Investigation of Spatial Control Strategies with Application to Advanced Heavy Water Reactor

This chapter begins with a brief history of nuclear energy generation and worldwide statistics along with current status in India. India has undertaken the nuclear power program. As a part of third stage of nuclear power program, the Advanced Heavy Water Reactor is designed in India. The overview of this neutronically large nuclear reactor is presented by emphasizing the need of spatial control. The chapter ends with a review of spatial control techniques applied to large nuclear reactors.

In this chapter, a nodal model representing the coupled core neutronics–thermal hydraulics behavior of Advanced Heavy Water Reactor (AHWR) is described. After linearization, the model equations are cast in standard linear state-space form and linear system properties are discussed. Then, a vectorized nonlinear model of AHWR is developed in the MATLAB/Simulink environment, which helps to understand the relationship between different variables of the system in a better way. Since the oscillations in spatial power are highly detrimental for harmless operation of large nuclear reactor, their presence in AHWR is examined for control purposes. It is demonstrated that the spatial control of AHWR is possible with the feedback of total power and nodal powers where regulating rods are located. Effect of output feedback on system stability is addressed using vectorized nonlinear model. Simulation results are generated for different transient conditions and the behaviors of delayed neutron precursor and xenon concentrations are also analyzed for each transient.

In this chapter, a state feedback-based control technique is explored for spatial control of Advanced Heavy Water Reactor (AHWR). The AHWR model with 90 state, 18 output, and 5 input variables is decomposed into slow and fast subsystems of orders 73 and 17, respectively, by two-stage linear transformation. As the fast subsystem is observed to be stable, controller is designed only for the slow subsystem and then composite controller is derived for the original system. Vectorized nonlinear model of AHWR is simulated with presented composite controller and performance is tested under various transient conditions. It is noticed that xenon oscillations are effectively suppressed and performance is found to be acceptable.

Controlling of large nuclear reactors is a challenging task due to the simultaneous presence of both the slow and the fast varying dynamic modes. However, as demonstrated in this chapter, the two-time-scale property of the system can be taken advantage of. In particular, the design of linear quadratic regulator for spatial power control of Advanced Heavy Water Reactor (AHWR) has been presented in this chapter. The singularly perturbed two-time-scale model of AHWR is decomposed into two comparatively lower order subsystems, namely, slow and fast subsystems of orders 73 and 17, respectively. Two individual optimal controllers are developed for both the subsystems and then a composite controller is obtained for original higher order system. This composite controller is applied to the vectorized nonlinear model of AHWR. From dynamic simulations of the nonlinear model of the reactor in representative transients, the suggested control scheme is found to be superior to other methods.

In this chapter, sliding mode control (SMC) is designed for spatial control of Advanced Heavy Water Reactor (AHWR). Nonlinear system of AHWR has 90 states, 18 outputs, and 5 inputs. When linearized, the model is observed to be highly stiff. Therefore, direct application of the control method to the full-order system results into numerical ill-conditioning. Hence, full-order system of AHWR is separated into slow and fast subsystems of dimensions 73 and 17, respectively, by direct block diagonalization and sliding mode controller design is carried out using simply slow subsystem states. Afterward, SMC for full-order system is formulated by straightforward linear transformation matrices. In this, it is also demonstrated that slow subsystem SMC results in a sliding mode motion for full-order system. Nonlinear dynamic simulations have been carried out to show efficacy and robustness of the technique.

In this chapter, spatial control of Advanced Heavy Water Reactor (AHWR) is achieved by fast output sampling (FOS) based control strategy. State feedback control designed using two time-scale approach is realized using FOS feedback gain. As a result, the system states are not needed for feedback. The effectiveness of the controller has been confirmed by nonlinear simulation of transient behavior of AHWR system. Overall controller performance is observed to be acceptable.

This chapter examines periodic output feedback (POF) control scheme for spatial control of Advanced Heavy Water Reactor (AHWR) based on three-time-scale decomposition. The numerically ill-conditioned system of AHWR is first decoupled into three subsystems of lower order, namely, slow, fast 1, and fast 2 by three-stage linear transformation and then a composite controller is designed which provides an output injection gain. Output injection matrix is then used to calculate POF gain, which is applied to the vectorized nonlinear system of AHWR to attain control of spatial power. Effectiveness of the presented control scheme is evaluated via simulations generated under various transient situations. Performance of this scheme is also compared with the fast output sampling control scheme.

In this chapter, design of discrete-time sliding mode control (DSMC) for spatial stabilization of Advanced Heavy Water Reactor (AHWR) is demonstrated. AHWR system is represented by 90 first-order nonlinear differential equations with 18 outputs and 5 inputs. Initially, highly ill-conditioned linear system of AHWR is transformed into block diagonal form to have separate slow, fast 1, and fast 2 subsystems. Fast 1 and fast 2 subsystems are observed to be stable, hence DSMC is designed using slow subsystem alone. The constant plus proportional rate reaching law and power rate reaching law are used for design purpose. This nonlinear multivariable model of AHWR is simulated with the designed controls and results are generated. Performances are compared under the same transient conditions.

Large nuclear reactors are prone to xenon oscillations in which despite the fact that the total power remains constant, the power distribution in the core may be nonuniform as well as it might experience unstable oscillations. Such oscillations affect the operation and control philosophy of core and could also drive issues related to safety. Thus, spatial control is required. In this chapter, several types of spatial controllers have been examined for Advanced Heavy Water Reactor (AHWR). Some of these designs are based on output feedback whereas the others are based on state feedback and both the conventional and modern control concepts have been investigated. The designs of controllers have been carried out using a 90th order model of AHWR, which is extremely stiff. As a result, straight forward application of these methods suffers with numerical ill-conditioning. Singular perturbation and time-scale methods have been applied whereby the design problem for the original high order system is decoupled into two or three subproblems, each of which is worked out independently. Nonlinear simulations have been carried out to get the transient responses of the system with all the controllers and their performances have been evaluated on the similar time scale.