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Reliability Assessment Unit Commitment with Uncertain Wind Power Read chapter Read first chapter

2013 | OriginalPaper | Chapter

Probabilistic Approaches for the Steady-State Analysis of Distribution Systems with Wind Farms

Authors : A. Bracale, G. Carpinelli, A. R. Di Fazio, A. Russo

Published in: Handbook of Wind Power Systems

Publisher: Springer Berlin Heidelberg

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Abstract

This chapter deals with probabilistic approaches for the steady-state analysis (probabilistic load flow) of distribution systems with wind farms. The probabilistic analysis is performed taking into account the randomness of both the distribution system loads and the wind energy production. Several approaches are presented to obtain the probability functions of state and dependent variables (e.g., voltage amplitudes and line flows). These approaches are mainly concentrated on wind farm probabilistic models, using one of the classical probabilistic techniques (e.g., Monte Carlo simulation, convolution process, and special distribution functions) to perform the probabilistic load flow. Numerical applications on a 17-bus balanced test distribution system and on an IEEE 34-bus unbalanced test distribution system are presented and discussed, considering the various wind farm models.

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previous chapter Deterministic Approaches for the Steady-State Analysis of Distribution Systems with Wind Farms
next chapter Advanced Control Functionalities for Grid Integration of Large Scale Wind Generation
Appendix
Available only for authorised users
Footnotes
1
As a reminder, given a random variable \( X \) with the pdf \( f\left( x \right) \), the moment of order n is defined as \( m_{n} = \int\nolimits_{ - \infty }^{\infty } {x^{n} f\left( x \right)\;dx} \), and the cumulant of order n is defined as \( \kappa_{n} = \left. {\frac{{d^{n} \varPsi \left( t \right)}}{{dt^{n} }}} \right|_{t = 0} \), where \( \varPsi \left( t \right) \) is the cumulant-generating function, i.e., the logarithm of the moment-generating function, if it exists.
 
2
In the authors’ opinion, the use of a normal pdf instead of the more popular Weibull pdf is justified by the considerations that they are interested to short-term predictions. In any case, they consider that the proposed approach can be extended to medium- and long-term predictions if the uncertainties of wind and loads are properly modelled.
 
3
As is well known, a stochastic process is defined as a model of a system that develops randomly in time according to probabilistic laws.
 
4
The use of the discrete Markov process to model wind speed (and then the wind farm) was proposed in the relevant literature both for the probabilistic power flow analysis and for the reliability analysis of distribution networks that have wind farms.
 
5
We note that not all authors consider the use of time series to be a strictly probabilistic approach. In fact, strictly speaking, unlike the Monte Carlo simulation, the input data are not derived from pdfs, but the time series of load and wind generation are directly applied. In the frame of this method, the steady-sate of the distribution system is simulated during a suitable time period (i.e., 1 week or 1 year). Using the active and reactive power curves of the WTGU (Fig. 1), the output power series can be obtained. From the load and wind generation time series, the corresponding state and dependent variables can be obtained by performing subsequent load flow calculations for each point; this approach was applied also in [9, 10].
 
6
In addition to the first-order Markov chain model, a second order model has been proposed to generate wind speed time series. For example, see [14].
 
7
A multi-state system (MSS) is a system that performs its mission with various levels of efficiency, referred as performance rates.
 
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Metadata
Title
Probabilistic Approaches for the Steady-State Analysis of Distribution Systems with Wind Farms
Authors
A. Bracale
G. Carpinelli
A. R. Di Fazio
A. Russo
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Book
Handbook of Wind Power Systems

Print ISBN: 978-3-642-41079-6

Electronic ISBN: 978-3-642-41080-2

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-642-41080-2_8