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. Wind site resourceIII. Turbine power
curveIV. Farm power curveV. Farm electric modelVI. Nearby wind farmsVII. Limits on reactive
power
VIII.Reactive Power Policy Constant power factor Automatic voltage control Scheduled Reactive
control Reactive power under
centralized control
IX. Effect on power lossesX. Uncertainty AnalysisXI. Conclusions
II. Wind site resource (Weibull distribution)
0 5 10 15 20 25 30Wind Speed ms0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
ytilibaborPytisneD
Probability Density Function PDFChart for shape parameter = 2Solid red => wind speed = 5 m/s
Dashed pink=>wind speed = 5,5 m/sDark blue => wind speed = 6 m/s
Light blue => wind speed = 6,5 m/sDotted green=>wind speed = 7 m/sYellow => wind speed = 7,5 m/s
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 curve measured at a pitch regulated turbine (from IEC 61400-12-1)
0 5 10 15 20 25 30Wind Speed ms
0.2
0.4
0.6
0.8
1
rewoPdtS.
veD.p.u. Power Output Std . Dev .
IV. Wind farm curve (IEC 61400-12-3)Declared (calculated) wind farm power curve by directional
sector (from IEC 61400-12-3, annex C)
0 5 10 15 20 25 30
Wind Speed ms0
0.2
0.4
0.6
0.8
1
rewoPtuptuOp.u.
Wind Farm Power curveIV. Wind farm (4 parameters adjusted curve)
woff
w25% w75% woff
25% 75%
nominal
25% 75%
2( ) (3) (3)2
wf SS cut off
wf Soff
w ww w wP
P w Tanh Ln Tanh Lnw w w
wf is the farm mean efficiency factor(referred to “unperturbated wind” of the site).
IV. Farm power distribution
0 0.2 0.4 0.6 0.8
Power output p.u.0.25
0.5
0.75
1
1.25
1.5
1.75
2
ytilibaborPytisneD
noitcnuF
Probability Density
IV. Farm power distribution
Chart for shape factor k = 2Solid red => wind speed = 5 m/s
Dashed pink=>wind speed = 5,5 m/sDark blue => wind speed = 6 m/s
Light blue => wind speed = 6,5 m/sDotted green=>wind speed = 7 m/sYellow => wind speed = 7,5 m/sDashed red => wind speed = 8 m/s
V. Model of the wind farm with one medium voltage circuit
V. Model of the wind farm with several medium voltage circuits
Usubstation
P g e n 2 Q g e n 2
I g e n e r a t o r I c i r c u i t M V 2 2 2
2 2 2
A B
C DC i r c u i t o
Ugenerator
P g e n 1 Q g e n 1
I g e n e r a t o r I c i r c u i t M V 1 1 1
1 1 1
A B
C DC i r c u i t o
Ugeneratorr
P g e n N Q g e n N
I g e n e r a t o r I c i r c u i t N c i r c
Ugenerator
N c i r c N c i r c
N c i r c N c i r c
A B
C DN c i r c
N c i r c b r a n c h e s i n t h e M V n e t w o r k o f t h e p a r k
S u b s t a t i o n
N 1 t u r b i n e s
N 2 t u r b i n e s
N N t u r b i n e s
V. Approximated equivalent model of the wind farm
Averaged model
WT WT
WT WT
WT WT
WT WT
shunt PCC P 0, Q 0
shunt PCC P 0, Q 0
series PCC shuntP 1, Q 0
series PCC seriesP 1, Q 0
G P
B
R =1- P -G
X =-Q +Y
Q
V. Fourth pole model & parameters of the farm
2 22WT WT
PCC WT series shunt PCC2PCC
P +QP =P -R -G U
U
2 22WT WT
PCC WT series shunt PCC2PCC
P +QQ =Q -X +B U
U
Utu
rbin
e
(ave
rage
)
PCC
, poi
nt o
f co
mm
on c
oupl
ing Pturbines
Qturbines
-Iturbine (average) -Igrid PCC
Equivalent circuit of the farm grid
Grid’s equivalent seen from wind farm
U0 ~
+
ZSC grid
Ugr
id P
CC
Zseries
Ysh
unt
VI. Power of nearby farms Nearby wind farms are supposed to be closely correlated a linear regression can be precise enough
j j i iP =P P Pjb j
j iji
sb r
s
• 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 powerLimits 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
Estimation of parameters from power flows:
WT WT
WT WT
sc serieseff worse 0
turbine0 P 1 p.u., Q 0
sc serieseff worse 0
turbine0 P 0, Q 1/ 3 p.u.
R +RR U U
U
X +X 1X U U
U 3
min 0 worse maxturbine
worse eff WT eff WTturbine
min eff WT eff WT max
U U U U
U R P X Q
U R P Q P U
eff WT eff WT max
eff WT eff WT min
R P Q P U
R P Q P U
Upper voltage limit :
Lower voltage limit :
VII. Loci of allowable power
PWT (p.u.)
QWT (p.u.)
max
eff
U
R
max
eff
U
X
min
eff
U
X
min
eff
U
R
over-voltage
under-voltage
over
cu
rren
t
Imax (p.u) Turbine limits
VIII. Reactive power policy Centralized control: stabilize voltage, power losses, balance reactive power flows…Constant power factor regulationAutomatic 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
-0.005 0 0.005 0.01 0.015 0.02 0.025
Voltage deviation at PCC p.u.0.1
0.2
0.3
0.4
0.5
ytilibaborPytisneD
tcnuF. Probability of Voltage deviations UPCC
-0.005 0 0.005 0.01 0.015 0.02 0.025Voltage deviation at PCC p.u.
0.1
0.2
0.3
0.4
0.5
ytilibaborPytisneD
tcnuF. Probability of Voltage deviations UPCC
Peak hours4 h/day
(Capacitive behaviour)
Medium hours
12 h/day(unity power factor)
Valley hours
8 h/day
VIII. Voltage deviation due to scheduled power factor (Spain)
-0.3 -0.2 -0.1 0 0.1 0.2Reactive Power at PCC , QPCCp.u.
0.1
0.2
0.3
0.4
0.5
ytilibaborPytisneD
tcnuF. Reactive Power at PCC , QPCC
-0.3 -0.2 -0.1 0 0.1 0.2Reactive Power at PCC , QPCCp.u.
0.1
0.2
0.3
0.4
0.5
ytilibaborPytisneD
tcnuF. Reactive Power at PCC , QPCC
Peak hours4 h/day
(Capacitive behaviour)Valley
hours8 h/day
VIII. Reactive power injection due to scheduled power factor (Spain)
0 0.2 0.4 0.6 0.8 1Active Power , PWT p.u.-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
evitcaeRrewoP,Q
TWp.u.
QWT capability at Wint Turbine
0 0.2 0.4 0.6 0.8 1Active Power , PWT p.u.-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
evitcaeRrewoP,Q
TWp.u.
QWT capability at Wint Turbine
VIII. Reactive power under centralized control
Simplistic example of realizable reactive power at a wind turbine
VIII. Availability of reactive power INJECTION for the example Probability of being able to INJECT capacitive power up to Qwt
0.2 0.3 0.4 0.5 0.6Qwt p.u.0
0.2
0.4
0.6
0.8
1
rPxamQ
twQAvailability or Q
Chart for shape parameter = 2Solid red => wind speed = 5 m/s
Dashed pink=>wind speed = 5,5 m/sDark blue => wind speed = 6 m/s
Light blue => wind speed = 6,5 m/sDotted green=>wind speed = 7 m/sYellow => wind speed = 7,5 m/s
VIII. Availability of reactive power ABSORPTION for the example
Probability of being able to ABSORB inductive power up to Qwt
-0.6 -0.4 -0.2 0Qwt p.u., inductive
0.2
0.4
0.6
0.8
1
rPnimQ
twQ
Availability of Q absortion
Chart for shape parameter = 2Solid red => wind speed = 5 m/s
Dashed pink=>wind speed = 5,5 m/sDark blue => wind speed = 6 m/s
Light blue => wind speed = 6,5 m/sDotted green=>wind speed = 7 m/sYellow => wind speed = 7,5 m/s
IX. Effect on power losses
2iloss, i i
i
222i 0,i P,i WT 0,i Q,i WT
loss losses, i loss Pwt=0, Qwt=0i
2 2P WT P WT Q WT Q WT
RP = S ;
U
S P +k P Q +k Q
P = P P +
+ a P + b P + a Q + b Q
Parameters aP, aQ, bP and bQ can be obtained from power flow runsAn analogue relationship can be established for losses on reactive power
X. Uncertainty of the resultsThe 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.
ConclusionsThis 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?