Hydrological scenario reduction for stochastic optimization in hydrothermal power systems

Aravena, Ignacio; Gil, Esteban

doi:10.1002/asmb.2027

Cited by 8 publications

(3 citation statements)

References 11 publications

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“…Renewable energy systems based on wind power, hydropower, thermal energy, and solar energy are indispensable for the sustainable and environmentally friendly development of modern human lives. PV systems have been used as one of the most effective renewable energy systems owing to their many advantages, such as abundance, being pollution free, and renewability as they directly convert sunlight into electricity through a simple solid‐state device .…”

Section: Introductionmentioning

confidence: 99%

An optimal switching approach toward cost‐effective control of a stand‐alone photovoltaic panel system under stochastic environment

Yoshioka

Yano

2019

Appl Stoch Models Bus & Ind

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The operation of a stand‐alone photovoltaic (PV) system ultimately aims for the optimization of its energy storage. We present a mathematical model for cost‐effective control of a stand‐alone system based on a PV panel equipped with an angle adjustment device. The model is based on viscosity solutions to partial differential equations, which serve as a new and mathematically rigorous tool for modeling, analyzing, and controlling PV systems. We formulate a stochastic optimal switching problem of the panel angle, which is here a binary variable to be dynamically controlled under stochastic weather condition. The stochasticity comes from cloud cover dynamics, which is modeled with a nonlinear stochastic differential equation. In finding the optimal control policy of the panel angle, switching the angle is subject to impulsive cost and reduces to solving a system of Hamilton‐Jacobi‐Bellman quasi‐variational inequalities (HJBQVIs). We show that the stochastic differential equation is well posed and that the HJBQVIs admit a unique viscosity solution. In addition, a finite‐difference scheme is proposed for the numerical discretization of HJBQVIs. A demonstrative computational example of the HJBQVIs, with emphasis on a stand‐alone experimental system, is finally presented with practical implications for its cost‐effective operation.

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Section: Introductionmentioning

confidence: 99%

An optimal switching approach toward cost‐effective control of a stand‐alone photovoltaic panel system under stochastic environment

Yoshioka

Yano

2019

Appl Stoch Models Bus & Ind

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“…Due to its importance, scenario reduction is applied in the most diverse areas of knowledge, namely in supply chain [7] and particularly in the scope of this research, in electricity markets [4]. In power systems, most applications of scenario reduction methods focus on unit commitment and short-term operation [8][9][10]. This paper addresses the scenario reduction in a two-stage stochastic optimization applied to the short-term trading of PV power in a DAM, reformulated as a mixed-integer linear programming approach.…”

Section: Introductionmentioning

confidence: 99%

Scenario Reduction for Stochastic Optimization Applied to Short-Term Trading of PV Power

Gomes¹,

Melício²,

Mendes³

2020

IFIP Advances in Information and Communication Technology

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This paper addresses the scenario reduction for stochastic optimization applied to short-term trading of photovoltaic (PV) power. Stochastic optimization becomes a useful technique when leading with problems involving uncertainty. Short-term trading of PV power in electricity markets is an example of a problem involving a high level of uncertainty, namely uncertain parameters as PV power and market prices. As the level of uncertainty raises and the optimization problem becomes more complex, the prerequisite of scenario reduction becomes crucial without losing the representativeness of the original scenarios. Thus, in this paper is proposed an effective scenario reduction algorithm based on backward method in order to obtain a profitable trading of PV power in electricity markets. The scenario reduction method is applied to a two-period scenario tree, i.e., a scenario fan including uncertainty on day-ahead market (DAM) prices, on imbalance prices and on PV power. Through a case study is analyzed the performance of the scenario reduction algorithm and the comparison with the original set of scenarios. The results show that the reduced set of scenarios still has a very high level of accuracy.

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“…Mathematical models based on stochastic control theory have been principal tools for finding solution strategies of environmental and ecological management problems. Aravena and Gil applied a scenario‐based stochastic dynamic programming method to planning of hydrothermal power systems. Abdel‐Hameed and Nakhi mathematically analyzed a tractable diffusion process model of reservoir dynamics from a long‐term perspective.…”

Section: Introductionmentioning

confidence: 99%

Robust stochastic control modeling of dam discharge to suppress overgrowth of downstream harmful algae

Yoshioka

Yaegashi

2017

Appl Stoch Models Bus & Ind

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The mathematical concept of multiplier robust control is applied to a dam operation problem, which is an urgent issue on river water environment, as a new industrial application of stochastic optimal control. The goal of the problem is to find a fit-for-purpose and environmentally sound operation policy of the flow discharge from a dam so that overgrowth of the harmful algae Cladophora glomerata Kützing in its downstream river is effectively suppressed. A minimal stochastic differential equation for the algae growth dynamics with uncertain growth rate is first presented. The performance index to be maximized by the operator of the dam while minimized by nature is formulated within the framework of differential games. The dynamic programming principle leads to a Hamilton-Jacobi-Bellman-Isaacs equation whose solution determines the worst-case optimal operation policy of the dam, ie, the policy that the operator wants to find. Application of the model to overgrowth suppression of Cladophora glomerata Kützing just downstream of a dam in a Japanese river is then carried out. Values of the model parameters are identified with which the model successfully reproduces the observed population dynamics. A series of numerical experiments are performed to find the most effective operation policy of the dam based on a relaxation of the current policy.

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Hydrological scenario reduction for stochastic optimization in hydrothermal power systems

Cited by 8 publications

References 11 publications

An optimal switching approach toward cost‐effective control of a stand‐alone photovoltaic panel system under stochastic environment

An optimal switching approach toward cost‐effective control of a stand‐alone photovoltaic panel system under stochastic environment

Scenario Reduction for Stochastic Optimization Applied to Short-Term Trading of PV Power

Robust stochastic control modeling of dam discharge to suppress overgrowth of downstream harmful algae

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