Comparison of different methods for solving a large scale, stochastic dynamic problem

1986 ◽  
pp. 982-991
Author(s):  
Ph. Torrion ◽  
J. Leveugle ◽  
C. Hery
Keyword(s):  
Dynamic Problem ◽  
Large Scale ◽  
Stochastic Dynamic

scholarly journals Combined Aggregated Sampling Stochastic Dynamic Programming and Simulation-Optimization to Derive Operation Rules for Large-Scale Hydropower System

Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 625
Author(s):  
Xinyu Wu ◽  
Rui Guo ◽  
Xilong Cheng ◽  
Chuntian Cheng
Keyword(s):  
Dynamic Programming ◽  
Stochastic Dynamic Programming ◽  
Large Scale ◽  
Simulation Optimization ◽  
Optimal Operation ◽  
Stochastic Dynamic ◽  
Operation Model ◽  
Two Stage ◽  
Operation Rules ◽  
Reservoir Systems

Simulation-optimization methods are often used to derive operation rules for large-scale hydropower reservoir systems. The solution of the simulation-optimization models is complex and time-consuming, for many interconnected variables need to be optimized, and the objective functions need to be computed through simulation in many periods. Since global solutions are seldom obtained, the initial solutions are important to the solution quality. In this paper, a two-stage method is proposed to derive operation rules for large-scale hydropower systems. In the first stage, the optimal operation model is simplified and solved using sampling stochastic dynamic programming (SSDP). In the second stage, the optimal operation model is solved by using a genetic algorithm, taking the SSDP solution as an individual in the initial population. The proposed method is applied to a hydropower system in Southwest China, composed of cascaded reservoir systems of Hongshui River, Lancang River, and Wu River. The numerical result shows that the two-stage method can significantly improve the solution in an acceptable solution time.

scholarly journals The Impact of Assuming Perfect Foresight When Planning Infrastructure in the Water–Energy–Food Nexus

2021 ◽  
Vol 3 ◽  
Author(s):  
Raphael Payet-Burin ◽  
Mikkel Kromman ◽  
Silvio J. Pereira-Cardenal ◽  
Kenneth M. Strzepek ◽  
Peter Bauer-Gottwein
Keyword(s):  
Economic Evaluation ◽  
Large Scale ◽  
Reasonable Assumption ◽  
Stochastic Dynamic ◽  
Total System ◽  
Perfect Foresight ◽  
Computational Costs ◽  
Infrastructure Investments ◽  
The Impact ◽  
High Uncertainty

Perfect foresight hydroeconomic optimization models are tools to evaluate impacts of water infrastructure investments and policies considering complex system interlinkages. However, when assuming perfect foresight, optimal management decisions are found assuming perfect knowledge of climate and runoff, which might bias the economic evaluation of investments and policies. We investigate the impacts of assuming perfect foresight by using Model Predictive Control (MPC) as an alternative. We apply MPC in WHAT-IF, a hydroeconomic optimization model, for two study cases: a synthetic setup inspired by the Nile River, and a large-scale investment problem on the Zambezi River Basin considering the water–energy–food nexus. We validate the MPC framework against Stochastic Dynamic Programming and observe more realistic modeled reservoir operation compared to perfect foresight, especially regarding anticipation of spills and droughts. We find that the impact of perfect foresight on total system benefits remains small (<2%). However, when evaluating investments and policies using with-without analysis, perfect foresight is found to overestimate or underestimate values of investments by more than 20% in some scenarios. As the importance of different effects varies between scenarios, it is difficult to find general, case-independent guidelines predicting whether perfect foresight is a reasonable assumption. However, we find that the uncertainty linked to climate change in our study cases has more significant impacts than the assumption of perfect foresight. Hence, we recommend MPC to perform the economic evaluation of investments and policies, however, under high uncertainty of future climate, increased computational costs of MPC must be traded off against computational costs of exhaustive scenario exploration.

The Approximate Solutions of FPK Equations in High Dimensions for Some Nonlinear Stochastic Dynamic Systems

2011 ◽  
Vol 10 (5) ◽  
pp. 1241-1256 ◽  
Author(s):  
Guo-Kang Er ◽  
Vai Pan Iu
Keyword(s):  
Large Scale ◽  
Joint Probability ◽  
Approximate Solutions ◽  
The State ◽  
Stochastic Dynamic ◽  
State Variables ◽  
High Dimensions ◽  
Polynomial Type ◽  
Fpk Equation ◽  
Stochastic Dynamic Systems

AbstractThe probabilistic solutions of the nonlinear stochastic dynamic (NSD) systems with polynomial type of nonlinearity are investigated with the subspace-EPC method. The space of the state variables of large-scale nonlinear stochastic dynamic system excited by white noises is separated into two subspaces. Both sides of the Fokker-Planck-Kolmogorov (FPK) equation corresponding to the NSD system is then integrated over one of the subspaces. The FPK equation for the joint probability density function of the state variables in another subspace is formulated. Therefore, the FPK equation in low dimensions is obtained from the original FPK equation in high dimensions and it makes the problem of obtaining the probabilistic solutions of large-scale NSD systems solvable with the exponential polynomial closure method. Examples about the NSD systems with polynomial type of nonlinearity are given to show the effectiveness of the subspace-EPC method in these cases.

Sign in / Sign up

Export Citation Format

Share Document