Reactive power injection strategies for wind energy

regarding its statistical nature

Joaquín Mur M.P. Comech joako@unizar.es mcomech@unizar.es

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?