基于风险分摊的多风电场机会约束机组组合求解方法

Joint Chance Constrained Unit Commitment With Wind Farms Based on Risk Sharing

在含风功率等新能源出力不确定性的联合机会约束机组组合问题中,如何将多维联合机会约束转化为确定性约束是求解此问题的关键。含多维随机变量的联合机会约束规划问题是非凸问题,难以直接求解。提出了一种考虑风电功率不确定性的基于改进风险分摊的联合机会约束机组组合问题求解方法。首先,建立了基于联合机会约束的考虑风电功率不确定性的机组组合模型,将机组组合的多维联合机会约束的风险水平(违反概率)按权重分摊给每个单维机会约束的风险水平,再利用散度函数和散度容差去修正每个单维机会约束的风险水平。然后,利用自适应带宽核密度估计拟合每个单维机会约束中随机变量的概率密度函数。最后,通过随机变量累积分布函数求逆的方法将这一系列的单维机会约束转化为确定性约束,从而实现将难以求解的联合机会约束转化为易于求解的确定性约束。仿真结果验证了上述方法的有效性以及相对于传统多维联合机会约束求解方法的优越性。

The simplification of the joint chance constraints into the deterministic constraints is the key to solve the unit commitment problem under the uncertainties of wind power and the other renewable energy outputs. The joint chance constrained programming problem with multi-dimensional random variables, as a nonconvex problem, is difficult to solve directly. In this paper, an improved method for the joint chance constrained unit commitment problem with wind farms based on risk sharing is proposed. Firstly, the joint chance constrained unit commitment model considering the wind power uncertainty is established. The joint chance constraints of the unit commitment are simplified into several one-dimensional chance constraints, and the risk levels(violation probability) of the joint chance constraints are allocated to every one-dimensional chance constraint according to the weights. Then the risk level of each one-dimensional chance constraint is corrected by using the divergence function and the divergence tolerance. The adaptive bandwidth kernel density estimation proposed is used to fit the probability density function of the random variable in each of the chance constraints. Finally, the series of one-dimensional chance constraints are transformed into the deterministic constraints by using the inverse method of the random variable cumulative distribution function so as to transform the joint chance constraints into the deterministic constraints, realizing the simplification. Simulation results verify the effectiveness of the proposed method and its superiority over the traditional multidimensional joint chance constraint.