Optimising the placement of fuel assemblies in a nuclear reactor core using the OSCAR-4 code system

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: • Fresh FAs may be loaded into the core • FAs already in the core may be exchanged with spare FAs kept in a pool (not fresh) • 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 letxdenote 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 fi(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 αifor objectives. • Multiobjective ICFMO problem is solved by minimising the distance between the objective vector F(x) = [ f1(x), f2(x), … , fn(x)] of a solution and the aspiration vector Α = [α1, α2, … , αn] 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 α1should 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! ≈ 4x1026 solutions).

9. The test scenario • Bi-objective optimisation problem: • Maximise excess reactivity(in order to maximise the cycle length) • 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. Results • 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. Reference solution Dominating 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 MultiobjectiveOptimisation, 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.