In the reactor stability analysis, first governing equations are established for normal and perturbed values of state variables from the plant dynamics codes and then the governing equations are linearized for the perturbed one. The equations are converted into a frequency domain by the Laplace transform and analyzed there. This is referred to as linear stability analysis and the procedure for it in the frequency domain is shown in Fig. 2.43.

In the figure, the system transfer function (closed-loop transfer function) is defined with the open-loop transfer functions, G(s) and H(s) The system stability is characterized by the poles of the transfer function (the roots of the characteristic equation in its denominator) and described by the decay ratio. The concept and the stability criteria are given in Fig. 2.44. For the system to be stable with damping, all the roots of the characteristic equation must have negative real parts. The decay ratio, which is defined as the ratio of two consecutive peaks of the impulse response of the oscillation for the represen­tative root (the root nearest to the pole axis), depends on the calculation mesh size. The decay ratio is determined by extrapolation to zero mesh size following calculations with different mesh size.

The following should be considered in the stability analysis of nuclear reactor design.

(i) Channel stability: This is thermal-hydraulic stability of the fuel cooling channel.

(ii) Core stability: This is the nuclear and thermal-hydraulic coupled stability where the whole core power (neutron flux) regularly oscillates as a fundamental mode due to the moderator density feedback

(iii) Regional stability: This is a kind of core stability and the neutron flux of each region oscillates as a high-order mode by reciprocally going up and down.

(iv) Plant stability

(v) Xenon stability (Xe spatial oscillation): This is a function of accumulation and destruction of FP Xe, and spatial change of neutron flux

The channel stability is thermal-hydraulic stability of single coolant channel in the core. The core stability is the nuclear and thermal-hydraulic coupled stability where the whole core power (neutron flux) regularly oscillates as a fundamental mode due to the moderator density feedback. The regional stabil­ity is a kind of core stability and the neutron flux of each region oscillates as a high-order mode by reciprocally going up and down. These three stabilities are inherent characteristics of nuclear reactors with a large change in moderator density in the core such as BWRs, and hence they are evaluated by the frequency-domain stability analysis. The plant stability is the stability of plant system including its control system and is evaluated by time-domain analysis using a plant dynamics analysis code. Xenon spatial oscillation is caused by accumulation and destruction of Xenon-135, and spatial change of neutron flux. The xenon stability is analyzed by the production and destruction equation of Xenon-135.