Parameters Selection Method of Circuit Breaker and Fault Current Limiter in Mesh-Type DC Microgrid

Circuit breaker (CB) and fault current limiter (FCL) are two major fault protection devices used in mesh-type DC microgrids. This paper proposes the parameters selection method to obtain a reliable and economic configuration scheme of CBs and FCLs applied in mesh-type DC microgrid. The breaking time of CB, the nominal breaking current of CB and the inductance of FCL are selected as three optimization parameters in an evaluation model. Since the reliability of fault protection scheme depends on whether the nominal breaking current of the CB is greater than the line current at the breaking moment of CB, it is necessary to accurately calculate the post-fault line current. Based on this, an accurate transient DC microgrid model is presented in this paper. And then, an improved non-dominated sorting genetic algorithm II (NSGA-II) is used to configure the parameters of CBs and FCLs quickly. Besides, a case study on six-terminal DC microgrid test system shows that the proposed method can obtain accurate post-fault line current and can achieve the parameters selection of CBs and FCLs.


I. INTRODUCTION
The DC microgrid is a promising application in the electric power system. Firstly, there are no concepts of phase and reactive power in DC microgrids, so that renewable power generation system can be connected to AC/DC hybrid distribution system through DC microgrid without considering phase synchronization [1]. Secondly, some devices (such as photovoltaics, energy storage) are more suitable to connect to the AC/DC hybrid distribution system through DC microgrid [2], [3]. Moreover, the application of DC microgrids enables transmission power can be flexibly controlled in AC/DC hybrid distribution system. It can ensure efficient access of devices during normal operation and can achieve fast cross-region power support in emergency situations [4]- [6]. Therefore, compared with the traditional AC grid, the DC microgrid has many advantages and grows rapidly.
Since the impedance of lines in DC microgrid is less than that in AC grid, the influence caused by short circuit fault The associate editor coordinating the review of this manuscript and approving it for publication was Hazlie Mokhlis .
in DC microgrid is more serious than that in AC grid [7], [8].
Since the faulty current in DC microgrid has no zero crossing, it is more difficult to cut off the faulty line than that in AC grid [1]. Thus, fault protection of DC microgrid has become a significant challenge for the development of AC/DC hybrid distribution system. There have been preliminary studies on fault protection of DC microgrid which generally use circuit breakers (CBs) to isolate the fault in DC microgrid [9]- [12]. The post-fault lines current in DC microgrid may increase rapidly and even exceed the nominal breaking current of CB before the breaking time [13]. To isolate faulty segment by CB successfully, the fault current limiter (FCL) has been used to limit the rise rate of faulty current after fault occurs in DC microgrid referring to the method of HVDC grid in [14].
The technology of CB and FCL was comprehensively reviewed [15]. CB is used to break faulty lines, and there are three types of CB, i.e., Mechanical CB (MCCB) [16], Solid-state CB (SSCB) [17] and Hybrid mechanical-solid CB (HMSCB) [18]. Since the MCCB uses the traditional AC mechanical breaking unit to break the faulty line, their fault interruption time is as slow as 30-100 milliseconds. This breaking speed cannot meet the requirements of DC microgrid. The SSCB uses the controllable breaking characteristics of solid-state switch to break the faulty line, which makes the SSCB can break the faulty line quickly. However, the SSCB has considerable conduction losses in steady state. The HMSCB combines the advantages of the previous two CBs. Current flows through the branch with mechanical switch in steady state and the branch with solidstate switch in faulty condition. This decrease the losses of HMSCB and breaks the faulty line rapidly. Due to the excellent performance of HMSCB, it is suitable for HVDC and DC microgrid. Thus, HMSCB was selected as the analysis object.
FCL is used to limit the faulty current and can be divided into three types, i.e., Resistive-superconducting FCL (SFCL) [19], Solid-state FCL (SSFCL) [20] and Inductortype FCL (IFCL) [7]. The current-limiting device in SFCL usually employs a superconducting resistor, which has a low resistance in steady state, and can be transformed into a high resistance when a fault occurs. Although SFCL has superior performance, special low-temperature device is required in SFCL. Thus, it is only suitable for HVDC, and still considered as immature and costly for DC microgrid. The current limiting principle of SSFCL is the same as the breaking principle of SSCB, so SSFCL can be regarded as an additional function of SSCB. Since the solid-state switch in SSFCL needs to be adjusted by the control system, there is a time delay in the current limiting, which cannot suppress the instantaneous rising of faulty current. In addition, since SSFCL is an additional function of SSCB, it is not suitable as a main current limiting device. IFCL can be regarded as a reactor connected in series in the line. Although the installation of IFCL will increase the electrical distance of DC system, IFCL has low cost and high reliability, and is very suitable for DC microgrids. On this basis, IFCL was selected as the analysis object.
With the development of DC microgrid, the topology of DC microgrid changes from radial-type [9] or ring-type [10]- [12] to mesh-type. The radial-type DC microgrid is the simplest DC microgrid, and there are no loops in the structure. Thus, there is no coupling relationship between the lines. The ring-type DC microgrid has a loop in the structure. This means that there are two paths for power transmission between any terminal and the fault position. The coupling of mesh-type DC microgrid is more significant than that in radial-type and ring-type DC microgrid, so that the mesh-type DC microgrid has a better redundancy, flexibility and reliability, and provides the possibility for the expansion of DC microgrid capacity. A comparison of those three types for post fault transient behavior is shown in Table 1. However, compared with radial-type and ring-type topologies, more CBs and FCLs need to be installed in mesh-type DC microgrid. Therefore, it is significant to develop parameters selection method of CBs and FCLs in mesh-type DC microgrid to protect DC microgrid accurately and quickly.
Different from DC microgrid, the selection of CBs and FCLs parameters in mesh-type AC grid has been widely studied. In order to implement the selection of CBs and FCLs in AC grids, the post-fault transient model is established firstly and the model of faulty current under the consideration of FCLs is developed. And then, the parameters of CBs and FCLs can be optimized by heuristic algorithms, i.e., genetic algorithm (GA) [21], [22], Particle Swarm Optimization (PSO) [23], [24], harmony search algorithm [25].
Based on the design method of CBs and FCLs parameters in AC grids, a parameters selection method of CBs and FCLs in DC microgrid is proposed in [13], in which an evaluation model of CBs and FCLs is established and solved by GA algorithm. Furthermore, analytical expressions of faulty current are deduced. However, not all parameters related to short circuit fault in CBs and FCLs are considered in the evaluation model in [13] (such as the breaking time of CBs). Besides, the transient model of DC microgrid in [13] lacks the consideration of the intermediate nodes.
Under this situation, a parameters selection method of CBs and FCLs in mesh-type DC microgrid is proposed in this paper. The main contributions of the proposed parameters selection method can be described as following: 1) An evaluation method considering all parameters of CBs and FCLs is developed, and the parameters in hybrid mechanical-solid CB and inductor-type FCL were optimized as an example; 2) An accurate transient DC microgrid model considering the intermediate nodes in mesh-type topology is established in difference equation form; 3) An improved NSGA-II algorithm considering the calculation of non-dominated sorting and crowding distance is proposed to accelerate convergence of iteration in the parameter selection.
The rest of this paper is organized as follows. Section II presents the parameters selection problem of CBs and FCLs in mesh-type DC microgrid. And the evaluation model of CBs and FCLs is introduced in Section III. Next, Section IV gives the process of parameters selection method, establishes the transient DC microgrid model, and improves the NSGA-II algorithm. And then, the proposed parameters selection method of CBs and FCLs is validated in Section V. Finally, Section VI draws the conclusion.

II. PROBLEM STATEMENT
In order to describe the mesh-type DC microgrid clearly, a six-terminal mesh-type DC microgrid test system is established in this section. And the operation principles of CB and FCL are shown in this test system.

A. SIX-TERMINAL DC MICROGRID TEST SYSTEM
Referring to the large onshore renewable power generation grid (DCS-A) in DCS-M [26], the schematic diagram of the  test system is shown in Fig. 1. There are six nodes in the meshtype DC microgrid test system. The nodes n 1 , n 2 , n 3 , n 5 and n 6 , which connect to voltage source converter (VSC) directly, are defined as ''real nodes''. The node n 4 , which connects to VSC indirectly, is defined as ''intermediate node''.
The parameters of DC lines include DC-links capacitance, lines resistance and lines inductance. Referring to [27], the parameters are set as follows. The DC-links capacitances of all nodes are 9000µF. The resistance and inductance of DC lines are proportional to their lengths and shown in Table 2.
The master-slave control is taken as the example control strategies to verify the parameters selection method proposed by this paper. A detailed description of the master-slave control can be found in [28]. DC-link voltage control is used in VSC connected to AC generator, while active power control is used in VSC connected to AC grid or wind farm. Based on that, the DC voltage reference of VSC 5 is set as 1000V. The input power references of VSC 1 , VSC 2 , VSC 3 are set as 100kW respectively. The output power reference of VSC 6 is set as 400kW. By calculating the steady-state power flow of the six-terminal mesh-type DC microgrid, the steady-state nodes voltage and lines current can be obtained, as shown in Table 3.

B. OPERATION PRINCIPLES OF CB AND FCL IN DC MICROGRID
Since the pole-to-pole fault is more serious than the pole-toground fault, the pole-to-pole fault is chosen as the analyzed fault in this paper. As shown in Fig. 1, CBs and FCLs are used as protection devices and installed at both ends of each DC line. Assuming that a short circuit fault occurs at the midpoint of b 24 (fault condition 1), and the faulty position is defined   As shown in Table 4, if the FCL is not equipped, the faulty segment cannot be broken by a CB with the breaking time T 2 (5ms) and the breaking capacity I CB1 (1800A). However, the faulty segment can be broken by reducing T 2 (5ms) to T 1 (3ms), increasing I CB1 (1800A) to I CB2 (2500A), or equipping 2mH FCL on the faulty line. This indicates that the breaking of fault segment is realized through the cooperation of CB and FCL.
The cost of each CB is related to the breaking time and the nominal breaking current. It should be noted that, the shorter the breaking time and the higher the nominal breaking current, the higher the cost of CB. And the cost of FCL is directly proportional to inductance of FCL. Though the faulty segment can also be broken by CB (3ms, 2500A) and FCL (2mH), this cooperation has the highest cost and the worst economy. Thus, it is significant to select suitable CBs and FCLs which take both reliability and economy into consideration.

III. EVALUATION MODEL OF CBS AND FCLS
The short circuit parameters of CBs and FCLs are analyzed in this section. Furthermore, referring to parameter selection principles of CBs and FCLs in AC grids [21]- [25], the objective functions and status conditions of that in mesh-type DC microgrid are established.

A. SHORT CIRCUIT PARAMETERS OF CB AND FCL
Various electrical devices have different functions and different working conditions, so the selection of parameters is also different.
CBs in DC microgrid need to select 8 parameters: nominal voltage, nominal current, thermal current, dynamic current, nominal breaking current, nominal closing current, breaking time, and close time. Among these 8 parameters, the parameters related to short circuit fault are nominal breaking current and breaking time. And these two parameters can be selected as the optimization object.
FCLs in DC microgrid need to select 7 parameters: nominal voltage, nominal current, thermal current, dynamic current, inductance, voltage drop during normal operation, and residual voltage after short circuit. Among these 7 parameters, the parameters related to short circuit fault are inductance, voltage drop during normal operation, and residual voltage after short circuit. And the inductance can be selected as the optimization object. The voltage drop during normal operation and residual voltage after short circuit are parameters that are used as constraints.

B. OBJECTIVE FUNCTION
The objective functions are divided into economy objective function and reliability objective function. The economy objective function includes the cost of CBs and FCLs. As the analysis in Section II.B, the cost of each CB is related to the breaking time and the nominal breaking current. The objective functions of CBs can be expressed as: where F i is the length of breaking time of CB i , I i is the nominal breaking current of CB i , N CB is the number of CBs. As the analysis in Section II.B, the objective function of FCLs can be expressed as: where X j is the inductance of FCL j , N FCL is the number of FCLs.
In order to sort schemes that cannot break the fault line reliably. The constraints of whether the current of line exceeds the breaking current are converting into a total objective function. Furthermore, this process is beneficial to find schemes that satisfy all constraints in iteration. The reliability objective function can be expressed as: where E i is the judgement of whether the current I i,line of line i exceeds the nominal breaking current I i,CB of CB i .
The status constraints are divided into power constraint, capacity constraints and voltage drop constraints. The power constraint means that the active power balance of each node. And power constraint can be expressed as: where U i is the voltage of node i, R ij is the resistance between node i and node j, N b is the number of lines connected to node i, P i is the power of node i injected from VSC.

2) INEQUALITY CONSTRAINTS
The capacity constraints refer to the selection range of CBs and FCLs parameters, which can be expressed as: where T i,CB is the breaking time of CB i . I i,CB is the nominal breaking current of CB i . X j,FCL is the inductance of FCL j . Symbols with superscripts of ''max'' or ''min'' represent the maximum limit or minimum limit of corresponding parameters.
The voltage drop constraints refer to the voltage drop during normal operation and residual voltage after short circuit. There is an upper limit of the voltage drop during normal operation, which can be expressed as (9). Meanwhile, there is a lower limit of the residual voltage after short circuit, which can be expressed as (10).
where U i is the voltage drop of node i, U i_re is the residual voltage of node i, U i_N is the nominal voltage of node i, A i is the upper limit of the voltage drop of node i, B i is the lower limit of the residual voltage of node i.

IV. PARAMETERS SELECTION METHOD
The parameters selection method of CBs and FCLs is described in detail in this section. Firstly, an accurate fault transient model of mesh-type DC microgrids is developed in this section. And it is the key to obtain the accurate expressions of post-fault lines current. Secondly, in order to optimize the parameters of CBs and FCLs, an improved NSGA-II algorithm is proposed in this section.     [29], [30]. Since the VSC control system is considered in the modeling, the VSC model becomes a nonlinear system and must be solved in difference equation form instead of differential form. Therefore, in order to obtain the transient model of the entire mesh-type DC microgrid, it is necessary to derive the DC line model in difference equation form.
The DC line model in difference equation form has already been deduced in [29], [30]. However, the DC line model in [29], [30]

2) DIFFERENCE EQUATIONS OF INTERMEDIATE NODES VOLTAGE
As shown in Fig. 1, intermediate nodes exist only in radialtype topology. Thus, the three-terminal radial-type DC microgrid shown in Fig. 5 is used as an example to analyze the relationship between intermediate nodes voltage and other variables.
The relationship between lines current and nodes voltage in three terminal radial-type DC microgrid can be expressed as: where u m is voltage of node m, i pq is current in line p-q and flowing from node p to node q. R pq and L pq are the resistance and inductance of line p-q respectively. Note that R qp and L qp equal to R pq and L pq in this paper.
Eliminating the change rate of current i 14   be expressed as: where k is iteration step time.
Referring to the derivation of three terminal structure, the difference equations of intermediate nodes voltage in an arbitrary mesh-type DC microgrid in matrix form can be expressed as: Since A 0 is a diagonal matrix, the diagonal element A ii can be expressed as: (19) where K is the number of lines connecting to the node. If j > i, g = 2. Else if j < i, g = 1.
Each element in B 0 can be expressed as: Each element in C 0 can be expressed as: where R b and L b are the resistance and inductance of the j th line in i 0 respectively.

3) DIFFERENCE EQUATIONS OF LINES CURRENT AND VSCs INJECTION CURRENT
Since the intermediate nodes voltage can be calculated by (18), the voltage at each node on both sides of a line can be calculated correspondingly. Therefore, the difference equations of each line current can be related to the nodes voltage at both ends of the line. And the difference equations of lines current can be expressed in matrix form as: where T is iteration step time. L 0 is an inductor matrix.
Both the matrix L 0 and R 0 are diagonal matrix. And the value of L ii (R ii ) is equal to the inductance (resistance) of the i th line in i 0 .
Each element in D 0 can be expressed as: According to KCL, the relationship between i c0 and i 0 can be expressed as:

4) MODEL MODIFICATION UNDER SHORT CIRCUIT FAULT
Assuming that a short circuit fault occurs in line p-q as shown in Fig. 6, the line p-q is divided into two new lines. The resistance R pq and inductance L pq are replaced by R pf , R qf and L pf , L qf respectively. The faulty position is considered as a new node. And the faulty resistance is R f . Under this situation, lines current matrix i 0 , VSCs injection current i c0 and all nodes voltage matrix u 0 need to be modified as: (27) The difference equations u M , i 0 , i c0 need to be modified as: where the dimension of A is M ×M. The dimension of B is M × (n+1). The dimension of C is M × (b+1). i pf and i qf are the current of line p-f and line q-f. F is a row vector, the dimension of F is 1×(b+1), the value of the element corresponding to i pf and i qf is 1, and the value of the remaining elements is VOLUME 9, 2021 Through the iteration calculation of DC line model and VSC model, the lines current in short circuit fault can be accurately calculated, which provides a basis for optimizing the parameters of CBs and FCLs.

C. IMPROVEMENT OF NSGA-II ALGORITHM
Since there are four optimization objectives of evaluation model, NSGA-II algorithm, which is a multi-objective algorithm, is selected as the optimization algorithm to solve this multi-objective optimization problem. Compared with single-objective algorithm, those four objective functions are independent of each other when solving the multi-objective function, and there is no need to consider the ''weight'' of each optimization objective. Moreover, the NSGA-II algorithm has fast non-dominated sorting, individual crowding distance, elite strategy, etc., which can be referred in [13].
In this paper, three parameters of CBs and FCLs need to be optimized. To avoid the dimensionality disaster caused by too many parameter combinations, the improved NSGA-II algorithm is proposed to accelerate iterative convergence.

1) IMPROVEMENT OF NON-DOMINATED SORTING
The configuration schemes corresponding to individuals, whose E i in (4) greater than 0, cannot remove all faulty lines reliably. And those schemes will not be adopted as the final configuration schemes. In order to accelerate the convergence, the priority of unsatisfied individuals needs to be lowered. Thus, the non-dominated numbers of those unsatisfied individuals are increased by 1 in this paper.

2) IMPROVEMENT OF CROWDING DISTANCE CALCULATION
The crowding distance of each individual can be expressed as the sum of the crowding distance under each objective function: where n is the number of individuals in the set. It should be noted that the value of reliability objective function is equal to 0 when the individual meets the requirement for removing the fault reliably, and the crowding distance of this individual is infinity in this condition. With the improvement of non-dominated sorting, the value of reliability objective function of all individuals is 0 in the set with a non-dominated sorting of 1. It means that the crowding distance is useless and cannot inherit individuals with lower density to the next generation. Therefore, the calculation of crowding distance should be improved, and only the crowding distances of the economy objective functions are calculated in this paper.

V. CASE STUDY
In order to validate the accuracy of transient calculation model and the feasibility of parameter selection method, the midpoint of b 24 (fault condition 1 in Fig. 1) and the terminals of DC lines (fault condition 2 in Fig. 1) are used as analyzed fault position respectively. Moreover, the fault resistance of both fault conditions is zero. The parameters of the mesh-type DC microgrid are given in Section II.A. The basic parameters of selection method include the limit of inequality constraints (shown in Table 5 ) and the parameters of NSGA-II algorithm (shown in Table 6 ). Note that calculation with larger value ranges has been done in advance to estimate the value ranges of parameters.

2) COMPARISON OF NSGA-II AND IMPROVED NSGA-II
In order to ensure the persuasiveness of the comparison, except for the two improvements in Section IV.C, the NSGA-II and the improved NSGA-II are the same. The number of optimal schemes which can cut off the faulty line 35520 VOLUME 9, 2021   reliably is shown in Fig. 8. When NSGA-II is used for solving the problem, the number of optimal schemes keeps changing. The maximum number of optimal schemes is 18 when iterating to 293 times. And the minimum number of optimal schemes is only 4 when iterating to 131 times. The change of the number of optimal schemes means that the optimal schemes may lose in iteration.
After the NSGA-II algorithm is improved, the number of optimal schemes increases as iteration. And 633 optimal schemes are obtained when iterating to 300 times. The increase in the number of optimal schemes effectively avoids the dimensionality disaster and prevents the algorithm from falling into the local optimal schemes.

3) CONVERGENCE OF CBs AND FCLs PARAMETERS
In the process of using NSGA-II to approach optimal scheme set, the total breaking time of CBs gradually increases, the total nominal breaking current of CBs decreases, and the total inductance of FCLs decreases. Thus, the convergence of CBs and FCLs can be obtained by observing the changes of those three objective functions. The changes of objective functions with iteration are shown as Fig. 9. According to Fig. 9, before 150 iterations, the total breaking time of CB raises, while the total nominal breaking current of CB and total inductance of FCL drop. After 150 iterations, those three objective functions remain almost constant and fluctuate over a small range. According to the changes of those three objective functions, the parameters of CBs and FCLs rapidly approximate to the optimal scheme set before 150 iterations and fluctuate around the optimal scheme set after 150 iterations.

4) OPTIMAL SCHEME SET OF CBs AND FCLs PARAMETERS
Through the iterative of NSGA-II, the optimal scheme set can be obtained. And with the help of the optimal scheme set, the Pareto front graph can be fitted out and shown as Fig. 10. It should be noted that through the improvement of NSGA-II in Section IV.C.1), the reliability objective indexes of all the schemes in the optimal scheme set are zero (f 4 = 0). So only three economic indexes need to be analyzed.
By observing Fig. 10, it can be found that the Pareto front graph obtained by those three objective functions is a VOLUME 9, 2021 FIGURE 10. The optimal scheme set and the pareto front graph.  three-dimensional surface, and the non-dominated optimal schemes are distributed on the surface. In the following, three of the obtained results are investigated, denoted as Case 1, Case2 and Case 3. The results of these cases are given in Table 7 and Table 8. And the comparisons of nominal breaking current of CBs and maximum fault current of lines are shown in Fig. 11. Note that the side with a smaller node number is assumed as the left side of a line. The other side is the right side of the line.
According to Table 7, these cases show the optimal choices with different preferences for objective functions. The total breaking time and total nominal breaking current of CB are increased from Case 1 to Case 3, while the inductance of FCL are reduced from Case 1 to Case 3.
As shown in Table 8, the parameters of CBs and FCLs in the three cases are also different. For example, the breaking times of CB on the left side of line 1-2 are 12ms, 3.6ms, 2.0ms respectively. The value in Case 1 is 3.3 times larger than Case 2 and 6 times larger than Case 3. As shown in Fig. 11, although CB and FCL of each candidate position are selected differently by the three cases, all those three cases meet the requirements of cutting off the line reliably.
Moreover, if the cost has a linear relationship with the total nominal breaking current of CB (C Total ), the proportional coefficient is 1. If the cost has a linear relationship with the total inductance of FCL (I Total ), the proportional coefficient is 1. If the cost is inversely proportional with the total breaking time of CB (T Total ), the proportional coefficient is 1000. The relationship between total cost (Cost Total ) and economic indexes can be expressed as: Cost Total = 1 × C Total + 1 × I Total + 1000/T Total (30) With the relationship of (30), the costs of the three cases are: 81.58(Case 1), 63.60(Case 2), 66.88(Case 3). And the optimal scheme is Case 2.
According to the above analysis, it can be known that the optimal scheme set and the Pareto front graph can be obtained by the improved NSGA-II. Besides, in actual application, the optimal scheme can be selected flexibly after getting the relationship between total cost and economic indexes.

VI. CONCLUSION
This paper proposes a parameters selection method of CBs and FCLs in mesh-type DC microgrids. Firstly, all parameters of CBs and FCLs are analyzed and five parameters related to short circuit fault are selected in the evaluation method. Moreover, the post-fault transient model of mesh-type DC microgrid is established to calculate the post-fault current of all lines accurately, in which the intermediate nodes in mesh-type DC microgrids are considered in the proposed method. And then, an improved NSGA-II algorithm, which is improved with the calculation of non-dominated sorting and crowding distance, is provided to optimize the parameters of CBs and FCLs. Besides, the parameters selection method is verified under a modified six-terminal DC microgrid test system. The result shows that the method proposed in this paper can be applied to various faulty DC microgrid analysis, since the method has consideration on both reliability and economy.