fati̇h onur hocaoğlu res_2015

8/18/2019 Fatıh Onur Hocaoğlu Res_2015

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MODELLING WIND AND PV DATA ANDSIZE OPTIMIZATION OF HYBRID

SYSTEMS USING ADVANCED

TECHNIQUES

Fatih Onur Hocaoglu

RES Winter School 2015



Outline

• Introduction to Wind/PV systems

• Wind Speed Modeling

• Solar Radiation Modeling• Hybrid System Sizing



Introduction to Wind/PV systems

WL ≤ WPV + WG + WB



Why Wind Speed Modeling

• Design of a proper wind energy system

(requires the prediction of wind speed

statistical parameters)

• Design of wind sensitive structures

• Air pollution studies



Model: Markov Processes

0 1ij

p

1

1ij

j

p

11 12 13 1

21 22 23 2

1 2 3

. . .

. . .

. . . . . . .

. . . . . . .

. . .

n

n

n n n nn

p p p p

p p p p

A

p p p p



Wind Speed Modeling using

Markov Approach

, 1, 2,...,ij

ij

ij

j

m p i j n

m




Markov Approach0.61 0.29 0.08 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.18 0.47 0.28 0.06 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.04 0.20 0.46 0.23 0.06 0.01 0.01 0.00 0.00 0.00 0.00 0.00 0.00

0.01 0.05 0.20 0.45 0.22 0.06 0.01 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.06 0.26 0.42 0.20 0.04 0.01 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.01 0.07 0.28 0.41 0.18 0.04 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.01 0.01 0.07 0.29 0.39 0.21 0.02 0.01 0.00 0.00 0.00

0.00 0.00 0.00 0.01 0.02 0.09 0.30 0.38 0.17 0.02 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.01 0.04 0.12 0.33 0.39 0.08 0.02 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.01 0.03 0.18 0.27 0.37 0.08 0.05 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.18 0.09 0.23 0.41 0.09 0.00

0.00 0.00 0.00 0.00 0.08 0.08 0.00 0.00 0.15 0.31 0.08 0.31 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00



Syntetic generation of wind speed

data




Markov Approach0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 ......

0.00 0.61 0.18 0.10 0.05 0.03 0.02 0.00 0.00 0.00 0.00 0.00 ......

0.00 0.25 0.24 0.24 0.14 0.06 0.04 0.01 0.00 0.00 0.00 0.00 ......

0.00 0.12 0.18 0.28 0.23 0.11 0.05 0.03 0.01 0.01 0.00 0.00 ......

0.00 0.05 0.11 0.15 0.23 0.19 0.12 0.07 0.02 0.03 0.00 0.00 ......

0.00 0.02 0.04 0.10 0.18 0.30 0.16 0.10 0.04 0.02 0.01 0.00 ......

0.00 0.01 0.03 0.05 0.10 0.17 0.28 0.17 0.10 0.04 0.02 0.01 ......

0.00 0.00 0.00 0.02 0.04 0.10 0.20 0.25 0.18 0.11 0.05 0.02 ......

0.00 0.00 0.00 0.00 0.02 0.06 0.12 0.23 0.25 0.13 0.10 0.05 ......

0.00 0.00 0.00 0.00 0.01 0.02 0.05 0.12 0.22 0.25 0.18 0.07 ......

0.00 0.00 0.00 0.00 0.00 0.01 0.03 0.05 0.13 0.22 0.23 0.16 ......

0.00 0.00 0.00 0.00 0.00 0.00 0.02 0.04 0.05 0.15 0.22 0.21 ......

...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ......




Markov Approach

1

k

ik ij

j

P p

ik P is transition probability in the i th row at the k th state




Markov Approach0.61 0.90 0.98 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

0.18 0.64 0.92 0.98 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

0.04 0.23 0.69 0.92 0.98 0.99 1.00 1.00 1.00 1.00 1.00 1.00 1.00

0.01 0.06 0.26 0.72 0.93 0.99 1.00 1.00 1.00 1.00 1.00 1.00 1.00

0.00 0.00 0.06 0.32 0.75 0.95 0.99 1.00 1.00 1.00 1.00 1.00 1.00

0.00 0.00 0.01 0.08 0.36 0.77 0.95 0.99 1.00 1.00 1.00 1.00 1.00

0.00 0.00 0.01 0.02 0.09 0.38 0.76 0.97 0.99 1.00 1.00 1.00 1.00

0.00 0.00 0.00 0.01 0.03 0.12 0.42 0.80 0.98 1.00 1.00 1.00 1.00

0.00 0.00 0.00 0.00 0.02 0.05 0.17 0.50 0.89 0.97 1.00 1.00 1.00

0.00 0.00 0.00 0.00 0.00 0.01 0.04 0.22 0.49 0.86 0.95 1.00 1.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.18 0.27 0.50 0.91 1.00 1.00

0.00 0.00 0.00 0.00 0.08 0.15 0.15 0.15 0.31 0.62 0.69 1.00 1.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 1.00 1.00 1.00




Markov Approach




Markov Approach

Observed DataGenerated Data from

Model-1

Generated Data from

Model-2

Min 0.00 0.02 0.00

Max 12.47 11.44 12.77

Mean 3.52 3.16 3.61

Median 3.35 2.95 3.47

Std 2.11 1.91 2.02




Markov Approach

0

5

10

15

20

1 3 5 7 9 11 13 15 17

Wind Speed (m/s)

Pro

bability(%)

Observed data Generated data from Model-1

Generated data from Model-2



Variation: Hidden Markov Models



Hidden Markov Models

'fatih'

< , fatih, , 0.3> == P( )=0.32 3 2 3

s s s s

E ={<x, ‘1’, x, 0.32> < x, ‘0’, x, 0.52> < x, ‘0’, y, 0.16> < y, ’1’, x, 1>}




The Problems that should be solved are,

1-) What is the probability of observed data O1,O2 ,…,OT ?Calculate P(O1,O2 ,…,OT |model )

2-) What state is most likely if we know the observation sequence? Findthe state sequence

q1,q2,…qT S.T P(q1,q2,…qT | O1,O2 ,…,OT , model )

3-) Given some data, how do we learn a good HMM to describe the

data



Viterbi Algorithm

1,

1

1, 1, 1

(1)

( ) ( ) , arg max ( ( )) ( )

( ) arg max ( )

t

t

i

c wi j k

i k ik

t t

s

s

t t s j P t P s s

t P s w




Hidden Markov Approach





( ).

in

n

oo

i j

o ij

n p s s

n p





Min Max Mean Median Std

Measured 0 11.4000 3.5277 3.3500 2.1279

Model Generated 0 11.9523 3.3191 1.8253 3.1638





Min Max Mean Median Std

Measured 0.11 8.2954 3.5277 3.4525 1.3917

Model Generated 0.2224 8.7660 3.5964 3.6058 1.5205



Solar Radiation Data Analysis




R R 2

x44

– x34

0.911 0.830

x44 –

x24 0.894 0.799

x44

– x14

0.898 0.806

x44

– x43

0.938 0.879

x44

– x42

0.807 0.651

x44

– x14

0.630 0.397

x44

– x33

0.870 0.760

x44

– x22

0.740 0.548




0 5 10 15 20 250

50

100

150

200

250

300

350

400



Optimal Coefficient Linear

Prediction Filters

,i j x , 1i j

x

1,i j x 1, 1 ?i j x




Prediction Filters

1 111 12 13

21 22 23 2 2

31 32 33 3 3

a r R R R

R R R a r

R R R a r

1 2 3

0a a a

1a R r




Prediction Filters

x11

x22 .

.

. .

.

xm1 . . . xmn

x12. . . . .x1n

.

.

1D-Filter 1

x11 x12

x22 .

.

. .

.

xm1 . . . xmn

. . . . .x1n

.

.

x11 x12

x22 .

.

. .

.

xm1 . . . xmn

.. .x1n

.

.

x11

x21 x22 .

.

. .

.

xm1 . . . xmn

. . . . .x1n x11

x21 x22 .

. . . . .x1n x11

x21 x22 .

.

. .

x41

xm1 . . . xmn

. . . . .x1n

x13

x31 x32 ... .

. . .

xm1 . . . xmn

x31

1D-Filter 4

1D-Filter 2

1D-Filter 5

1D-Filter 3

1D-Filter 6




Prediction Filters

x11

x21

x12

x22 .

.

. .

.

xm1 . . . xmn

. . . . .x1n

x22 x21

x13

.

. .

.

xm1 . . . xmn

x11 x12 . x1n

2D-Filter 2 2D-Filter 3

x21

x12

.

. .

.

xm1 . . . xmn

x11 . x1n

2D-Filter 1

x22

2

1 1

1( ( , ) ( , ))

N M

i j

RMSE Rad i j Rad i j NM



Testing the Performance of 2D

Approach using OCLPF




Approach using NNs

Input Layer Output Layer Hidden Layer

i1 o


i1

i2

o


i2

i3

i1

o




Approach using NNs

0 10 20 30 40 50 60 70 80 90 10010

-2

10-1

100

Asama

P e r f o r m a n s

Performans: 0.0153904



Results

OCLPF

NNs

Train Data Test Data

RMSE RMSE RMSE

1-D Filter1/NN1 58.53 0.94 58.80 0.93 62.64 0.94

1-D Filter2/NN2 45.02 0.96 41.86 0.97 39.79 0.98

1-D Filter3/NN3 44.36 0.96 44.70 0.96 43.73 0.97

1-D Filter4/NN4 67.05 0.91 69.30 0.90 74.32 0.91

1-D Filter5/NN5 61.94 0.92 63.95 0.92 67.63 0.92

1-D Filter6/NN6 76.49 0.88 60.83 0.93 63.64 0.93

2-D Filter1/NN7 46.56 0.96 45.58 0.96 47.98 0.96

2-D Filter2/NN8 40.23 0.97 35.42 0.98 34.57 0.98

2-D Filter3/NN9 39.37 0.97 42.15 0.97 43.15 0.97



It is obvious from the literature that prediction performance increases in case of

different meteorological parameters are employed as inputs of models.

(Zarzalejo et al., 2005; Yorukoglu and Celik, 2006; Psiloglou and Kambezidis, 2007; Li et al.,

2010; Kaplanis and Kaplani, 2010; Pandey and Soupir, 2012; Inman et al., 2013;......)

Multi Dimensional Filter Approach







Zi,j Zi,j+1

Zi+1,j

Ži+1,j+1=

?

How can we use this template?




1, 1,1 , ,1 1 , 1,1 2 1, ,1 3 , ,2 1 , 1,2 2 1, ,2 3 , ,3 1

, 1,3 2 1, ,3 3

i j i j i j i j i j i j i j i j

i j i j

Z Z a Z a Z a Z b Z b Z b Z c

Z c Z c

1, 1,1

1, 1,1 1, 1,1

i ji j i j

Z Z

1 2 3 1 2 3 1 2 3

0

a a a b b b c c c

11 12 13 14 15 16 17 18 19

21 22 23 24 25 26 27 28 29

31 32 33 34 35 36 37 38 39

41 42 43 44 45 46 47 48 49

51 52 53 54 55 56 57 58 59

61 62 63 64 65 66 67 68 69

71 72 73 74 75 76

81 82 83 8

91 92 93

r r r r r r r r r

r r r r r r r r r

r r r r r r r r r

r r r r r r r r r

r r r r r r r r r

r r r r r r r r r

r r r r r r

r r r r

r r r

1 1

2 2

3 3

1 4

2 5

3 6

77 78 79 1 7

4 85 86 87 88 89 2 8

94 95 96 97 98 99 3 9

a r

a r

a r

b r

b r

b r

r r r c r

r r r r r c r

r r r r r r c r

1.a R r

+1,+1,12

=1

=1




Performance Evaluat ion :

March 1, 2012 – Febuary

1, 2013




Deney Sonuçları:

1 Mart 2012 – 28 Şubat

0 2000 4000 6000 80000

200

400

600

800

1000

1200

1400

Zaman (Saat)

Ex

traterrestrialIşınım(W/m

)

0 2000 4000 6000 80000

200

400

600

800

1000

1200

Zaman (Saat)

G

ü n e ş I ş ı n ı m ı ( W / m 2 )

0 2000 4000 6000 8000 10000-20

-10

0

10

20

30

40

50

Zaman (Saat)

Sıcaklık

(0C

)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000-300

-200

-100

0

100

200

300

Zaman (Saat)

Extraterrestrialışınımınbirincide

recedentürevi

0 2000 4000 6000 8000 10000-800

-600

-400

-200

0

200

400

600

800

Zaman (Saat)

G ü n e ş ı ş ı n ı m ı n ı n b i r i n c i d e r e

c e d e n t ü r e v i

0 1000 2000 3000 4000 5000 6000 7000 8000 9000-15

-10

-5

0

5

10

15

20

Zaman (Saat)

S ı c a k l ı ğ ı n

b i r i n c i d e r e c e d

e n

t ü r e v i





Data Employed

Mevcut very ile 1 saat sonrasının

tahmini (Filtre 1-4-7)

Model 1 Solar Radiation R(i+1)=a∗R(i)

Data Employed

Mevcut very ile 1 saat sonrasının


Model 2 Temperature- Solar Radiations R(i+1)=a∗R(i)+b∗S(i)

Model 3

Extraterrestrial Radiations- Solar

Radiations

R(i+1)=a∗R(i)+b∗E(i)

Model 4

Future Extraterrestrial

Radiations- Solar Radiations

R(i+1)=a∗R(i)+b∗E(i+1)

Model 5

First order derivative oftemperature- Solar Radiations

R(i+1)=a∗R(i)+b∗( ∂S(i) )/∂t

Model 6

First order derivative of

temperature- Solar Radiation

R(i+1)=a∗R(i)+b∗( ∂E(i) )/∂t

Model 7

First order derivative of

radiation- Solar radiation

R(i+1)=a∗R(i)+b∗( ∂R(i) )/∂t

Model 8

First order derivative of future

extraterrestrials- Solar radiation

R(i+1)=a∗R(i)+b∗( ∂E(i+1) )/∂t





Kullanılan veriler Mevcut very ile 1 saat sonrasının


Model 9

Sıcaklık-Extraterrestrial Işınım-

Güneş Işınımı R(i+1)=a∗R(i)+b∗E(i)+c∗S(i)

Model 10

Sıcaklık-Gelecek ExtraterrestrialIşınım- Güneş Işınımı

R(i+1)=a∗R(i)+b∗E(i+1)+c∗S(i)

Model 11

Geçmiş-Şimdiki ExtraterrestrialIşınım- Güneş Işınımı

R(i+1)=a∗R(i)+b∗E(i-1)+c∗E(i)

Model 12

Şimdiki-Gelecek Extraterrestrial

Işınım- Güneş Işınımı R(i+1)=a∗R(i)+b∗E(i)+c∗E(i+1)

Model 13

Extraterrestrial Işınım veSıcaklığın 1. mertebeden türevi –

Güneş Işınımı R(i+1)=a∗R(i)+b∗∂E(i)/∂t+c∗∂S(i)/∂t

Model 14

Gelecek Extraterrestrial Işınım veSıcaklığın 1.mertebeden türevi-Güneş Işınımı

R(i+1)=a∗R(i)+b∗∂E(i+1)/∂t+c∗∂S(i)/∂t




Resul ts:

RMSE(W/m2) MBE(W/m2)

Filter-1 Filter-2 Filter-3 Filter-1 Filter-2 Filter-3

Model-1 103,056 106,13 71,617 -8,7688 -9,4984 -15,4211



Model-2

101,896

104,941

69,974

5,9120

0,7507

-1,0896

Model-3

98,102

92,387

61,064

0,8737

5,1521

4,1404 Model-4 77,766 98,786 63,871 -8,9170 0,6794 7,7531

Model-5 90,512 105,799 68,820 7,1283 -8,9790 -1,6505

Model-6

65,858

105,838

60,990

4,2371

-9,5205

0,4748

Model-7 85,346 104,909 67,558 13,5672 -8,3142 -5,5875

Model-8 65,556 105,815 61,780 -0,7808 -9,5960 1,2491



Model-9 97,922 92,387 60,842 1,3655 4,9215 4,7141

Model-10 76,603 98,607 62,504 -7,1460 4,8505 1,3850

Model-11 65,187 92,107 X 0,5263 5,7969 X

Model-12 63,390 93,261 X -5,5989 1,3302 X

Model-13 65,667 105,247 60,739 4,1965 -0,7403 3,9799

Model-14

64,767

105,685

61,118

-1,0290

-8,8602

6,2795




Model-3 98,102

Model-4 77,766

Resul ts:

Model-2 101,896

Model-5

90,512

Model-3 98,102

Model-6 65,858

Extraterrestrial ışınımın mevcut değeri yerinegelecek değerinin kullanıldığı durum

Sıcaklık yerine türevinin kullanıldığı durum

Extraterrestrial ışınım yerine türevinin kullanıldığıdurum

Model-9

97,922

Model-10 76,603

Model-11 65,187

Model-12 63,390

Model-13 65,667

Model-14

64,767

R(i+1)=a R(i)+b E(i)+c S(i)

R(i+1)=a

R(i)+b

E(i+1)+c

S(i)

R(i+1)=a

R(i)+b

E(i-1)+c

E(i)

R(i+1)=a

R(i)+b

E(i)+c

E(i+1)

R(i+1)=a

R(i)+b

∂E(i)/∂t+c

∂S(i)/∂t

R(i+1)=a R(i)+b ∂E(i+1)/∂t+c ∂S(i)/∂t




Resul ts:

0 200 400 600 800 1000 12000

100

200

300

400

500

600

700

800

900

1000

Ölçülen Güneş Işınım Değeri (W/m2)

TahminEdilenGüneşIşınımDeğeri(W/m

2 )





05

1015

2025

0

100

200

300

400-1000

-500

0

500

1000

SaatGün

TahminHatası(W/m

2 )




Results:

It is possible to use different meteorological parameters ralated with solar

radiaion data in case proposed multi dimensional approach is used.

14 different models with 9 different templates are proposed.

It is obtained that future and past values of extraterrestrial radiation carry

important information for the prediction model.

It is observed that the performance of the prediction is increased in case the

first and second order derivatives of solar radiation values are employed.

In solar radiation prediction one day before values also carry information about

prediction. On the other hand one hour before values carry much moreinformation.


Analytical Modeling Approach for



Analytical Modeling Approach for

Solar Radiation Data

Novel Analytical Modeling




Approach for Solar Radiation Data






2 2( )( ) x b c g x ae

2 2 2 21 1 2 2( ) ( )

1 2( ) x b c x b c

g x a e a e






a b c

D1 285.6000 12.9500 2.7280

D2 226.7000 13.4000 2.8410

D3 301.8000 12.9500 2.7710 D4 235.1000 12.1700 2.8930

D5 201.1000 14.5600 1.8690

D6 229.7000 12.7800 3.0010

D7 134.3000 13.2700 3.2470

D8 122.9000 12.9200 3.4460

D9 298.9000 12.1100 2.8850

D10 103.1000 12.3000 3.3970






1 Source Gauss 2 Source Gauss

D1 0.9907 0.9981

D2 0.982 0.9971

D3 0.9881 0.9986

D4 0.9596 0.9949

D5 0.9242 0.9974

D6 0.9136 0.9889

D7 0.9293 0.9907

D8 0.9561 0.9964

D9 0.9882 0.9899

D10 0.9155 0.9978






1-Source

Gauss

2-source

Gauss

RMSE 57.20 105.25

A novel modeling approach using



A novel modeling approach using

extraterrestrial solar radiations



Extraterrestrial Formulation

2sin( ) / 24 I C R

sin( ) sin( )sin( ) cos( ) cos( )cos( ) L D L D h

15( 12)ch h

2D Representation of



2D Representation of

Extraterrestrial Data

Modeling Solar Radiations from




Extraterrestrial Radiations





Extraterrestrial Radiations

Novel Hybrid (Wind/PV) Sizing




Algorithm

WL ≤ WPV + WG + WB





Algorithm

PV m m f pc P A P I

0

ci

r ci r

r ci

w r ci

ci co

V V P V V V

V V

P P V V V

V V ve V V





Algorithm

( ) ( 1) ( ( ) ( ) )Wg Gw Pv GP LDSOC t SOC t N E t N E t E

( ) Max

SOC t SOC

( ) Min

SOC t SOC

/ f LLP T T





Algorithm

( , , ) ( , ) Pv Wg bat Pv Wg Q N N N F N N





Algorithm

• For any number of Pv ( ) and any number ofwind generator ( ) are

calculated and versus t are

plotted This curve is named as characteristic

curve of remaining-deficient energies.

• For all time t , the following sum is calculated for

accumulation of the characteristic curve

• The time periods in which the sum in Eq. Above

is negative are counted.

Pv N

Wg N ( ) ( ) ( )

Gw GP LDt

E t E t E t

( ) ( ) ( )Gw GP LD

E t E t E t

1

( ( ) ( ) ( ))Gw GP LD

t

E t E t E t





Algorithm

• The collected count from previous step is divided to

the total considered period of time to find LLP

• Here constitutes a subset of the longest

time period satisfying the inequality in the numerator.

1

#( ( ( ) ( ) ( ))) 0Gw GP LD

t

E t E t E t

LLP T

1, 2,...,T



Capacity Calculation Illustration

-30

-20

-10

0

10

20

30

40

50

60

Remaining/D

eficit

Energies(W)

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31

t (Day)





Algorithm

• Where OC is the optimum capacity of batteries, N is

the length of x[t] sequence for which is greaterthan zero, and NUM is the length of N for the

maximum accumulation

0

arg max [ ] 0 N

N t

NUM x t

0

[ ]

N

t

OC x t

0 [ ]

N

t

x t



E i l S d



Experimental Study



Thank You

Fatih Onur Hocaoglu

fati̇h onur hocaoğlu res_2015

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