Predicting islanding operation of grid connected PV inverters

G.A.Smith, l?A.Onions and D.G. Infield

Abstract: Increasing numbers of photovoltaic arrays are being connected to the power utility through power electronic inverters. Ths has raised potential problems of network protection. If, due to the action of the inverter or inverters, the local network voltage and frequency remain within regulatory limits when the utility is disconnected, then islanding is said to occur. Many methods to prevent this have been proposed and a SPICE-based model and analysis of the system are presented, specifically aimed at predicting the effectiveness of two of these. These are: active frequency drift, which causes the inverter current to be generated slightly lower or higher in frequency than the frequency of the terminal voltage, and slip mode frequency shift, which controls the phase angle of the inverter current as a function of the frequency deviation of the terminal voltage from that of the normal network frequency. Experimental verification of the model is provided. Active frequency drift using frequency speed-up rather than speed-down is shown to be preferable for inductive loads, but conditions that resulted in islanding could be predicted. Slip mode frequency shift proved to be a more robust anti- islanding protection technique.

1 introduction

The installation of photovoltaic (PV) arrays connected to the utility through power electronic inverters has raised concern about safety and protection should islanding occur. Islanding refers to the situation where local embed- ded generators continue to maintain the local network volt- age and frequency within regulatory limits after disconnection of the power utility. Islanding is undesirable because it poses a safety hazard to utility service personnel and can lead to asynchronous reclosure which can damage equipment. The low power rating and cost of PV inverters has prompted the development of electronic techniques to prevent islanding. Many of these techniques have been fully described and analysed by a number of authors [IH]. This paper addresses two of the techques.

I. I Active frequency drift (AFD) Inverters that use this technique output current to the util- ity at a frequency slightly lower or lugher than the temiinal frequency. The inverter uses circuits to detect the zero crossing of the network voltage, computes its frequency and introduces a small increaseldecrease in the frequency of the output current. This is of no significant consequence during normal operation, when the utility is connected as the inverter current is reset each cycle of the network volt- age. However, when the utility is disconnected, the terminal voltage sensed is due to the inverter output current and the load impedance, and thus the frequency, should increment upldown to exceed preset shutdown levels.

0 IEE, 2000 IEE Proceedings online no. 20000004 DOI: 10.1049/igepa:20000004 Paper fmt received 8th July and in revised form 21st September 1999 The authors are with the Centre for Renewable Energy Systems Technology, Department of Electronic and Electrid Engineering, Loughborough Univer- sity, Loughborough, LEI 1 3TU, UK

1.2 Slip mode frequency shift (SMS) The slip (or slide) mode frequency shift makes the phase angle between the inverter output current and the terminal voltage a function of the deviation of the terminal fre- quency from nominal. If, for instance, when the utility is disconnected the terminal frequency increases by a small amount, then the phase angle of the inverter current is increased by the power electronics, whch reduces the time to the next zero crossing of the terminal voltage. Ths is interpreted by the inverter controller as a further increase in frequency, so giving a further phase increase, etc. Similarly, a phase reduction is used for frequency deviations below nominal. The technique is said to be operating in an unsta- ble mode and so the terminal frequency will rapidly exceed allowable limits when the inverter will be shut down.

Clearly the effectiveness of such techniques is dependent on the settings of the inverter control functions and on the load impedance on the local network. It is with ths in mind that a SPICE-based model has been developed that will allow these aspects to be investigated, and so to deter- mine whether and why islanding can occur under specified operating conditions. This model will be described and its operation with different loads analysed. Some verification of the model will be presented from experiments with a pro to type inverter.

2 SPICE model

In order to investigate islanding the SPICE model does not need to simulate the high frequency switching behaviour of the inverter. The model is therefore based on representing the inverter simply as a current source whose output can be controlled in phase and frequency with respect to its termi- nal voltage. The basis of the simulation is shown in Fig. 1.

A voltage source representing the grid can be discon- nected at a prescribed time. The load can be any combina- tion of R, C, and L. The inverter is a voltage controlled current source, whose value, without any anti-islanding

I IEE Proc.-Electr. Power Appl., Vol. 147, No. 1. January 2000

1 inverter

E 9 sample- hold I T I continuous

romp t

iae controlled current

zero crossing . v-sin(2rr/T2l(time-T1)

source

-

Fig.

terms, is detemned from the equation

'U = sin(27r/Ta)(time - TI) (1) where T2 is the period of the last cycle, i.e. 1% TI is the time in the simulation at whch each positive zero crossing of the terminal voltage is detected, and time = the total time into the simulation. Thus, each time a positive zero crossing is detected (time - T I ) will be zero and another sin- ewave is started.

Terms can now be included to provide for active fre- quency drift and slip-mode frequency shift.

(2) where f = UT2, Sf = the increase in frequency each cycle, and k2/T2 represents a time equivalent to the phase shift (set by k2) at the current operating frequency. The phase shift k2 can be made a function of the frequency deviation for evaluation of the SMS method. The inverter output current will be given by

(3) where kl is the gain of the current source.

If islanding is to occur, then the terminal voltage must remain within prescribed limits when the utility is discon- nected. Then the inverter current through the load resist- ance, RIO&, should be set to a value to achieve this, i.e. k l . RIO& = rated peak voltage of the network.

'U = sin(27r)(f + s f ) ( t ime - TI + ka/Ta)

i = Icl sin(27r)(f + s f ) ( t ime - TI + Ica/Ta)

2.1 Control function for active frequency drift The active frequency drift technique is based on the inverter running at a constant power factor (usually unity) so the term k2 can be made zero. Thus the control equation will be

'U = sin(27r)(f + bf)(time - TI) (4) In order that the inverter current commences a new sine- wave cycle at the end of a cycle of load voltage, a negative to positive transition of the latter is detected and used to sample a voltage, VR1, ramping linearly at 1.0 V per cycle of the rated network frequencyf,. Thus, TI , the time into the simulation at which this transition occurs, will be given by VRllfr, and so (time - T I ) will be zero and a new sine- wave will start.

The frequency of the new sinewave will be that of the previous cycle plus an increment, Sf; set by the inverter electronics. The frequency of the last cycle, f, is obtained by sampling a voltage, Vm, ramping at the same rate as V,,

but which is reset directly after the sample is taken. Thus, T2 will be given by Vmfp Fig. 2 shows SPICE results for a frequency speed-up rate of 0.5Wcycle operating on a 50Hz system with the utility switched off after 100ms.

LOOVr ut i l i tv voltoae ~~

-1oov oV(VI:+) oV(invcurrentI* 100 v V ( 0 )

I ' , 1- frequency

SEL>> 50 Hzl 1 , ' I

100ms 150ms 200 ms 250ms oV(frequency1 t ime

Fig.2 Activefrequency driji

2.2 Control function for slip mode frequency shift The slip mode frequency shift method starts a new cycle of inverter current on the negative to positive transition of the load voltage. The phase angle of the current is controlled as a function of the deviation of the frequency of the last cycle from the nominal operating frequency of the utility. It is suggested [5] that a sinusoidal function should be used to provide a phase advance for increases in frequency and phase retard for reductions in frequency.

The control equation will be

'U = sin(27r/Tz)(time - T I + k z / T z ) (5) where TI and T2 are found as described earlier.

If a phase shft of 8" is required then k2 = 01360 and divi- sion by T2 gives the time equivalent of this angle at the operating frequency of the last cycle. If the phase shift is to be a sinusoidal function of the deviation of the frequency from the rated frequency of the network, f,, as shown in Fig. 3, then

8 = 8, sin [.(f - fr)/2(fm - f r ) ] (6) wheref, is the frequency at which the maximum phase shift 19, occurs.

leod

Fig. 3 SI@ mode smusoidalfrequency shift

When the utility is disconnected, operation will move through the unstable region shown in Fig. 3 towards a sta- ble operating point, where the load phase angle matches the phase shift of the inverter. Provided the unstable region includes the inverter frequency trip levels then islanding will not occur.

The model was used to represent a resistive load case, load 2 in Fig. 3, operating on a 50Hz network with 0, set at 10" and v, -f,> = 3Hz. The results are shown in Fig. 4

IEE Proc.-Electr. Power Appl., Vol. 147, No. I , January 2000 L

in which the utility was disconnected after 120ms. The phase shift of the inverter current reaches 10" at a fre- quency of 47Hz after a further 240ms and arrives at a steady state of 0" and 44Hz as is expected from Fig. 3.

phose, deg

-1 ov O V I 0 V(phose)

SEL>> 50Hzz L2 Hz

frequency

160ms200ms 250ms 300ms 350ms Looms 150ms 500ms o V ( frequency) time

Fig.4 Slip moukfreyuency sh$

The complete SPICE circuit is shown in Fig. 5. The crossover detector, based on mono-stables, operates the switches in the sample-hold circuits for T,, T2 when nega- tive to positive transitions of the load terminal voltage are detected.

3 Islanding with active frequency drift

The SPICE model was used to investigate the active fre- quency drift technique with two types of load, single stored energy types, i.e. R-L and R-C loads, and resonant loads.

inverter outDut current

3. I R-L and R-C loads with frequency speed- up/down As an example, an analysis is given for the R-C case. The waveforms relating to circuit operation with this type of load are shown in Fig. 6 for a frequency speed-up mode of operation. After the utllity has been disconnected, the load voltage is in phase with the inverter current and the preset speed-up rate would increase the next cycle of inverter cur- rent to coincide with A. If, however, the load includes capacitance, then the terminal voltage will lag the inverter current and the effective speed-up rate would be less than the set value giving a frequency coinciding with B. In order to study the effectiveness of the speed-up circuit the loads chosen must ensure that the load voltage remains within specification. If, for example, the operating limits of load voltage are +lo% of rated voltage VR, and the inverter is operating at rated current IR, then

(7) where 14 is the magnitude of the load impedance = Nd(1 + (oCR)~). If R is chosen so that IR.R = VR, then OC VRl I R 5 0.48, SO

c 5 0 . 4 8 I ~ / W v ~ (8) Thus, C can be chosen to ensure the load voltage is within limits when investigating the speed-up technique.

With an RC load the terminal voltage leads the inverter current by a phase angle q3 c OCR that can be related to an equivalent frequency change, Sf; based on 50Hz. Thus the effective frequency speed-up wdl be less than the inverter set rate of Si, i.e. SAa = S i - Sf As the frequency

1 crossover detector

I *O

frequency 2.36 t sin ((6.283 tV(A1)) t ( l ime-V(A2) r 0.02)) A3

inver ter output act ive frequency dr i f t

current source 50 /V(A3)

G1

I I select mode

- IOUS I I I sl ide mode frequency

sh i f t ( 1

Fig. 5 SPICE circuit

IEE Proc.-Elecfr. Poner Appl., Vol. 147, No. I , January 2000 3

increases, so the phase angle increases and the effective speed-up rate decreases. Fig. 7 shows a SPICE result for a resistive capacitive load meeting the requirements of eqns. 7 and 8 with the speed-up rate of the inverter set at OAHdcycle. Note that the resulting speed-up increments are less than the set value and get increasingly smaller as the frequency increases, and may well reach zero before in- built trip limits are reached, i.e. islanding will occur. Simi- larly, for R-L loads the effective frequency will be increased, i.e. 6jern = Sfi + 6f; which will aid the speed-up process and improve protection. The converse will be true if speed-down is used with inductive loads reducing the speed down rate. So speed-up is the preferred operating mode as most loads are inductive.

V

presetspeed -up ?>capacitive load

I capactive load

I resistive Load preset speed-up

inverter j current

I t , I /J"i voLtoge

: I

1 : :

Fig. 6 Voltage und current wavefimsjbr R cmd R C loah

L9.9Hzl I

Os 0.2s 0.4s 0.6s 0.8s 1.0s 1.2s l.Ls 0 V(frequency1 t ime

Resirtivexapucitive load with speed-up Fig. 7

3.2 Resonant loads with frequency speed-up/ down The circuit waveforms for a resonant RLC load are shown in Fig. 8. At B in Fig. 8 the net current is zero, so

i R + i L + i c = 0 (9) If the load voltage has a peak value Vp then

wL, and substitution gives iR = 4 Vp sin6)/R, ic = wC. Vp cos6 and iL = 4 V p cos@/

t a n 0 = R(wC - l / w L )

The time equivalent to 6, i.e. 6t, is 6t = 6/2$, so

27rfbt = tan-'(R(wC - l / w L ) )

(10)

(11)

l i

I ' *gk-

B A Fig.8 Voltage und current wcrveformsfor on RLC load

Islanding will occur when 6t is the same as that set by the inverter speed-up circuits. Let 6f be the change in frequency per second set by the speed-up circuit in the inverter. Based on the rated frequency of the network, J;., the increment in frequency per cycle, sf,, will be 6Jji.. So

6t = l / f - l / ( f + S f c ) (12) Substituting into eqn. 11 gives

27rbfc / ( f+Sfc) = tan- '(R(2rfC- 1/257fL)) (13) which, for small angles, can be approximated to

27rSfc/(f + S f c ) = ( R ( 2 T f C - 1/2.irfL))

f 3 + S f c - (f," + b f C / R C ) f - Sfcf," = 0

(14) Solving for f and replacing 1/2dLC by,Jb, the resonant fre- quency, gives

(15) Neglecting the second and fourth terms, islanding will occur when the frequency is given by

f ( 2 s l a n d i n g ) (f," + 6fc/RC)1'2 (16) SPICE results were taken for R = 14452 corresponding

to the rated power of a 400W inverter operating at 240V, with C = 5pF and L chosen to givefo values close to the rated frequency of the network, A., of 50Hz. The SPICE results are given in Fig. 9 and can be compared with the calculated results in Table 1.

60- 58 56

- -

I" 5 L - 5 5 2 - f 50- g L a - - L 6 - L

LL -

cose 5 1 cose 3

0 0.1 0.2 0.3 0.L 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.L 1.5 time,s

Fig.9 SPICE resultsfor Tdle 1

Note that a load with a resonant frequency f o > ,f, is net inductive at f,, i.e. cases 3 and 4. A frequency shift up, case 3, will cause an over-frequency trip to occur sooner than for a resistive load, case 5. However, a frequency shift down, case 1, could result in islanding. Again, with loads

IEE Proc.-Electr. Power Appl. . Vol. 147, No. I , Juiiuury 2000 4

generally inductive the frequency shift-up technique appears to be best. The predicted and SPICE modelled results agree well, giving confidence to the use of the model with any form of complex load.

Table 1: Results for the active frequency drift technique

0.93

1 46 +20 +0.4 51.7 51.2 2 46 -20 -0.4 39.5 40 3 54 +20 +0.4 58.9 58.4 4 54 -20 -0.4 48.6 49 5 - +20 +0.4 Resistive load only

6 - -20 -0.4 Resistive load only

4

The slip mode frequency shift technique was studied for the loads in Table 1 using a sinusoidal control function as shown in eqn. 6, with O,,, set at 10" and V;, -5) set at 3Hz. The results for the resistive load case have already been shown in Fig. 4 where steady state operation occurs, as would be expected, at 44Hz and zero phase shft. An alter- native steady state point would have been at 56Hz.

Case 1 in Table 1 corresponds to a net capacitive load at J;, which, from Fig. 3, should cause the inverter frequency to fall towards a stable operating point. The SPICE results in Fig. 10 clearly show operation through 47Hz and lo" shift to a steady state at 44Hz and -0.9" shift, and the inverter frequency trips would have operated to prevent islanding. Note that with a positive Sf the active frequency drift mode of operation resulted in islanding at a frequency near to f , .

-lov OV; phose,deg

Islanding with slip mode frequency shift

oV( phose

frequency

switched off ot 120mS

-100ms 150ms 200ms 250ms 300ms 350ms LOOms oV (frequency) t ime

Fig. 10 Slip tnocikjrquency SA$ - cme 1. Tubk 1

frequency SEL>> 50Hz, I

100ms 150ms 200ms 250ms 300ms 350ms L00ms o V (frequency) time

Fig. 1 1 Slip nzodefiepency sh$ - case 3, Tuble I

Similarly, the net inductive load of case 3 caused the inverter frequency to increase, resulting in steady state

IEE ProcElectr. Poivw Appl., Vol. 147, No. I . January 2000

operation at 55.8Hz and +0.93" shift, as suggested in Fig. 3 and shown in Fig. 11. The effect of choosing a smaller value for e,, i.e. 2", is to reduce the rate at which the fre- quency changes and to reduce the steady state frequency, provided there is still an intersection of the load line and the control function on the second quadrant of the sine- wave. The results are given in Fig. 12 and can be compared with those of Fig. 11. The slip mode frequency shift method seems to be particularly effective, with no cases of islanding being observed.

" O V I 0.71

OVI r' * oV (phose

55 ..

frequency

50Hz 100ms 200ms 300ms LOOms 500ms 600ms 700ms

0 V(frequency1 time

Fig. 12 Slip mode frequency SI@ - cme 3, reduced gain

5 Experimental results

A prototype inverter was available operating with active frequency drift. Ths was operated with a load resistance that gave rated terminal voltage at rated current. Thus, the terminal voltage would remain withm specification when the utility supply was disconnected. Operating on a supply of 50Hz with a frequency ramp-up rate of SHds, the inverter tripped out at 52Hz after 250ms. However, when additional parallel L and C loads were added to givefo val- ues close to 50Hz, islanding was observed as shown in Figs. 13 and 14. Table 2 shows the comparison between islanding frequencies predicted by theory and those obtained experimentally. The results are in close agreement, despite the difficulty in determining precise values for all the load elements.

52r

L81 0 5 10 15 20 25 30 35 LO

time,s Fi . I 3 Experimental results for active frequency drij with RLC load ( fo = 483"z)

52

2- .5- 511 _. "

.... LEI I

0 5 10 15 20 25 30 35 LO t ime ,s

Fi .I4 Experimental results for active frequency drift with RLC load (& = 47%r.,,

5

Table 2: Experimental results (AFD)

case fo, H~ af ~d~ hislanding) F(islanding)

Fig. 8 48.9 8 49.1 e 50.5

calculated experimental

Fig.9 47.9 8 48.0 = 49.5

6 Conclusions

A SPICE model has been developed that will allow the effectiveness of anti-islanding techniques to be assessed for PV inverters connected to a power utility. Two protection techniques have been studied - active frequency drift and slip mode frequency shlft. The former increments the inverter frequency and the latter introduces a phase shift. Both techniques have been well reported. Analysis has shown that there are load situations that will result in islanding if the active frequency drift techtuque is used. However, these may fall outside what may be considered practically realisable. Nevertheless, it has been shown that for lagging kVAr loads, the frequency increase rather than decrease mode of operation is to be preferred. The SPICE model based on representing the inverter as a simple con-

trollable current source has given results that agree with analysis. The slip mode frequency shift method appears to be the most reliable as islanding did not seem to be possible for any load situation. Although the SPICE model was only used to investigate the above two techniques it is easily adaptable to other control and anti-islanding strategies.

References

ROPP, M.E., BEGOVIC, M., and ROHATGI, A.: ‘Prevention of islanding in grid connected photovoltaic systems’, Prog. Photovolt., Res. Appl.. 1999, 7, (I), pp. 39-59 JONES, R.A., SIMS, T.R., and IMECE, A.F.: ‘Investigation of potential islanding of a selfcommutated static power converter in pho- tovoltaic systems’, IEEE Trans. Energy Convers., 1990, 5, (4), pp. 6 2 4 63 1 VACHTSEVANOS, G., and KANG, H.: ‘Simulation studies of islanded behaviour of gridconnected photovoltaic systems’, ZEEE Tram. Energy Convers., 1989, 4, (2), pp. 177-183 RANADE, S.J., PRASAD, N.R., OMICK, S., and KAZDA, L.F.: A study of islanding in utility connected residential photovoltaic sys- tems, part 1: models and analytic methods’, ZEEE Trans. Energy Con- vers., 1989, 4, (3), pp. 4 3 W 5 YWUMA, S., ICHINOSE, T., KIMOTO, K., ITAMI, T.,

HARA, S., IOKA, S., and KUNIYOSHI, M.: ‘A high speed fre- quency shift method as a protection for islanding phenomena of utility interactive PV systems’, Sol. Energy Mater. Sol. Cells, 1994, 35, (14), pp. 477486

AMBO,T., OKADO,C., NAKAJIMA, K., HOJO, S., SHINO-

6 IEE Proc-Electr. Power Appl., Vol. 147, No. 1, January 2000