基于多项式混沌展开的电力系统概率可用输电能力评估

Probabilistic Available Transfer Capacity Evaluation of Power Systems Using Polynomial Chaos Expansion

大规模开发和利用风能有利于实现电力系统清洁低碳转型,是实现国家“碳达峰、碳中和”战略目标的重要技术手段,但风电出力的强不确定性对电力系统区域间可用输电能力(available transfer capability,ATC)评估带来了全新的挑战,传统用于求解计及风电出力不确定性的概率ATC评估模型在计算效率和计算精度方面均存在一定的不足。为此,该文提出一种基于多项式混沌展开(polynomialchaos expansion,PCE)的电力系统概率ATC评估方法,该方法首先构建基于机会约束的电力系统概率ATC评估模型;然后,根据风电出力预测误差的概率分布特征,选择对应的正交多项式为基函数以近似风电出力预测误差及电力网络中与之相关联的其他随机变量;进一步,借助Galerkin投影和基于一阶矩、二阶矩的机会约束转化方法,将所构建的机会约束模型的概率约束转化为确定性约束,实现基于机会约束的概率ATC评估模型向易于求解的确定性优化模型的转化;进而,将概率ATC评估模型的求解问题转化为ATC的最优多项式逼近系数的求解问题,根据求得的最优多项式逼近系数和选取的基函数计算电力系统ATC的概率分布特征;最后,通过修改后的PJM-5节点测试系统、IEEE-118节点测试系统及吉林西部电网实际算例验证了所提基于多项式混沌展开的电力系统概率ATC评估方法的准确性和有效性。

The growing uncertainty level caused by the increasing penetration of wind power generation poses a formidable challenge in the available transfer capability(ATC)evaluation of bulk power systems.The existing probabilistic ATC(PATC)calculation methods can solve the ATC of power system with the increasing uncertain wind power,but they may fail in the computational accuracy or efficiency.To handle this challenge,a Polynomial Chaos Expansion(PCE)based chance-constrained PATC calculation method is developed in this paper.The chance-constrained PATC model is formulated,and the polynomial basis is determined according to the probabilistic distributions of wind power forecasting error.Using the determined polynomial basis,the wind power forecasting error and its dependent network variables are represented by the PCE,and the formulated chance-constrained PATC model can be further reformulated as a one-shot deterministic ATC model by using the PCE with the Galerkin projection and moment-based chance constraint representation.Hence,the reformulated ATC model casts the chance-constrained PATC model as a finite dimensional nonlinear program(NLP)with the PCE coefficients as decision variables,and the optimal PCE coefficients can be achieved by solving the reformulated ATC model via the existing optimization solver.Using the solved optimal PCE coefficients and determined polynomial basis,the probabilistic characteristics(e.g.,mean,variance,probability distribution)of PATC can be obtained.Numerical studies on the modified PJM 5-bus test system,modified IEEE 118-bus test system and western Jilin power grid validate the proposed PCE-based PATC method,achieving accurate estimation for the probabilistic characteristics of PATC with a high efficiency.