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Register a new userA Data-Driven Sparse Polynomial Chaos Expansion Method to Assess Probabilistic Total Transfer Capability for Power Systems with Renewables
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Added by
Xiaoting Wang
Publication date
2020
fields
Electronic Engineering
and research's language is
English
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The increasing uncertainty level caused by growing renewable energy sources (RES) and aging transmission networks poses a great challenge in the assessment of total transfer capability (TTC) and available transfer capability (ATC). In this paper, a novel data-driven sparse polynomial chaos expansion (DDSPCE) method is proposed for estimating the probabilistic characteristics (e.g., mean, variance, probability distribution) of probabilistic TTC (PTTC). Specifically, the proposed method, requiring no pre-assumed probabilistic distributions of random inputs, exploits data sets directly in estimating the PTTC. Besides, a sparse scheme is integrated to improve the computational efficiency. Numerical studies on the modified IEEE 118-bus system demonstrate that the proposed DDSPCE method can achieve accurate estimation for the probabilistic characteristics of PTTC with a high efficiency. Moreover, numerical results reveal the great significance of incorporating discrete random inputs in PTTC and ATC assessment, which nevertheless was not given sufficient attention.
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Polynomial chaos expansions (PCEs) have been used in many real-world engineering applications to quantify how the uncertainty of an output is propagated from inputs. PCEs for models with independent inputs have been extensively explored in the literature. Recently, different approaches have been proposed for models with dependent inputs to expand the use of PCEs to more real-world applications. Typical approaches include building PCEs based on the Gram-Schmidt algorithm or transforming the dependent inputs into independent inputs. However, the two approaches have their limitations regarding computational efficiency and additional assumptions about the input distributions, respectively. In this paper, we propose a data-driven approach to build sparse PCEs for models with dependent inputs. The proposed algorithm recursively constructs orthonormal polynomials using a set of monomials based on their correlations with the output. The proposed algorithm on building sparse PCEs not only reduces the number of minimally required observations but also improves the numerical stability and computational efficiency. Four numerical examples are implemented to validate the proposed algorithm.
The surrogate model-based uncertainty quantification method has drawn a lot of attention in recent years. Both the polynomial chaos expansion (PCE) and the deep learning (DL) are powerful methods for building a surrogate model. However, the PCE needs to increase the expansion order to improve the accuracy of the surrogate model, which causes more labeled data to solve the expansion coefficients, and the DL also needs a lot of labeled data to train the neural network model. This paper proposes a deep arbitrary polynomial chaos expansion (Deep aPCE) method to improve the balance between surrogate model accuracy and training data cost. On the one hand, the multilayer perceptron (MLP) model is used to solve the adaptive expansion coefficients of arbitrary polynomial chaos expansion, which can improve the Deep aPCE model accuracy with lower expansion order. On the other hand, the adaptive arbitrary polynomial chaos expansions properties are used to construct the MLP training cost function based on only a small amount of labeled data and a large scale of non-labeled data, which can significantly reduce the training data cost. Four numerical examples and an actual engineering problem are used to verify the effectiveness of the Deep aPCE method.
Uncertainties exist in both physics-based and data-driven models. Variance-based sensitivity analysis characterizes how the variance of a model output is propagated from the model inputs. The Sobol index is one of the most widely used sensitivity indices for models with independent inputs. For models with dependent inputs, different approaches have been explored to obtain sensitivity indices in the literature. Typical approaches are based on procedures of transforming the dependent inputs into independent inputs. However, such transformation requires additional information about the inputs, such as the dependency structure or the conditional probability density functions. In this paper, data-driven sensitivity indices are proposed for models with dependent inputs. We first construct ordered partitions of linearly independent polynomials of the inputs. The modified Gram-Schmidt algorithm is then applied to the ordered partitions to generate orthogonal polynomials with respect to the empirical measure based on observed data of model inputs and outputs. Using the polynomial chaos expansion with the orthogonal polynomials, we obtain the proposed data-driven sensitivity indices. The sensitivity indices provide intuitive interpretations of how the dependent inputs affect the variance of the output without a priori knowledge on the dependence structure of the inputs. Three numerical examples are used to validate the proposed approach.
In this paper, we investigate conventional communication-based chaotic waveforms in the context of wireless power transfer (WPT). Particularly, we present a differential chaos shift keying (DCSK)-based WPT architecture, that employs an analog correlator at the receiver, in order to boost the energy harvesting (EH) performance. We take into account the nonlinearities of the EH process and derive closed-form analytical expressions for the harvested direct current (DC) under a generalized Nakagami-m block fading model. We show that, in this framework, both the peak-to-average-power-ratio of the received signal and the harvested DC, depend on the parameters of the transmitted waveform. Furthermore, we investigate the case of deterministic unmodulated chaotic waveforms and demonstrate that, in the absence of a correlator, modulation does not affect the achieved harvested DC. On the other hand, it is shown that for scenarios with a correlator-aided receiver, DCSK significantly outperforms the unmodulated case. Based on this observation, we propose a novel DCSK-based signal design, which further enhances the WPT capability of the proposed architecture; corresponding analytical expressions for the harvested DC are also derived. Our results demonstrate that the proposed architecture and the associated signal design, can achieve significant EH gains in DCSK-based WPT systems. Furthermore, we also show that, even by taking into account the nonlinearities at the transmitter amplifier, the proposed chaotic waveform performs significantly better in terms of EH, when compared with the existing multisine signals.
In this work, we investigate differential chaos shift keying (DCSK), a communication-based waveform, in the context of wireless power transfer (WPT). Particularly, we present a DCSK-based WPT architecture, that employs an analog correlator at the receiver in order to boost the energy harvesting (EH) performance. By taking into account the nonlinearities of the EH process, we derive closed-form analytical expressions for the peak-to-average-power-ratio of the received signal as well as the harvested power. Nontrivial design insights are provided, where it is shown how the parameters of the transmitted waveform affects the EH performance. Furthermore, it is demonstrated that the employment of a correlator at the receiver achieves significant EH gains in DCSK-based WPT systems.
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