Optimal Coordination of Overcurrent Relays in Microgrids Considering a Non-Standard Characteristic

Abstract

The optimal coordination of overcurrent relays (OCRs) has recently become a major challenge owing to the ever-increasing participation of distributed generation (DG) and the multi-looped structure of modern distribution networks (DNs). Furthermore, the changeable operational topologies of microgrids has increased the complexity and computational burden to obtain the optimal settings of OCRs. In this context, classical approaches to OCR coordination might no longer be sufficient to provide a reliable performance of microgrids both in the islanded and grid-connected operational modes. This paper proposes a novel approach for optimal coordination of directional OCRs in microgrids. This approach consists of considering the upper limit of the plug setting multiplier (PSM) as a variable instead of a fixed parameter as usually done in traditional approaches for OCRs coordination. A genetic algorithm (GA) was implemented to optimize the limits of the maximum PSM for the OCRs coordination. Several tests were performed with an IEC microgrid benchmark network considering several operational modes. Results showed the applicability and effectiveness of the proposed approach. A comparison with other studies reported in the specialized literature is provided showing the advantages of the proposed approach.

1. Introduction

The proliferation of small-scale rotary machines and distributed generation (DG) units within distribution networks (DNs) has brought new opportunities in the diversification of the energy basket and a better use of natural resources which promotes sustainability. Microgrids are a powerful alternative to satisfy the growing energy demand with a positive impact in power networks improving the overall efficiency. However, the high penetration of DG causes bidirectional power flows and currents that change the traditional dynamic interaction between loads and generators [1,2,3,4]. Such interaction makes the problem of protection coordination even more complex.

Protection systems in microgrids must deal with the following two aspects: (a) the dynamic behavior that is usually presented due to intermittent energy resources and (b) the microgrid operation mode which can be connected or disconnected from the main power grid [5,6]. Microgrids are reconfigurable electric power systems with variable levels of current fault and bidirectional power flows [7]. Microgrids have changed the traditional paradigm of radial DNs into non-radial and flexible systems. Therefore, finding a protection scheme that ensures speed, selectivity and reliability has become one of the most challenging tasks in microgrids operation planning [8].

Overcurrent relays (OCRs) are the most extended protection systems due to their efficiency, simplicity, and ease of installation. Nevertheless, their proper incorporation and coordination in microgrids is still an emerging research topic [1,2,9,10]. Selection and design of coordination protection schemes are essential for appropriate control and reliable operation of microgrids [6]. Recently, many researchers have focused their efforts in implementing optimization techniques to find an appropriate protection coordination scheme that features minimum operation time while guaranteeing reliability and security [11,12].

In [13], the authors proposed an index to measure the impact on OCRs coordination when DG units are included. The directional OCRs coordination problem is also analyzed in [14] in DNs with high participation of DG. The authors of [15] proposed a methodology for OCRs coordination which includes the N-1 security criterion. In [16], a multi-objective swarm optimization algorithm for OCRs coordination in microgrids was presented. In [17], the authors proposed an online adaptive coordination protection scheme for directional OCRs. Such a scheme uses smart electronic devices and a communication channel to obtain real time information for updating the relays configuration. This approach was intended for DNs with dynamically changing operating conditions which includes loss of loads, generations, and lines. In [18], the authors proposed an adaptive coordination protection scheme. In this case, a hybrid artificial neural network and a support vector machine model were used for the state recognition of the microgrid. Based on the state recognition, the protective settings of the network were dynamically modified to enhance the reliability of the network. However, the schemes presented in [17,18] are usually expensive and their implementation tends to be complex [19].

In [20], the concept of non-standard features for overcurrent protection coordination in power systems is described. Non-standard features are those not described neither in IEEE nor in IEC (international electrotechnical commission) standards. Technological advances in protective equipment have formed the basis for the new generation of digital overcurrent relays that allow alternative approaches to the standard protection schemes. The continuous growth of power systems makes the protection coordination an increasingly complex problem. Then, non-standard features arise as an alternative to improve the safety and reliability of electrical power systems. In [21], the authors presented a protection coordination approach taking into account the installation of future photovoltaic systems with any penetration level and different locations along the distribution feeder. Basically, the authors of [21] modified the existing characteristic curve of the overcurrent protection. The characteristic curve can be modified by varying the constants of the curve while keeping the time multiplying setting (TMS) and pick up current fixed.

Modern DNs present changeable operational modes that increase the complexity to obtain the optimal settings of directional OCRs. To tackle this problem, the authors of [11] proposed an alternative to the conventional protection coordination approach, adding a new constraint that takes into account the Plug Setting Multiplier (PSM). PSM is the ratio between the fault current seen by the relay and the pick up current. The tripping characteristic of overcurrent relays is limited by the PSM value. The standard characteristic curves of commercial relays are generally defined in a region where the minimum value is 1.1 times the PSM, whereas the maximum value is 20 times the PSM value. The DG units in microgrids considerably increase the short circuit level. Therefore, for different faults, this maximum value defined for PSM might be exceeded, affecting the sensitivity of the protections and causing loss of the coordination protection scheme. The new constraint introduced in [11] considers the above-mentioned conditions by setting the maximum value of 20 times the PSM.

In [12], the authors considered the constraint proposed in [11] and also used a non-standard curve for improving the performance of the OCRs protection. Such a non-standard curve modifies the region defined by the characteristic curve. In this case, they considered a value of 100 times the PSM for its maximum value which allows improving the performance of the protection coordination.

Modern DNs require more intelligent and adaptive protection schemes. In this context, non-standard and user-defined characteristics of directional OCRs must be explored aiming to find coordination schemes adaptable to the new challenges imposed by modern DNs. This paper is aligned with this trend by proposing a novel approach for the coordination of directional OCRs in microgrids. The proposed approach improves and complements the non-standard characteristic described in [11,12]. In this case, the maximum limit of the PSM is treated as a variable instead of a parameter, as usually considered in conventional approaches. Although considering the PSM as a variable makes the coordination process more complex, it also expands the search space of coordination alternatives and improves the performance of the overall protection scheme, being applicable to DNs with high penetration of intermittent DG and several operational modes. Results obtained with the proposed methodology are compared with those reported in [11,12] using an IEC microgrid benchmark network. In all scenarios analyzed, the proposed methodology presented a better performance of the protection scheme.

This paper is organized as follows. Section 2 presents the mathematical model for coordination of directional OCRs in microgrids. Section 3 describes the methodology for obtaining the limits of the non-standard characteristic curve. Section 4 presents the results and a comparative analysis. Finally, Section 5 presents the conclusions and highlights the most relevant aspects of our research work.

2. Mathematical Formulation

2.1. Objective Function

The objective function given by Equation (1) aims at minimizing the operation time of the OCRs ensuring coordination between the main and back up relays. In this case, m and n are the number of relays and faults in the system, respectively, whereas $t_{if}$ corresponds to the operation time of relay i when the fault f occurs.

$$\begin{array}{c}\hfill Min\sum _{i=1}^m\sum _{f=1}^n{t}_{if}\end{array}$$

(1)

2.2. Coordination Criteria

When a fault takes place, both the backup and primary OCRs identify the fault occurrence. The backup OCR is in charge of tripping the fault in case the primary OCR misses to isolate the fault. Equation (2) illustrates this condition. In this case, $t_{jf}$ is the operation time of the backup relay j when fault f occurs, and $t_{if}$ is the operation time of the primary relay i for the same fault. The coordination time interval $CTI$ is the period of time allowed for the backup protection to operate. This time is determined by the operating time of the relay, the operating time of circuit breakers and the overshooting time. Typical $CTI$ values are within the range of 0.2 to 0.5 s. The $CTI$ considered in this study is 0.3 for comparative purposes.

$$\begin{array}{c}\hfill t_{jf}-t_{if}\ge CTI\end{array}$$

(2)

2.3. Relay Characteristic

The ORCs considered in this study present a normal inverse characteristic as indicated by Equation (3). In this case, A and B are constant parameters of the curve, $TM{S}_i$ is the time multiplying setting of relay i, and $PS{M}_{if}$ is the ratio between the fault current $I_{fi}$ and the pick up current $ipicku{p}_i$ given by Equation (4).

$$\begin{array}{c}\hfill t_{if}=\frac{A.TM{S}_i}{PS{M}_{if}^B-1}\end{array}$$

(3)

$$\begin{array}{c}\hfill PS{M}_{if}=\frac{I_{fi}}{ipicku{p}_i}\end{array}$$

(4)

2.4. Bonds in Relay Operation Time

Equation (5) indicates the operating time limits of the OCRs. In this case, $t_{imin}$ and $t_{imax}$ are the minimum and maximum operating time of relay i, respectively.

$$\begin{array}{c}\hfill t_{imin}\le t_{if}\le t_{imax}\end{array}$$

(5)

2.5. Bonds on the TSM and Pick Up Current for Each Relay

In the conventional approach of protection coordination, the $TSM$ is the main decision variable. Equation (6) represents the minimum and maximum limits of $TSM$ for relay i given by $TM{S}_{imin}$ and $TM{S}_{imax}$, respectively. Similarly, Equation (7) represents lower and upper limits of the pickup current $ipicku{p}_i$, denoted as $ipicku{p}_{imin}$ and $ipicku{p}_{imax}$, respectively.

$$\begin{array}{c}\hfill TM{S}_{imin}\le TM{S}_i\le TM{S}_{imax}\end{array}$$

(6)

$$\begin{array}{c}\hfill ipicku{p}_{imin}\le ipicku{p}_i\le ipicku{p}_{imax}\end{array}$$

(7)

2.6. New Constraints on PSM

When obtaining the $TMS$ for each OCR, the maximum value of $PSM$$\left(PS{M}_{imax}\right)$ must be taken into account, which is the highest current level of the IEC normally inverse curve programmed in the industrial protective relay before the definite time region of the curve. Equation (8) was introduced in [11] to constrain and limit the $PSM$. This consideration is not taken into account in traditional protection coordination approaches. The authors in [11] considered 1.1 and 20 as minimum and maximum limits of $PSM$, respectively. On the other hand, in [12], the authors modify the upper limit of $PSM$ to 100. In this paper, $PS{M}_{imax}$ is considered as a variable ranging between $\alpha$$PSM$ and $\beta$$PSM$. The values of $\alpha$ and $\beta$, selected by the authors in this paper, were 5 and 100, respectively. Parameter $\beta$ was set in 100 since it was the maximum PSM suggested in [12]. Parameter $\alpha$ was set to 5 in order to guarantee a setting in which the inverse characteristic curve of the current would not loss its main feature. Figure 1 illustrates the proposed non-standard characteristic for primary and backup OCRs coordination and the difference with the approaches considered in [11,12].

$$\begin{array}{c}\hfill PS{M}_{imin}\le PS{M}_{if}\le PS{M}_{imax}\end{array}$$

(8)

$$\begin{array}{c}\hfill \alpha \le PS{M}_{imax}\le \beta \end{array}$$

(9)

3. Methodology

The model given by (1)–(9) was solved using a genetic algorithm (GA) implemented in Matlab. Genetic algorithms are metaheuristics that mimic Darwinian evolution in which the fittest individuals have greater chance to transmit their genes into the next generation. Other metaheuristic techniques have also been used for solving the optimal coordination of protections, such as particle swarm optimization [22,23] and differential evolution [24]. GAs have shown to be effective in tackling the overcurrent protection coordination problem as indicated in [25,26,27]. The flowchart of the GA procedure is depicted in Figure 2.

The process that was implemented to solve the problem of directional OCRs coordination is as follows. Step 1: The test network is modeled using the Digsilent Power Factory software. Step 2: Several operational modes (OMs) are configured in the test network. Step 3: Short-circuit currents are calculated for different fault locations for every OM, using the Digsilent Power Factory software. Step 4: The short-circuit currents obtained in Step 3 are used as input parameters to the GA for the protection coordination. Step 5: The protection coordination model (Equations (1)–(9)) is solved for each OM using the proposed GA approach. Step 6: A set of parameters for the OCRs coordination is obtained for each OM. Alternatively, it is possible to modify Step 5 and obtain a single set of coordination parameters suitable for all OMs.

3.1. Initial Population

The GA starts with an initial set of candidate solutions known as population. Each individual within the population is represented by a vector that codifies a possible solution to the problem. In this case, every element of the vector corresponds to a setting of $TMS$ and $PS{M}_{imax}$ for each relay. In the proposed protection coordination model, $TMS$ and $PSMimax$ are the decision variables. The length of the vector corresponds to twice the number of relays present in the test network. The GA implemented generates the initial population randomly considering the minimum and maximum limits of the decision variables. Figure 3 depicts an example of a candidate solution. In this case, the candidate solution indicates that the TMS of relays 1, 2, and n must be set to 0.05, 1, and 0.9, respectively. Also, the maximum PSM limits for the same relays must be set to 16, 20, and 40, respectively.

3.2. Fitness Evaluation

Each solution candidate has an associated cost or value of the objective function. In the GA, this value is referred to as the fitness of the individual. Once a given number of solution candidates are proposed, their associated costs or fitness are evaluated. In this case, the objective function given by Equation (1) represents the operation time of the OCRs. The objective function is evaluated for each individual and these are classified from best to worst. To enforce constraints, the objective function of unfeasible candidate solutions is penalized. The best solution candidates are those with the lowest value of the objective function.

3.3. Tournament Selection

After the evaluation of the objective function, some individuals are chosen among the best to generate new possible solutions. For this case, a selection by tournament is implemented which consists of randomly selecting two pairs of individuals and choosing the individual with the best fitness. There are as many tournaments as individuals. The best individuals go through the next stages of crossover and mutation.

3.4. Crossover

The crossover or recombination is the stage of the algorithm in which parents exchange their genetic material to generate new individuals. In this case, the crossover is performed over two winners of the tournament (parents), then their bits are crossed at a random position of the vectors generating two new individuals (offspring). In this case, each new individual preserves part of the genetic material of both parents. Figure 4 illustrates the crossover stage.

3.5. Mutation

Mutation consists of small variation of the new individuals, performed with a given probability. The mutation stage introduces diversification and allows the algorithm to eventually escape from local optimal solutions. In the mutation process, one of the offspring is randomly selected with a given probability, then one of its bits is changed. In this case, the current value of the bit is randomly changed within its limits.

3.6. New Generation

Once the recombination and mutation processes are finished, the population of offspring and parents is grouped together. The fitness of each individual is then used for selecting the new population. As the new population will be twice the initial one, half of the individuals are discarded (those with the poorest performance) and a new generation is ready for the next iteration of the algorithm.

3.7. Stopping Criteria

Two stopping criteria are considered in the GA: (1) a predefined maximum number of iterations, and (2) a maximum number of iterations without an improvement of the objective function. If either of these two criteria occurs, the algorithm stops.

4. Tests and Results

To prove the effectiveness of the proposed approach, a benchmark IEC microgrid that integrates different DG technology types was considered. The parameters of the microgrid, depicted in Figure 5, can be consulted in [28]. Four OMs, as described in

Table 1. Microgrid operational modes.

Operational Mode	Grid	DG1	DG2	DG3	DG4
OM1	on	off	off	off	off
OM2	on	on	on	on	on
OM3	on	on	on	off	off
OM4	off	on	on	on	on

were analyzed. In the first operational mode, the DG units are disconnected from the microgrid and the load is supplied through the main grid. In the second one, all DG units operate along with the main source of the grid. In the third operational mode, the demand of the microgrid is fed via the main grid along with DG1 and DG2. Finally, in the fourth operational mode, the microgrid is operated in islanded mode, employing all DG units and disconnected from the main utility.

The test system was implemented in DIgSILENT PowerFactory. Five three-phase faults at lines DL-1, DL-2, DL-3, DL-4, and DL-5 were considered. The short circuit levels for these faults are illustrated in Figure 5. F1 represents a fault at line DL-5, and F2 and F3 are faults at lines DL-4 and DL-2, respectively. F4 represents a fault at line DL-1 and F5 represents a fault at line DL-3. Note that every system operator determines the types of faults and locations to be evaluated in order to establish the protection coordination. In this case, the aforementioned faults were selected for comparative purposes with [11,12]. Nevertheless, any other set of faults can be considered. Calculations and tests were performed according to the recommendations of the IEEE Standard 242 which is widely used for overcurrent protections coordination [29].

The results obtained with the proposed approach regarding the coordination of the directional OCRs, were compared with the ones reported in [11,12]. The transformation ratios of current transformers $RCT$ and pickup currents $i_{pickup}$ are shown in

Table 2. $RCT$ and $i_{pickup}$ for each relay.

Relay	$\mathit{RCT}$	${\mathit{i}}_{\mathit{pickup}}$
R1	400	0.50
R2	400	0.50
R3	400	0.50
R4	400	0.50
R5	400	0.50
R6	400	0.50
R7	1200	1.00
R8	400	0.50
R9	400	0.50
R10	400	0.50
R11	400	0.65
R12	400	0.50
R13	400	0.88
R14	400	0.65
R15	400	0.55

.

IEEE Standard 242 [29] recommends that the coordination time between the main relay and the backup relay $CTI$ must be equal or greater than 0.2 seconds. This paper considers a $CTI$ of 0.3 seconds for comparative purposes. For the operation time of the OCRs, the IEC Normal Inverse curves with constants A and B of 0.14 and 0.02, respectively, were considered. Relays are labeled with numbers ranging from 1 to 15 preceded by the letter R. Figure 6 shows the location of each relay. For the fault cases analyzed, letter “P” was assigned for main relays, whereas letter “B” was assigned to for backup relays.

Several tests were performed for the parameter tuning of the GA. The combination of parameters that presented the best results were population of 100, number of generations of 1000, crossing rate of 0.7, and mutation rate of 0.3. In all scenarios under analysis, CB-LOOP1 was considered to be open (see Figure 6).

4.1. Results for Operational Mode 1

In this operational mode, the microgrid is connected to the main grid while all DG units are disconnected (see Table 1). In this case, simulations were performed for the five different faults previously described.

Table 3. Coordination parameters for OM1.

Relay	${\mathit{TMS}}_{\mathit{i}}$ [11]	${\mathit{PSM}}_{\mathit{imax}}$ [11]	${\mathit{TMS}}_{\mathit{i}}$ [12]	${\mathit{PSM}}_{\mathit{imax}}$ [12]	${\mathit{TMS}}_{\mathit{i}}$ [Proposed]	${\mathit{PSM}}_{\mathit{imax}}$ [Proposed]
R1
R2	0.128	20	0.1283	100	0.050	58.003
R3
R4	0.256	20	0.2591	100	0.1787	86.38
R5
R6	0.391	20	0.4024	100	0.3223	75.15
R7	0.335	20	0.2895	100	0.2060	5.00
R8
R9
R10	0.1283	20	0.1283	100	0.050	92.37
R11
R12	0.1320	20	0.0101	100	0.050	76.82
R13
R14
R15
T(s)	7.53		6.64		4.99

presents the results obtained with the proposed model and the ones reported in [11,12]. The $TMS$ and $PS{M}_{imax}$ is presented for each relay as well as the sum of operating times for all relays $T\left(s\right)$ (objective function). Note that the proposed model presents faster operating times guaranteeing coordination of backup and main OCRs. All relays presented different $PS{M}_{imax}$ values. Particularly, relay R7 has a $PS{M}_{imax}$ lower than the $PS{M}_{imax}$ obtained in [11,12]. This allows improving the operating times of all relays.

Table 4. Operation times for OM1.

Fault	Relays	[11]	[12]	[Proposed]
F1	RP1
	RP2	0.29	0.303	0.1165
	RB4	0.59	0.606	0.4165
	RB13
F2	RP3
	RP4	0.58	0.54	0.3732
	RB1
	RB6	0.86	0.84	0.6732
	RB15
F3	RP5
	RP6	0.88	0.72	0.5819
	RB7	1.18	1.02	0.8819
	RB8
	RB15
F4	RP8
	RP12	0.29	0.2	0.1044
	RB5
	RB7	1.59	1.37	0.9786
	RB11
F5	RP9
	RP10	0.29	0.28	0.1165
	RB6	0.91	0.88	0.7514
	RB14
	RB15

presents the operation times of the main and backup relays for each fault. Note that in all cases the proposed approach presents lower operation times than those reported in [11,12].

4.2. Results for Operational Mode 2

In this operational mode, all DG units operate in the microgird along with the main source of the grid. The coordination parameters of the OCRs obtained with the GA for this operational mode are shown in

Table 5. Coordination parameters for OM2.

Relay	${\mathit{TMS}}_{\mathit{i}}$ [11]	${\mathit{PSM}}_{\mathit{imax}}$ [11]	${\mathit{TMS}}_{\mathit{i}}$ [12]	${\mathit{PSM}}_{\mathit{imax}}$ [12]	${\mathit{TMS}}_{\mathit{i}}$ [Proposed]	${\mathit{PSM}}_{\mathit{imax}}$ [Proposed]
R1	0.173	20	0.1736	100	0.1370	54.58
R2	0.132	20	0.1391	100	0.0500	51.33
R3	0.086	20	0.0868	100	0.0500	56.99
R4	0.265	20	0.2782	100	0.1891	94.94
R5	0.172	20	0.1720	100	0.1148	16.50
R6	0.397	20	0.4010	100	0.3198	87.16
R7	0.338	20	0.2839	100	0.2439	48.10
R8	0.265	20	0.2226	100	0.1911	84.82
R9	0.069	20	0.0695	100	0.0500	53.94
R10	0.132	20	0.1413	100	0.0500	67.99
R11	0.280	20	0.2437	100	0.2175	34.54
R12	0.132	20	0.1503	100	0.0500	80.58
R13	0.194	20	0.1936	100	0.1669	93.88
R14	0.116	20	0.1159	100	0.0998	94.46
R15	0.186	20	0.1704	100	0.1359	32.75
T(s)	19.18		17.48		13.66

. The $TMS$ and $PS{M}_{imax}$ values for each relay, along with the sum of operating time of all relays $T\left(s\right)$, are presented. Note that with the proposed coordination approach, all relays presented different $PS{M}_{imax}$ values, and the operation time $T\left(s\right)$ is lower than the one reported in [11,12], which consider a fixed $PS{M}_{imax}$. Results presented in

Table 6. Operation times for OM2.

Fault	Relays	[11]	[12]	[Proposed]
F1	RP1	0.56	0.55	0.4454
	RP2	0.29	0.299	0.1078
	RB4	0.59	0.59	0.4078
	RB13	0.86	0.86	0.7454
F2	RP3	0.29	0.29	0.1723
	RP4	0.6	0.52	0.3556
	RB1	0.59	0.58	0.4723
	RB6	0.9	0.82	0.6556
	RB15	0.89	0.82	0.6556
F3	RP5	0.45	0.45	0.3039
	RP6	0.9	0.7	0.5618
	RB7	1.19	1.0	0.8618
	RB8	1.0	1.0	0.8618
	RB15	0.97	0.97	0.7775
F4	RP8	1.0	0.94	0.8229
	RP12	0.29	0.29	0.0995
	RB5	0.6	0.59	0.3995
	RB7	1.74	1.44	1.25
	RB11	1.23	1.23	1.12
F5	RP9	0.29	0.25	0.2152
	RP10	0.29	0.29	0.1059
	RB6	0.95	0.95	0.7668
	RB14	0.59	0.57	0.5152
	RB15	1.22	1.22	0.9755

show the operation times of main and backup relays for each fault. Note that lower operation times are also obtained with the proposed model, guaranteeing coordination among main and backup relays.

4.3. Results for Operational Mode 3

In this operational mode, the microgrid is connected to the main network, DG1 and DG2 units are connected, and DG3 and DG4 units are disconnected. The parameters of the OCRs coordination, obtained with the GA, are presented in

Table 7. Coordination parameters for OM3.

Relay	${\mathit{TMS}}_{\mathit{i}}$ [11]	${\mathit{PSM}}_{\mathit{imax}}$ [11]	${\mathit{TMS}}_{\mathit{i}}$ [12]	${\mathit{PSM}}_{\mathit{imax}}$ [12]	${\mathit{TMS}}_{\mathit{i}}$ [proposed]	${\mathit{PSM}}_{\mathit{imax}}$ [proposed]
R1
R2	0.092	20	0.092	100	0.0500	51.72
R3
R4	0.227	20	0.227	100	0.1855	71.96
R5	0.087	20	0.090	100	0.0608	36.71
R6	0.356	20	0.362	100	0.3232	65.84
R7	0.312	20	0.264	100	0.2027	5.00
R8	0.207	20	0.207	100	0.1925	16.55
R9
R10	0.0847	20	0.084	100	0.0500	86.69
R11	0.2626	20	0.231	100	0.2186	74.38
R12	0.1320	20	0.145	100	0.0500	87.83
R13
R14
R15	0.1670	20	0.154	100	0.1373	60.46
T(s)	14.04		12.67		10.71

indicating $TMS$ and $PS{M}_{imax}$ for each relay, as well as the total operation time $T\left(s\right)$. It can be observed that implementing the proposed approach reduces the total operation times from 14.04 and 12.67 seconds (with the methodologies reported in [11,12], respectively) to 10.71 seconds. Also, all relays present different $PS{M}_{imax}$ values. Particularly, relay R7 has a $PS{M}_{imax}$ lower than the one obtained in [11,12], which allows improving the operating times of all relays and maintains the coordination times of main and backup relays.

Results presented in

Table 8. Operation times for OM3.

Fault	Relays	[11]	[12]	[Proposed]
F1	RP1
	RP2	0.200	0.200	0.1107
	RB4	0.508	0.502	0.4107
	RB13
F2	RP3
	RP4	0.508	0.44	0.3625
	RB1
	RB6	0.807	0.74	0.6625
	RB15	0.800	0.73	0.6625
F3	RP5	0.42	0.42	0.2878
	RP6	0.80	0.63	0.5677
	RB7	1.10	0.93	0.8677
	RB8	1.10	0.93	0.8677
	RB15	0.84	0.78	0.6958
F4	RP8	1.05	0.89	0.8286
	RP12	0.29	0.298	0.1025
	RB5	0.67	0.64	0.4025
	RB7	1.52	1.28	0.9899
	RB11	1.35	1.19	1.1286
F5	RP9
	RP10	0.19	0.19	0.1107
	RB6	0.83	0.84	0.7551
	RB14
	RB15	1.10	0.99	0.9030

show the operating times of main and backup relays for each fault. Note that operation times of main and backup protections were lower in all cases with the proposed approach.

4.4. Results for Operational Mode 4

In this case, the microgrid is operating in islanded mode and the load is supplied by the DG units.

Table 9. Coordination parameters for OM4.

Relay	${\mathit{TMS}}_{\mathit{i}}$ [11]	${\mathit{PSM}}_{\mathit{imax}}$ [11]	${\mathit{TMS}}_{\mathit{i}}$ [12]	${\mathit{PSM}}_{\mathit{imax}}$ [12]	${\mathit{TMS}}_{\mathit{i}}$ [proposed]	${\mathit{PSM}}_{\mathit{imax}}$ [proposed]
R1	0.173	20	0.1730	100	0.1370	57.41
R2	0.105	20	0.1050	100	0.0500	32.61
R3	0.086	20	0.0860	100	0.0500	55.99
R4	0.211	20	0.2110	100	0.1571	90.12
R5	0.209	20	0.2090	100	0.1552	49.59
R6	0.181	20	0.1812	100	0.1510	47.70
R7
R8	0.247	20	0.2476	100	0.2176	83.93
R9	0.069	20	0.0695	100	0.050	61.34
R10	0.112	20	0.1124	100	0.050	53.98
R11	0.264	20	0.2645	100	0.2395	40.79
R12	0.104	20	0.1050	100	0.050	42.65
R13	0.193	20	0.1930	100	0.1669	32.32
R14	0.115	20	0.1159	100	0.0998	95.86
R15	0.177	20	0.1771	100	0.1476	76.22
T(s)	15.56		15.56		12.63

presents the results of the OCRs coordination obtained with the GA. As with the previous operational modes, the proposed approach results in lower total operation time $T\left(s\right)$ when compared to the results presented in [11,12]. Also, all relays have different $PS{M}_{imax}$ values. Results presented in

Table 10. Operation times for OM4.

Fault	Relays	[11]	[12]	[Proposed]
F1	RP1	0.56	0.56	0.4454
	RP2	0.29	0.29	0.1400
	RB4	0.59	0.59	0.4400
	RB13	0.86	0.86	0.7454
F2	RP3	0.29	0.29	0.1723
	RP4	0.55	0.55	0.4121
	RB1	0.59	0.59	0.4723
	RB6	0.85	0.85	0.7121
	RB15	0.85	0.85	0.7121
F3	RP5	0.55	0.55	0.4106
	RP6	0.81	0.81	0.6809
	RB7
	RB8	1.10	1.10	0.9809
	RB15	1.01	1.01	0.8447
F4	RP8	1.06	1.06	0.9367
	RP12	0.29	0.29	0.1426
	RB5	0.59	0.59	0.4426
	RB7
	RB11	1.37	1.37	1.2367
F5	RP9	0.29	0.29	0.2152
	RP10	0.29	0.29	0.1330
	RB6	1.00	1.00	0.8707
	RB14	0.59	0.59	0.5152
	RB15	1.00	1.00	0.9706

show the operation times of main and backup relays for each fault.

4.5. Results Considering All Operational Modes Simultaneously

So far, a different set of coordination parameters for the OCRs has been obtained for each OM in Section 4.1, Section 4.2, Section 4.3 and Section 4.4. However, the proposed approach can also be used to obtain a single set of coordination parameters suitable for all OMs.

Table 11. Coordination parameters considering all OMs.

Relay	${\mathit{TMS}}_{\mathit{i}}$	${\mathit{PSM}}_{\mathit{imax}}$
R1	0.1371	47.93
R2	0.0500	70.71
R3	0.0500	91.64
R4	0.1892	77.20
R5	0.1552	94.85
R6	0.3007	18.92
R7	0.2816	70.13
R8	0.3673	48.50
R9	0.0500	24.84
R10	0.0500	58.53
R11	0.3644	36.61
R12	0.0500	82.74
R13	0.1669	9.890
R14	0.0998	53.91
R15	0.2042	33.25

shows a set of coordination parameters, obtained with the proposed GA, that is suitable for all OMs. Note that all relays also present a different $PS{M}_{imax}$.

Table 12. Operation times for all OMs with a single set of parameters.

Fault	Relays	OM1	OM2	OM3	OM4
F1	RP1		0.4455		0.4455
	RP2	0.1165	0.1078	0.1107	0.1400
	RB4	0.4410	0.4079	0.4188	0.5298
	RB13		0.7400		0.7452
F2	RP3		0.1723		0.1723
	RP4	0.3951	0.3556	0.3697	0.4962
	RB1		0.4724		0.4724
	RB6	0.6951	0.6951	0.6951	1.4176
	RB15		0.9848	0.9848	0.9848
F3	RP5		0.4106	0.7340	0.4106
	RP6	0.6951	0.6951	0.6951	1.3554
	RB7	0.9950	0.9950	0.9950
	RB8		1.6556	1.6556	1.6556
	RB15		1.1681	1.0343	1.1681
F4	RP8		1.5810	1.5810	1.5810
	RP12	0.1044	0.0995	0.1025	0.1426
	RB5		0.5397	1.0265	0.4425
	RB7	1.3372	1.4540	1.3748
	RB11		1.88	1.8810	1.8810
F5	RP9		0.2152		0.2152
	RP10	0.1165	0.1059	0.1107	0.1330
	RB6	0.7009	0.7209	0.7024	1.7332
	RB14		0.5152		0.5152
	RB15		1.4655	1.3423	1.3423

presents the operation times of the main and backup relays for each fault. In this case, the coordination between main and back up relays is also guaranteed.

A comparison of operation times for different OMs using multiple and a single set of coordination parameters is presented in

Table 13. Total operation time for each operational mode.

	Multiple Parameters			Single Set of Parameters
Operational Modes	$\mathit{T}\left(\mathit{s}\right)$ [11]	$\mathit{T}\left(\mathit{s}\right)$ [12]	$\mathit{T}\left(\mathit{s}\right)$ [proposed]	$\mathit{T}\left(\mathit{s}\right)$ [proposed]
OM1	7.53	6.64	4.99	5.59
OM2	19.18	17.48	13.66	17.88
OM3	14.04	12.67	10.71	15.81
OM4	15.56	15.56	12.63	17.97

. Operation times reported in columns 2 through 4 in Table 13 consider an independent set of parameters for each OM as described in Section 4.1, Section 4.2, Section 4.3 and Section 4.4. Note that for all OMs the proposed approach presents lower operation times (column 4). On the other hand, the operation times presented in column 5 are computed considering a single set of parameters suitable for all OMs. Such a single set of parameters results in different operation times depending on the OM of the microgrid. As expected, obtaining a single set of coordination parameters suitable for all OMs results in higher operation times, as shown in column 5 of Table 13. Note that the works in [11,12] do not present a single set of coordination parameters suitable for all OMs, which does not allow a direct comparison with the results of the proposed approach. Despite this, note that the proposed approach outperforms the results of [12] in OM1 and OM2 and the ones of [11] in OM1 even when considering a single set of coordination parameters for all OMs.

4.6. Results Considering a Meshed Topology

To show the versatility of the proposed approach a meshed topology was also considered. In this case, switches CB-LOOP1 and CB-LOOP2 were closed to obtain a loop in the microgrid.

Table 14. Coordination parameters for a meshed topology under different OMs.

	OM1		OM2		OM3		OM4
Relay	${\mathit{TMS}}_{\mathit{i}}$	${\mathit{PSM}}_{\mathit{imax}}$	${\mathit{TMS}}_{\mathit{i}}$	${\mathit{PSM}}_{\mathit{imax}}$	${\mathit{TMS}}_{\mathit{i}}$	${\mathit{PSM}}_{\mathit{imax}}$	${\mathit{TMS}}_{\mathit{i}}$	${\mathit{PSM}}_{\mathit{imax}}$
R1	0.1523	62.49	0.2222	74.68	0.1770	60.01	0.2263	76.17
R2	0.3141	92.30	0.0998	89.11	0.2132	58.91	0.0500	38.98
R3	0.0830	70.29	0.1180	68.27	0.0930	64.68	0.1403	55.10
R4	0.4345	79.63	0.2315	85.70	0.3409	69.12	0.1382	44.76
R5	0.0500	75.98	0.0500	61.24	0.0500	79.17	0.1224	66.87
R6	0.5509	88.45	0.3412	66.10	0.4434	82.72	0.0807	28.69
R7	0.3889	59.91	0.2651	72.17	0.3251	53.34	0.4573	41.51
R8	0.3563	30.43	0.1166	85.08	0.2468	85.88	0.1460	83.54
R9	0.2537	40.93	0.2439	48.69	0.2519	79.63	0.1831	77.46
R10	0.3091	72.63	0.0977	49.06	0.2096	56.05	0.0500	81.30
R11	0.6930	43.95	0.1349	70.24	0.1662	60.04	0.1669	60.39
R12	0.3330	90.40	0.2514	89.68	0.2992	58.68	0.0500	83.67
R13	0.8610	71.69	0.2901	74.48	0.8610	34.40	0.1897	18.86
R14	0.7621	30.07	0.1250	32.12	0.1818	35.07	0.1564	12.46
R15	0.2748	22.99	0.1508	91.34	0.1971	5.00	0.1376	52.92
T(s)	29.44		27.11		30.51		20.53

presents the coordination parameters and the total operation time $T\left(s\right)$ for each OM, whereas

Table 15. Operation times for different OMs considering a meshed topology.

Fault	Relays	OM1	OM2	OM3	OM4
F1	RP1	0.42167	0.49191	0.44203	0.59823
	RP2	0.78298	0.22738	0.50076	0.17005
	RB4	1.08311	0.52745	0.80070	0.47003
	RB10	2.92315		2.52986
	RB11		0.83453	0.92618	0.89816
	RB12	1.0030	0.83790	0.92858
	RB13		0.79193		0.89824
	RB14		0.83438		0.89812
F2	RP3	0.35933	0.33954	0.33184	0.48932
	RP4	0.88455	0.42828	0.65143	0.36016
	RB1	0.65936	0.63937	0.63157	0.78926
	RB6	1.18450	0.72834	0.95144	0.66051
	RB9	1.18465	0.72843	0.95148	0.66030
	RB15		0.72841	0.95132	0.66008
F3	RP5	0.18404	0.11982	0.13543	0.32499
	RP6	1.01170	0.61973	0.81014	0.37051
	RB3	0.48396	0.41991	0.43563	0.62527
	RB7	1.31161	0.91978	1.11021
	RB8	1.31152	0.91975	1.11007	0.67032
	RB9	1.51116	0.87956	1.20111	0.82953
	RB15		0.90261	1.09567	0.77153
F4	RP8	1.08912	0.28141	0.66302	0.40801
	RP12	0.71574	0.53209	0.63773	0.20710
	RB2	1.38922	0.58116	0.96309
	RB5				0.50699
	RB7	1.57438	1.15475	1.36610
	RB10	1.38930	0.58115	0.96305
	RB11		1.15750	1.12595	1.06701
	RB13		2.04715		1.04401
	RB14		1.19148		1.08042
F5	RP9	0.70720	0.54431	0.63357	0.48849
	RP10	0.76892	0.22198	0.49124	0.16809
	RB2	3.19678		3.00190
	RB3				0.99023
	RB6	1.31087	0.83507	1.07630
	RB11		0.84417	0.93385	0.90272
	RB12	1.00700	0.84437	0.93361
	RB13		1.56726		0.90241
	RB14		0.84453		0.90340
	RB15		0.96945	1.22515	0.72047

presents the operation time of the main and backup relays. Protection coordination of OCRs in a meshed topology is a more complex task; therefore, higher operation times where obtained when compared to the previous results that considered a radial configuration.

5. Conclusions

Given the complex nature of current distribution networks, the ever-increasing presence of renewable-based DG in microgrids require more intelligent and adaptive protection schemes. In a context in which microgrids are expected to operate in various operational modes, traditional approaches to OCRs coordination may not be reliable for certain topologies of the microgrid. In this paper, a new approach for optimal coordination of OCRs in microgrids is proposed. The proposed approach considers a variable upper limit of the plug setting multiplier achieving a proper coordination in less time than traditional approaches. A genetic algorithm was used to solve the proposed coordination model. Several tests were performed on a IEC benchmark microgrid which features different types of DG units under several operation modes. A comparison was made with other models proposed in the specialized literature showing the applicability and effectiveness of the proposed approach. In all operational modes of the microgrid, the coordination obtained with the proposed model presented lower operation times. This work also shows that the employment of numerical protective devices along with the implementation of metaheuristics can be used to explore non-standard and user-defined characteristics of directional OCRs to ensue a more adequate protection coordination of microgrids.