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

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 control problem of xenon-induced spatial oscillations of a PWR in the axial direction during a load following operation is investigated. The system models are described by a one-group diffusion equation with xenon and temperature feedbacks, iodine and xenon dynamic equations, and heat conduction processes. Control is implemented by full-length and part-length control rods and the boron concentration. In order to achieve the control purpose, control models are formulated as the design problem of robust servo systems for distributed parameter reactor systems. The total thermal power and the axial offset are chosen as outputs to be controlled. The control systems consist of servo compensators and stabilizing compensators. They are designed based on finite-dimensional systems which are constructed by linearizing around steady states, approximating by the Galerkin method, and reducing dimensions via the singular perturbation method. A new and simple computational algorithm to obtain an approximate solution of steady-state neutron balance is developed via the perturbation method. Some results of numerical simulations are shown in order to discuss the effectiveness of the theory developed in this paper. In particular, it is shown that the designed servo systems are robust against model errors with linearization and modal truncation. >

A new approach to control of xenon spatial oscillation during load follow operation via robust servo systems

This paper investigates the control problem of xenon spatial oscillations in the axial direction during load following operations of a nuclear reactor. The system model is described by a one-group diffusion equation with xenon and power feedbacks and iodine-xenon dynamic equations and controlled by full-length and part-length control rods. In order to achieve the control purpose we formulate the control model as the design problem of robust servo systems for distributed parameter reactor systems. Hence the total thermal power and the axial offset are chosen as outputs to be controlled. The control law is designed based upon finite-dimensional systems which are constructed by linearizing around steady states, approximating by the Galerkin approximate method and reducing dimensions via the singular perturbation method. From a computational point of view a simple computational algorithm to obtain an approximate solution of the steady state neutron balance is developed via the perturbation method. Some result...

https://www.tandfonline.com/doi/pdf/10.1080/18811248.1990.9731189

Control of Xenon Spatial Oscillations during Load Follow of Nuclear Reactor via Robust Servo Systems

Previous work done on reactor kinetics and control in load-following operation modes available in open literature is reviewed. The analysis is focused on, however not limited to pressurized water reactors. Different approximations of the time-dependent neutron transport problem as well as different control algorithms are described in detail and compared. Due to lack of published information the majority of the comparisons was done on qualitative level. In order to facilitate future testing and intercomparisons of models and algorithms, two so-called reference scenarios with time-dependent power demand are defined: a scenario to test the limitations of the load-following capabilities of the nuclear facilities and a second, quasi-realistic scenario.

/pdf/an-overview-of-power-reactor-kinetics-and-control-in-load-2x44c02t.pdf

An overview of power reactor kinetics and control in load-following operation modes

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

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