Enhancements to the Cumulant Method for Probabilistic Optimal Power Flow Studies

Tamtum, A.; Schellenberg, A.; Rosehart, William

doi:10.1109/tpwrs.2009.2030409

Cited by 60 publications

(44 citation statements)

References 11 publications

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“…The wind power output can be modeled as a negative load, and its power factor is kept constant [5]. References [36,37] built the model of CM for P-OPF with the load at each bus as a random input variable. In this paper, wind power output is also treated as a random input variable and incorporated into the computational model.…”

Section: Traditional CM For P-opfmentioning

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: Traditional CM For P-opfmentioning

confidence: 99%

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

Deng

Zhang

2017

Energies

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“…For example, in [22] a chance-constrained optimal power dispatch strategy is developed for transmission systems, using cumulant-based stochastic models. The Gram-Charlier expansion method is applied in [22], [26], [27] to approximate the distribution of state variables; however, it reduces the accuracy of stochastic modelling. Such reduced accuracy could be inevitable in large transmission systems; but it may not be acceptable at distribution level, which is where we focus on in this paper.…”

Section: B Comparison To Related Literaturementioning

confidence: 99%

“…To this aim, we approximate the chance constraints in (25) and (27) with some convex bounds in the form of their expected values, specifically by using the Markov Bounds [52]. We then compare the two approaches for the same set-up and objectives of Section IV-A.…”

Section: E Comparison With Scenario-based Stochastic Optimizationmentioning

confidence: 99%

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Energy Storage Planning in Active Distribution Grids: A Chance-Constrained Optimization with Non-Parametric Probability Functions

Akhavan-Hejazi

Mohsenian‐Rad

2016

IEEE Trans. Smart Grid

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Abstract-By considering the specific characteristics of random variables in active distribution grids, such as their statistical dependencies and often irregularly-shaped probability distributions, we propose a non-parametric chance-constrained optimization approach to operate and plan energy storage units in power distribution girds. In particular, we develop new closedform stochastic models for the key operational parameters in the system. Our approach is analytical and allows formulating tractable optimization problems. Yet, it does not involve any restricting assumption on the distribution of random parameters, hence, it results in accurate modeling of uncertainties. Different case studies are presented to compare the proposed approach with the conventional deterministic and parametric stochastic approaches, where the latter is based on approximating random variables with Gaussian probability distributions.

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“…PPF methods mainly include three categories: simulation methods [5][6][7], approximate methods [8][9][10][11], and analytical methods [12][13][14][15][16]. Among simulation methods, the Monte Carlo simulation method (MCSM) is an outstanding representation, and it is regarded as a standard to evaluate the accuracy and efficiency of other PPF methods.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Power Flow Method Considering Continuous and Discrete Variables

2017

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This paper proposes a probabilistic power flow (PPF) method considering continuous and discrete variables (continuous and discrete power flow, CDPF) for power systems. The proposed method-based on the cumulant method (CM) and multiple deterministic power flow (MDPF) calculations-can deal with continuous variables such as wind power generation (WPG) and loads, and discrete variables such as fuel cell generation (FCG). In this paper, continuous variables follow a normal distribution (loads) or a non-normal distribution (WPG), and discrete variables follow a binomial distribution (FCG). Through testing on IEEE 14-bus and IEEE 118-bus power systems, the proposed method (CDPF) has better accuracy compared with the CM, and higher efficiency compared with the Monte Carlo simulation method (MCSM).

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Enhancements to the Cumulant Method for Probabilistic Optimal Power Flow Studies

Cited by 60 publications

References 11 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

Energy Storage Planning in Active Distribution Grids: A Chance-Constrained Optimization with Non-Parametric Probability Functions

Probabilistic Power Flow Method Considering Continuous and Discrete Variables

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