The load flow problem is fundamental to characterize the equilibrium behavior of a power system. Uncertain power injections such as those due to demand variations and intermittent renewable resources will change the system’s equilibrium unexpectedly, and thus potentially jeopardizing the system’s reliability and stability. Understanding load flow solutions under uncertainty becomes imperative to ensure the seamless operation of a power system. In this work, we propose a non-parametric probabilistic load flow (NP-PLF) technique based on the Gaussian Process (GP) learning to understand the power system behavior under uncertainty for better operational decisions. The technique can provide “semi-explicit” form of load flow solutions by implementing the learning and testing steps that map control variables to inputs. The proposed NP-PLF leverages upon GP upper confidence bound (GP-UCB) sampling algorithm. The salient features of this NP-PLF method are: i) applicable for power flow problem having power injection uncertainty with an unknown class of distribution; ii) providing probabilistic learning bound (PLB) which further provides control over the error and convergence; iii) capable of handling intermittent distributed generation as well as load uncertainties. The simulation results performed on the IEEE 30-bus and IEEE 118-bus system show that the proposed method can learn the voltage function over the power injection subspace using a small number of training samples. Further, the testing with different input uncertainty distributions indicates that complete statistical information can be obtained for the probabilistic load flow problem with an average percentage relative error of the order of $10^{-3}$% on 50,000 test points.

潮流问题对于表征电力系统的平衡行为至关重要。不确定的功率注入（例如由于需求变化和间歇性可再生资源引起的功率注入）会意外地改变系统的平衡，从而有可能危害系统的可靠性和稳定性。必须了解不确定性下的潮流解决方案，以确保电力系统的无缝运行。在这项工作中，我们提出了一种基于高斯过程（GP）的非参数概率潮流（NP-PLF）技术，以了解电力系统在不确定性条件下的行为，以获得更好的运行决策。该技术可以提供“半显性”通过实施将控制变量映射到输入的学习和测试步骤来形成潮流解决方案。拟议的NP-PLF利用GP上限置信度（GP-UCB）采样算法。NP-PLF方法的显着特征是：i）适用于具有未知分布类别的功率注入不确定性的潮流问题；ii）提供概率学习界限（PLB），它进一步提供对错误和收敛的控制；iii）能够处理间歇性分布式发电以及负荷不确定性。在IEEE 30总线和IEEE 118总线系统上进行的仿真结果表明，该方法可以使用少量训练样本来学习功率注入子空间上的电压函数。更多，$\mathrm{1个}{0}^{-3}$50,000个测试点的％。