Probabilistic Power Flow Analysis Based on the Stochastic Response Surface Method

Ren, Zhouyang; Li, Wenyuan; Billinton, R.; Yan, Wei

doi:10.1109/tpwrs.2015.2461159

Cited by 145 publications

(120 citation statements)

References 22 publications

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“…From (19), if the power system bus number is R, the state variables of bus voltage and branch flow (i.e. v i and z i ) can be formulated as:…”

Section: Modified Cumulant Calculationmentioning

confidence: 99%

“…This method greatly enhances the calculation speed and is able to accurately approximate the PDF or CDF of output variables [13][14][15][16][17]. Based on the GC theory, several improved approaches were employed to address PLF analysis, such as the stochastic collocation interpolation [18], and polynomial chaos expansion [19,20]. However, the GC expansion based PLF (GC-PLF) calculation method may mistakenly obtain negative values in tail regions of PDF, which limits system planners to determine line security and maximum power rating [21,22].…”

Section: Introductionmentioning

confidence: 99%

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Maximum entropy based probabilistic load flow calculation for power system integrated with wind power generation

Sui

Hou

Jia

et al. 2018

J. Mod. Power Syst. Clean Energy

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Distributed generation including wind turbine (WT) and photovoltaic panel increased very fast in recent years around the world, challenging the conventional way of probabilistic load flow (PLF) calculation. Reliable and efficient PLF method is required to take into account such changing. This paper studies the maximum entropy probabilistic density function reconstruction method based on cumulant arithmetic of linearized load flow formulation, and then develops a maximum entropy based PLF (ME-PLF) calculation algorithm for power system integrated with wind power generation (WPG). Comparing to traditional Gram-Charlier expansion based PLF (GC-PLF) calculation method, the proposed ME-PLF calculation algorithm can obtain more reliable and accurate probabilistic density functions (PDFs) of bus voltages and branch flows in various WT parameter scenarios. It can solve the limitation of GC-PLF calculation method that mistakenly gaining negative values in tail regions of PDFs. Linear dependence between active and reactive power injections of WPG can also be effectively considered by the modified cumulant calculation framework. Accuracy and efficiency of the proposed approach are validated with some test systems. Uncertainties yielded by the wind speed variations, WT locations, power factor fluctuations are considered.

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“…From (19), if the power system bus number is R, the state variables of bus voltage and branch flow (i.e. v i and z i ) can be formulated as:…”

Section: Modified Cumulant Calculationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Maximum entropy based probabilistic load flow calculation for power system integrated with wind power generation

Sui

Hou

Jia

et al. 2018

J. Mod. Power Syst. Clean Energy

View full text Add to dashboard Cite

show abstract

“…Then, calculate the probability distribution of discrete vector according to Equations (13) and (14).…”

Section: Implementation Procedures Of Cdpfmentioning

confidence: 99%

“…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%

“…PDFs and CDFs of power flow responses can be obtained by CM accurately and efficiently for PPF problems [19,20]. Nonetheless, errors based on CM still exist, and mainly consist of two classes: (1) linearization errors-when non-linear power flow equations are linearized into linear power flow equations by ignoring high-order terms of Taylor series expression, linearization errors are formed [21]; and (2) series expansion errors-when series diverge, such as the Gram-Charlier series (GCS) [22], PDFs will appear negative or CDFs will be more than 1 [14]. In a word, two types of errors are mainly derived from the fluctuation of stochastic variables.…”

Section: Introductionmentioning

confidence: 99%

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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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Probabilistic power flow analysis based on arbitrary polynomial chaos expansion of bus voltage phasor

Laowanitwattana

Uatrongjit

2020

Int Trans Electr Energ Syst

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Summary An increasing penetration of renewable energy sources, such as solar farms and wind farms, necessitates a usage of statistical analysis and modeling for efficient operation and planning of the power systems. The probabilistic power flow (PPF) analysis based on the generalized polynomial chaos expansion (gPCE) technique has been applied to investigate the effects of random parameters in the power system network. Nevertheless, the gPCE‐based methods can be applied to the systems whose random parameters belong to specific probability distributions. If there exists a correlation among random parameters, then a decorrelation technique, for example, a copula function, is required. In this paper, a new approach for PPF analysis based on the arbitrary polynomial chaos expansion (aPCE) has been proposed. A set of basic polynomial functions used in this method is constructed using the recorded dataset of random parameters. The dependency of these uncertain parameters is decoupled by the whitening transformation. Instead of applying the aPCE to the required power system responses such as active power flow, current magnitude, etc, the proposed method uses the aPCE to construct a surrogate model of each bus voltage phasor. The bus voltage phasor model can then be employed to compute other power system responses without performing power flow analysis of the original power system. The proposed technique has been implemented and demonstrated in a MATLAB environment. On the basis of the numerical experiments with the modified IEEE 14‐bus and 118‐bus systems, the results indicate that the proposed method can achieve better accuracy and use less computation time than the techniques based on the gPCE with Gaussian copula function.

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Probabilistic Power Flow Analysis Based on the Stochastic Response Surface Method

Cited by 145 publications

References 22 publications

Maximum entropy based probabilistic load flow calculation for power system integrated with wind power generation

Maximum entropy based probabilistic load flow calculation for power system integrated with wind power generation

Probabilistic Power Flow Method Considering Continuous and Discrete Variables

Probabilistic power flow analysis based on arbitrary polynomial chaos expansion of bus voltage phasor

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