The neutron kinetics equations (Eqs. 6 11 and 6.12) that were applied to zero-power reactors also hold for power reactors However, additional relations exist here between reactor power and reactivity because the former is high enough to cause effects on the latter (see Fig. 6.4). This feedback of reactor power to reactivity is the

—*K+>

Fig. 6.4—Relations between the feedback and the zero — power transfer functions which make up the transfer func­tion of a power reactor

important characteristic of power-reactor dynamics. As might be expected, transfer-function measurements are used to obtain information about this feedback.

Equations that relate power to reactivity can be numerous and complex, depending on the system. Specific forms for boiling — and pressunzed-water reactors have been summarized 74 Where commonly a set of linear differential equations adequately represent the system, the feedback transfer function from power to reactivity may be written

kfb(s) Y’ rijd+TgS)

nfs)/N “ H(S) " 2j 7‘ П k (1 + Tlks)
1

where s = ICO and the values of т are time constants associated with a system variable that has a feedback reactivity change of y, percent for a 1% power change (in the limit of very slow transients).

The transfer function between an external excitation reactivity, kln, such as an oscillator rod, and the reactor power is the solution of Eqs 6 14 and 6.17 if к = 1 + kln + kfb is used

G0(s)

1 — G0(s) H(s)

Since G0 is well known, this equation is generally used to obtain H(s) or G(s) from the other