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Improved Monte Carlo techniques for distributed generation impact evaluation

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Abstract

The integration of emerging technologies associated with renewable sources of electrical energy introduces new uncertainties into the operation and planning of the electrical power system (EPS). In this context, the Monte Carlo method (MCM) is a widely used technique for addressing uncertainties in distributed generation (DG) impact analysis. However, this method demands a high computational effort, which tends to increase with the dimensionality of the problem and the correlations among random variables. For this reason, this work investigates some of the main Monte Carlo-based techniques for improving computational efficiency in DG impact assessment, namely Latin Hypercube Sampling (LHS), Quasi-Monte Carlo (QMC) and Importance Sampling (IS). These methods are applied in a case study involving an IEEE feeder connected to DG, and the simulations are conducted via the OpenDSS software. The results show enhancements in both precision and convergence when compared to Crude Monte Carlo (CMC). Additionally, the implementation of the hybrid technique IS-QMC demonstrates that the combination of these methods can lead to superior outcomes.

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Availability of data and materials

The complete data of the IEEE 13-bus feeder can be found in [33].

Notes

  1. The critical value is the number such that \( \varphi (z_{\gamma } ){\text{~}} = {\text{~}}\gamma \), where \( \varphi \) is the standard normal cumulative distribution function (CDF). For example, for a 95% confidence level, \(\alpha {\text{ ~}} = {\text{~}}0.05 \) and the critical value is \( z_{{1 - 0.05/2}} = z_{{0.975}} = {\text{~}}\varphi ^{{ - 1}} \left( {0.975} \right){\text{~}} = {\text{~}}1.96 \)

  2. Halton is the multidimensional generalization of the (one-dimensional) Van Der Corput sequence. Equations (8) and (9) also apply to Van Der Corput.

  3. The CMC estimator with updated weights differs from the IS estimator because, although the updated weights are already incorporated into the random sampling of the model states, (2) is used to calculate the estimator instead of (11). The IS estimator obtained via (11) is shown in Fig. 13. The CMC estimator with updated weights is illustrated in Fig. 12 only to clarify the IS operation, having no practical meaning in its current form.

  4. The confidence interval and its margin of error are defined in (4) and (5), respectively.

  5. Unlike the analysis shown in Figs. 9, 10 and 11, in which the estimator (coefficient β) was obtained for 100 MCM simulations, in Fig. 14 the cumulative average was calculated in a single MCM simulation over 1,000 iterations, such that the cumulative average in the last iteration considers the values estimated in previous iterations.

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Funding

This study was financed in part by Fundação Carlos Chagas de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ) and by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq/INERGE), Brazil.

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Authors and Affiliations

  1. Graduate Program in Electrical and Telecommunications Engineering (PPGEET), Federal Fluminense, University (UFF), Niterói, RJ, 24210-240, Brazil

    Tiago P. Abud & Bruno S. M. C. Borba

  2. Electrical Engineering Department, Federal University of Technology – Parana (UTFPR), Apucarana, PR, 86812-460, Brazil

    Renan S. Maciel

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  1. Tiago P. Abud
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  2. Renan S. Maciel
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  3. Bruno S. M. C. Borba
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T. A. involved in conceptualization, methodology, investigation, computational simulation, and writing of the original manuscript. R. M. took part in conceptualization, supervision, and manuscript review. B. B. involved in conceptualization, supervision, manuscript review, and funding acquisition.

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Correspondence to Tiago P. Abud.

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Abud, T.P., Maciel, R.S. & Borba, B.S.M.C. Improved Monte Carlo techniques for distributed generation impact evaluation. Electr Eng (2024). https://doi.org/10.1007/s00202-024-02336-5

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