Analyses of Experimental Power-Reactivity Feedback Transfer Functions for a Natural Circulation Boiling Water Reactor

Mathematical Description of Feedback

“…This function satisfies the same boundary condition as the temperature, so that, for every r' in the core and for all t > 0, we have #(r f l ,r';*) =0 (17) where r s is a point on the surface. In order to solve (12), we may substitute n^r\t)=A(r't)Ur) (18) and obtain…”

“…32). The shift of the average power level is calculated by SP 0 = P 0 \im[so 7 k ext (s)L(s)] (18) which is obtained from (4.4, Eq. 32) by replacing Z(s) by L(s).…”

“…The time constants are determined by resolving [18] the experimental amplitude and phase responses of the feedback into the Bode diagram [18,19] (break-frequency method). The number of time constants to be included in (20) The knowledge of H(P 0 , ico) can in certain cases be used to determine even the nonlinear form of the feedback functional, as shown by…”

“…The main point in this extrapolation technique is that the time constants and H(P 0 , 0) are usually slowly varying, monotonic functions of P 0 . A combination of this method with a crude feedback model was successfully used to predict the 40-MW performance of the EBWR by Deshong and Lipinski[18,20].The critical power level P c can be predicted by extrapolating the "gain" and "phase" margins from low-power measurements. The gain margin is equal to (1 -| P 0 ZH |) at a frequency for which the argument of -ZH is 180 deg, and the phase margin measures the deviation from 180 deg of the phase angle of -ZH when | P 0 ZH | = 1.…”

“…Both of these quantities require a complete knowledge of H(P 0 , ico) at various power levels as a function of frequency. This technique was used by Deshong and Lipinski[18] to predict the instability threshold of EBWR.…”