A Parallel Probabilistic Load Flow Method Considering Nodal Correlations

Liu, Juhua; Hao, Xudong; Cheng, Peifen; Fang, Wanliang; Niu, Shuanbao

doi:10.3390/en9121041

Cited by 12 publications

(8 citation statements)

References 33 publications

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“…In this paper, the Cholesky decomposition algorithm [33,44] is applied to convert correlated variables to independent variables. This algorithm is a reasonable solution for a normal distribution vector with a mean of zero [45].…”

Section: The Methods Of Handling Correlations Among Input Variablesmentioning

confidence: 99%

A Novel Probabilistic Optimal Power Flow Method to Handle Large Fluctuations of Stochastic Variables

Deng

Zhang

2017

Energies

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Abstract:The traditional cumulant method (CM) for probabilistic optimal power flow (P-OPF) needs to perform linearization on the Karush-Kuhn-Tucker (KKT) first-order conditions, therefore requiring input variables (wind power or loads) varying within small ranges. To handle large fluctuations resulting from large-scale wind power and loads, a novel P-OPF method is proposed, where the correlations among input variables are also taken into account. Firstly, the inverse Nataf transformation and Cholesky decomposition are used to obtain samples of wind speeds and loads with a given correlation matrix. Then, the K-means algorithm is introduced to group the samples of wind power outputs and loads into a number of clusters, so that in each cluster samples of stochastic variables have small variances. In each cluster, the CM for P-OPF is conducted to obtain the cumulants of system variables. According to these cumulants, the moments of system variables corresponding to each cluster are computed. The moments of system variables for the total samples are obtained by combining the moments for all grouped clusters through the total probability formula. Then, the moments for the total samples are used to calculate the corresponding cumulants. Finally, Cornish-Fisher expansion is introduced to obtain the probability density functions (PDFs) of system variables. IEEE 9-bus and 118-bus test systems are modified to examine the proposed method. Study results show that the proposed method can produce more accurate results than traditional CM for P-OPF and is more efficient than Monte Carlo simulation (MCS).

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Section: The Methods Of Handling Correlations Among Input Variablesmentioning

confidence: 99%

A Novel Probabilistic Optimal Power Flow Method to Handle Large Fluctuations of Stochastic Variables

Deng

Zhang

2017

Energies

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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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“…The authors of [29] proposed a probabilistic power flow calculation method by combining a semi-invariant and Gram-Charlier series expansion. In the literature [30], a probabilistic power flow algorithm based on a stochastic configuration point method was proposed based on the uncertainty quantization theory. In the literature [31], the Monte Carlo method was used as the reference value, and the power system with wind and PV power generation was considered as the analysis object.…”

Section: Introductionmentioning

confidence: 99%

Solar PV Grid Power Flow Analysis

et al. 2019

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As the unconstrained integration of distributed photovoltaic (PV) power into a power grid will cause changes in the power flow of the distribution network, voltage deviation, voltage fluctuation, and so on, system operators focus on how to determine and improve the integration capacity of PV power rationally. By giving full consideration to the static security index constraints and voltage fluctuation, this paper proposes a maximum integration capacity optimization model of the PV power, according to different power factors for the PV power. Moreover, the proposed research analyzes the large-scale PV grid access capacity, PV access point, and multi-PV power plant output, by probability density distribution, sensitivity analysis, standard deviation analysis, and over-limit probability analysis. Furthermore, this paper establishes accessible capacity maximization problems from the Institute of Electrical and Electronics Engineers (IEEE) standard node system and power system analysis theory for PV power sources with constraints of voltage fluctuations. A MATLAB R2017B simulator is used for the performance analysis and evaluation of the proposed work. Through the simulation of the IEEE 33-node system, the integration capacity range of the PV power is analyzed, and the maximum integration capacity of the PV power at each node is calculated, providing a rational decision-making scheme for the planning of integrating the distributed PV power into a small-scale power grid. The results indicate that the fluctuations and limit violation probabilities of the power system voltage and load flow increase with the addition of the PV capacity. Moreover, the power loss and PV penetration level are influenced by grid-connected spots, and the impact of PV on the load flow is directional.

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A Parallel Probabilistic Load Flow Method Considering Nodal Correlations

Cited by 12 publications

References 33 publications

A Novel Probabilistic Optimal Power Flow Method to Handle Large Fluctuations of Stochastic Variables

A Novel Probabilistic Optimal Power Flow Method to Handle Large Fluctuations of Stochastic Variables

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

Solar PV Grid Power Flow Analysis

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