Application of artificial neural networks to CPCS axial power distribution synthesis

Abstract

The core protection calculator system (CPCS) is installed in digital nuclear power plants (NPPs) to initiate a trip to prevent violation of the departure from nucleate boiling ratio (DNBR) and local power density (LPD) safety limits. To calculate the DNBR and LPD, the CPCS uses core axial power distribution and various operation parameters, and to calculate the core axial power distribution, a shape annealing matrix (SAM) and cubic spline interpolation are used. However, the current core axial power distribution synthesis methods have an inherent limitation in calculating all of the power shapes: center peak, flat type, and saddle type. There have been few studies on enhancing the accuracy of core axial power distribution synthesis in the CPCS, and reactor trips still occur or additional penalties are still imposed on the CPCS due to inaccuracies in the current method. This paper proposes artificial neural networks combined with a simulated annealing method for calculation of the core axial power distribution in the CPCS to solve the current method`s deficiencies. The simulated annealing method complements the artificial neural networks to find the global optimum solution. The proposed artificial neural networks are typical multilayer/feed-forward networks, and a hyperbolic tangent function was used as an ANN activation function. As a learning algorithm, we used back-propagation, which is a typical supervised learning method, to obtain weights. For the performance index, the core axial power distribution root-mean-square error was calculated using the 20 nodes target axial power and 20 nodes generated axial power. We used 300 randomly selected cases out of 4800 test cases for training to obtain weights and the remaining cases were used for testing. Validation was performed for the reload core and initial core: Hanul unit 4 cycles 8 and 10, Hanbit unit 4 cycle 13 and Shin-kori unit 1 cycle 1. As a result of the study, the core axial power distribution RMS error was decreased by about 60% for the maximally decreased case for design data and the RMS error was decreased from 15.11% to 6.44% for Hanul unit 4 cycle 8 end of cycle operation data. Our method also correctly calculated the BERR(i) penalties and hot pin axial shape index uncertainty. This method had a good fit for the online data, and had an especially good performance when an allowance level of 8% was exceeded. All of the RMS errors calculated by the artificial neural networks combined with the simulated annealing method were lower than 8% and were very stable for the entire cycle. If the operation data were used additionally when the weights were produced, the RMS error could be reduced 2.2%P more. By using the proposed method in the CPCS, the accuracy of core axial power distribution synthesis will be enhanced and unintended reactor trips caused by inaccuracy of the core axial power distribution synthesis can be prevented. Finally, the reliability of the CPCS will be enhanced.