非侵入式低秩近似法的概率潮流计算
Probabilistic Power Flow Calculation using Non-intrusive Low-rank Approximation Method
摘要：
提出了一种基于低秩近似（LRA）的非侵入式概率潮流（PPF）分析方法，该方法能够准确、高效地估计出系统的概率特性（如，平均值，方差，概率密度函数）的PPF解决方案。该方法的目的是通过少量的潮流计算，建立一个与PPF解在物理上等价的代理。通过利用保留的张量积形式的一元多项式的基础上，一个顺序的校正更新计划，使未知数的总数是线性的，而不是指数的随机输入的数量。因此，LRA方法是特别有前途的处理高维问题，大量的随机输入。对IEEE 39节点、118节点和1354节点系统的数值研究表明，与Monte Carlo仿真相比，该方法能够以更少的计算量获得PPF解的精确概率特性。即使与多项式混沌展开方法相比，LRA方法也可以达到相当的精度，而LRA方法更能够处理高维问题。此外，数值结果表明，随机性所带来的可再生能源资源和负荷可能不可避免地影响调度/规划方案的可行性。
英文摘要：
In this paper, a novel non-intrusive probabilistic power flow (PPF) analysis method based on the low-rank approximation (LRA) is proposed, which can accurately and efficiently estimate the probabilistic characteristics (e.g., mean, variance, probability density function) of the PPF solutions. This method aims at building up a statistically-equivalent surrogate for the PPF solutions through a small number of power flow evaluations. By exploiting the retained tensor-product form of the univariate polynomial basis, a sequential correction-updating scheme is applied, making the total number of unknowns to be linear rather than exponential to the number of random inputs. Consequently, the LRA method is particularly promising for dealing with high-dimensional problems with a large number of random inputs. Numerical studies on the IEEE 39-bus, 118-bus, and 1354-bus systems show that the proposed method can achieve accurate probabilistic characteristics of the PPF solutions with much less computational effort compared to the Monte Carlo simulations. Even compared to the polynomial chaos expansion method, the LRA method can achieve comparable accuracy, while the LRA method is more capable of handling higher-dimensional problems. Moreover, numerical results reveal that the randomness brought about by the renewable energy resources and loads may inevitably affect the feasibility of dispatch/planning schemes.
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