Optimal groundwater management models are based on the hydraulic equations of the aquifer system. These equations relate the state variables of the groundwater system, the head, and the decision variables that control the magnitude, location, and timing of pumping, or artificial recharge. For the unconfined aquifer these management models are large-scale, nonlinear programming problems. A differential dynamic programming (DDP) algorithm is used for unsteady, nonlinear, groundwater management problems. Due to the stagewise decomposition of DDP, the dimensionality problems associated with embedding the hydraulic equations as constraints in the management model are significantly reduced. In addition, DDP shows a linear growth in computing effort with respect to the number of stages or planning periods, and quadratic convergence. Several example problems illustrate the application of DDP to the optimal control of nonlinear groundwater hydraulics.

Optimal control of nonlinear groundwater hydraulics using differential dynamic programming

This investigation is to review advanced technologies for modeling and control of reactor cores in nuclear power plants for electricity generation. A reactor core in a nuclear power plant is the key part as the hot source with radioactivity nuclear fuel, which possesses security risks and economic potential. Incapacity of a nuclear power plant to carry out desired control of its core can result in either higher operating costs or a reduction in system security and reliability, and the implementation of desirable control for the core can improve security and effectiveness of the nuclear power plant. Generally speaking, the reactor core control contains the power (or coolant temperature) control and axial power difference (namely power distribution) control of the core. The core power control is to regulate the core power, and the core load following control is to regulate the core power and axial power difference simultaneously. Modeling reactor cores is the inevitable preliminary work for research of reactor core control. Over the decades, continuous work has been devoted to the research of including modeling, power and load following control for reactor cores. In this paper, the review on advanced technologies for modeling, power and load following control of reactor cores is presented. Modeling approaches for reactor cores are reviewed such as the point reactor core modeling. Power control methods for reactor cores are reviewed such as the feedback control with a state observer. Load following control techniques for reactor cores are reviewed such as Mode A, Mode G, Mode T, Mechanical Shim and advanced control methods of containing multivariable frequency control, etc. The review in this paper can contribute to comprehend the past work with respective advantages, and then exploit novel research directions for development of nuclear power plants.

Modeling and control of nuclear reactor cores for electricity generation: A review of advanced technologies

Nodal dynamics modeling of AP1000 reactor for control system design and simulation

A receding horizon control method is applied to the axial power distribution control in a pressurized water reactor. The basic concept of receding horizon control is to solve on-line, at each sampl...

Design of a Receding Horizon Control System for Nuclear Reactor Power Distribution

A model predictive controller is designed to control thermal power in a nuclear reactor. The basic concept of the model predictive control is to solve an optimization problem for finite future time steps at current time, to implement only the first optimal control input among the solved control inputs, and to repeat the procedure at each subsequent instant. A controller design model used for designing the model predictive controller is estimated every time step by applying a recursive parameter estimation algorithm. A 3-dimensional nuclear reactor analysis code, MASTER that was developed by Korea Atomic Energy Research Institute (KAERI), was used to verify the proposed controller for a nuclear reactor. It was known that the nuclear power controlled by the proposed controller well tracks the desired power level and the desired axial power distribution.

Design of a Nuclear Reactor Controller Using a Model Predictive Control Method

The problem of extending that part of the fuel life cycle during which a reactor is capable of sustaining load-follow operation is formulated as an optimal control problem. A two-node model representation of pressurized water reactor dynamics is used, leading to a set of non-linear ordinary differential equations. Differential Dynamic Programming is used to solve directly the resulting nonlinear optimization problem and obtain the trajectories of soluble boron concentration and control rod insertion. Results of computations performed for a reference reactor are presented, showing how the optimal control policy stretches the capability of the reactor to follow an average daily load curve towards the end of the fuel life cycle.

Extension of Load Follow Capability of a PWR Reactor by Optimal Control

The problem of controlling the spatial flux distribution in a reactor is formulated as an optimization problem. A nodal representation of the distributed parameter system that results in a set of non-linear ordinary differential equations is used. This non-linear optimal control problem is solved directly by Differential Dynamic Programming. Several numerical examples are presented to show the efficiency of the method, the short computational time needed for convergence, and the wide range of sudden demands that can be handled.

A Method of Optimization of Flux and Xenon Fluctuations in a Nuclear Reactor

Optimal Control of a PWR Reactor to Extend Load Follow Capability

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Extension of Load Follow Capability of a PWR Reactor by Optimal Control

A Method of Optimization of Flux and Xenon Fluctuations in a Nuclear Reactor

Optimal Control of a PWR Reactor to Extend Load Follow Capability