Chronological Probability Model of Photovoltaic Generation

Ren, Zhouyang; Yan, Wei; Zhao, Xuetong; Li, Wenyuan; Yu, Jie

doi:10.1109/tpwrs.2013.2293173

Cited by 49 publications

(30 citation statements)

References 20 publications

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“…However, these well-defined distribution functions perform well only with a prior assumption that PV generation and load satisfy a certain distribution, which can hardly hold for various PV generation and load scenarios. Therefore, nonparametric kernel density estimation [24,25], which is suitable for arbitrary distribution, is used in this paper.…”

Section: Marginal Distributions Of Pv and Loadmentioning

confidence: 99%

Probabilistic duck curve in high PV penetration power system: Concept, modeling, and empirical analysis in China

et al. 2019

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The concepts of probabilistic duck curve and probabilistic ramp curve are proposed.• The probabilistic duck curve is modeled considering dependencies among PV and loads. A B S T R A C TThe high penetration of photovoltaic (PV) is reshaping the electricity net-load curve and has a significant impact on power system operation and planning. The concept of duck curve is widely used to describe the timing imbalance between peak demand and PV generation. The traditional duck curve is deterministic and only shows a single extreme or typical scenario during a day. Thus, it cannot capture both the probability of that scenario and the uncertainty of PV generation and loads. These weaknesses limit the application of the duck curve on power system planning under high PV penetration. To address this issue, the novel concepts of probabilistic duck curve (PDC) and probabilistic ramp curve (PRC) are proposed to accurately model the uncertainty and variability of electricity net load and ramp under high PV penetration. An efficient method is presented for modeling PDC and PRC using kernel density estimation, copula function, and dependent discrete convolution. Several indices are designed to quantify the characteristics of the PDC and PRC. For the application, we demonstrate how the PDC and PRC will benefit flexible resource planning. Finally, an empirical study on the Qinghai provincial power system of China validates the effectiveness of the presented method. The results of PDC and PRC intuitively illustrate that the ramp demand and the valley of net load face considerable uncertainty under high PV penetration. The results of flexible resource planning indicate that retrofitting coal-fired units has remarkable performance on enhancing the power system flexibility in Qinghai. In average, reducing the minimal output of coal-fired units by 1 MW will increase PV accommodation by over 4 MWh each day.

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Section: Marginal Distributions Of Pv and Loadmentioning

confidence: 99%

Probabilistic duck curve in high PV penetration power system: Concept, modeling, and empirical analysis in China

et al. 2019

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“…This is illustrated with a case study wherein the European LV test feeder is used with an increasing amount of PV generation. The PV generation is modelled based on a model for the creation of PV time series [23]. The generated PV time series for the times between 12:00 and 14:00 is added to the distribution of the household load between these two times to create the Gaussian mixture distribution of the load as illustrated in Fig.…”

Section: Resultsmentioning

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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“…The stochastic samples of power flow responses (such as voltage magnitude, line flow, network loss, or any other response) can be obtained by substituting stochastic samples of into the polynomial chaos expansion. With these samples, a nonparametric kernel density estimation method [22] is applied to estimate the probability distributions of power flow responses. No series expansion is needed.…”

Section: Estimating the Probability Distributions Of Power Flow Rementioning

confidence: 99%

“…The probability density function can be estimated using the following kernel density function estimation [22]. Mathematically, it has been proved that when the sample size is reasonably large, in (10) will converge to [25]:…”

Section: Appendixmentioning

confidence: 99%

Probabilistic Power Flow Analysis Based on the Stochastic Response Surface Method

Ren

Billinton

et al. 2016

IEEE Trans. Power Syst.

Self Cite

145

111

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This paper proposes a probabilistic power flow analysis technique based on the stochastic response surface method. The probability distributions and statistics of power flow responses can be accurately and efficiently estimated by the proposed method without using series expansions such as the Gram-Charlier, Cornish-Fisher, or Edgeworth series. The stochastic continuous input variables following normal distributions such as loads or non-normal distributions such as photovoltaic generation and wind power and their multiple correlations can be easily modeled. The correctness, effectiveness and adaptability of the proposed method are demonstrated by comparing the probabilistic power flow analysis results of the IEEE 14-bus and 57-bus standard test systems obtained from the proposed method, the point estimate method, and the Monte Carlo simulation method.Index Terms-Photovoltaic generation, probabilistic power flow, stochastic response surface method, wind power.

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Chronological Probability Model of Photovoltaic Generation

Cited by 49 publications

References 20 publications

Probabilistic duck curve in high PV penetration power system: Concept, modeling, and empirical analysis in China

Probabilistic duck curve in high PV penetration power system: Concept, modeling, and empirical analysis in China

Gaussian Mixture Based Probabilistic Load Flow For LV-Network Planning

Probabilistic Power Flow Analysis Based on the Stochastic Response Surface Method

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