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Short-term load forecast plays an important role in the day-to-day operation and scheduling of generating units. Season and temperature are the most important factors that affect the load change, but random factors such as big sport events or popular TV shows can change demand consumption in particular hours, which will lead to sudden load changes. A weighted time-variant slide fuzzy time-series model (WTVS) for short-term load forecasting is proposed to improve forecasting accuracy. The WTVS model is divided into three parts, including the data preprocessing, the trend training and the load forecasting. In the data preprocessing phase, the impact of random factors will be weakened by smoothing the historical data. In the trend training and load forecasting phase, the seasonal factor and the weighted historical data are introduced into the Time-variant Slide Fuzzy Time-series Models (TVS) for short-term load forecasting. The WTVS model is tested on the load of the National Electric Power Company in Jordan. Results show that the proposed WTVS model achieves a significant improvement in load forecasting accuracy as compared to TVS models.


Introduction
Load forecast has been a research topic for many decades and the accuracy of load forecast is crucial to electricity power industry due to its direct influence on generating planning.Short-term load forecast means the forecast time lead is in the range of hours to a few days ahead, which plays an important role in the day-to-day operation and scheduling of generating units.There are many factors that affect the load changes, such as calendar, weather, economical and random factors.For short-term load forecast, weather and random factors are the most important factors.Season and temperature are have the most influence to the load due to the fact that changes in temperature results in direct changes in energy consumption by heating and cooling appliances.Random factors such as big sport events or popular TV shows can change demand consumption in particular hours, which will lead to sudden load changes.A number of load forecasting models have been presented in the last decades.These models can be divided into traditional approaches [1] and the artificial intelligence methods [2].The former include regression models, time series models et al, and the latter provided many new tools for the forecasting of shortterm load such as neural networks [3][4][5], fuzzy logic [6,7], support vector machines [8], expert systems [9], hybrid method [10,11] et al.In recent years, many researchers have used fuzzy time series models to handle load forecasting problems [12][13][14][15].Liu et al. proposed a Timevariant Slide Fuzzy Time-series Model (TVS) for shortterm load forecasting [13], the TVS model only uses historical data to predict the load changes.Taking into account the affect of season, temperature, and random factors, a Weighted Time-variant Slide Fuzzy Time-series Forecasting Model (WTVS) is presented.The WTVS model is divided into three parts, including the data preprocessing, the trend training and the load forecasting.In the data preprocessing stage, the impact of random factors will be weakened by smoothing the history data.In the trend training and load forecasting stage, the seasonal factor and the weight of history data are introduced into the TVS model.The WTVS model is tested on the load of the National Electric Power Company in Jordan.Results show that the WTVS model achieves a significant improvement in load forecasting accuracy as compared to TVS models.

Time-Variant Fuzzy Time-Series
A fuzzy set A defined in the universe of discourse ,where A f is the membership function of the fuzzy set A , , f u denotes the degree of membership of be longing to the fuzzy set be the universe of discourse and also a subset of .It is assumed that i is defined on and , simultaneously and the relations are time variant.The

 is a timevariant fuzzy time series and the relation can be expressed as
, where is a time parameter affecting the forecast , which is the analysis window of time-variant models.

WTVS Model
This study aims to improve short-term load forecasting using an adaptive algorithm to adjust the analysis window automatically in the training phase of weighted historical data and heuristic rules for forecasting in the testing phase.The WTVS model includes the following steps: 1) Preprocessing historical data, 2) defining and partitioning the universe of discourse, 3) defining fuzzy sets and fuzzifying time series, 4) establishing fuzzy relationships and 5) forecasting and defuzzifying forecasting results.These steps consist of three parts: preprocessing phase, training phase and testing phase.The preprocessing phase is used to eliminate the impact of random factors by smoothing the historical data.The training phase is used for data learning.Two values are computed in each round based on the selected analysis window sizes and the value with higher prediction accuracy is determined as the forecasting value.In this process, a sequence of the analysis windows is obtained.The selection of analysis window is determined by the following adaptive algorithm (Algorithm 1).The testing phase is used for forecasting accuracy test.Two values are computed by Algorithm 3 for every testing data based on the selected analysis window sizes of testing phase.Taking into account the affect of seasonal factor, a heuristic method is proposed to select the analysis window sizes of testing phase and determine the forecasting value based on the sequence of analysis window obtained in training phase.The structure of the WTVS model is presented in Figure 1.
In the following, details of each step is described.
Step 1. Preprocessing the historical load.Random factors may cause sudden load changes.We will smooth these sudden load changes by the following method when the absolute difference value of the load is higher than a threshold.The threshold is defined as Threhold 3 1 Step 2. Fuzzified the revised historical load.
(1) Define the universe of discourse th, the midpoint of is .
Step 3. Establishing fuzzy relationships of time and and group the fuzzy time-series.
In the training phase, the fuzzy relationship is supposed to be i j A A  .In the testing phase, the fuzzy relationship is supposed to be .# i A  Generally, the trend of load in summer and winter is shown in Tables 1 and 2, respectively.For example, in summer, we can conclude that from 1 to 6 o'clock, the load have the downward trend, while from 7 to 12 o'clock, the load have the upward trend.These trends can be used to revise the forecast in the forecasting phase.
In the training phase, each round calculates values For 1 and For 2 and compares the two values to actual value Act with the better one as the forecasting load.The analysis window is determined by Algorithm 1.The computations of For 1 and For 2 are carried out by Algorithm 2. In the testing phase, the forecasting load is determined by Algorithm 3.
Algorithm 1. (slide analysis window) , where and S  are the sizes of the initial window.Flag . 1 n  (2) If the prediction accuracy computed by 1 i S  is higher than that of i , then slide the analysis window forward and the size of the analysis window plus 1, and flag .Otherwise, slide the analysis window backward and the size of the analysis window minus 1, and flag .
be the middle value of interval u .j (1) Select two initial window sizes and and   F t is the actual load at time .
Then    , and 1 s s   .Else    , and s s  .
(3) Consider the trend of load change and the sequence of flags which obtained in training phase, there are the following heuristic rules: , and the actual load at time t is bigger than that of time 1 t  , then the load at time 1 t  has the trend of increasing.At the same time pay attention to the trend in Tables 1 and 2, the forecast value is max ,and the actual load at time is smaller than that of time t 1 t  , then the load at time 1 t  has the trend of decreasing.At the same time pay attention to the trend in Tables 1 and 2, the forecast value is min

 
For 4 For 3 . 3) Else, the forecast value is the arithmetic average of For 3 and For 4.
(4) Slide the window until the end of the whole forecasting data.the purpose of the comparisons of the predictive accuracy, we use the mean absolute percentage error (MAPE) as the index of forecasting accuracy.MAPE can be defined as

Experiments and Analysis
The load of the National Electric Power Company in Jordan [12] is chosen for model validation.An empirical analysis is conducted to validate the performance of WTVS model by comparing the forecasted load with that of TVS model [13].Considering the time and season factors, we choose the data from 1 to 24 in each day as our research data.The data are divided into two parts: the training data (from 1 to 20) and the forecasting data (from 21 to 24).Table 3

Conclusions
In this paper a weighted time-variant slide fuzzy timeseries model for short-term load forecasting is proposed.The proposed model is tested for forecasting efficacy on the load of the National Electric Power Company in Jordan.Some of the heuristic knowledge generated by the WTVS model in the training phase is used to forecast unknown future values.The experimental results show that the WTVS model is more accurate than TVS model.The advantages of the WTVS model are as follows.1) External factors were considered in WTVS model.In the data preprocessing phase, the impact of random factors is weakened by smoothing the historical data.In the trend training and load forecasting phase, the seasonal factor was introduced into TVS model.
2) The most recent data from the prediction load has the greater impact.The weighted historical data are considered in WTVS model.

A
and fuzzify the data.

3 )
Repeat step (2) until the end of the training data.Algorithm 2. (training phase) Suppose that the fuzzy relationship of time and is

Table 1 . Load trend in summer.


Table 5
lists the load in 23/5 and 29/6 and the corresponding revised load by preprocessing.For shows the different forecasting accuracy in

Table 5 . Comparison under different numbers of intervals in forecasting phase.
forecasting phase under different numbers of intervals.It is shown that the forecast accuracy is influenced by the length of intervals. the