Probabilistic load flow calculation using cumulants and multiple integrals

Wu, Wei; Wang, Keyou; Li, Guojie; Jiang, Xiuchen; Wang, Zhiming

doi:10.1049/iet-gtd.2015.1129

Cited by 34 publications

(18 citation statements)

References 28 publications

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“…PPF analysis methods can be generally divided into analytical methods and numerical methods. The former includes cumulant methods [4], [5], point estimation methods [6], [7], cornish-fisher expansion [8], [9] and the generalized polynomial chaos method [10]. These analytical methods is considered to be computational tractable since they directly integrate the probabilistic distribution of uncertainty factors (e.g., renewable energy source and load) into a few deterministic power flow models.…”

Section: B Literature Review and Backgroundmentioning

confidence: 99%

Fast Calculation of Probabilistic Power Flow: A Model-Based Deep Learning Approach

Yang

et al. 2020

IEEE Trans. Smart Grid

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Probabilistic power flow (PPF) plays a critical role in the analysis of power systems. However, its high computational burden makes practical implementations challenging. This paper proposes a model-based deep learning approach to overcome these computational challenges. A deep neural network (DNN) is used to approximate the power flow calculation process, and is trained according to the physical power flow equations to improve its learning ability. The training process consists of several steps: 1) the branch flows are added into the objective function of the DNN as a penalty term, which improves the generalization ability of the DNN; 2) the gradients used in back propagation are simplified according to the physical characteristics of the transmission grid, which accelerates the training speed while maintaining effective guidance of the physical model; and 3) an improved initialization method for the DNN parameters is proposed to improve the convergence speed. The simulation results demonstrate the accuracy and efficiency of the proposed method in standard IEEE and utility benchmark systems. Index Terms-Model-based deep learning, initialization methods, deep neural networks, probabilistic power flow.

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Section: B Literature Review and Backgroundmentioning

confidence: 99%

Fast Calculation of Probabilistic Power Flow: A Model-Based Deep Learning Approach

Yang

et al. 2020

IEEE Trans. Smart Grid

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“…The cumulants [26][27][28][29] of a probability distribution are a set of quantities that provide an alternative to the moments of the distribution. The moments determine the cumulants in the sense that any two probability distributions whose moments are identical will have identical cumulants as well, and similarly the cumulants determine the moments.…”

Section: Cumulants Of Random Variablesmentioning

confidence: 99%

Chance-Constrained Real-Time Dispatch with Renewable Uncertainty Based on Dynamic Load Flow

Bie

Zhang

et al. 2017

Energies

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Abstract:In this paper, a comprehensive real-time dispatch model considering renewable uncertainty based on dynamic load flow (DLF) is proposed. Through DLF, the primary and secondary frequency regulation amount caused by the variation of renewable energy as well as the line flow when primary and secondary regulation are deployed can be obtained easily. Not only the frequency constraints, but also the regular constraints like generator production limits and line flow limits are respected under both primary and secondary frequency regulation. To solve the dispatch problem with renewable uncertainty, chance-constrained programming based on cumulants and Cornish-fisher expansions (CCP-CMCF) is adopted to get the probability of holding the chance constraints and then the real-time dispatch model can be transformed into a quadratic programming. The simulation results show that the dispatch model proposed in this paper can deal with both primary and secondary regulation well and has a fast computation speed.

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“…Cumulant method (CM) [7]- [16] is the representative of the analytical method. It can easily and efficiently calculate the cumulants of the output random variables (ORVs) based on the linearized load flow model and the characteristics of the cumulant.…”

Section: Introductionmentioning

confidence: 99%

“…It can easily and efficiently calculate the cumulants of the output random variables (ORVs) based on the linearized load flow model and the characteristics of the cumulant. Although CM performs well in terms of efficiency, its accuracy is less impressive: a considerable error is observed when the input random variables (IRVs) are highly discrete [16].…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Load Flow Based on Bivariate Dimension Reduction and Johnson System

Zhang

Yin

2020

IEEE Access

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A probabilistic load flow (PLF) is an effective tool that helps describe the uncertainty of power system operation. However, when confronting random variables with non-Gaussian distributions and highly discrete characteristics, existing PLF methods have difficulty balancing efficiency and accuracy. Therefore, a novel approach based on bivariate dimension reduction (BDR) and the Johnson system is proposed herein. BDR is used to estimate the moments of output random variables (ORVs). Because BDR considers the joint effect of input random variables, it significantly reduces the estimation error for high-order moments in particular. In addition, a strategy to improve BDR efficiency is proposed. The Johnson system is used to obtain the probability distributions of ORVs as it has better adaptability and accuracy than the series expansion method. Case studies including comparisons between this approach and others found in the literature were conducted, and the results obtained showed that the proposed method has better performance than previous approaches. INDEX TERMS Bivariate dimension reduction, Johnson system, probabilistic load flow, renewable energy source.

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Probabilistic load flow calculation using cumulants and multiple integrals

Cited by 34 publications

References 28 publications

Fast Calculation of Probabilistic Power Flow: A Model-Based Deep Learning Approach

Fast Calculation of Probabilistic Power Flow: A Model-Based Deep Learning Approach

Chance-Constrained Real-Time Dispatch with Renewable Uncertainty Based on Dynamic Load Flow

Probabilistic Load Flow Based on Bivariate Dimension Reduction and Johnson System

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