Novel grid-connected photovoltaic inverter

S.Saha V.P.Sundarsingh

Indexing terms: Solar photovoltaic, Inverter, Utility interface, Energy conversion

Abstract: Detailed analysis and simulation results of a novel solar photovoltaic inverter configuration interconnected to the grid are presented. From the simulation results it is confirmed that the harmonic distortion of the output current waveform of the inverter fed to the grid is within the stipulated limits laid down by the utility companies. Typical hardware aspects are also discussed in detail and the applicability of the design is verified.

List of symbols

dt , = incremental OFF period of the transistors dt ON = incremental ON period of the transistors f , = switching frequency or the transistors IO = RMS value of the inverter output current (iL1,oFF)f = final current through the inductor L1 during

the OFF period of the transistors T1 and T2 (iL1,OFF)i = initial current through the inductor L1

during the OFF period of the transistors TI and T2 = final current through the inductor L1 during the ON period of the transistors T1 and T2 = initial current through the inductor L1 during the ON period of the transistors TI and T2

(iL& = instantaneous peak current through the inductor Ll

(iL2)f = final current through the inductor L2 (iL2)i = initial current through the inductor L2 P, (100%) = power transferred to the grid at 100%

insolation P, (50%) = power transferred to the grid at 50% inso-

lation TON = total ON period of the transistors vc = voltage across the capacitor C ( Vc), = instantaneous peak voltage across the

capacitor C v s = solar panel voltage at any instant

1 Introduction

Since the cost of solar cells has not decreased apprecia- bly, it is often said that the photovoltaic plants of small

(i,,,,,)f

(iLl,oN)i

0 IEE, 1996 IEE Proceedings online no. 19960054 Paper first received 8th February 1995 and in final revised form 11th Sep- tember 1995 The authors are with I.I.T. Powai, Bombay 400 076, India

IEE Proc.-Gener. Trunsm. Distrib.. Vol. 143, No. 2, Murch 1996

capacity between 1 and 5kW are suited for remote areas only, far away from the grid. However, these iso- lated stand-alone photovoltaic plants require a battery pack for energy storage thereby increasing the net elec- tricity cost further. Additionally, regular day-to-day maintenance of these batteries presents major problem. On the other hand, a photovoltaic plant with an utility interactive inverter does not need an expensive and inefficient battery storage. As a result, installation of small, individual grid-connected photovoltaic systems between 1 and 2kW, having a solar panel at the roof top, has generated considerable interest in recent years in several countries. In such a system, during the day- time, a residential consumer sells electricity to the util- ity when the output of the photovoltaic plant is greater than the AC power needed by the residential load. Sim- ilarly, at a certain instant, if the solar power output is less than the power taken from the utility, a residential consumer buys the excess energy requirements from the utility. The idea of a single energy meter in a grid-con- nected photovoltaic system (i.e. for buying as well as selling electricity) has a major disadvantage since the cost of generating electrical energy through solar pho- tovoltaics is at least three times greater than any other form of conventional energy. The disadvantage may be overcome by adopting two energy meter systems together with a subsidy, as is the case in many coun- tries. With grid-connected systems, low-rating photo- voltaic plants are becoming increasingly popular. Hence, the effort to develop a low cost, reliable and rugged single phase inverter for this application has gained credibility.

As mentioned in [l], a typical utility interactive pho- tovoltaic inverter has to satisfy a number of design characteristics. These are: (i) The photovoltaic system voltage should not exceed 1OOV. Otherwise, insulation failure may occur and the safety and protection of a person will be in danger. (ii) The current harmonic distortion fed to the grid by the solar photovoltaic utility interactive inverter should not exceed the limit permitted by public utility laws. (iii) Care should be taken to control the radio interfer- ence generated due to high frequency switching of the power devices in the inverter. (iv) The solar photovoltaic plant should be discon- nected from the grid at times of too low an insolation. (v) The inverter should be equipped with a maximum power point tracker to be able to get the maximum power possible from the phoiovoltaic generator at any time. (vi) During a power failure, an isolator should discon- nect the photovoltaic inverter from the grid and con- nect it to an emergency load.

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Such a system is described in [2, 31 for inverters operat- ing at 20kHz. This paper, however, describes another novel grid-connected single phase photovoltaic inverter configuration satisfying all these design considerations.

2 Proposed novel configuration

The schematic diagram or the novel utility interactive solar photovoltaic inverter is shown in Fig. 1. The operation of the inverter consists in transferring the solar energy intermittently to an inductor and then feeding it to the mains so that a sinusoidal mains cur- rent is obtained. In this scheme, both the transistors T1 and T, are either turned ON or OFF simultaneously. When they are turned ON, energy is stored in the Inductor L1 and the current flowing through it ramps up to a finite value as shown in loop I of Fig. 2.

L2

Fig. 1 Novel configuration of grid connected solar photovoltaic inverter

Fig.2 Current loop I when transistors are ON

Fig.3 Current loop 11 when tramistors are OFF

L2

Fig.4 Current Loop III when transistors are OFF as well as ON

The equation for loop I, neglecting collector-emitter saturation voltage VCE(sat) of the transistors, is given by

(1)

(2)

dz - - vs

d t O N

V S

L1 ( i L 1 , O N ) f zr (ZL1,ON)i + -TON

The ON and OFF durations of the transistors TI and T2 should be designed such that the entire energy stored in the inductor Ll during its ON period is com- pletely used during its OFF period. Thus, the current flowing through inductor L1 will be discontinuous and (iLl,oN)l will always be zero at the start of every ON period of the transistors.

lmmediately after the transistors are turned OFF, diodes D1 and D2 start conducting and the capacitor C starts charging up through loop I1 as shown in Fig. 3. The equation for loop 11, negiecting the diode drop, is written as

( 3 )

(4) VC L1 ( i L 1 , O F F ) i = ( i L 1 , O F F ) f - -dtOPF

During this OFF period, loop 111, as shown in Fig. 4, which feeds energy to the mains, will come into action only if V, is greater than V, sin at, where V, sin at is the source voltage. The corresponding loop equation is given by

+V,sinwt-V, = O (5) L2 - d i L 2

d t O F F

OFF (ZL,)~ = ( 2 ~ ~ ) ~ + (V, - V,sinwt)-

L2

During dt,, the change in the capacitor voltage, AVc, is given by

I C

c - C - -d tOFF

In eqn. 7, I, is the capacitor current and is expressed as IC = iL1 - iL2 where iLl and iL2 are the average values of the currents flowing through the inductors L1 and L2, respectively, during the incremental period dt0FF. Thus, the capacitor voltage has to be updated continu- ously for the solution of eqns. 4 and 6. During the OFF period of the transistors, the current through inductor L2 starts increasing, whereas the current flow- ing through inductor L1 starts decreasing since the energy stored in it is used to feed power to the mains as well as to charge capacitor C and inductor L,. At a cer- tain instant, the current flowing through inductor L2 will be greater than that flowing through L1 and capac- itor C starts discharging. The current flowing through the inductor L1 will become zero at that particular time when all the energy in it is used and loop I1 will be out of action. This is again followed by the ON period of the transistors during which time loop I11 will still be in action, feeding back energy to the mains. Now, during the ON period of the transistors, the current through the inductor L2 starts decreasing and is calculated from eqn. 6 where dtoFF is replaced by dtoN. The free- wheeling diode FD of loop I11 will conduct only after the voltage V, across the capacitor C becomes zero. Thus, by solving these equations, the functioning of the inverter can be studied. The above inverter configura- tion does not have an isolation between the mains and the solar cells which is essential for safety and protec- tion. For this, a modified scheme incorporating isola- tion is shown in Fig. 5. To ensure that the current fed back to the mains is a sine current with a specified rip- ple content, simulation of the photovoltaic utility inter- active inverter is carried out by step by step method with the help of eqns. 1-7.

IEE Proc -Gener Transm Distrib , Vol 143, No 2, March 1996 220

3 Simulation result

In the simulation algorithm, emphasis is given to the following control statements during the determination of the ON and OFF periods for the transistors T1 and T2. These are: (i) The energy stored in the inductor L1 during the ON period of the transistors should be fully dissipated in the OFF period. (ii) The current fed back to the mains during the tran- sistor OFF period should rise to a maximum value sat- isfying the condition I , = I,, sin cot and during the transistor ON period, decrease to a minimum value sat- isfying the condition I, = I,, sin at, where Iml is greater than Im2. (iii) The initial and final value of the voltage across the capacitor C after a half cycle should be equal. (iv) The current fed back to the mains should reach zero sufficiently ahead of 10 ms during a half cycle so that the corresponding pair of thyristors conducting during this time can commutate naturally and the next pair of thyristors can take over the conduction process.

Fig. 5 Grid connected solar photovoltaic inverter with isolation

15

- 10

= 5

Q

C I

U

Z o ," - 5

2 -10

3

c L

.-

-I 5 0 0.004 0.008 0.012 0.016 0.020

lime, s Simulated sinusoidal output current waveform of 2kW inverter at Fig.6

maximum insolation

120

Q 100

'- 80

E 5 60

i

C

U L

3 40

.c 20

0

3 U

0 0.002 0.004 0.006 0.008 0.010 time, s

Fig.7 insolution

Current flowing through inductor Ll of 2kWinverter ut muximum

Under these boundary conditions, simulation is car- ried out for a 2kW as well as a 1kW photovoltaic inverter interfaced with the utility. The solar panel volt- age at maximum insolation is taken as 1OOV. The 2kW

IEE Proc -Gener Transm Distvih , Vu1 143, No 2 Murch 1996

photovoltaic inverter interfaced with a single phase utility of 240V should have an output RMS current of 8.33A at maximum insolation The peak value of the output inverter current under this condition is 11.78A. Hence, for a ripple of lA, Iml and Im2 should be 12.28A and 11.28A, respectively. The step width cho- sen for the simulation is l ps. For a 2kW inverter con- figuration, the optimum values obtained for L1, L2 and C obeying all the boundary conditions (i) to (iv) are found to be 0.175mH, 12.5mH and 5pF, respectively.

Table 1: ON and OFF durations of 2kW photovoltaic inverter

no. Transistor Transistor ON period, p OFF period, ps

1 43 322

2

3

4

5 6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

47 155

59 151

71 141

83 133

94 122

105 113

116 106

126 97

135 89

144 83

151 74

158 69

165 66

170 61

174 58

178 57

180 55

182 57

182 57

181 58

180 63

177 66

174 73

169 79

163 86

156 93

149 104

141 116

132 130

121 141

110 156

98 171

86 195

72 219

57 1264

Simulation shows that the switching frequency U,) of the transistors should be 3.6kHz, and the ON and OFF periods of the transistors in a lOms half cycle are listed in Table 1. The switching pattern of the transis- tors gives an unique pulse width modulation which is very near to a sinusoidal PWM. The simulated sinusoi- dal output current waveform of the 2kW inverter at maximum solar insolation is shown in Fig. 6. Fig. 7

22 1

Table 2: Simulation results of 2kW and 1 kW inverters

Max output, Percentage of

kW

2 0.175 12.5 5 36 100 102 560 8.33 lessthan 2%

75 76 470 4.52 lessthan3%

50 51 400 2.05 lessthan4%

1 0.35 25 1.5 34 100 53 750 4.16 lessthan4%

75 40 575 2.26 lessthan5%

50 26 450 0.98 lessthan 6%

L,, mH L,, mH C, pF fs, kHz V,, V (ill),, A (VJ,, V /o, A 3rd, 5th, ..., 15th harmonic

shows that the current flowing through the inductor L1 during a half cycle is discontinuous. The simulated voltage of the capacitor C is plotted in Fig. 8 which shows that the initial and final voltage across it during a half cycle are equal. Keeping the ON and OFF peri- ods of the transistors identical and boundary condi- tions same, simulation is also carried out for the 2kW inverter at lower solar insolation level assuming the solar panel voltage to be 75 and 5QV. Under these con- ditions, parameters such as the instantaneous peak inductor current (i,,),, instantaneous peak capacitor voltage ( VC), and output inverter current Io are calcu- lated and listed in Table 2. Further, for a similar inverter of 1kW all the above mentioned simulated parameters are also listed in Table 2. Simulation results of both the inverters show that the maximum output current of the inverter or the maximum inverter power output decreases by a constant factor with a decrease in the solar insolation. This constant factor is approxi- mately given by (VJVms)2 where V, is the solar panel voltage at any instant and V,, is the maximum solar panel voltage.

z 500 >U

8 400 0 c - 9 300 b g zoo 9

.-

Q

100

n 0 0.002 0.004 0.006 0.008 0.010

time, 5 Voltage across capacitor C of 2 kW inverter at maximm insola- Fig.8

tion

4 Harmonic distortion

A solar photovoltaic inverter connected to the grid should strictly abide by the guidelines laid down by the utility companies in different countries. One such speci- fication is discussed by Duffey and Stratford in [4]. Table 3 specifies the harmonic current limits that a grid connected photovoltaic inverter is allowed to inject into an utility system as discussed in this article. From this Table, it is evident that as the capacity of the photo- voltaic inverter decreases with respect to the size of the power system to which it is connected, larger percent- age of harmonic current can be injected into the utility system. Table 4 lists the quality of voltage that the util- ity must furnish to the consumer. A utility will be able to furnish the voltage as listed in Table 4 provided the

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harmonic currents fed by the numerous photovoltaic inverters, various power electronic equipment and non- linear loads into a distribution feeder are limited in accordance with Table 3. It is to be noted that the volt- age distortion at the point of common coupling (PCC) depends on the highly inductive internal impedance of the AC source and the magnitude of the injected cur- rent harmonics. Thus, it is essential to estimate the har- monic contents generated by the present scheme.

Table 3: Harmonic current limits for nonlinear loads at the point of common coupling (PCC) with other loads at voftages of 2.4 to 69 kV

Maximum harmonic current distortion as percentage of fundamental

Harmonic order (odd harmonics)

IscllL < I 1 11<h<17 17<h<23 23<h<35 35<h THD

0.3 5.0

0.5 8.0

1.5 0.6 <20 20-50 7.0 3.5 2.5 1 .o 50-100 10.0 4.5 4.0 1.5 0.7 12.0

100-1000 12.0 5.5 5.0 2.0 1.0 15.0

>IO00 15.0 7.0 6.0 2.5 1.4 20.0

4.0 2.0

where I , = maximum short circuit current at PCC / l = maximum fundamental frequency load current at PCC THD = total harmonic distortion

For PCCs from 69 to 138kV, the limits are 50% of the limits above. A case-by-case evaluation is required for PCCs of 138kV and above

Table 4: Harmonic voltage limits for power producers (public utilities or cogenerators)

Harmonic voltage distortion as percentage at PCC

2.3-69kV 69-138kV >138kV

Maximum for individual 3.0 1.5 1 .o harmonic

Total harmonic distortion 5.0 2.5 1.5 (THD)

The magnitude of the harmonic distortion in the out- put current of the proposed grid connected solar pho- tovoltaic inverter at various solar insolation levels is determined by the FFT (fast Fourier transform) func- tion defined in Matlab 386 by feeding the current waveform generated by the simulation at 1 ps intervals. This interval is within the requirements of the package. Fig. 9 shows the plot of power spectral density against frequency as generated by the package for the simu- lated output current waveform of the 2kW inverter at the maximum solar insolation. The magnitude of the harmonic distortion of the output current for the 2kW

IEE Proc -Gener Transm Distrib , Vol 143, No 2, March 1996

and 1 kW photovoltaic inverters at various solar insola- tion levels are listed in Table 2. Since the maximum current ripple is specified as 1A for both the inverters in the simulation, the harmonic distortion of the output current is higher for the 1kW solar photovoltaic inverter. This can be reduced by specifying a propor- tionally lesser ripple current as an input parameter dur- ing simulation. From the simulation results it is verified that the harmonic current distortion generated by both the 2kW and 1kW inverters is well within the stipu- lated limits mentioned in the specifications, if the ratio of Zsc/Il is greater than 20. However, reduced ripple content, resulting in lower harmonic current distortion can be obtained for the solar photovoltaic inverters of different kilowatt capacity by suitably altering the val- ues of the inductor L1, L2, and capacitor C. But, this calls for higher switching frequency of the power tran- sistors TI and T2 of the inverter.

0 500 1000 1500 2000 2500 frequency, Hz

Fig.9 inverter at maximum insolation

Power speetral aknsity of oulput current waveform of 2 kW

5 Hardware aspects

For implementing the hardware, a 1 kW solar panel is considered such that its output voltage is lOOV and capable of delivering a current of 10A at the maximum solar insolation. For a 1 kW inverter, it is seen from the simulation result that the instantaneous peak current flowing through inductor L1 is 53A at lOOV and the corresponding maximum ON period of the transistors is 186p. Hence, a capacitor C, is connected across the solar panel to supply this peak current. For a 5% volt- age change at the output of the solar panel throughout

a half cycle, the value of C, is found approximately to be 10 OOOpF.

The schematic hardware diagram is shown in Fig. 10. From this Figure, it is evident that the ON and OFF durations of the transistors during a half cycle are stored in EPROM 2716. EPROM 2716 has 2K x 8 bits. Out of all the available bits, 2000 bits are only accessed in a half cycle. For this, the address lines of the EPROM is connected to the output of a 12-bit binary ripple counter IC 4040. The clock frequency of the 12-bit binary ripple counter should be 200kHz for generating a 50Hz inverter frequency. This clock fre- quency is synchronised with the mains frequency by IC 4046 acting in phase locked loop (PLL) mode. For this, the mains frequency and the clock frequency divided by 4000 are fed to the input pin and the phase comparator pin of IC 4046, respectively. The EPROM is pro- grammed in such a fashion that the output of the data bus Do is high during the ON period of the transistors and low during the OFF period. Synchronisation with the mains frequency is also assured by resetting IC 4040 during the zero crossing of the mains waveform. The output of the EPROM is fed to a driver and then to the base of transistors TI and T2. The zero crossing detector (ZCD) which senses the mains voltage, is also used to fire the appropriate thyristor pairs during every half cycle. However, under fault conditions, a case may arise where the output current of the inverter is not zero at the end of a half cycle. To alleviate this prob- lem, the output current is also sensed and the opposite pair of thyristors are fired only after the output current has reached zero. This is assured by the current condi- tioning unit.

In this scheme, complex control strategies are avoided by simply keeping the ON and OFF period of the transistors constant for all values of insolation. For achieving maximum power tracking, the following strategy can be adopted. To begin with, the ON and OFF durations for the transistors are selected at 50% insolation level for maximum power transfer from the solar panel to the grid. Then at 100% insolation, for transferring the power, the inverter voltage must be increased according to the formula given by

For most of the low cost solar panels, this calls for

~ 240V inverter

, 11 ,rLi$!y base drive of thyristor

Fig. 10

IEE Proc-Gener. Transm. Distrib., Vol. 143, No. 2, March 1996 223

operating the panel beyond the maximum power point, that is, in the drooping region of ZIV characteristics of the solar panel. This obviously results in a loss of use- ful power from the solar panel. After studying the low cost panel characteristics, it is observed than the loss may be in the range of 5 to 10%. Finally, the inverter should be isolated from the utility when the solar panel voltage is less than 50V, since the generation becomes highly distorted.

6 Conclusion

Simulation results and hardware design aspects show the feasibility of the novel photovoltaic inverter con- nected to the utility. Further, adoption of a simple con- trol strategy should make the inverter more reliable. The cost of this inverter will also be relatively low as minimum number of power devices are used to execute this configuration and, optimum component values of L1, L2 and C obtained from simulation result are used. It is also evident from the simulation result, that the

harmonic distortion of the output inverter current waveform at different solar panel voltage levels can be maintained within the specified regulation limits of the utility. All the above advantages have made the inverter configuration highly suitable for grid con- nected photovoltaic application.

References

CRAMER, G., and GREBE, R.: ‘Grid connection of PV plants in the power range from 2 kW to 1 MWp’. Proceedings of the 11 th E.C. photovoltaic solar energy conference, Montreux, Switzer- land, October 1992, pp. 1151-1154 CUK, S., and MIDDLEBROOK, R.D.: ‘High-frequency isolated 4 kW photovoltaic inverter for utility interface’. Power conversion international, May 1984, pp. 2611.8 STEIGERWALD, R.L., FERRARO, A., and TURNBULL, F.G.: ‘Application of power transistors to residential and interme- diate rating photovoltaic array power conditioners’, IEEE Trans. Ind. Appl., 1983, 19, (2), pp. 254-267 DUFFEY, C.K., and STRATFORD, R.P.: ‘Update of harmonic standard IEEE - 519 IEEE recommended practices and require- ments for harmonic control in electric power systems’. IEEEiIAS 35th petroleum and chemical industry conference (PCIC), Dallas, TX, September 1988, pp. 249-255

224 IEE Proc.-Cener. Transm. Distrib., Vol. 143, No. 2, March 1996