J. Cent. South Univ. Technol. (2008) 15: 726-732

DOI: 10.1007/s11771-008-0134-4

A novel recurrent neural network forecasting model for power intelligence center

LIU Ji-cheng(刘吉成), NIU Dong-xiao(牛东晓)

(School of Business Administration, North China Electric Power University, Beijing 102206, China)

Abstract: In order to accurately forecast the load of power system and enhance the stability of the power network, a novel unascertained mathematics based recurrent neural network (UMRNN) for power intelligence center (PIC) was created through three steps. First, by combining with the general project uncertain element transmission theory (GPUET), the basic definitions of stochastic, fuzzy, and grey uncertain elements were given based on the principal types of uncertain information. Second, a power dynamic alliance including four sectors: generation sector, transmission sector, distribution sector and customers was established. The key factors were amended according to the four transmission topologies of uncertain elements, thus the new factors entered the power intelligence center as the input elements. Finally, in the intelligence handing background of PIC, by performing uncertain and recursive process to the input values of network, and combining unascertained mathematics, the novel load forecasting model was built. Three different approaches were put forward to forecast an eastern regional power grid load in China. The root mean square error (E_RMS) demonstrates that the forecasting accuracy of the proposed model UMRNN is 3% higher than that of BP neural network (BPNN), and 5% higher than that of autoregressive integrated moving average (ARIMA). Besides, an example also shows that the average relative error of the first quarter of 2008 forecasted by UMRNN is only 2.59%, which has high precision.

Key words: load forecasting; uncertain element; power intelligence center; unascertained mathematics; recurrent neural network

1 Introduction

So far, many methods have been used to improve the accuracy of load forecasting, such as expert system, artificial neural networks^[1-3], fuzzy analysis^[4], and rough set^[5]. However, those methods do not consider the impact of uncertainties. Dealing with uncertainty is an important aspect of power network planning. Some methods have been used to analyze uncertain information, for example, stochastic method^[6], fuzzy method, grey method^[7]. Those methods can effectively deal with random, fuzzy, and interval uncertainty. But they cannot deal with the other side of uncertain information, i.e. unascertained information^[8-10].

Firstly, on the basis of general project uncertain element transmission theory (GPUET) and considering the three characteristics of unascertained information, uncertain elements were classified. Secondly, in order to deal with uncertain information effectively and rapidly in power network planning, theoretical frameworks of power intelligence center (PIC) were established, and the corresponding mathematical definition and basic operation were given. Based on this, the UMRNN     was raised. Finally, forecasting comparisons of various methods were presented, and an example verified the efficiency of UMRNN.

2 Uncertain element definition and its mathematical operations

The GPUET^[11] is a three-dimensional structure model, which includes project application dimension, transmission path dimension and method dimension. The project application dimension mainly includes economic evaluation, comprehensive evaluation of projects, network planning; the method dimension contains analytical method, simulation, and combination and so on; and the transmission path consists of relationship, tree, hierarchical and network type, which is shown in Fig.1.

According to the basic definition of the GPUET, the uncertain element can be divided into three types: stochastic uncertain element (SUE), fuzzy uncertain  element (FUE), grey uncertain element (GUE). However, uncertain element of unascertained information, which has widely been used in network planning, has not been defined. Based on this, a new uncertain element (UE) was defined and applied to the power network planning and the next section’s model: power intelligence centre.

Fig.1 Structures of uncertain element transmission path

Real member of unascertained information is x₀ in unascertained mathematics, and unascertained information could be uniquely confirmed by the degree of belief distribution function F(x). F(x) represents distribution of subjective probability and subjective degree of the membership in different instances. So unascertained information could be expressed by a generalized number that is an interval number with addition information and is called ‘unascertained number’.

Its definition is as follows^[8]. If function F(x) satisfies the following conditions in interval [a, b]: 1) F(x) is a non-decreasing continuous function in (-∞, +∞); 2) 0≤F(x)≤1; 3) when x＜a, F(x)=0, and when x＞b, F(x)≡F(b)≤1, [a, b] and F(x) will constitute an unascertained number recorded as {[a, b], F(x)}. [a, b] is the distribution interval of unascertained number and F(x) is the distribution function. The number of F(x) is confidence level of x₀ at interval (-∞, x), and the confidence level of x₀ at interval (x_i, x_j) is F(x_i)- F(x_j).

The mathematic operations of unascertained number can refer to Ref.[8], and in this section only addition and multiplication were defined as follows.

If {[a, b], F(x)} and {[c, d], G(x)} are mutually independently continuous unascertained numbers, the following equation will be got:

 (1)

where  H(x) is the distribution of sum, and  uncertain element {[a+c, b+d], H(x)} is the sum of {[a, b], F(x)} and {[c, d], G(x)}.

Furthermore, define

  (2)

where

  (3)

is the distribution of product.

3 Power intelligence center (PIC) based on uncertain element transmission theory

The putting forward of PIC is inspired by enterprise dynamic alliance and business intelligence center^[12]. Business intelligence originated in 1990s, which is the process of collecting, synthesizing, filtering, analyzing, transmitting, comprehensively using all the enterprise’s internal and external data and making them converse into information and knowledge. Business intelligence center is based on business intelligence. The core is ‘leader’ enterprise of enterprise dynamic alliance. Its premise is to achieve the goal of promoting enterprise dynamic alliance, and its internal role in the union members is decision support, coordination and management. Its external role is representative of the interests of the organizational unit. Therefore, power generation, power transmission, the distribution sector and customers are combined, and power dynamic alliance is established according to dynamic alliance, which is adapted to power sector. At the same time, PIC is established on the basis of structure of power dynamic alliance, the main indicators of power grid are analyzed intelligently, such as load, price, etc. Load is the most important indicator to be forecasted when considering uncertain elements. When dealing with uncertain elements, different uncertain degrees^[11] are calculated for different network structure, which is based on GPUET model and different types of uncertain element^[11]. The load should be forecasted more preciously through adjusting the parameters of intelligence center by uncertain degree. The structure of uncertain processing of PIC is shown in Fig.2.

4 Novel uncertain element transmission neural network forecasting model for PIC based on unascertained mathematics

Recurrent neural networks are neural networks with one or more feedback loops. Elman’s recurrent neural network is one of them, and its capability of processing is better than that of recurrent neural network. On the basis of Elman’s recurrent neural network structure, uncertain element was cited, then the novel recurrent neural network based on unascertained mathematics (UMRNN) was proposed.

UMRNN network contains a recurrent connection

Fig.2 Structure of uncertain processing of PIC

layer formed by the layer from hidden neurons to convergence units. Those convergence units store output units of hidden neurons for one time step, and then feed them back to the input layer. Besides, the input layer of UMRNN includes two sections: one is the data needed to be forecasted, the other one is the size of uncertain element in PIC. The size of uncertain element with real number expression can be converted into unascertained number expression by means of the following transforming relation^[8]

 (a∈R)                      (4)

where  R is the real number set, and all unascertained number set is∈R. Let a correspond to the unascertained number {[a, a], F_a(t)}, that is, a?{[a, a], F_a(t)}. This relationship is expressed by K. The mathematical operation of unascertained number is the same as definition of Section 2. Then, UMRNN model is shown in Fig.3.

In Fig.3, x_i(t-1) is the ith data predicted before processing recurrent neural network; {[r_i, r_i], is the ith uncertain element; w_{ai, j} is the weight from the ith waiting node to the jth node of the hidden layer;  is the weight from the ith uncertain element to the jth node of the hidden layer; z_i(t) is the ith data predicted through weighting and improving uncertain element; Φ is process function of neural network, which may be linear function or sigmoid; x_i(t) is the ith data to be predicted after completing recurrent network improvement;  is the weight of the ith node from hidden layer to output layer; s(t) is the function after weighting; y(t) is the forecast data or vector. Variables in Fig.3 can be expressed mathematically as

 j=1, …, n          (5)

                             (6)

                              (7)

Fig.3 PIC Intelligence handing background based on UMRNN

                               (8)

Since there is no feedback in the output layer of Elman’s network, the weight update for this layer is done by standard error backpropagation:

                  (9)

where  μ is the step size parameter; e(t) is the standard error. For hidden layer, there exists

    (10)

If is defined as partial derivative of state variable x_k(t), whose weight Δw_{ai, j}(t) can be revised as

      (11)

can be extended as follows:

      (12)

where  δ_kj is Kronecker delta, and

                        (13)

Similarly,

   (14)

      (15)

Those recursive equations describe process of nonlinear dynamical learning, whose initial conditions are specified as

                         (16)

5 Example

To demonstrate effectiveness and accuracy of the proposed algorithm, power load which is one of the critical factors of PIC was predicted mainly, and other factors such as price, customer credit risk and so on were not analyzed. According to monthly largest electricity load data of a province power grid load in East China from May 2005 to December 2007, and considering meteorological factors that impact the load, for example, temperature, humidity, etc, experts evaluation values of those factors impacting on load were chosen as uncertain element input variables of UMRNN. Load was respectively forecasted by traditional time-series model ARIMA, neural network model BPNN, and UMRNN model. During the forecasting process, on one hand, load from July 2007 to December 2007 was forecasted on the basis of actual load from May 2005 to June 2007, and the forecasted accuracies of those three forecasting approaches were compared through analyzing their errors. On the other hand, according to the data from May 2005 to December 2007, the load of January 2008 to April 2008 was forecasted by the most precise model, and then the errors were analyzed through the latest observed data in the first quarter of 2008.

Data were analyzed by computer (AMD Athlon X2 1.8G, 2G memory), operation system was Windows Vista, data training platform was Matalb7.0, and initial and time series analysis data were processed by SPSS13.0. When data were trained by the neural network, training numbers of BPNN and UMRNN were set to  hidden layer functions of neural network were all set to sigmoid functions, output function was linear function, and output was a node. Because the more the hidden layer neurons are, the higher the accuracy close to the target function is, the hidden layer neurons number of NN was equal to 20, momentum factor was equal to 0.2, learning factor was equal to 1.0. In addition, the input data of neural network could be standardized in the following expression:

                       (17)

where  x(t) is the actual load at time t; x′(t) is the standardized load; x_max(t) is the maximum of actual load; x_min(t) is the minimum of actual load.

In order to measure the forecast accuracy of those models, the definitions of three errors were used: the relative error (E_R), the standard deviation error (E_SD), and the root mean square error (E_RMS). These three errors could be expressed by the following formulas:

                           　(18)

　                  (19)

　            (20)

where  x(t) is the actual load at time t; is the forecasted load at time t; n is the number of data to be forecasted.

According to the analysis of PIC and UMRNN, and based on the data from May 2005 to June 2007, the load data from July 2007 to December 2007 were forecasted by ARIMA, BPNN and UMRNN, and the errors were calculated. The results are listed in Tables 1 and 2.

Table 1 Actual and forecasted load from July 2007 to December 2007 using three different approaches

Table 2 Errors of load from July 2007 to December 2007 by using three different approaches

It can be seen from Tables 1 and 2 that the forecasted load of BPNN is closer to the actual load data than that of ARIMA. Although ARIMA considers seasonal change, BPNN can improve forecasting accuracy according to the constantly training network. In addition, forecasting data of UMRNN are closer to actual values than those of BPNN because in the construction of neural network, not only impact of uncertain elements is considered, but also noise of the input data can be dealt with in the recurrent structure network. The corresponding curves from July 2007 to December 2007 are shown in Fig.4.

Fig.4 Forecasting and actual curves at load using ARIMA, BPNN, UMRNN from July 2007 to December 2007

Comparing E_R of those three models, the relative error of UMRNN is the least. For example, the forecasted E_R in August 2007 as follows: E_R of ARIMA is 6.37%, that of BPNN is 3.79%, and that of the UMRNN is 2.13%. Obviously, forecasting precision of UMRNN is the highest. Besides, as for E_SD and E_RMS of those three models, BPNN has the highest E_SD, which shows that data forecasted by BPNN has greater volatility, and its network structure needs to be improved. The size of E_RMS is used to measure the forecast precision, 100 is basis point of E_RMS. And the closer the absolute value to 100, the higher the forecast precision. Tables 1 and 2 show that the forecast accuracy of UMRNN is 3% higher than that of BPNN, and 5% higher than that of ARIMA.

According to above analysis, it can be seen that the proposed model in this work has better forecast precision. In addition, the useful information for the future can be stored in Elman’s network, and compared with other neural network structures (RBF network, ART network). Elman’s network can produce patterns of space classification and the change relations in time-domain model. Therefore, Elman’s network can forecast the load more efficiently and flexibly^[13]. The load of first six months in 2008 was forecasted by load data from May 2005 to December 2007. The corresponding curves of load forecast are shown in Fig.5. The corresponding data of load forecasted are shown in Table 3.

After investigation, the latest load data of this province power grid are those in April 2008, and the new loads have been added to the curve to compare forecasting data with the observed data. The relative errors of the first four months for load forecasting in 2008 are listed on Table 3, and the average relative error is about 2.59%.

Fig.5 Load curve using UMRNN from January 2008 to June 2008

Table 3 Observed and forecasted load from January 2008 to June 2008 using UMRNN model

6 Conclusions

1) The general project uncertain element is classified by unascertained information. Four basic transmission paths are put forward, which lay foundation for processing unascertained information in power network planning.

2) A new dynamic alliance collaborative decision-making model is established. A new concept of power intelligence center (PIC) is proposed, which combines generation sector, transmission sector, distribution sector, and customers together through uncertain element transmission theory to deal with all kinds of uncertain elements in power network planning.

3) A series of mathematical definitions and operations of uncertain element are given. According to those operations and combining with Elman’s recurrent neural network, a novel load forecasting model is developed. Example shows that UMRNN model has a higher forecasting accuracy than the traditional ARIMA and BPNN, and the average relative error shows that UMRNN greatly improves the forecasting accuracy. The E_RMS of UMRNN is -99.98, and those of BPNN and ARIMA are -99.95 and -99.93, respectively. Obviously, the UMRNN is the best model.

4) PIC needs to combine with other intelligent tools when it is impacted by stochastic, fuzzy and grey uncertain elements. Blind information processing which combines those three models together will be paid much attention to in the future work.

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(Edited by CHEN Wei-ping)

Foundation item: Projects(70572090, 70373017) supported by the National Natural Science Foundation of China

Received date: 2008-04-12; Accepted date: 2008-06-23

Corresponding author: LIU Ji-cheng, Associate professor, Doctoral candidate; Tel: +86-13601030970; E-mail: ljc29@163.com