Linear stability analysis of a nuclear reactor using the lumped model

Abstract

The sta bil ity anal y sis of a nu clear re ac tor is an im por tant as pect in the de sign and op er a tion of the re ac tor. A sta ble neutronic re sponse to per tur ba tions is es sen tial from the safety point of view. In this pa per, a gen eral meth od ol ogy has been de vel oped for the lin ear sta bil ity anal y sis of nu clear re ac tors us ing the lumped re ac tor model. The re ac tor ki net ics has been mod elled us ing the point ki net ics equa tions and the re ac tiv ity feed backs from fuel, cool ant and xe non have been mod elled through the ap pro pri ate time de pend ent equa tions. These gov ern ing equa tions are linearized con sid er ing small per tur ba tions in the re ac tor state around a steady op er at ing point. The char ac ter is tic equa tion of the sys tem is used to es tab lish the sta bil ity zone of the re ac tor con sid er ing the re ac tiv ity co ef fi cients as pa ram e ters. This meth od ol ogy has been used to iden tify the sta bil ity re gion of a typ i cal pres sur ized heavy wa ter re ac tor. It is shown that the pos i tive re ac tiv ity feed back from xe non nar rows down the sta bil ity re gion. Fur ther, it is ob served that the neu tron ki net ics pa ram e ters (such as the num ber of de layed neu tron pre cur sor groups con sid ered, the neu tron gen er a tion time, the de layed neu tron fractions, etc.) do not have a sig nif i cant in flu ence on the lo ca tion of the sta bil ity bound ary. The sta bil ity bound ary is largely in flu enced by the pa ram e ters gov ern ing the evo lu tion of the fuel and cool ant tem per a ture and xe non con cen tra tion.