A Rapid Method for Optimization of Linear Systems with Storage

Bannister, CH; Kaye, R.J.

doi:10.1287/opre.39.2.220

Cited by 31 publications

(20 citation statements)

References 1 publication

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“…A dual approach to dynamic programming was formulated by George [1986, 1990] and has the advantage of constructing the optimal solution directly and hence reducing the computational requirements, and a very similar technique was developed by Bannister and Kaye [1991] and further developed by Kaye and Travers [1997]. Kaye and Travers refer to this approach as a "constructive dynamic programming" (CDP) technique, and we will use that term here in order to distinguish it from the rather different technique which has been developed by Pereira and Pinto [1991] under the name of stochastic dual DP.…”

Section: Introductionmentioning

confidence: 65%

A constructive dual dynamic programing for a reservoir model with correlation

Yang¹,

Read²

1999

Water Resources Research

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Abstract. The reservoir management problem for a hydrothermal power system is well suited to modeling via dynamic programing. In this paper we describe a dual approach which we term "constructive dynamic programming" (CDP) which has been successfully applied to optimize releases in a stochastic two-reservoir model of the New Zealand power system. That model ignores serial correlations of inflows, though, and hence assumes that current inflow observations do not have any impact on future release decisions. Tests show, however, that better decision rules can be produced by accounting for inflow correlation. Hence we have developed an extension to the standard CDP to explicitly deal with serial correlation of reservoir inflows, and we report on those extensions also. IntroductionThe reservoir management problem for a hydrothermal power system is to decide how much water should be released in each period so as to minimize the expected operational cost, including the fuel cost of thermal plants, and the cost of shortages, should they occur. In economic terms the basic principle of reservoir management is to continue generation until the marginal value of releasing water is equal to the fuel cost of the most expensive thermal station used to meet residual demand after hydro generation or during a shortage the value of meeting loads which would otherwise not be serviced. The marginal value of the water in stock depends on the optimal utilization of that stock in future periods. Because all reservoirs have limited storage capacities and because the inflows are uncertain, water management becomes quite complex.Dynamic programming (DP) has been widely used in reservoir management. This is mainly due to its ability to handle nonlinear and stochastic features which characterize many reservoir systems. A drawback with traditional DP is that it can only provide a discrete approximation for problems with a continuous state space. Problems involving several "state variables" (in this case reservoir storage) also run into serious computational difficulties, the so called "curse of dimensionality."A dual approach to dynamic programming was formulated by Read and George [1986, 1990] and has the advantage of constructing the optimal solution directly and hence reducing the computational requirements, and a very similar technique was developed by Bannister and Kaye [1991] and further developed by Kaye and Travers [1997]. Kaye and Travers refer to this approach as a "constructive dynamic programming" (CDP) technique, and we will use that term here in order to distinguish it from the rather different technique which has been developed by Pereira and Pinto [1991] under the name of stochastic dual DP. CDP is more accurate than primal DP when finding a solution using the same number of grid points, be- In CSDP the optimal release rules are expressed by a set of guidelines consisting of the locus over time of storage levels (S t) whose marginal water values (MWV) are equal to the fuel costs of particular thermal stations. This discussi...

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Section: Introductionmentioning

confidence: 65%

A constructive dual dynamic programing for a reservoir model with correlation

Yang¹,

Read²

1999

Water Resources Research

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“…Constraints (4) are ramp-down constraints, i.e., they limit the maximum decrease in power attainable at time instant t. We remark that this formulation is more general than those usually considered (cf. Bannister and Kaye 1991, Fan et al 2002, Travers and Kaye 1998, not only because the cost functions need not be piecewise linear, but also because we allow different limits t + and t − for ramp-up and ramp-down constraints, and we allow them to depend on the time instant t.…”

Section: Formulationmentioning

confidence: 99%

“…The approach is based on the following idea: redefine the state space of the dynamic programming procedure so that computation of the state costs reduces to a convex (although harder than in the standard case) problem, the economic dispatch with ramping constraints (ED). The efficiency is obtained by using a constructive dynamic programming procedure that solves (ED) with a piecewise-linear cost function, similar to that of Bannister and Kaye (1991) and Travers and Kaye (1998). Thus, two nested dynamic programming procedures are employed to obtain an overall efficient approach.…”

Section: Introductionmentioning

confidence: 99%

Solving Nonlinear Single-Unit Commitment Problems with Ramping Constraints

Frangioni

Gentile

2006

Operations Research

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We present a dynamic programming algorithm for solving the single-unit commitment (1UC) problem with ramping constraints and arbitrary convex cost functions. The algorithm is based on a new approach for efficiently solving the single-unit economic dispatch (ED) problem with ramping constraints and arbitrary convex cost functions, improving on previously known ones that were limited to piecewise-linear functions. For simple convex functions, such as the quadratic ones typically used in applications, the solution cost of all the involved (ED) problems, consisting of finding an optimal primal and dual solution, is O n 3 . Coupled with a special visit of the state-space graph in the dynamic programming algorithm, this approach enables one to solve (1UC) with simple convex functions in O n 3 overall.

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“…While these tools have been applied, for example, to extend the solution of the optimal energy storage problem from a deterministic setting [6] to a stochastic one [7], [8], the existing literature on the implications for individual flexible consumers in more practical scenarios is relatively narrow.…”

Section: Introductionmentioning

confidence: 99%

Optimal Consumption Policies for Power-Constrained Flexible Loads Under Dynamic Pricing

Materassi

Bolognani

Roozbehani

et al. 2015

IEEE Trans. Smart Grid

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This paper analyzes the response of an individual consumer with a flexible demand for electricity to exogenous and stochastic electricity prices. The contributions of this paper are twofold. First, we propose a comprehensive model for which the optimal policy can be explicitly computed. The proposed consumer model features a time varying bound on power consumption, the presence of a nondeferrable load profile, the presence of a load profile that can be deferred up to a deadline, and the possibility of curtailment. Second, we describe the algorithm that, via explicit backward iterations of the Bellman equation, returns the optimal response of such consumer in a very general energy market scenario featuring a correlated/nonstationary price process and multiple energy procurement sources.

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A Rapid Method for Optimization of Linear Systems with Storage

Cited by 31 publications

References 1 publication

A constructive dual dynamic programing for a reservoir model with correlation

A constructive dual dynamic programing for a reservoir model with correlation

Solving Nonlinear Single-Unit Commitment Problems with Ramping Constraints

Optimal Consumption Policies for Power-Constrained Flexible Loads Under Dynamic Pricing

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