Probabilistic Load Flow for Power Grids With High PV Penetrations Using Copula-Based Modeling of Spatially Correlated Solar Irradiance

Renewable energy sources, such as wind, solar and hydro, are increasingly incorporated into power grids, as a direct consequence of energy and environmental issues. These types of energies are variable and intermittent by nature and their exploitation introduces uncertainties into the power grid. Therefore, probabilistic analysis of the system performance is of significant interest. This paper describes a new approach to Probabilistic Load Flow (PLF) by modifying the Two Point Estimation Method (2PEM) to cover some drawbacks of other currently used methods. The proposed method is examined using two case studies, the IEEE 9-bus and the IEEE 57-bus test systems. In order to justify the effectiveness of the method, numerical comparison with Monte Carlo Simulation (MCS) method is presented. Simulation results indicate that the proposed method significantly reduces the computational burden while maintaining a high level of accuracy. Moreover, that the unsymmetrical 2PEM has a higher level of accuracy than the symmetrical 2PEM with equal computing burden, when the Probability Density Function (PDF) of uncertain variables is asymmetric.

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Probabilistic Load Flow Method Based on Modified Latin Hypercube-Important Sampling

Energies ◽

10.3390/en11113171 ◽

2018 ◽

Vol 11 (11) ◽

pp. 3171 ◽

Cited By ~ 3

Author(s):

Quan Li ◽

Xin Wang ◽

Shuaiang Rong

Keyword(s):

Distributed Generation ◽

Large Scale ◽

Sampling Method ◽

Latin Hypercube Sampling ◽

Load Flow ◽

Power Grids ◽

Latin Hypercube ◽

Importance Sampling Method ◽

Probabilistic Load Flow ◽

Probabilistic Load

The growing amount of distributed generation has brought great uncertainty to power grids. Traditional probabilistic load flow (PLF) algorithms, such as the Monte-Carlo method (MCM), can no longer meet the needs of efficiency and accuracy in large-scale power grids. Latin Hypercube Sampling (LHS) develops a sampling efficiency and solves the correlation problem of distributed generation (DG) access nodes for accuracy analyses. In this paper, a modified Latin Hypercube-Important Sampling method is proposed for higher efficiency and precision by using the importance sampling method before LHS and the Cholesky decomposition method in correlation calculations. The simulation results are presented using a modified IEEE 30-bus system and are compared with traditional MCM and LHS.

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Probabilistic Load Flow Approach Considering Dependencies of Wind Speed, Solar Irradiance, Electrical Load and Energy Exchange with a Joint Probability Distribution Model

Energies ◽

10.3390/en13071727 ◽

2020 ◽

Vol 13 (7) ◽

pp. 1727

Author(s):

Marie-Louise Kloubert

Keyword(s):

Wind Speed ◽

Solar Irradiance ◽

Energy Exchange ◽

Joint Probability ◽

Load Flow ◽

Joint Probability Distribution ◽

Electrical Load ◽

Transmission Grid ◽

Probabilistic Load Flow ◽

Probabilistic Load

The modelling of stochastic feed-ins and demands becomes essential for transmission grid operation and planning due to the extension of renewable energy sources (RES). Neglecting the correlation between uncertain variables and/or oversimplifying the distribution through the assumption of Normal distributions leads to the inaccurate determination of future network states. Therefore, the uncertainties need to be accurately modelled in order to be used in a probabilistic load flow approach. This paper analyses the characteristics of wind speed and solar irradiance for different locations throughout countries and models the dependencies between them. In addition, the total electrical load and the energy exchange between neighbouring countries are analysed. All of these uncertainties are modelled together in a high-dimensional joint probability distribution using pair-copula constructions. The model is applied to generate samples and determine the probability of extreme events, e.g. high RES production and low demand. The probability for rather high load (>65 GW) and low RES production with wind speed less than 3 m/s and solar irradiance less than 100 W m ² at 90% of all stations is e.g. 0.064%. In addition, the model is integrated in a probabilistic load flow approach in order to analyse the German transmission grid for a future scenario of the year 2025. With the copula, samples are generated as an input for the Monte Carlo simulation approach. The approach enables the assessment of planned HVDC lines. When considering the HVDC lines, the load on the AC lines can be significantly reduced.

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