The first important problem, which is encountered in this research, is modeling of the reactor kinetic system. Many mathematical methods have been developed for system modeling and numeric calculation. For nuclear reactor time-spatial kinetics, some classical methods such as point kinetic method, finite difference method, nodal method and modal expansion approximation are set up for modeling processes [17]. All these methodologies are developed to analyze spatial-time dependent kinetics. These methods can be used for static and dynamic analysis of nuclear reactors. A number of new or advanced numerical methods have been developed in nuclear reactor physics analysis, such as advanced nonlinear iteration nodal method, finite element analysis method and Monte Carlo method[18]. These methods can be used to develop spatial kinetic models of nuclear reactors in good manner, which can provide the more detailed information on reactor characteristics. More specifically, 3-D kinetic models can be established. However, the applications are not amenable when used in control problems. As it is known, control problems often need models described in the form of ordinary differential equations. Not only most of the advanced numerical methods mentioned above, but also the finite difference and nodal methods, are represented in a PDE manner. These features limit the application of these methods to control problems. A cell nerve net method can be taken into account to solve partial differential equations of nuclear diffusion theory, but it’s very
complicated and not the mainstream application[19].
Point kinetic model is very useful in small and medium size reactors, where the entire dynamic characteristics of the reactor can be approximated as a single point and the internal behavior of the core can be ignored. However, in cases where the internal behaviors within large reactors are required to be considered, this method cannot be used. Specifically for local dynamic analysis in large reactors, point kinetic method is definitely unsuitable to do the analysis. In A. Tiwari and H. Javidnia’s research [14], simplified nodal method is operated on modeling of CANDU nuclear reactors. Each of 14 liquid control zones of CANDU reactor is treated as a large point and all internal physics properties are assumed to be homogenous. This model can reflect the zone dynamic responses as each zone works as a unit. But it cannot represent the detailed information within the zones, such that it cannot reflect the accurate 3-D dynamics. This kind of reactor model might be improved by adding more nodes to the original model. For example, each zone (a node) of 14 liquid control zones can be divided into subzones where fine point kinetic nodes can be used. Nevertheless, the problem becomes more complex since more reactivity coefficients need to be calculated, and even if this is successfully resolved, the order of the kinetic equations will be increased, which makes the control problems more difficult.
Modal expansion approximation method can be suggested [20]-[22]. The suggested approach is to synthesize the spatial flux distributions, delayed neutron precursor
concentrations, Xenon and Iodine concentrations by a time-weighted sum of spatial flux modes [22]. These flux modes are eigenfuntions of the steady-state diffusion equation and satisfy the bi-orthogonality conditions. The flux modes can be prepared by using the multidimensional diffusion codes. Modal method with only a few flux modes can achieve as accurate results as the finite differential or nodal method does, when dealing with the basic transient analysis. In case of complex transient analysis with large reactivity perturbations, a high-order modal model is required. However, the increased order also brings to the simulations computational burdens which cannot be anticipated. Thus, the balance of the model order and the computational burden has to be considered and evaluated.
Classical control methods such as PID controller are often used in the design of conventional feedback control for nuclear power plants [7]. However, modern multivariable control theories have been widely used in other technological systems [23]. There is no evidence showing that comparison has been performed between classical and modern control methods with applications to a commercial reactor. Advanced multivariable control methods, such as optimum control and adaptive control, have been used in different research areas of nuclear reactor control, including control of spatial-time flux distribution, load following and Xenon transient [24-31]. In this research, since the 3-D reactor neutronic kinetic model belongs to a MIMO dynamic system with multiple internal variables, it is difficult to use traditional methods such as PID to design
the feedback control system. However, modern control method can take into account such a complex coupled dynamic system. As for the proposed 3-D power level control problem, the objective is to achieve optimal performance criterion and meanwhile maintain the stability of the closed-loop system with the least amount of the control-signal energy. To achieve the above objectives, a linear quadratic regulator (LQR) feedback control scheme is employed to solve the 3-D control problem.
The steps of this research can be represented as follows.
systematically study CANDU reactor kinetics and control
establish the reactor neutronic kinetic model by using modal synthesis method
compare the reactor modal model with the coupled point kinetic model
decompose the simulation platform of CANDU reactor regulating system by
using MATLAB/SIMULINK
develop new simulation platform for the CANDU RRS, integrating the modal
synthesis reactor model
evaluate the performance of new RRS simulation platform by validating the
simulation results with the power plant data and comparing the results against those of couple point kinetic model
design an optimum control algorithm for CANDU reactor 3-D power level
control and analyze the simulation results