Optimal management of pumped hydroelectric production with state constrained optimal control

Picarelli, Athena; Vargiolu, Tiziano

doi:10.1016/j.jedc.2020.103940

Cited by 10 publications

(6 citation statements)

References 33 publications

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“…Control with state constraints is well-studied for dynamic programming. 42,58,59 However, it has not been well-studied for maximum principle; especially, the boundary discontinuity of the admissible range of controls hinders us from directly applying it to solving optimal control problems. We tackle this issue by considering sub-optimal controls imposing the constraint only in the forward dynamics.…”

Section: Objectives and Contributionsmentioning

confidence: 99%

“…In the non‐LQ case, state constraints of the dynamics, such as non‐negativity of the outflow discharge and water volume, are additionally considered. Control with state constraints is well‐studied for dynamic programming 42,58,59 . However, it has not been well‐studied for maximum principle; especially, the boundary discontinuity of the admissible range of controls hinders us from directly applying it to solving optimal control problems.…”

Section: Introductionmentioning

confidence: 99%

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Towards control of dam and reservoir systems with forward–backward stochastic differential equations driven by clustered jumps

Yoshioka

2022

Adv Control Appl

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We deal with a new maximum principle‐based stochastic control model for river management through operating a dam and reservoir system. The model is based on coupled forward–backward stochastic differential equations (FBSDEs) derived from jump‐driven streamflow dynamics and reservoir water balance. A continuous‐time branching process with immigration driven by a tempered stable subordinator efficiently describes clustered inflow streamflow dynamics. This is a completely new attempt in hydrology and control engineering. Applying a stochastic maximum principle to the dynamics based on an objective functional for designing cost‐efficient control of dam and reservoir systems leads to the FBSDEs as a system of optimality equations. The FBSDEs under a linear‐quadratic ansatz lead to a tractable model, while they are solved numerically in the other cases using a least‐squares Monte‐Carlo method. Optimal controls are found in the former, while only sub‐optimal ones are computable in the latter due to a hard state constraint. Model parameters are successfully identified from a real data of a river in Japan having a dam and reservoir system. We also show that the linear‐quadratic case can capture the real operation data of the system with underestimation of the outflow discharge. More complex cases with a realistic time horizon are analyzed numerically to investigate impacts of considering the environmental flows and seasonal operational purposes. Key challenges towards more sophisticated modeling and analysis with jump‐driven FBSDEs are discussed as well.

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Section: Objectives and Contributionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Towards control of dam and reservoir systems with forward–backward stochastic differential equations driven by clustered jumps

Yoshioka

2022

Adv Control Appl

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“…The expectation and variance of the terminal value of the optimally controlled process are also very close to their theoretical values. In the case of a conditional mean-field interaction, a close problem is solved by [40]. For instance X max = 0 corresponds to the much simpler problem without storage nor control of the valuation of a wind power park.…”

Section: Problem Averagementioning

confidence: 99%

A level-set approach to the control of state-constrained McKean-Vlasov equations: application to renewable energy storage and portfolio selection

Germain¹,

Pham²,

Warin³

2021

Preprint

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“…This difficulty can be overcome by accordingly modifying the corresponding HJB equation at the boundaries. For related problems, see Picarelli and Vargiolu (2020).…”

Section: Dam-reservoir System Managementmentioning

confidence: 99%

Mathematical and Computational Approaches for Stochastic Control of River Environment and Ecology: From Fisheries Viewpoint

Yoshioka

2021

Computational Management

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We present a modern stochastic control framework for dynamic optimization of river environment and ecology. We focus on a fisheries problem in Japan, and show several examples of simplified optimal control problems of stochastic differential equations modeling fishery resource dynamics, reservoir water balance dynamics, benthic algae dynamics, and sediment storage dynamics. These problems concern different phenomena with each other, but they all reduce to solving degenerate parabolic or elliptic equations. Optimal controls and value functions of these problems are computed using finite difference schemes. Finally, we present a higher-dimensional problem of controlling a dam-reservoir system using a semi-Lagrangian discretization on sparse grids. Our contribution shows the state-of-art of modeling, analysis, and computation of stochastic control in environmental engineering and science, and related research areas.

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Optimal management of pumped hydroelectric production with state constrained optimal control

Cited by 10 publications

References 33 publications

Towards control of dam and reservoir systems with forward–backward stochastic differential equations driven by clustered jumps

Towards control of dam and reservoir systems with forward–backward stochastic differential equations driven by clustered jumps

A level-set approach to the control of state-constrained McKean-Vlasov equations: application to renewable energy storage and portfolio selection

Mathematical and Computational Approaches for Stochastic Control of River Environment and Ecology: From Fisheries Viewpoint

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