碳捕集中考虑碳价概率分布拟合抽样误差的超分位数–鲁棒优化方法

Superquantile-robust Optimization Method Considering Fitting and Sampling Error of Random Carbon Price Used in Carbon Capture

碳捕集优化中随机规划方法以概率分布表达碳价的波动趋势,而这种碳价概率分布应考虑拟合、抽样误差。因此引入含松弛变量的不确定集合表示该误差范围,运用鲁棒优化方法解决超分位数法中分布误差不确定问题,提出超分位数-鲁棒优化模型。推导了超分位数-盒式鲁棒碳捕集优化模型,并采用蒙特卡洛模拟、拉格朗日转换求解。仿真结果表明:在碳捕集优化问题中,误差不确定性增大会导致碳捕集成本增加,但该成本低于利用超分位数法优化与追加误差成本之和,且超分位数-鲁棒法能够获得更高的碳捕水平。超分位数-鲁棒法碳捕集模型,考虑了上述误差,具有良好的经济和低碳效益。也可用于解决其他需考虑概率分布误差的随机优化问题。

The stochastic programming method in carbon capture optimization expresses the fluctuation trend of carbon price with probability distribution,and the carbon price probability distribution should consider the fitting and sampling error.Therefore,the uncertainty set with slack variables is introduced to represent the error range.The robust optimization method is used to solve the uncertainty problem of distributed error in the superquantile method.A hyper-quantitative-robust optimization model is proposed.A model for optimizing carbon capture level using superquantile-robust with box uncertainty set is established.Proposed model is processed by Monte Carlo and Lagrange Duality for solution.The simulation results show that the increase of error uncertainty will lead to an increase in carbon capture cost in the carbon capture optimization problem,but the cost is lower than the total costs of adding errors for surperquantile method optimization,and the superquantile-robust method is able to achieve higher levels of carbon capture.The superquantile-robust carbon capture model consider the above error,it has good economic and low carbon benefits.Also,this model is applicable to other stochastic optimization problems that need to consider the probability distribution errors.