Estimated Power Output of PV Generating Station · V PV6 V PV5 V PV4 V PV3 V PV2 V PV1 MPP 1 MPP 2...

89

ESTIMATED POWER OUTPUT OF PHOTOVOLTAIC GENERATING

STATION

Abir Chatterjee and Ali Keyhani

1 Abstract

For planning and designing a photovoltaic (PV) generating station, the power

available from it must be known. The output of the PV station varies with environmental

conditions of temperature and irradiance at a given time. The voltage level of the station

is also a function of temperature and irradiance along with the current drawn from the PV

array [1]. For operation control, the utility company must know how much power is

available from the PV station from power flow studies and scheduling. In this report, the

power available from 80 kW PV station as a function of time of day is presented for two

locations.

To obtain power from a PV station, the irradiance and temperature data must be

known as a function of time. However, irradiance on a particular day depends on the

angle the sun makes with the PV panels, the air mass and the cloud cover [2]. Forecast of

irradiance can be made by the meteorologists, which is used for operations control.

However, to plan a PV station, long-term forecasts must be made on the available power

from the PV station. In this report, method to estimate the power available from PV is

presented. For two locations, the performance of the PV station in terms of power/energy

output is presented.

90

The voltage at which the PV array operates is a function of temperature and

irradiance. As the temperature goes up and irradiance goes down, the voltage of the array

decreases as shown in Figure 1. If the voltage drops below a certain cutoff, the power

electronic converters are not able to convert power to required voltage level. However, if

there are multiple converters with lower output voltage levels, power which would have

not been available at lower voltage can be extracted. It is shown that for lower power

range of the PV, the voltage of the boost converter and in the DC voltage of the inverter

must have lower values for the PV station to supply power to the grid. Comparison is

made between the amount of power available from PV station with and without boost

converter. When the voltage of the PV array is lower with lower irradiance and higher

temperature, the PV panels are connected to power converters with lower voltage rating

making the PV station able to capture power at lower voltages which would not have

been to be captured with higher voltage.

It is demonstrated that the power available from the PV station during dawn and

dusk and in the days when the sky is overcast can be substantially increased with

converters of lower voltage rating.

91

PPV

VPV

Increasing irradiance and decreasing

temperature

VPV6 VPV5 VPV4 VPV3 VPV2 VPV1

MPP1

MPP2

MPP3

MPP4

MPP5

MPP6

Converter set 1

Converter set 2

Converter set 3

Figure 1. Voltage-current characteristic of PV for varying irradiance and temperature

2 Topology of PV station

A PV station is connected to the load it supplies through power electronic

converters. There can be one or multiple stages of conversion of power output from the

PV to the magnitude and frequency at which the load is rated. Two possible topologies

have been presented in this report for the study of power available from PV stations as

shown in Figure 2. In Figure 1(a), the PV array is connected to the inverter through a

boost conveter. The advantage of this topology is the boost converter provides a stable

and high voltage for the inverter, therefore, the inverter is rated at a lower current rating

for the same power level.

92

To reduce cost of the boost converter, the PV may be directly conneted to the

inverter as shown Figure 1(b). In both the topologies, two sets of power converters rated

at two voltage levels are used. When the irradiance is high and the temperature is low,

converters with higher voltages are used. Conversely, when the irradiance is low and the

temperature is high, converters with lower voltage rating are used. This arrangement

makes it possible to capture power for longer times.

When the voltage of the PV array is between VPV1 and VPV3 shown in Figure 1,

converter set with highest voltage level is switched on (see Figure 2). However, with this

set of converters will not be able to convert power at a voltage level below VPV3. A

sensor senses the voltage of the PV array and turns the controllable switches for converter

set 1 off and turns on the controllable switch of set 2. This set is able to convert power

between VPV3 and VPV6. Converter set 3 is connected to the system and the other

converter sets are disconnected when the array voltage falls below VPV6 through the

action of controllable switches. Reasonable number of sets of converters should be

available for different voltage levels. The number of sets is decided by the additional

amount of power available from the new set of converters and the associated cost with it.

93

dcVL

S

D

CVin VO

+ -

-

+ iL+

-

VL

RPVV

dcVL

S

D

CVin VO

+ -

-

+ iL+

-

VL

RPVV

dcVL

S

D

CVin VO

+ -

-

+ iL+

-

VL

RPVV

(a) continued Figure 2. Topology of PV based DG: (a) Topology 1: power flow from PV to grid, boost converter used to boost PV voltage (b) Topology 2: When PV voltage is high enough to be connected directly to the inverter without a boost converter

93

94

Figure 2 continued

dcVPVV

dcVPVV

dcVPVV

(b)

94

95

2.1 PV Station with Boost Converter and Inverter

The voltage of the PV array may not be sufficient for the inverter to operate for

most of the day. Therefore, a boost converter is used to step up the PV array voltage to a

value that is above lower cut-off voltage for the inverter. This topology has been shown

in Figure 1(a). In a boost converter, the switch is operated to force the inductor current to

conduct to the output side and thereby boosting the voltage. The output voltage of the

boost converter is given by (1) [3]:

δ−=

1V

V PVdc (1)

where δ is the duty ratio of the switch.

The relationship between the input and output voltage as given in (1) is under the

assumption that the current in the inductor of the boost converter is never zero that is

continuous conductance mode. The limit to continuous conductance is given by (2) [3]:

2II L

avgLΔ

=, (2)

where IL,avg is average inductor current and ΔIL.

Substituting the values from the PV station quantities into (2) we obtain (3).

96

s

PVPV fL2

VI

..

min

δ=

or

PV

sPV

VfLI2 ... min=δ

(3)

where Lmin is minimum boost converter inductance for continuous conduction, fs is

switching frequency.

From (3), it is seen that the duty ratio δ is limited by the switching frequency, the

voltage and current of the PV array and the inductance of the boost converter. With the

value of δ limited, the boost step up ratio is also limited as given by (1). This practically

limits the output voltage of the boost converter for a given PV array voltage. Since the

input voltage of the inverter should be maintained at sufficiently high value, the PV array

will not be able to provide power to the grid below a certain array voltage hence limiting

the output of the PV station to only certain times of the day when the irradiance is high

and temperature is low. Therefore, at times when the PV voltage is low, it is connected to

a different set of converters with lower step up voltage and therefore, making it capable

of capturing power at lower voltage levels.

2.2 PV Station with Direct Connection to Inverter

In this topology, shown in Figure 1(b), the DC voltage at the input of the inverter,

which is PV array voltage, must be above a cutoff value so that space vector modulation

97

is able to produce modulate AC voltage in its linear modulation range from zero to one.

The output line-to-line voltage of the inverter ViL-L is given by:

adc

LL M2

VVi .=− (4)

where Vdc is the input voltage of the inverter and Ma is the modulation index varying

between zero and one.

If the inverter is directly connected to the PV array, then Vdc is equal to the PV

array voltage VPV. Since the output of the inverter voltage is determined by the grid

voltage and the transformer turns ratio, therefore, the DC voltage of the inverter input is

limited to the case when Ma = 1 and the minimum DC voltage is given by:

LLdc Vi2V −= .min, (5)

Therefore, for power to be supplied to the grid, the PV array voltage must be

above Vdc, min. If the voltage of the PV falls below this value due to decrease in irradiance

or increase in temperature, then the PV station must be connected to lower voltage levels.

In other words, as the temperature and irradiance varies in a day, the PV station will be

able to be in service only during those times of the day when the voltage of the array is

above the cutoff value.

98

3 Problem Formulation

The irradiance of received on a horizontal surface is given by Ihor:

{ }φδ+ωφδ= sin.sincos.cos.cos.. ohor ESI (6)

where S is solar constant, δ is the declination angle, ϕ is the latitude of the location and ω

is solar hour angle. However, with a tilt angle β, the irradiance on the module is changed

as given in [4]:

( ) ( ){ }β−φδ+ωβ−φδ= sin.sincos.cos.cos.. ohor ESI (7)

However, (6) and (7) give the irradiance on a surface that is located outside the

earth’s atmosphere. As the rays of the sun pass through the atmosphere, some of the

components get diffused; others get absorbed into the atmosphere. A fraction reaches the

surface of the earth is available to the panels [2]. Using (7) and scaling it down from the

irradiation data available at the location, the irradiance on the panels at is calculated for

different times of the day. With the irradiance estimated and the average temperature of

the day available from meteorological records, the power, voltage and current output

from the array is estimated using the maximum power point estimation.

99

4 Case Study for PV Stations at Different Locations

The amount of power available from a PV is a function of location, time

of the year and the weather conditions at the location. Two sample cases have been

selected for the case study: Kolkata, India and Columbus, Ohio. Both the topologies of

the PV power plant have been considered for the study with different levels of voltages at

the input and output of the inverter. In each case, Wednesdays of each week have been

chosen as sample days. The voltage, current and power profile of the PV is made for each

day and the total energy available on those days from the PV station has been tabulated.

When the PV station consists of both boost converter and inverter, the boost

converter output voltage maintained at 480 V DC with a switching frequency of 5 kHz

and inductance of 5 mH, and inverter output voltage at 240 V. When the PV station

consists of only inverter, the line-to-line voltage is maintained at 240 V AC. The low

voltage level is half the value of the high voltage level specified above.

Data of PV module produced by Mitsubishi Electric, PV-MF165EB3, is used to

simulate a 80 kW PV station with 15 modules connected in series to form a string and 32

strings connected in parallel to form an array. The datasheet values provided by the

manufacturer’s datasheet are given in Table 1.

Isc Voc Vmpp Impp ns Ki Kv 7.36 A 30.4 V 24.2 V 6.83 A 50 0.057% -0.346

Table 1 Datasheet values of PV-MF165EB3 panel at STC

100

Voltage, current and power of an 80 kW PV station as a function of irradiance and

temperature is shown in Figure 3.

010

2030

4050

6070

80

0100

200300

400500

600700

800900

1000150

200

250

300

350

400

450

temperature (oC)irradiance (W/m2)

VPV

(V)

(a)

010

2030

4050

6070

80

0100

200300

400500

600700

800900

10000

50

100

150

200

250


I PV (A

)

(b) continued Figure 3. Voltage, current, and power output of 80 kW PV stations with and without boost converter as a function of irradiance and temperature: (a) PV voltage (b) PV current (c) PV output power without boost converter (d) PV power output with boost converter

101

Figure 3 continued

010

2030

4050

6070

80

0100

200300

400500

600700

800900

10000

10

20

30

40

50

60

70

80

90


PPV

(kW

)

(c)

010

2030

4050

6070

80

0100

200300

400500

600700

800900

10000

10

20

30

40

50

60

70

80

90


PPV

(kW

)P P

V(k

W)

(d)

4.1 Case 1: Kolkata, India

The voltage, current, and power profiles of on different days of the year have been

presented in Figure 4 and Figure 6 from irradiation and temperature data available for PV

station with and without boost converter respectively for Kolkata, India. The average

temperature data used for Kolkata, India is listed in Table 2.

102

Date Jan 5

Jan 12

Jan 19

Jan 26

Feb 2

Feb 9

Feb 16

Feb 23

Mar 2

Mar 9

Mar 16

Mar 23

Mar 30

Temperature (°C)

17 14 18 21 20 24 28 22 22 28 27 30 27

Date Apr 6

Apr 13

Apr 20

Apr 27

May 4

May 11

May 18

May 25

Jun 1

Jun 8

Jun 15

Jun 22

Jun 29

Temperature (°C)

27 30 30 28 28 30 32 30 30 32 28 30 27

Date Jul 6

Jul 13

Jul 20

Jul 27

Aug 3

Aug 10

Aug 17

Aug 24

Aug 31

Sep 7

Sep 14

Sep 21

Sep 28

Temperature (°C)

28 30 28 31 30 28 27 31 29 30 29 28 30

Date Oct 5

Oct 12

Oct 19

Oct 26

Nov 2

Nov 9

Nov 16

Nov 23

Nov 30

Dec 7

Dec 14

Dec 21

Dec 28

Temperature (°C)

30 30 28 27 25 24 26 24 22 22 20 16 16

Table 2. Average temperature of Kolkata, India for different days of the year

103

6 8 10 12 14 16 180

500

1000

Irrad

ianc

e (W

/m2 )

6 8 10 12 14 16 18250

300

350

400

VPV

(V)

6 8 10 12 14 16 180

100

200

I PV (A

)

6 8 10 12 14 16 180

20

40

60

PPV

(kW

)

time of day (hr)

week 1week 2week 3week 4week 5week 6week 7week 8week 9week 10week 11week 12week 13

(a) continued Figure 4. Irradiance, voltage, current and power profile of a 80 kW PV station at Kolkata, India with both boost converter and inverter for all seasons, Vdc: 480 V, ViL-L: 240 V, fs: 5 kHz, Lboost: 5 mH: (a) winter quarter (b) spring quarter (c) summer quarter (d) autumn quarter

104

Figure 4 continued

5 10 15 200

500

1000

Irrad

ianc

e (W

/m2 )

5 10 15 20250

300

350

VPV

(V)

5 10 15 200

100

200

I PV (A

)

5 10 15 200

20

40

60

PPV

(kW

)

time of day (hr)


(b) continued

105

Figure 4 continued

5 10 15 200

200

400

600

Irrad

ianc

e (W

/m2 )

5 10 15 20250

300

350

VPV

(V)

5 10 15 200

50

100

150

I PV (A

)

5 10 15 200

20

40

60

PPV

(kW

)

time of day (hr)


(c) continued

106

Figure 4 continued

6 8 10 12 14 16 180

500

1000

Irrad

ianc

e (W

/m2 )

6 8 10 12 14 16 18250

300

350

400

VPV

(V)

6 8 10 12 14 16 180

50

100

150

I PV (A

)

6 8 10 12 14 16 180

20

40

60

PPV

(kW

)

time of day (hr)


(d)

107

5 10 15 20 25 30 35 40 45 50

200

300

400

500

week

PPV

(kW

h)

5 10 15 20 25 30 35 40 45 5010

20

30

40

week

Tem

pera

ture

(o C)

1 2 3 4 5 6 7 8 9 10 11 121

2

3

4

5

6

7

month

irrad

iatio

n (k

Wh/

m2 /d

ay)

Figure 5. Power generated and irradiation received by a 80 kW generating station with both boost converter and inverter located at Kolkata, India for the weeks through a year

The power output from a PV station depends on the time of the year. The position

of the sun changes from month to month in a year increasing or decreasing the irradiance

of the location. It also depends on the weather at the location. For example in Kolkata,

India located at 22° N, the irradiance available from the sun increases as summer is

approached. Therefore, the power and irradiation are maximum during the summer

months of April and May. However, as monsoon sets in during the months of June

through September, the sky is mostly overcast and the power available decreases. With

autumn setting in which is followed by winter and spring, with clearer skies during

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October through March, the power availability in those months increases. However, since

the sun is not directly overhead at these times of the year, the power output is lower than

that of summer months of April and May when the sun is directly overhead. The

irradiation and power available from a 80 kW PV station is shown in Figure 5.

6 8 10 12 14 16 180

500

1000

Irrad

ianc

e (W

/m2 )

6 8 10 12 14 16 18250

300

350

400

VPV

(V)

6 8 10 12 14 16 180

100

200

I PV (A

)

6 8 10 12 14 16 180

20

40

60

PPV

(kW

)

time of day (hr)


(a) continued Figure 6. Irradiance, voltage, current and power profile of a 80 kW PV station at Kolkata, India with only inverter for all seasons, ViL-L: 240 V: (a) winter quarter (b) spring quarter (c) summer quarter (d) autumn quarter

109

Figure 6 continued

5 10 15 200

500

1000

Irrad

ianc

e (W

/m2 )

5 10 15 20250

300

350

VPV

(V)

5 10 15 200

100

200

I PV (A

)

5 10 15 20-1

0

1

PPV

(kW

)

time of day (hr)


(b) continued

110

Figure 6 continued

5 10 15 200

200

400

600

Irrad

ianc

e (W

/m2 )

5 10 15 20250

300

350

VPV

(V)

5 10 15 200

50

100

150

I PV (A

)

5 10 15 20-1

0

1

PPV

(kW

)

time of day (hr)


(c) continued

111

Figure 6 continued

6 8 10 12 14 16 180

500

1000

Irrad

ianc

e (W

/m2 )

6 8 10 12 14 16 18250

300

350

400

VPV

(V)

6 8 10 12 14 16 180

50

100

150

I PV (A

)

6 8 10 12 14 16 180

20

40

60

PPV

(kW

)

time of day (hr)


(d)

From Figure 4 and Figure 6 it is observed that the PV station with boost converter

is able to supply powers to the grid during most times of the day except few minutes after

sunrise and before sunset. However, the energy available from the PV station involving

only inverter, the times for which the power is available is shorter. For spring and

summer months, the power available from a station involving only inverter is zero since

the voltage of the PV decreases to a level below the cutoff value of 340 V DC due to

higher temperatures in those months. The power available from the PV station with boost

112

converter is greater than that when boost converter is not used. The energy in kWh that is

available from the PV station is tabulated in Table 3.

Date Jan 5

Jan 12

Jan 19

Jan 26

Feb 2

Feb 9

Feb 16

Feb 23

Mar 2

Mar 9

Mar 16

Mar 23

Mar 30

MPPT with Boost

380 378 363 348 410 389 368 366 445 416 404 385 379

MPPT with Inverter

354 368 320 237 347 0 0 218 334 0 0 0 0

Date Apr 6

Apr 13

Apr 20

Apr 27

May 4

May 11

May 18

May 25

Jun 1

Jun 8

Jun 15

Jun 22

Jun 29

MPPT with Boost

431 424 424 428 419 415 411 415 342 338 345 342 347

MPPT with Inverter

0 0 0 0 0 0 0 0 0 0 0 0 0

Date Jul 6

Jul 13

Jul 20

Jul 27

Aug 3

Aug 10

Aug 17

Aug 24

Aug 31

Sep 7

Sep 14

Sep 21

Sep 28

MPPT with Boost

301 298 302 297 308 312 314 307 311 296 297 299 296

MPPT with Inverter

0 0 0 0 0 0 0 0 0 0 0 0 0

Date Oct 5

Oct 12

Oct 19

Oct 26

Nov 2

Nov 9

Nov 16

Nov 23

Nov 30

Dec 7

Dec 14

Dec 21

Dec 28

MPPT with Boost

319 330 346 361 334 347 355 369 382 345 352 360 359

MPPT with Inverter

0 0 0 0 0 0 0 0 247 177 274 342 341

Table 3. Energy output from a 80 kW PV station in kWh in Kolkata, India on different days of the year for PV station with both boost converter and inverter; and a 80 kW PV station with inverter only Vdc: 480 V, ViL-L: 240 V, fs: 5 kHz, Lboost: 5 mH

113

The voltage of the PV array is a function of temperature and irradiance. As the

temperature increases and the irradiance decreases, the PV voltage decreases. Therefore,

the PV arrays are not able to supply the inverter or the grid below a certain voltage level.

To utilize the power available from the PV station under these conditions, separate boost

converter and inverters with lower voltage rating must be designed. Table 4 presents the

additional energy available from the PV station with reduced voltage level.

5 10 15 20 25 30 35 40 45 500

50

100

150

200

250

300

350

400

450

week

Ene

rgy

(kW

h)

5 10 15 20 25 30 35 40 45 500

0.2

0.4

0.6

0.8

1

week

Ene

rgy

(kW

h)

Figure 7. Additional energy output from a 80 kW PV station in kWh in Kolkata, India on different days of the year when the voltage of the boost converter is reduced from 480 V DC to 240 V DC and the inverter voltage is reduced from 240 V AC to 120 V AC

114

Date Jan 5

Jan 12

Jan 19

Jan 26

Feb 2

Feb 9

Feb 16

Feb 23

Mar 2

Mar 9

Mar 16

Mar 23

Mar 30

MPPT with Boost

0 0.08 0 0.08 0 0 0.18 0.41 0 0.42 0.10 0.18 0

MPPT with Inverter

25.6 10.1 42.7 111 62.9 388 368 148 110 416 404 385 378

Date Apr 6

Apr 13

Apr 20

Apr 27

May 4

May 11

May 18

May 25

Jun 1

Jun 8

Jun 15

Jun 22

Jun 29

MPPT with Boost

0 0.48 0.32 0.38 0.33 0.05 0 0 0 0.44 0.36 0 0.11

MPPT with Inverter

430 424 424 428 419 415 410 414 341 338 345 341 347

Date Jul 6

Jul 13

Jul 20

Jul 27

Aug 3

Aug 10

Aug 17

Aug 24

Aug 31

Sep 7

Sep 14

Sep 21

Sep 28

MPPT with Boost

0.44 0.43 0 0.08 0.83 0.13 0 0.70 0.02 0 0.20 0 0.04

MPPT with Inverter

301 298 301 297 308 312 313 307 311 295 297 298 296

Date Oct 5

Oct 12

Oct 19

Oct 26

Nov 2

Nov 9

Nov 16

Nov 23

Nov 30

Dec 7

Dec 14

Dec 21

Dec 28

MPPT with Boost

0 0 0 0 0.05 0.36 0.26 0.29 0.03 0.17 0.22 0.12 0

MPPT with Inverter

318 329 345 360 334 347 355 369 135 168 78.2 18.1 17.5

Table 4. Additional energy output from a 80 kW PV station in kWh in Kolkata, India on different days of the year when the voltage of the boost converter is reduced from 480 V DC to 240 V DC and the inverter voltage is reduced from 240 V AC to 120 V AC

The irradiance and temperature at a particular location are not stable from year to

year. They vary widely even from day to day. The irradiance drops rapidly during

overcast conditions. During these periods of time, if the voltage level of the converters is

high, then the converters will not be able to capture power for entire days. However, if

there are other sets of converters with lower voltage levels, then, during these times,

115

power can be generated at the PV stations. Table 5 presents the additional power

available from the PV station when converters sets with two voltage levels are used. It is

observed that the power available from the PV station with boost converter is able to

capture power at wide voltage range and therefore, the additional power available is

negligible. However, for the PV station without boost converter additional power

available with two sets of converters is high when the irradiance decrease and the

temperature increases as shown in Table 5. From Table 5 it is seen that the additional

energy available over a year with two sets of converters is 32 MWh in one year when

boost converter is not used as opposed to 130 MWh available when the temperature and

irradiation are normal. However, further analysis shows negligible improvement in power

when boost converter is used. When the number of converters is increased to 3, the

additional power available is negligible over 2 converters.

116

Date Jan 5

Jan 12

Jan 19

Jan 26

Feb 2

Feb 9

Feb 16

Feb 23

Mar 2

Mar 9

Mar 16

Mar 23

Mar 30

MPPT with Boost

0 0 0 0 0 0 0 0 0 0 0 0 0

MPPT with Inverter

82 81 78 74 88 83 78 78 96 89 86 82 81

Date Apr 6

Apr 13

Apr 20

Apr 27

May 4

May 11

May 18

May 25

Jun 1

Jun 8

Jun 15

Jun 22

Jun 29

MPPT with Boost

0 0 0 0 0 0 0 0 0 0 0 0 0

MPPT with Inverter

92 90 90 91 89 88 87 88 72 71 73 72 73

Date Jul 6

Jul 13

Jul 20

Jul 27

Aug 3

Aug 10

Aug 17

Aug 24

Aug 31

Sep 7

Sep 14

Sep 21

Sep 28

MPPT with Boost

0 0 0 0 0 0 0 0 0 0 0 0 0

MPPT with Inverter

63 62 63 62 64 65 66 64 65 62 62 63 62

Date Oct 5

Oct 12

Oct 19

Oct 26

Nov 2

Nov 9

Nov 16

Nov 23

Nov 30

Dec 7

Dec 14

Dec 21

Dec 28

MPPT with Boost

0 0 0 0 0 0 0 0 0 0 0 0 0

MPPT with Inverter

67 69 73 76 70 73 75 78 81 73 74 76 76

Table 5. Additional Energy output from a 80 kW PV station in kWh in Kolkata, India on different days of the year when the voltage of the boost converter is reduced from 480 V DC to 240 V DC and the inverter voltage is reduced from 240 V AC to 120 V AC when irradiance decreases to one-fourth and the temperature is 10° C higher

4.2 Case 2: Columbus, Ohio

The voltage, current, and power profiles of on different days of the year have been

presented in Figure 8 and Figure 10 form irradiation and temperature data available for

PV station with and without boost converter respectively. When the PV station consists

of both boost converter and inverter, the boost converter output voltage maintained at 480

117

V DC with a switching frequency of 5 kHz and inductance of 5 mH, and inverter output

voltage at 240 V. When the PV station consists of only inverter, the line-to-line voltage is

maintained at 240 V AC. The voltage level for low voltage rating is half of the high

voltage rating. The average temperature for different days of the year for Columbus, Ohio

is presented in Table 6.

Date Jan 5

Jan 12

Jan 19

Jan 26

Feb 2

Feb 9

Feb 16

Feb 23

Mar 2

Mar 9

Mar 16

Mar 23

Mar 30

Temperature (°C)

-6 -6 -1 1 -2 -11 7 -3 2 7 8 11 0

Date Apr 6

Apr 13

Apr 20

Apr 27

May 4

May 11

May 18

May 25

Jun 1

Jun 8

Jun 15

Jun 22

Jun 29

Temperature (°C)

10 9 12 19 8 23 12 22 24 27 17 23 20

Date Jul 6

Jul 13

Jul 20

Jul 27

Aug 3

Aug 10

Aug 17

Aug 24

Aug 31

Sep 7

Sep 14

Sep 21

Sep 28

Temperature (°C)

26 23 27 26 26 22 21 24 22 16 18 20 13

Date Oct 5

Oct 12

Oct 19

Oct 26

Nov 2

Nov 9

Nov 16

Nov 23

Nov 30

Dec 7

Dec 14

Dec 21

Dec 28

Temperature (°C)

15 15 10 16 11 10 7 6 1 -1 8 11 -1

Table 6. Average temperature of Columbus, Ohio for different days of the year

118

6 8 10 12 14 16 180

500

1000

Irrad

ianc

e (W

/m2 )

6 8 10 12 14 16 18300

350

400

450

VPV

(V)

6 8 10 12 14 16 180

50

100

150

I PV (A

)

6 8 10 12 14 16 180

20

40

60

PPV

(kW

)

time of day (hr)


(a) continued Figure 8. Irradiance, voltage, current and power profile of a 80 kW PV station at Columbus, Ohio with both boost converter and inverter for all seasons, Vdc: 480 V, ViL-L: 240 V, fs: 5 kHz, Lboost: 5 mH: (a) winter quarter (b) spring quarter (c) summer quarter (d) autumn quarter

119

Figure 8 continued

5 10 15 200

500

1000

Irrad

ianc

e (W

/m2 )

5 10 15 20250

300

350

400

VPV

(V)

5 10 15 200

100

200

I PV (A

)

5 10 15 200

20

40

60

PPV

(kW

)

time of day (hr)


(b) continued

120

Figure 8 continued

5 10 15 200

500

1000

Irrad

ianc

e (W

/m2 )

5 10 15 20250

300

350

400

VPV

(V)

5 10 15 200

100

200

I PV (A

)

5 10 15 200

20

40

60

PPV

(kW

)

time of day (hr)


(c) continued

121

Figure 8 continued

6 8 10 12 14 16 180

500

1000

Irrad

ianc

e (W

/m2 )

6 8 10 12 14 16 18300

350

400

VPV

(V)

6 8 10 12 14 16 180

50

100

150

I PV (A

)

6 8 10 12 14 16 180

20

40

60

PPV

(kW

)

time of day (hr)


(d)

122

5 10 15 20 25 30 35 40 45 50

200

300

400

500

week

PPV

(kW

h)

5 10 15 20 25 30 35 40 45 50

-10

0

10

20

30

40

week

Tem

pera

ture

(o C)

1 2 3 4 5 6 7 8 9 10 11 121

2

3

4

5

6

7

month

irrad

iatio

n (k

Wh/

m2 /d

ay)

Figure 9. Power generated, temperature and irradiation received by a 80 kW generating station with both boost converter and inverter located at Columbus, Ohio for the weeks of a year

A plot of power available from an 80 kW PV station with both boost converter

and inverter located at Columbus, Ohio is given in Figure 9. It is observed that the power

available increases from January to June when the apparent motion of the sun is towards

the northern hemisphere increasing the irradiance and the power output of the PV station.

After June, as the sun apparently moves towards the southern hemisphere, the zenith

angle of the sun increases and reaches its maximum value in December which is seen to

have the least irradiation and power output from the PV station. It is observed that since

123

Columbus, Ohio is located away from the tropics at 40° N and it is further north of

Kolkata, India, the amount of irradiation received at Columbus, Ohio is substantially

lesser than that of Kolkata. The peak value, however, is higher than that in Kolkata

because when the sun is making least zenith angle, there is no cloud cover unlike Kolkata

during the monsoons staring from June (see Figure 5).

6 8 10 12 14 16 180

500

1000

Irrad

ianc

e (W

/m2 )

6 8 10 12 14 16 18300

350

400

450

VPV

(V)

6 8 10 12 14 16 180

50

100

150

I PV (A

)

6 8 10 12 14 16 180

20

40

60

PPV

(kW

)

time of day (hr)


(a) continued Figure 10. Irradiance, voltage, current and power profile of a 80 kW PV station at Columbus, Ohio with only inverter for all seasons, ViL-L: 240 V: (a) winter quarter (b) spring quarter (c) summer quarter (d) autumn quarter

124

Figure 10 continued

5 10 15 200

500

1000

Irrad

ianc

e (W

/m2 )

5 10 15 20250

300

350

400

VPV

(V)

5 10 15 200

100

200

I PV (A

)

5 10 15 200

20

40

60

PPV

(kW

)

time of day (hr)


(b) continued

125

Figure 10 continued

5 10 15 200

500

1000

Irrad

ianc

e (W

/m2 )

5 10 15 20250

300

350

400

VPV

(V)

5 10 15 200

100

200

I PV (A

)

5 10 15 200

20

40

60

PPV

(kW

)

time of day (hr)


(c) continued

126

Figure 10 continued

6 8 10 12 14 16 180

500

1000

Irrad

ianc

e (W

/m2 )

6 8 10 12 14 16 18300

350

400

VPV

(V)

6 8 10 12 14 16 180

50

100

150

I PV (A

)

6 8 10 12 14 16 180

20

40

60

PPV

(kW

)

time of day (hr)


(d)

It is observed from Figure 8 and Figure 10 that PV station with boost converter is

able to supply more power to the grid than without boost converter. It is also observed

that the PV station with only inverter at Columbus, Ohio is able to generate more power

than that of Kolkata, India because the operating temperature is less in Columbus, Ohio.

The total energy in kWh available from the location for each day is tabulated in Table 7.

Date Jan 5

Jan 12

Jan 19

Jan 26

Feb 2

Feb 9

Feb 16

Feb 23

Mar 2

Mar 9

Mar 16

Mar 23

Mar 30

127

MPPT with Boost

261 249 231 215 329 316 270 263 377 342 319 297 297

MPPT with Inverter

261 250 231 215 329 316 270 263 377 339 311 282 295

Date Apr 6

Apr 13

Apr 20

Apr 27

May 4

May 11

May 18

May 25

Jun 1

Jun 8

Jun 15

Jun 22

Jun 29

MPPT with Boost

382 379 370 355 448 415 434 413 446 438 459 446 452

MPPT with Inverter

369 369 352 271 440 179 418 244 0 0 413 218 365

Date Jul 6

Jul 13

Jul 20

Jul 27

Aug 3

Aug 10

Aug 17

Aug 24

Aug 31

Sep 7

Sep 14

Sep 21

Sep 28

MPPT with Boost

431 439 432 437 394 405 412 412 423 352 356 361 384

MPPT with Inverter

0 225 0 0 0 257 306 0 295 314 302 281 366

Date Oct 5

Oct 12

Oct 19

Oct 26

Nov 2

Nov 9

Nov 16

Nov 23

Nov 30

Dec 7

Dec 14

Dec 21

Dec 28

MPPT with Boost

283 305 339 361 197 213 232 249 270 197 194 193 202

MPPT with Inverter

249 277 339 344 182 209 232 249 270 197 194 193 202

Table 7. Energy output from a 80 kW PV station in kWh in Columbus, Ohio on different days of the year for PV station with both boost converter and inverter; and a 80 kW PV station with inverter only Vdc: 480 V, ViL-L: 240 V, fs: 5 kHz, Lboost: 5 mH Date Jan Jan Jan Jan Feb Feb Feb Feb Mar Mar Mar Mar Mar

128

5 12 19 26 2 9 16 23 2 9 16 23 30 MPPT with Boost

0.41 0.79 0 0 0.17 0 0.10 0 0.38 0.61 0.19 0 0.41

MPPT with Inverter

0.41 0 0 0 0.17 0 0.10 0 0.34 3.61 8.19 14.9 0.41

Date Apr 6

Apr 13

Apr 20

Apr 27

May 4

May 11

May 18

May 25

Jun 1

Jun 8

Jun 15

Jun 22

Jun 29

MPPT with Boost

0 0 0 0 0 0 0.37 0 0 0.33 0.25 0.15 0.88

MPPT with Inverter

12.7 9.7 17.7 83.7 7.8 235.7 16.4 168 445 438 46 228 87.9

Date Jul 6

Jul 13

Jul 20

Jul 27

Aug 3

Aug 10

Aug 17

Aug 24

Aug 31

Sep 7

Sep 14

Sep 21

Sep 28

MPPT with Boost

0 0 0.36 0.31 0 0.30 0.01 0 0.09 0 0 0.21 0

MPPT with Inverter

430 213 432 437 393 148 106 411 128 37.7 53.7 80.2 17.9

Date Oct 5

Oct 12

Oct 19

Oct 26

Nov 2

Nov 9

Nov 16

Nov 23

Nov 30

Dec 7

Dec 14

Dec 21

Dec 28

MPPT with Boost

0.11 0.28 0.47 0.02 0 0 0 0.25 0.24 0 0 0 0

MPPT with Inverter

34.1 28.2 0.47 17.0 14.9 3.76 0 0.25 0.24 0 0 0 0

Table 8. Additional energy output from a 80 kW PV station in kWh in Columbus, Ohio on different days of the year when the voltage of the boost converter is reduced from 480 V DC to 240 V DC and the inverter voltage is reduced from 240 V AC to 120 V AC

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5 10 15 20 25 30 35 40 45 500

50

100

150

200

250

300

350

400

450

week

Ene

rgy

(kW

h)

5 10 15 20 25 30 35 40 45 500

0.2

0.4

0.6

0.8

1

week

Ene

rgy

(kW

h)

Figure 11. Additional energy output from a 80 kW PV station in kWh in Columbus, Ohio on different days of the year when the voltage of the boost converter is reduced from 480 V DC to 240 V DC and the inverter voltage is reduced from 240 V AC to 120 V AC

Table 9 presents the additional power available from the PV station when

converters sets with two voltage levels are used. It is observed that the power available

from the PV station with boost converter is able to capture power at wide voltage range

and therefore, the additional power available is negligible. However, for the PV station

without boost converter additional power available with two sets of converters is high

when the irradiance decrease and the temperature increases as shown in Table 9. From

Table 9 it is seen that the additional energy available over a year with two sets of

130

converters is 25 MWh in one year when boost converter is not used vis-à-vis 124 MWh

maximum power available from the location when the irradiance and temperature are

normal. However, further analysis shows negligible improvement in power when boost

converter is used. When the number of converters is increased to 3, the additional power

available is negligible over 2 converters.

Date Jan

5 Jan 12

Jan 19

Jan 26

Feb 2

Feb 9

Feb 16

Feb 23

Mar 2

Mar 9

Mar 16

Mar 23

Mar 30

MPPT with Boost

0 0 0 0 0 0 0 0 0 0 0 0 0

MPPT with Inverter

23 28 48 45 61 63 57 56 81 73 68 63 63

Date Apr 6

Apr 13

Apr 20

Apr 27

May 4

May 11

May 18

May 25

Jun 1

Jun 8

Jun 15

Jun 22

Jun 29

MPPT with Boost

0 0 0 0 0 0 0 0 0 0 0 0 0

MPPT with Inverter

82 81 79 75 97 88 94 88 95 93 99 95 97

Date Jul 6

Jul 13

Jul 20

Jul 27

Aug 3

Aug 10

Aug 17

Aug 24

Aug 31

Sep 7

Sep 14

Sep 21

Sep 28

MPPT with Boost

0 0 0 0 0 0 0 0 0 0 0 0 0

MPPT with Inverter

92 94 92 93 84 86 88 88 91 75 76 77 82

Date Oct 5

Oct 12

Oct 19

Oct 26

Nov 2

Nov 9

Nov 16

Nov 23

Nov 30

Dec 7

Dec 14

Dec 21

Dec 28

MPPT with Boost

0 0 0 0 0 0 0 0 0 0 0 0 0

MPPT with Inverter

60 64 72 77 41 44 48 52 57 41 40 40 42

Table 9. Additional Energy output from a 80 kW PV station in kWh in Columbus, Ohio on different days of the year when the voltage of the boost converter is reduced from 480 V DC to 240 V DC and the inverter voltage is reduced from 240 V AC to 120 V AC when irradiance decreases to one-fourth and the temperature is 10° C higher

131

It is seen from Figure 3 that the voltage of the PV array decreases with increase in

temperature linearly and decreases with decreasing irradiance nonlinearly. The effect of

temperature on voltage of the array is more dramatic than that of irradiance. Therefore,

for locations with higher mean temperature the PV station is able to operate for a longer

time when the voltage of the converters is lower. Hence, additional power output at lower

voltage is higher for Kolkata, India is greater than that of Columbus, Ohio as seen from

Table 4 and Table 8. Therefore, for locations with higher temperature, lower voltages of

operation should be adopted.

5 Summary

The expected power output from a PV station should be known for operation

planning and systems control. Voltage, current and power output of the PV array is a

nonlinear function of temperature and irradiance. Depending on the operating conditions

at the location of the PV station, the power output varies from sun rise to sun set. Low

irradiance and high temperature causes the PV array voltage to decrease to a point when

power can no longer be extracted. To have power available for longer times, two sets of

converters is used at different voltage levels. It is observed that the additional power

available with two voltage level topology is substantially more for topologies without

boost converter and there is a marginal improvement in additional power availability in

the topology involving boost converter. In this report the voltage, current and power

profile of a PV station is presented. It is shown that if different converter sets are used at

different operating conditions, the power output of the PV station is increased. Case study

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has been performed for PV station located at Kolkata, India and Columbus, Ohio for each

weak of the year. Is has been shown that the amount of additional power available is

substantially more when two sets of converters are used over one set of converters when

the irradiance is low and temperature is high. However, improvement of power output is

negligible when three converters are used over two. The amount of additional power

available with 2 sets of converters when there is no boost converter with irradiance one

fourth of the normal and temperature 10° C higher is 32 MWh for Kolkata, India which is

an increase from 130 MWh under normal conditions and 25 MWh for Columbus, Ohio,

which is an increase from 124 MWh from normal conditions with PV station rated at 80

kW. However, the available additional power will increase with the increase in rating of

the power station.

References

[1] D. Sera, R. Teodorescu, and P. Rodriguez, “PV panel model based on datasheet values,” IEEE International Symposium on Industrial Electronics, pp. 2392 – 2396, Jun. 2007.

[2] T. Markvart, Solar Electricity, West Sussex, England: Wiley, 1994, pp. 11 – 16. [3] S. Liu, J. Liu, H. Mao, and Y. Zhang, “Analysis of Operating Modes and Output

Voltage Ripple of Boost DC–DC Converters and Its Design Considerations”, IEEE Trans. Power Electronic, vol. 23, no. 4, pp. 1813 – 1821, Jul 2008

[4] M. Iqbal, An Introduction to Solar Radiation, New York: Academic Press, 1983, pp. 1 – 84

133

Appendix function [time, I, Vmpp_, Impp_, Pmpp_i, Pmpp_b] = Irr_multiple_days(j, day_num, temp, betha) %% Irradiation and optimal tilt angle at a location data_Columbus_OH %data_Kolkata_India %% quarter, tilt angle and ground reflectivity g = 0.5; % for semi bare ground reflectivity Lboost = 5e-3; % inductance of boost converter fs = 5e3; % swtching frequency of boost converter VacL2L = 240/2; % line to line voltage at inverter output Vboost = 480/2; % boost converter output voltage S=1367; %w/m2 global irradiation day = zeros(1,52); for i = 1:52 day(i) = 5 + 7*(i-1); end delta=23.45*sind(360*(284+day(day_num))/365); % Calculating declination angle % Calculate the sunset angle x = -tand(L)*tand(delta); if abs(x) > 1 if x > 0 x = 1; else x = -1; end end ws = acos(x); % Finding sunset angle y = -tand(L-betha)*tand(delta); if abs(y) > 1 if y > 0 y = 1; else y = -1; end end ws1=acos(y); % Finding sunset angle for tilted surface wo=min(ws,ws1); % Calculating extraterrestrial irradiation Bo=(24/pi)*S*(1+.0333*cos(2*pi*day(day_num)/365))*(cosd(L)*cosd(delta)*sin(ws)+ws*sind(L)*sind(delta)); if Bo == 0 % no sunrise

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DD = GI(j); % radiation on surface is all diffusion B = 0; else KT=GI(j)/Bo; % clearness index DD=GI(j)*(1-1.13*KT); % diffuse irradiation BB=GI(j)-DD; % beam(direct irradiation) B=BB*(cosd(L-betha)*cosd(delta)*sin(wo)+wo*sind(L-betha)*sind(delta))... /(cosd(L)*cosd(delta)*sin(ws)+ws*sind(L)*sind(delta)); end D=DD*0.5*(1+cosd(betha)); % diffused irradiation on tilted surface R=DD*0.5*g*(1-cosd(betha)); % reflection irradiation on tilted surface G=B+D+R; % total global irradiation lim = 2; w = -wo*180/pi+lim:2*(wo*180/pi-lim)/100:wo*180/pi-lim; % hour angle form sunrise to sunset time = 12+12/180*w; % converting the hour angle to time of day I = abs(S*(1+.0333*cos(2*pi*day(day_num)/365))*(cosd(L-betha)*cosd(delta)*cosd(w) + sind(delta)*sind(L-betha))); % irradiance out side atmosphere B1=(24/pi)*S*(1+.0333*cos(2*pi*day(day_num)/365))*(cosd(L-betha)*cosd(delta)*sin(ws)+ws*sind(L-betha)*sind(delta)); % irradiation out side atmosphere I = I*G/B1; % scaling the extra-terristrial irradiance to the data at location I = I/4; %% Calculating MPP for j = 1:length(I) [Vmpp_(j) Impp_(j)] = MPP(I(j), temp); end % power with MPPT inverter for j = 1:length(time) if Vmpp_(j)/sqrt(2) >= VacL2L+5 % DC voltage of inverter is greater than line2line AC Pmpp_i(j) = Impp_(j)*Vmpp_(j); else Pmpp_i(j) = 0; end end % power with MPPT boost converter duty = 1-Vmpp_/Vboost; % duty ratio Lmin = duty.*Vmpp_/2./Impp_/fs; % for continuous conduction for j = 1:length(time) if Lboost >= Lmin(j) % boost inductance greater than Lmin Pmpp_b(j) = Impp_(j)*Vmpp_(j);

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else Pmpp_b(j) = 0; end end end %% Generates the maximum power point from irradiance and temperature function [Vmpp_ Impp_] = MPP(G_given, temp) array = 1; % 1: array, 0: module %% Datasheet values Data_PVMF165EB3 %% Array sepcifications: 5 kW Nss = 15; % Npp = 32; % tolerance = 1e-6; %% STC T = Tstc; G = Gstc; %% Array value adjustment if array Isc = Isc*Npp; Ki = Ki*Npp; Voc = Voc*Nss; Kv = Kv*Nss; Impp = Impp*Npp; Vmpp = Vmpp*Nss; ns = ns*Nss; end %% Initialization Rs = 0; Rsh = 1000; %% Calculate parameters [Iph, Io, A, Rs, Rsh, iteration] = PV_parameter_calculation(Isc, Voc, Impp, Vmpp, ns, Tstc, Rs, Rsh, tolerance); % Change in environmantal conditions T = 273 + temp; [Iph_ Io_ Isc_ Voc_ Vmpp_ Impp_] = PV_env_change(Isc,Voc,Vmpp,Impp,ns,Tstc,Gstc,Ki,Kv,Kp,G_given,T,A,Rs,Rsh); Vmpp_ = real(Vmpp_); Impp_ = real(Impp_); end

Estimated Power Output of PV Generating Station · V PV6 V PV5 V PV4 V PV3 V PV2 V PV1 MPP 1 MPP 2...

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Transcript of Estimated Power Output of PV Generating Station · V PV6 V PV5 V PV4 V PV3 V PV2 V PV1 MPP 1 MPP 2...