基于二阶锥最优潮流的机会约束分布鲁棒优化研究

Chance-constrained Distributional Robust Optimization Based on Second-order Cone Optimal Power Flow

新能源及负荷的不确定性会影响电力系统的安全运行,目前很多基于直流潮流的经济调度研究考虑了不确定性,而考虑不确定性的交流最优潮流值得进一步研究。因此,该文工作包括二阶锥最优潮流模型(second-order cone alternating current optimal power flow model,SOC-ACOPF)、基于分布鲁棒的最优潮流模型(second-order cone alternating current optimal power flow model based on the distributional robust optimization,DR-SOC-ACOPF)的建立及求解方法。首先,通过引入的松弛变量对潮流非线性部分进行二阶锥松弛,提出了最优潮流的二阶锥求解方法,并额外添加松弛上限约束限制二阶锥松弛的误差。其次,将节点功率的不确定性与潮流表达、泰勒展开结合,推导了不确定量的关系方程,以此结合机会约束构造方法及方差区间估算,建立了可直接求解的二阶锥最优潮流的机会约束分布鲁棒优化模型,此方法具有较强的鲁棒性,且计算过程易处理。最后,通过多个IEEE算例验证了所提方法的有效性。

The uncertainty of new energies and load affects the safe operation of the power system. Currently, many economic dispatch studies based on DC power flow have considered such uncertainty, while the AC optimal power flow considering uncertainty is worthy of further study. Thus, the work of this paper includes the establishment and solution of the second-order cone alternating current optimal power flow model(SOC-ACOPF) and the second-order cone alternating current optimal power flow model based on the distributional robust optimization(DR-SOC-ACOPF). Firstly, through the introduced relaxation variables, the nonlinear part of the power flow is relaxed by the second-order cone, thus the second-order cone solution method for the optimal power flow is proposed. Besides, the upper limit constraint of relaxation is added to restrict the relaxation error. Secondly, the uncertainty of the node power is combined with the power flow equations and Taylor expansion to derive the relationship equations of the uncertainty variables. The construction method of chance constraint and the interval estimation of variance are integrated to the equations to build the chance-constrained distributional robust optimization of second-order cone optimal power flow that can be directly solved. This method has strong robustness and the calculation is computationally tractable. Finally, the effectiveness of the proposed method is verified by multiple IEEE cases.