Constant monitoring of the state of the core ensures safe operation of a nuclear reactor. This article examines the reconstruction of the energy release in the core of a nuclear reactor on the basis of the indications of height sensors. Situations where some sensors fail are not rare. Any reduction in the number of sensor indications increases the error. However, the missing measurement information can be reconstructed by mathematical methods, and replacement of the failed sensors can be avoided. The simplest algorithm for reconstruction missing indications consists in approximating the height distribution by harmonic functions. However, the coeffi cients of these functions are found to be correlated. It is suggested that a set of natural functions determined by means of statistical estimates obtained from archival data be constructed. The procedure proposed makes it possible to reconstruct the fi eld even with a signifi cant loss of measurement information.Safe and effi cient operation of a nuclear reactor is secured by constantly monitoring the state of the core, including the energy release, by means of sensors used for in-reactor monitoring. In VVER, direct-charge sensors (DCS) are united into neutron-measurement channels with seven sensors uniformly arranged along the height in each channel [1]. Radial and height sensors comprised of four extended sensitive sections for monitoring the energy release (SMER) are installed in RBMK [2]. Situations where some in-reactor sensors fail are not rare in the practice of operating nuclear reactors. If a sensor fails, then the use of its indications is prohibited. For example, if more than one section of a RBMK sensor fails, then the detector is considered to be 'prohibited'. A neutron measurement channel in VVER is prohibited upon failure of more than two sensors.A reduction in the number of in-reactor monitoring sensor indications on the basis of which the energy release in the reactor core is reconstructed results in a larger determination error and requires modifi cation of the standard reconstruction algorithm. We note that in VVER the sensors can be replaced only between runs while in RBMK they can be replaced 'on the fl y' without stopping the reactor, but this complicates the work because not just the sensor but the entire fuel assembly must be replaced so that actually unplanned refueling is performed.The missing measurement information can be restored by mathematical methods and premature replacement of the failed detectors can thereby be avoided, which is also expedient economically. For this, it is proposed that the missing sensor indications be calculated by fi tting the known points using functions determined on the basis of archival data. We shall clarify this for the following example.

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A method of determining the coolant flowrate in an RBMK process channel on the basis of activity information is examined. A mathematical model of coolant activation in the RBMK channel and an algorithm for determining the flowrate in the channel with an imprecise flowmeter are described. The results of tests of the computational-measurement system to determine the coolant flowrate in the No. 1 unit of the Kursk nuclear power plant are presented (area of application and error in flowrate determination).The coolant flowrate through a process channel is one of the important parameters that determine the safe operation of a power-generating unit with an RBMK reactor. Standard monitoring of the flowrate is accomplished with ShTORM-32M ball-type flowmeters placed on water pipelines carrying coolant to each process channel [1]. During operation of the flowmeters, the flowrate error due to mechanical wear of a ball and the rocking track, change of the flow regime, and other reasons increases [2]. In the practice of RBMK operation, there arise situations where flowmeters malfunction or their indications cannot be trusted. This imposes additional limitations on the operating regime of the reactor, including during refueling operations or power increase after brief shutdowns.It is important to determine the flowrate in a process channel by a method which is independent of the standard method, for example, based on activation of the water coolant by fast neutrons according to the reactions 16 O(n, p) 16 N 7 and 17 O(n, p) 17 N 7 .The induced activity of the water in the core depends on the fast-neutron flux density, i.e., the power of the channel, at the point of measurement of the radioactivity -on the coolant delivery time, i.e., on the flowrate if the distance to the measuring point is known. Thus, the coolant activity carries information on the power and the flowrate. This fact has attracted the attention of investigators in application to vessel reactors with pressurized water [3]; at present the radiation method is successfully implemented abroad as a standard and additional monitoring system. The successful use of information on singlephase coolant activity in PWR has initiated an investigation of the possibility of using a similar approach for RBMK with boiling coolant [4].

Situations where several fuel assemblies become unsealed can occur during the operation of RBMK reactors. The existing sanitation rules for designing and operating nuclear electric power plants determine the maximum admissible level of the emissions. For example, a plant must be shut down if the yearly maximum admissible emission is reached before it has operated for one calendar year. At the same time, it is possible to have a situation where several fuel assemblies with different energy output and with different total emissions not exceeding the maximum admissible level are unsealed at the same time. Then there arises the question of determining the sequence in which the unsealed fuel assemblies should be extracted with the minimum loss of total energy production.Let there be N unsealed fuel assemblies. The energy production of each fuel assembly by this time is E 0i , the operating time of each assembly is t 0i , and the emissions are x i . If the ith fuel assembly is left in the core for an additional time ∆t i , then the energy production is E(t 0i + ∆t i ). Let the maximum energy production E m of a fuel assembly be reached at time t m . If the fuel assembly is removed after time ∆t i , then the loss of energy production of the ith fuel assembly will be ∆E i = E m --E(t 0i + ∆t i ) the total loss of energy production with all unsealed fuel assemblies removed isThe problem is to find a sequence for removing the fuel assemblies, i.e., ∆t 1 , ..., ∆t N , that minimizes the total loss of energy production and does not violate the limitation on the total emission of radionuclides P.The mathematical problem is stated as follows: we must find (1) under the constraints(3)x t P i i i N ∆ ≤ = ∑ 2 ; min ( ) ,..., ∆ ∆ = ∆ ∆ ∑ t t i i i N N E t 1 1 S E t i i i N = ∆ ∆ = ∑ ( ).

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