A unified framework for modeling slow response self-powered neutron detectors with discrete-time state-space representation

Slow response self-powered neutron detectors (SPNDs) with Vanadium and Rhodium emitters have found wide application in nuclear power plants for in-core flux mapping as well as power regulation. When used as input to power regulation system or protection system, the detector signals must undergo time compensation to counteract the inherent delay associated with beta decay. There has been a number of compensation techniques developed for Vanadium, Rhodium and other slow response SPNDs, including both analog and digital approaches. However, it is noticed that a majority of these compensation techniques are based on Laplace and z-transformations, which inevitably requires some kind of approximation to map from s-domain to z-domain. In other words, the prevailing approaches are neither straightforward nor accurate due to complex manipulations of representations in different domains. Moreover, the reported methods are generally developed in a case by case fashion, without addressing the issue with a generalized approach such that applies to all kinds of slow response SPNDs. To overcome these limitations and deficiency, we propose in this paper a unified framework to model slow response SPNDs with discrete-time state-space representation. The proposed method eliminates complicated manipulations in s and z domain; and achieves accurate compensation without approximation by means of state-space representation of SPND dynamics and advanced digital signal processing techniques in both continuous and discrete domain. The derived discrete-time state-space SPND model also readily facilitates application of state-of-the-art signal processing algorithms such as Kalman filtering, which has been proved to be highly accurate and effective for similar applications.