Study On CANDU Refuelling Optimization Method And Feasibility Study Of Pwr Loading Pattern Search Via Direct Optimization

Fuel load/reload optimization is very important for economical and safe operation of a nuclear reactor. It is a complicated optimization problem. In this paper, based on the integer programming method, both CANDU refuelling optimization and feasibility of PWR core loading pattern search via direct optimization are investigated.In the first part of this paper, CANDU reactor refuelling optimization is investigated. Based on the on-power refuelling characteristic of a CANDU reactor, refuelling channel selection problem is solved into two steps with the aftereffect of channel refueling taking into consideration and core calculation model being employed in each step. At the first step, candidate channel selection model is developed which is based on a zero-dimensional core model with time-average channel power sharing. The objective function of the model is minimizing the number of discharged bundles, while core excess reactivity and regional reactivity balance are used as main constraints. By solving this model, candidate channels for successive 16 weeks are selected simultaneously. Then the candidates for the first few weeks are fed to the second step for subsequent weekly refuelling schemes optimization. At the second step, weekly refuelling schemes optimization model is developed based on the Linear Sensitivity Matrix (LSM) method. The objective function is maximizing the average discharge burnup, with operation limits of key safety related parameters as main constraints. Specific channels as well as their refuelling sequences for the coming week are determined simultaneously by solving this model. LSM method is proposed in order to develop a numerical tool for the fast evaluation of different CANDU refuelling schemes. Verification results demonstrate that LSM is capable of gaining accurate results and runs very fast for evaluating a refuelling scheme. At both steps, mixed integer programming (MIP) models are developed. Commercial programming solver ILOG CPLEX is used to solve these models. The method is applied to unit 1 of Third Qinshan Nuclear Power Company (TQNPC) to perform refuelling simulation. Comparisons between simulation data and history operation data show that the proposed CANDU refuelling optimization method can deepen the average fuel discharge burnup (up to 176.54 MWh/kgU) and save fuel bundles (32 bundles), with core power distribution approaching time-averaged value and no channel and bundle power limits exceeded. Thus the proposed method has the potential to be implemented at TQNPC.In the second part, the feasibility of loading pattern search via direct optimization is investigated. To resolve the time-consuming issue of the proposed method, the original HHLP method is linearized. Accordingly, direct optimization model is developed based on the HHLP linearization method. Numerical results show that the accuracy of direct optimization model deteriorates when the perturbed LP is far from the reference LP. Then the issue of how to select reference LP is discussed. Finally, an iterative method is proposed. That is, the model is firstly solved from arbitrary reference LP. As iteration proceeds, the reference LP is updated with the latest optimum LP. The process is carried out until optimum LP converges. Several loading pattern search problems for a 2-loop PWR core, including cases considering the fuel depletion and burnable absorber effects, are tested with the objective function of maximizing k-effective while limiting the peak assembly (fuel pin) power. Numerical results demonstrate that the direct optimization method is very effective and the results are good although it can not guarantee finding out the global optimum. Meanwhile, the method can significantly speed up the process of LP searching.