As a reference power distribution for investigating power distribution flattening by a burnable poison design, and fuel loading and control rod patterns, the Haling distribution [19] may be used. It is based on the principle that if a power distribution can be kept constant through the operating cycle by proper man­agement of burnable poison and movable control rods, the peak-to-average value will be at a minimum. In derivation of the principle, it was assumed that the infinite multiplication factor of a fuel assembly is a decreasing function of burnup and variation in the flux-to-power ratio with burnup is small or a decreasing function of burnup. This assumption leads to a concludion that in comparison with the case of a constant power distribution through the operat­ing cycle, a slightly smaller power peaking for a period of the operating cycle will require fuel burning by reactor operation under a high power peaking for another period.

In a given fuel design, the Haling distribution of the fuel arrangement can be obtained from calculation of an initial power distribution shape and repeated calculations between the power distribution shape and burnup distribution. The repeated calculations finally give a consistent distribution between power and burnup. If this power distribution shape can be realized during the operating cycle by adjusting the burnable poison distribution in fresh fuel and the insertion amount and position of control rods, namely, the neutron absorber distribution, it will give a minimum power peaking.

This principle is useful in designing the control rod pattern during the operating cycle. For a given fuel arrangement, cycle length, and effective multiplication factor at EOC, a corresponding Haling distribution and the necessary infinite multiplication factor in each location of the core are obtained. The reactivity worth to be controlled by control rods and burnable poisons is found by taking the difference between the infinite multiplication factor distri­bution at BOC and the one necessary for the Haling distribution. The insertion location and depth of control rods are determined based on the difference. The insertion and withdrawn of control rods are actually discrete and the Haling distribution cannot be achieved strictly. The Haling distribution is, however, useful as a target plan for control rod operation.

A big advantage in using the Haling distribution for setting the control rod pattern is to be able to separately handle the fuel loading patterns over several cycles and the control rod pattern in the cycle of interest when the reactor is operated. In other words, when the fuel loading pattern is planned, the power distribution during reactor operation dose not need to be predicted based on a detailed control rod pattern, but is assumed to have a Haling distribution, in which the number of fresh fuel assemblies and the location change of reloading fuel assemblies are determined by evaluating the fuel burnup.

The nuclear design of the fuel assembly, namely, the design of the fuel enrichment zoning and burnable poison distribution in the fuel assembly, is optimized generally based on the fuel burnup distribution at an equilibrium cycle to exclude the singularity of a specific operating cycle. The Haling distribution has been used in design of the equilibrium cycle core and evalua­tion of fuel discharge burnup and required enrichment.