Harmonic Dual-Setting Directional Overcurrent Protection for Inverter-Based Islanded Microgrids

Limited fault currents in inverter-interfaced islanded microgrids impose immense challenges on conventional overcurrent protection schemes. This paper proposes a sensitive and selective protection scheme for islanded microgrids using a third harmonic voltage generated by inverter-interfaced distributed generators (IIDGs). The generated harmonic voltage results in a harmonic layer formed during short-circuit faults and is decoupled from the fundamental fault current, i.e., limited by IIDGs. Further, the generated harmonic voltage is adaptively adjusted based on fault severity to enhance protection sensitivity and obtain a universal set of relays’ settings. The proposed protection scheme utilizes harmonic directional overcurrent relays (HDOCRs) equipped with a dual-setting time-current-voltage setting that sense the generated harmonic voltages and currents at the relay location to ensure optimal protection coordination (OPC) of islanded microgrids. The OPC with the proposed dual-setting is formulated as a constrained nonlinear program to determine the optimal forward and reverse relays’ settings. The proposed scheme is tested on the Canadian benchmark urban distribution system and compared to the conventional protection scheme, which relies only on a single time-current-voltage trip characteristic. The results ensure the ability of the proposed scheme to protect islanded microgrids without communication and its capability to reduce relays’ operation times.


I. INTRODUCTION
Integration of distributed generators (DGs) into distribution networks results in active distribution networks characterized by bidirectional power flow and can evolve into microgrids. Islanded microgrids powered by synchronous generators have higher fault current levels than those powered by inverter-interfaced DGs (IIDGs), which limit their output currents to 150% of the inverter's rated current [1]. These low fault currents have an adverse impact on the available protection devices, such as overcurrent relays and render their coordination troublesome or infeasible [2], [3]. Moreover, the The associate editor coordinating the review of this manuscript and approving it for publication was Qiang Li . IIDG controllers adversely impact the existing commercial directional elements [3]. Thus, a reliable relaying scheme is required.
Numerous non-communication methods are proposed to tackle inverter-interfaced islanded microgrid protection challenges. Faults in islanded microgrids are detected by monitoring the inverter's current transient response [4]. In [5], faults are detected and classified based on a data-mining decision tree created using wavelet transform and the extracted features from sequence and phase currents. Reference [6] proposes a digital protection scheme that detects faults based on the transient wavelet energy of the superimposed current using a wavelet transform algorithm. However, the proposed method requires communication. The study in [7] utilizes negative-sequence components to achieve protection coordination based on a definite-time grading method to protect islanded microgrids. Nonetheless, unbalanced loading conditions may challenge the negative-sequence-based protection schemes. An overcurrent protection scheme equipped with dual-setting time-current-voltage directional overcurrent relays (DOCRs) for distribution systems powered by DGs is suggested [8]. Despite the scheme's capability to handle reverse DG fault currents, it considers only synchronousbased DGs. The authors of [9] propose to increase the IIDGs fault currents by integrating supercapacitors to obtain a single set of relays' settings for grid-connected and islanded modes. However, supercapacitors introduce an extra cost. Virtual impedance-fault current limiters are employed in the IIDG control scheme to protect inverter switches from overcurrent and achieve protection coordination [10]. An overcurrent protection scheme for microgrids is proposed in [11] utilizing a non-standard trip characteristic.
Communication-assisted protection schemes have also been proposed to address microgrid protection challenges [12], [13], [14]. In [12], a protection scheme based on mathematical morphology is proposed in which faults are detected utilizing current traveling waves. The travelingwave-based protection schemes are immune against fault current levels but require high-frequency instrument transformers. An adaptive directional overcurrent relay is proposed for microgrid protection in [13], utilizing the superimposed positive and negative-sequence components. However, the relay's pickup current has to be accurately set to avoid nuisance tripping. A protection scheme is proposed in [14], where two sets of relay settings are obtained based on network configuration to ensure proper coordination. Differentialbased protection schemes are also suggested using the difference in negative-sequence impedance angle [15], power flow [16], relays' output binary state [17], and measured impedance [18]. The methods in [15], [16], [17], and [18] require communication infrastructure often unavailable in microgrids, comes with an extra cost, and may suffer from latency.
The flexibility of the IIDG controllers makes them a venue for recent research to fulfill different protection objectives [19], [20], [21], [22]. These studies employ the IIDG controller to inject harmonics to assist in islanded microgrids protection. In [19], the IIDG controller injects a fifth harmonic used for fault detection. A droop impedance is used to limit the fundamental fault current to enable the coordination of upstream and downstream relays in a radial islanded microgrid. However, existing commercial relays may indicate incorrect fault directions [2], [3]. Moreover, [19] does not consider bidirectional fault currents. The study in [20] proposes a protection scheme for islanded microgrids that utilize harmonic-DOCRs (HDOCRs). The IIDG control scheme is modified to include a function that makes the IIDG injects an n th order harmonic current synthesized by the respective HDOCRs. The HDOCRs measure the injected harmonic currents at different locations, which are employed to attain protection coordination. However, the harmonic-based method of [20] utilized time-domain simulations to achieve protection coordination. Using simulations to solve for the system's steady-state values is time-consuming, computationally expensive, and limited to relatively small test systems. Reference [21] proposed utilizing the IIDG controllers to inject a pattern of three synthetic harmonics. A directioncomparison protection scheme is then designed based on the cosine similarity. However, the pattern injection settings need updating under network contingencies. A harmonic-based protection scheme is proposed in [22], in which a harmonic function is added to the IIDGs controllers to generate a synthetic harmonic voltage in the event of faults. The resulting harmonic voltages and currents are used to develop harmonic distance relays. Yet, studies [19], [20], [21], [22] employ time-domain simulations to obtain steady-state values for the short-circuit currents measured by the protective relays.
In [23] and following fault inception, the IIDG controller generates a constant third harmonic voltage, resulting in harmonic fault currents. The optimal protection coordination (OPC) of the developed HDOCRs is attained based on the locally measured harmonic voltages and currents. However, the constant harmonic voltage generation may result in fault currents being less than the relays' pickup current. Furthermore, using a single relay trip characteristic for forward and reverse fault directions may lead to higher relays' operation times.
This paper focuses on inverter-based islanded microgrids protection, which is challenging due to the low fault current levels. An OPC algorithm is developed based on an adaptive harmonic voltage generated by IIDGs, which makes microgrid protection independent of the limited fundamental current during faults. The paper's original contributions are summarized as follows: • Opposed to the constant harmonic voltage methods available in the literature, an adaptive characteristic is utilized to generate harmonic voltage to produce tangible fault current measurements for a broader range of fault resistances. Using adaptive harmonic voltage enhances protection sensitivity.
• A new OPC formulation involving a two-stage algorithm is developed for islanded microgrids. In the first stage, the algorithm evaluates various characteristics for harmonic voltage generation (i.e., linear, piecewise linear, and parabolic) to maximize the harmonic voltage, resulting in more tangible harmonic currents. In addition, the piecewise linear harmonic voltage characteristic further reduces the total relays' operation time.
• In the second stage, the harmonic voltages and currents are used to achieve protection coordination utilizing HDOCRs equipped with dual time-current-voltage characteristics. A wide range of fault resistances up to the maximum voltage sag defined by the IEEE Standard 1547 is simultaneously considered in the proposed OPC. Compared to the study, which adopts constant harmonic VOLUME 11, 2023 voltage generation, the dual-setting protection scheme significantly reduces the relays' total operation time (by up to 62.69%) and handles reverse fault currents without communication.
The low voltage ride-through (LVRT) is enforced on the fundamental layer, i.e., based on fundamental frequency voltages and currents. On the other hand, the proposed harmonic-based protection scheme is developed for the harmonic layer, which is decoupled from the fundamental layer; therefore, it is not impacted by the LVRT.

II. PROPOSED HARMONIC-BASED PROTECTION
This paper proposes a protection scheme that triggers a harmonic voltage generation at the inverter's terminals upon fault detection. Consequently, harmonic current flows from IIDGs to the fault location. The deliberately generated harmonic currents are decoupled from the fundamental currents. Further, the decoupled harmonic currents can be discriminated from load harmonic currents. Then, HDOCRs are utilized to measure the harmonic voltages and currents to achieve OPC for islanded microgrids.

A. IIDG CONTROLLER AND HARMONIC GENERATION CHARACTERISTIC
The modulation index, m, of the IIDG is augmented with a harmonic modulation index, m h , before being fed to the pulse width modulation (PWM) block, as illustrated by Fig. 1(a). m h determines the magnitude of the adaptive generated harmonic voltage at the inverter's terminals and h pertains to the order of the individual injected harmonic. An asterisk indicates the reference signals, and δ denotes the instantaneous angle of the system angular frequency ω.
As shown in Fig. 1(a), neither the magnitude nor the angle of the generated harmonic voltage is regulated by the IIDG droop controller [ Fig. 1(b)] or PQ controller [ Fig. 1(c)]. By setting the angular frequency, ω * , and magnitude of m h , two decoupled layers (i.e., fundamental and harmonic) are formed during faults. Therefore, the HDOCRs operate based on the measured harmonic currents that are not impacted by the IIDGs' limited fundamental current. On the other hand, the IIDG controller limits the inverter's current in the fundamental layer, resulting in a constant current source model for the IIDG.
Faults can be detected by monitoring the sag in the IIDG terminal voltage, the IIDG terminal voltage, the negative-sequence component of the terminal voltage, the zero-sequence current at the high-voltage side of the coupling transformer, changes in impedance at the inverter terminals, and the inverter current waveform transient response [4], [23]. Additionally, combinations of multiple methods have been investigated in the literature to ensure the reliability of fault detection [24], [25]. Fault detection is well-established in the literature and industry.
Upon fault detection, binary variables k a , k b , and k c are set at 1.0, activating the respective harmonic generation system as shown in Fig. 1. These variables switch to zero once the fault is cleared to deactivate the harmonic generation system. Therefore, the harmonic injection exists only during faults. HDOCRs are then coordinated based on the measured harmonic voltages and currents. It is worth mentioning that injected harmonics have a minor effect on power quality since the fault condition typically lasts for a short time. Other system applications, such as microgrid islanding detection, have employed limited harmonics injection for a short period of time [26]. The proposed harmonic generation system injects synthetic harmonics designed with a phase shift δ, as displayed in Fig. 1, which is different from load harmonics that have a phase shift of hδ. Further, while the load third-harmonics appear as zero-sequence components, their synthetic counterparts are positive-sequence components. Thus, the proposed HDOCRs can differentiate between load harmonics and generated harmonics.
Fault currents change based on fault severity, i.e., the fault resistance and location. Establishing a deliberate harmonic current flow during faults can be attained by a constant or adaptive harmonic voltage generation. However, the constant harmonic voltage may fail to produce sensible fault currents for a broader range of fault resistances, especially at the farthest point from the IIDG's terminals. This paper proposes a scheme that ensures reliable protection coordination for higher fault resistances in islanded microgrids. Employing an adaptive harmonic voltage generation produces higher harmonic fault currents for high resistive faults.
The harmonic voltage is adapted to faults such that its maximum and minimum magnitudes are generated during high resistive fault at the feeder end and bolted fault at the IIDG terminals, respectively. The sample microgrid displayed in Fig. 2 is considered to elaborate on the harmonic voltage generation. Fig. 3 depicts the equivalent circuit of the sample microgrid in the harmonic layer. In Fig. 3, v h 1 and v h 2 denote the generated harmonic voltages at the IIDGs' inverter terminals. Z h f , Z h tr , and Z h line are the filter's, transformer's, and line's impedances in the harmonic domain, respectively. The  superscript h indicates harmonic quantities. Fault F results in harmonic currents I h F 1 and I h F 2 . However, fault F may results in an unappreciable harmonic fault current measured by relay R 2 , considering a high resistive fault. In this case, I h F 2 is expected to be low because IIDG2 is far away from the fault location.
Fault severity can be inferred by sensing the voltage sag, V o , in the fundamental layer at the IIDG's terminals, i.e., where V min is the lowest normal IIDG output voltage and V f o denotes the IIDG output voltage during faults, which is lower than V min . V min is set at 0.88 per unit (pu) as recommended by the IEEE Standard 1547 [1]. V f o is obtained using PSCAD/EMTDC simulations. The extreme fault scenarios are bolted and high resistive faults at the IIDG's terminals and the farthest point from IIDG on the respective feeder, resulting in the maximum and minimum V o , respectively. Promoting higher harmonic voltage generation at the IIDG's terminals that adapt to fault severity leads to higher harmonic currents at high resistive faults. Three harmonic voltage characteristics are proposed (i.e., linear, piecewise linear, and quadratic), tested, and compared, as displayed in Fig. 4 and defined respectively by (2)-(4).
where |v h | is the generated harmonic voltage magnitude at the inverter's terminals. The slope, k 1 , of the linear characteristic is calculated using the endpoints representing the minimum, ⌊v h ⌋, and maximum,⌈v h ⌉, magnitudes of v h , respectively. Unlike the linear characteristic, the piecewise linear characteristic (3) represents four-line segments based on fault harshness, i.e., high, moderate-high, moderate-low, or severe, as indicated in Fig. 4. The slope for each line segment is calculated using its endpoints having the ordinates y 1 , y 2 , and y 3 . For example, the slope of the second segment is calculated using the points (0.2, y 1 ) and (0.5, y 2 ). The coefficients k 2 , k 3 , and k 4 are the quadratic characteristic coefficients. The boundaries of each characteristic are set such that v h is at its maximum value for the highest resistive fault and at its minimum value for bolted fault at the IIDG's terminals.
The main objective of the adaptive harmonic voltage generation is to maximize the generated voltage based on fault severity while maintaining the IIDG output current below or equal to its maximum allowable value, I max DG , i.e., 1.5 pu, according to [1]. Thus, an objective function is defined to maximize the sum of all generated harmonic voltages, V h , i.e., where m is the IIDG index, M is the total number of IIDGs, and v h mlr f is the individual IIDG's generated harmonic voltage due to a fault at location l involving fault resistance r f . L and R tot are the total numbers of fault locations and resistances, respectively. In this paper, faults at the near and far ends of lines are considered. Thus, the total number of fault locations, L, is twice the number of lines. On the other hand, the total number of fault resistances, R tot , is six, with values equal to 0.1 , 1 , 3 , 5 , 10 , and 15 . All characteristics are bounded by lower and upper bounds defined by Equality constraints are set at the endpoints of the adaptive quadratic characteristic by replacing V o in (4) with zero, which determines k 4 as and substituting V max o for V o in (4) as follows: Enforcing the equality constraints in (8) and (9) ensures that the generated harmonic voltage is between ⌊v h ⌋ and ⌈v h ⌉. In addition, k 2 and k 3 are bounded by lower and upper limits and optimized by the proposed OPC algorithm to obtain the minimum relays' operation times.
where lb and ub are the lower and upper bounds of k 2 and k 3 . The authors of [27] compared and applied several meta-heuristic techniques to the expansion planning problem. The extensive investigation in [27] concludes that the genetic algorithm (GA) outperforms other meta-heuristic methods in solving nonlinear problems, such as generation expansion planning. Furthermore, it exhibits superior performance compared to other meta-heuristic techniques in terms of execution time and accuracy. Hence, this paper employed the GA in MATLAB to optimize the piecewise linear and quadratic characteristics parameters and investigate its impact on relays' operation times. In other words, the GA is used to solve a subproblem and the main problem is the OPC which is solved using the interior-point algorithm.
Harmonic voltage generation at the inverter's terminals can be achieved by directly changing the harmonic modulation signals. The minimum generated voltage is adapted when a bolted fault is applied at the IIDG's terminals, such that the amplitude of the peak output current does not exceed I max DG to protect the inverter's switches from excessive current. Further, the fundamental current is limited by the current limiter in the current control loop. Thus, the constraints imposed on the lowest injected harmonic current, I h low , can be established by where I fund sat is the saturated fundamental fault current, set at 1.2 pu. IIDG's fault current contribution is typically limited to 150% of its rated current [2]. Setting the fundamental current at 120% leaves a room of 30% for the harmonic current generation during bolted faults. The maximum generated voltage is adjusted when a high fault resistance, R ′ flt , is applied at the farthest point from the IIDG's terminals such that it results in the highest harmonic fault current, I h high . The IIDGs operate near their nominal current at high resistive faults, allowing 50% room for the harmonic current. Therefore, ⌈v h ⌉ can be approximated by where Z feed is the impedance between the IIDG's terminals and the farthest point on the feeder. R ′ flt is network-dependent and is obtained using PSCAD/EMTDC simulations. The fault resistance is increased in incremental steps to attain the minimum voltage sag V o , which is calculated as in (1). The fault resistance that has resulted in the minimum V o is R ′ flt = 15 .

B. TRIP CHARACTERISTICS OF HDOCRs
Typically, overcurrent protection schemes adopt the inversetime-current (ITC) characteristic, according to the IEC standard 60255-151 [29]. Applying the standard ITC for the HDOCR results in a harmonic ITC (HITC) characteristic defined by where TDS r and I h pr are the time dial setting and the harmonic pickup current for relay r, respectively. I h flr denotes the harmonic fault current measured by relay r for a fault location l. t lr is the operation time of relay r for a fault location l. A and B are constants that determine the HDOCR characteristic. Assuming the standard ITC characteristic, the constants A and B are 0.14 and 0.02, respectively. The authors of [29] proposed a time-current-voltage (TCV) characteristic to enhance the relays' operation times, employing fundamental currents. Therefore, to enhance the operation time of HDOCR, the TCV characteristic is implemented in the harmonic layer. The operation time for the harmonic TCV (HTCV) characteristic can be obtained as where v h flr is the harmonic fault phase voltage measured by relay r for a fault location l and K is a constant parameter.

C. THE HARMONIC DIRECTIONAL ELEMENT
The HDOCRs measure harmonic fault voltages and currents; therefore, they can identify the fault's current direction [22]. The directional element can be implemented using where T h r is the developed torque by relay r. δ h vr and δ h Ir pertain to the phase angles of the relay's measured harmonic voltage and current, respectively, and δ h Z denotes the angle of the harmonic impedance of the protected line. The relay's harmonic torque angle is represented by δ h r . The harmonic directional element logic is given by The harmonic directional element is utilized along with the harmonic voltages and currents measured by HDOCRs to implement the proposed protection scheme.

III. HARMONIC SHORT-CIRCUIT CALCULATIONS
As a prerequisite step, short-circuit current calculations (SCC) should be performed for OPC. This paper adopts the modified nodal method (MNM) initially proposed in [30] and applied by [22] as an SCC method. The MNM is selected due to its superior computational capabilities that offer flexible modeling of all system components and handling different system topologies. Further, the MNM has an outstanding performance compared to the backward-forward sweep and current injection methods used to solve the power flow problem in distribution networks [31].
The SCC method developed in [21] is employed and denoted in this paper by the harmonic short-circuit current calculation (HSCC) method. The bus admittance matrix is a function of the harmonic order and models the microgrid buses, including virtual fault buses. The relationship between voltages and currents in the HSCC is given by where Y h N is the harmonic bus admittance matrix neglecting the harmonic voltage sources' contributions. N denotes the total number of system buses, including the virtual fault locations and the IIDGs' internal buses. u is the total number of components that are not included in Y h N . V h N and I h u comprise the unknown bus harmonic voltages and the unknown harmonic currents, respectively. V h u and I h N define the magnitudes of the known independent harmonic voltages and the known injected harmonic currents, respectively. The matrices B 1 and B 2 are determined by the voltage sources and their connection to system buses. B 1 is a binary matrix with an element equal to zero if the respective element of I h u is not related to the corresponding nodal equation and 1.0 otherwise. B 2 is also a binary matrix with elements equal to 1.0 only if the corresponding elements of V h N and V h u are equal. B 3 is a square matrix defined by source type (i.e., dependent or independent).
Since IIDGs generate only harmonic voltages, (18) can be rewritten as u defines the number of independent harmonic voltage sources regulated by IIDGs. 0 N and 0 u are columns with N zeros and u × u matrix with all its elements equal to zero, respectively. The off-diagonal elements of Y h N are calculated as z h ij denotes line ij impedance (i.e., between buses i and j) and is calculated by where R ij and L ij are the resistance and inductance of line ij, respectively. The diagonal elements of Y h N are given by Then, the harmonic fault current is obtained using the nodal harmonic voltages during the fault: where v h fi and v h fj are the harmonic voltages of buses i and j during a fault, respectively.

IV. PROPOSED PROTECTION COORDINATION
This section explains the proposed OPC problem formulation and provides a description of the OPC program.

A. OPC PROBLEM FORMULATION
In contrast to the conventional directional relays, which operate only in a forward direction, the dual-setting directional relays can operate in both forward and reverse directions utilizing two different settings. This paper proposes an HDOCR equipped with a dual-setting TCV characteristic for islanded microgrid overcurrent protection to enhance the relays' total operation time. The operation times of the dual-setting HDOCR are defined as where t lr,fwd , TDS r,fwd , and K r,fwd pertain to the relay operation time for a fault location l, time dial setting, and constant parameter for the forward operation, respectively. Likewise, t lr,rev , TDS r,rev , and K r,rev are the relay operation time for a fault location l, time dial setting, and constant parameter for the reverse operation, respectively. The main aim of protection coordination is to minimize the HDOCRs' total operation time while satisfying the coordination constraints. Thus, the objective function is defined as follows: lr,fwd + t b k lr,rev ))) (28) VOLUME 11, 2023 where l is the fault location with a total number of L locations, and r is the relay identifier with R as the total number of relays. p and b k denote the primary and the k th backup relay, respectively. t p lr,fwd , t b k lr,fwd , t p lr,rev , and t b k lr,rev are computed for each relay r, employing the harmonic fault voltages and currents calculated using the HSCC.
The OPC program considers a set of constraints to be satisfied to ensure a feasible solution for the forward and reverse operation of every HDOCR. For the HDOCRs coordination purposes, the relay settings and coordination constraints should be included in the OPC program. The constraints imposed on the relay settings are TDS min ≤ TDS r,fwd , TDS r,rev ≤ TDS max ∀r (29) where TDS min and TDS max denote the lower and upper bounds of TDS r,fwd and TDS r,rev , respectively, with values set at 0.01 and 1.0. K min and K max are the minimum and maximum values for K r,fwd and K r,rev , respectively. K min and K max are equal to 0 and 4.0, respectively. TDS min and TDS max are selected as 0.01 and 1.0 such that the relay's operation time is neither equal to zero nor a magnified value. Whereas K min is set at zero such that the exponent function in (26) and (27) is equal to 1.0 (i.e., reverting to the ITC trip characteristic). The OPC is solved using a wide range of values for K max up to 10. However, the values of K max , which are greater than 4.0, resulted in infeasible solutions. Hence, K max is set at 4.0.
A minimum coordination time interval (CTI) should be maintained between the operation of primary and backup relays. CTI is set at 0.2 s as recommended by the IEEE Standard 242-2001. Hence, the CTI constraints are formulated as follows: The IEEE Standard 519 mandates a maximum harmonic current distortion of 0.04 pu for harmonic orders 3-11 during normal operation. Further, the accuracy of CT measurements is guaranteed if the measured currents are equal to or above 0.05 pu [32]. Hence, to distinguish the generated harmonics and guarantee accurate measurements, the pickup current of the HDOCR is selected to have a value of 0.1 pu. Finally, a constraint on the minimum relay operation time is enforced through the following constraint: t p lr,fwd , t b k lr,fwd ≥ t min ∀r t p lr,rev , t b k lr,rev ≥ t min ∀r (32) where t min is the minimum relay operation time set to 20 ms [33].

B. OPC PROGRAM
The algorithm starts by building the bus admittance matrix Y h N , which includes the fault location as a virtual bus and is formulated for each fault location. The OPC program enfolds two stages, as illustrated by the flow chart depicted in Fig. 5. The first stage aims at maximizing the generated harmonic voltage to promote higher harmonic currents at high fault resistances. In Stage I, the harmonic adaptive linear characteristic is employed. Then, the GA available in the MATLAB optimization toolbox is used to obtain optimized values for the adaptive characteristic coefficients (i.e., piecewise linear and quadratic) starting with an initial guess. Then, the HSCC is employed to obtain bus voltages during faults for several fault resistances utilizing the optimized harmonic generation characteristic. Next, the bus voltages obtained are used to calculate the lines' short-circuit currents. Finally, the harmonic short-circuit currents and voltages are mapped to their respective relays.
The harmonic short-circuit currents and voltages are used in Stage II, employing the interior-point algorithm to obtain the optimal relays' settings TDS fwd , TDS rev , K fwd , and K rev that guarantee OPC. Next, the total operation times for fault conditions are computed. The procedure is repeated until there is no significant change in the relays' total operation times (i.e., maximum iterations). The nonlinear constraints formulated using the harmonic short-circuit currents and voltages resulting from involving several fault resistances are considered simultaneously in the solution. The solution obtained results in a single relays' settings that guarantee optimal coordination under all fault scenarios. The OPC program was executed using a computer with a Core-i7, 2.3-GHz processor, and 16-GB RAM. The proposed OPC program can approach an optimal relays' settings in 20.16 s for the piecewise linear characteristic compared to 9.06 s for the quadratic characteristic.
The protection coordination requires calculating the shortcircuit currents and solving the OPC optimization problem, which are done offline; therefore, the processing time is not a priority. The HDOCR operates when it measures a fault current that exceeds its pickup current (i.e., 0.1 pu). Moreover, since the proposed harmonic-based protection scheme is communication-free, it is designed with that in mind by solving the OPC problem for a wide range of fault resistances simultaneously (0. 1 -15 ). This results in a universal set of dual relays' settings that work with all fault scenarios on the microgrid (i.e., the relays' settings are not updated online). Further, the total IIDGs rating is 1.25 times the microgrid load. Thus, the relays' settings are tuned once and do not need an update unless the microgrid demand approaches the total generation.

V. PERFORMANCE EVALUATION A. TEST SYSTEM
The performance of the proposed protection scheme is assessed on the microgrid displayed in Fig. 6. The microgrid is a part of the Canadian urban benchmark distribution system [34]. The IIDGs are connected to the test microgrid via 2.5-MVA and 3.5-MVA, 480 V/12.47 kV, dYG transformers with Z t = 0.0012 + j0.05 pu. Faults (F 1 -F 16 ) at the near and far ends are marked as indicated in Fig. 6. Each line hosts two primary relays due to the bidirectional power flow. As a result, 16 HDOCRs are used for overcurrent protection.
It is worth noting that Relays R 8 and R 16 are equipped with only forward trip characteristics because they provide protection against fault currents contribution by the respective IIDG (i.e., unidirectional power flow).

B. THE HARMONIC LAYER MEASUREMENTS
The islanded microgrid in Fig. 6 is simulated using PSCAD/EMTDC, and a bolted fault at F 10 is considered to demonstrate the operation of the proposed protection scheme. The fault is detected by monitoring the change in the IIDG output voltage. IIDGs reduce their output voltages upon fault  inception to limit their output currents. As a consequence, a severe network-wide voltage sag dominates in the microgrid. A harmonic voltage is superimposed on the faulted phase once a voltage sag below 0.88 pu is detected at the IIDG's terminals. Fig. 7(a) displays the IIDG1 output current during F 10 . This current enfolds a 3 rd harmonic component excited by the superimposed 3 rd harmonic voltage and a fundamental component. A fast Fourier transform (FFT) is used to extract the positive-sequence 3 rd harmonic current, depicted in Fig. 7(b). The IIDGs' harmonic fault currents flow towards the fault at F 10 . As a result, the harmonic current measured by R 4 is the sum of IIDG1's and IIDG2's injected harmonic currents, as demonstrated in Fig. 8. Another fault scenario at F 1 is considered to illustrate the sensitivity of the proposed protection scheme to a high resistive fault (R ′ flt = 15 ). Fig. 9 shows the 3 rd harmonic current measured by the primary relay R 1 . The harmonic torque angles of R 2 and R 3 are displayed in Fig. 10. The relays R 2 and R 3 identify a forward and a reverse fault, respectively, as noted by the angles in Fig. 10. Since the harmonic pickup current is exceeded for F 1 , relays R 4 , R 6 , and R 8 are triggered due to the identification of VOLUME 11, 2023 34637 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.    a forward fault. Therefore, R 1 and R 2 are designed to have the fastest operation times for a fault at their primary protection zone.
A case study is conducted to assess the performance of the proposed method under asymmetrical faults. Singleline-to-ground (SLG), line-to-line (LL), and double-line-toground (DLG) are applied with bolted fault at F 1 to illustrate the capability of the proposed harmonic voltage generation method in producing tangible harmonic currents during unbalanced faults. Fig. 11 displays the harmonic fault currents measured by R 1 during bolted SLG, LL, DLG, and balanced faults at F 1 , respectively. The harmonic fault current in the faulted phases exceeds the pickup current (i.e., 0.1 pu). Hence, the proposed protection scheme can deal with all fault types.
C. OPC USING CONSTANT AND ADAPTIVE HARMONIC VOLTAGE GENERATION Fig. 12 compares the relays' total operation times for constant and adaptive harmonic voltage generation considering relays equipped with only the forward trip characteristic. First, the OPC is solved using constant harmonic voltage generation [21], optimized for faults with zero resistance and up to the highest fault resistance (R ′ flt ). Although the OPC is feasible in all fault scenarios, the relays' total operation times have high values, as noted by the dark bars in Fig. 12. Then, the OPC is solved by employing a linear adaptive   harmonic voltage generation optimized for bolted to the highest resistance faults. The results in Fig. 12 reveal that the adaptive harmonic protection scheme has two advantages: (i) a significant reduction of up to 62.69% in the relays' total operation time, and (ii) OPC feasibility up to R ′ flt . Table 1 displays the optimal settings of TDS and K obtained for all HDOCRs of the test microgrid by solving the OPC problem utilizing constant and adaptive harmonic voltages. The solution leads to different optimal settings.   Table 2 reports the relays' total operation times adopting different adaptive v h characteristics and the dual-setting. Testing various adaptive v h characteristics aims to obtain the minimum relays' total operation times. The results demonstrate that optimized characteristic coefficients further reduce the total relays' operation time compared to the linear characteristic. The minimum relays' total operation times for high resistive faults are obtained using the piecewise linear characteristic. The optimal dual-setting obtained achieved OPC for bolted faults and up to 15 fault resistance. Furthermore, Table 2 displays the total operation times, which reflects the sum of operation times for the individual primary and backup relays in both directions (i.e., forward and reverse). In contrast, Fig. 12 displays the total operation times representing the sum of the individual primary and backup relays' operation times in the forward direction. Table 3 lists the relays' optimal settings for forward and reverse fault directions obtained from solving the OPC problem employing the piecewise linear characteristic. The relay's optimal settings, along with the calculated harmonic voltages and short-circuit currents are used to obtain the relay's operation time.
The relays' operation times are obtained using the optimal dual-settings displayed in Table 3. Table 4 reports a break- down of the relays' operation times in response to bolted faults. The primary and backup relay sets are adequately coordinated with CTIs of at least 0.2 s. Furthermore, the backup relays on the lines adjacent to the faulty line have the same operation times, instantly enabling the fault's clearance from both sides. Table 5 displays the relays' operation times in response to selected faults involving 15 fault resistance. The results are obtained using the same optimal dual-setting of Table 4. Using the same settings confirms the capability of the proposed dual-setting protection scheme to achieve OPC up to high fault resistance and its sensitivity to high resistive faults. The primary and backup relays remain coordinated without violating the minimum value of the CTI.

D. LC FILTER DESIGN
The filter's resonant frequency is typically designed to be ten times the line frequency and one-half the switching frequency [35]. The resonant frequency is between the 17 th and 28 th harmonics when adding the feeder inductance to the filter inductance [36]. To avoid resonance, the frequency of the injected signal must be lower than the resonant frequency by a sufficient margin [19], [20]. As a result, the lowest available low-order harmonics are the second and third harmonics. The proposed method employs the third-harmonic because the second-harmonic is the dominant frequency during unbalanced transients [37]. Numerous fault conditions at various locations were tested in this paper, and in all scenarios, the relays' harmonic currents were higher than the pickup current. Thus, the IIDG filter did not attenuate the harmonic current of the relays or caused relay's malfunction.

E. CONTINGENCIES
A case study is conducted using the test microgrid in Fig. 6 to demonstrate the efficacy of the proposed adaptive harmonicbased dual-setting directional overcurrent protection. Fig. 13 displays the harmonic currents measured by primary protection relays (i.e., R 1 and R 2 ) under IIDG3 outage and during a bolted fault at F 1 . The harmonic currents measured by both relays are higher than the pickup current. Fig. 14 shows the harmonic currents measured by R 1 and R 2 while line 2-3 is out of service and during a bolted fault at F 1 . The harmonic current measured by R 1 is higher than the pickup current, while R 2 senses no harmonic current because it is connected to an open end during the contingency. Thus, the proposed algorithm can handle contingencies.

F. QUALITATIVE ASSESSEMENT
A case study is conducted to show time-domain simulations and relays' response during a bolted fault F 7 applied at t = 1 s. The harmonic voltage generation is triggered upon fault   detection. Consequently, harmonic fault currents flow toward the fault location. Fig. 15(a) displays the harmonic current magnitudes measured by the primary relay R 15 and backup relay R 13 . The primary relay R 15 initiates a trip signal and fault F 7 is isolated in 0.219 s after fault inception, as illustrated in Fig. 15(b). If R 15 does not operate (due to a relay malfunction), the backup relay R 13 operates after a delay of 0.2 s and clears F 7 in 0.419 s following the fault occurrence. The delayed operation of R 13 allows R 15 to respond (in 0.219 s) and maintain the coordination time interval (CTI = 0.2 s). Once the considered bolted fault F 7 is isolated, the harmonic current ceases, as demonstrated by Fig. 15(a). Fig. 15(c) shows the voltages at bus 6 and bus 7. The voltages restore their nominal values after the fault clearance. Table 6 compares the proposed protection method with the harmonic protection schemes in [19], [20], [21], [22], and [23]. The proposed method capitalizes on the IIDG's controller flexibility in generating adaptive harmonic voltage (i.e., no external circuitry). As a result, it is communication-free, with enhanced sensitivity to high resistance faults, and does not require harmonic function upgrade.

VI. CONCLUSION
The limited fault current contributions from IIDGs introduce formidable protection challenges in islanded microgrids. Consequently, conventional overcurrent protection may fail to distinguish between normal load and short-circuit currents. This paper addresses this issue by proposing a harmonic-based protection scheme that does not rely on communication to ensure reliable overcurrent protection of islanded microgrids. Once a fault is detected, a harmonic current flow is established by utilizing the IIDG controller to generate adaptive harmonic voltages based on fault severity. The adaptive harmonic voltage is optimized to maximize the harmonic current flow during faults, thus, reducing the relays' total operation time. The resulting harmonic voltages and currents are measured locally by relays and employed to identify the fault direction. The relay settings with respect to harmonics are optimally determined using a developed OPC program. A universal set of dual-settings that maintain HDOCRs coordination is obtained utilizing the HTCV characteristic and a harmonic directional element. The proposed dual-setting overcurrent protection scheme does not necessitate updating the relays' settings. In addition, the sensitivity is improved across a wide range of fault resistances because of the adaptively generated harmonic voltage. The results highlight the proposed protection scheme's performance in terms of selectivity, sensitivity to fault resistance, and proper coordination of primary and backup relay pairs. Further, it operates on local measurements. The proposed protection scheme provides inexpensive and reliable overcurrent protection for islanded microgrids powered by IIDGs. Further, the adaptive harmonic voltage reduces the total relays' operation time and achieves coordination for bolted to high resistance faults.