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Currently, the increasing wind power penetration, with consequent randomness and variability, presents great challenges to power system planning and operation. Probabilistic power flow (PPF) has been developed to calculate the power flow under uncertain circumstances. However, the current wind power models are subject to specific probability distributions, limiting their accuracies in wider applications. Additionally, the cumulant method (CM)-based PPF, if nonlinear relationship is considered in, would face an impractically high computational complexity. To address these problems in modeling and cumulant calculation, this article proposes a novel generalized density/distribution fitting method (GDFM) combining with the Copula function to establish a joint probability model for wind power generation. A special impulse- mixed probability density (IMPD) integration method is also introduced to derive the input cumulants from the model. Finally, a fast cumulant method (FCM) is proposed to reduce the computational burden of output cumulant calculation while retaining a high accuracy in a nonlinear context. Case study on the IEEE-118 test system validates the effectiveness of the proposed methods, and a real application to a provincial power grid in China provides some useful power flow risk information for decision making. The whole FCM-based PPF scheme can be helpful for future power flow examination in power system planning and operation.

As increasing penetration of renewable energy, stochastic power flow method becomes an essential tool to analyze the randomness and variation in power system. Conventional methods cannot count in the correlation between input random variables, which will lead to obvious error in most cases. Consequently, it’s necessary to study enhanced methods, and also conduct comparisons among them to provide criteria for method selection. This paper builds up the basic frame of stochastic power flow methods considering correlation and compares them, especially two typical cumulant methods in aspects of accuracy, efficiency and complexity. Useful conclusions are obtained for further study and application.

As increasing integration of stochastic factors such as renewable energy, storage system and controllable load, the consequent randomness and variability bring great challenges to power system planning and operation. Probabilistic power flow (PPF) is proposed to deal with those uncertainties by means of probability distributions and probabilistic methods. However, some stochastic factors like energy storage and controllable load are subject to the control strategies, which makes their distributions and correlations vary a lot and adds difficulties to PPF analysis. To address the problem, this paper combines alternative control strategies, a novel polynomial distribution fitting method and the Copula function theory to establish a general probability model. Based on the model, an enhanced probabilistic power flow procedure with all of these stochastic factors and correlations is performed, and a subsequent evaluation scheme for transmission expansion plans are developed. Case study shows that the proposed PPF method can help make more reasonable and reliable decisions to transmission expansion plans under multiple stochastic factors.

As increasing penetration of renewable energy, the unpredictable randomness and variability of generation pose challenges to power system planning and operation. Probabilistic power flow (PPF) is emerging as a valid method to deal with uncertainty of generation outputs. However, the conventional PPF methods considering correlated generations can only derive the probability distribution of single node voltage or transmission line power, failing to cover the correlation between multiple voltages and powers, which is also significant in power flow analysis. To address the problem, this paper proposed an enhanced cumulant-based probabilistic power flow method for correlation mining in order to obtain more detailed probability characteristics of node voltages and transmission powers. Test results showed that the proposed method performed better than common PPF methods in combined or conditional events analysis, thus is more practical for operation analysis and decision making.

With increasing renewable energies integrated into power grid, the variability and uncertainty in power system are becoming dramatic and unpredictable. Probabilistic Power Flow was proposed to handle the uncertainties, by introducing random variables with specific probability distributions into calculation. However, the current PPF usually adopts correlation coefficient matrix as its correlation model, which is incomplete for probabilistic modelling. And the deterministic distributions in PPF cannot fully describe the randomness of renewable energy. To address the problem, this paper proposed a fuzzy Copula model for building a more complete and real probability model. And based on the fuzzy model, a whole scheme of Fuzzy Probabilistic Power Flow (FPPF) was established. Case study showed that FPPF can help obtain more possible distribution scenarios of objective random variables, indicating its superior reliability and practicability than conventional PPF.

Nowadays with enlargement of power grid and increasing renewable energy integration, uncertainties and randomness challenge traditional power system analysis methods. Scenarios are widely applied to deal with power system uncertainties. Especially power flow examination in transmission expansion planning needs typical scenarios to verify normal power flow, and provide useful information for auxiliary planning strategies by studying typical extreme scenarios. In order to perform large-scale and multidimensional scenario analysis in power flow examination, this paper proposes an improved initial-center-refined and weighted K-means (ICRW K-means) method to improve efficiency and reduce computational time. Taking extreme scenarios into account, an extreme scenario reduction method is presented to retain typical extreme scenarios, maintaining more features of scenario reduction results. A real network is studied using proposed ICRW K-means and extreme scenario reduction method to perform power flow examination in transmission expansion planning. Numerical results demonstrate the effectiveness of proposed method, providing suggestions for auxiliary planning strategies to enhance power grid in resisting extreme conditions and reducing economic losses.