Optimal determination of the number,capacity and location of DGs to improve the coordination of overcurrent relays in distribution networks

Abstract

Increasing the penetration rate of DG (Distributed Generation) units has various advantages for the network. In addition to various advantages, the use of DGs has problems, such as the emergence of protection problems in the network, which is caused by the increase in the penetration rate of DG units. To maximize the benefits of DGs, such as reducing network power losses, it is necessary to choose their location and capacity correctly. To lessen the adverse effects of DGs in the network, it is also necessary to find the optimal location and capacity of Fault Current Limiters. Then, the optimal number of DGs was determined, the number of FCLs was changed from one to five, and the effects on the results of the problem were investigated and the optimal number was determined. Finally, by knowing the number of FCLs and DGs, their optimal location and capacity were determined simultaneously. In this paper, by placing three FCLs, the protection problems caused by the presence of DGs have been solved. It can be seen that one of the most suitable locations to install these limiters is in series with distributed generation sources and at the beginning of the feeder. Finally, by adjusting the settings of three overcurrent relays and implementing appropriate values for FCL, the protection issues have been resolved.

Keywords

distributed generation fault current limiters over current relays genetic algorithm

1. Introduction

The design of distribution networks typically follows a ring configuration, although they function radially. Prior to the integration of DG resources into the distribution system, this network operated unidirectionally with power flowing from power plants to transmission substations, then to super distribution substations, and finally to loads. The incorporation of DGs on the consumers’ side alters the power flow through the lines as well as affects voltage levels at various network points. Proper and optimal placement of DGs in the distribution network can enhance network characteristics, while incorrect placement may yield negative outcomes. Therefore, prior to DG installation, a thorough investigation into their impact on line currents, voltage profiles, network reliability, changes in short-circuit currents, and harmonic injection is essential.

The introduction of DGs alters voltage levels at different points in the network. Therefore, determining the maximum injected power from DGs must ensure that all network points maintain voltage within permissible ranges. Neglecting this consideration may lead to overvoltages in the network. The integration of DGs raises short-circuit current levels in the distribution network, necessitating careful management to ensure that the injected power from DGs does not exceed protective equipment capacity. Methods to prevent short-circuit level escalation in the network are crucial. Failure to limit fault current requires replacing power switches with higher-capacity ones, incurring significant costs. Even with switch replacement, preventing short-circuit currents from passing through the first few cycles after a fault occurs is challenging, underscoring the importance of reducing short-circuit levels through appropriate methods.

Fault current limitation involves employing methods or devices in the network to restrict fault currents before they reach peak values, allowing existing power switches to effectively interrupt them. Figure 1 illustrates a short-circuit current waveform with and without a fault current limiter. The initial peak of fault current exceeds the steady-state level, potentially causing severe mechanical stresses at fault inception. Therefore, the primary objective of an FCL is to limit fault current at the first peak of the fault occurrence.

Figure 1.

The short-circuit current waveform in the presence and absence of an FCL.

The methods of limiting fault current can generally be classified from several perspectives. From one angle, these methods fall into two broad categories: active and passive. Within the active category, network impedance increases only during fault conditions, whereas within the passive category, network impedance remains consistently high both during normal operation and fault conditions. From a more comprehensive standpoint, limitation methods can be further divided into two groups. The first group comprises structural methods, which aim to reduce and limit fault current through modifications to the network arrangement. The second group consists of instrumental methods, where fault current limitation is achieved by adding elements to the system.

The fault current limiter is a device that shows very little self-resistance in the normal working mode of the network and has very little effect on the network. When a fault occurs, this equipment puts a large resistance in the fault path, thereby increasing the impedance of the fault path and, as a result, reducing the short circuit current. If an FCL is placed in the path that feeds the fault DG, it will reduce the current flowing to the fault location by the DG. As a result, the effectiveness of DG in fault currents is reduced and the stated protection disadvantages due to the addition of DG to the network will be removed to a great extent. The ideal fault current limiter should have the ability to limit the fault current at its first peak and withstand the imposed voltage and current stresses in the distribution network. In normal conditions, this limiter has low impedance and losses and low voltage drops, but in the event of a fault, it shows a very large impedance. The return time of this limiter after an error should be the minimum possible value. The cost of its installation and repair should be low and the time between two periodic repairs should be long.¹ The transition time from normal conditions to fault conditions should be as fast as possible to protect against the fault current. However, a sudden change in impedance will increase the unsafe voltage in the circuit. The time of 2 to 4 milliseconds is the right time to prevent overvoltage during impedance change.²

As stated, one of the problems caused by the increase in the penetration rate of DGs in the network is the change in the range of fault currents and as a result creating problems in the network protection system. In this section, some of the methods presented in different sources and papers to face this problem will be reviewed. According to the studies that were conducted, three general methods are used to face the challenge of increasing the penetration rate of DGs.

It is assumed that the protection plan in the system will not be changed. Based on this and according to the restrictions that this issue creates, the maximum capacity of DG units and their suitable location are determined.

According to distributed generation units that are going to be added to the network or have been added, new settings of protective relays are determined. In this case, the characteristics of distributed generation units are assumed to be known and it is necessary to get updated protection system settings.

In this case, the goal is to obtain the maximum penetration of DGs, and the coordination constraints of protective relays are also part of the constraints of the problem. In this case, unlike the first and second cases, both the capacity and location of distributed generation units and the settings of protection relays are assumed to be unknown to achieve the highest level of dispersed generation unit penetration.

1.1. Solutions based on the stability of the protection plan

In papers that employ this concept, protective constraints such as the coordination constraint of protective relays are taken into account, and the location and maximum capacity of distributed generation units are determined based on these constraints. In this scenario, it is assumed that the existing protection plan will remain unchanged.

In reference,³ a genetic algorithm is utilized to determine the optimal placement of distributed generation sources and to ascertain the maximum allowable capacity for each unit. The objective function of the problem is defined based on the reduction of losses, maximizing the total distributed generation capacity, lessening fault current levels, as well as improving voltage, all without altering the protection plan. Compliance with voltage levels and coordination between protective equipment are the two primary conditions of the problem. The proposed method is implemented on an 11 kV feeder consisting of 47 nodes. Reference⁴ employs a specialized genetic algorithm to identify the maximum capacity of distributed production. This method represents a refined model of a genetic algorithm, addressing the issue where solutions obtained from the algorithm may be locally optimal. This investigation aims to select the maximum capacity of distributed generation units in such a way that no changes are required in relay settings, location, or quantity. The objective function considered in this paper is to achieve the maximum production capacity, with the sole constraint being coordination between relays. In reference,⁵ the objective function for determining the maximum capacity of distributed generation units, both synchronous and inverter types, is defined. Constraints considered in the problem are categorized into relay coordination constraints and harmonic constraints. Coordination constraints such as disruption of the protection system and incorrect shutdown commands due to the addition of distributed generation units are addressed in this reference. Reference⁶ utilizes a genetic algorithm to locate DG units and determine their appropriate capacity. The authors claim that employing the method described in this paper to determine the location and capacity of DG units will improve network parameters such as voltage profile, power loss, and short-circuit levels. An important feature of this method is its consideration of transient short-circuit fault currents resulting from DG unit connection or disconnection from the network. Reference⁷ introduces adverse effects such as loss of coordination between overcurrent relays, loss of sensitivity, reorientation of protective equipment, and temporary overvoltages resulting from the addition of DG units to the system. In this paper, software analysis is used to calculate penetration coefficients of dispersed production for different types of distributed generation, aiming to prevent the occurrence of each adverse effect separately. To avoid creating a lack of coordination between the overcurrent relays, the function characteristics of downstream and upstream overcurrent relays are intersected. Reference⁸ presents a method to determine the optimal location of DG units to achieve the highest penetration coefficient for these units. A genetic algorithm is employed to identify the optimal location and capacity of DG units. The objective of this investigation is to determine the maximum capacity and location of distributed generation units without necessitating changes to protection constraints. In reference,⁹ a method is proposed to determine the appropriate location and capacity of Fault Current Limiters to minimize three-phase short-circuit currents at the lowest cost. The method used in this reference to solve the problem is the paper swarm Optimization (PSO) algorithm. The model presented in this reference is implemented on a modified IEEE 33-bus network with DGs. Reference¹⁰ addresses the introduction of DG units as a potential disruptor to the protection system. To mitigate the negative impacts of adding DG units, this paper discusses the optimal placement of DG units, their optimal capacities, and the optimal sizing of fault current limiters placed in series with the units. To tackle this issue, a specialized type of genetic algorithm known as NSGA-II is employed. The paper considers three adverse effects resulting from the increase in the penetration coefficient of DG units on the protection system: an increase in the level of short-circuit current, incorrect trips, and blinding of the protection system. To address these adverse effects, the paper focuses on determining the appropriate sizing of the fault current limiter.

In reference,¹¹ the method of reducing the negative effects of increasing the penetration rate of scattered products in the network is the location of scattered products. To reduce the effect of these generators on the fault current, a fault current limiter has been considered in series with each distributed generation and their optimal impedance has been found. The method used in this investigation is utilized to resolve the Coyote Optimization Algorithm (COA) issue. Reference¹² considers the addition of DG to the network as the cause of the loss of coordination between the network protection system and the solution to this problem is the addition of DG along with the FCL in series with it in the network. The intended purpose considered for this issue is to minimize the network losses and the difference between the short-circuit current before and after adding DG. The method utilized to resolve the issue is the PSO algorithm. In this paper, determining the best place for DGs and their capacity with the objective function of minimizing network losses as well as the constraints of limited DG capacity and bus voltage has been discussed.

1.2 Solutions based on providing new protection settings

In papers employing the method of providing new protection settings to address the challenge of increasing the penetration rate of distributed generation units, it is initially assumed that the production rate and capacity of distributed generation units are at a certain level. Subsequently, a suitable protection plan is proposed for different capacity values of DG units.

In reference,¹³ the impact of adding DG on the coordination between overcurrent relays is investigated. The genetic algorithm is utilized to coordinate the overcurrent relays. The proposed method in this paper is implemented on a three-basin sample system. This algorithm is executed once by considering a penetration factor of 4% for one DG unit and once by considering a penetration factor of 8% for 2 DG units. In either case, the TMS and Ip adjustment values for the overcurrent relays are obtained to ensure coordination between the relays in the network in the event of a three-phase short-circuit fault in each bus. Reference¹⁴ explores the effect of adding a DG unit to a distribution network with a medium voltage level. With the addition of the DG unit, the coordination between the overcurrent relays is compromised. In this paper, attempts are made to adjust the settings of the overcurrent relays with the addition of the DG unit and to establish coordination between the relays using adaptive relays. The coordination method involves calculating new settings for the protective relays when the DG unit is added to the system. These settings are then communicated to the relay through a communication link. These new setpoints are designated as Contiguous Function Chart (CFC) inputs for the relay. Based on the logic programmed in the CFC of each relay, the appropriate Time Current Characteristic (TCC) of each relay is determined. Newer digital relays feature multiple TCCs. Depending on the diffusion coefficient of the distributed generation unit and the new conditions, each relay selects the appropriate characteristic. Reference¹⁵ considered the addition of DG units in the distribution network as the cause of the disruption of coordination between overcurrent relays. The relays considered in this reference are all of the fixed time type and only two adjustment parameters of pick-up current and operation time can be defined for them. In this paper, to solve the problem of loss of coordination in the case of adding a distributed generation unit, the fault characteristics in the network with a high penetration coefficient for the DG unit have been analyzed, and the effect of voltage on the protection during the fault has also been investigated. In reference,¹⁶ one of the effects of adding photovoltaic units in the network is the loss of coordination between overcurrent relays. To solve this problem, first, without changing the settings of the protective relays, photovoltaic units with different penetration coefficients and with different positions have been placed in the network and the performance of the relays has been checked. In the following, according to the standard relay performance charts, the backup relay performance chart has been selected in such a way that coordination is not lost in the worst case. In the algorithm used in this paper, the calculations and settings are done in offline mode and they only make changes in the backup relay settings. As a result, there is no need for adaptive relays and programmable relays. In reference,¹⁷ the effect of adding DG units on the loss of coordination between overcurrent relays has been investigated. The method presented in this reference to solve the problem of loss of coordination is to use the overcurrent relay coordination tool. This tool has been developed by DIGSILENT Programming Language (DPL) in DIGSILENT software and is used to coordinate overcurrent relays if there are DG units in the system. The output of this tool is the pick-up current value as well as the TDS (Time Dial Setting) for the overcurrent relay. In reference,¹⁸ the issue of two-way power flow in radial networks resulting from the addition of a distributed generation unit is investigated. This bidirectional power flow leads to the loss of coordination between protection relays. The authors address this problem by employing reverse power relays in the system. These relays detect the reverse power flow in the network, identifying faults and disconnecting the DG unit from the network accordingly. By disconnecting the DG unit, coordination between the current relays is preserved. Although this method requires changes to the protection system and the addition of relays, the penetration level of the DG unit does not affect its effectiveness. This method ensures coordination between overcurrent relays regardless of the penetration level. In reference,¹⁹ the addition of distributed production units to the network and changes in their penetration levels are identified as factors influencing the short-circuit current level, leading to a loss of coordination between overcurrent relays in the network. In this reference, using constraint reduction techniques, the problem of optimum coordination of overcurrent relays is framed and addressed as a linear programming problem. The objective function in this problem is defined to minimize the total operation time of the main and backup relays for all positioning modes of the DG units in the network, considering buses near and far from the fault location to determine the TDS (Time Dial Setting) values.

1.3 The solution is based on achieving the maximum penetration of DG with new protection settings

In the papers employing this method, the aim is to determine the location and capacity of DG units to achieve the highest penetration coefficient. Contrary to the assumption of not altering the protection plan, finding a new protection plan is also a goal in this problem category, where coordination constraints are also taken into account. Essentially, in these papers, both the specifications of the DG unit and the settings of the protective relays are unknown.

Reference²⁰ addresses the increase in DG penetration coefficient along with challenges like elevated harmonic distortions, variations in short-circuit levels, and changes in current as detected by current transformers, which can lead to malfunctions in the protection system. This paper employs a genetic algorithm to determine the maximum penetration of DG units for achieving a more suitable voltage profile, reducing losses, and limiting THD (Total Harmonic Distortion). Finally, optimal setting values for overcurrent relays are obtained based on the DG penetration rate. The considered DG units in this paper include synchronous and inverter types. In reference,²¹ the aim is to determine the highest penetration coefficient of DG units along with their location and type, while considering power balance limitations, bus voltage limitations, THD and IHD limitations, overcurrent relay operation time limitations, and protection coordination limitations. The problem of finding the maximum penetration rate of DG units is formulated as a non-linear programming problem and implemented on the IEEE 30-bus standard system.

Unlike previous discussions focusing solely on the benefits of distributed production, this paper emphasizes reducing the adverse effects of DG through Fault Current Limiters (FCLs) by selecting their installation location and capacity accurately. Various methods have been provided by different authorities to determine the optimal arrangement of FCLs. However, in these references, the assumption is made that the network structure, location, and capacity of DGs are known, with little attention paid to the discussion of the location of DGs. This paper aims to provide a model for obtaining the optimal location and capacity of both DGs and FCLs. By solving the optimization problem to determine the optimal location and capacity of DGs, followed by identifying the optimal location and capacity of FCLs after determining the network structure, DGs’ detrimental effects on the defense mechanism are reduced, enabling the network to leverage the benefits of DGs while mitigating their adverse effects.

2. Simulated system

The studied network is the reference distribution network,²² whose single-line diagram is illustrated in Figure 2. This network comprises 19 buses, 18 lines, and 18 overcurrent relays. It is fed through the upstream post located at bus 1 with an impedance of 0.53 + j3.2 Ohms. The voltage level of the network is 20 kV. Detailed line information is provided in Table 1.

Figure 2.

Simulated system.

Table 1.

The results of fault classification.

Line number	R (Ω)	X(Ω)	Line number	R (Ω)	X(Ω)
1	0.67	0.53	10	0.72	0.64
2	0.8	0.69	11	0.37	0.42
3	0.59	0.59	12	0.69	0.53
4	0.69	0.59	13	0.27	0.24
5	0.48	0.53	14	0.69	0.53
6	0.67	0.69	15	0.72	0.53
7	0.72	0.53	16	0.64	0.75
8	0.8	0.69	17	0.8	0.81
9	0.72	0.64	18	0.72	0.53

To compute the short-circuit currents, the methodology outlined in reference²³ is employed. Conceptualizing the calculation of fault currents as a “black box,” its inputs encompass the network configuration, line impedance, matrix of main and backup relays, as well as the location and capacity of distributed generation sources and fault current limiters. The output of this black box comprises three-phase short-circuit currents passing through the main and backup relays for faults occurring at the initiation of the protection zone of each main relay, along with two-phase short-circuit currents passing through the main and backup relays for faults with resistance at the termination of the protection zone of each main relay. In instances requiring the computation of short-circuit currents in the reverse direction, the output of the black box is the minimum and maximum short-circuit currents passing through the main and backup relays in the reverse direction. It's important to note that to compute the short-circuit current within the black box according to reference,²³ the process involves calculating short-circuit currents by creating a virtual bus at the fault occurrence point on the line and figuring out the network's impedance matrix.

3. The proposed method to find the optimal location and capacity of DGs and FCLs

One of the advantages of using DGs is the reduction of network power losses. Therefore, when determining the optimal location and capacity of DGs, it is essential to ensure that these factors are chosen to achieve the greatest reduction in network losses. Additionally, the cost associated with using DGs must be considered during selection. While employing FCLs on all buses would be ideal for limiting error currents, it is both costly and impractical. Therefore, when selecting FCLs, it is important to consider the cost of these devices and choose their location and capacity to minimize expenses as much as possible.

3.1. The objective function of the problem

To solve the problem, the following two objective functions are defined:

\begin{aligned} J_{1} & = w_{2} \frac{1}{l} \sum_{k = 1}^{l} \sum_{i = 1}^{N_{L}} P_{i . k}^{L o s s} + \sum_{k = 1}^{l} \sum_{i = 1}^{N_{D G}} (C 1_{D G} \times P_{D G . i . k}) + \sum_{i = 1}^{N_{D G}} (C 2_{D G} \times P_{D G . i . k}) + \sum_{k = 1}^{l} (C_{k} \times P_{s l a c k_{k}}) \end{aligned}

(1)

\begin{aligned} J_{2} & = w_{1} \sum_{i = 1}^{N_{f c l}} (Z_{f c l_{i}}) \end{aligned}

(2)

In the first objective function, N_L represents the number of lines in the network, L represents the load levels, and

P_{i, k}^{L o s s}

represents the loss of the i-th line at the k-th load level. This study considers four load levels per day: during the first 6 h, the load is 30% of the rated load; in the second 6 h, it is 60% of the rated load; in the third 6 h, it equals the rated load; and in the fourth 6 h, it is 90% of the nominal load.²⁴

N_DG indicates the number of DG units placed in the network, C1 _DG indicates the cost of operation, repairs, and maintenance of DG, C2 _DG indicates the cost of purchasing and installing DG, P_DG_,i,k indicates the production power of the i-th DG at the k-th load level, and P_DG_,i represents the capacity of the i-th DG.

P_slack_,k represents the amount of power purchased from the upstream network at the k-th load level to meet the required power of the network under study. If there are no DGs in the network, all the power required by the network is purchased from the upstream network. However, with the addition of DGs to the network, the amount of power purchased will decrease depending on the capacity of the DGs. Including this term in the objective function ensures that the proper penetration coefficient of DGs is determined to minimize costs. In other words, this term helps create a balance between the power produced by DGs and the power purchased from the upstream network to minimize costs.

In the second objective function, the parameter Z_fcli represents the FCL impedance in the i-th bus, and N_fcl represents the number of buses in which FCL is placed.

Given that this study considers daily load levels, the values assigned to the coefficients w1, kc, and w2 are calculated to express the cost of the objective function in dollars per day.

3.2. Problem constraints

3.2.1. FCL impedance selection constraint

Z_{f c l}^{m a x} \leq Z_{f c l_{i}} \leq Z_{f c l}^{m a x}

(3)

In this clause, the impedance limits of FCLs are specified. The upper and lower limits of this condition are determined according to the types of FCLs available in the electricity industry. Based on the information provided in reference²⁵ and considering the voltage range of power distribution networks, the upper limit of the impedance value is set at 8 Ω, while the lower limit value is established at 5 Ω. Additionally, it is noted that the FCL resistance is 0.005 ohms under normal operating conditions.

3.2.2. Bus voltage constraint

V^{m i n} \leq V_{i} \leq V^{m a x}

(4)

In this constraint, the permissible voltage limits of buses are examined after DG placement. A minimum allowable decrease or increase in voltage of 5% is considered.

3.2.3. Maximum capacity constraints of DGs

\sum_{i = 1}^{N_{D G}} P_{D G . i} \leq C \times \sum_{i = 1}^{n b} P_{L o a d . i}

(5)

It limits the maximum capacity utilized for DGs. In various papers and references, this numerical limit is considered to be between 20 and 100 percent of the nominal load. In this research, various coefficients for DG penetration have been assumed, and the results obtained for different penetration coefficients have been compared.

3.2.4. The constraint on selecting the capacity of DG units

This constraint will restrict the capacity of each DG unit. The minimum and maximum capacity of each DG unit depends on the type of unit as well as its design and construction. In this research, to explore all potential scenarios, real numbers within the industry's available upper and lower limits for DG units have been considered.

P_{D G . i}^{m i n} \leq P_{D G . i} \leq P_{D G . i}^{m a x}

(6)

3.2.5. The constraints on the balance of active and reactive powers in the network

The last 6 constraints concern the equilibrium between reactive and active power as well as establishing a correlation between bus voltage and the power flowing through them. In these relationships, PDi and QDi represent the values of active and reactive loads connected to bus i, and Pi and Qi denote the net active and reactive power injected into each bus. This is the result of subtracting the active and reactive load from the sum of the active and reactive powers determined by different lines or sources entering each bus.

\begin{aligned} P_{i} = \sum_{j = 1}^{n b} V_{i} V_{j} (G_{i j} C O S (δ_{i} - δ_{j}) + B_{i j} \sin (δ_{i} - δ_{j})) \end{aligned}

(7)

\begin{aligned} Q_{i} = \sum_{j = 1}^{n b} V_{i} V_{j} (G_{i j} s i n (δ_{i} - δ_{j}) - B_{i j} \cos (δ_{i} - δ_{j})) \end{aligned}

(8)

\begin{aligned} P_{s_{i}} + P_{D G_{i}} - P_{D_{i}} = P \end{aligned}

(9)

\begin{aligned} Q_{s_{i}} + Q_{D G_{i}} - Q_{D_{i}} = Q_{i} \end{aligned}

(10)

\begin{aligned} P_{S l a c k} + \sum_{i = 1}^{n b} P_{D G_{i}} - \sum_{i = 1}^{n b} P_{D_{i}} - P_{L o s s} = 0 \end{aligned}

(11)

\begin{aligned} Q_{S l a c k} + \sum_{i = 1}^{n b} Q_{D G_{i}} - \sum_{i = 1}^{n b} Q_{D_{i}} - Q_{L o s s} = 0 \end{aligned}

(12)

3.3. Genetic algorithm (GA)

The genetic algorithm is extensively utilized in solving optimization dilemmas. To employ the genetic algorithm in problem-solving, an initial population comprising K chromosomes is initially generated, with each chromosome representing a potential solution to the problem. Subsequently, utilizing the fitness operator, the optimality of each chromosome is evaluated. Following this, based on the fitness values computed in the previous step, chromosomes are selected, and an intermediate population is generated. This intermediate population also comprises K chromosomes. Eventually, the mutation and crossover operators are applied to the chromosomes of the intermediate population. Upon the application of these operators, the intermediate population replaces the initial population. The aforementioned steps of fitness evaluation, selection, mutation, crossover, and replacement are iteratively executed. Figure 3 illustrates a simplified flowchart depicting the functioning of the genetic algorithm. MATLAB software toolbox is employed to tackle the optimization problems addressed in this paper using the genetic algorithm.

Figure 3.

Flowchart of genetic algorithm operation.

4. Results

4.1. Optimal number of DGs

Table 2 presents the results obtained from solving the problem for various numbers of DGs. Through load distribution calculations, the loss of the sample network without DGs and FCLs is determined to be 202.51 kW. According to Table 2, when there are 2 DGs in the network, their optimal penetration rate is approximately 89%, resulting in a loss reduction to 61.88 kW, equivalent to 8% of the network losses before DG addition. Consequently, network losses are reduced by 92%. With three DGs, the penetration rate is 87%, leading to a 95% loss reduction. The presence of 4 DGs achieves a loss reduction of 95.6% with a DG penetration rate of 91%. Furthermore, with 5 DGs, losses decrease to 96.2%, with a DG penetration rate of about 29%. These instances demonstrate that increasing the number of DGs correlates with loss reduction. Notably, the increase in loss reduction from 3 to 5 DGs is only 2.6 kW, indicating the diminishing impact of adding more than 3 DGs on loss reduction.

Table 2.
Network losses for different numbers of DGs.

Number of DGs DG capacity in MW (Location) FCL capacity in ohms (Location) Network losses (KW)

2 1.7(3)-1.6(8) 7(3)-5(8) 16.88

3 1.12 (3)-0.87(8)-1.221(17) 6(3)-5(8)-5(10-17) 9.71

4 1.09(6)-0.76(8)-0.71(17)-0.81(3) 5(6)-5(8)-5(10-17)-6(3) 8.24

5 0.9(6)-0.67(8)-0.55(17)-0.70(3)-0.6(9) 5(6)-5(8)-5(10-17)-6(3)-5(7-9) 7.11

Number of DGs	DG capacity in MW (Location)	FCL capacity in ohms (Location)	Network losses (KW)
2	1.7(3)-1.6(8)	7(3)-5(8)	16.88
3	1.12 (3)-0.87(8)-1.221(17)	6(3)-5(8)-5(10-17)	9.71
4	1.09(6)-0.76(8)-0.71(17)-0.81(3)	5(6)-5(8)-5(10-17)-6(3)	8.24
5	0.9(6)-0.67(8)-0.55(17)-0.70(3)-0.6(9)	5(6)-5(8)-5(10-17)-6(3)-5(7-9)	7.11

4.2. Optimal location and capacity of DGs

To address the problem, the objective function J₁ is initially tackled, taking into account the constraints. The outcome of solving this problem is the identification of the optimal location and capacity of DGs. The results pertaining to the location and capacity of DGs are detailed in Table 3.

Table 3.
The results obtained for the location and capacity of DGs.

DG Bus No Capacity (MW)

3 1.32

8 0.81

17 1.1

DG Bus No	Capacity (MW)
3	1.32
8	0.81
17	1.1

4.3. Optimal number of FCLs

The analysis was conducted with the assumption of having 3 DGs. The impact of varying the number of FCLs from one to five on the problem's outcomes was explored in this section. The maximum penetration rate of DGs in the network was assumed to be 100%. By determining the number of FCLs and DGs, their optimal location and capacity were concurrently obtained. Table 4 presents the results for different numbers of FCLs.

Table 4.
Network losses and cost of FCLs for different numbers of FCLs.

Number of FCLs DG capacity in MW (Location) FCL capacity in ohms (Location) Daily cost of FCLs ($) Network losses (KW)

1 1.21 (3)-0.97(8)-1.16(17) 8(3) 422.4 9.84

2 1.123 (3)-0.75(8)-1.117(17) 6(3)-7(8) 686 11.01

3 1.12 (3)-0.87(8)-1.221(17) 6(3)-5(8)-5(10-17) 844.8 9.71

4 1.11 (3)-0.86(8)-1.231(17) 6(6)-5(8)-5(10-17)-5(3) 1108.8 9.94

5 1.13 (3)-0.88(8)-1.110(17) 6(6)-5(8)-5(10-17)-5(3)-5(7-9) 1372.8 10.07

Number of FCLs	DG capacity in MW (Location)	FCL capacity in ohms (Location)	Daily cost of FCLs ($)	Network losses (KW)
1	1.21 (3)-0.97(8)-1.16(17)	8(3)	422.4	9.84
2	1.123 (3)-0.75(8)-1.117(17)	6(3)-7(8)	686	11.01
3	1.12 (3)-0.87(8)-1.221(17)	6(3)-5(8)-5(10-17)	844.8	9.71
4	1.11 (3)-0.86(8)-1.231(17)	6(6)-5(8)-5(10-17)-5(3)	1108.8	9.94
5	1.13 (3)-0.88(8)-1.110(17)	6(6)-5(8)-5(10-17)-5(3)-5(7-9)	1372.8	10.07

According to the outcomes described in Table 4, the number of FCLs does not significantly affect system losses or the location and capacity of DGs. The capacity of distributed generation units with different numbers of FCLs varies slightly, attributed to the impact of FCLs on the obtained results. Additionally, considering the lower cost of using FCLs compared to other system costs, increasing their number will not have a substantial effect on the total cost. For instance, increasing the number of FCLs from 1 to 3 resulted in a cost increase of $422.4, which represents only 2.9% of the total project cost with 3 FCLs.

4.4. Optimal location and capacity of FCLs

After solving the problem using objective function 1J to determine the optimal location as well as the capacity of three DGs in the network, along with the specified number of FCLs, objective function 2J was then optimized to determine the FCLs’ ideal placement and capacity, considering the constraints. The outcomes of solving the problem with objective function 2J are presented in Table 5.

Table 5.
Network losses and cost of FCLs for different numbers of FCLs.

FCL capacity(Ω) FCL location

6 Series with DG on bus 3

5 Series with DG on bus 8

5 The beginning of the feeder between busses 10 and 17

FCL capacity(Ω)	FCL location
6	Series with DG on bus 3
5	Series with DG on bus 8
5	The beginning of the feeder between busses 10 and 17

4.5. Loss of protection coordination due to increased short circuit level

The amount of fault current passing through the main and backup relays before and after the addition of DG can be observed in Table 6. It is evident that after incorporating DG into the network, the fault current passing through all relays increases. Furthermore, the fault current flowing through the primary and backup relays in the radial network is equal when DG is not present, but this balance is disrupted in the presence of DG. Consequently, there is an inconsistency between the operation of the main and backup overcurrent relays when a fault occurs. In this scenario, the operation time of the relays and the difference in operation time between the main and backup relays have been calculated, as shown in Table 7. Notably, in 9 cases out of the total, the protection coordination interval is not established between the primary relay's operation period and the backup, signifying the loss of protection coordination in the network.

Table 6.
Fault current through the relays before and after adding DG to the network.

Main relay current Backup relay current Main relay current Backup relay current

Main Backup Before After Before After Main Backup Before After Before After

1 - 3553 3553 - - 10 8 1979 3009 1979 3009

2 1 2940 3467 2940 2939 11 5 2084 3383 2084 2951

3 1 2941 4142 2941 2939 12 6 2066 3130 2066 2599

4 3 2465 3795 2465 3264 13 6 2068 3134 2068 2602

5 2 2377 3555 2377 2715 14 7 1817 2880 1817 2454

6 3 2465 3264 2465 3264 15 7 1817 2454 1817 2454

7 5 2083 2950 2083 2950 16 12 1809 2587 1809 2587

8 2 2375 3981 2375 2712 17 12 1809 2586 1809 2586

9 8 1979 3009 1979 3009 18 15 1607 2089 1607 2089

		Main relay current	Backup relay current			Main relay current	Backup relay current
1	-	3553	3553	-	-	10	8	1979	3009	1979	3009
2	1	2940	3467	2940	2939	11	5	2084	3383	2084	2951
3	1	2941	4142	2941	2939	12	6	2066	3130	2066	2599
4	3	2465	3795	2465	3264	13	6	2068	3134	2068	2602
5	2	2377	3555	2377	2715	14	7	1817	2880	1817	2454
6	3	2465	3264	2465	3264	15	7	1817	2454	1817	2454
7	5	2083	2950	2083	2950	16	12	1809	2587	1809	2587
8	2	2375	3981	2375	2712	17	12	1809	2586	1809	2586
9	8	1979	3009	1979	3009	18	15	1607	2089	1607	2089

Table 7.

The difference in the operation time of the main and backup relay in the presence of DG.

Main	Backup	$Δ T^{m a x}$	$Δ t^{m i n}$	Main	Backup	$Δ T^{m a x}$	$Δ t^{m i n}$
1	-	-	-	10	8	0.196	0.580
2	1	0.380	1.312	11	5	0.541	1.611
3	1	1.012	1.779	12	6	0.270	0.885
4	3	0.566	1.886	13	6	0.440	1.219
5	2	0.748	0.854	14	7	0.410	1.255
6	3	0.220	0.764	15	7	0.216	0.673
7	5	0.204	0.668	16	12	0.208	0.615
8	2	1.046	1.934	17	12	0.207	0.628
9	8	0.196	0.579	18	15	0.228	0.647

After establishing the location, numbers, and magnitude of impedance for each FCL, and considering I_pickup before DG addition as the lower limit of regulation current, the issue of protection coordination with DGs and FCLs present is addressed. The results of solving this problem utilizing a genetic algorithm are presented in Table 8. Subsequently, with suitable FCL values on the lines, we readdress the protection coordination issue in the network, this time with both DGs and FCLs simultaneously, and illustrate the outcomes in Table 9.

Table 8.

Protection settings of overcurrent relays in the presence of DG and FCL simultaneously.

Relay No	TMS	I-pickup	Type of characteristic curve	Relay No	TMS	I-pickup	Type of characteristic curve
1	0.4855	408.13	VI^a	10	0.0508	50.38	EI
2	0.5393	290.78	VI	11	0.0515	51.50	EI
3	0.6759	204.14	VI	12	0.4619	93.75	VI
4	0.0500	51.00	EI^b	13	0.0501	51.53	EI
5	0.6913	180.23	VI	14	0.0502	51.08	EI
6	0.5331	158.83	VI	15	0.3917	95.26	VI
7	0.5567	140.12	VI	16	0.0500	51.64	EI
8	0.5803	83.17	VI	17	0.0500	52.04	EI
9	0.0500	52.39	EI	18	0.0502	50.35	EI

Very Inverse (VI).

Extremely Inverse (EI).

Table 9.

Operation time difference between main and backup relay in the presence of DG and FCL simultaneously.

Main	Backup	$Δ T^{m a x}$	$Δ t^{m i n}$	Main	Backup	$Δ T^{m a x}$	$Δ t^{m i n}$
1	-	-	-	10	8	0.301	0.862
2	1	0.300	1.651	11	5	0.780	2.290
3	1	0.437	2.166	12	6	0.300	0.972
4	3	0.757	2.440	13	6	0.557	1.541
5	2	0.300	1.297	14	7	0.563	1.675
6	3	0.301	1.042	15	7	0.301	0.938
7	5	0.301	0.993	16	12	0.300	0.869
8	2	0.724	2.883	17	12	0.300	0.888
9	8	0.301	0.861	18	15	0.300	0.846

The results demonstrate that the integration of FCLs has effectively addressed the challenges posed by the presence of DGs, leading to optimal coordination within the network.

5. Comparative evaluation with existing methods

In this section, we provide a comparative analysis of the proposed method with recent studies on distributed generation (DG) and fault current limiter (FCL) optimization in distribution networks. The reviewed papers employ various optimization techniques, including genetic algorithms and particle swarm optimization, to enhance relay coordination, reduce network losses, and manage fault currents (Table 10).

Table 10.
Comparative evaluation with existing methods.

Ref. Algorithm/ method Main objective Evaluation metrics Network type Strengths Weaknesses

³ Genetic Algorithm Optimization of DG locations and capacities without altering protection scheme Loss reduction, voltage profile improvement, fault current level reduction 11KV network with 47 nodes Maintains existing protection scheme, minimizing system changes Limited flexibility, as it does not account for adaptive relay settings

⁵ Genetic Algorithm Maximum DG capacity without changing relay coordination Relay coordination, loss reduction, harmonic constraints Distribution network with fixed relays Maintains relay coordination with high DG penetration Focus on relay coordination only, with limited attention to overall network performance

⁹ PSO Optimization of FCL locations and capacities to reduce fault currents Three-phase fault current reduction with minimum cost IEEE 33-bus network Cost-effective approach to mitigate high fault currents Does not address DG placement, potentially affecting network optimization

¹⁰ NSGA-II Optimization of DG and FCL placement to mitigate negative impacts of DGs Fault current level reduction, prevention of incorrect trips Distribution network with DGs Multi-objective optimization handles protection issues and fault currents effectively Increased complexity in solving multi-objective problem, leading to longer processing times

¹³ Genetic Algorithm Relay re-coordination for a given DG penetration level Relay coordination, reduced relay operation time 3-bus distribution network Effective in adjusting relay settings dynamically with DG addition Limited to predefined DG penetration levels; not applicable for large-scale networks

²⁶ Comprehensive Review Analysis of challenges in relay coordination with DG integration Relay miscoordination, protection reliability Various distribution networks Extensive review covering recent contributions and challenges in DG protection Primarily theoretical; lacks practical application examples

²⁷ PSO Optimization of DG placement and sizing for improved reliability and loss reduction Power losses, system reliability Modified IEEE 13-bus network Effective in reducing losses with multiple DG types; real-world scenarios Limited to small-scale network; does not cover relay protection explicitly

²⁸ PSO-based Coordination Relay protection coordination with DGs and FCLs for enhanced stability Relay coordination, fault current minimization Standard IEEE test systems Effective combination of DGs and FCLs to maintain protection with high DG penetration High computational requirements for large systems

²⁹ Genetic Algorithm Integrated DG and FCL placement for relay coordination improvement Relay miscoordination, censitivity loss Active distribution network Optimized settings help mitigate DG-induced protection issues Complex configuration for realtime network adaptability

This paper Genetic Algorithm Optimization of DG and FCL locations and capacities to reduce losses and improve relay coordination Network loss reduction, improved relay coordination, fault current reduction 19-bus network Comprehensive approach with simultaneous optimization of DGs and FCLs; effective in improving network reliability Computational complexity due to dual optimization (DG and FCL)

Ref.	Algorithm/ method	Main objective	Evaluation metrics	Network type	Strengths	Weaknesses
³	Genetic Algorithm	Optimization of DG locations and capacities without altering protection scheme	Loss reduction, voltage profile improvement, fault current level reduction	11KV network with 47 nodes	Maintains existing protection scheme, minimizing system changes	Limited flexibility, as it does not account for adaptive relay settings
⁵	Genetic Algorithm	Maximum DG capacity without changing relay coordination	Relay coordination, loss reduction, harmonic constraints	Distribution network with fixed relays	Maintains relay coordination with high DG penetration	Focus on relay coordination only, with limited attention to overall network performance
⁹	PSO	Optimization of FCL locations and capacities to reduce fault currents	Three-phase fault current reduction with minimum cost	IEEE 33-bus network	Cost-effective approach to mitigate high fault currents	Does not address DG placement, potentially affecting network optimization
¹⁰	NSGA-II	Optimization of DG and FCL placement to mitigate negative impacts of DGs	Fault current level reduction, prevention of incorrect trips	Distribution network with DGs	Multi-objective optimization handles protection issues and fault currents effectively	Increased complexity in solving multi-objective problem, leading to longer processing times
¹³	Genetic Algorithm	Relay re-coordination for a given DG penetration level	Relay coordination, reduced relay operation time	3-bus distribution network	Effective in adjusting relay settings dynamically with DG addition	Limited to predefined DG penetration levels; not applicable for large-scale networks
²⁶	Comprehensive Review	Analysis of challenges in relay coordination with DG integration	Relay miscoordination, protection reliability	Various distribution networks	Extensive review covering recent contributions and challenges in DG protection	Primarily theoretical; lacks practical application examples
²⁷	PSO	Optimization of DG placement and sizing for improved reliability and loss reduction	Power losses, system reliability	Modified IEEE 13-bus network	Effective in reducing losses with multiple DG types; real-world scenarios	Limited to small-scale network; does not cover relay protection explicitly
²⁸	PSO-based Coordination	Relay protection coordination with DGs and FCLs for enhanced stability	Relay coordination, fault current minimization	Standard IEEE test systems	Effective combination of DGs and FCLs to maintain protection with high DG penetration	High computational requirements for large systems
²⁹	Genetic Algorithm	Integrated DG and FCL placement for relay coordination improvement	Relay miscoordination, censitivity loss	Active distribution network	Optimized settings help mitigate DG-induced protection issues	Complex configuration for realtime network adaptability
This paper	Genetic Algorithm	Optimization of DG and FCL locations and capacities to reduce losses and improve relay coordination	Network loss reduction, improved relay coordination, fault current reduction	19-bus network	Comprehensive approach with simultaneous optimization of DGs and FCLs; effective in improving network reliability	Computational complexity due to dual optimization (DG and FCL)

6. Conclusions

Papers discuss various solutions to address the protection challenges posed by the addition of Distributed Generation (DG) units in the network. These solutions are categorized into three main approaches: maintaining the stability of the existing protection plan, implementing new protection settings, and achieving maximum DG penetration while adjusting protection settings. Among these, methods focusing on the stability of the protection plan have received significant attention. Some references have concentrated on finding the optimal placement and capacity of fault current limiters (FCLs), employing two main strategies. Firstly, when the locations and capacities of DGs are known, the task becomes determining the optimal locations and capacities of FCLs. Secondly, after determining the locations and capacities of DGs, FCLs are installed in series with DGs, and their optimal placements and capacities are calculated. In this particular study, the initial step involved determining the number and optimal capacities of DGs. Subsequently, by installing three FCLs, protection issues were addressed. It was observed that one of the most effective locations for these limiters was in series with the DGs and at the beginning of the feeder. Finally, the protection challenges were resolved by adjusting the settings of three overcurrent relays and selecting suitable FCL values.

Footnotes

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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