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
Chair Electric Power Networks and Renewable Energy Sources
04.-05. October 2006, Roskilde2
Motivation and Aim of the Work
Description of the Problem
Coherency Approaches for Power System Reduction
Reduction Approaches for Wind Farms
Summary
Outline
Chair Electric Power Networks and Renewable Energy Sources
04.-05. October 2006, Roskilde3
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
Chair Electric Power Networks and Renewable Energy Sources
04.-05. October 2006, Roskilde4
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
Chair Electric Power Networks and Renewable Energy Sources
04.-05. October 2006, Roskilde5
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
Chair Electric Power Networks and Renewable Energy Sources
04.-05. October 2006, Roskilde6
Sub-System 1
Sub-System 2to be reduced
Coherency Approaches for System Reduction
Chair Electric Power Networks and Renewable Energy Sources
04.-05. October 2006, Roskilde7
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
Chair Electric Power Networks and Renewable Energy Sources
04.-05. October 2006, Roskilde8
Coherency Approaches for System Reduction
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
Chair Electric Power Networks and Renewable Energy Sources
04.-05. October 2006, Roskilde9
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)
Chair Electric Power Networks and Renewable Energy Sources
04.-05. October 2006, Roskilde10
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
Chair Electric Power Networks and Renewable Energy Sources
04.-05. October 2006, Roskilde11
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
Chair Electric Power Networks and Renewable Energy Sources
04.-05. October 2006, Roskilde12
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
Chair Electric Power Networks and Renewable Energy Sources
04.-05. October 2006, Roskilde13
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
Chair Electric Power Networks and Renewable Energy Sources
04.-05. October 2006, Roskilde14
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
Chair Electric Power Networks and Renewable Energy Sources
04.-05. October 2006, Roskilde15
Implementation of Reduced State Space Model
Chair Electric Power Networks and Renewable Energy Sources
04.-05. October 2006, Roskilde16
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
Chair Electric Power Networks and Renewable Energy Sources
04.-05. October 2006, Roskilde17
Thank You For Your Attention !