Nonlinear Treatment of Large Perturbation in Power Reactor Stability

Mathematical Description of Feedback

“…Several attempts were made to obtain the high-power describing function in the past, with disagreement in the final results [21][22][23][24]. The result obtained here agrees with that obtained by Wasserman [24] in 1962.…”

“…Since f^Z du 8(u) = 1, and the integral of power is energy, Q must be equal to the unit of energy. Mathematically, G(t) is the first derivative + of the functional 8k t [p] at p = 0, i.e., (22) as can be seen from (20) with p(u) = e 8(u).…”

“…The constant term in (22) gives rise to the constant feedback reactivity at the equilibrium power level, i.e., (23) Hence, the incremental feedback reactivity becomes …”

Nonlinear Oscillations and Stability of a Nuclear Reactor with Two Reactivity Feedbacks

“…He recognized that a negative reactivity bias was necessary for sustained power oscillations; however, he failed to consider in the solution the change in average neutron density from low power to high power operation. Sandmeier (1959) contributed to the solution of the problem by including the change in average neutron density which Nelkin had omitted.…”

“…This is necessary in his work because H(s) is calculated for P while Torlin defined p in terms of P. The factor is o v 13 not needed here since p is the incremental power about P . The deviation between P and Pq which is a shift in the mean equilibrium neutron density caused by the nonlinearities in the system is discussed by several authors (Sandmeier 1959, Smets 1964. For a linear system, the shift is not present; P = P^ and P/PQ = 1.…”