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DC/DC

solar cell array

voltage converter (maximum power point tracker (MPPT))

batteries

contact grid

n p

rear contact

1.5 1

0.5

dark0

0.5

Current / A

1

1.5

2

2.5

3

3.5 0

illuminated0.1 0.2 0.3 0.4 Voltage / V 0.5 0.6

0.7

0.8

3.5

3

2.5

output current I / A

2

1.5

1

0.5

0

0

20

40

60 80 100 120 output voltage V / V (number of cells in series z = 168)

3.5

3

2.5

output current I / A

2

1.5

1

0.5

0

0

20

40

60

80 output voltage V / V

100

120

140

(number of cells in series z = 168)

300 250

output power P / W200

150

100

50

0

0

20

40

60 80 100 120 output voltage V / V (number of cells in series z = 168)

350

300

250

output power P / W

200

150

100

50

100 120 140 (number of cells in series z = 168)

0

0

20

40

60

80 output voltage V / V

4

output current I / A3

2

1

0

0

20

40

60 output voltage V / V

80

100

120

300 250

output power P / W

200 150 100 50 0 0

20

40

60 output voltage V / V

80

100

120

solar panel

geometric face

blocking diode bypass diode

photovoltaic cell

switch position:

closed

open

1 0.9 0.8 0.7 conversion ratio M(D) 0.6 0.5 0.4 0.3 0.2 0.1 0 0

0.1

0.2

0.3

0.4

0.5 0.6 duty ratio D

0.7

0.8

0.9

1

10 9 8 7 conversion ratio M(D) 6 5 4 3 2 1 0 0

0.1

0.2

0.3

0.4

0.5 0.6 duty ratio D

0.7

0.8

0.9

1

5

4.5 4

3.5

conversion ratio

3 2.5 2 1.5 1 0.5 0 0

0.1

0.2

0.3

0.4

0.5 0.6 duty ratio

0.7

0.8

0.9

1

1 0.95 0.9 0.85 0.8

efficiency

0.75 0.7 0.65 0.6 0.55 0.5 1

1.5

2

2.5

3 3.5 conversion ratio

4

4.5

5

5.5

0 1 2 3 conversion ratio M(D) 4 5 6 7 8 9 10 0

0.1

0.2

0.3

0.4

0.5 0.6 duty ratio D

0.7

0.8

0.9

1

0

0.5 1 1.5

conversion ratio

2 2.5 3 3.5 4 4.5 5 0

0.1

0.2

0.3

0.4

0.5 duty ratio

0.6

0.7

0.8

0.9

1

1 0.95 0.9 0.85 0.8efficiency

0.75 0.7 0.65 0.6 0.55 0.5 5

4.5

4

3.5

3 2.5 2 conversion ratio

1.5

1

0.5

0

DC/DC converter

solar cell array

load

k

PWM

300

tracking with P&O algorithm path of real MPP250

output power P / W200

150

100

50

0

0

20

40

60 80 100 120 output voltage V / V (number of cells in series z = 168)

Slow RC Circuit

"1"

J K

clk Multiplier Fast RC Circuit

Q

Integrator

Comparator Flip Flop

300

250

Power ripple200

output power P / W

150

100

50

0

0

20

40

60 output voltage V / V

80

100

120

Voltage ripple

current [A]

voltage [V]

solar panel

V

0 controller display

dctodc converter

battery

1 voltage V 2 current I 3 series resistance Rs 4 number of cells in series 1 30 parallel resistance Rp u 1 Rp current

1000 Insolation [W/m^2] Iph(T)

Insolation [W/m^2] Temperature [K]

1 Current [A]

Voltage [V] 1 parallel resistancecurrent I Voltage V Temperature [K]

Current I Voltage V series resistance Rs number of cells in series Rp current

diode1 current

T

7*8*5 number of cells series resistance Rscurrent I Voltage V Temperature [K]

number of cells in series

15e3

series resistance Rs

Diode 1

Cell temperature [degr.C] 25T

diode2 current number of cells in series series resistance Rs

TDiode 2

T

absolute temperature 273 offset

1

(Rbs*Rbp*Cbp*Rb1*Cb1)s 2+(Rbp*Rb1*Cb1+Rb1*Rbp*Cbp+Rbs*Rb1*Cb1+Rbs*Rbp*Cbp)s+(Rbs+Rb1+Rbp) (Rbp*Cbp*Rb1*Cb1)s 2+(Rbp*Cbp+Rb1*Cb1)s+1 battery impedance

1

3

1

du/dt derivative

1

gain 1 u

2

1 1

2

2

Il(V,I,D)

Ib(Il,Vb)

3

V(Il,Vb,D)

1 1 2

controller

490 power P / W 480 470 460 160 voltage V / V 155 150 145 bvoltage Vb / V 110 105 100 95 0.7 duty ratio D 0.68 0.66 0.64 0 500 1000 1500 2000 2500 3000 time t / 0.1s 3500 4000 4500 5000 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

482.02 power P / W 482.01 482 481.99 53 482.02 power P / W 482.01 482 481.99 53 0.688 duty ratio D 0.687 0.686 0.685 0.684 53 53.2 53.4 53.6 53.8 54 time t / s 54.2 54.4 54.6 54.8 55

53.2

53.4

53.6

53.8

54

54.2

54.4

54.6

54.8

55

53.2

53.4

53.6

53.8

54

54.2

54.4

54.6

54.8

55

485 power P / W 480 475 470 4900 165 voltage V / V 160 155 150 4900 3.2 current I / A 4910 4920 4930 4940 4950 4960 4970 4980 4990 5000 4910 4920 4930 4940 4950 4960 4970 4980 4990 5000

3

2.8 4900 0.7 duty ratio D 0.69 0.68 0.67 4900

4910

4920

4930

4940

4950

4960

4970

4980

4990

5000

4910

4920

4930

4940

4950 4960 time t / 0.001s

4970

4980

4990

5000

192.81 power P / W 192.8 192.79 192.78 45 192.81 power P / W 192.8 192.79 192.78 45

45.02

45.04

45.06

45.08

45.1

45.12

45.14

45.16

45.18

45.2

45.02

45.04

45.06

45.08

45.1

45.12

45.14

45.16

45.18

45.2

duty ratio D

0.376

0.374

0.372 45

45.02

45.04

45.06

45.08

45.1 time t / s

45.12

45.14

45.16

45.18

45.2

194 power P / W 192 190 188 88 66 voltage V / V 64 62 60 88 3.2 current I / A 3.1 3 2.9 88

88.2

88.4

88.6

88.8

89

89.2

89.4

89.6

89.8

90

88.2

88.4

88.6

88.8

89

89.2

89.4

89.6

89.8

90

88.2

88.4

88.6

88.8

89 time t / s

89.2

89.4

89.6

89.8

90

193 192 power P / W

191

190

189 88.8

88.82

88.84

88.86

88.88

88.9

88.92

88.94

88.96

88.98

89

0.39

0.38 duty ratio D

0.37

0.36

0.35 88.8

88.82

88.84

88.86

88.88

88.9 time t / s

88.92

88.94

88.96

88.98

89

385.7 power P / W 385.6 385.5 385.4

385.3 50 385.7 power P / W 385.6 385.5 385.4 385.3 50

50.02

50.04

50.06

50.08

50.1

50.12

50.14

50.16

50.18

50.2

50.02

50.04

50.06

50.08

50.1

50.12

50.14

50.16

50.18

50.2

duty ratio D

0.458

0.456

0.454 50

50.02

50.04

50.06

50.08

50.1 time t / s

50.12

50.14

50.16

50.18

50.2

386

385 power P / W

384

383

382 99

99.02

99.04

99.06

99.08

99.1

99.12

99.14

99.16

99.18

99.2

0.46

duty ratio D

0.455

0.45

0.445 99

99.02

99.04

99.06

99.08

99.1 time t / s

99.12

99.14

99.16

99.18

99.2

482.015

power P / W

482.01

482.005

482 70

70.02

70.04

70.06

70.08

70.1

70.12

70.14

70.16

70.18

70.2

0.688

0.687 duty ratio D

0.686

0.685

0.684 70

70.02

70.04

70.06

70.08

70.1 time t / s

70.12

70.14

70.16

70.18

70.2

482.1 482.05 power P / W 482 481.95 481.9 481.85 481.8 27.7 27.75 27.8 27.85 27.9 27.95 28

0.685 0.684 duty ratio D 0.683 0.682 0.681 0.68 27.7

27.75

27.8

27.85 time t / s

27.9

27.95

28

482.02 power P / W 482.01 482 481.99 481.98 95 95.02 95.04 95.06 95.08 95.1 95.12 95.14 95.16 95.18 95.2

duty ratio D

0.688 0.687 0.686 0.685 0.684 95 95.02 95.04 95.06 95.08 95.1 time t / s 95.12 95.14 95.16 95.18 95.2

490 power P / W 480 470 460 450 34.9 0.7 duty ratio D 0.69 0.68 0.67 34.9 34.91 34.92 34.93 34.94 34.95 34.96

34.97

34.98

34.99

35

34.91

34.92

34.93

34.94

34.95 time t / s

34.96

34.97

34.98

34.99

35

290.5

290

power P / W

289.5

289

288.5 29.7

29.8

29.9

30

30.1

30.2

30.3

601 600

insolation S / W/m

2

599 598 597 596 595 29.7 29.8 29.9 30 time t / s 30.1 30.2 30.3

insolation S / W/m

1000 800 600 15 20 25 30 35

2

500

power P / W

400 300 200 15 160

20

25

30

35

voltage V / V

140 120 100 80 15 1 20 25 30 35

duty ratio d

0.9 0.8 0.7 0.6 15 20 25 time t / s

30 35

505 504

insolation S / W/m

2

503 502 501 500 499 24.9 25 25.1 25.2 25.3 25.4 25.5

242

241.5

power P / W

241

240.5

25 25.1 25.2 25.3 25.4 25.5

240 24.9

0.685

0.68

duty ratio d

25 25.1 25.2 time t / s 25.3 25.4 25.5

0.675

0.67

0.665 24.9

insolation S / W/m2

1000

800

600 19 20 21 22 23 24 25 26 27

200

power P / W

150

20 21

100 19 70

22 23 24 25 26 27

voltage V / V

65 60 55 50 19 20 21

22 23 24 25 26 27

0.45

duty ratio d

0.4 0.35 0.3 19

20 21 22 23 time t / s 24 25 26 27

temperature T / C

44.4 44.3 44.2 44.1 44 32.2 32.3 32.4 32.5 32.6 32.7 32.8 32.9 33 33.1 33.2

449

power P / W

448.8

448.6 32.2 32.3 32.4

32.5 32.6 32.7 32.8 32.9 33 33.1 33.2

panelvoltage V / V

148 147.5 147 146.5 146 32.2 0.735 32.3 32.4 32.5 32.6 32.7

32.8

32.9

33

33.1

33.2

dutyratio d

0.73 0.725 0.72 32.2

32.3 32.4 32.5 32.6 32.7 time t / s 32.8 32.9 33 33.1 33.2

42.6

temperature T / C

42.4

42.2 27.5 27.6 27.7 27.8 27.9 28 28.1 28.2 28.3 28.4 28.5

power P / W

225.4 225.3 225.2 225.1 225 27.5 27.6 27.7 27.8 27.9 28 28.1 28.2 28.3 28.4 28.5

panelvoltage V / V

148.2 148 147.8 147.6 147.4 27.5 27.6 27.7 27.8

27.9 28 time t / s 28.1 28.2 28.3 28.4 28.5

temperature T / C

43.5 43 42.5 42 26.5

27

27.5

28

226

power P / W

225.5 225 224.5 224 26.5 27 27.5 28

panelvoltage V / V

149 148 147 146 26.5

27 27.5 28

0.69

dutyratio d

0.685

0.68 26.5

27 time t / s 27.5 28

dutyratio d panelvoltage V / V power P / W

400 200 50 160 140 120 100 150 200 250 300

50

100

150

200

250

300

0.8 0.75 0.7 0.65 50 100 150 200 250 300 110 105 100 95 50 100 150 200 250 300

insolation S / W/m2 bat.voltage V / V b temperature T / C

1000 500 50 50 40 30 100 150 200 250 300

50

100

150 time t / s

200

250

300

duty ratio d panelvoltage V / V power P / W

400 200 50 155 150 145 50 100 150 200 250 300 100 150 200 250 300

0.75 0.7

0.65insolation S / W/m2 bat.voltage V / V b temperature T / C

50

100

150

200

250

300

110 105 100 95 50 100 150 200 250 300

1000 500 50 50 40 30 100 150 200 250 300

50

100

150 time t / s

200

250

300

dutyratio d panelvoltage V / V power P / W

400 200 50 160 140 120 100 150 200 250 300

50

100

150

200

250

300

0.8 0.75 0.7 0.65 50 100 150 200 250 300 110 105 100 95 50 100 150 200 250 300

insolation S / W/m2 bat.voltage V / V b temperature T / C

1000 500 50 50 40 30 100 150 200 250 300

50

100

150 time t / s

200

250

300

dutyratio d panelvoltage V / V power P / W

400 200 50 100 150 200 250 300 160 140 120 50 0.9 0.8 0.7 50 100 150 200 250 300 100 150 200 250 300

insolation S / W/m2 bat.voltage V / V b temperature T / C

110 105 100 95 50 100 150 200 250 300

1000 500 50 50 40 30 100 150 200 250 300

50

100

150 time t / s

200

250

300

280 260 240

power P / W

230 235 240 245 250 time t / s 255 260 265 270 275

220 200 180 160 140 120

1 I

1 V

V I I D Il Il Il Il Ib Vb D Vb V

2 D

D

2 Ib

Il(V,I,D)

Ib(Il,Vb)

3 Vb

V(Il,Vb,D)

1 V

Il V I Il I D Vb V

1 I 2 D 3 Vb

Il(V,I)

V(Il,Vb,D)Il Vb D Ib

2 Ib

Ib(Il,Vb,D)

V

Il Il D Vb V

1 V

1 I 2 D 3 Vb

I

I D

Il(V,I)

V(Il,Vb,D)Il Vb D Ib

2 Ib

Ib(Il,Vb,D)

1 I 2 V ZeroOrder HoldPk

Sum

MuxPk Pk Vk1 Vk1

Mux truth table 0.001 Sum1 1 D

>=0

1 V 2 I ZeroOrder Hold

P

SumPk

Pk1 Pk1

Vk

algorithm

Pk

1 Gain 1 D

1 IdI

0 AND NOT ==

==

2 VdV

[215] IC NOT Product AND ==I/V dI Out dV

0

NOT

1 0

>= >= MuxdeltaV

0.001 dV

1 D

truth table

192.806 192.804 power P / W

192.802

192.8

192.798 44.2

44.22

44.24

44.26

44.28

44.3

44.32

44.34

44.36

44.38

44.4

0.377

0.376 duty ratio D

0.375

0.374

0.373 44.2

44.22

44.24

44.26

44.28

44.3 time t / s

44.32

44.34

44.36

44.38

44.4

192.82 192.8 power P / W 192.78 192.76 192.74 192.72 192.7 43.8 43.82 43.84 43.86 43.88 43.9 43.92 43.94 43.96 43.98 44

0.375

0.374 duty ratio D

0.373

0.372

0.371 43.8

43.82

43.84

43.86

43.88

43.9 time t / s

43.92

43.94

43.96

43.98

44

385.65

power P / W

385.6

385.55

385.5 60

60.02

60.04

60.06

60.08

60.1

60.12

60.14

60.16

60.18

60.2

0.458

0.457 duty ratio D

0.456

0.455

0.454 60

60.02

60.04

60.06

60.08

60.1 time t / s

60.12

60.14

60.16

60.18

60.2

385.65 385.6 power P / W 385.55 385.5 385.45 385.4 385.35 385.3 50 50.02 50.04 50.06 50.08 50.1 50.12 50.14 50.16 50.18 50.2

0.458 0.457 duty ratio D 0.456 0.455 0.454 0.453 50

50.02

50.04

50.06

50.08

50.1 time t / s

50.12

50.14

50.16

50.18

50.2

192.806 power P / W 192.804 192.802 192.8 99 0.377 duty ratio D 0.376 0.375 0.374 0.373 99 99.02 99.04 99.06 99.08 99.1 time t / s 99.12 99.14 99.16 99.18 99.2

99.02

99.04

99.06

99.08

99.1

99.12

99.14

99.16

99.18

99.2

193 power P / W 192 191 190 189 51 0.39 duty ratio D 0.38 0.37 0.36 51 51.01 51.02 51.03 51.04 51.05 51.06 51.07 51.08 51.09 51.1

51.01

51.02

51.03

51.04

51.05 time t / s

51.06

51.07

51.08

51.09

51.1

385.7 power P / W 385.6 385.5 385.4 90

90.05

90.1

90.15

90.2

90.25

90.3

90.35

90.4

duty ratio D

0.458

0.456

0.454 90

90.05

90.1

90.15

90.2 time t / s

90.25

90.3

90.35

90.4

386 power P / W 385 384 383 382 45 45.05 45.1 45.15 45.2 45.25 45.3 45.35 45.4

0.46 duty ratio D

0.455

0.45 45

45.05

45.1

45.15

45.2 time t / s

45.25

45.3

45.35

45.4

241.6 241.5 power P / W

241.4

241.3

241.2 29.9

30

30.1

30.2

30.3

30.4

30.5

0.655

dutyratio d

0.65

0.645

0.64 29.9

30

30.1

30.2 time t / s

30.3

30.4

30.5

power P / W

200 150 100 50 50 70 60 50 100 150 200 250 300

panelvoltage V / V

50

100

150

200

250

300

0.55 0.5 0.45 0.4 0.35 50 105 100 95 100 150 200 250 300

insolation S / W/m2 bat.voltage V / V

b

dutyratio d

50

100

150

200

250

300

1000 800 600 400 200 50 40 30

temperature T / C

50

100

150

200

250

300

50

100

150 time t / s

200

250

300