aggregation of wind farms for power system analysis

Chair Electric Power Networks and Renewable Energy Sources

04.-05. October 2006, Roskilde1

Aggregation of Wind Farms for Power System

Analysis

Krzysztof Rudion

Otto-von-Guericke-University Magdeburg

Prof. Z. A. Styczynski

EAWE Seminar on Wind Energy in Europe

04. – 05. October 2006, Roskilde



Motivation and Aim of the Work

Description of the Problem

Coherency Approaches for Power System Reduction

Reduction Approaches for Wind Farms

Summary

Outline



Still increasing number of WT in power systems

The impact of a single WT on the grid operation can be neglected

But, the impact of large scale wind farms can be crucial to the stable operation of the power system

Consideration of many small WTs in power system analysis is difficult because of the model size what can lead to long simulation times

To analyse the operation of the power system the behaviour of the wind farm in the PCC is important

Therefore, wind farms can be approximated by an equivalent model with similar dynamic behaviour in the PCC

Motivation and Aim of the Work



Description of the Problem – WT Types

Constant Speed WT with Squirrel Cage Induction Generator

Variable Speed WT with Doubly Fed Induction Generator

Variable Speed WT with Converter Driven Synchronous Generator



Description of the Problem – WT Models

P3w

2TTur cvRπρ

2

1P

Mechanical Power of WT:

dt

dψψωIRV dS

qSSdSSdS

dt

dψψωIRV qS

dSSqSSqS

dt

dψψωsIRV dR

qRSdRRdR

dt

dψψωsIRV qR

dRSqRRqR

EMS TT

dt

dωJ

DFIG Mathematical ModelStator Equations:

Rotor Equations:

Equation of Motion:

WT Mathematical Model Drive Train Model

WT Controllers

wr

Swrwr

2H

αKT

dt

dω

m

wrSm

2H

T - αK

dt

dω

)ω(ωf2πdt

dαmwr

Pitch Controller

Machine-Side Converter Controller

Grid-Side Converter Controller



Sub-System 1

Sub-System 2to be reduced

Coherency Approaches for System Reduction




G

G

GG

G1 G2

G3

G4

G1

G2

G3

G4

Voltage-White-Noise

Sub-System Iremainingunchanged

Sub-System IIto be reduced

Slip




Zd (s)

Zd eq (s)

Note: q-axis analog

s=1 Zd“ = R“ + jX“ (subtransient)s=.01 Zd‘ = R‘ + jX‘ (transient)s~0 Zd = R + jX (synchronous)

Yeq“ = Y1“ + Y2“ + ... + Yn“Yeq‘ = Y1‘ + Y2‘ + ... + Yn‘Yeq = Y1 + Y2 + ... + Yn

from 1/Yeq , 1/Yeq‘ , 1/Yeq“ :

Raeq, Xhdeq, Rfdeq, Xfdeq, RDdeq, XDdeq

i

ii

iiAeqA SSTT

ii

ieqeq jQPjQP



Approaches of Wind Farm Reduction

Reduction Approaches for WF

Reduction of WT number

Description of WT group (or whole wind farm) using a

rescaled unit with equivalent parameters

(equivalent model preserve the

physical structure of WT)

Reduction of wind park model order

Wind park complexity reduction using mathematical methods(equivalent model can lose physical

structure)



Methods for Wind Farm Equivalencing

PCC

Wind Direction“West East”

Wind Direction“South North”

Detailed Wind Park

1 2 …………. n 1

2

3

m

......

1

2

3



PCC

Wind Direction“South North”

PCC

Wind Direction“West East”

Methods for Wind Farm Equivalencing

Equivalent Wind Park

n

1i

m

1jji,EQ

n

1i

m

1jji,EQ

PP

SS

Power of the Equivalent Wind Turbine:

1

2



Mathematical Reduction Methods

There are many different mathematical approaches for system order reduction, e.g.:

Modal truncation

Balanced reduction techniques

Optimal Hankel-norm approximation

Singular perturbations method

Most of the methods were developed for linear systems

The analysis of non-linear system is difficult and therefore non-linear models are often linearized

Two methods were found that were used for order reduction in correspondence to the wind generation:

Singular perturbations

Optimal Hankel-norm approximation



Singular Perturbations Theory

Useful for prediction of steady-state as well as transient behaviour

Method based on the decomposition of the system variables into slow and fast according to their dynamics

The order of the system is reduced through neglecting the fast or slow dynamic phenomena (depending on analysis objective)

The effects of the neglected dynamics are calculated in the separated time scales and are reintroduced as a boundary layer corrections

The reduction retains the physical meaning of the variables

Separation of the slow and fast system variables can be problematic

Method can be used for order reduction of single wind turbine



Hankel-norm approximation

Based on the observability and controllability of the system that are defined as:

dteBBeW tA

0

TAtC

T

dteCCeW At

0

TtAO

T

On the basis of Hankel singular values the influence of state variables on the input – output behaviour of the system can be determined

States that have low influence can be neglected

Advantageous is that the order of the reduced system can be defined a priori

Disadvantage is that reduced models lose the physical interpretation

Controllability gramian

Observability gramian



Implementation of Reduced State Space Model



Summary - Next Steps

Reduced model of the wind farm is needed

There are many different mathematical reduction methods available

Analysis of the usability of the existing mathematical methods

Test simulations of the chosen methods

It should be checked if combination of mathematical order reduction methods with aggregation methods can be performed



Thank You For Your Attention !

aggregation of wind farms for power system analysis

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