**2. A review of previous works**

Certain days load model (formal and informal vacations) is completely different from load model of working days of week (Saturday to Wednesday), but is very similar to its near Fridays. Short-term load forecasting by using fuzzy system cannot have a good function for load forecasting of days by itself since load model of special off-days has a big difference to a usual days. As usual days load model is different regarding the surface and the shape of curve, therefore we need an expert system for adjusting the primary forecasting which apply necessary information for results correction by using an expert person's experience.

On the other hand the power price is a signal with high frequency at competitive market; multi season changes, calendar effect weekends and formal vacation) and the high percentage of unusual prices are mostly during periods of demand increase [8]. The behavior of load curve for different week days is different and in sequential weeks is similar to each other. In this paper, authors use ARMA1 and ANFIS2 models for power signal forecasting. A compound method is also suggested in [9] based on neural network that forecast power price and load simultaneously. In [10, 11], PSO3 has been used for forecasting that in these papers it is in the form of long-term. In [12], the method of neural network learning and SVR4 is presented in order to a faster forecasting. A local learning method is introduced here and KNN5 is used for model optimizing. In [13], power load model is also mentioned as a non-linear model and a method is suggested that has the capability of non-linear map.

This paper purpose is introducing SVR with a new algorithm for power load forecasting. SVR and ANN are used for error reduction.

### **2.1 Short-term load forecasting methods**

As we use short term load forecasting in our method, review some important methods here.

A large variety of statistical and artificial intelligence techniques have been developed for short-term load forecasting [17].

*Similar-day approach*. This approach is based on searching historical data for days within one, two, or three years with similar characteristics to the forecast day. Similar characteristics include weather, day of the week, and the date. The load of a similar day is considered as a forecast. Instead of a single similar day load, the forecast can be a linear combination or regression procedure that can include several similar days. The trend coefficients can be used for similar days in the previous years.

*Regression methods*. Regression is the one of most widely used statistical techniques. For electric load forecasting regression methods are usually used to model the relationship of

<sup>1</sup> Autoregressive moving average

<sup>2</sup> Adaptive Neural- Fuzzy Inference System

<sup>3</sup> Particle swarm optimization

<sup>4</sup> Support vector regression

<sup>5</sup> K-nearest neighbor

consumed load was considered by entering Mashhad climate information gathered from

Certain days load model (formal and informal vacations) is completely different from load model of working days of week (Saturday to Wednesday), but is very similar to its near Fridays. Short-term load forecasting by using fuzzy system cannot have a good function for load forecasting of days by itself since load model of special off-days has a big difference to a usual days. As usual days load model is different regarding the surface and the shape of curve, therefore we need an expert system for adjusting the primary forecasting which apply necessary information for results correction by using an expert person's experience. On the other hand the power price is a signal with high frequency at competitive market; multi season changes, calendar effect weekends and formal vacation) and the high percentage of unusual prices are mostly during periods of demand increase [8]. The behavior of load curve for different week days is different and in sequential weeks is similar to each other. In this paper, authors use ARMA1 and ANFIS2 models for power signal forecasting. A compound method is also suggested in [9] based on neural network that forecast power price and load simultaneously. In [10, 11], PSO3 has been used for forecasting that in these papers it is in the form of long-term. In [12], the method of neural network learning and SVR4 is presented in order to a faster forecasting. A local learning method is introduced here and KNN5 is used for model optimizing. In [13], power load model is also mentioned as a non-linear model and a

This paper purpose is introducing SVR with a new algorithm for power load forecasting.

As we use short term load forecasting in our method, review some important methods here. A large variety of statistical and artificial intelligence techniques have been developed for

*Similar-day approach*. This approach is based on searching historical data for days within one, two, or three years with similar characteristics to the forecast day. Similar characteristics include weather, day of the week, and the date. The load of a similar day is considered as a forecast. Instead of a single similar day load, the forecast can be a linear combination or regression procedure that can include several similar days. The trend coefficients can be

*Regression methods*. Regression is the one of most widely used statistical techniques. For electric load forecasting regression methods are usually used to model the relationship of

weather forecasting department of the province.

method is suggested that has the capability of non-linear map.

SVR and ANN are used for error reduction.

**2.1 Short-term load forecasting methods** 

used for similar days in the previous years.

short-term load forecasting [17].

Autoregressive moving average

Particle swarm optimization

Support vector regression

K-nearest neighbor

Adaptive Neural- Fuzzy Inference System

 1

2

3

4

5

**2. A review of previous works** 

load consumption and other factors such as weather, day type, and customer class. Engle et al. [18] presented several regression models for the next day peak forecasting. Their models incorporate deterministic influences such as holidays, stochastic influences such as average loads, and exogenous influences such as weather. References [19], [20], [21], [22] describe other applications of regression models to loads forecasting.

*Time series*. Time series methods are based on the assumption that the data have an internal structure, such as autocorrelation, trend, or seasonal variation. Time series forecasting methods detect and explore such a structure. Time series have been used for decades in such fields as economics, digital signal processing, as well as electric load forecasting. In particular, ARMA (autoregressive moving average), ARIMA (autoregressive integrated moving average), ARMAX (autoregressive moving average with exogenous variables), and ARIMAX (autoregressive integrated moving average with exogenous variables) are the most often used classical time series methods. ARMA models are usually used for stationary processes while ARIMA is an extension of ARMA to non-stationary processes. ARMA and ARIMA use the time and load as the only input parameters. Since load generally depends on the weather and time of the day, ARIMAX is the most natural tool for load forecasting among the classical time series models. Fan and McDonald [23] and Cho et al. [24] describe implementations of ARIMAX models for load forecasting. Yang et al. [25] used evolutionary programming (EP) approach to identify the ARMAX model parameters for one day to one week ahead hourly load demand forecast. Evolutionary programming [26] is a method for simulating evolution and constitutes a stochastic optimization algorithm. Yang and Huang [27] proposed a fuzzy autoregressive moving average with exogenous input variables (FARMAX) for one day ahead hourly load forecasts.

*Neural networks*. The use of artificial neural networks (ANN or simply NN) has been a widely studied electric load forecasting technique since 1990 [28]. Neural networks are essentially non-linear circuits that have the demonstrated capability to do non-linear curve fitting. The outputs of an artificial neural network are some linear or nonlinear mathematical function of its inputs. The inputs may be the outputs of other network elements as well as actual network inputs. In practice network elements are arranged in a relatively small number of connected layers of elements between network inputs and outputs. Feedback paths are sometimes used. In applying a neural network to electric load forecasting, one must select one of a number of architectures (e.g. Hopfield, back propagation, Boltzmann machine), the number and connectivity of layers and elements, use of bi-directional or unidirectional links, and the number format (e.g. binary or continuous) to be used by inputs and outputs, and internally.

The most popular artificial neural network architecture for electric load forecasting is back propagation. Back propagation neural networks use continuously valued functions and supervised learning. That is, under supervised learning, the actual numerical weights assigned to element inputs are determined by matching historical data (such as time and weather) to desired outputs (such as historical electric loads) in a pre-operational "training session". Artificial neural networks with unsupervised learning do not require preoperational training. Bakirtzis et al. [29] developed an ANN based short-term load forecasting model for the Energy Control Center of the Greek Public Power Corporation. In the development they used a fully connected three-layer feed forward ANN and back propagation algorithm was used for training.

A Multi Adaptive Neuro Fuzzy Inference System for

inputs to outputs (i.e. curve fitting).

Short Term Load Forecasting by Using Previous Day Features 341

an input has associated with it a certain qualitative ranges. For instance a transformer load may be "low", "medium" and "high". Fuzzy logic allows one to (logically) deduce outputs from fuzzy inputs. In this sense fuzzy logic is one of a number of techniques for mapping

Among the advantages of fuzzy logic are the absence of a need for a mathematical model mapping inputs to outputs and the absence of a need for precise (or even noise free) inputs. With such generic conditioning rules, properly designed fuzzy logic systems can be very robust when used for forecasting. Of course in many situations an exact output (e.g. the precise 12PM load) is needed. After the logical processing of fuzzy inputs, a "defuzzification" process can be used to produce such precise outputs. References [37], [38],

*Support vector machines*. Support Vector Machines (SVMs) are a more recent powerful technique for solving classification and regression problems. This approach was originated from Vapnik's [40] statistical learning theory. Unlike neural networks, which try to define complex functions of the input feature space, support vector machines perform a nonlinear mapping (by using so-called kernel functions) of the data into a high dimensional (feature) space. Then support vector machines use simple linear functions to create linear decision boundaries in the new space. The problem of choosing an architecture for a neural network is replaced here by the problem of choosing a suitable kernel for the support vector machine [41]. Mohandes [42] applied the method of support vector machines for short-term electrical load forecasting. The author compares its performance with the autoregressive method. The results indicate that SVMs compare favorably against the autoregressive method. Chen et al. [43] proposed a SVM model to predict daily load demand of a month. Their program was the winning entry of the competition organized by the EU Load NITE network. Li and Fang

The load forecasting art is in selecting the most appropriate way and model for and the closest ones to the existing reality of the network among different methods and models of load forecasting, by studying and analyzing the last procedure of load and recognizing the effective factors sufficiently and maximizing each of them, and then in this way it forecasts different time periods required for the network with an acceptable approximation. It should be accepted that there is always some error in load forecasting due to the accidental load behavior but never this error should go further than the acceptable and tolerable limit. Relative accuracy has a particular importance in load forecasting in power industry. Especially when load forecasting is the basis of network development planning and power plant capacity. Since, any forecasting with open hand causes extra investment and the installation capacity to be useless and vice versa any forecasting less than real needs, faces the network with shortage in production and damages the instruments due to extra load. Consumed load model is influenced by different parameters such as weather, vacations or holidays, working days of week and etc. in order to build a short-term load forecasting system, we should consider the influence of different parameters in load forecasting, which it can be full field by a correct selection of system entries. Selection of these parameters depends on experimental observations and is influenced by the environment conditions and

[39] describe applications of fuzzy logic to electric load forecasting.

[44] also used a SVM model for short-term load forecasting.

**3. Consumed load model** 

is determined by trial and error.

Input variables include historical hourly load data, temperature, and the day of the week. The model can forecast load profiles from one to seven days. Also Papalexopoulos et al. [30] developed and implemented a multi-layered feed forward ANN for short-term system load forecasting. In the model three types of variables are used as inputs to the neural network: season related inputs, weather related inputs, and historical loads. Khotanzad et al. [31] described a load forecasting system known as ANNSTLF. ANNSTLF is based on multiple ANN strategies that capture various trends in the data. In the development they used a multilayer perceptron trained with the error back propagation algorithm. ANNSTLF can consider the effect of temperature and relative humidity on the load. It also contains forecasters that can generate the hourly temperature and relative humidity forecasts needed by the system. An improvement of the above system was described in [32]. In the new generation, ANNSTLF includes two ANN forecasters, one predicts the base load and the other forecasts the change in load. The final forecast is computed by an adaptive combination of these forecasts. The effects of humidity and wind speed are considered through a linear transformation of temperature. As reported in [32], ANNSTLF was being used by 35 utilities across the USA and Canada. Chen et al. [4] developed a three layer fully connected feed forward neural network and the back propagation algorithm was used as the training method. Their ANN though considers the electricity price as one of the main characteristics of the system load. Many published studies use artificial neural networks in conjunction with other forecasting techniques (such as with regression trees [26], time series [33] or fuzzy logic [34]).

*Expert systems*. Rule based forecasting makes use of rules, which are often heuristic in nature, to do accurate forecasting. Expert systems, incorporates rules and procedures used by human experts in the field of interest into software that is then able to automatically make forecasts without human assistance.

Expert system use began in the 1960's for such applications as geological prospecting and computer design. Expert systems work best when a human expert is available to work with software developers for a considerable amount of time in imparting the expert's knowledge to the expert system software. Also, an expert's knowledge must be appropriate for codification into software rules (i.e. the expert must be able to explain his/her decision process to programmers). An expert system may codify up to hundreds or thousands of production rules. Ho et al. [35] proposed a knowledge-based expert system for the shortterm load forecasting of the Taiwan power system. Operator's knowledge and the hourly observations of system load over the past five years were employed to establish eleven day types. Weather parameters were also considered. The developed algorithm performed better compared to the conventional Box-Jenkins method. Rahman and Hazim [36] developed a site-independent technique for short-term load forecasting. Knowledge about the load and the factors affecting it are extracted and represented in a parameterized rule base. This rule base is complemented by a parameter database that varies from site to site. The technique was tested in several sites in the United States with low forecasting errors.

The load model, the rules, and the parameters presented in the paper have been designed using no specific knowledge about any particular site. The results can be improved if operators at a particular site are consulted.

*Fuzzy logic*. Fuzzy logic is a generalization of the usual Boolean logic used for digital circuit design. An input under Boolean logic takes on a truth value of "0" or "1". Under fuzzy logic

Input variables include historical hourly load data, temperature, and the day of the week. The model can forecast load profiles from one to seven days. Also Papalexopoulos et al. [30] developed and implemented a multi-layered feed forward ANN for short-term system load forecasting. In the model three types of variables are used as inputs to the neural network: season related inputs, weather related inputs, and historical loads. Khotanzad et al. [31] described a load forecasting system known as ANNSTLF. ANNSTLF is based on multiple ANN strategies that capture various trends in the data. In the development they used a multilayer perceptron trained with the error back propagation algorithm. ANNSTLF can consider the effect of temperature and relative humidity on the load. It also contains forecasters that can generate the hourly temperature and relative humidity forecasts needed by the system. An improvement of the above system was described in [32]. In the new generation, ANNSTLF includes two ANN forecasters, one predicts the base load and the other forecasts the change in load. The final forecast is computed by an adaptive combination of these forecasts. The effects of humidity and wind speed are considered through a linear transformation of temperature. As reported in [32], ANNSTLF was being used by 35 utilities across the USA and Canada. Chen et al. [4] developed a three layer fully connected feed forward neural network and the back propagation algorithm was used as the training method. Their ANN though considers the electricity price as one of the main characteristics of the system load. Many published studies use artificial neural networks in conjunction with other forecasting techniques (such as with regression trees [26], time series

*Expert systems*. Rule based forecasting makes use of rules, which are often heuristic in nature, to do accurate forecasting. Expert systems, incorporates rules and procedures used by human experts in the field of interest into software that is then able to automatically

Expert system use began in the 1960's for such applications as geological prospecting and computer design. Expert systems work best when a human expert is available to work with software developers for a considerable amount of time in imparting the expert's knowledge to the expert system software. Also, an expert's knowledge must be appropriate for codification into software rules (i.e. the expert must be able to explain his/her decision process to programmers). An expert system may codify up to hundreds or thousands of production rules. Ho et al. [35] proposed a knowledge-based expert system for the shortterm load forecasting of the Taiwan power system. Operator's knowledge and the hourly observations of system load over the past five years were employed to establish eleven day types. Weather parameters were also considered. The developed algorithm performed better compared to the conventional Box-Jenkins method. Rahman and Hazim [36] developed a site-independent technique for short-term load forecasting. Knowledge about the load and the factors affecting it are extracted and represented in a parameterized rule base. This rule base is complemented by a parameter database that varies from site to site. The technique

The load model, the rules, and the parameters presented in the paper have been designed using no specific knowledge about any particular site. The results can be improved if

*Fuzzy logic*. Fuzzy logic is a generalization of the usual Boolean logic used for digital circuit design. An input under Boolean logic takes on a truth value of "0" or "1". Under fuzzy logic

was tested in several sites in the United States with low forecasting errors.

[33] or fuzzy logic [34]).

make forecasts without human assistance.

operators at a particular site are consulted.

an input has associated with it a certain qualitative ranges. For instance a transformer load may be "low", "medium" and "high". Fuzzy logic allows one to (logically) deduce outputs from fuzzy inputs. In this sense fuzzy logic is one of a number of techniques for mapping inputs to outputs (i.e. curve fitting).

Among the advantages of fuzzy logic are the absence of a need for a mathematical model mapping inputs to outputs and the absence of a need for precise (or even noise free) inputs. With such generic conditioning rules, properly designed fuzzy logic systems can be very robust when used for forecasting. Of course in many situations an exact output (e.g. the precise 12PM load) is needed. After the logical processing of fuzzy inputs, a "defuzzification" process can be used to produce such precise outputs. References [37], [38], [39] describe applications of fuzzy logic to electric load forecasting.

*Support vector machines*. Support Vector Machines (SVMs) are a more recent powerful technique for solving classification and regression problems. This approach was originated from Vapnik's [40] statistical learning theory. Unlike neural networks, which try to define complex functions of the input feature space, support vector machines perform a nonlinear mapping (by using so-called kernel functions) of the data into a high dimensional (feature) space. Then support vector machines use simple linear functions to create linear decision boundaries in the new space. The problem of choosing an architecture for a neural network is replaced here by the problem of choosing a suitable kernel for the support vector machine [41]. Mohandes [42] applied the method of support vector machines for short-term electrical load forecasting. The author compares its performance with the autoregressive method. The results indicate that SVMs compare favorably against the autoregressive method. Chen et al. [43] proposed a SVM model to predict daily load demand of a month. Their program was the winning entry of the competition organized by the EU Load NITE network. Li and Fang [44] also used a SVM model for short-term load forecasting.
