Power load forecasts based on hybrid PSO with Gaussian and adaptive mutation and Wv-SVM

https://doi.org/10.1016/j.eswa.2009.05.011Get rights and content

Abstract

This paper presents a new load forecasting model based on hybrid particle swarm optimization with Gaussian and adaptive mutation (HAGPSO) and wavelet v-support vector machine (Wv-SVM). Firstly, it is proved that mother wavelet function can build a set of complete base through horizontal floating and form the wavelet kernel function. And then, Wv-SVM with wavelet kernel function is proposed in this paper. Secondly, aiming to the disadvantage of standard PSO, HAGPSO is proposed to seek the optimal parameter of Wv-SVM. Finally, the load forecasting model based on HAGPSO and Wv-SVM is proposed in this paper. The results of application in load forecasts show the proposed model is effective and feasible.

Introduction

The theoretical study of load forecasting of power systems started in the middle of last century, simultaneously with the flourishing of system identification and modern control theories, etc. Before that, because the scales of power systems were limited and there were many uncertain factors, the study of load forecasting had not taken shape. It was not until the 1980s that the theoretical study of mid-long term load forecasting began to occur, and a series of forecasting methods, such as AR algorithm, MA algorithm, General Exponential Smoothing algorithm, ARMA algorithm and ARIMA algorithm, had been successively developed and are widely accepted in the load forecasting of power systems at present (Chenhui, 1987). With the improvement of the grey system, manual neural network, expert system, genetic algorithm (Wu, Yan, & Yang, 2008a) and other theories and methods, the method of mid-long term load forecasting of power systems has continuously improved (Benaouda et al., 2006, Liang, 1997, Santos et al., 2007, Topalli et al., 2006, Ying and Pan, 2008). In general, most of the algorithms above are based on the time series.

Recently, SVM which was developed by Vapnik (1995) is one of the methods that receives increasing attention with remarkable results in the field of load forecasting (Hong, 2009, Pai and Hong, 2005, Wu et al., 2009). The main difference between NN and SVM is the principle of risk minimization. ANN implements empirical risk minimization (ERM) to minimize the error on the training data, while SVM implements the principle of structural risk minimization (SRM) by constructing an optimal separating hyper-plane in the hidden feature space, and using quadratic programming to find a unique solution. SVM has yielded excellent generalization performance that is significantly better than that of competing methods in load forecasts (Hong, 2009, Pai and Hong, 2005, Wu et al., 2009). However, for our used kernel functions so far, the SVM cannot approach any curve in L2(Rn) space (quadratic continuous integral space), because the kernel function which is used now is not the complete orthonormal base. This character lead the SVM cannot approach every curve in the L2(Rn) space. Similarly, the regression SVM cannot approach every function. Therefore we need find a new kernel function, and this function can build a set of complete base through horizontal floating and flexing. As we know, this kind of function has already existed, and it is the wavelet functions. The SVM with wavelet kernel function is called by wavelet SVM (WSVM). Reviewing the load forecasts literatures about support vector machine technique (Hong, 2009, Pai and Hong, 2005, Wu et al., 2009), little has been written about in the literature on application of Wv-SVM to load forecast research field.

However, the confirmation of unknown parameters of the Wv-SVM is complicated process. In fact, it is a multivariable optimization problem in a continuous space. The appropriate parameter combination of models can enhance approximating degree of the original series. Therefore, it is necessary to select an evolutionary algorithm to seek the optimal parameters of Wv-SVM. These unknown parameters have a great effect on the generalization performance of Wv-SVM. An appropriate parameter combination corresponds to a high generalization performance of Wv-SVM. Particle swarm optimization (PSO), which is an evolutionary computation technique developed by Kennedy and Eberhart (1995), is considered as an excellent technique to solve the combinatorial optimization problems (Lin et al., 2008, Shen et al., 2007, Wu et al., 2009, Wu et al., 2009, Wu, 2009, Wu et al., 2008b; Wu and Yan, 2009, Wu and Yan, in press; Yuan and Chu, 2007, Yang et al., 2007, Zhao and Yang, 2009).

PSO is based on the metaphor of social interaction and communication such as bird flocking. Original PSO is distinctly different from other evolutionary-type methods in a way that it does not use the filtering operation (such as crossover and mutation) and the members of the entire population are maintained through the search procedure so that information is socially shared among individuals to direct the search towards the best position in the search space. One of the major drawbacks of the standard PSO is its premature convergence. To overcome the shortage, there have been a lot of reported works focused on the modification PSO such as in (Lin et al., 2008, Shen et al., 2007, Wu et al., 2008b, Yuan and Chu, 2007, Zhao and Yang, 2009) to solve the parameter selection problems of SVM, but little attention is given in Wv-SVM. And then, a hybrid PSO with adaptive mutation and Gaussian mutation (HAGPSO) is proposed to optimize the parameters of Wv-SVM in this paper.

Based on the above analysis, a new load forecasting model based and Wv-SVM is proposed in this paper. Their superiority over traditional model is verified in numerical simulation. The rest of this paper is organized as follows. Section 2 introduces Wv-SVM. HAGPSO is arranged in Section 3. In Section 4 the steps of HAGPSO and forecasting method are described. Section 5 gives experimental simulation and results. Conclusions are drawn in the end.

Section snippets

Wavelet kernel theory

Let us consider a set of data points (x1,y1),(x2,y2),,(xl,yl), which are independently and randomly generated from an unknown function. Specifically, xi is a column vector of attributes, yi is a scalar, which represents the dependent variable, and l denotes the number of data points in the training set.

The support vector’s kernel function can be described as not only the product of point, such as K(x,x)=K(<x·x>), but also the horizontal floating function, such as K(x,x)=K(x-x). In fact, if

Hybrid particle swarm optimization

The confirmation of unknown parameters of the Wv-SVM is complicated process. In fact, It is a multivariable optimization problem in a continuous space. The appropriate parameter combination of models can enhance approximating degree of the original series Therefore, it is necessary to select an intelligence algorithm to get the optimal parameters of the proposed models. The parameters of Wv-SVM have a great effect on the generalization performance of Wv-SVM. An appropriate parameter combination

The procedures of HAGPSO and Wv-SVM

The HAGPSO algorithm is described in steps as follows:

Algorithm 1

  • Step 1.

    Data preparation: Training, validation, and test sets are represented as Tr, Va, and Te, respectively.

  • Step 2.

    Particle initialization and PSO parameters setting: Generate initial particles. Set the PSO parameters including number of particles (n), particle dimension (m), number of maximal iterations (kmax), error limitation of the fitness function, velocity limitation (Vmax), and inertia weight for particle velocity (w0), Gaussian distribution (N(0,

Experiment

To analyze the performance of the proposed HAGPSO algorithm, the forecast of power load series by means of the intelligence system based on HAGPSO and Wv-SVM is studied. To compare the performance of HAGPSO algorithm, the standard PSO is also adopted to optimize the parameters of Wv-SVM. The better algorithm will give the better combinational parameters of Wv-SVM. Therefore, there is a good forecasting capability provided by the better combinational parameters in the regression estimation of Wv

Conclusion

In this paper, a new load forecasting model based on HAGPSO and Wv-SVM is proposed. A new version of PSO, viz., hybrid particle swarm optimization with adaptive mutation and Gaussian mutation (HAGPSO), is also proposed to optimize the parameters of Wv-SVM. The performance of the HAGPSOWv-SVM is evaluated by means of forecasting the data of power loads, and the simulation results demonstrate that the Wv-SVM is effective in dealing with many dimensions, nonlinearity and finite samples. Moreover,

References (26)

Cited by (49)

  • A hybrid method based on neural network and improved environmental adaptation method using Controlled Gaussian Mutation with real parameter for short-term load forecasting

    2019, Energy
    Citation Excerpt :

    Higashi and Iba [53] combined Gaussian mutation with particle swarm optimization to avoid stagnation problem. Wu [54] proposed a new forecasting model based on hybrid PSO and SVM. PSO has been combined with Gaussian and adaptive mutation to enhance the efficiency of PSO.

  • Hybrid bio-Inspired computational intelligence techniques for solving power system optimization problems: A comprehensive survey

    2018, Applied Soft Computing Journal
    Citation Excerpt :

    These two drawbacks are tackled by hybrid CI techniques by incorporating bio-inspired optimization methods [146,148,150,154,155]. Support vector Machine (SVM)-based hybrid techniques used in load forecasting optimization [136,142,145,152] can effectively solve the practical problems of nonlinearity, high dimension, small sample size and local minimum point. The objective function of the UC problem is to minimize the system operation cost (SOC), where the SOC includes the fuel cost and the transition cost of all the generating units over the entire scheduling horizon [159].

View all citing articles on Scopus
View full text