An analytical method to solve the probabilistic load flow considering load demand correlation using the DC load flow

Villanueva, Daniel; Feijóo, Andrés; Pazos, José Luis Echarte

doi:10.1016/j.epsr.2014.01.003

Cited by 56 publications

(30 citation statements)

References 25 publications

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“…Step (7) Determine the vector of discrete input variables according to Equations (11) and (12). 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%

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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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Section: Implementation Procedures Of Cdpfmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Probabilistic Power Flow Method Considering Continuous and Discrete Variables

2017

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“…For the probabilistic modeling of DG, different DGs might obey different distributions. For example, the Weibull distribution [23,24] is usually used for the wind speed model as shown in Equation (16), and the probabilistic expression and control strategy for wind power generation can be obtained through Equations (16) and (17):…”

Section: Probabilistic Modeling Of Power System Uncertaintiesmentioning

confidence: 99%

A Parallel Probabilistic Load Flow Method Considering Nodal Correlations

et al. 2016

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Abstract:With the introduction of more and more random factors in power systems, probabilistic load flow (PLF) has become one of the most important tasks for power system planning and operation. Cumulants-based PLF is an effective algorithm to calculate PLF in an analytical way, however, the correlations among the nodal injections to the system level have rarely been studied. A novel parallel cumulants-based PLF method considering nodal correlations is proposed in this paper, which is able to deal with the correlations among all system nodes, and avoid the Jacobian matrix inversion in the traditional cumulants-based PLF as well. In addition, parallel computing is introduced to improve the efficiency of the numerical calculations. The accuracy of the proposed method is validated by numerical tests on the standard IEEE-14 system, comparing with the results from Correlation Latin hypercube sampling Monte Carlo Simulation (CLMCS) method. And the efficiency and parallel performance is proven by the tests on the modified IEEE-300, C703, N1047 systems with distributed generation (DG). Numerical simulations show that the proposed parallel cumulants-based PLF method considering nodal correlations is able to get more accurate results using less computational time and physical memory, and have higher efficiency and better parallel performance than the traditional one.

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“…Application to medium voltage networks with the amount of variable loads limited to mostly the distributed renewable energy resources has been performed [8] [9]. For the DC load flow, a probabilistic load flow based on cumulants and Gram-Charlier expansion has already been applied [10]. For the LV network, the DC simplifications will not hold.…”

Section: Introductionmentioning

confidence: 99%

Gaussian Mixture Based Probabilistic Load Flow For LV-Network Planning

Nijhuis

Gibescu

Cobben

2017

IEEE Trans. Power Syst.

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Abstract-Due the many uncertainties present in the evolution of loads and distributed generation, the use of probabilistic load flow in low voltage (LV) networks is essential for the evaluation of the robustness of these networks from a planning perspective. The main challenge with the assessment of LV-networks is the sheer number of networks which need to be analysed. Moreover, most loads in the LV-network have a volatile nature and are hard to approximate using conventional probability distributions. This can be overcome by the use of a Gaussian mixture distribution in load modelling. Taking advantage of its radial nature and high R/X ratios, the LV-network can be analysed more efficiently from a computation viewpoint. By the application of simplifications defined in this paper, the backwards-forwards load flow can be solved analytically. This allows for the direct computation of the load flow equations with a Gaussian mixture distribution as load. When using this new approach, the required calculation time for small networks can be decreased to 3% of the time it takes to generate a similar accuracy with a Monte Carlo approach. The practical application of this load flow calculation method is illustrated with a case study on PV penetration.

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An analytical method to solve the probabilistic load flow considering load demand correlation using the DC load flow

Cited by 56 publications

References 25 publications

Probabilistic Power Flow Method Considering Continuous and Discrete Variables

Probabilistic Power Flow Method Considering Continuous and Discrete Variables

A Parallel Probabilistic Load Flow Method Considering Nodal Correlations

Gaussian Mixture Based Probabilistic Load Flow For LV-Network Planning

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