1. Optimising the placement of fuel assemblies in a nuclear reactor core using the OSCAR-4 code system EB Schlünz, PM Bokov & RH Prinsloo Radiation and Reactor Theory The South African Nuclear Energy Corporation (Necsa) Energy Postgraduate Conference 2013 iThemba Labs, Cape Town 11 – 14 Augustus 2013

2. Overview  Introduction ICFMO problem description OSCAR core calculation system  Optimisation module for ICFMO Constraint handling Objective function Optimisation algorithm  Application of the optimisation module and results SAFARI-1 research reactor The test scenario  Conclusion

3. Introduction: ICFMO At the end of an operational cycle, depleted fuel assemblies (FAs) are discharged from a reactor core. The following may then occur before the next operational cycle commences: 1.Fresh FAs may be loaded into the core 2.FAs already in the core may be exchanged with spare FAs kept in a pool (not fresh) 3.The placement of FAs in the core may be changed, resulting in a fuel reconfiguration (or shuffle) The in-core fuel management optimisation (ICFMO) problem then refers to the problem of finding an optimal fuel reload configuration for a nuclear reactor core. A single objective, or multiple objectives, may be pursued during ICFMO, subject to certain safety and/or utilisation constraints.

4. Introduction: OSCAR-4  The OSCAR code system has been used for several years as the primary calculational tool to support day-to-day operations of the SAFARI-1 research reactor in South Africa.  It is a deterministic core calculation system which utilises response- matrix methods for few-group cross-section generation in the transport solution, and multigroup nodal diffusion methods for the three-dimensional global solution.  A new ICFMO support feature has been developed for the OSCAR-4 system (the latest version of the code), namely an optimisation module with multiobjective capabilities.

5. Constraint handling Let J be the number of constraints in an ICFMO problem and let x denote a candidate solution. Without loss of generality, the constraint set may be formulated as If a candidate solution violates any constraint, a corresponding penalty value is incurred which is related to the magnitude of the constraint violation. The penalty function adopted in the optimisation module is defined as

6. Objective function  Single, as well as multiobjective, ICFMO problem formulations incorporated.  Let n be number of different objectives, let f i (x) denote parameter value of objective i returned by OSCAR-4 after the evaluation of candidate solution x.  Augmented weighted Chebychev goal programming approach implemented as scalarising objective function – introduces concept of aspiration levels α i for objectives.  Multiobjective ICFMO problem is solved by minimising the distance between the objective vector F(x) = [ f 1 (x), f 2 (x), …, f n (x)] of a solution and the aspiration vector Α = [α 1, α 2, …, α n ] according to the Chebychev norm.  Therefore, we minimise the function  For a single objective formulation (i.e. n = 1), the max operator may be disregarded, the value of ρ may be set to zero and α 1 should be unattainable value.

7. Optimisation algorithm  Harmony search algorithm  Metaheuristic technique inspired by the observation that the aim of a musical performance (e.g. jazz improvisation) is to search for a perfect state of harmony.  Population-based method, creating single solution during each iteration.  The algorithm maintains a memory structure containing the best-found solutions during its search.  New solutions are then generated based on these solutions in the memory, according to certain operators.

8. The SAFARI-1 research reactor  Utilised for nuclear and materials research (e.g. neutron scattering, radiography and diffraction) as well as irradiation services (e.g. isotope production and silicon doping).  There are 26 fuel loading positions, and 26 available FAs were considered (at most 26! ≈ 4x10 26 solutions).

9. The test scenario  Bi-objective optimisation problem: 1.Maximise excess reactivity (in order to maximise the cycle length) 2.Minimise relative power peaking factor (safety consideration)  Three safety-related constraints are incorporated  Optimisation algorithm executed for 900 iterations (required 2.5 days of computation time on PC)  Five independent computational runs using different random seeds (initial solutions) were performed  Conglomerated results presented here  Optimisation results are compared to a typical operational reload strategy

10. Results

11. Reference solutionDominating solution  The dominating solution yields an improvement of 18.8% in excess reactivity, and an improvement of 0.64% in relative power peaking factor over the reference solution.

12. Conclusion  New ICFMO support feature for OSCAR-4 has been presented.  A scalarising objective function has been implemented to suitably model the multiple objectives of the ICFMO problem.  Results indicated the optimisation feature is effective at producing good reload configurations from cycle to cycle, within an acceptable computational budget.  Automation of searching for reload configurations, and good quality configurations obtained by this optimisation feature may greatly aid in the decision making of a reactor operator tasked with designing reload configurations.

13. References [1]G. Stander, R.H. Prinsloo, E. Müller & D.I. Tomašević, 2008, OSCAR-4 code system application to the SAFARI-1 reactor, Proceedings of the International Conference on the Physics of Reactors (PHYSOR ‘08), Interlaken, Switzerland. [2]T.J. Stewart, 2007, The essential multiobjectivity of linear programming, ORiON, 23(1), pp. 1-15. [3]K. Miettinen, 1999, Nonlinear Multiobjective Optimisation, Kluwer Academic Publishers, Boston (MA). [4]Z.W. Geem, J.H. Kim & G.V. Loganathan, A new heuristic optimization algorithm: Harmony search, Simulation, 76(2), pp. 60-68.