Research and Application of Multidimensional Dynamic Programming in Cascade Reservoirs Based on Multilayer Nested Structure

AbstractThe multidimensional dynamic programming (MDP) algorithm is a traditional method used to solve cascade reservoir operation optimization (CROO) problems, but the high dimensionality called the curse of dimensionalitycannot be ignored. In order to alleviate this problem, this paper proposes a new MDP algorithm named multilayer nested multidimensional dynamic programming (MNDP), which is based on a multilayered, nested structure. MNDP is mainly used to deal with computer memory space and computation complexity problems of MDP in CROO, and its recursive equation of reverse recursion calculation and specific calculation steps are presented in detail. This paper takes the cascade reservoirs of the Li Xianjiang River in China as an example to solve the CROO problem with the proposed MNDP. By comparing with the dynamic programming with successive approximations (DPSA) method, MNDP presents better performance in terms of power generation and the assurance rate in wet, normal, dry, and average years. The gl...

[1]  Malabika Basu,et al.  A simulated annealing-based goal-attainment method for economic emission load dispatch of fixed head hydrothermal power systems , 2005 .

[2]  M. Janga Reddy,et al.  Multipurpose Reservoir Operation Using Particle Swarm Optimization , 2007 .

[3]  Wei Wang,et al.  Study on the optimal hydropower generation of Zhelin reservoir , 2013 .

[4]  Chang Shian Chen,et al.  Multiobjective Planning of Surface Water Resources by Multiobjective Genetic Algorithm with Constrained Differential Dynamic Programming , 2007 .

[5]  Wu Zening.  Discussion on application of coopetive coevolution of differential evolution algorithm to optimal operation of cascaded reservoirs , 2012 .

[6]  Ximing Cai,et al.  Improved Dynamic Programming for Reservoir Operation Optimization with a Concave Objective Function , 2012 .

[7]  Zhu-ge Yi-si,et al.  The Application of DDDP Method to Optimal Operation for Cascade Reservoirs Based on State Transformation Matrix , 2010, 2010 International Conference on Computational and Information Sciences.

[8]  Ying Li,et al.  Numerical Solution of Continuous-State Dynamic Programs Using Linear and Spline Interpolation , 1993, Oper. Res..

[9]  M. Mathlouthi,et al.  Emploi de la série chronologique des événements secs générés dans l'optimisation de la gestion des barrages / Use of generated time series of dry events for the optimization of small reservoir operation , 2009 .

[10]  Leon S. Lasdon,et al.  Solving nonlinear water management models using a combined genetic algorithm and linear programming approach , 2001 .

[11]  K. D. W. Nandalal,et al.  Dynamic Programming Based Operation of Reservoirs: Applicability and Limits , 2007 .

[12]  Miguel A. Mariño,et al.  Reservoir Operation by Linear and Dynamic Programming , 1983 .

[13]  Chao-Lung Chiang,et al.  Optimal economic emission dispatch of hydrothermal power systems , 2007 .

[14]  Malabika Basu,et al.  An interactive fuzzy satisfying method based on evolutionary programming technique for multiobjective short-term hydrothermal scheduling , 2004 .

[15]  Mohammad Karamouz,et al.  Fuzzy-State Stochastic Dynamic Programming for Reservoir Operation , 2004 .

[16]  Christine A. Shoemaker,et al.  Estimating Maximal Annual Energy Given Heterogeneous Hydropower Generating Units with Application to the Three Gorges System , 2013 .

[17]  Samer Takriti,et al.  A decomposition approach for the fuel-constrained economic power-dispatch problem , 1999, Eur. J. Oper. Res..

[18]  Arie Hordijk,et al.  On the convergence of the average expected return in dynamic programming , 1974 .

[19]  A. A. El-Keib,et al.  Environmentally constrained economic dispatch using the LaGrangian relaxation method , 1994 .

[20]  Yuan-Yih Hsu,et al.  A hybrid artificial neural network-differential dynamic programming approach for short-term hydro scheduling , 1995 .

[21]  Sh. Momtahen,et al.  Direct Search Approaches Using Genetic Algorithms for Optimization of Water Reservoir Operating Policies , 2007 .

[22]  R. Bellman.  Dynamic programming. , 1957, Science.

[23]  Jianshi Zhao,et al.  Improved Dynamic Programming for Hydropower Reservoir Operation , 2014 .

[24]  K. D. W. Nandalal,et al.  Dynamic Programming Based Operation of Reservoirs: Incremental dynamic programming in optimal reservoir operation , 2007 .

[25]  S. Yakowitz.  Dynamic programming applications in water resources , 1982 .

[26]  Christine A. Shoemaker,et al.  Applying Experimental Design and Regression Splines to High-Dimensional Continuous-State Stochastic Dynamic Programming , 1999, Oper. Res..

[27]  Omid Bozorg Haddad,et al.  Reservoir Operation for Simultaneously Meeting Water Demand and Sediment Flushing: Stochastic Dynamic Programming Approach with Two Uncertainties , 2013 .

[28]  K. Hindi,et al.  Dynamic economic dispatch for large scale power systems: a Lagrangian relaxation approach , 1991 .

[29]  Paresh Chandra Deka,et al.  Fuzzy Neural Network Modeling of Reservoir Operation , 2009 .

[30]  Derong Liu,et al.  Generalized adaptive dynamic programming algorithm for discrete-time nonlinear systems: Convergence and stability analysis , 2013, 2013 IEEE Third International Conference on Information Science and Technology (ICIST).

[31]  Liu Zhao.  Discussion on the application of differential evolution algorithm for optimal operation of cascade reservoirs , 2008 .

[32]  Ji Chang-ming.  Optimal Reservoir Rule Curve Based on Ant Colony Optimization , 2007 .

[33]  Hao Wang,et al.  Use of parallel deterministic dynamic programming and hierarchical adaptive genetic algorithm for reservoir operation optimization , 2013, Comput. Ind. Eng..

[34]  Wan Fang.  Study of optimal operation chart of cascade reservoirs based on linking simulation with differential evolution algorithm , 2008 .

[35]  Chun-Lung Chen,et al.  Non-convex economic dispatch: A direct search approach , 2007 .

[36]  S. Baskar,et al.  Hybrid real coded genetic algorithm solution to economic dispatch problem , 2003, Computers & electrical engineering.

[37]  Liu Fang.  Application of Ant Colony Algorithm for Hydropower Dispatching Function Optimization , 2011 .

[38]  L. Papageorgiou,et al.  A mixed integer quadratic programming formulation for the economic dispatch of generators with prohibited operating zones , 2007 .

[39]  Qiuye Sun,et al.  Adaptive dynamic programming-based optimal control of unknown nonaffine nonlinear discrete-time systems with proof of convergence , 2012, Neurocomputing.

[40]  L. Liao,et al.  Convergence in unconstrained discrete-time differential dynamic programming , 1991 .

[41]  R. J. Kaye,et al.  Dynamic dispatch by constructive dynamic programming , 1998 .

[42]  Paulo Chaves,et al.  Stochastic Fuzzy Neural Network: Case Study of Optimal Reservoir Operation , 2007 .

[43]  B. J. Cory,et al.  A homogeneous linear programming algorithm for the security constrained economic dispatch problem , 2000 .

[44]  Huifeng Zhang,et al.  Optimal Operation of Large-Scale Cascaded Hydropower Systems in the Upper Reaches of the Yangtze River, China , 2014 .

[45]  Richard N. Palmer,et al.  Optimal Drought Management Using Sampling Stochastic Dynamic Programming with a Hedging Rule , 2011 .

[46]  Wen‐Cheng Huang,et al.  Diagnostic Checking in Stochastic Dynamic Programming , 1993 .

[47]  Abdelkrim El Mouatasim.  Boolean Integer Nonlinear Programming for Water Multireservoir Operation , 2012 .