A Nondestructive Islanding Detection Method Based on Adaptive and Periodic Disturbance on Reactive Power Output of Inverter-Based Distributed Generation

In order to detect islanding nondestructively, an islanding detection method for microgrid is proposed based on adaptive and periodic disturbance on the reactive power output of inverter-based distributed generation (DG). The first two parts of the disturbance in a cycle form a symmetric triangular shape and the disturbance can adaptively adjust its peak value and cycle time for two purposes. One is to minimize the total amount of the disturbance.The other is to guarantee that the absolute value of the rate of change of frequency (ROCOF) is constant during islanding, which can be utilized to be a criterion to detect islanding.Themethod can be applied on the DG either operating at a unity power factor or generating both active and reactive power simultaneously. Moreover, it helps to avoid the serious transient process during control strategy transformation of the DG for microgrid islanded operation. According to the anti-islanding test system in the IEEE Std. 929-2000 and IEEE Std. 1547-2003, several study cases are carried out in the PSCAD/EMTDC environment. The simulation results show that the proposed method can detect islanding rapidly and nondestructively. Moreover, it also performs effectively for the system with multiple DGs.


Introduction
The inverter-based distributed generation (DG) uses renewable energy such as wind power, photovoltaics, and microturbine to supply power [1].It is being widely researched and applied to meet the targets of environmental protection and harmonious development of the power industry.Microgrid usually contains the DG, the load, and control devices based on a certain topology structure [2][3][4].It can realize the effective management of the DG and fully mine its value for the benefits of both the grid and users [5,6].
Islanding is a condition in which a portion of the utility system that contains both the DG and load continues operating while this portion is electrically separated from the main utility [7,8].There are two types of islanding: (1) intentional islanding and (2) inadvertent islanding.According to the control strategy in advance, intentional islanding forms in a controlled manner to make good use of the DG and improve the power supply reliability [8,9].This operation mode is not studied in this paper.On the contrary, inadvertent islanding can lead to power quality problems, serious equipment damage, and even safety hazards to utility operation personnel [10].Therefore, the DG has to detect islanding rapidly and effectively in this case to prevent the damage mentioned above.
Generally, the islanding detection methods can be mainly classified into three categories: (1) passive methods; (2) active methods; and (3) communication-based methods.Communication-based methods rely on power line carrier communications and do no harm to the power quality of the power system with the negligible nondetection zone (NDZ), but the cost is much higher than the other two types of methods and the operations are more complex as well [11].Therefore, passive and active methods have been well developed.
Passive methods determine the islanding condition by measuring system parameters such as magnitude of the voltage at the point of common coupling (PCC), the PCC voltage frequency, and phase jump [12].Over/underfrequency protection (OFP/UFP) and over/undervoltage protection (OVP/UVP) are the most widely used passive islanding detection methods.According to GB/T 19939-2005 (China), the voltage thresholds are typically set at 0.85 pu and 1.1 pu, while the frequency thresholds are set at 49.5 Hz and 50.5 Hz (50 Hz is the rated frequency of the power system) [13].Passive methods are easy to implement and do no harm to the power quality of the power system, but they may fail to detect islanding when the local load consumption closely matches the power output of the DG [14].
In order to reduce or eliminate the NDZ, active methods rely on injecting intentional disturbances or harmonics into some DG parameters to identify whether islanding has occurred [15][16][17].Active methods mainly include the active frequency drift (AFD), slip-mode frequency shift (SMS), and Sandia frequency shift (SFS) methods, which can create a continuous trend to change the frequency during islanding [18][19][20].Though active methods suffer smaller NDZs, the presence of disturbances during normal operation will sacrifice power quality and reliability of the power system.Moreover, some active methods have difficulty in maintaining synchronization of the intentional disturbances.Therefore, they may not work owing to the averaging effect when applied in multiple-DG operation [21,22].
Islanding detection methods based on reactive power control are more attractive.With the designed reactive power reference for the DG, these methods can be easily implemented.The NDZ can be reduced or even eliminated with proper design.Moreover, these methods do not cause current distortion during the normal operation [23].
An islanding detection method relying on equipping the DG interface with a - characteristic was proposed in [24].It was hard to guarantee that the slope of the DG - curve, which was a preset and fixed value, would be steeper than that of the load curve.Thus, the method might fail to detect islanding in some cases.Reference [25] presented an islanding detection method based on intermittent bilateral reactive power variation and the frequency was forced to deviate to the thresholds during islanding.Compared with the method in [25], the proposed method in [26] was improved by only generating unilateral reactive power variation in each variation period and reducing the reactive power output based on the load's resonance frequency.However, if the islanding occurred when the reactive power variation was equal to zero, it would not be detected rapidly with the detection time probably up to a whole variation cycle 1.8 s.Moreover, when the methods were applied to multiple DGs, the synchronization of the reactive power variation might not be guaranteed and the methods would fail to detect islanding.
The methods in [24][25][26] were designed for the DG operating at a unity factor during the normal operation.However, the DG was also explored to compensate reactive power simultaneously for power factor improvement [27,28], as well as the voltage regulation [29,30].The method in [31] was designed for this kind of DG.With the designed reactive power reference, the DG continuously and partly compensated the load reactive power consumption, thus forcing the frequency to rise or drop until the frequency deviated outside the OFP/UFP limits.However, the detection speed varied and it would be too slow if the load consumed little reactive power.Most active methods aim to force the frequency to deviate outside the OFP/UFP limits to detect islanding.However, the abnormal frequency after detection makes the control strategy transformation of the DG for microgrid islanded operation hard.Therefore, a nondestructive islanding detection method for microgrid is proposed in this paper.The method relies on the periodic disturbance on the reactive power output of the DG.The disturbance in a cycle has three parts with equal duration and the first two parts of the disturbance form a symmetric triangular shape.Accordingly, the frequency deviates in a symmetric triangular shape without exceeding its limits.In addition, the disturbance in the next cycle can adaptively adjust its peak value and cycle time according to the frequency in the third part of the disturbance in last cycle.The design is for two purposes: (1) minimizing the total amount of disturbance and (2) making sure that the absolute value of the ROCOF is constant during islanding, which can be utilized to be a criterion to detect islanding.The method has the universal nature.It can be applied on the DG either operating at a unity power factor or generating both active and reactive power simultaneously.Moreover, it performs effectively as well for the system with multiple DGs.Due to the method's nondestructive effect on the frequency, it helps to avoid the serious transient process during control strategy transformation of the DG for microgrid islanded operation.

Recommended Generic System
Modeling and Basic Relationship Analysis Active methods aim to detect islanding when the local load consumption closely matches the DG output power.Due to the fact that the detection time is short, the DG output power can be considered to be constant during the detection.Therefore, using a constant dc source behind a three-phase inverter, the DG is usually designed as a constant power source.

SPWM Switch signals
Based on the dual close loop control structure in the - synchronous reference frame, the DG can control the active and reactive power output independently.The block diagram of the DG interface control is shown in Figure 2. It mainly contains the phase-locked loop (PLL), the outer power control loop, and the inner current control loop.The PLL offers the voltage phase angle as a benchmark phase to realize synchronous Park transformation.In addition, it can calculate the frequency of the PCC voltage as well, which can be utilized to judge whether islanding occurs or not according to the OFP/UFP.In the outer power control loop, according to PI regulators, the errors between active and reactive power output of the DG and their preset values are transformed into the reference values of active and reactive current, respectively.In the inner current loop, the errors between the measured and reference - values of the DG current are also passed through PI regulators.Meanwhile, the feed-forward compensation from the - voltages at the PCC realizes the decoupled control of the - components of the DG current as well as the DG active and reactive power output.According to the Park transformation, the output of the inner current control loop is transformed into the reference values of the output voltage of the DG.Then, the triggering pulses on the inverter switches are gained by sinusoidal pulse-width modulation (SPWM).
The instantaneous active and reactive power output of the DG can be written in terms of the - axis components as follows [32]: where   and   represent the - components of the PCC voltage and   and   are the - components of the DG current.Under the balanced network conditions, the abovementioned - components are constant.

Basic Relationship Analysis.
When the DG and its local load are connected to the utility grid, the power flows and the active and reactive power consumed by the RLC load can be expressed as follows: where RLC represent the load resistance, inductance, and capacitance and  PCC and  are the root mean square (RMS) of the single-phase voltage at the PCC and its frequency, respectively.In addition, (3) can also be written in terms of the RLC load's resonant frequency ( 0 ) and quality factor (  ) as follows [26]: and the  0 and   can be expressed as follows: It can be inferred from (2) that when islanding occurs, the PCC voltage falls or rises according to the active power mismatch Δ (Δ =  Load −  DG ).If the active power of the DG is set constant, the active power mismatch can be expressed as follows [33]: and Δ can be expressed as where  PCC and  * PCC represent the PCC voltage before and after islanding, respectively.
If the DG operates at a unity power factor, the reactive power consumed by the local load will be equal to zero after islanding.Therefore, the value of the frequency after islanding is equal to that of  0 according to (4).In order to force the frequency after islanding to deviate to a certain value (such as 50 Hz or the frequency threshold values 50.5 Hz and 49.5 Hz), the additional amount of the reactive power can be derived according to (4) as follows: where  tar represents the target value of frequency,  1 is the reactive power with the frequency equal to  tar , and  1 represents the frequency after islanding with its value equal to that of  0 in this case.
On the other hand, if the DG generates both active and reactive power simultaneously, the value of  1 depends on both active and reactive power mismatches [34].In order to force the frequency after islanding to deviate to its threshold in this case, the additional amount of the reactive power can be derived as where  2 is the reactive power with the frequency equal to  tar for the DG of this kind.Since the change of  0 around 50 Hz has negligible impact on the value of Δ 2 ,  0 could be set as 50 Hz and ( 9) can be rewritten as follows: On the basis of islanding detection standards, the power factor   of the RLC load is set as 2.5.Assuming that  DG is equal to 1, Figure 3 illustrates the relationship between  1 and Δ when  tar is set as 50 Hz and the threshold values 49.5 Hz and 50.5 Hz according to (8) and (10).It can be seen from Figure 3 that (1) no matter whether the DG operates at a unity factor or generates active and reactive power simultaneously, the Δ- 1 curves are the same; (2) the Δ- 1 curves show the approximately linear characteristic for the period between 49.5 Hz and 50.5 Hz; (3) when  1 is greater than or equal to 50 Hz, the additional reactive power can be calculated with Frequency after islanding (Hz) Additional reactive power f tar is set as the lower limit 49.5 Hz.
f tar is set as the upper limit 50.5 Hz.
f tar is set as 50 Hz. tar equal to 50.5 Hz.And the additional reactive power can be calculated with  tar equal to 49.5 Hz when  1 is smaller than 50 Hz.Therefore, the additional reactive power is within ±5%  DG .

Proposed Nondestructive Islanding Detection Method Based on Adaptive and Periodic Disturbance on the Reactive Power Output of the DG
Traditional active methods usually force the frequency to deviate outside the OFP/UFP limits to detect islanding.However, the abnormal frequency makes the control strategy transformation of the DG for microgrid islanded operation hard.In this paper, a nondestructive islanding detection method for microgrid is proposed, which can keep the frequency in the normal operating range and avoid the serious transient process during the control strategy transformation of the DG.
It can be seen from ( 6), (8), and (10) that the active power mismatch makes the voltage change after islanding, while the frequency variation depends on the reactive power mismatch no matter whether the DG operates at a unity power factor or generates active and reactive power simultaneously.Thus, periodic disturbance on the reactive power output of the DG can be utilized to detect islanding.In addition, islanding should be detected rapidly with the minimum reactive power disturbance.Therefore, the proposed method includes three key points: (1) maintaining the frequency in the normal operating range; (2) designing proper criterions to detect islanding rapidly; and effectively (3) minimizing the total amount of the disturbance by adaptively adjusting its peak value and cycle time.
According to the study on the relationship between the reactive power mismatch and the frequency variation after islanding in Section 2, the Δ- 1 curve shows the approximately linear characteristic for the period between 49.5 Hz and 50.5 Hz.Therefore, the disturbance in a cycle is designed to be divided into three parts with equal duration and the first two parts form a symmetric triangular shape.Accordingly, the frequency deviates in a symmetric triangular shape without exceeding its limits after islanding when the periodic disturbance is added on reactive power output of the DG.The reactive power disturbance in a complete cycle can be expressed as follows: where Δ peak and  are the peak value and cycle time of the disturbance, respectively.The first two parts are the rise/fall or fall/rise sections of the symmetric triangular, respectively.Whether the rise section or the fall section starts first depends on the sign of Δ peak .If Δ peak is positive, the first part of the disturbance is the rise section of the triangular shape.In addition, the peak value and cycle time of the disturbance in this cycle can be calculated according to the frequency in the third part of the disturbance in the last cycle.As for the third part of the disturbance in a cycle, the disturbance value is set as zero.This part aims to obtain the value of  1 , which is the frequency without disturbance after islanding.Then, the peak value and cycle time of the disturbance in the next cycle can be calculated, which is introduced in detail afterwards.
In order to keep the frequency in its normal range during islanding and reduce the NDZ, the frequency corresponding to the peak value of the disturbance is set as the frequency threshold (50.5 Hz or 49.5 Hz).Therefore, if islanding occurs, the frequency will deviate from  1 to its threshold, return back to  1 afterwards, and repeat the abovementioned process periodically.As mentioned in Section 2, the peak value of the disturbance on the reactive power output will be within ±5%  DG if proper threshold value is chosen for  1 .However, the peak value of the disturbance decreases along with the increasing value of  1 .If  1 is close to the frequency threshold, the peak value of the disturbance will be small.The method might fail to detect islanding in this condition.Therefore, the frequency corresponding to the peak value of the disturbance is set as 50 Hz when  1 is close to the frequency threshold (such as when  1 is above 50.25 Hz or below 49.75 Hz).If islanding occurs in this condition, the frequency will deviate from  1 to 50 Hz, return back to  1 afterwards, and repeat the abovementioned process periodically.According to (8), the peak value of the disturbance can be calculated as follows for the DG operating at a unity power factor: As for the DG generating the active and reactive power simultaneously, the peak value of the disturbance can be obtained as follows according to (10): On the other hand, the cycle time of the disturbance should be properly designed as well.The design of the cycle time has two purposes: (1) minimizing the total amount of the disturbance; (2) making sure that the absolute value of the ROCOF is constant in the triangular parts of the disturbance when islanding occurs.Assuming that the cycle time is  1 when  1 is 50 Hz, the frequency deviates to 50.5 Hz after onethird of the cycle time  1 .Therefore, the absolute value of the ROCOF is equal to 1.5/ 1 (Hz/s).If  1 is not equal to 50 Hz, the cycle time of the disturbance can be obtained as follows: It can be seen from ( 14) that the cycle time also depends on the value of  1 and it changes adaptively to shorten the duration of the disturbance and keep the absolute value of the ROCOF equal to 1.5/ 1 .The value of  1 is preset.When the first part of the disturbance in a cycle starts, it is checked whether the absolute value of the ROCOF is equal to 1.5/ 1 or not.If the absolute value of the ROCOF is equal to 1.5/ 1 and the situation lasts for the time preset in advance, islanding will be nondestructively detected based on this criterion with the frequency in its allowable range.Assuming that  DG is equal to 1 and  1 is set as 0.3 s, the adaptive and periodic disturbance on the reactive power output of the DG with different values of  1 is shown in Figure 4.
When the method is applied to multiple DGs, the effectiveness of the method based on above criterion depends on whether or not the disturbances on the reactive power output of DGs are synchronous.If the disturbances are synchronous, the criterion mentioned above will still be satisfied after islanding and islanding will be detected effectively.However, if the disturbances are asynchronous, the total amount of the disturbances will be inadequate to force the frequency to deviate to its target value (50.5 Hz, 49.5 Hz, or 50 Hz).Accordingly, the absolute value of the ROCOF will be smaller than 1.5/ 1 .Therefore, additional criterion is needed for multiple-DG operation in case of the disturbance asynchrony based on the characteristic in this situation.The values of  1 calculated by DGs are the same after islanding because DGs are in the same islanding system.Therefore, the peak values and cycle time of the disturbances and the frequency's target value are the same as well.Moreover, according to the proposed method, the disturbance in a cycle is designed to have three parts with equal duration.Therefore, the frequency will deviate periodically after islanding and its cycle time is always equal to that of the disturbance no matter whether the disturbances are synchronous or not.This characteristic can be utilized as the additional criterion to detect islanding when the disturbances are asynchronous in multiple-DG operation.The detection time with this criterion is a little bit longer than that based on the absolute value of the ROCOF and its duration, but it is much shorter than 2 s as the IEEE standard required.
Therefore, both criterions are configured in the DG.If either one of both criterions is satisfied, islanding will be detected rapidly and effectively no matter whether the disturbances on the reactive power output of both DGs are synchronous or not.

Performance of the Proposed Method during Islanding
In this section, several study cases are simulated on the power systems computer-aided design (PSCAD)/EMTDC based on the system in Figure 1.The main system parameters are given in Table 1.Adopting the interface control presented in Figure 2, the DG performs as a constant power source.The designed disturbance is added on the reactive power output of the DG.The frequency is 50 Hz before islanding and  1 is set as 0.3 s.The islanding is initiated at  = 0.3 s.The performance of the proposed islanding detection method is tested under different conditions.

Application on the DG Operating at a Unity Power Factor.
To examine the performance of the proposed method when it is applied on the DG operating at a unity power factor, three test cases are designed with different values of RLC load as shown in Table 2.There are no active and reactive (2) the first part of the disturbance in this cycle is half completed.When the disturbance value in this cycle is equal to zero, the value of  1 can be obtained again.Then, the peak value and cycle time of the disturbance in the next cycle can be calculated.For the DG operating at a unity power factor, the value of  1 is equal to that of  0 during islanding and the value of the DG reactive power output is equal to that of the disturbance as well.
For the first scenario, Figure 5 illustrates the PCC frequencies and the DG reactive power output of three cases, respectively.It can be seen from Figure 5 that the sudden change of the load reactive power consumption (from the rated reactive power consumption to 0 Var) in Cases 2 and 3 leads to transient processes of the frequencies.The values of  1 in three cases are 50 Hz, 49.8 Hz, and 50.2 Hz, respectively.Accordingly, the peak values of the disturbance in the next cycle are −10 kVar (−5%  DG ), 6 kVar (3%  DG ),  and −6 kVar (−3% DG ) and cycle time is 0.3 s, 0.18 s, and 0.18 s.Corresponding to the first two parts of the disturbance in a cycle, the frequency is forced to deviate in a triangular shape.When the first part of the disturbance in a cycle starts, it is checked whether the absolute value of the ROCOF is equal to 5 (Hz/s) or not.If the absolute value of the ROCOF is equal to 5 and the situation lasts for 10 ms, islanding is detected nondestructively.Islanding can be detected within 110 ms for three cases in this scenario.Afterwards, when the disturbance value is equal to zero, the control strategy transformation of the DG for microgrid islanded operation can be implemented to avoid the serious transient process.
Figure 6 illustrates the PCC frequencies and the DG reactive power output of three cases for the second scenario, respectively.When islanding occurs, the peak value and cycle time of the disturbance at that time have been determined according to the normal system frequency 50 Hz.They will not change until the next disturbance period for all the three cases.For both Cases 1 and 2, where the values of  1 are not larger than 50 Hz, the frequencies are within the normal range after islanding and islanding detection time is within 60 ms.However, the value of  1 in Case 3 is 50.2Hz and the maximum frequency after islanding reaches up to 50.7 Hz, which corresponds to the peak value of the disturbance calculated according to 50 Hz.The frequency deviates outside its upper threshold 50.5 Hz and the passive OFP/UFP method can detect islanding within 50 ms.The DG transforms its control strategy for microgrid islanded operation when the disturbance value is equal to zero for three cases.
For the situations like Case 3 in the second scenario, the maximum frequency should be as small as possible to make the power quality better.In order to realize this target, the proposed method can be further improved.When the frequency is detected to just begin to be above 50.5 Hz, the value of the disturbance at that time Δ thr is captured.Then, the value of the disturbance is maintained to be Δ thr for a while.The duration of this situation can be calculated as follows: According to the improved method, the PCC frequencies and the DG reactive power output of three cases in the second scenario are shown in Figure 7. Compared with the frequency of Case 3 as shown in Figure 6, it is approximately equal to 50.5 Hz after the transient process.Therefore, the improved method can guarantee the better power quality for the situations like Case 3 in the second scenario.

Application on the DG Generating Active and Reactive
Power Simultaneously.This part aims to verify the effectiveness of the proposed method when it is applied on the DG generating active and reactive power simultaneously.As  shown in Table 3, three test cases are also designed with different values of DG reactive power output.These values are the DG reactive power output without considering the disturbance.The RLC load's power factor is set to 0.95 with the rated active and reactive power equal to 200 kW and 65.74 kVar, respectively.Therefore, the values of  1 are different in these three cases due to different reactive power mismatches.Like in Section 4.1, the two scenarios are simulated as well in this part.Figure 8 illustrates the PCC frequencies and the DG reactive power output of three cases in the first scenario.The values of  1 of three cases are 50 Hz, 49.84 Hz, and 50.14 Hz, respectively.Accordingly, the peak values of the disturbances in the next cycle are −10 kVar (−5%  DG ), 6.8 kVar (3.4%  DG ), and −7.2 kVar (−3.6%DG ) and the cycle time of the disturbances is 0.3 s, 0.204 s, and 0.216 s.Moreover, it can be seen that the absolute values of the ROCOF in three cases are equal to 5 (Hz/s) when the first parts of the disturbances in the next cycle start after islanding, and the duration of these situations is over 10 ms.Therefore, islanding can be detected effectively within 110 ms in these three test cases.
On the other hand, Figure 9 illustrates the PCC frequencies and the DG reactive power output of three cases in the second scenario, respectively.Like the second scenario in Section 4.1, the frequencies of Cases 1 and 2 are within their normal ranges.The absolute values of the ROCOF are equal to 5 (Hz/s) during the second parts of the disturbances after islanding, and the duration of these situations is over 10 ms.Therefore, islanding can be detected effectively within 60 ms in Cases 1 and 2. In addition, the frequency of Case 3 deviates outside its upper threshold and islanding can be detected by the passive OFP/UFP method.The value of the frequency is approximately equal to 50.5 Hz after the transient process with the improved method and the frequency is kept within its normal range afterwards.islanding effectively for the DG either operating at a unity power factor or generating active and reactive power simultaneously in both scenarios.Therefore, the performance of the proposed method is only tested on the system with both DGs operating at a unity power factor in this part.Both DGs connect with their own local load, respectively, and then connect together at the PCC.The parameters of the local RLC load are the same with those in Case 1 of Section 4.1.Moreover, considering that the disturbances on the reactive power output of both DGs might be asynchronous, two scenarios are simulated as well in this part: (1) the disturbances on the reactive power output of both DGs are synchronous; (2) the disturbance on the reactive power output of one DG lags by 0.03 s (0.1) behind that on the reactive power output of the other one.Figure 10 presents the frequency and the separate and total reactive power output of both DGs in the first scenario, respectively.Due to the disturbance synchronization, the frequency can deviate to its threshold 50.5 Hz and the absolute value of the ROCOF is equal to 5 (Hz/s).Therefore, islanding can be detected within 110 ms for this scenario.
Figure 11 presents the frequency and the separate and total reactive power output of both DGs in the second scenario, respectively.When islanding occurs, there is a sudden change of the load reactive power consumption (from 0 Var to the current value of the total reactive power).Therefore, the frequency goes through a transient process.In addition, the total amount of the disturbances is inadequate to force the frequency to deviate to 50.5 Hz because the disturbances on the reactive power output of both DGs are asynchronous.It can be seen from Figure 11 that when the triangular wave parts of the disturbances start, the frequency deviates periodically with the cycle time equal to 0.3 s.Islanding can be detected within 400 ms for this scenario, which is still far less than the 2 s as the standard required.

Conclusion
According to the relationship between the reactive power mismatch and the frequency deviation, a nondestructive islanding detection method based on adaptive and periodic disturbance on the reactive power output of the DG is proposed in this paper.The disturbance in a cycle is designed to have three parts.The first two parts form a symmetric triangular shape.Accordingly, the frequency deviates in a symmetric triangular shape when islanding occurs.This design guarantees that the frequency is within its normal range during islanding.The value of the third part of the disturbance is equal to zero.According to the frequency in this part, the disturbance in the next cycle can adaptively adjust its peak value and cycle time.
Therefore, the total amount of the disturbance is the minimum.The absolute value of the ROCOF is constant during islanding, which can be utilized to be a criterion to detect islanding rapidly.Afterwards, when the disturbance value is equal to zero, the control strategy of the DG for microgrid islanded operation can be implemented to avoid the serious transient process.In addition, the method has the universal nature.It can be applied on the DG either operating at a unity power factor or generating both active and reactive power simultaneously.Furthermore, it also performs effectively for the system with multiple DGs.

Figure 2 :
Figure 2: The block diagram of the DG interface control.

Figure 3 :
Figure 3: The Δ- 1 curves when  tar is set as 50 Hz and the threshold values.

Figure 4 :
Figure 4: The adaptive and periodic disturbance with different values of  1 .

3 Case 3 :Figure 5 :
Figure 5: The PCC frequencies and reactive power output of the DG in the first scenario.

3 Figure 6 :
Figure 6: The PCC frequencies and reactive power output of the DG in the second scenario.

3 Figure 7 : 3 Figure 8 :
Figure 7: The PCC frequencies and reactive power output of the DG in the second scenario with the improved method.

Figure 10 :
Figure 10: The PCC frequency and the separate and total reactive power output of both DGs in the first scenario.

Figure 11 :
Figure 11: The PCC frequency and the separate and total reactive power output of both DGs in the second scenario.

Table 1 :
Parameters of the study system.

Table 2 :
Parameters of the RLC load.The values of the load's resonant frequency  0 in these three cases are different.The frequency is 50 Hz before islanding.Therefore, the disturbance, whose peak value and cycle time have been determined with  1 equal to 50 Hz, will last for a while (not longer than a cycle) until the next cycle after islanding.Considering the unpredictability of its duration, two scenarios are simulated: (1) the third part of the disturbance in this cycle just starts;

Table 3 :
Parameters of the RLC load and DG reactive power output without the disturbance.
4.3.Multiple-DG Operation.According to the simulation results in Sections 4.1 and 4.2 the methods can detectFigure 9: The PCC frequencies and reactive power output of the DG in the second scenario with the improved method.