Optimising the placement of fuel assemblies in a nuclear reactor core using the OSCAR-4 code systemEB Schlünz, PM Bokov & RH

Prinsloo

Radiation and Reactor TheoryThe South African Nuclear Energy

Corporation (Necsa)

Energy Postgraduate Conference 2013iThemba Labs, Cape Town

11 – 14 Augustus 2013

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

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 core2. 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.

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.

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

.,,1,)( JjHxh jj

otherwise.

if where ,

0

)()(

)()()(1

jjj

jj

j

J

jj

HxhH

Hxh

xpxpxP

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 αi for 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 α1 should be unattainable value.

)()()(max1

,,1xPxf

k

wxf

k

wz

n

iii

i

iii

i

i

nin

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.

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).

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

Results

2.7 2.8 2.9 3 3.1 3.2 3.3 3.410.5

11

11.5

12

12.5

13

13.5

14

14.5

15

Nondominated solutions (feasible)

Nondominated setBest foundReference

Relative power peaking factor

Excess r

ea

cti

vit

y (

$)

Results

Reference solution Dominating 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.

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.

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.