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On a Probability Distribution Convolution Approach to Clear-Sky Index and a Generalized Ångström Equation
Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Solid State Physics. (BEESG)
Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Solid State Physics. (BEESG)
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We show that by modeling solar beam irradiance approximately as a simple Bernoulli distribution and diffuse irradiance as a Gamma distribution, a generalized Ångström equation relating solar irradiation to sunshine hours follows directly as aconsequence of the convolution of beam and diffuseirradiance distributions into a distribution for the clear-sky index.

National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:uu:diva-242441OAI: oai:DiVA.org:uu-242441DiVA: diva2:783460
Available from: 2015-01-26 Created: 2015-01-26 Last updated: 2017-10-27Bibliographically approved
In thesis
1. Distributed Photovoltaics, Household Electricity Use and Electric Vehicle Charging: Mathematical Modeling and Case Studies
Open this publication in new window or tab >>Distributed Photovoltaics, Household Electricity Use and Electric Vehicle Charging: Mathematical Modeling and Case Studies
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Technological improvements along with falling prices on photovoltaic (PV) panels and electric vehicles (EVs) suggest that they might become more common in the future. The introduction of distributed PV power production and EV charging has a considerable impact on the power system, in particular at the end-user in the electricity grid.

In this PhD thesis PV power production, household electricity use and EV charging are investigated on different system levels. The methodologies used in this thesis are interdisciplinary but the main contributions are mathematical modeling, simulations and data analysis of these three components and their interactions. Models for estimating PV power production, household electricity use, EV charging and their combination are developed using data and stochastic modeling with Markov chains and probability distributions. Additionally, data on PV power production and EV charging from eight solar charging stations is analyzed.

Results show that the clear-sky index for PV power production applications can be modeled via a bimodal Normal probability distribution, that household electricity use can be modeled via either Weibull or Log-normal probability distributions and that EV charging can be modeled by Bernoulli probability distributions. Complete models of PV power production, household electricity use and EV home-charging are developed with both Markov chain and probability distribution modeling. It is also shown that EV home-charging can be modeled as an extension to the Widén Markov chain model for generating synthetic household electricity use patterns. Analysis of measurements from solar charging stations show a wide variety of EV charging patterns. Additionally an alternative approach to modeling the clear-sky index is introduced and shown to give a generalized Ångström equation relating solar irradiation to the duration of bright sunshine.

Analysis of the total power consumption/production patterns of PV power production, household electricity use and EV home-charging at the end-user in the grid highlights the dependency between the components, which quantifies the mismatch issue of distributed intermittent power production and consumption. At an aggregate level of households the level of mismatch is shown to be lower.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2015. 93 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1224
Keyword
Distributed Photovoltaics, Household Electricity Use, Electric Vehicle Charging, Markov Chain Modeling, Probability Distribution Modeling, Data Analysis, Self-Consumption, Grid Interaction.
National Category
Energy Systems
Research subject
Engineering Science
Identifiers
urn:nbn:se:uu:diva-243159 (URN)978-91-554-9162-8 (ISBN)
Public defence
2015-03-27, Polhemsalen, Ångström Laboratory, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2015-03-04 Created: 2015-02-05 Last updated: 2015-03-12Bibliographically approved

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Munkhammar, JoakimWidén, Joakim

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