Modified Q–f Droop Curve Method for Islanding Detection with Zero Non-Detection Zone

In this paper, a modified Q-f droop curve method for inverter-based distributed generator is proposed. The proposed method has merits such as detecting islanding with zero non-detection zone, negligible effects on power quality and simple implementation. A new parameter is embedded in the reactive power reference to accelerate the frequency deviation at the point of common coupling, until the islanding is detected. Therefore, a passive under/over frequency relay will be simply sufficient to detect islanding within the permissible limit. The proposed method is modelled with computer-aided design SIMULINK/MATLAB environment. The proposed method is analysed for operation with unity and non-unity power factors. The performance is validated for various loading quality factors with a negligible change in detection time. In addition, it is confirmed that the proposed system is stable under unbalanced loading and switching conditions. The proper operation of proposed islanding detection method under multi distributed generators connection is validated. The results of the hardware experimentations are presented to confirm the proposed method analysis and simulations.


I. INTRODUCTION
One of the serious concerns of electrical network utilities is an unintentional islanding in grid as it can cause a hazard for utility line-workers and damaging distributed generator (DG) particularly during the DG reconnection [1]. In addition, for distributed generators in a microgrid, an unintentional islanding detection is important to transfer the operation safely and smoothly into islanded mode [2]. IEEE 1547 considers the islanding detection and its respective parameters, which includes detection time, quality factor and voltage/frequency thresholds. The islanding detection methods are classified into remote and local methods [3]. The latter can be further divided into passive and active methods. Remote methods are based on communication systems to monitor the network circuit breaker or recloser, when they are open during islanding. In [4], the islanding detection signal has been combined with a voltage unbalance of PCC voltage to help the local method for islanding detection.The main advantage of communication-based methods is that, zero non-detection zone (NDZ) is achievable. However, the communication link adds complexity, cost and reliability issues [5]. The passive methods include under/over voltage , under/over frequency, voltage phase jump detection or voltage vector shift, changes in voltage and current of total harmonic distortion and rate of change of frequency [5]. When the power mismatch between the local load and DG is too small, the amount of frequency or voltage deviation will not be large enough to trigger the islanding detection method [6]- [8]. In [9]. a passive islanding detection method was introduced, which is based on phasor measurement unit (PMU). It has a good performance for islanding detection, however its detection time can be longer than active islanding detection methods. In [10], a passive islanding detection method was modelled based on components of the voltage signals. The islanding detection time is short with zero NDZ, however it needs more performance investigation with different loading quality factors and multi DGs connection. Signal processing methods have been developed to improve the operation of passive islanding detection methods [11]. However, their weakness under transient operation is the main challenge. In [12], a passive islanding detection method with logistic regression method, which is based on machine learning technique has been introduced. It has a good performance, howerver the system has nit been tested for higher loading quality factors and multi DGs connection. In [13], an intelligent islanding detection method was presented, which is categorised under passive methods. It has an effective performance for islanding detection, although its operation under non-unity power factor of DG for different loading quality factors has not been considered. In active methods, a small disturbance is injected into the point of common coupling (PCC) and then monitoring the DG electrical variables such as voltage and frequency to detect islanding. The most common active islanding detection methods with frequency deviation are active frequency drift [14], Sandia frequency shift [15] and slipmode frequency shift [16]. The active methods have smaller NDZ, however they can degrade the power quality at the PCC [17]. In [18], a method based on active frequency drift was proposed, which has been modified by the positive feedback, to improve the islanding detection performance. However, it does not show the effectiveness of the method for different loading quality factors. Recently, active methods based on reactive power variation (RPV) have received noticeable consideration due to their high performance and simple implementation [19]- [26]. Nevertheless, the RPV methods still poses many challenges to attract noticeable research attention e.g. shortening the detection time and reduction the effect on the power quality. In [19], a Q-f droop curve was embedded in the control algorithm to deviate the frequency during islanding. A conservative loading quality factor value has been set at 7.4 in the reactive power reference equation. The results confirm that higher loading quality factors will lead to increase the detection time or even to fail the islanding detection. The setting of the loading quality factor is based on a trial and error, which makes difficult the setting of this method for different rated active power of DGs and/or different grid frequencies and respective UOF thresholds. In [20] and [21], the proposed islanding detection methods were based on intermittent bilateral and unilateral variation of reactive power reference, respectively. In these two methods, DG reactive power was changed periodically. The main advantage is that zero NDZ is achievable. However, a synchronization of periodic RPV based methods for multi DG connection is difficult. In [20], the loading quality factor was set at 2.5, whereas based on IEEE Std. 929-2000 [33], it can be 2.5 or less. Therefore, an effective performance for a wide range of loading quality factors has not been presented. The presented islanding detection method in [22], was based on the relationship between the reactive power disturbances and the frequency variation during islanding. The reactive power disturbances were configured periodically at two sets with different amplitude and duration time. Its advantage is a good islanding detection for the DG operation either at unity power factor or supplying reactive power for its local load with zero NDZ. As two sets of disturbances were periodic, its disadvantage is similar with [20] and [21]. In [22], the loading quality factor was set at 2.5 for all test cases during unity power factor of DG performance. The performance has not been shown under different loading quality factors and their impact on detection time. In [23], an intelligent controller method was introduced for islanding detection. The controller deviates the frequency by adding a disturbance signal in the d-axis current when islanding happens. It has a rapid islanding detection speed, although, it still suffers from NDZ. Also, in [23] the islanding detection has been tested with only one value of loading quality factor. In [24], the presented islanding detection method was based on the inverter's q-axis current controller, which was modelled with a continuous periodic reference current of a small value. The PCC frequency is deviated with respect to the variation of reference current during islanding. Also, an average absolute frequency deviation value was proposed during an islanding condition. The advantage of this method is its ability to detect islanding, when active and reactive powers mismatch are zero. Although, its performance under multi DG connection has not been investigated. The islanding detection algorithm in [25] was presented to eliminate NDZ during a reactive power mismatch by deviating the frequency beyond the thresholds. This method has zero NDZ, however it may degrade the power quality. In [25], the loading quality factor is set at 1, which is less than 2.5 as the higher value for the determined loading quality factor by [33]. In [26], a hybrid method was presented based on reactive power variation and four passive criteria. Despite of rapid islanding detection time with zero NDZ, this method has complexity due to using various criteria. Also, in [26], the parameters of reactive power reference were set based on Q f = 2.5. It means the performance of reactive power reference is different and the islanding detection time might be longer. The islanding detection method in [27] was proposed to eliminate the current static error in frequency shift islanding detection method. It has a fast detection time with a very good performance. It needs more investigation under multi DGs connection mode. In [28], a hybrid method including voltage unbalance/Total Harmonic Distortion and bilateral reactive power variation was introduced. It has a fast detection time; however, its performance under multi DGs connection has not been considered. It can be concluded that research efforts in literature have focused for operation with one value for loading quality factor, whereas the loading quality factor can be changed in a wide range of load parameters. On the other hand, the setting of parameters in some methods is based on trial and error. Therefore, with changing the system frequency or UOF thresholds, a revised setting is required, which is time consuming. In this paper, a modified Q-f droop curve method is proposed which its reactive power reference is set based on the converter rated power output, loading quality factor, load resonant frequency and UOF thresholds. The proposed method is examined under different loading conditions and various loading quality factors. Its ability for islanding detection with zero NDZ and rapid detection time is presented. Also, its implementation for multi DG connection is demonstrated. The contributions of the paper are as follows: 1) proposed a modified islanding detection method. 2) the experimental validation of the proposed islanding detection method for both static and dynamic loads. The rest of this paper is organized as follows. Section II presents the islanding basic system modelling. Section III provides the proposed islanding detection method. Section IV presents performance and simulation results of the proposed method. Section V demonstrates the experimentally validation of the proposed islanding detection method, which is tested under different load conditions.

II. ISLANDING BASIC SYSTEM MODELLING
The system under investigation is illustrated in Figure 1. It consists of a three-phase grid, a parallel three-phase RLC load and an inverter-based DG, which is modelled as a constant DC source behind a three-phase inverter. The DG interface control structure comprises two controllers as shown in Figure 2. The first control loop is an inner current controller to regulate the current while the second control loop is an outer power controller to regulate the active/reactive powers. The instantaneous active and reactive powers can be presented in terms of the dq axis components [29], as (1) and (2).
The active and reactive powers for the RLC load, when the grid is connected to PCC can be calculated as in (3) and (4). Also, active and reactive powers of the load can be expressed based on active/reactive powers of the grid and DG as in (5) and (6): where, ΔP and ΔQ are the power mismatch between DG and load, which are provided by the grid, as shown in Figure 1.
In grid connected operation, the PCC frequency is determined by the grid. However, after islanding, the PCC frequency is stabilized at resonant frequency when the DG is running at unity power factor. In that case, the reactive power of the load is moving towards zero, thus: If the resonant frequency is within the under/over frequency (UOF) thresholds, then it will not be detected by the UOF relay. Another important parameter that affects the NDZ is the loading quality factor (Q f ). It is defined as the ratio of the maximum stored energy to the dissipated energy.
Also, the quality factor can be expressed as in (10).
According to IEEE Std. 929-2000 [33] requirement, Q f is set at 2.5 for an islanding detection test. However, the islanding detection method must provide an effective performance for all amounts of Q f < 2.5 as well. The relationship between loading quality factor, reactive power mismatch and frequency thresholds can be obtained as in (11) [31]: where, f grid is the grid frequency, f min and f max are the upper and lower frequency thresholds of UOF relay. As shown in (11), P DG Q f for DG rated power and loading quality factor can be equal for DG with different rated powers and loading quality factors. For example, the multiplication of a DG with P DG = 100 kW and Q f = 2.5 is same as a DG with P DG = 200 kW and Q f = 1.25. Therefore, inequality in (11) for a DG with maximum quality factor (Q f = 2.5) is not able to guarantee proper islanding detection for other DGs with different rated powers. For this reason, any islanding detection method must be examined for various loading quality factors, lower and higher than 2.5, to validate its effectiveness with different DG rated powers.

III. PROPOSED MODIFIED Q-f DROOP CURVE METHOD FOR ISLANDING DETECTION
As mentioned in the introduction, RPV is an attractive islanding detection method, which the reactive power of DG varies after the grid disconnection and it drifts the PCC frequency beyond the UOF relay threshold. In [19], the load reactive power has been calculated as in (12).
As expressed in (12), the load Q-f equation has been calculated as a function of the load's resonant frequency. Also, the DG reactive power reference has been defined by: where, the values of k 1 and k 2 have been considered for constant P DG and Q f . It means that for different P DG rated values, different Q f values have to be used, which is difficult and relies on a trial and error approach. Therefore, it is essential to find an optimized method for calculating k 1 and k 2 , which depends on grid and load parameters rather than trial and error. Also, in [19], f res does not have any role for calculation of k 2 . On the other word, for any UOF thresholds or any grid frequency, k 2 is not changed and it is a constant value. It is another challenge, which makes it difficult to operate in other system frequencies.
In [25], another reactive power reference equation has been proposed to enhance the performance as in (14).
where, k 1 is a positive constant value and k 2 is set below or above the frequency threshold depending on PCC phase voltage during islanding. However, the value of k 1 has been specified for a constant P DG and Q f by trial and error. Therefore, it is not suitable for different loading quality factors. In both methods above, it is difficult to find optimum values for k 1 and k 2 to detect islanding for different DG rated powers. Also, in [25] with a high value for k 1 , which is equal 1000, the power quality might be degraded. If there is a reactive power mismatch between DG output and local loads, when islanding happens, the reactive power mismatch makes a change in the frequency of the PCC voltage. Therefore, after islanding, the frequency of PCC voltage is shifted to a new value, f PCC ′ . In that case, the inductive parameters of the load can be represented by L + ΔL and C + ΔC [30] as illustrated in Figure 3. Accordingly, the resonant frequency is modified as [30]: The ratio of resonant frequency without and with power mismatch can be expressed: For simplicity, ( ≈ 0), then (16) can be: On the other hand, equation (10) can be expressed as: Also (8) can be expressed as: With substitution (19) in (18): Similarly, it can be obtained: = Thus: The effect of resonant frequency on reactive power mismatch can be represented as: With substitution (22) in (23): Then, For simplicity, (1 + ∆ ≈ 1), and with substitution (25) in (17): Equation (26) can be rewritten as: The curve between the load reactive power and PCC frequency is approximately linear within the UOF thresholds. To formulate a linear relation between PCC frequency and DG reactive power reference, a new equation is proposed with the same parameters of equation (27) to deviate the PCC frequency after the grid disconnection as in (28).
where, 1 = − ( − ) 2 and 2 = Also, equation (28) should be modified in such that the DG reactive power reference is equal to the pre-set original reactive power reference during the grid connected mode as in (29): Using equation (29), the PCC frequency will be deviated outside the UOF thresholds after grid disconnection even if there is no active/reactive power mismatch between the load and DG. Therefore, zero non-detection zone is achievable (NDZ =0) when islanding occurs. Also, the proposed reactive power reference equation is a function of the grid parameters, UOF thresholds, and loading quality factor. Thus, the proposed islanding detection method enables to detect islanding for any value of PCC frequency and no need for trial and error to choose Q f . Since f res−modified can be set based on upper and lower limits of UOF relay, equation (29) is split into two equations. When the PCC frequency is below the grid frequency, f res−modified is set at the upper threshold of UOF relay, whereas for PCC frequency equal or above the grid frequency, it is set at the lower threshold of UOF relay. The DG reactive power reference at upper limit of UOF is called Q ref−upper and for the lower limit is Q ref−lower . The proposed reactive power reference equation's slope is design to provide a higher negative slope than the load curve. Therefore, after islanding, when the PCC frequency is below the grid frequency, the reactive power reference value (equation (29)) is more than the reactive power of the load.
In that case, the PCC frequency moves toward the lower value in order to increase the load's reactive power. Then, the PCC frequency is drifted beyond the lower threshold and islanding can be detected smoothly. Correspondingly, when the PCC frequency is above the grid frequency, the reactive power reference value is less than the load reactive power.
The PCC frequency has to move toward the upper value in order to draw the load's reactive power toward the reference reactive power. This result in that the PCC frequency is pushed to be more than the upper threshold and finally islanding is detected. Figure 4 is the flowchart of the proposed islanding method.

V. PERFORMANCE AND SIMULATION RESULTS OF THE PROPOSED ISLANDING DETECTION METHOD
In this section, several cases are designed and modelled by using MATLAB/SIMULINK software to utilize the system shown in Figure 1. The grid and DG parameters are presented in Table 1. An island event is formed at t = 0.5 s, and the PCC frequency is 50 Hz before islanding. Equation (29) is used to calculate the upper and lower limits of the DG reactive power reference as in (30) and (31).
where, = . based on IEEE Std. 929-2000 [33], and − is set at the upper or lower limits of the frequency thresholds, which are 50.5 Hz and 49.3 Hz, respectively.

A. PROPOSED ISLANDING DETECTION METHOD PERFORMANCE WITH DIFFERENT and
In order to comprehensively validate the proposed islanding detection method, several loading quality factors with different reactive power references are included. Also, the impact of PCC frequency variation after islanding, when it is close or equal to the grid frequency (the most difficult case) is tested. The simulated cases parameters at unity and non-unity power factors are shown in Table 2.  Figure 5 parts (a), (b), and (c) show the PCC frequency response, which is set at 49.8 Hz, 50 Hz, and 50.2 Hz respectively after islanding. Each case is tested at different four loading quality factors, while the DG operates with unity power factor. Figure 5 (a) illustrates that after the grid disconnection, the PCC frequency (f PCC = 49.8 Hz) is less than the grid frequency, and the value of load reactive power is less than the proposed reactive power reference value. Thus, the frequency will decrease to increase the load's reactive power. The PCC frequency is finally drifting beyond the UOF threshold and islanding is detected. Figure 5 (b) presents the most difficult case, when the mismatch of active and reactive powers between load and DG is zero. For the loading quality factors equal 1, the PCC frequency is deviated beyond the upper threshold. In that case, after the grid disconnection, the proposed islanding detection method draws the PCC frequency to the upper threshold. With increasing the loading quality factor to 2.5, 3.5, and 4.5, the PCC frequency is deviated outside the lower frequency threshold. It is due to a small variation of PCC frequency toward the frequency below 50 Hz after the grid disconnection. For higher loading quality factors, the slope of load curve is increased, and approaches to the proposed method's slop curve. This increases the detection time. In Figure 5 (c), after the grid disconnection, the PCC frequency (f PCC = 50.2 Hz) is more than the grid frequency and the value of load reactive power is more than the proposed reactive power reference value. As a result, the frequency will increase to decrease the load's reactive power. The PCC frequency is finally drifting beyond the upper threshold and islanding is detected. In order to test the proposed islanding detection method for other operating conditions, Figure 6 shows the frequency response when the DG operation is set with non-unity power factor (Q ref−original = 10 kVAr). The load parameters are adjusted in such that the mismatch of active and reactive powers is almost zero as shown in Table 2. The PCC frequencies are selected to make around zero power mismatch condition after islanding for different loading quality factors. In that case, the PCC frequency drops below 50 Hz after the grid disconnection. Then, the proposed detection method forces the PCC frequency to move towards to the lower thresholds until islanding is detected.  Table 3 shows the detection time of the proposed islanding detection method compared to conventional methods [19], [25] and [26] for all cases in Figure 5 and Figure 6. It confirms that the detection time for all cases is faster than the required detection time (2 s) as recommended by IEEE Std. 929-2000 [33]. It shows also that the most rapid detection time is achieved when the PCC frequency is above the grid frequency. It is due to the less difference between the upper frequency threshold (50.5 Hz) and the grid frequency (50 Hz) compared with the lower frequency threshold (49.3 Hz). The islanding detection method in [19] fails to detect islanding when the PCC frequency is set at 49.8 Hz or 50.2 Hz for after islanding and loading quality factor is above 1. Also, it fails to detect islanding when the PCC frequency is set at 50 Hz with unity power factor or DG is working with non-unity power factor. It is due to a higher slope for the load curve, when the loading quality factor rises. In that case, the presented reactive power reference curve in [19] does not have high slope enough compared with the load to deviate PCC frequency after the grid disconnection. It is getting worse for zero power mismatch conditions. Also, as previously mentioned, k 2 in reactive power reference [19] is not updated. In [25], the islanding detection method can detect the islanding. However, parameter k 1 has been set with a constant value without any relation to the loading quality factor or the rated active power of DG. Thus, for different loading quality factors, particularly for the higher of them, the detection time becomes longer. The islanding detection method in [26] is able to detect islanding for all cases, but the detection time is longer than the proposed method. The parameters of reactive power reference [26] were set based on Q f = 2.5. Therefore, with changing the loading quality factor, the setting of reactive power reference is changed. It makes the detection time longer. Therefore, the proposed Q-f droop curve method has better results, particularly for the higher loading quality factors compared with [19], [25] and [26].

B. PROPOSED ISLANDING DETECTION METHOD PERFORMANCE WITH UNBALANCED LOADS
To test the effect of unbalanced loading on the proposed islanding detection method, two phases of the load resistance are set at 115 kW (R a = R b = 1.39 Ω), whereas the third phase is set at 100 kW (R c = 1.6 Ω). The unbalanced load is considered for both unity and non-unity power factors of DG operation. Also, it is simulated for the most difficult cases, when the PCC frequency after islanding is equal 50 Hz as shown in Table 4.  Figure 7 shows that the proposed islanding detection method is able to detect islanding for both unity and non-unity power factor of DG operation with almost zero power mismatch. The PCC frequency measured for after islanding with different values of loading quality factors is deviated toward below threshold of frequency. Also, it shows that with increasing the loading quality factors, the detection time becomes longer. It is due to the slope of load curve rising for higher loading quality factors and approaching to the proposed method's slop curve.   Table 5 shows the detection time of the proposed islanding detection method for unbalanced loading compared to conventional methods [19], [25] and [26]. It confirms that the detection time for all cases is faster than the required detection by IEEE Std. 929-2000 [33]. The islanding detection method in [19], when the PCC frequency is set at 50 Hz for unbalanced load during islanding, it is not able to detect islanding. Also, for DG operation with non-unity power factor and unbalanced load conditions, it is only able to detect islanding, when loading quality factor is equal to 1. Similar to the previous part, for zero power mismatch the presented method in [19] is not able to detect islanding. In the other word, after islanding, PCC frequency deviation is not big enough to be moved beyond the UOF threshold. It is due to improper setting of k 1 and k 2 for reactive power reference presented in [19]. In [25], the detection time is longer than the proposed method's detection time. As previously mentioned, the parameters in this method has been set for the loading quality factor equal 1. Thus, with increasing the loading quality factor, the detection time is increased. The islanding detection method in [26] is able to detect islanding for all cases, however its detection time is longer than the proposed method. Similar to the previous part, the proposed Q-f droop curve method has faster islanding detection without any fail, when a DG operates with both unity and non-unity power factor under the unbalanced load conditions. It is one of the main significant advantages of proposed method, particularly for the higher loading quality factors compared with [19], [25] and [26].

C. PROPOSED ISLANDING DETECTION METHOD PERFORMANCE WITH MOTOR LOAD
As realistic loads, such as motors constitute a substantial portion of the distribution system [32], the performance of the proposed islanding detection method is tested with an induction motor and resistance load as shown in Figure 8. The proposed method should be able to recognize between islanding detection and motor starting to avoid any unnecessary disconnection from the grid. Also, the proposed method must be capable to disconnect a dynamic load, such as motor from the DG, when islanding occurs. The motor's torque is set at full load mode. The parameters of motor load chosen for the simulation are listed in Table 6.  Four cases are simulated. As shown in Figure 9 (a) in two cases, the load resistance power is set at 80 kW. In those two cases, the motor is in steady state condition or the motor is in transient (starting time is set at 0.49 s, which is 0.01 s before the grid disconnection). Also, Figure 9 (b) illustrates two cases, when the load resistance power is set at 100 kW and the motor conditions is as similar as the aforementioned conditions.
(a) (b) In Figure 9 (a), after the grid disconnection, when the resistance load and motor starting time is as the same, PCC frequency is deviated above the upper threshold limit, when islanding occurs. It is due to the bigger value of DG rated active power (100 kW) compared to resistance and motor load active power. Therefore, the PCC voltage rises. When the motor starting time is very close to the grid disconnection time, the motor inrush current makes a voltage dip at the PCC voltage. Therefore, PCC frequency is deviated at the longer time. In Figure 9 (b), during the grid disconnection, when the resistance load and motor starting time is as the same, PCC frequency is deviated under the lower threshold limit. It is due to the smaller value of DG rated active power compared to resistance and motor load active power. Therefore, the PCC voltage drops. When the motor starting time is very close to the grid disconnection time, the motor inrush current is added to the PCC voltage reduction and it causes a shorter VOLUME XX, 2017 9 detection time. Table 7 shows the detection times for Figure  9.

D. PROPOSED ISLANDING DETECTION METHOD PERFORMANCE IN LOAD SWITCHING CONDITIONS
In this section, the proposed islanding detection method is tested under load switching conditions. The proposed method should be able to maintain PCC voltage and frequency within permissible limit during load switching and avoidance any inessential disconnection from the grid. An additional load is added to the circuit presented in Figure 1.
The additional load is switched on at t = 0.5 s then turned off at t=1 s. The response of PCC voltage and frequency are investigated for four loading cases as presented in Table 8. For all additional load cases, DG is operating with active rated power (100 kW) and loading quality factor equal 2.5 during grid connection. As presented in Figure 10, voltage and frequency are deviated, when the additional load is switched on and off within the UOV/UOF thresholds, whereas before and after switching the voltage and frequency operate at their rated values. Therefore, the proposed islanding method during load switching does not impact on the power system performance during normal conditions.

E. PROPOSED ISLANDING DETECTION METHOD PERFORMANCE IN MULTIPLE DGs CONNECTION
The proposed islanding detection method is further tested for multiple DGs connection. The proposed method should be able to show its ability for islanding detection for multiple DGs connection with negligible effect on the power quality. Figure 11 shows multiple DGs connection to the grid with their respective local loads. As it shows, when circuit breaker 1 is close and circuit breaker 2 is open, DG1 and DG2 with their relative local loads are connected to the grid. When both circuit breaker 1 and circuit breaker 2 are close three DGs and their loads are connected to the grid with underground cable. Each DG operates at unity power factor with rated active power equal to 100 kW. The values of load parameters are set based on loading quality factor equal of 2.5 with operation at 50 Hz, and underground cable parameters is set based on 200 m length. The loads and cable parameters are illustrated in Table 9 and Table 10 respectively.  Figure 12 (a) illustrates the PCC frequencies at PCC1 and PCC2 for two DGs connection. Figure 12 (a) confirms the islanding is properly detectable for both DGs. Also, Figure  12 (b) presents PCC frequencies at PCC1, PCC2 and PCC3 for three DGs connection. Figure 12 shows that proposed islanding method is able to detect islanding in each of the abovementioned conditions at the same time with a negligible difference regardless the cable connection between DGs. This means that there is a synchronization in islanding detection between multiple DGs connection. It is worth noting that multiple DGs connection is tested for the most difficult case, when the resonant frequency is same as the grid frequency for all loads with zero power mismatch. In case of presence a power mismatch between the load and DG, the detection time is shorter than the tested conditions in this study. Therefore, the proposed islanding detection method is able to detect islanding effectively and rapidly for multiple DGs which are located in a distance from each other in a microgrid with a negligible impact on power quality during grid connection. The detection time for two and three DGs is tabulated in Table 11.

A. PROPOSED ISLANDING DETECTION METHOD PERFORMANCE WITH DIFFERENT
In this subsection, the proposed islanding detection method is tested under different loading quality factors. The experimental setup parameters are listed in Table 12. Figure  13 shows the experimental setup of the circuit. As shown in Table 12, the inductive and capacitive reactance of the load have been set in such that the reactive power of the load is equal zero. Also, the DG operation has been considered with unity power factor, thus the reactive power mismatch between the load and DG is zero (∆Q = 0). Also, the load resistance is set so as the load active power is equal to DG rated active power, therefore active power mismatch is zero as well (∆P = 0). These conditions are considered for different loading quality factors as the most difficult cases.   Figure 14 shows the performance of experimental circuit, when loading quality factor is set at 1. In this case, active and reactive power mismatch between the load and DG are zero, also the resonant frequency is 50 Hz at the instant of the grid disconnection. As illustrated in Figure 14, the proposed islanding detection method is able to detect the islanding in105 ms for the most difficult case. However, the presented method in [19] fails to detect the islanding as shown in Figure 15. Figure 16 depicts the frequency response of the proposed islanding detection method at different loading quality factors. As it shows the proposed islanding detection method succeeds to detect the islanding under different loading quality factors. The detection time for different loading quality factors is given in Table 13.

B. PROPOSED ISLANDING DETECTION METHOD PERFORMANCE WITH MOTOR LOAD
In this subsection, the performance of the proposed islanding detection method is experimentally evaluated with an induction motor load, which is parallel with a resistance load. The experimental setup is illustrated in Figure 17. Also, the load parameters are shown in Table 14. During this test, the input power of induction motor has been set at 345 W. The power of the load resistance is adjusted at 450 W during case 1, and 530 W during case 2. Also, the DG active power is set at 845 W.   Figure 18 shows the frequency response, when the total load powers including induction motor and the resistance load in case 1 are less than the DG active power. In that case, the PCC frequency rises after the grid disconnection. Therefore, the proposed islanding detection method accelerates the PCC frequency to move up beyond the upper UOF threshold until islanding is detected within 70 ms. Figure 19 shows the frequency response, when the total load powers including induction motor and the resistance load in case 2 are more than the DG active power. It means that the PCC frequency drops after the grid disconnection. As a result, the proposed islanding detection method forces the PCC frequency to move down beyond the lower UOF threshold for islanding detection in a very short time, which is 60 ms.

V. CONCLUSION
A modified Q-f droop curve method for islanding detection has been proposed in this paper. The proposed method has been designed such that the inverter-based DG maintains its stable operation during grid-connected, whereas it is unstable when an islanding occurs. The design of proposed method is based on the grid frequency, UOF thresholds, loading quality factor and rated active power of DG, which are easily available. Thus, the proposed method enables to be implemented for any DG and grid frequency values without a need for trial and error to choose the system parameters. An UOF relay is sufficient to detect efficiently and rapidly islanding using the proposed method, which reduces the complexity of the detection method. The proposed method has zero NDZ for a wide range of loading quality factors and zero power mismatch between the load and DG. In addition, it has the capability of maintaining stable operation under unbalanced load and load switching conditions. There is no degradation with multiple DGs equipped to the proposed method on the islanding.