Near-maximum-power-point-operation (nMPPO) design of photovoltaic power generation system

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Near-maximum-power-point-operation (nMPPO) design

of photovoltaic power generation system

B.J. Huang

*

_{, F.S. Sun, R.W. Ho}

Department of Mechanical Engineering, National Taiwan University, Taipei 106, Taiwan, ROC Received 15 April 2003; received in revised form 5 June 2005; accepted 29 June 2005

Available online 25 August 2005

Communicated by: Associate Editor Arturo Morales-Acevedo

Abstract

The present study proposes a PV system design, called ‘‘near-maximum power-point-operation’’ (nMPPO) that can maintain the performance very close to PV system with MPPT (maximum-power-point tracking) but eliminate hard-ware of the MPPT. The concept of nMPPO is to match the design of battery bank voltage Vsetwith the MPP

(maxi-mum-power point) of the PV module based on an analysis using meteorological data. Three design methods are used in the present study to determine the optimal Vset. The analytical results show that nMPPO is feasible and the optimal Vset

falls in the range 13.2–15.0 V for MSX60 PV module. The long-term performance simulation shows that the overall nMPPO eﬃciency gnMPPOis higher than 94%. Two outdoor ﬁeld tests were carried out in the present study to verify

the design of nMPPO. The test results for a single PV module (60Wp) indicate that the nMPPO eﬃciency gnMPPOis

mostly higher than 93% at various PV temperature Tpv. Another long-term ﬁeld test of 1 kWp PV array using nMPPO

shows that the power generation using nMPPO is almost identical with MPPT at various weather conditions and Tpv

variation from 24C to 70 C.

Keywords: MPPT; nMPPO; Meteorological data; PV; Field test; Statistical analysis

1. Introduction

A photovoltaic power generation system requires a maximum-power-point tracking (MPPT) to control the photovoltaic arrays to operate at the maximum-power point (MPP) of the PV module in order to obtain the best power generation eﬃciency. The MPPT can be achieved from a power electronic device that utilizes a DC/DC

converter to adjust the output voltage of the PV array at MPP. Several control schemes were proposed by many researchers, for examples, the step-up methods (Salameh and Taylor, 1990) and the step-down methods (Salameh et al., 1991). The present study proposes a new design concept, called ‘‘near-maximum-power-point operation’’ (nMPPO) that can keep the performance very close to MPPT but eliminate hardware of the MPPT.

Fig. 1shows the I–V curves measured outdoors using natural sunlight for the PV module MSX-60 (polycrys-talline PV) manufactured by Solarex. The P–V curves shown in Fig. 2 reveal that the peak voltages at the maximum-power-points are within a narrow range, 0038-092X/$ - see front matter 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.solener.2005.06.013

*_{Corresponding author. Tel.: +886 2 2362 4790; fax: +886 2}

2364 0549.

E-mail address:[email protected](B.J. Huang).

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about 14–16 V. Similar phenomenon occurs in many PV modules.

The idea of nMPPO is to use the voltage provided by battery bank to keep the PV at a voltage near the MPP, as shown inFig. 3. The battery bank has dual functions, i.e., PV voltage control and energy storage. By matching the voltage of battery bank with MPP in design, a PV system with nMPPO can obtain a performance very close to MPPT. Even if the operating point is not exactly the MPP of the PV module, the loss caused by the mis-match will be very small. The problem remained to be solved is how to choose the voltage of the battery bank for an nMPPO. A statistical analysis was carried out in the present study for determining a proper design volt-age of battery bank that best matches the PV module under local meteorological condition.

2. Performance analysis of PV system with nMPPO 2.1. Performance of a PV module

The design of a PV system with nMPPO requires the information of local meteorological data and the

perfor-mance curves of the PV module. In the present study, we used Solarex MSX60 as an example. The performance curves of MSX60 are shown inFigs. 1 and 2. They are measured outdoors using natural sunlight. The charac-teristic equation of the module at a ﬁxed PV temperature TPVcan be expressed as Eq.(1):

Ipv¼ IgdS Is exp Vpvþ RsIpv VT 1 Vpvþ RsIpv Rsh . ð1Þ For MSX60 at 45C, the parameters in Eq. (1) are determined experimentally as Igd= 3.92· 103A m2/

W; Is= 5.25· 1011A; VT= 0.747 V; Rs= 1.09 X;

Rsh= 999 X. The solid lines drawn inFigs. 1 and 2are

based on Eq.(1)using the above parameters. To correct the performance deviation due to temperature change, Eq.(2)is used.

Ipv¼ Ioþ aðTpv ToÞ;

Vpv¼ Voþ bðTpv ToÞ RsðIpv IoÞ KIpvðTpv ToÞ;

ð2Þ where Ipv and Vpv are the current and voltage of PV

module at PV temperature Tpv, Ioand Voare the current

Nomenclature

Ea accumulated power generation at S over

cer-tain period of time, J

EMPP expected ideal daily total PV power

genera-tion at MPP, kW h

EnMPPO measured daily total PV power generation

with nMPPO, kW h

Etotal daily total incident solar radiation energy,

MJ/m2

Ig= IgdS light current of PV module in speciﬁc solar

radiation, A Iload current of load, A

InMPPO nMPPO operating current, A

Ipv output current of PV module, A

Ipv(Si) current through PV module at Vsetand Si, A

Is saturation current of diode, A

Ns occurrence frequency of S, dimensionless

Nv number of occurrence of Vmax,

dimension-less

Pmax power generation of PV module at

maxi-mum-power point, W

pv probability function of Vmaxdeﬁned in Eq.

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PVpvðSiÞ power generation at Siin use with nMPPO,

W

Rs inner series resistance of PV voltage, X

Rsh inner shunt resistance of PV voltage, X

S solar radiation intensity incident upon PV surface, W m2

SE value of S at maximum Ea, W m2

Si solar radiation intensity incident upon PV

surface at sequence i, W m2 Tpv temperature of PV module,C

Vdiode voltage loss of the blocking diode, V

VE MPP voltage of the PV module for a given

SE, V

Vload battery bank voltage (load voltage), V

Vmax output voltage of PV module at

maximum-power point, V

Vmp most probable value of Vmax, V

VnMPPO nMPPO operating voltage, V

Voﬀ energy management system: load-oﬀ

volt-age, V

Von energy management system: load-on

volt-age, V

Vover energy management system: overcharge

voltage, V

Vpv output voltage of PV module, V

Vrecover energy management system: system recovery

voltage, V

Vset design voltage of PV system with nMPPO, V

VT thermal voltage of diode, V

g0_nMPPO daily nMPPO efficiency defined in Eq.(11) gnMPPO total nMPPO efficiency defined in Eq.(5)

go long-term nMPPO eﬃciency deﬁned in Eq.

(3)

and voltage of PV module at a reference temperature To

(45C). The coeﬃcients a, b and K are determined experimentally and listed in Table 1. The performance curves of PV module can thus be calculated for any gi-ven PV temperature Tpv and solar radiation intensity

S, using Eqs.(1) and (2).

2.2. Performance of a PV module at maximum-power point

Fig. 2and the performance equations, Eqs. (1) and (2), imply that, for a given solar radiation intensity (S) incident upon the PV module and module temperature MSX-60 Tpv = 45ºC 3.5 S=750 W/m2 3 700 650 600 2.5 550 500 450 2 Ipv (A) 1.5 300 1 ₂₀₀ 0.5 150 0 10 12 14 16 18 20 0 2 4 6 8 Vpv(V)

Fig. 1. I–V curves of MSX60.

MSX-60 40 Tpv = 45ºC S=750 W/m2 700 35 650 600 30 550 25 500 Ppv (W) 20 450 300 15 200 10 150 5 MPP locus 0 4 12 16 18 20 0 2 6 8 10 14 Vpv (V) Fig. 2. P–V curve of MSX60.

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Tpv, there exists an output voltage of the PV module,

de-noted Vmax, at which the PV output power is maximum

Pmax. Using Eqs.(1) and (2), we can calculate the

varia-tion of Vmaxand Pmaxwith S and Tpvand draw the

re-sults inFigs. 4 and 5.

2.3. Statistical analysis of local meteorological data An analysis can be carried out to determine the total power generation at various PV output voltage for an

nMPPO. Before doing so, we analyze the occurrence fre-quency of S using local meteorological data. The top of Fig. 6is the occurrence frequency of S in Tainan area (southern part of Taiwan) that is based on 15,096 data points of hourly solar radiation intensity from January 1, 1980 to December 31, 1983. The hourly data S has been converted to the value corresponding to solar radi-ation incident upon a tilted surface of 25 that is the best installation angle for that area. The statistics used a dis-crete value of S with 10 W/m2increment. Similar calcu-lation was also carried out for Taipei (north part of Taiwan) using 6809 hourly data points for S > 0 from August 1, 1999 to September 30, 2001, provided by Cen-tral Weather Bureau, Taiwan. The results are shown in the bottom ofFig. 6. It is seen that the weather is quite diﬀerent in these two areas. Tainan is located at latitude Blocking diode + IPV ILoad Vdiode IVset PV array + Load VPV Vset Battery -- _V PV VMPP = Vset + Vdiod

Fig. 3. Schematic diagram of nMPPO Vsetdesign.

Table 1

Temperature coeﬃcients in Eq.(2)for MSX60 PV module

a(A/C) b(V/C) K (X/C) 2.24 · 103 _{5.51 · 10}2 _6.01_{· 10}3 0 100 200 300 400 500 600 700 800 900 1000 10 11 12 13 14 15 16

Solar radiation intensity, S (W/m2) Vmax (volt) T_pv= 25ºC T_pv= 35ºC T_pv= 45ºC T_pv= 55ºC T_pv= 65ºC T_pv= 75ºC

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22.5 that is in tropical region, while Taipei is located at latitude of 25 that is in subtropical region.

2.4. Design analysis of a PV system with nMPPO based on local meteorological data

The output voltage of a PV module at maximum-power point, Vmax, is the desired operating point of a

PV system. The design concept of nMPPO (Fig. 3) is to ﬁx the output voltage of PV module at a value near Vmax that can generate a maximum power. However,

the output voltage of a PV module at maximum-power point, Vmax, varies with S. A statistical analysis is thus

necessary in order to determine an optimum Vsetthat

can generate maximum power. Three design methods are employed: (1) based on a Vmaxat maximum

obtain-able energy, (2) based on the most probobtain-able Vmax, and

(3) by direct searching Vset.

2.4.1. nMPPO design based on Vmaxat maximum

obtainable energy

Fig. 6 indicates that the distribution of occurrence frequency Ns of S varies at diﬀerent locations. Using

Figs. 5 and 6, we can calculate the accumulated power generation Ea(S) using Eq.(3)from a PV module

oper-ated at a given solar radiation intensity S and at a cor-responding maximum-power point (MPP), over certain period of time with hourly-mean meteorological data.

EaðSÞ ¼ PmaxðSÞ Ns 1 h; ð3Þ

where Ea(S) is the accumulated power generation at S;

Pmax(S) is the MPP power generation of PV module at

S, according to Fig. 5; Nsis the occurrence frequency

of S.

The integral of the Eacurve over S is the maximum

total power generated by the PV module over certain period of time. That is,

Etot¼

Z 1 0

EaðSÞ dS; ð4Þ

Pmax(S) as well as Ea(S) represents the power output of a

PV module in use with an ideal MPPT device. Hence, Etotcan be treated as the baseline for nMPPO to

com-pare the performance. The tracking behavior of an ideal MPPT makes the PV module operate at the maximum-power point all the time. In an nMPPO, a ﬁxed operat-ing voltage is used. Thus, an optimal voltage has to be determined.

If the voltage of the nMPPO is ﬁxed at Vset, we can

define the total nMPPO efficiency for the specific dura-tion as the ratio of actual accumulated power generadura-tion to the power generation operating at MPP all the time, in discrete form: gnMPPO P1 i¼1½PVpvðSiÞ IpvðSiÞ Vdiode 1 h P1 i¼1EaðSiÞ ð5Þ or define the nMPPO loss as

enMPPO 1 gnMPPO; ð6Þ 0 100 200 300 400 500 600 700 800 900 1000 0 5 10 15 20 25 30 35 40 45 50 55 Pmax (Watt) T_pv= 25ºC T_pv= 35ºC T_pv= 45ºC T_pv= 55ºC T_pv= 65ºC T_pv= 75ºC

Solar radiation intensity, S (W/m2) Fig. 5. Variation of Pmaxwith solar radiation intensity S.

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where

Vpv¼ Vsetþ Vdiode; ð7Þ

Ipv¼ Isetþ Iload; ð8Þ

where PVpvðSiÞ is the power generation at Siin use with

nMPPO; Vdiodeis the voltage loss of the blocking diode

(Fig. 3); Ipv(Si) is the current through PV module at Vset

and Si.

Fig. 7 shows that, Ea has a maximum value at

S = 640 W/m2in Tainan area and at S = 530 W/m2in Taipei area. The value of S with maximum Eais denoted

as SE. For a given SE, there exists an MPP voltage of the

PV module, VE, according toFig. 5.Table 2lists the

va-lue of VEat diﬀerent SE.

If the voltage Vset of the nMPPO is ﬁxed at

VE, i.e. Vset= VE, we can calculate the nMPPO

eﬃciency according to Eq. (5). It can be seen from Table 2that the nMPPO eﬃciency is around 95% for Vdiode= 0.7 V. This is very close or even better than

that of the actual MPPT since the ideal MPPT is hardly obtained. It is interesting to note that VE at

various Tpv falls in a narrow range (13.2–14.5 V) and

VE are almost identical for Tainan and Taipei areas

at various Tpv.

2.4.2. nMPPO design based on the most probable Vmax

It can be seen fromFigs. 4 and 5that there exists a Vmax as well as Pmaxat a S. Hence, the occurrence

fre-350 Tainan 300 250 200 150 100 50

Total data points: 15,096 0 0 100 200 300 400 500 600 700 800 900 1000 S 180 Taipei 160 140 120 100 80 60 40

Total data points: 6,809 20 0 0 100 200 300 400 500 600 700 800 900 1000 S Ns (times) Ns (times)

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quency or probability function pv of Vmax can be

deﬁned and calculated using Eq.(9)and the meteorolog-ical data: pvðVmaxÞ ¼ NvðVmaxÞ R1 0 NvðVmaxÞ dVmax ; ð9Þ

where Nvis the number of occurrence of Vmaxat certain

period of time.Fig. 8indicates that the most probable value (Vmp) of Vmaxis 14.2 V in both Tainan and Taipei

areas at Tpv= 45C. The number of occurrence of

9000

T

pv

=

35oC Tainan 8000 7000 45oC 6000 5000

E

a (W -h r) 4000 3000 55oC 2000 1000 640 0 100 200 300 400 500 600 700 800 900 1000 0

S

(W/m2) 3000 Taipei 2500

T

pv

=

35oC

4

5oC 2000

E

a (W -h r) 1500

5

5oC 1000 500 530 0 200 400 500 600

S

(W/m2) 900 1000 100 0 300 700 800

Fig. 7. Accumulated power generation at diﬀerent S.

Table 2

nMPPO eﬃciency at Vset= VE

Tpv(C) SE(W/m 2

) VE(V) gnMPPO(%) enMPPO(%)

Tainan area (Vset= VE)

35 640 14.2 94.42 5.58

45 640 13.7 94.57 5.43

55 640 13.2 94.18 5.82

Taipei area (Vset= VE)

35 530 14.5 94.77 5.23

45 530 13.9 94.78 5.22

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Vmax= 14.2 V in Tainan area is 2951 out of 15,096 total

data points, i.e. the probability of Vmax= 14.2 V is

19.5%.

The nMPPO eﬃciency based on the most probable value (Vmp) of Vmaxis calculated and presented inTable

3. It can be seen from Table 3 that the nMPPO eﬃciency for the speciﬁc duration is around 94% for Vdiode= 0.7 V. This is very close to the result of the

aforementioned ﬁrst design method. It is interesting to note that the values of Vset (=Vmp) at various Tpvare

identical in Tainan and Taipei areas and falls in a nar-row range (13.8–15.0 V).

2.4.3. nMPPO design by direct searching Vset

Another nMPPO design is by a direct searching method to determine the optimal Vset. For a Tpv,

giv-ing a value of Vset, we can calculate the nMPPO

eﬃciency gnMPPOaccording to Eq.(5)using the

meteo-rological data S. An optimum set voltage Vg can thus

be obtained as shown inTable 4. The results listed in

0.20 (14.2, 0.19)

Tainan area

MSX-60

0.18 0.16 0.14 0.12 pv 0.10 0.08 0.06 0.04 0.02 0 11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16 Vmax (V) 0.35

Taipei area

(14.2, 0.28) 0.30 0.25 0.20 pv 0.15 0.1

MSX-60

0.05 0 12 12.5 13 13.5 14 14.5 15 15.5 16 11 11.5 Vmax (V)

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Table 4 show that the nMPPO eﬃciency gnMPPO

for Vset= Vg is around 95% for Vdiode= 0.7 V.

Fig. 9 shows the variation of power generation loss (compared to an ideal MPPT) with Vg. It is

notice-able that Vg at various Tpv falls in a narrow range

(13.5–14.5 V) and are identical in Tainan and Taipei areas.

The analytical results from the above three design methods indicate that nMPPO is feasible and Vsetfalls

in 13.2–15.0 V for MSX60 for a wide range of Tpv.

3. Experimental veriﬁcation of nMPPO using a single PV module

An experiment was carried out in the present study to verify the feasibility of nMPPO. The experimental setup is shown inFig. 10. A Solarex MSX60 (60 Wp) was used as the PV module which is installed at a tilted angle 23 facing south. The above design analysis has shown that Vsetat various Tpvfalls in a narrow range (13.2–15.0 V).

A conventional 12VDC battery is thus adopted as the voltage setup Vsetdevice as well as an energy storage

de-vice for nMPPO. For battery safe operation, the voltage

will vary between 11.5 V and 13.5 V depending upon the state of charge of battery. Thus, Vsetis ﬂoating instead

of a ﬁxed value, due to the battery charge and discharge control. The aforementioned analytical results indicate that Vset will decrease with increasing Tpv. For

Tpv> 45C, the optimum Vset will be less than 14 V

which is very close to the battery performance (11.5– 13.5 V) and the real situation of the experimental PV system as well.

A DC fan was used as the load. The voltage drop of the blocking diode is 0.7 V. The charge and discharge of the battery is controlled by a PC. Solar radiation inten-sity incident upon the PV module surface S is measured by a pyranometer. The output current from PV is mea-sured by a Hall sensor. The voltages of PV module and battery are measured by a data logger (Yokogawa HR3880). The temperature of PV module is measured using T-type thermocouple. The experiment is con-trolled by the PC, including data acquisition, measure-ment, and control. The measurements are taken every 2 s and data are recorded in the PC for further analysis. The purpose of the present experiment is to measure the daily nMPPO eﬃciency gnMPPOaccording to Eq.(5),

which can be written as gnMPPO Pn i¼1½PVpvðSiÞ IpvðSiÞ Vdiode 2 s Pn i¼1PmaxðSiÞ 2 s ; ð10Þ

where the summation can be over a sequence of data in certain period of time; Pmax(Si) is the power output of

the PV module in use with an ideal MPPT device that is calculated using Eqs. (1) and (2) and the measured Siand Tpv.

In order to distinguish the eﬀect of Tpv, the test

re-sults shown in Table 5 are calculated from the data screened from all the instantaneous data at Tpv± 2C.

It is seen that the summation of power generation at var-ious Tpvis very close to the expected ideal power

gener-ation at MPP and the total nMPPO eﬃciency, gnMPPO,

is 93%. This is acceptable since an actual MPP tracking controller will not be perfect in tracking the MPP of the PV module and there are some energy losses in the con-trol circuits and in the imperfect MPPT concon-trol algorithm.

Some errors may exist in the test due to the measument errors and dynamic responses. The temperature re-sponse of the PV module is much slower than the sampling time of the measurement (2 s). The tempera-ture probe used to measure Tpvis mounted on the back

surface of the PV module. A delay eﬀect from the solar cell to the back surface may exist and causes the errors in measuring the power generation PVpv. Another source of

error may result from Eqs.(1) and (2)used for the cal-culation of ideal MPP power generation at given S and Tpv. The formulas are subject to some errors since

they are derived from an outdoor performance test. This could cause error in calculating Pmax(Si). The above

Table 4

Performance of nMPPO based on a Vset(=Vg) obtained from

the direct searching method

Tpv Vg(V) gnMPPO(%) enMPPO(%)

Tainan area (Vset= Vg)

35 14.5 94.68 5.32

45 14.0 94.63 5.37

55 13.5 94.33 5.67

Taipei area (Vset= Vg)

35 14.5 94.77 5.23

45 14.0 94.86 5.14

55 13.5 94.55 5.45

Table 3

Performance of nMPPO based on the most probable Vmax

Tpv(C) Vmp(V) gnMPPO(%) enMPPO(%)

Tainan area (Vset= Vmp)

35 15.0 93.71 6.29

45 14.2 94.26 5.74

55 13.8 93.77 6.23

Taipei area (Vset= Vmp)

35 15.0 94.47 5.33

45 14.2 94.76 5.24

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error sources may lead to the error in the determination of gnMPPO, especially at low solar radiation periods.

Fig. 11is the instantaneous performance of nMPPO at a partly-cloudy day. For further comparison, a single module PV system is tested simultaneously using an-other MSX60 module with a MPPT controller. The lab-oratory-made MPPT controller is designed based on the

step-up algorithm (Salameh and Taylor, 1990). It can be seen that the power generation PVpv of the PV system

with nMPPO is very close to the system with MPPT. The nMPPO keeps the PV output voltage Vpvat a nearly

constant value around 12.7 V as compared to the track-ing behavior in MPPT that has larger variation. The lar-ger deviation of PVpv between nMPPO and MPPT at

x 104

10

Tainan area Tpv= 45oC 31.1%

9

8

nMPPO Power Loss (Watt-hr)

7 20.8% 19.2% 6 17.1% 5 13.6% 4 10.3% _11.4% 3 7.66% 2 _7.01% 5.81% _5.37% 1 13 12 12.5 13.5 14 14.5 15 15.5 16 11.5 11

PV Voltage Set, Vset (V)

3 x 104 Tpv= 45oC 30.89% Taipei area 2.5 21.92% 2

nMPPO Power Loss (Watt-hr)

18.27% 17.96% 1.5 14.72% 11.38% 1 8.42% _10.02% 6.16% 0.5 6.1% 5.14% 0 12 12.5 13 13.5 14 14.5 15 15.5 16 11 11.5

PV Voltage Set, Vset (V)

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high radiation periods (S > 600 W/m2) is caused by the high PV temperature (around 60C). The analytical re-sults shown inTables 2–4indicate that the optimum set voltage Vsetdecreases with increasing PV temperature.

Therefore, the set voltage Vsetat 12 V in the experiment

may be too high at Tpv> 60C and causes a lower

power generation as compared to MPPT. The high PV temperature obtained in the experiment also implies that the cooling of PV module is poor due to low wind speed. Actually, this condition takes place not very often in Taipei area.

At cloudy day, the test result ofFig. 12shows that the power generation of nMPPO is almost identical with that of the MPPT. It is noted that Tpvis mostly kept

be-low 50C. The set voltage Vsetat 12 V in the experiment

is very close to the MPP.Figs. 11 and 12also show that PVpvand Ipvin both systems are always in phase with

so-lar radiation variation S.

4. Long-term field test of nMPPO using 1 kWp PV array For further verification of the nMPPO in real appli-cation, a field test using a 1 kWp PV array was carried

out. Fig. 13shows the hardware conﬁguration of the system. The instruments used are the same as that de-scribed previously. The 1kWp PV array consists of 16 MSX60 modules with 4 modules connected in series and 4 in parallel. The output power of the PV system was connected to a 48 V battery bank through a block-ing diode. The nMPPO operation can thus be achieved via the designed battery bank voltage. To consume the power generated from the PV array when the battery is fully charged, an 800 W-load is connected in parallel to the battery. This 800 W load is made of electric light bulbs for lighting.

The battery bank voltage was automatically regu-lated by the charge and discharge control using an en-ergy management system based on PC. According to Table 4, the optimum Vsetwill be 13.5 V at Tpv= 55C

for a single PV module. For this ﬁeld test with 4 PV modules connected in series, Vset will be 54 V. Here,

the battery voltage Vload includes the voltage drop of

the blocking diode, 2 V, in the PV array, i.e. Vload= Vdiode+ VnMPPO. The energy management

sys-tem is designed to switch oﬀ the 800W-load for protect-ing the battery bank from over dischargprotect-ing when the battery bank voltage Vloaddrops to Voﬀ= 46 V, which

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is the low-charge condition for the battery bank. The control system switches on the 800W-load when the battery bank voltage Vload reaches Von= 52 V. When

the battery bank voltage rises to over-charging voltage Vover= 57.6 V, the energy management system will

temporally cut oﬀ the PV connection from system to protect the battery bank from over-charging. Until the battery bank voltage drop to recover voltage Vrecover= 56 V, the energy management system will

reconnect PV array to the battery bank. That is, during the test, each PV module will operate at a narrow volt-age range (about 12–14 V) that is around the MPP of the PV module. This also coincides with the analytical results of nMPPO.

The ﬁeld test was monitored by a data acquisition system. The output current and voltage of the PV

array, solar incident radiation, ambient temperature, PV temperature etc. are measured every 10 seconds and the time-average values are recorded every 10 min. The daily total power generation from PV array EnMPPO was then calculated. For comparison,

the expected daily PV power generation at MPP (EMPP) is deﬁned as the accumulated MPP power

gen-eration if the PV is running at the MPP exactly. EMPP

is calculated using the performance equations of MSX60, Eqs.(1) and (2), and the measured PV tem-perature (Tpv) and solar radiation intensity (S) in a

day. EMPP is thus an ideal power generation at

MPP. The daily eﬃciency of nMPPO gnMPPO is then

deﬁned as the ratio of the daily total power generation using nMPPO and the ideal power generation at MPP, according to Eq.(5), which can be written as Table 5

nMPPO test results screened for diﬀerent Tpv

Date Summation of PV power generation (J) Summation of power input to battery (J) Expected PV MPP power generation (J) nMPPO eﬃciency gnMPPO(%) Tpv= 55 ± 2C 1/18 34751.5 32592.4 34427.7 94 1/19 34005.7 31902.5 33714.8 94 1/21 1183.8 1125.4 1100.9 100 1/22 4186.5 3978.3 3799.3 100 1/24 8066.0 7645.3 7605.9 100 1/31 171039.8 159828.8 165118.7 96 2/06 92631.8 86469.0 88569.6 97 2/09 103889.3 96810.0 99043.3 97 2/15 233349.5 217680.6 245887.7 88 Total 683,104 638,032 679,268 93.9 Tpv= 35 ± 2C 12/10 3433.4 3220.9 3327.5 96 12/16 8696.1 8145.2 9212.7 88 12/18 9807.8 9168.9 10546.6 86 12/22 15157.2 14167.6 15682.6 90 1/16 51409.8 48235.9 49181.9 98 1/18 39271.7 37192.1 36753.2 100 1/19 78031.6 74067.4 79570.0 93 1/20 71063.8 67544.9 71964.7 93 1/21 73965.3 70296.9 75522.4 93 1/22 71363.9 67806.8 73369.6 92 1/24 66035.8 62770.7 70731.9 88 1/30 6744.5 6276.5 6461.6 97 1/31 4893.4 4586.8 4817.0 95 2/06 55727.2 52417.2 57016.7 91 2/08 55895.7 52566.8 57175.6 91 2/09 66893.0 62520.6 67270.9 92 2/10 5378.4 5031.0 5246.6 95 2/11 7845.8 7261.8 7408.3 98 2/15 54592.3 51377.7 56085.7 91 Total 683,104 704,656 757,346 93.0

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0 20 40 60 80 100 120 140 160 180 200 0 200 400 600 800 S (W/m 2) 2001/05/21 (Taipei) 0 20 40 60 80 100 120 140 160 180 200 20 40 60 80 Tpv ( o C) 0 20 40 60 80 100 120 140 160 180 200 10 12 14 16 18 Vpv (V) Time (min) nMPPO MPPT nMPPO MPPT 0 20 40 60 80 100 120 140 160 180 200 0 1 2 3 4 Ipv (A) 0 20 40 60 80 100 120 140 160 180 200 0 10 20 30 40 0 20 40 60 80 100 120 140 160 180 200 0 10 20 30 Pbat (W) Time (min) nMPPO MPPT nMPPO MPPT MPPT nMPPO P Vpv (W)

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gnMPPO

Pn

i¼1½VpvðSiÞ Vdiode IpvðSiÞ 10 min

Pn

i¼1PmaxðSiÞ 10 min

¼ Pn

i¼1VBattðiÞ IpvðSiÞ 10 min

Pn

i¼1PmaxðSiÞ 10 min

¼EnMPPO EMPP

; ð11Þ Table 6shows a list of ﬁeld test data. As we can see, EnMPPO is very close to EMPP, and Tpv varied from

24C to over 70 C, due to the variation of incident solar radiation and ambient temperature. The operat-ing voltage of the nMPPO varied in an acceptable

range, which is affected by the energy management system and balance of energy flow.Fig. 14shows that the daily nMPPO efficiency, gnMPPO, is higher than

90% for most of the test days.Fig. 15is the compari-son of EnMPPOand EMPPT at various daily total solar

irradiance.

The total nMPPO eﬃciency, go, for the long-term

performance is deﬁned as go¼ P EnMPPO P EMPP . ð12Þ 0 50 100 150 200 250 300 30 40 50 60 Tpv ( o C) 0 50 100 150 200 250 300 0 200 400 600 800 S (W/m 2) 2001/05/17 (Taipei) MPPT nMPPO Time (min) 0 50 100 150 200 250 300 0 20 40 P Vpv (W) 0 50 100 150 200 250 300 0 1 2 3 Ipv (A) 0 50 100 150 200 250 300 10 12 14 16 18 Vpv (V) MPPT Time (min) MPPT nMPPO nMPPO nMPPO MPPT

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The ﬁeld test starts from September 25, 2003 to July 12, 2004. The test results are summarized inTable 7. It indi-cates that the long-term total nMPPO eﬃciency go is

over 99% as compared to the same PV array in use with an ideal MPPT at the same weather conditions. Some data inTable 6andFig. 15show that the power output of nMPPO is slightly higher than that of the ideal MPPT. This is due to errors in measurement and in cal-culating the power output at MPP using Eqs.(1) and (2) with the measured data.

An actual MPP tracking controller conventionally available will not be perfect in tracking the MPP of the PV array since there are some energy losses due to the control circuits (hardware) and the imperfect con-troller algorithm (software). The present nMPPO reveals superior to the conventional MPPT control of the PV array since nMPPO can generate power very near the MPP of the PV array.

5. Discussions and conclusion

The present study proposes a sequence of procedure to verify the feasibility of nMPPO for local meteorology and chosen PV module and to choose optimal operating voltage range. We can implement the nMPPO by choos-ing battery bank very carefully with proper blockchoos-ing diode, and operating the system with an energy manage-ment system. The operating voltage of nMPPO will ﬂoat in a desired working range near MPP, even if PV tem-perature (Tpv) varied with incident solar radiation (S)

and ambient temperature.

The design of nMPPO that eliminates the power electronic hardware as used in MPPT has been veriﬁed analytically and experimentally in Taiwan area. Three design methods are proposed in the present study in

order to determine an optimal Vset: (1) based on a

Vmax at maximum obtainable energy, (2) based on

the most probable Vmax, and (3) by direct searching

Vset. The analytical results from three design

meth-ods show that nMPPO is feasible and Vset falls in a

narrow range 13.2–15.0 V for MSX60 for a wide range of Tpv. Both analytical and experimental results show

that the eﬃciency of nMPPO is very close to that of MPPT.

The test results for a single PV module (60 Wp) indi-cate that the total nMPPO eﬃciency gnMPPO is higher

than 93% at various Tpv. This is acceptable since an

ac-tual MPPT controller will not be perfect in tracking the MPP of the PV array and there are some energy losses in the control circuits and in the imperfect MPPT control algorithm.

The long-term ﬁeld test of 1 kWp PV array using nMPPO shows that the total nMPPO eﬃciency gnMPPO

is over 99% at various weather condition and Tpvin

Tai-pei area. As can be noticed fromTable 6, during the test period, Tpvvaried from 24C to over 70 C, due to the

variation of incident solar radiation and ambient temperature.

The energy losses of an nMPPO include the blocking diode loss and the mismatch of MPP of the PV module. The energy loss will depend on the weather conditions, including variations of solar radiation intensity and wind speed etc. The analytical results from a simulation using local meteorological data have shown that the long-term performance of nMPPO can be very close to that of MPPT. The nMPPO eﬃciency is higher than 94% if the battery voltage Vset is properly designed.

The design procedure of an nMPPO system is not very complicated. The performance curve of the PV module can be provided directly from the manufac-turer. This can simplify the design process a great deal.

Data logger _PC 1kWp PV system VLoad ILoad Relay InMPPO 800W Load 48V Battery VnMPPO

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Long-term ﬁeld test results of 1 Wp PV array with nMPPO

Test date nMPPO performance nMPPO operating condition

Total incident radiation, Etotal(MJ/m2) Expected daily ideal PV power generation at MPP, EMPP (kW h) Measured daily PV power generation with nMPPO, EnMPPO(kW h) PV daily eﬃciency EnMPPO/ Etotal(%) nMPPO daily eﬃciency EnMPPO/ EMPP(%) Average diode (V) Maximum Vpv(V) Minimum Vpv(V) Average Vpv(V) Maximum Tpv(C) Minimum Tpv(C) Average Tpv(C) 2003/09/25 16.38 3.41 3.37 9.16 98.9 1.83 60.1 49.5 54.3 65.5 26.0 49.7 2003/09/26 4.83 1.17 1.02 9.10 87.8 1.57 53.5 50.2 52.4 42.6 26.1 32.6 2003/09/27 9.21 2.09 1.86 8.82 89.1 1.77 53.5 47.7 50.8 53.6 26.9 40.8 2003/09/28 22.71 4.55 4.75 9.37 104.4 1.70 55.1 49.8 53.0 69.0 24.1 53.7 2003/09/29 22.00 4.45 4.59 9.35 103.1 1.74 55.4 50.2 53.1 68.0 25.4 53.2 2003/09/30 22.50 4.50 4.66 9.28 103.4 1.78 55.5 50.1 53.2 69.0 24.8 54.8 2003/10/01 17.67 3.66 3.53 8.95 96.4 1.72 53.8 48.2 51.5 72.3 24.4 51.6 2003/10/02 19.11 3.97 3.87 9.08 97.6 1.78 54.6 48.3 52.0 68.3 25.9 51.1 2003/10/03 19.26 3.95 3.95 9.21 100.0 1.91 55.3 48.0 52.5 66.9 26.7 51.5 2003/10/04 2.76 0.60 0.57 7.84 95.0 1.96 55.1 48.3 52.4 39.2 24.3 29.0 2003/10/05 13.00 2.89 2.69 9.17 93.0 1.89 53.5 48.4 51.1 60.0 26.9 41.6 2003/10/06 8.16 1.96 1.72 9.29 87.9 2.02 53.5 48.5 51.3 56.3 26.2 34.3 2003/10/07 3.67 0.89 0.77 8.67 86.1 1.98 53.2 49.1 52.0 35.8 25.1 30.1 2003/10/08 8.89 2.00 1.82 8.97 90.6 2.30 56.8 48.9 51.9 59.0 28.8 40.5 2003/10/09 11.31 2.52 2.28 8.87 90.6 2.02 53.8 48.5 51.3 60.4 25.6 43.7 2003/10/10 21.87 4.37 4.53 9.26 103.5 2.20 56.4 49.2 53.7 68.5 26.8 55.8 2003/10/11 17.45 3.44 3.49 8.91 101.5 2.18 56.3 49.2 53.4 69.9 27.6 52.9 2003/10/12 15.48 3.28 3.09 8.93 94.3 2.07 54.4 49.2 52.0 67.9 25.4 49.7 2003/10/13 8.69 1.86 1.76 8.88 94.7 1.86 53.9 48.7 51.7 64.0 28.0 45.8 2003/10/14 2.43 0.53 0.54 8.01 100.8 1.59 53.5 49.3 52.0 30.3 24.4 27.0 2003/10/15 1.83 0.43 0.40 8.21 92.6 1.61 53.3 49.0 52.5 29.2 22.5 25.2 2003/10/16 11.72 2.81 2.40 9.07 85.2 2.12 59.0 47.9 51.4 45.8 22.3 36.9 2003/10/17 17.51 3.72 3.63 9.26 97.6 1.89 56.4 47.8 52.7 67.2 21.3 46.0 2003/10/18 17.71 3.83 3.70 9.33 96.6 1.99 54.7 47.5 51.7 60.2 20.5 44.7 2003/10/19 14.04 3.11 2.91 9.22 93.5 1.95 55.8 49.3 52.3 59.6 25.1 43.3 2003/10/20 18.48 3.92 3.77 9.10 96.0 2.11 56.3 48.1 52.4 64.9 22.3 47.0 2003/10/21 17.88 3.82 3.73 9.31 97.5 2.08 57.7 48.7 53.2 60.5 23.8 45.9 2003/10/22 17.55 3.77 3.55 9.02 94.2 2.40 56.1 48.3 52.5 61.8 18.5 46.1 2003/10/23 7.30 1.60 1.50 8.77 93.9 2.03 55.1 48.8 52.3 63.3 19.7 35.5 2003/10/24 20.91 4.31 4.37 9.33 101.2 2.09 59.6 48.6 54.2 65.2 18.2 48.7 2003/10/25 22.63 4.61 4.70 9.30 102.0 2.03 60.5 48.3 54.9 65.6 15.2 50.2 2003/10/26 20.60 4.33 4.31 9.37 99.5 1.95 58.7 48.0 53.3 63.6 18.0 48.7 2003/10/27 17.04 3.56 3.39 8.85 95.1 2.02 55.1 48.3 52.0 66.8 20.4 49.1 2003/10/28 20.32 4.20 4.16 9.16 99.1 2.02 58.0 48.3 53.3 66.1 19.0 50.3 2003/10/29 18.63 3.99 3.74 8.99 93.8 2.72 58.9 47.9 53.9 60.8 24.6 47.9 Total 511.53 108.10 105.12 9.01 97.2 1.97 55.8 48.7 52.5 59.6 23.7 44.4 B.J. Huang et al. / Solar Energy 80 (2006) 1003–1020

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Nevertheless, the design procedure of nMPPO can be further standardized for application in various areas. The nMPPO is a reliable and economical design that can be adopted in many PV systems. The battery used

in the nMPPO has dual functions, i.e., voltage control and energy storage. For a grid-connected system, the method of nMPPO design is still applicable in the design of PV operating voltage. 0 20 40 60 80 100 120 140 0 5 10 15 20 25

Daily total irradiance, (MJ/m2_day)

Daily nMPPO efficiency (%)

Fig. 14. Daily nMPPO eﬃciency.

0 1 2 3 4 5 6 0 5 10 15 20 25

Daily total irradiance, (MJ/m2_day)

PV power generation (KWh/day)

MPPT nMPPO

Fig. 15. Daily power output comparison for nMPPO and MPPT.

Table 7

Long-term ﬁeld test results of 1 kWp PV array with nMPPO (2003/9/25–2004/7/12) Total incident solar

radiation (MJ/m2₎

Total power generation with ideal MPPT (kW h)