Transcript Statistical model of wind farms for power flow

Reactive power injection
strategies for wind energy
regarding its statistical nature
Joaquín Mur M.P. Comech
[email protected]
[email protected]
I. Introduction: presentation
layout
II.
III.
IV.
V.
VI.
VII.
Wind site resource
VIII.Reactive Power Policy

Constant power factor
Turbine power curve

Automatic voltage control
Farm power curve

Scheduled Reactive control
Farm electric model

Reactive power under
Nearby wind farms
centralized control
Limits on reactive
IX. Effect on power losses
power
X. Uncertainty Analysis
XI. Conclusions
II. Wind site resource
Probability Density
Probability
Density
(Weibull distribution)
Function
PDF
0.14
Chart for shape parameter = 2
Solid red
=> wind speed = 5 m/s
0.12
Dashed pink=>wind speed = 5,5 m/s
0.1
Light blue => wind speed = 6,5 m/s
Dotted green=>wind speed = 7 m/s
Yellow
=> wind speed = 7,5 m/s
Dark blue
0.08
=> wind speed = 6 m/s
0.06
0.04
0.02
0
0
5
10
Wind
15
Speed
20
m s
25
30
III. Wind turbine
(IEC 61400-12-1)
Power curve measured at a pitch regulated turbine (from IEC 61400-12-1)
III. Snapshoot of turbines in a farm
Power
Output
Std . Dev .
Power Std. Dev. p.u.
Power curve measured at a pitch regulated turbine (from IEC 61400-12-1)
1
0.8
0.6
0.4
0.2
0
5
10
Wind
15
Speed
20
m s
25
30
IV. Wind farm curve
(IEC 61400-12-3)
Declared (calculated) wind farm power curve by directional sector
(from IEC 61400-12-3, annex C)
IV. Wind farm
Wind
(4 parameters adjusted curve)
Farm Power curve
Power Output
p.u.
1
woff
0.8
0.6
P
Pwf ( wS )  nominal
2
0.4

w25%  w75%

wf wS 


2
Tanh  Ln(3)
w25%  w75%




0.2



wS  wcut off
  Tanh  Ln(3)
woff



wf is the farm mean efficiency factor
(referred to “unperturbated wind” of
the site).
0
0
5
w25%
10w75% 15
Wind Speed
20
m s
25
woff
30

 
 
IV. Farm power distribution
Probability(PowerWF  pWF ) =
shape
 

woff



2
p
WF


ArcTanh  1 
  wcut off 



= 1  Exp 

Ln (3)
Pnominal  


 


scale






shape
 




w25%  w75%
w25%  w75%
2 pWF



ArcTanh
1

 



 Exp   
2
Ln (3)
P


nominal  
 



scale
wf



 

Probability Density Function
IV. Farm power distribution
Probability
2
Density
Chart for shape factor k = 2
Solid red
=> wind speed = 5 m/s
1.75
Dashed pink=>wind speed = 5,5 m/s
1.5
Dark blue
=> wind speed = 6 m/s
Light blue => wind speed = 6,5 m/s
Dotted green=>wind speed = 7 m/s
Yellow
=> wind speed = 7,5 m/s
Dashed red => wind speed = 8 m/s
1.25
1
0.75
0.5
0.25
0
0.2
0.4
0.6
0.8
Power output
p.u.
V. Model of the wind farm with one
medium voltage circuit
V. Model of the wind farm with
several medium voltage circuits
Icircuit MV 1
Icircuit MV 2
Igenerator
 A2 B2 


 C2 D2 Circuito2
Igenerator
Ugeneratorr
Substation
 A1 B1 


 C1 D1 Circuito1
N1 turbines
Pgen1
Qgen1
N2 turbines
Ugenerator
Usubstation
Pgen2
Qgen2
Ncirc branches in the MV network of the park
Icircuit Ncirc  ANcirc
Igenerator
Ugenerator

 CNcirc
BNcirc 

DNcirc Ncirc
NN turbines
PgenN
QgenN
V. Approximated equivalent model of
the wind farm
Averaged model
Substation
Averaged model of MV net
Isubstation MV  A
net MV
I generator average
Ugenerator average
Usubstation

 Cnet MV
Bnet MT   1 0 
.
Dnet MT   0 N
Pturbine
Qturbine
V. Fourth pole model & parameters
of the farm
Grid’s equivalent
seen from wind farm
Equivalent circuit of the farm grid
Zseries
Uturbine
2
WT
WT
Bshunt  QPCC P U0,PCC
Q
2
-G shunt U PCC
2
R series =1- PPCCPPWT21,+Q
-G
shunt
Q WT
0
X series =- Q PCC
2
WT 0
WT
Q PCC =Q WT -Xseries
 Pturbines
 Qturbines
2
G shunt   PP
PCC
WTP +Q
0, Q WT
0
PPCC =PWT -R series
(average)
-Iturbine (average)
Yshunt
PCC, point of
common coupling
~
U0
+
Ugrid PCC
ZSC grid -Igrid PCC
WT
U
WT
2
PWT 1, PCC
Q WT 0
+Bshunt U PCC
+Yseries
2
VI. Power of nearby farms
Nearby wind farms are supposed to be closely
correlated  a linear regression can be precise
enough

Pj =Pj  b j Pi  Pi

b j  rij
sj
si
• Pi and Pj are the average power output in park “j”
(estimated farm) and “i” (reference farm);
• rij is the experimental correlation coefficient;
• si and sj are the standard deviation of power in
farms i and j.
• Qi and Qj must be estimated based on each farm reactive
control
VII. Limits on reactive power
Limits provided by the turbine manufacturer.

Second edition of IEC 61400-21 will include a section
devoted to the reactive power capability and the ability to
participate in an automatic voltage control scheme.
Allowable voltage at the turbines.


The wind turbine that is electrically farer from PCC will
suffer the greatest voltage deviations of the wind farm.
Voltage at turbines is dependent on UPCC
Current limit in series elements (lines,
transformers, etc) and grid bottlenecks.


Slow thermal dynamics, grid congestion…
Usually, some degree of overload is allowed.
VII. Voltage at electrically farer turbine
U min  U0  U worse  U max
turbine
U worse  R eff PWT  X eff Q WT
turbine
U min  R eff PWT  Qeff PWT  U max
Estimation of parameters from power flows:
R sc +R series
 U worse
 U0
U0
turbine P 1 p.u., Q 0
WT
WT
Upper voltage limit :
X +X
1
 sc series  U worse
 U0
U0
3 turbine PWT 0, QWT 1/ 3 p.u.
Lower voltage limit :
R eff 
X eff
R eff PWT  Qeff PWT  U max
R eff PWT  Qeff PWT  U min
VII. Loci of allowable power
ov
c u er
rr
en
t
QWT (p.u.)
ove
r
Imax (
Umin
R eff
U max
X eff
p.u)
-vo
ltag
e
Turbine
limits
U
un
der X
-vo
lta
ge
min
eff
U max
R eff
PWT
(p.u.)
VIII. Reactive power policy
Centralized control: stabilize voltage, power losses,
balance reactive power flows…
Constant power factor regulation
Automatic voltage control
Scheduled reactive control



Current model in Spain, power factor depending on hours
Improvement if weekdays and holidays would be
considered
Improvement if target is based on reactive power, not on
power factor
Probability Density Funct.
VIII. Voltage deviation due to
scheduled
power
factor (Spain)
Probability
of Voltage deviations
0.5
0.4
0.3
Valley
hours
8 h/day
0.2
U PCC
Mediu
m hours
12
h/day Peak hours
(unity
4 h/day
power (Capacitive
factor) behaviour)
0.1
-0.005
0
0.005
0.01 0.015
Voltage deviation
at PCC
0.02 0.025
p.u.
Probability Density Funct.
VIII. Reactive power injection due
to scheduled power factor (Spain)
0.5
Reactive
0.4
0.3
0.2
Valley
hours
8 h/day
Power
at PCC , Q PCC
Peak hours
4 h/day
(Capacitive
behaviour)
0.1
-0.3
-0.2
-0.1
0
0.1
0.2
Reactive
Power at PCC , Q PCC p.u.
VIII. Reactive power under
centralized control
Simplistic example of realizable reactive power at a wind
turbine
Q WT capability
at Wint
Turbine
0.6
Reactive Power, QWT
p.u.
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
0
0.2
0.4
0.6
Active Power , P WT
0.8
p.u.
1
VIII. Availability of reactive power
INJECTION for the example
Probability of being able to INJECT capacitive power up to Qwt
Availability
or Q
1
Pr Qmax
Qwt
0.8
0.6
Chart for shape parameter = 2
Solid red
=> wind speed = 5 m/s
Dashed pink=>wind speed = 5,5 m/s
0.4
0.2
Dark blue
=> wind speed = 6 m/s
Light blue => wind speed = 6,5 m/s
Dotted green=>wind speed = 7 m/s
Yellow
=> wind speed = 7,5 m/s
0
0.2
0.3
Qwt
0.4
p.u.
0.5
0.6
VIII. Availability of reactive power
ABSORPTION for the example
Probability of being able to ABSORB inductive power up to Qwt
Availability
of Q absortion
Qwt
1
0.8
Pr Qmin
0.6
Chart for shape parameter = 2
Solid red
=> wind speed = 5 m/s
Dashed pink=>wind speed = 5,5 m/s
Dark blue
0.4
0.2
=> wind speed = 6 m/s
Light blue => wind speed = 6,5 m/s
Dotted green=>wind speed = 7 m/s
Yellow
=> wind speed = 7,5 m/s
-0.6
Qwt
-0.4
-0.2
p.u., inductive
0
IX. Effect on power losses
Ri 2
Ploss, i = Si ;
Ui
Si   P0,i +k P,i PWT    Q 0,i +k Q,i Q WT 
2
2
Ploss =  Plosses, i  Ploss
Pwt=0, Qwt=0
2
+
i
2
+ a P PWT + b P PWT + a Q Q WT + b Q Q WT
2
Parameters aP, aQ, bP and bQ can be obtained from power flow
runs
An analogue relationship can be established for losses on
reactive power
X. Uncertainty of the results
The main source of errors are:
Adjustment of wind resource to a Weibull
distribution.
The uncertainty of the farm power curve.
Simplistic model of the power curve with only
two or four parameters.
Approximations done in the model of the grid
(for example, considering U0 constant).
Availability of turbines and network.
Conclusions
This work shows a statistical model of wind farms
and a methodology for adjusting its parameters.
This model has been used to assess the grid
impact of a wind farm reactive power during
normal operation.
Several reactive power control strategies are
analyzed.
The uncertainty of the final data due to the
approximations made is studied. The accuracy
can be increased if non-parametric models of
farm power curve and wind resource is employed.
Questions?