基于群集智能与算法融合的电力负荷组合预测
|
摘要
电力负荷预测是电力系统进行规划设计的基础,是电力系统运行的经济性与可靠性的保证。由于电力负荷本身具有一定的不确定性、非线性、随机性等内在特点,负荷预测一直是学术研究的前沿与热点问题。随着电力市场的发展,负荷变化规律的复杂程度增加,而传统的单一预测方法自适应能力较差,问题的复杂性与求解方法的局限性之间的矛盾更加突出,预测不一定能得到满意的结果,因此,组合预测的探讨成为当今负荷预测的研究重点之一。组合预测能综合更多信息,增强单一的预测方法之间的互补,能够更完整的描述负荷的发展规律,达到提高预测精度的目的。组合预测思路主要有两方面：其一,从模型自身的优化与完善的角度,提出将学习算法和单一预测技术相结合的组合预测,用学习算法优化单一预测模型的相关参数以提高预测模型的预测精度。其二,将多种单一预测方法得到结果按一定方式结合起来,综合利用各种预测方法所提供的相关信息,并在综合这些信息的基础之上进行最优组合。
本文针对电力负荷自身特点,引入群集智能优化计算方法以及组合预测技术,对电力负荷预测的理论与方法进行研究,取得了一定具有理论意义和实用价值的成果,主要研究工作与成果如下：
(1)针对负荷预测中对单一预测模型进行优化的问题,研究群集智能优化计算方法及其改进,提出一种新的自适应粒子群算法(FAPSO),该算法根据粒子适应值的变化动态调整惯性权重ω的数值,平衡粒子的探索和开发两种搜索行为,提高粒子搜索能力的自适应性。同时在算法中加入极值扰动策略,防止算法陷入局部最优。对FAPSO算法进行了收敛性分析与收敛性测试,由仿真结果可知,与经典粒子群算法PSO比较,FAPSO具有更快的收敛速度与更可靠的全局收敛性。
(2)提出一种由惯性权重递减型粒子群优化算法(LWPSO)与径向基函数神经网络(RBF)相结合的组合预测模型,应用粒子群算法的全局搜索能力搜索RBF神经网络的最优网络输出权值,从而达到优化RBF神经网络预测模型的目的。并利用虚拟仪器开发平台(LabVIEW)的强大数组处理能力和直观的编程方式实现了基于LWPSO优化的RBF神经网络,将训练好的网络对某实际电网进行了日整点负荷预测。仿真结果表明,该方法具有良好的预测精度和稳定性。
(3)针对有限样本信息下的负荷预测问题,提出基于自适应粒子群算法FAPSO与支持向量机SVM相结合的组合预测模型。用FAPSO算法来优化SVM模型的相关参数,通过实例仿真与分析表明,与传统的通过交叉验证试算或遗传算法等确定SVM参数的方法相比,该方法不仅有较快的运算收敛速度,而且在预测精度和稳定性等方面都有一定程度提高。
(4)研究粒子群算法PSO与模拟退火算法SA的自学习融合,提出新的优化算法NSAPSO,即在粒子群算法的寻优过程中加入模拟退火思想,结合SA算法的随机接受准则有效弥补经典粒子群算法在求解复杂问题较易陷入局部最优的缺点,使得算法在具有高效搜索的同时,能选择接受非最优解进而有能力跳出局部最优。同时在算法中加入极值扰动,增加粒子的多样性,进一步改善算法性能。由仿真测试结果,NSAPSO在对复杂多峰问题的寻优过程中体现出很好的收敛性能。
(5)针对多单一预测模型的组合问题,提出基于自学习融合算法NSAPSO与SVM模型结合的组合方式,对单一模型实现分时段变权重非线性组合,用SVM的非线性回归学习能力描述多个单一预测模型的非线性组合关系,其优点在于不用确定描述输入输出关系的具体函数表达式,避免了传统组合方式中加权系数的复杂的求取问题,同时尽可能地满足了组合方法中的非线性、变权值的需求。仿真结果证明,该组合预测模型降低了传统单一预测模型的预测风险,同时有较高的预测精度和可靠性。
Load forecasting is important for power system planning and design, system operation and management. It is the guarantee for the reliability and economic operation of electric power system. The intrinsic features of the electricity load are nonlinear, uncertainty, and randomness. For a long period scholars dedicated themselves to the research work of load forecasting technique and many effective methods have been proposed. However, the rules of load forecasting have become more complex with the development of electricity market and the traditional prediction way establish single model and has poor adaptive abilities. Traditional load forecasting method which using a single model to predict in complex conditions has obviously become less capable for the prediction task and may not be able to get the satisfactory results. Hence, the conflict between the complexity of the problem and the limitations of solving methods is more prominent. The combination Forecasting has become a focus for the research which can be integrated more information and enhanced the adaptive capability. The ideas for the combination can be summed up in two main aspects:Firstly, improve the performance of prediction model by the combination with the optimal algorithm. The algorithm is used to optimize the prediction models for better performance in forecasting. Secondly, the combination of different single prediction models by given each model certain weight. The combination model can integrate relevant information given by each model and improve the accuracy of load forecasting.
In this paper, we deeply study the theories and methods of the load forecasting by adopting the virtual forecasting technique, swarm intelligence algorithm and combination forecasting theory, and obtain a series of conclusions which have theoretical and practical value. The main research and innovative results are as follows:
(1) According to the optimization problem of the prediction model, describes the process of the standard particle swarm algorithm optimization and then proposed the improved particle swarm optimization(FAPSO). In particle swarm optimization, the search process must include explore and develop. The inertia weight needs larger step for global search at first, then the inertia weight requires gradually reduce for the local search. Take the changes of weight followed with the particles'fitness change. Map the changes in inertia weight by the exponential function. The disturbance for extreme value also added in the algorithm. The convergence analysis and the corresponding function tests for this self-adaptive particle swarm algorithm showed that the performance of FAPSO is better than that of the traditional particle swarm algorithm.
(2) This paper proposes particle swarm optimization algorithm with weight linearity reduced (LWPSO) combined with Radial Basis Function (RBF) neural network model for short term load forecasting. The global search capability of particle swarm is used to optimize the weight of Radial Basis Function neural network. Implement the process by using LabVIEW for its powerful array processing capabilities and intuitionist way of programming. Simulation results show that the prediction accuracy and stability are better than that of the traditional one.
(3) In view of the sample limited problem of load forecasting, the paper discussed support vector machine load forecasting model based on the improved particle swarm (FAPSO) optimization. The impact of the parameters for support vector machine is analyzed and then proposed FAPSO algorithm to optimize the relevant parameters of support vector machine which is found to overcome the shortcoming of the traditional way. The simulation shows that this method has faster convergence speed, and better performance compared with the traditional support vector machine parameter determination method.
(4) The global convergence capability of simulated annealing (SA) and the efficiency of particle swarm search are combined as fusion algorithm in the way of self-study. Proposed the fusion algorithm NSAPSO with the disturbance for extreme value added in. SA has the ability of choosing to receive the bad solution in order to have the ability to leap out the local optimization. The simulation shows that this algorithm has better performance for global convergence.
(5) In view of the problem of the combination of different single prediction models, support vector machines based on NSAPSO is proposed for nonlinear combined model. The model avoid the complex way of solving the weighting coefficient in the traditional combination way and it can fit with the requirement of non linear, variable weight requirement. It has a good performance and practice value for short term load forecasting.
本文针对电力负荷自身特点,引入群集智能优化计算方法以及组合预测技术,对电力负荷预测的理论与方法进行研究,取得了一定具有理论意义和实用价值的成果,主要研究工作与成果如下：
(1)针对负荷预测中对单一预测模型进行优化的问题,研究群集智能优化计算方法及其改进,提出一种新的自适应粒子群算法(FAPSO),该算法根据粒子适应值的变化动态调整惯性权重ω的数值,平衡粒子的探索和开发两种搜索行为,提高粒子搜索能力的自适应性。同时在算法中加入极值扰动策略,防止算法陷入局部最优。对FAPSO算法进行了收敛性分析与收敛性测试,由仿真结果可知,与经典粒子群算法PSO比较,FAPSO具有更快的收敛速度与更可靠的全局收敛性。
(2)提出一种由惯性权重递减型粒子群优化算法(LWPSO)与径向基函数神经网络(RBF)相结合的组合预测模型,应用粒子群算法的全局搜索能力搜索RBF神经网络的最优网络输出权值,从而达到优化RBF神经网络预测模型的目的。并利用虚拟仪器开发平台(LabVIEW)的强大数组处理能力和直观的编程方式实现了基于LWPSO优化的RBF神经网络,将训练好的网络对某实际电网进行了日整点负荷预测。仿真结果表明,该方法具有良好的预测精度和稳定性。
(3)针对有限样本信息下的负荷预测问题,提出基于自适应粒子群算法FAPSO与支持向量机SVM相结合的组合预测模型。用FAPSO算法来优化SVM模型的相关参数,通过实例仿真与分析表明,与传统的通过交叉验证试算或遗传算法等确定SVM参数的方法相比,该方法不仅有较快的运算收敛速度,而且在预测精度和稳定性等方面都有一定程度提高。
(4)研究粒子群算法PSO与模拟退火算法SA的自学习融合,提出新的优化算法NSAPSO,即在粒子群算法的寻优过程中加入模拟退火思想,结合SA算法的随机接受准则有效弥补经典粒子群算法在求解复杂问题较易陷入局部最优的缺点,使得算法在具有高效搜索的同时,能选择接受非最优解进而有能力跳出局部最优。同时在算法中加入极值扰动,增加粒子的多样性,进一步改善算法性能。由仿真测试结果,NSAPSO在对复杂多峰问题的寻优过程中体现出很好的收敛性能。
(5)针对多单一预测模型的组合问题,提出基于自学习融合算法NSAPSO与SVM模型结合的组合方式,对单一模型实现分时段变权重非线性组合,用SVM的非线性回归学习能力描述多个单一预测模型的非线性组合关系,其优点在于不用确定描述输入输出关系的具体函数表达式,避免了传统组合方式中加权系数的复杂的求取问题,同时尽可能地满足了组合方法中的非线性、变权值的需求。仿真结果证明,该组合预测模型降低了传统单一预测模型的预测风险,同时有较高的预测精度和可靠性。
Load forecasting is important for power system planning and design, system operation and management. It is the guarantee for the reliability and economic operation of electric power system. The intrinsic features of the electricity load are nonlinear, uncertainty, and randomness. For a long period scholars dedicated themselves to the research work of load forecasting technique and many effective methods have been proposed. However, the rules of load forecasting have become more complex with the development of electricity market and the traditional prediction way establish single model and has poor adaptive abilities. Traditional load forecasting method which using a single model to predict in complex conditions has obviously become less capable for the prediction task and may not be able to get the satisfactory results. Hence, the conflict between the complexity of the problem and the limitations of solving methods is more prominent. The combination Forecasting has become a focus for the research which can be integrated more information and enhanced the adaptive capability. The ideas for the combination can be summed up in two main aspects:Firstly, improve the performance of prediction model by the combination with the optimal algorithm. The algorithm is used to optimize the prediction models for better performance in forecasting. Secondly, the combination of different single prediction models by given each model certain weight. The combination model can integrate relevant information given by each model and improve the accuracy of load forecasting.
In this paper, we deeply study the theories and methods of the load forecasting by adopting the virtual forecasting technique, swarm intelligence algorithm and combination forecasting theory, and obtain a series of conclusions which have theoretical and practical value. The main research and innovative results are as follows:
(1) According to the optimization problem of the prediction model, describes the process of the standard particle swarm algorithm optimization and then proposed the improved particle swarm optimization(FAPSO). In particle swarm optimization, the search process must include explore and develop. The inertia weight needs larger step for global search at first, then the inertia weight requires gradually reduce for the local search. Take the changes of weight followed with the particles'fitness change. Map the changes in inertia weight by the exponential function. The disturbance for extreme value also added in the algorithm. The convergence analysis and the corresponding function tests for this self-adaptive particle swarm algorithm showed that the performance of FAPSO is better than that of the traditional particle swarm algorithm.
(2) This paper proposes particle swarm optimization algorithm with weight linearity reduced (LWPSO) combined with Radial Basis Function (RBF) neural network model for short term load forecasting. The global search capability of particle swarm is used to optimize the weight of Radial Basis Function neural network. Implement the process by using LabVIEW for its powerful array processing capabilities and intuitionist way of programming. Simulation results show that the prediction accuracy and stability are better than that of the traditional one.
(3) In view of the sample limited problem of load forecasting, the paper discussed support vector machine load forecasting model based on the improved particle swarm (FAPSO) optimization. The impact of the parameters for support vector machine is analyzed and then proposed FAPSO algorithm to optimize the relevant parameters of support vector machine which is found to overcome the shortcoming of the traditional way. The simulation shows that this method has faster convergence speed, and better performance compared with the traditional support vector machine parameter determination method.
(4) The global convergence capability of simulated annealing (SA) and the efficiency of particle swarm search are combined as fusion algorithm in the way of self-study. Proposed the fusion algorithm NSAPSO with the disturbance for extreme value added in. SA has the ability of choosing to receive the bad solution in order to have the ability to leap out the local optimization. The simulation shows that this algorithm has better performance for global convergence.
(5) In view of the problem of the combination of different single prediction models, support vector machines based on NSAPSO is proposed for nonlinear combined model. The model avoid the complex way of solving the weighting coefficient in the traditional combination way and it can fit with the requirement of non linear, variable weight requirement. It has a good performance and practice value for short term load forecasting.
引文
[1]康重庆,夏清,刘梅.电力系统负荷预测.北京：中国电力出版社,2007.
[2]R.J. Piers, K.Adamson.Methodologies for Load Forecasting.3rd International IEEE Conference,2006,800-806.
[3]赵希正.中国电力负荷特性分析与预测. 北京：中国电力出版社,2002.
[4]康重庆,夏清,张伯明.电力系统负荷预测研究综述与发展方向的探讨.电力系统自动化,2004,28(17)：1-11.
[5]Ranaweera D K, Karady G G, Farmer R G Economic impact analysis of load forecasting. IEEE Transactions on Power Systems,1997,12(3):1388-1392.
[6]Douglas A P, Breipohl A M, Lee F N, et al. Risk due to load forecast uncertainty in short term power system planning. IEEE Transactions on Power Systems,1998, 13(4):1493-1499.
[7]O'N eill-Carrillo E, Heydt G T, Kostelich E J. Chaotic phenomena in power systems:detection and applications. Electric Machines and Power Systems,1999, 27(1):79-91.
[8]Bates J M,Granger CW J. The Combination of Forecasts.Operational Research Quarterly,1969,20(4):451-468.
[9]Bunn D W. Forecasting with More than one Moderl. Journal of Forecasting, 1989,8(3):161-166.
[10]牛东晓,曹树华,赵磊等.电力负荷预测技术及其应用.北京：中国电力出版社,1998
[11]孙洪波. 电力网络规划. 重庆：重庆大学出版社,1996.
[12]徐国祥,胡清友.统计预测和决策. 上海：上海财经大学出版社,2005.
[13]方仍存.电力系统负荷区间预测[博士学位论文].武汉：华中科技大学,2008.
[14]陈玉祥,张汉亚.预测技术与应用.北京：机械工业出版社,1985.
[15]Shyh-Jier Huang, Kuang-Rong Shih. Short-term load forecasting via ARMA model identification including non-Gaussian process considerations. IEEE Transactions on Power Systems,2003,18(2):205-215.
[16]刘晨辉.电力系统负荷预报理论与方法.哈尔滨：哈尔滨工业大学出版社,1987.
[17]孙明玺.现代预测学.杭州：浙江教育出版社,1998.
[18]焦李成.神经网络系统理论.西安：西安电子科技大学出版社,1989.
[19]谢开贵,李春燕,周家启.基于神经网络的负荷组合预测模型研究.中国电机工程学,2002,22(7)：85-89.
[20]Hippert H.S., Pedreira C.E., Souza, R.C.. Neural networks for short-term load forecasting:A review and evaluation. IEEE Transactions on Power Systems,2001, 16(1):44-55.
[21]邓聚龙. 灰色系统理论教程. 武汉：华中理工大学出版社,1990.
[22]V.N. Vapnik, S.E. Golowich, A.J. Smola. Support vector machine for function approximation, regression estimation and signal procession. Neural Information Procession System,1996,Vol.9:281-287
[23]V.N. Vapnik. Statistical learning theory. New York:Wiley,1998.
[24]V.N. Vapnik. The Nature of Statistical Learning Theory.New York:Springer.,1995.
[25]白鹏,张喜斌,张斌,等.支持向量机理论及工程应用实例.西安：西安电子科技大学出版社,2008.
[26]Tamimi M, Egbert R. short term electric load forecasting via fuzzy neural collaboration. Electric Power Systems Research,2000,56(3):243-248.
[27]邰能灵,侯志俭,李涛,蒋传文,宋炯.基于小波分析的电力系统短期负荷预测方法.中国电机工程学报,2003,23(1)：45-50.
[28]谢敬东,唐国庆,徐高飞等.组合预测方法在电力负荷预侧中的应用.中国电力,1998,31(6)：3-5.
[29]Chang-il K, In-keun Y, Song Y H. Kohonen neural network and wavelet transformbased approach to short-term load forecasting. Electric Power Systems Research,2002,63(2):169-176.
[30]Srinivasan D, Swee S T, Chang C S, et al. Parallel neural network-fuzzy Expert system strategy for short-term load forecasting:system implementation andperformance evaluation. IEEE Transactions on Power Systems,1999, 14(3):1100-1105.
[31]康重庆,夏清,沈渝,等.电力系统负荷预测的综合模型.清华大学学报,1999,39(1)：8-11.
[32]Chongqing Kang,Xu Cheng,Qing Xia,et al. Novel Approach Considering Load-relative Factors in Short-term Load Forecasting. Electric Power Systems Research,2004,70(2):99-107.
[33]Bunn D W. Forecasting load and prices in competitive power Markets. Proceedings of IEEE,2000,88 (2):163-169.
[34]邹斌,周浩,李晓刚.电力市场原理与实践.北京：北京大学出版社,2006.
[35]Bonabeau E, Morigo M. Theraulaz. Swarm intelligence:from natural to artificial syatems. New York, Oxford University Press,1999.
[36]J. Kennedy, R. Eberhart.Swarm Intelligence. Morgan:Kaufmann Publishers,2001.
[37]Parrish,J.K. Edelstein-Keshet,L. Complexity,pattern, and evolutionary trade-offs in animal aggregation. Science,1999,284(2):99-101.
[38]GB Ermentrout,L. Edelstein-Keshet,Cellular automata approaches to biological modeling. Journal of Theoretical Biology,1993,160:97-133.
[39]Chandramouli V, Raman H. Multireservoir modeling withdynamic programming and neural networks. Journal of Water Resources Planning and Management,2001, 127(2):89-98.
[40]徐心和,么健石.有关行为主义人工智能研究综述.控制与决策,2004,19(3)：241-246.
[41]J Kennedy, R Eberhart.Particle swarm optimization[C]. In Proceeding of IEEE International Conference on Neural Networks,1995,1942-1948.
[42]J. Kennedy, R. Eberhart. Particle swarm optimization. Proceedings of the Sixth International Symposium on 4-6 Oct.1995,39-43..
[43]J. Kennedy, R. Eberhart. A new optimizer using particle swarm theory. In Proceeding sixth International Symposium on Micro Machine and Human Science, 1995,39-43.
[44]段晓东,王存睿,刘向东.粒子群算法及其应用.辽宁：辽宁大学出版社,2007
[45]R. Eberhart., Y.Shi, Particle swarm optimization:developments,applications and resources. Proceedings of IEEE Congress on Evolutionary Computation. Piscataway,2001,81v86.
[46]Kennedy,J.The behavior of particles.7th Annual Conference on evolutionary programming,San Diego,USA.1998,581-591.
[47]Eberhart R C, Kennedy J. A New optimizer using particle swarm theory. in: Proceedings of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan,1995:39-43.
[48]R. Eberhart,Y.Shi. Comparing inertia weights and constriction factors in particle swarm optimiaztion.2000 Congress on evolutionary computing,vol.l,.84v88.
[49]Kennedy J, Eberhart R C. Particle swarm optimization. in:Proceedings of the IEEE International Joint Conference on Neural Networks, IEEE Press,1995,1942-1948.
[50]Carlisle,A.and Dozier,G.An Off-The-Shelf PSO.Proceedings of the 2001 Workshop on Particle Swarm Optimization,2001,1-6.
[51]Clerc M, Kennedy J. The particle swarm:Explosion,stability and convergence in multi-dimensional complex space. IEEE Trans on Evolutionary Computation,2002, 6(1):58-73.
[52]Trelea I C. The particle swarm optimization algorithm:Convergence analysis and parameter selection.Information Processing Letters,2003,85(6):317-325.
[53]刘洪波,王秀坤,谭国真.粒子群算法的收敛性分析及其混沌改进算法.控制与决策,2006,21(6)：636-645.
[54]莫愿斌.粒子群优化算法的扩展与应用[博士学位论文]. 杭州：浙江大学,2006.
[55]Y.Shi, R.Eberhart.Parameter Selection in particle swarm optimization, Evolutionary Programming, Lecture Notes in Computer Science, Springer,1998:1447-1471.
[56]Y.Shi, R. Eberhart. A modified particle swarm optimization.IEEE International Conference of Evolutionary Computation,Anchorage,Alaska,May 1998,581-591.
[57]Ho K L, Hsu Y-Y, Yang C-C. Short-term load forecasting using a multilayer neural network with an adaptive learning algorithm. IEEE Transactions on Power systems, 1992,7(1):141-149.
[58]丁军威,孙雅明.基于混沌学习算法的神经网络短期负荷预测.电力系统自动化,2000,24(2)：32-35.
[59]Srinivasan D. Evolving artificial neural networks for short term load forecasting. Neurocomputing,1998,23(1):265-276.
[60]Bakirtzis A G, Theocharis J B, Kiartzis S J, et al. Short-term load forecasting using fuzzy neural networks. IEEE Transactions on Power Systems,1995, 10(3):1518-1523.
[61]牛东晓,邢棉,谢宏,等.短期电力负荷预测的小波神经网络模型的研究.电网技术,1999,23(4)：21-24.
[62]Park D C, EI-Sharkawi M A, Marks R J. Electric load forecasting using artificial neural network. IEEE Transactions on Power Systems,1991,6(2):442-449.
[63]Lee K Y, Cha Y T, Park J H. Short term load forecasting using an artificial neural network. IEEE Transactions on Power Systems,1992,7(1):124-130.
[64]Mori H, Yuibara A. Deterministic annealing clustering for ANN-based short-term load forecasting. IEEE Transactions on Power Systems,2001,16(3):545-551.
[65]徐秉铮,张百灵,韦岗.神经网络理论与应用.广州：华南理工大学出版社,1995.
[66]夏昌浩,向学军,胡翔勇.基于RBF神经网络和天气数据的负荷预测虚拟仪器设计.继电器,2007,35(2)：29-30.
[67]高山,单渊达.基于径向基函数网络的短期负荷预测.电力系统自动化,1999,23(5)：31-34.
[68]Hippert H S, Pedreira C E, Souza R C. Neural networks for short-term load forecasting:a review and evaluation. IEEE Transactions on Power Systems,2001, 16(1):44-55.
[69]Alsayegh 0 A. Short-term load forecasting using seasonal artificial neural networks. International Journal of Power and Engery Systems,2003,23(3):137-142.
[70]Ranaweera D K, Hubele N F, Paplexopoulos A D. Application of radial basis function neural network model for short-term load forecasting. IEEE Proceedings-Generation Transmission and Distribution,1995,142(1):45-50.
[71]Chang-il K, In-keun Y, Song Y H. Kohonen neural network and wavelet transform based approach to short-term load forecasting. Electric Power Systems Research, 2002,63(2):169-176.
[72]Chiu S L. Fuzzy model identification based on cluster estimation. Journal of Intelligent and Fuzzy Systems,1994,2(3):67-278.
[73]吴兴华,周晖.基于减法聚类及自适应模糊神经网络的短期电价预测. 电网技术,2007,31(19)：70-71.
[74]Vittorio Manirzzo.Genetic evolution of the topology and weight distri-bution of networks.IEEE Trans on Neural Networks,1994; 5(1):39-53.
[75]纪震,廖惠连,吴青华.粒子群算法及应用.北京：科学出版社,2009.
[76]Ning Lu, Jianzhong Zhou. Particle Swarm Optimization-Based RBF Neural Network Load Forecasting Model. Asia-Pacific Power and Energy Engineering Conference 2009.
[77]侯国屏.LabVIEw7.1编程与虚拟仪器设计.北京：清华大学出版社,2005.
[78]扬乐平,李海涛, 肖相生.LabView程序设计与应用. 北京：电子工业出版社,2001,262-270.
[79]Robert H. Bishop著,乔瑞萍,林欣等译.LabVIEW6i实用教程.北京：电子工业出版社,2003.
[80]岑文辉,雷友坤,谢恒.应用人工神经网络与遗传算法进行短期负荷预测.电力系统自动化,1997,21(3)：29-32.
[81]陈耀武,汪乐宇,龙洪玉.基于组合式神经网络的短期电力负荷预测模型.中国电机工程学报,2001,21(4)：79-82.
[82]潘峰,程浩忠,杨镜非,等.基于支持向量机的电力系统短期负荷预测.电网
技术,2004,38(21)：39-42.
[83]李元诚,方廷健,于尔铿.短期负荷预测的支持向量机研究.中国电机工程学报,2003,23(6)：55-59.
[84]Ning Lu, Jianzhong Zhou, Yaoyao He, et. all. Particle Swarm Optimization for Parameter Optimization of Support Vector Machine Model. The Second International Conference on Intelligent Computation Technology and Automation, 2009,283-286.
[85]谢宏,魏江平,刘鹤立短期负荷预测中支持向量机模型的参数选取和优化方法.中国电机工程学报,2006,26(2)：17-22.
[86]WangJingmin,Zhou Yamin,Chen Xiaoyu.Electricity load forecasting based on support vector machines and simulated annealing particle swarm optimization algorithm.Proceedings of the IEEE International Conference on Automation and Logistics,Jinan,China,2007,2836-2841
[87]T M Mitchell,曾华军,等译.机器学习.北京：机械工业出版社,2003.
[88]Cortes C,Vapnik V. Support vector networks. Machine Learning,1995,20(2): 273-297.
[89]郑永康.相空间重构与支持向量机结合的短期负荷预测研究[博士学位论文].成都：西南交通大学,2008.
[90]Chen Bojuen,Chang Mingmei.Load forecasting using support vector machines:a study on EUNITE competition 2001. IEEE Trans on Power Systems, 2004,19(4):1812-1830.
[91]Zhang Ming-guang. Short-term load forecasting based on support vector machines regression.Proceedings of the Fourth International Conference on Machine Learning and Cybernetics,Guangzhou,2005,8:4310-4314.
[92]J.A.Jordaan, A.Ukil. Load forecasting with support vector machines and semi-parametric method. The 8th Intelligent Data Engineering and Automated Learning, Birmingham,UK,2007,258-267.
[93]康立山,谢云,尤矢勇等.非数值并行算法--模拟退火算法.北京：科学出版社,2000.
[94]Wang Youhua, Yan Weili, et al. Adaptive simulated annealing for the optimal design of electromagnetic devices. IEEE Trans. on Magnetics,1996,32(3): 1214-1217.
[95]Hao Chen, Nicholas S.Flann and Daniel W.Watson.Parallel Genetic Simulated Annealing:A Massively Parallel SIMD Algorithm. Parallel and Distributed Systems, 1998,9(2):126-136.
[96]M.Lundy,A.Mess.Convergence of an Annealing Algorithm. Mathematical programming,1986, Vol34:111-123.
[97]Xi Ziqing and Zhou Keding. An improved simulated annealing algorithm and its application in global optimization of structure of a transformer core. Proc. of ICEF'2000, Tianjing,2000:322-324.
[98]李波.基于粒子群与模拟退火协同进化方法的电力系统无功优化[硕士学位论文].济南：山东大学,2008.
[99]王丽芳,曾建潮.基于微粒群算法与模拟退火算法的协同进化方法.自动化学报,2006,32(4)：630v636.
[100]Solis F,Wets R. Minimization by random search techniques.Mathematics of Operations Research,1981,6(5):19-30.
[101]Bates J M,Granger CW J. The Combination of Forecasts.Operational Research Quarterly,1969,20(4):451-468.
[102]Bunn D W. Forecasting with More than one Moderl. Journal of Forecasting,1989,8(3):161-166.
[103]Anandalingam G, Chen L. Linear Combination of Forecasts:A General Bayesian Model. Journal of Forecasting,1989,8(3):199-213.
[104]谢敬东,唐国庆,徐高飞,等.组合预测方法在电力负荷预测中的应用.中国电力,1998,31(6)：3-5.
[105]Bunn D w. A Bayesian Approach to the Linera Combination of Forecasts.Operations Research Quarterly,1975,26(2):325-329.
[106]谢开贵,李春燕,周家启.基于神经网络的负荷组合预测模型研究.中国电机工程学报,2002,22(7)：85-89.
[107]唐小我,曹长修.组合预测方法研究.控制与决策,1993,8(1)：35-38.
[108]Bunn D W. Forecasting load and prices in competitive power Markets. Proceedings of IEEE,2000,88 (2):163-169.
[109]康重庆,夏清,沈渝,等.电力系统负荷预测的综合模型.清华大学学报,1999,39(1)：8-11.
[110]俞集辉,李春燕,谢开贵.基于遗传算法的短期负荷组合预测模型.电网技术,2001,25(8)：20-23.
[111]谢开贵,李春燕,周家启.基于神经网络的负荷组合预测模型研究中国电机工程学报,2002,22(7)：85-89.
[112]张亚军,刘志刚,张大波.一种基于多神经网络的组合负荷预测模型电网技术.电网技术,2006,30(21)：21-25.
[113]Ning Lu, Jianzhong Zhou, Yaoyao He, et. all. Simulated Annealing Theory based Particle Swarm Optimization for Support Vector Machine Model in Short-Term Load Forecasting. International Conference on Information Engineering and Computer Science,2009.Wuhan,China
[2]R.J. Piers, K.Adamson.Methodologies for Load Forecasting.3rd International IEEE Conference,2006,800-806.
[3]赵希正.中国电力负荷特性分析与预测. 北京：中国电力出版社,2002.
[4]康重庆,夏清,张伯明.电力系统负荷预测研究综述与发展方向的探讨.电力系统自动化,2004,28(17)：1-11.
[5]Ranaweera D K, Karady G G, Farmer R G Economic impact analysis of load forecasting. IEEE Transactions on Power Systems,1997,12(3):1388-1392.
[6]Douglas A P, Breipohl A M, Lee F N, et al. Risk due to load forecast uncertainty in short term power system planning. IEEE Transactions on Power Systems,1998, 13(4):1493-1499.
[7]O'N eill-Carrillo E, Heydt G T, Kostelich E J. Chaotic phenomena in power systems:detection and applications. Electric Machines and Power Systems,1999, 27(1):79-91.
[8]Bates J M,Granger CW J. The Combination of Forecasts.Operational Research Quarterly,1969,20(4):451-468.
[9]Bunn D W. Forecasting with More than one Moderl. Journal of Forecasting, 1989,8(3):161-166.
[10]牛东晓,曹树华,赵磊等.电力负荷预测技术及其应用.北京：中国电力出版社,1998
[11]孙洪波. 电力网络规划. 重庆：重庆大学出版社,1996.
[12]徐国祥,胡清友.统计预测和决策. 上海：上海财经大学出版社,2005.
[13]方仍存.电力系统负荷区间预测[博士学位论文].武汉：华中科技大学,2008.
[14]陈玉祥,张汉亚.预测技术与应用.北京：机械工业出版社,1985.
[15]Shyh-Jier Huang, Kuang-Rong Shih. Short-term load forecasting via ARMA model identification including non-Gaussian process considerations. IEEE Transactions on Power Systems,2003,18(2):205-215.
[16]刘晨辉.电力系统负荷预报理论与方法.哈尔滨：哈尔滨工业大学出版社,1987.
[17]孙明玺.现代预测学.杭州：浙江教育出版社,1998.
[18]焦李成.神经网络系统理论.西安：西安电子科技大学出版社,1989.
[19]谢开贵,李春燕,周家启.基于神经网络的负荷组合预测模型研究.中国电机工程学,2002,22(7)：85-89.
[20]Hippert H.S., Pedreira C.E., Souza, R.C.. Neural networks for short-term load forecasting:A review and evaluation. IEEE Transactions on Power Systems,2001, 16(1):44-55.
[21]邓聚龙. 灰色系统理论教程. 武汉：华中理工大学出版社,1990.
[22]V.N. Vapnik, S.E. Golowich, A.J. Smola. Support vector machine for function approximation, regression estimation and signal procession. Neural Information Procession System,1996,Vol.9:281-287
[23]V.N. Vapnik. Statistical learning theory. New York:Wiley,1998.
[24]V.N. Vapnik. The Nature of Statistical Learning Theory.New York:Springer.,1995.
[25]白鹏,张喜斌,张斌,等.支持向量机理论及工程应用实例.西安：西安电子科技大学出版社,2008.
[26]Tamimi M, Egbert R. short term electric load forecasting via fuzzy neural collaboration. Electric Power Systems Research,2000,56(3):243-248.
[27]邰能灵,侯志俭,李涛,蒋传文,宋炯.基于小波分析的电力系统短期负荷预测方法.中国电机工程学报,2003,23(1)：45-50.
[28]谢敬东,唐国庆,徐高飞等.组合预测方法在电力负荷预侧中的应用.中国电力,1998,31(6)：3-5.
[29]Chang-il K, In-keun Y, Song Y H. Kohonen neural network and wavelet transformbased approach to short-term load forecasting. Electric Power Systems Research,2002,63(2):169-176.
[30]Srinivasan D, Swee S T, Chang C S, et al. Parallel neural network-fuzzy Expert system strategy for short-term load forecasting:system implementation andperformance evaluation. IEEE Transactions on Power Systems,1999, 14(3):1100-1105.
[31]康重庆,夏清,沈渝,等.电力系统负荷预测的综合模型.清华大学学报,1999,39(1)：8-11.
[32]Chongqing Kang,Xu Cheng,Qing Xia,et al. Novel Approach Considering Load-relative Factors in Short-term Load Forecasting. Electric Power Systems Research,2004,70(2):99-107.
[33]Bunn D W. Forecasting load and prices in competitive power Markets. Proceedings of IEEE,2000,88 (2):163-169.
[34]邹斌,周浩,李晓刚.电力市场原理与实践.北京：北京大学出版社,2006.
[35]Bonabeau E, Morigo M. Theraulaz. Swarm intelligence:from natural to artificial syatems. New York, Oxford University Press,1999.
[36]J. Kennedy, R. Eberhart.Swarm Intelligence. Morgan:Kaufmann Publishers,2001.
[37]Parrish,J.K. Edelstein-Keshet,L. Complexity,pattern, and evolutionary trade-offs in animal aggregation. Science,1999,284(2):99-101.
[38]GB Ermentrout,L. Edelstein-Keshet,Cellular automata approaches to biological modeling. Journal of Theoretical Biology,1993,160:97-133.
[39]Chandramouli V, Raman H. Multireservoir modeling withdynamic programming and neural networks. Journal of Water Resources Planning and Management,2001, 127(2):89-98.
[40]徐心和,么健石.有关行为主义人工智能研究综述.控制与决策,2004,19(3)：241-246.
[41]J Kennedy, R Eberhart.Particle swarm optimization[C]. In Proceeding of IEEE International Conference on Neural Networks,1995,1942-1948.
[42]J. Kennedy, R. Eberhart. Particle swarm optimization. Proceedings of the Sixth International Symposium on 4-6 Oct.1995,39-43..
[43]J. Kennedy, R. Eberhart. A new optimizer using particle swarm theory. In Proceeding sixth International Symposium on Micro Machine and Human Science, 1995,39-43.
[44]段晓东,王存睿,刘向东.粒子群算法及其应用.辽宁：辽宁大学出版社,2007
[45]R. Eberhart., Y.Shi, Particle swarm optimization:developments,applications and resources. Proceedings of IEEE Congress on Evolutionary Computation. Piscataway,2001,81v86.
[46]Kennedy,J.The behavior of particles.7th Annual Conference on evolutionary programming,San Diego,USA.1998,581-591.
[47]Eberhart R C, Kennedy J. A New optimizer using particle swarm theory. in: Proceedings of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan,1995:39-43.
[48]R. Eberhart,Y.Shi. Comparing inertia weights and constriction factors in particle swarm optimiaztion.2000 Congress on evolutionary computing,vol.l,.84v88.
[49]Kennedy J, Eberhart R C. Particle swarm optimization. in:Proceedings of the IEEE International Joint Conference on Neural Networks, IEEE Press,1995,1942-1948.
[50]Carlisle,A.and Dozier,G.An Off-The-Shelf PSO.Proceedings of the 2001 Workshop on Particle Swarm Optimization,2001,1-6.
[51]Clerc M, Kennedy J. The particle swarm:Explosion,stability and convergence in multi-dimensional complex space. IEEE Trans on Evolutionary Computation,2002, 6(1):58-73.
[52]Trelea I C. The particle swarm optimization algorithm:Convergence analysis and parameter selection.Information Processing Letters,2003,85(6):317-325.
[53]刘洪波,王秀坤,谭国真.粒子群算法的收敛性分析及其混沌改进算法.控制与决策,2006,21(6)：636-645.
[54]莫愿斌.粒子群优化算法的扩展与应用[博士学位论文]. 杭州：浙江大学,2006.
[55]Y.Shi, R.Eberhart.Parameter Selection in particle swarm optimization, Evolutionary Programming, Lecture Notes in Computer Science, Springer,1998:1447-1471.
[56]Y.Shi, R. Eberhart. A modified particle swarm optimization.IEEE International Conference of Evolutionary Computation,Anchorage,Alaska,May 1998,581-591.
[57]Ho K L, Hsu Y-Y, Yang C-C. Short-term load forecasting using a multilayer neural network with an adaptive learning algorithm. IEEE Transactions on Power systems, 1992,7(1):141-149.
[58]丁军威,孙雅明.基于混沌学习算法的神经网络短期负荷预测.电力系统自动化,2000,24(2)：32-35.
[59]Srinivasan D. Evolving artificial neural networks for short term load forecasting. Neurocomputing,1998,23(1):265-276.
[60]Bakirtzis A G, Theocharis J B, Kiartzis S J, et al. Short-term load forecasting using fuzzy neural networks. IEEE Transactions on Power Systems,1995, 10(3):1518-1523.
[61]牛东晓,邢棉,谢宏,等.短期电力负荷预测的小波神经网络模型的研究.电网技术,1999,23(4)：21-24.
[62]Park D C, EI-Sharkawi M A, Marks R J. Electric load forecasting using artificial neural network. IEEE Transactions on Power Systems,1991,6(2):442-449.
[63]Lee K Y, Cha Y T, Park J H. Short term load forecasting using an artificial neural network. IEEE Transactions on Power Systems,1992,7(1):124-130.
[64]Mori H, Yuibara A. Deterministic annealing clustering for ANN-based short-term load forecasting. IEEE Transactions on Power Systems,2001,16(3):545-551.
[65]徐秉铮,张百灵,韦岗.神经网络理论与应用.广州：华南理工大学出版社,1995.
[66]夏昌浩,向学军,胡翔勇.基于RBF神经网络和天气数据的负荷预测虚拟仪器设计.继电器,2007,35(2)：29-30.
[67]高山,单渊达.基于径向基函数网络的短期负荷预测.电力系统自动化,1999,23(5)：31-34.
[68]Hippert H S, Pedreira C E, Souza R C. Neural networks for short-term load forecasting:a review and evaluation. IEEE Transactions on Power Systems,2001, 16(1):44-55.
[69]Alsayegh 0 A. Short-term load forecasting using seasonal artificial neural networks. International Journal of Power and Engery Systems,2003,23(3):137-142.
[70]Ranaweera D K, Hubele N F, Paplexopoulos A D. Application of radial basis function neural network model for short-term load forecasting. IEEE Proceedings-Generation Transmission and Distribution,1995,142(1):45-50.
[71]Chang-il K, In-keun Y, Song Y H. Kohonen neural network and wavelet transform based approach to short-term load forecasting. Electric Power Systems Research, 2002,63(2):169-176.
[72]Chiu S L. Fuzzy model identification based on cluster estimation. Journal of Intelligent and Fuzzy Systems,1994,2(3):67-278.
[73]吴兴华,周晖.基于减法聚类及自适应模糊神经网络的短期电价预测. 电网技术,2007,31(19)：70-71.
[74]Vittorio Manirzzo.Genetic evolution of the topology and weight distri-bution of networks.IEEE Trans on Neural Networks,1994; 5(1):39-53.
[75]纪震,廖惠连,吴青华.粒子群算法及应用.北京：科学出版社,2009.
[76]Ning Lu, Jianzhong Zhou. Particle Swarm Optimization-Based RBF Neural Network Load Forecasting Model. Asia-Pacific Power and Energy Engineering Conference 2009.
[77]侯国屏.LabVIEw7.1编程与虚拟仪器设计.北京：清华大学出版社,2005.
[78]扬乐平,李海涛, 肖相生.LabView程序设计与应用. 北京：电子工业出版社,2001,262-270.
[79]Robert H. Bishop著,乔瑞萍,林欣等译.LabVIEW6i实用教程.北京：电子工业出版社,2003.
[80]岑文辉,雷友坤,谢恒.应用人工神经网络与遗传算法进行短期负荷预测.电力系统自动化,1997,21(3)：29-32.
[81]陈耀武,汪乐宇,龙洪玉.基于组合式神经网络的短期电力负荷预测模型.中国电机工程学报,2001,21(4)：79-82.
[82]潘峰,程浩忠,杨镜非,等.基于支持向量机的电力系统短期负荷预测.电网
技术,2004,38(21)：39-42.
[83]李元诚,方廷健,于尔铿.短期负荷预测的支持向量机研究.中国电机工程学报,2003,23(6)：55-59.
[84]Ning Lu, Jianzhong Zhou, Yaoyao He, et. all. Particle Swarm Optimization for Parameter Optimization of Support Vector Machine Model. The Second International Conference on Intelligent Computation Technology and Automation, 2009,283-286.
[85]谢宏,魏江平,刘鹤立短期负荷预测中支持向量机模型的参数选取和优化方法.中国电机工程学报,2006,26(2)：17-22.
[86]WangJingmin,Zhou Yamin,Chen Xiaoyu.Electricity load forecasting based on support vector machines and simulated annealing particle swarm optimization algorithm.Proceedings of the IEEE International Conference on Automation and Logistics,Jinan,China,2007,2836-2841
[87]T M Mitchell,曾华军,等译.机器学习.北京：机械工业出版社,2003.
[88]Cortes C,Vapnik V. Support vector networks. Machine Learning,1995,20(2): 273-297.
[89]郑永康.相空间重构与支持向量机结合的短期负荷预测研究[博士学位论文].成都：西南交通大学,2008.
[90]Chen Bojuen,Chang Mingmei.Load forecasting using support vector machines:a study on EUNITE competition 2001. IEEE Trans on Power Systems, 2004,19(4):1812-1830.
[91]Zhang Ming-guang. Short-term load forecasting based on support vector machines regression.Proceedings of the Fourth International Conference on Machine Learning and Cybernetics,Guangzhou,2005,8:4310-4314.
[92]J.A.Jordaan, A.Ukil. Load forecasting with support vector machines and semi-parametric method. The 8th Intelligent Data Engineering and Automated Learning, Birmingham,UK,2007,258-267.
[93]康立山,谢云,尤矢勇等.非数值并行算法--模拟退火算法.北京：科学出版社,2000.
[94]Wang Youhua, Yan Weili, et al. Adaptive simulated annealing for the optimal design of electromagnetic devices. IEEE Trans. on Magnetics,1996,32(3): 1214-1217.
[95]Hao Chen, Nicholas S.Flann and Daniel W.Watson.Parallel Genetic Simulated Annealing:A Massively Parallel SIMD Algorithm. Parallel and Distributed Systems, 1998,9(2):126-136.
[96]M.Lundy,A.Mess.Convergence of an Annealing Algorithm. Mathematical programming,1986, Vol34:111-123.
[97]Xi Ziqing and Zhou Keding. An improved simulated annealing algorithm and its application in global optimization of structure of a transformer core. Proc. of ICEF'2000, Tianjing,2000:322-324.
[98]李波.基于粒子群与模拟退火协同进化方法的电力系统无功优化[硕士学位论文].济南：山东大学,2008.
[99]王丽芳,曾建潮.基于微粒群算法与模拟退火算法的协同进化方法.自动化学报,2006,32(4)：630v636.
[100]Solis F,Wets R. Minimization by random search techniques.Mathematics of Operations Research,1981,6(5):19-30.
[101]Bates J M,Granger CW J. The Combination of Forecasts.Operational Research Quarterly,1969,20(4):451-468.
[102]Bunn D W. Forecasting with More than one Moderl. Journal of Forecasting,1989,8(3):161-166.
[103]Anandalingam G, Chen L. Linear Combination of Forecasts:A General Bayesian Model. Journal of Forecasting,1989,8(3):199-213.
[104]谢敬东,唐国庆,徐高飞,等.组合预测方法在电力负荷预测中的应用.中国电力,1998,31(6)：3-5.
[105]Bunn D w. A Bayesian Approach to the Linera Combination of Forecasts.Operations Research Quarterly,1975,26(2):325-329.
[106]谢开贵,李春燕,周家启.基于神经网络的负荷组合预测模型研究.中国电机工程学报,2002,22(7)：85-89.
[107]唐小我,曹长修.组合预测方法研究.控制与决策,1993,8(1)：35-38.
[108]Bunn D W. Forecasting load and prices in competitive power Markets. Proceedings of IEEE,2000,88 (2):163-169.
[109]康重庆,夏清,沈渝,等.电力系统负荷预测的综合模型.清华大学学报,1999,39(1)：8-11.
[110]俞集辉,李春燕,谢开贵.基于遗传算法的短期负荷组合预测模型.电网技术,2001,25(8)：20-23.
[111]谢开贵,李春燕,周家启.基于神经网络的负荷组合预测模型研究中国电机工程学报,2002,22(7)：85-89.
[112]张亚军,刘志刚,张大波.一种基于多神经网络的组合负荷预测模型电网技术.电网技术,2006,30(21)：21-25.
[113]Ning Lu, Jianzhong Zhou, Yaoyao He, et. all. Simulated Annealing Theory based Particle Swarm Optimization for Support Vector Machine Model in Short-Term Load Forecasting. International Conference on Information Engineering and Computer Science,2009.Wuhan,China