Performance Assessment of Islanding Detection for Mul-ti-inverter Grid-connected Photovoltaic Systems

doi:10.4236/epe.2013.54B287

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Energy and Power Engineering, 2013, 5, 1517-1520

doi:10.4236/epe.2013.54B287 Published Online July 2013 (http://www.scirp.org/journal/epe)

Performance Assessment of Islanding Detection for Mul-

ti-inverter Grid-connected Photovoltaic Systems

Xing Zhang, Dong Xie

College of Electric and Automation, Hefei University of Technology, Hefei, China

Email: [email protected], [email protected]

Received 2013

ABSTRACT

Islanding detection is an essential function for safety and reliability in grid-connected Distributed Generation Systems

(DGS). Passive and active islanding detection methods have been analyzed in literature considering DGS with only one

inverter connected to the utility. With the big scale application of photovoltaic (PV) power systems, islanding detection

technology of multi-inverter DGS has been paid more attention. This paper analyzes the performance of diverse island-

ing detection methods in multiple inverters grid-connected PV systems. Non-Detection Zones (NDZ) of multi-inverter

systems in a load parameter space are used as analytical tool. The paper provides guidance for the islanding detection

design in multiple grid-connected inverters.

Keywords: Photovoltaic Power Systems; Islanding Detection; Multi-inverter; Non-Detection Zones

1. Introduction

One problem for photovoltaic (PV) power system is is-

landing effect. When the grid is tripped for breakdown or

overhaul, the PV system remains independent running

status connected with the local load, this kind of phe-

nomenon is called the islanding effect. This phenomenon

will threaten the safety of power maintainer and power

equipment. Therefore, the PV system must have island-

ing detection function to prevent the occurrence of is-

landing effect [1-2].

Two types of islanding detection methods (IDMs), the

passive and active methods, have so far been developed.

Among them, the active methods include Active Fre-

quency Drifting (AFD) method, Active Frequency Drift-

ing with Positive-Feedback (AFDPF) method, Slip-

Mode Frequency Shifting (SMS) method and so on. Now

the researches on IDM are mostly in single-inverter PV

systems. With the development of economy and tech-

nology, multi-inverter PV systems will be used more

extensively. So the researchers have paid more attention

to the IDMs of multi-inverter systems. According to the

analysis of non-detection zones (NDZs) in Qf×f0

frame[3], this paper investigates the performance of

IDMs in multi- inverter PV systems, so as to provide a

reference for the islanding detection design in multiple

grid-connected inverters.

2. Performance Analysis of Idms for Mul-

ti-Inverter Operating in Parallel

2.1. Part of Inverters Adopt Passive IDMs

The inverters in grid-connected PV systems usually use

sinusoidal current control model based on the unit power

factor [4]. So, in multi-inverter systems, the

grid-connected inverters equipped with passive IDMs

can be regard as a negative resistance which transport the

active power to grid, the negative resistance together

with the local load is equivalent to resistance Req, i.e.

 (1)

where R is the local load, k is the proportion of active

power which is output by inverters equipped with passive

IDMs relative to overall active power consumed by the

local load. After the equivalent disposal, Req's quality

factor Qfeq may be represented as:

feq eq

QRC





 (2)

where Qf is the original quality factor of the local load. It

can be shown that Req's quality factor equals to 1/(1-k)

times of Qf . That is to say, if the inverters equipped with

passive IDMs provide 50% active power to local load (k

= 0.5), the equivalent quality factor Qfeq equals to

2Qf .Thus, if the single-inverter systems equipped with

active IDMs can successfully detect the islanding when

Qf ≤ 2.5, the multi-inverter systems can detect the is-

landing only if Qf ≤ 1.25, this means the NDZ has shifted

towards the left. Obviously, this kind of situation in-

X. ZHANG, D. XIE

1518

creased the probability of islanding occurrence.

2.2. Inverters Equipped with AFD and SMS

IDMs

Taking two grid-connected inverters for example, sup-

pose that the proportion of active power for the local load

provided by the inverter equipped with AFD IDM is

KAFDpu, and then the proportion of active power provided

by the inverter equipped with SMS IDM is (1-KAFDpu).

Therefore, the two inverter’s current is

2sin(2

AFD AFDpuAFD

iKIft



) (3)

2(1) sin(2)

SMS AFDpuSMS

iKIft



 (4)

where θAFD is the current initial phase angle of the in-

verter equipped with AFD IDM, andθSFS is the current

initial phase angle of the inverter equipped with SMS

IDM[5-6]. As per definition:

(2) 2

AFD

 





 (5)

where tz is the dead area time inserted into the output

current of inverter equipped with AFD IDM, f is the last

period frequency of inverter output voltage, Δf is the

frequency shifting of inverter output voltage;

sin 2

SMS m









 









(6)

whereθm is the maximum phase shifting of output cur-

rent of inverter equipped with SMS IDM, fm is frequency

when θm arise, fg is the frequency of grid, f is the last

period frequency of inverter output voltage.

According to (3) and (4), if the two parallel inverters

are equivalent to one inverter, the initial phase angle of

equivalent inverter’s total output current is

1sin(1) sin

tan()

cos(1) cos

AFDpu AFDAFDpuSMS

INV

AFDpu AFDAFDpuSMS











(7)

Thus, the NDZ in Qf×f 0 frame is determined by the

criteria as follows



tan( )0

INV



f

(8)

IfΔf in AFD IDM is 1Hz,θm is 10° and( fm – fg) is 3Hz

in SMS IDM, the sketch map of NDZ for PV system

with both AFD and SMS IDMs is shown in Figure 1.

There one sees that the NDZ is enlarged along with the

augment of KAFDpu, which proportion of local load’s ac-

tive power provided by the inverter equipped with AFD

IDM.

Figure 1. NDZ of a system with both AFD and SMS IDMs.

2.3. Inverters equipped with AFD and AFDPF

IDMs

The AFD IDM shifts the system operating frequency

towards the enhanced direction without considering if the

local load is capacitor or inductor. But the AFDPF IDM

will shift system operating frequency towards enhanced

or descended direction, which is decided by local load’s

capacitive or inductive characteristic. Therefore, the mul-

ti-inverter PV systems equipped with both AFD IDM and

AFDPF IDM, will have mutual influence.

Still taking two grid-connected inverters for example,

suppose that the proportion of active power for the local

load provided by the inverter equipped with AFD IDM is

KAFDpu, and then the proportion of active power provided

by the inverter equipped with AFDPF IDM is (1-KAFDpu).

Therefore the two inverter’s current is [7]

AFD

2sin[2

AFD AFDpu

iKIft



] (9)

AFDPF AFDPF

2(1) sin(2)

AFDpu

iKIft



 (10)

where θAFD is the current initial phase angle of the in-

verter equipped with AFD IDM, and θAFDPF is the current

initial phase angle of the inverter equipped with AFDPF

IDM. According to definition,

(2 )()

AFDPF

fcfk







  (11)

where cf0 is the initial chopping factor, k is the posi-

tive-feedb-ack gain. The θAFD is the same as last section,

thus the initial phase angle of equivalent inverter’s total

output current is:

)

coscostan

sinsintan

(tan 2

AFDPFAFD

INV







 (12)

where 1

sin ()

AFDpu





. Similarly, as per (8), when



= 1 Hz, 0 = 0.03, k = 0.06，the sketch map of

NDZ for PV system with both AFD and AFDPF IDMs

can be shown in Figure 2. Figure 2 displays that the

NDZ is enlarged along with the increase of KAFDpu. It

X. ZHANG, D. XIE 1519

Figure 2. NDZ of a system with both A FD and AFDPF IDMs .

means that if local load augments the proportion of active

power provided by the inverter equipped with AFD IDM,

the NDZ will be enlarged[8].

2.4. Inverters Equipped with both AFDPF IDMs

There is measuring error when sensors measure the fre-

quency of voltage, so the frequency measured in the two

inverters supposed to be f1 = f + Δfe and f2 = f – Δfe re-

spectively. When use the AFDPF IDMs, if the actual

frequency f more than reference frequency f0, as a result

of the positive-feedback, frequency f will further rise,

otherwise f will drop. Therefore, the system operating

frequency of these two inverters changes reversely be-

cause of the sensors measuring error. Thus, the islanding

detection function of the two inverters disturbs mutually,

namely has the so-called dilution effect, and the prob-

ability of islanding occurrence is enlarged. The impact of

measuring error on NDZ is analyzed as follows [9].

In order to have a convenient analysis, the initial

chopping cf0 and positive-feedback gain k of the two

inverters are supposed to be the same. First, the two in-

verters are equivalent to one inverter, the output current

of equivalent inverter is:



11 2

2sin(2) sin(2)

INVAFDPF AFDPF

ift ft

 



(13)

If the value of Δfe is small enough, we can obtain the

approximate expression

12 1

2 cos()sin(2)

2sin(2 )

AFDPFAFDPFAFDPF AFDPF

INV

INV INV

iI ft

Ift

 









(14)

where

(

AFDPF AFDPF

INV cfk f

 







Compared with (15) and (11), two expressions are the

same. It means that because of frequency measuring error,

the positive-feedback perturbations produced by the two

inverters counteract mutually, but the initial chopping

and positive-feedback gain still exist, the frequency posi-

tive-feedback can still be triggered, the effect of island-

ing detection is not affected. Therefore, the NDZ for

systems of multi-inverters equipped with AFDPF IDMs

is approximately the same as the NDZ for systems of

single-inverter equipped with identical IDMs. According

to (8), the NDZ for systems of two inverters equipped

with AFDPF IDMs is shown in Figure 3.

2.5. Inverters Equipped with Both SMS IDMs

First, still supposed the frequency of the two inverters

has sensor measuring error, and the error is +Δfe and –Δfe

respectively, i.e. the error amplitude is the same and error

polarity is opposite. Then the output current of equivalent

inverter is



11 2

2sin(2) sin(2)

INVSMS SMS

iftft

 



(16)

If the value of Δfe is small enough, we can obtain the

approximate expression

12 1

2cos()sin(2)

2sin(2 )

SMS SMSSMS SMS

INV

INV INV

iI ft

Ift

 









(17)

where

sin( )

INV meq









 (18)

cos( )

meq m









 (19)

)



(15) Figure 3. NDZ of a system with two AFDPF IDM inverters.

X. ZHANG, D. XIE

1520

Figure 4. NDZ of a system with two SMS IDM inverters.

The (6) express the current initial phase angle of sin-

gle-inverter system equipped with SMS IDMs. Com-

pared with (19) and (6), we may see that the frequency

measuring error will reduce the amplitude of maximum

phase shifting angle θm, it means that the positive-feed-

back perturbations produced by the two inverters coun-

teract mutually, and the NDZ will increase, so the per-

formance of islanding detection will drop. However,

even if the measuring error Δfe takes a relatively big val-

ue (0.5 Hz), and fm – fg =3Hz, the maximum phase shift-

ing angle θmeq drops only 3.4% compared with θm, there

isn’t obvious change for the NDZ. Figure 4 shows the

NDZ for different Δfe (θm = 10°

、

m – fg =3Hz). This

figure indicates that though the frequency measuring

error makes the perturbation produced by the two invert-

ers counteract mutually, it almost has no impact on per-

formance of islanding detection[9].

3. Conclusions

Synthesizing the above analysis, for the islanding de-

tection performance of the multi-inverter grid-connected

PV systems, we may draw the following conclusion:

First, when part of inverters in system adopt active

IDMs, the others use passive IDMs, the application of

passive IDMs enlarges the NDZ, and increases probabil-

ity of islanding; Second, when part of inverters in system

adopt AFD IDMs, the others use positive-feedback

based active IDMs, such as SMS and AFDPF IDMs, the

NDZ will be enlarged and hence increase the possibility

of islanding if we magnify the proportion of load active

power provided by inverters equipped with AFD IDM;

Third, when all the inverters in system adopt AFDPF

IDMs or SMS IDMs, though the sensor measuring error

makes the perturbation produced by the inverters coun-

teract mutually, it almost has no impact on islanding de-

tection performance even if in the worst situation(The

inverters have identical error amplitude and opposite

error polarity).

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