase accuracyobtain an optimized execution schedule. 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.

Apar

The STLF system from theused in this researches, during testing, is that developed by the UMH ^{[128]}, which was implementhere is not previous worked 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 ^{[15]} ^{[32]}.

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).

(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.

The result obtained by applying the proposed algorithm is a schedule, which defines the predictions to be executed 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. Therefore, the major benefit of applying the algorithm is the error reduction sparing us from calculations with worse errors than previous ones already executed. In this way, it can be applied to a system that is organized by time intervals and it is possible to choose which intervals to predict in each hour of the day.

The Figure 1 shows abhout scheduling forw to use the algorithm in a forecasting systems. The mentioned research. First, the maximum number of predictions that can be calculated per interval is obtained, which depends on available time and computing power. At the same time, the previous year can be predicted to calculate historical ^{[16][17][18][19][20][21][22][23][29][30][31]}error are the most similar works wcords. Finally, the algorithm is applied to obtain a schedule that will serve to forecast load during the next year.

**Figure 1.** Process summary.

Other schedulich tackleng alternatives have been tested to compare the performance of the predictioposed algorithm. They are explained in Table 1.

**Table 1. Scheduling options.**

Ton measure evaluation or the computhe value of a prediction, a numerical indicator called accuracy improvement expectational burden, which is required to decide the most useful (AIE) is used. As the name suggests, it reflects the expectation of improvement in accuracy of a predicted demand if it is recalculated. To calculate this parameter, historical records of predictions and then schedule thecalculated under the same conditions are used; that is, forecast execution.

Ts calculated at the same time a coof day with the same advance period.

The impulementer needs tod algorithm prioritizes the hourly forecast a set of future intervals depends on three vas according to larger AIE over the results of a full year, so only the first N values will be predicted in order to adhere to the time allowed.

Before executiables: the time required to load new input data (ng 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.

I)n order to test the proposed algorithm, the number of future intervals to forecast (n), and the time requirede year 2019 has been predicted. The accuracy average has been calculated for all the advances of all the hours of the year. Random selection performs worse for almost all cases; it is also inconsistent, so it is ruled out as a candidate. On the contrary, the proposed algorithm offers significantly better precision than the rest of the methods.

The year 2019 has been predicto compute each ed with every method. In most advances, the optimized algorithm performs better than other methods. As a final result, the year 2019 has been prediction (P). Soed with the current REE schedule, the algorithm, and by calculating all future hours. Except for the ninth day in advance, the run time (t) can be obtained with the Equalgorithm always offers better accuracy. The Optimized Algorithm has a global improvement compared to the current schedule.

Lastion (1).

$$$$

A-day selection and example applied to this equation is toptimized algorithm manage to 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 REE. It requires future load of 19 electrical regions, n. 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 wouldill 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 N of forecasts.

This research prhas desented the need for a method toveloped an algorithm that organizes the calculation schedule of a STLF system alongthroughout the day. The schedule must beobtained is adapted to the computational capacity of the computer while actually increasing the system accuracy. The main idea couldethodology 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 Spother hanish TSOd, according to results, the main ^{[12]}.

Icon addtrition, solvingbution of the work is to reduce the computational burden problemload of a predictive system without sacrificing accuracy. This will allow a transition to the quarter-hour system with an optimal execution schedule.

This respapearch showr offers a first approach to improveing 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.

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