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Stochastic Dynamic Programming (stochastic + dynamic_programming)

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Engineering66%

Selected Abstracts

Incorporating Penalty Function to Reduce Spill in Stochastic Dynamic Programming Based Reservoir Operation of Hydropower Plants

IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING, Issue 5 2010
Deependra Kumar Jha Non-member
Abstract This paper proposes a framework that includes a penalty function incorporated stochastic dynamic programming (SDP) model in order to derive the operation policy of the reservoir of a hydropower plant, with an aim to reduce the amount of spill during operation of the reservoir. SDP models with various inflow process assumptions (independent and Markov-I) are developed and executed in order to derive the reservoir operation policies for the case study of a storage type hydropower plant located in Japan. The policy thus determined consists of target storage levels (end-of-period storage levels) for each combination of the beginning-of-period storage levels and the inflow states of the current period. A penalty function is incorporated in the classical SDP model with objective function that maximizes annual energy generation through operation of the reservoir. Due to the inclusion of the penalty function, operation policy of the reservoir changes in a way that ensures reduced spill. Simulations are carried out to identify reservoir storage guide curves based on the derived operation policies. Reservoir storage guide curves for different values of the coefficient of penalty function , are plotted for a study horizon of 64 years, and the corresponding average annual spill values are compared. It is observed that, with increasing values of ,, the average annual spill decreases; however, the simulated average annual energy value is marginally reduced. The average annual energy generation can be checked vis-à-vis the average annual spill reduction, and the optimal value of , can be identified based on the cost functions associated with energy and spill. © 2010 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [source]

RESERVOIR OPERATION ANI EVALUATION OF DOWNSTREAM FLOW AUGMENTATION,

JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION, Issue 3 2001
Mahesh Kumar Sahu
ABSTRACT: Operation of a storage-based reservoir modifies the downstream flow usually to a value higher than that of natural flow in dry season. This could be important for irrigation, water supply, or power production as it is like an additional downstream benefit without any additional investment. This study addresses the operation of two proposed reservoirs and the downstream flow augmentation at an irrigation project located at the outlet of the Gandaki River basin in Nepal. The optimal operating policies of the reservoirs were determined using a Stochastic Dynamic Programming (SDP) model considering the maximization of power production. The modified flows downstream of the reservoirs were simulated by a simulation model using the optimal operating policy (for power maximization) and a synthetic long-term inflow series. Comparing the existing flow (flow in river without reservoir operation) and the modified flow (flow after reservoir operation) at the irrigation project, the additional amount of flow was calculated. The reliability analysis indicated that the supply of irrigation could be increased by 25 to 100 percent of the existing supply over the dry season (January to April) with a reliability of more than 80 percent. [source]

Optimal eradication: when to stop looking for an invasive plant

ECOLOGY LETTERS, Issue 7 2006
Tracey J. Regan
Abstract The notion of being sure that you have completely eradicated an invasive species is fanciful because of imperfect detection and persistent seed banks. Eradication is commonly declared either on an ad hoc basis, on notions of seed bank longevity, or on setting arbitrary thresholds of 1% or 5% confidence that the species is not present. Rather than declaring eradication at some arbitrary level of confidence, we take an economic approach in which we stop looking when the expected costs outweigh the expected benefits. We develop theory that determines the number of years of absent surveys required to minimize the net expected cost. Given detection of a species is imperfect, the optimal stopping time is a trade-off between the cost of continued surveying and the cost of escape and damage if eradication is declared too soon. A simple rule of thumb compares well to the exact optimal solution using stochastic dynamic programming. Application of the approach to the eradication programme of Helenium amarum reveals that the actual stopping time was a precautionary one given the ranges for each parameter. [source]

Incorporating Penalty Function to Reduce Spill in Stochastic Dynamic Programming Based Reservoir Operation of Hydropower Plants

IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING, Issue 5 2010
Deependra Kumar Jha Non-member
Abstract This paper proposes a framework that includes a penalty function incorporated stochastic dynamic programming (SDP) model in order to derive the operation policy of the reservoir of a hydropower plant, with an aim to reduce the amount of spill during operation of the reservoir. SDP models with various inflow process assumptions (independent and Markov-I) are developed and executed in order to derive the reservoir operation policies for the case study of a storage type hydropower plant located in Japan. The policy thus determined consists of target storage levels (end-of-period storage levels) for each combination of the beginning-of-period storage levels and the inflow states of the current period. A penalty function is incorporated in the classical SDP model with objective function that maximizes annual energy generation through operation of the reservoir. Due to the inclusion of the penalty function, operation policy of the reservoir changes in a way that ensures reduced spill. Simulations are carried out to identify reservoir storage guide curves based on the derived operation policies. Reservoir storage guide curves for different values of the coefficient of penalty function , are plotted for a study horizon of 64 years, and the corresponding average annual spill values are compared. It is observed that, with increasing values of ,, the average annual spill decreases; however, the simulated average annual energy value is marginally reduced. The average annual energy generation can be checked vis-à-vis the average annual spill reduction, and the optimal value of , can be identified based on the cost functions associated with energy and spill. © 2010 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [source]

Shortest path stochastic control for hybrid electric vehicles

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 14 2008
Edward Dean Tate Jr
Abstract When a hybrid electric vehicle (HEV) is certified for emissions and fuel economy, its power management system must be charge sustaining over the drive cycle, meaning that the battery state of charge (SOC) must be at least as high at the end of the test as it was at the beginning of the test. During the test cycle, the power management system is free to vary the battery SOC so as to minimize a weighted combination of fuel consumption and exhaust emissions. This paper argues that shortest path stochastic dynamic programming (SP-SDP) offers a more natural formulation of the optimal control problem associated with the design of the power management system because it allows deviations of battery SOC from a desired setpoint to be penalized only at key off. This method is illustrated on a parallel hybrid electric truck model that had previously been analyzed using infinite-horizon stochastic dynamic programming with discounted future cost. Both formulations of the optimization problem yield a time-invariant causal state-feedback controller that can be directly implemented on the vehicle. The advantages of the shortest path formulation include that a single tuning parameter is needed to trade off fuel economy and emissions versus battery SOC deviation, as compared with two parameters in the discounted, infinite-horizon case, and for the same level of complexity as a discounted future-cost controller, the shortest-path controller demonstrates better fuel and emission minimization while also achieving better SOC control when the vehicle is turned off. Linear programming is used to solve both stochastic dynamic programs. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Modeling the operation of multireservoir systems using decomposition and stochastic dynamic programming

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 3 2006
T.W. Archibald
Abstract Stochastic dynamic programming models are attractive for multireservoir control problems because they allow non-linear features to be incorporated and changes in hydrological conditions to be modeled as Markov processes. However, with the exception of the simplest cases, these models are computationally intractable because of the high dimension of the state and action spaces involved. This paper proposes a new method of determining an operating policy for a multireservoir control problem that uses stochastic dynamic programming, but is practical for systems with many reservoirs. Decomposition is first used to reduce the problem to a number of independent subproblems. Each subproblem is formulated as a low-dimensional stochastic dynamic program and solved to determine the operating policy for one of the reservoirs in the system. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006 [source]

Stochastic optimization for the ruin probability

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003
Manfred Schäl Prof. Dr. rer. nat.
The Cramér-Lundberg insurance model is studied where the risk process can be controlled by reinsurance and by investment in a financial market. The performance criterion is the ruin probability. The problem can be imbedded in the framework of discrete-time stochastic dynamic programming. Basic tools are the Howard improvement and the verification theorem. Explicit conditions are obtained for the optimality of employing no reinsurance and of not investing in the market. [source]

Flexible and Robust Implementations of Multivariate Adaptive Regression Splines Within a Wastewater Treatment Stochastic Dynamic Program

QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 7 2005
Julia C. C. Tsai
Abstract This paper presents an automatic and more robust implementation of multivariate adaptive regression splines (MARS) within the orthogonal array (OA)/MARS continuous-state stochastic dynamic programming (SDP) method. MARS is used to estimate the future value functions in each SDP level. The default stopping rule of MARS employs the maximum number of basis functions Mmax, specified by the user. To reduce the computational effort and improve the MARS fit for the wastewater treatment SDP model, two automatic stopping rules, which automatically determine an appropriate value for Mmax, and a robust version of MARS that prefers lower-order terms over higher-order terms are developed. Computational results demonstrate the success of these approaches. Copyright © 2005 John Wiley & Sons, Ltd. [source]