**1. Introduction**

Nowadays, with the increasing demand for electric energy, distributed generations (DGs), such as photovoltaics, wind turbines, and fuel cells, play significant roles in power systems [1,2]. Since the DG in the microgrid is close to the load, the line loss is reduced and the energy e fficiency is improved, which makes a grea<sup>t</sup> contribution to the reduction of carbon dioxide emissions in the world [3,4]. As the majority of DGs are connected to the grid via power electronic inverters, which is called inverter-interfaced DG (IIDG), new challenges have risen in energy management, planning, and design, as well as control and protection. E ffective microgrid protection is the primary prerequisite for the reliable operation of a microgrid [5,6].

Considering the unique fault characteristics, the conventional protection methods used in distribution systems are considered no longer su fficiently e ffective [7]. Firstly, the fault current level is strict by the current limiter of the inverter, which introduces challenges to the majority of conventional

current-based protection methods [8]. Secondly, a microgrid has two di fferent operational modes, i.e., a grid-connected mode and islanding mode, which causes notably di fferent fault levels [9]. Thirdly, as microgrids can have multiple DGs, the fault current direction may be changed, which brings di fficulties in the relay setting and coordination [10]. Furthermore, the inverter control methods alter the relationship of the output voltage and current compared with the synchronous generator and inherently increases the risk of compromising the performance of the conventional protection method [11].

Many researchers have put forward e fforts to improve the performance of the microgrid protection system. Some of them focus on protection with the communication channel [12,13]. Slemaisardoo et al. [12] proposed a di fferential protection method using a non-nominal frequency current during the fault, which can better detect the microgrid fault than conventional over-current protection. Aghdam et al. [13] proposed a di fferential protection method based on variable tripping times, and a multi-agent protection scheme was designed to improve the coordination of adjacent relays. Except for di fferential protection, some papers [14–16] used the data from multiple measurement points to classify and optimize the corresponding protection parameters based on the state change of the microgrid topology and DGs. Communication-based methods are reasonable solutions for microgrid protection. However, the reliability of this type of protection highly relies on the communication facilities and performance; also, it is not an economic solution.

Some research focused on protection methods that do not rely on communication. In [17], a new directional relay using amplitude and phase of sequence components in the network is proposed. In [18], a new zero-sequence direction protection for microgrid ground faults is proposed. Huang et al. [19] proposed an inverse-time impedance protection method, which is not a ffected by changes in the microgrid short-circuit level. In [20], an adaptive distance protection method based on the auxiliary coe fficient is proposed to solve the influence of DG on the measured impedance of the relay. Some researchers proposed improved over-current protection methods by considering the fault characteristics of the microgrid [21–23]. Muda and Jena [21] proposed an adaptive over-current protection method by increasing the fault current during the fault. The superposition current of both the positive and negative sequences was applied to amplify the value of the fault current. In [22], an adaptive over-current protection method that diagnosed the microgrid operating mode from the voltage analysis is proposed. El-Naily et al. [23] designed a new pickup current constraint based on the influence of DG on over-current protection so as to overcome the low-fault-level problem. Besides, some papers proposed methods using fault current limiters (FCLs) to limit the short-circuit level of the microgrid [24,25]. In [24], FCLs are used to limit the fault current contribution of the main grid, and the genetic algorithm is used to solve the optimal coordination of the protection. In [25], a new hybrid method that combined the Cuckoo optimization algorithm and linear programming (COA–LP) was applied to solve the coordination of the microgrid protection. Although the use of FCLs can ensure the reliability and selectivity of traditional over-current protection, the investment of additional equipment increases the cost of protection and lacks economic e fficiency.

With the development of artificial intelligence technology, some smart protection methods were also developed in recent years [26–28]. Kar et al. [26] proposed a di fferential protection scheme based on data mining to adapt to the operating mode and topology changes of the microgrid. In [27], an adaptive protection scheme based on machine learning was proposed, which can adaptively modify the protection parameters for di fferent operating conditions. Mishra and Rout [28] proposes a di fferential protection scheme based on Hilbert–Huang transform (HHT) and machine learning, in which HHT was used for feature extraction and machine learning used to classify the fault. These methods can effectively solve the relay setting and coordination problems, but the reliability and fastness of some smart algorithms are di fficult to guarantee.

Although massive smart and sophisticated protection methods have been developed, the simple over-current relay (OCR), which has the characteristics of good performance, simple principles, and a low cost, is still widely used in low-voltage power grids. In practice, a lot of existing microgrid projects utilize the over-current relay as their main and backup protection methods [29]. However, some challenges are still not overcome. Firstly, the over-current relays utilized in a microgrid are mainly time-inverse over-current relays, the operation time of which is inversely proportioned to the fault current. Due to the low fault-current level of the microgrid, the operational speed of this type of relay is di fficult to be satisfactory. Secondly, a microgrid typically has multiple DGs located in di fferent branches, which may bring di fficulty in relay coordination. Furthermore, the alteration of the operation modes of the microgrid will notably change the fault level and challenge the relay settings.

Therefore, to overcome the limitations of the conventional over-current protection methods discussed above, this paper proposes an improved inverse-time over-current (I-ITOC) protection method. A compound fault acceleration factor based on low voltage and the measured impedance was developed to improve the speed of the relay. Then, the coordination of protection is optimized by using the beetle antenna search (BAS) algorithm. Compared with the conventional over-current method, the proposed method notably improves the operation speed. Furthermore, as the proposed method does not require extra devices, it is potentially more economic and easier to implement in the field.

The rest of the paper is organized as follows: In Section 2, the compound fault acceleration factor and the I-ITOC protection method are explained. The optimal configuration of the protection parameters is described in Section 3, and case studies with simulation comparison analyses are presented in Section 4.

## **2. Improved Inverse-Time Over-Current Protection Method Based on the Compound Fault Acceleration Factor**

#### *2.1. Introduction to the Inverse-Time Over-Current Relay*

The inverse-time over-current relay (ITOCR) has the ability to reflect the severity of faults, and its operation time is inversely proportioned to the fault current. According to the standard IEC 60255 [30], the operation characteristic equation of the ITOCR is defined as follows:

$$t = \frac{A}{\left(\frac{I\_f}{I\_P}\right)^\alpha - 1} \times \text{TDS} \tag{1}$$

where *t* is the relay's operation time, *A* is the constant coe fficient, α is the inverse-time curve shape coe fficient, *If* is the magnitude of the fault current measured by the relay, Time Dial Setting (TDS) is the time dial setting, and *Ip* is the setting of the relay's pickup current.

However, due to the changes in the operating mode of the microgrid, the limitations of the power electronics in contributing to the fault current in the microgrid, and the significant impact of the DGs' control strategy and capacity on the fault output current, there are significant di fferences in fault current values in the microgrid under di fferent modes. Since the operation time of a conventional ITOCR is closely related to the fault current, the large variations in fault level will significantly a ffect the performance of the conventional ITOCR. Therefore, in order to ensure the satisfactory speed of the ITOCR in di fferent modes of the microgrid, it is necessary to improve the conventional ITOC protection method.

#### *2.2. Development of the Compound Fault Acceleration Factor for Over-Current Protection of a Microgrid*

When the microgrid is operating in the grid-connected mode, the bus voltage and frequency are regulated by the upstream main grid. When the microgrid is switched to the islanded mode, one or some main DGs will be used to maintain the bus voltage and frequency stability. In the event of a fault, the closer the fault point is to the relay installation point, the more serious the voltage drop of the relay will be. Thus, the voltage drop of the relays can reflect the distance from the fault point to the installation of the relay.

As shown in Figure 1, when one fault occurs downstream of the relay R2 (point *f*), constructing the coefficient of the fault voltage based on the characteristics of the bus fault voltage, and the fault voltage coefficient *U*∗*i*of the relay R*i*, can be defined in Equation (2):

$$\mathcal{U}I\_i^\* = 1 - \left| \frac{\mathcal{U}I\_i^{\text{fault}} - \mathcal{U}I\_i^{\text{prefault}}}{\mathcal{U}I\_i^{\text{prefault}}} \right| \tag{2}$$

where *U*prefault *i* and *U*fault *i* are the pre-fault voltage and the fault voltage to the relay R*i*, respectively. The fault position on the line influences the value of *U*∗*i* . The closer the relay is to the point of fault, the smaller *U*∗*i*is, and *U*∗*i*is less than 1 for all possible scenarios.

**Figure 1.** Simplified microgrid model.

In addition, according to the principle of distance protection, the measured impedance of the relay reflects the distance between the relay and the point of fault, and the fault impedance coefficient *Z*∗*i* can be constructed as follows:

$$Z\_i^\* = \frac{|Z\_L|}{|Z\_{Ri}|} \tag{3}$$

where *ZL* is the line impedance, which is the total impedance between the bus PCC (BUS1) to the end of the branch (BUS3). *ZRi* is the measured impedance of the relay Ri. Please note that calculation of *ZRi* changes with different fault types; also, the closer the relay is to the point of fault, the larger the fault impedance coefficient *Z*∗*i*is. *Z*∗*i*is greater than 1 for all possible scenarios.

By combing Equations (2) and (3), the operation characteristic equation and new TDS of the I-ITOC protection method is obtained in (4) and (5), where *Mi* in (6) represents the compound fault acceleration factor.

$$t\_i = \frac{A}{\left(\frac{I\_{f,i}}{I\_{p,i}}\right)^{\alpha\_i} - 1} \times \text{TDS}\_i^\* \tag{4}$$

$$\rm{TDS}^\*\_{i} = \rm{TDS}^\*\_{i} \times M\_i \tag{5}$$

$$M\_{\bar{i}} = \frac{\mathcal{U}\_{\bar{i}}^{\*}}{Z\_{\bar{i}}^{\*}} \tag{6}$$

Compared with the conventional ITOCR, the speed of the improved inverse-time over-current relay (ITOCR) can be improved as *Mi* is less than 1 for the majority of scenarios. The following section, Section 2.3, will discuss a few scenarios in which *Mi* is greater than 1. In the case of the islanded mode of the microgrid, due to the influence of the DG capacity, the DG's maintain bus voltage capability is weaker than that of the main grid. Therefore, the compound fault acceleration factor *Mi* in the islanded mode is smaller than that of the grid-connected mode. Inherently, the influence of a low fault level on the protection operation time during the island mode can be further reduced.

#### *2.3. E*ff*ect of DG on the Compound Fault Acceleration Factor*

The presence of DGs in the microgrid can change the fault current flowing through the relay, which will result in a different operation time by applying the ITOC. Besides, the fault current of the

DG may also affect the fault measurement impedance of the backup relay. In Figure 1, when a fault occurs downstream of the relay R2, the impedance measured by the relays R1 and R2 can be obtained by Equations (7) and (8):

$$Z\_{R1} = Z\_1 + Z\_f + Z\_{DG}^\* \tag{7}$$

$$Z\_{\mathbb{R2}} = Z\_f \tag{8}$$

where

$$Z\_{\rm DG}^\* = \frac{I\_{\rm DG2}}{I\_{\rm BUS1}} \times Z\_f \tag{9}$$

In Equations (7) and (8), *ZR*1 and *ZR*2 are the measured impedance of the relay R1 and R2, *Zf* is the impedance between relay R2 and fault point *f*, and *<sup>Z</sup>*<sup>∗</sup>*DG* is the contribution impedance of DG2's fault current to relay R1. In Equation (9), *IBUS*1 is the fault current flowing through BUS1 and *IDG*2 is the fault current of the DG2.

When the fault occurs in the grid-connected mode, *IBUS*1 will typically be much greater than *IDG*2, and *<sup>Z</sup>*<sup>∗</sup>*DG* can be ignored. When the fault occurs in the microgrid islanded mode, the magnitude of |*IDG*2/*IBUS*1| is affected by the DG control strategy and the severity of the fault. Since the phase angle of |*IDG*2/*IBUS*1| is between −90◦ and 90◦ [19], *ZR*1 is still greater than *ZR*2, and the fault impedance coefficient *Z*∗1 and *Z*∗2 measured by the relays R1 and R2 still satisfies the criteria that *Z*∗2 is greater than *<sup>Z</sup>*<sup>∗</sup>1.

However, when the capacity of the DG is relatively large, the fault current of the DG may cause may cause the protection measurement impedance *ZRi* to be greater than the set impedance *ZL*, inherently affecting the speed of the protection. Therefore, the compound fault acceleration factor *Mi* and the I-ITOC protection method is improved, which can be expressed in Equations (10) and (11).

$$M\_i = \frac{U\_i^\*}{1 + Z\_i^\*} \tag{10}$$

where

$$Z\_i^\* = \begin{cases} 1 & Z\_i^\* < 1 \\ & |Z\_L / Z\_{Ri}| & Z\_i^\* \ge 1 \end{cases} \tag{11}$$

In order to maintain the acceleration effect of *Mi* when the contribution of DG to the protection measurement impedance is too large, the denominator of *Mi* is changed, and 1 is taken when the fault impedance coefficient *Z*∗*i*is less than 1.

#### **3. Protection Coordination Optimization Based on the Beetle Antennae Search Algorithm**

Due to the unique fault characteristics in the microgrids and the influence of the DG, the conventional settings of the ITOCR cannot be directly applied for effective microgrid protection. Figure 2a,b are the protection operation characteristics curve of the conventional ITOCR under different operation modes of the microgrid.

As shown in Figure 2a, if the settings are configured based on the grid-connected operational mode, the speed of the relay in the islanded mode could be too slow due to the reduced fault level; as shown in Figure 2b, if the settings are calculated based on the islanded operational mode, the coordination time interval (*CTI*) of the adjacent relays in the grid-connected mode could be too small to ensure the coordination of protection. In addition, the contribution of the DG to the fault current flowing through the relay also affects the coordination of the relay. Therefore, in order to ensure the selectivity and speed of I-ITOCR in different operation modes of the microgrid, it is necessary to optimize the parameters of each relay.

**Figure 2.** Operation time in different modes of the microgrid: (**a**) Parameters are set according to the grid-connected mode; (**b**) parameters are set according to the islanded mode.

## *3.1. Coordinated Optimization of the I-ITOCRs*

The I-ITOCR operating characteristic equation is shown in Equation (6). In general, parameters A and α are fixed for a certain relay and the parameters *Ip*·*<sup>i</sup>* and *TDSi* need to be set. In this paper, in order to reduce the impact of current changes and achieve optimal coordination, the index α*i* is also added as the optimization variable. The objective function of the optimization problem is formulated in Equation (12), which represents the sum of the operation time for I-IOCR considering both the grid-connected and islanded operation modes of the microgrid.

$$\min\_{I\_{p, \mathcal{A}, TDS}} \mathcal{F} = \sum\_{m=1}^{2} \sum\_{n=1}^{4} \left( \sum\_{k=1}^{K} \left( t\_{pr \cdot k}^{i} + \sum\_{j=1}^{2} t\_{hc \cdot k}^{ij} \right) \right) \tag{12}$$

where m denotes the operation mode of the microgrid, and the numbers 1 and 2, respectively, indicate the grid-connected and islanded modes of the microgrid; *n* represents different fault types; *k* represents the different fault conditions, here being the first and end fault of each line; *i* represents the primary relay and *j* represents the backup relay to the primary relay *I*; and *t* denotes the operation time of the relays, with *tipr*·*k* denoting the operation time of the primary relay and *tijbc*·*k* denoting the operation time of the backup relay.

The total operation time of the I-IOCRs is reduced by obeying their constraints as follows.
