Transient Modeling Method for Faulty DC Microgrid Considering Control Effect of DC/AC and DC/DC Converters

The accurate transient modeling of faulty DC microgrids is the basis of fault detection, fault location and fault isolation. AC/DC and DC/DC converters keeps their normal control strategies until the fault is detected. However, in existing researches, the influence of the control effect of converters is normally being ignored in the transient characteristics of DC microgrids. This omission reduces the accuracy of the faulty transient model. Thus, this paper proposes a transient modeling method for faulty DC microgrid considering control effect of different DC/AC and DC/DC converters. Firstly, the transient characteristics of different converters (including voltage source converter, boost circuit, bidirectional chopper circuit and buck circuit) are analyzed. And then, the faulty transient model of ring-type DC microgrid is established. Furthermore, the correctness of proposed modeling method is verified by comparing with the Control-hardware-in-loop (CHIL) test system. The results show that the proposed method can not only improve the accuracy of transient analysis of faulty DC microgrid, but also enhance the calculation efficiency.


I. INTRODUCTION
The DC microgrid, which belongs to DC distribution system, is a promising concept in power system [1]. Compared with traditional AC distribution grids, DC microgrids have two unique advantages: 1) There is no concept of ''phase'' in DC microgrids, which means that the phase synchronization does not need to be considered when AC distributed renewable energies (DERs) are connected [2]; 2) Using DC microgrids to connect with DC devices (such as photovoltaic (PV), energy storage (ES)) can reduce the use of power electronic switches, which makes the distribution systems more efficient and economical [3]. Thus, DC microgrids have been widely used in isolated islands power supply [4], [5], distributed generators (DG) connection [6], [7], asynchronous AC grid interconnection [8], urban power supply [9], electric vehicle [10], [11] and data centers [12], etc. However, DC fault protection has become a great challenge for DC microgrids [13].
Fault detection, fault isolation and fault location are the three basic elements of fault protection. Accurate transient The associate editor coordinating the review of this manuscript and approving it for publication was Salvatore Favuzza . modeling of the faulty DC microgrid is helpful for the selection of the threshold in fault detection [14] and the selection of the parameters of protection devices in fault isolation [15]. Meanwhile, to achieve fault location, the faulty currents obtained by the transient modeling can be used as reference signals to compare with the sampled signals [16]. Therefore, the transient modeling of faulty DC microgrids is the key to provide the analysis basis of fault detection, fault location and fault isolation. The fault characteristic analysis of DC microgrids can be divided into transient analysis for system structures and transient analysis for AC/DC or DC/DC converters.
The system structures of DC microgrids include radial structure, ring structure and mesh structure [17]. The topologies of radial structure are simple. And each line is decoupled. Thus, the fault loops of radial structure can be regarded as resistance-inductance (RL) loops composed of short circuit fault resistance, faulty line resistance and faulty line inductance [18], [19]. In the ring structure, there are two paths between the fault point and any node. Reference [20] disconnects the ring structure from the position, where farthest from the fault point. The simplified ring structure is equivalent to a radial structure centered on the fault point. The complexity VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ of the mesh structure is the highest, since the lines are coupled with each other. In [21], the matrix expressions of the lines currents in the mesh structure are derived. Furthermore, to make the matrix solvable, the Dijkstra's path algorithm is used to eliminate the virtual nodes in the matrix. In [15], the Kirchhoff voltage and current equations in the mesh-type DC microgrid are given in the form of difference equations. And the lines currents are iterated automatically. In summary, the transient characteristics of various system structures have been analyzed. Also, accurate transient models have been established. Voltage source converters (VSCs) and various DC/DC converters are the most commonly used converters in DC microgrids. Firstly, as analyzed in [18]- [22], the transient current being injected from VSCs can be divided into three parts: 1) The discharge current of DC-link capacitor of VSCs; 2) The discharge current provided by the line inductance through the freewheeling diode in VSCs; 3) Short circuit current provided by the AC system through the freewheeling diode in VSCs. Unlike VSCs, there are various DC/DC converter topologies connected with different control objects. The numerical analysis for a DC microgrid with PV was derived in [23]. The results show that the contribution of PV to faults cannot be neglected. Bidirectional chopper circuit is normally used to connect with an ES in DC microgrid [24]. The analysis in [24] shows that the ES contributes to faults when the ground faults occur. The equivalent circuits at different stages of DC/DC converters connected with PV and ES were established in [25]. Moreover, comprehensive comparisons among them have also been investigated. Overall, there have existing researches on the transient modeling of converters in the faulty situation. However, the currents being injected from converters were ignored during the period from fault occurrence to fault detection in previous researches, which reduces the accuracy of fault transient model.
The period from fault occurrence to fault detection is the most important stage on fault transient analysis.
And depending on the severity of fault, the time scale of this period ranges from a few milliseconds to tens of milliseconds. For better performance on fault detection, location and isolation, it is necessary to consider the contribution of currents being injected from converters. Since the fault is not detected, the switches in converters are not blocked at this period. And the control systems keep the normal control strategy at this period. To figure out the contribution of fault current being injected from converters, it is necessary to analyze the control effect of converters on the fault transient characteristic.
Under this situation, the transient modeling and analysis of power electronic converters in faulty DC microgrids are accomplished in this paper. The main contributions of this paper can be described as following: 1) The transient responses of power electronic converters (VSC, boost circuit, buck circuit and bidirectional chopper circuit) are modelled and analyzed; 2) A transient modeling method for faulty ring-type DC microgrids is proposed. In addition, the proposed method can be implemented by computer automatically and applied in fault detection, fault location and other situations easily.
The rest of this paper is organized as follows: Section II presents the transient fault analysis problem for DC microgrids; Section III analyzes the transient characteristics of DC/AC converter and DC/DC converter in a faulty ring-type DC microgrid; The numerical analysis of the error between the transient calculation model and the Control-hardwarein-loop (CHIL) test system is completed in Section IV; Section V draws the conclusion.

II. PROBLEM STATEMENT A. RING-TYPE DC MICROGRID WITH DISTRIBUTED ENERGIES ACCESS
The classic ring-type DC microgrids connected with the distributed energies is taken as the case study in this paper. The schematic of the ring-type DC microgrid is shown in Fig. 1  Assuming that a fault occurs at t 0 . Firstly, the fault will be detected at t 1 by the fault detection devices. Once the fault is detected, the fault isolation devices will be enabled and the switches in converters will be blocked immediately. The fault isolation devices will isolate faulty line at t 2 to ensure the normal operation of other healthy lines. While the fault position will be located at t 3 to ensure the fault be repaired timely. The accurate transient modeling of the DC microgrid during the period from fault occurrence to fault detection is helpful for the selection of the threshold in fault detection and the selection of the parameters of isolation devices. Meanwhile, the faulty currents and nodes voltages obtained by the transient modeling can be used as reference signals compared with the sampled signals in fault location. The use in fault detection and fault location can be found in [26]. While, the use for the selection of parameters of isolation devices can be found in [27]. The control systems in converters will keep their normal control strategies during the period from fault occurrence to fault detection. And the control systems affect the changes of the currents i cov being injected from converters. However, as shown in Fig. 3, the currents i cov are ignored during the period from fault occurrence to fault detection in previous researches [18]- [25], which will reduce the accuracy of fault transient analysis. Thus, it is necessary to establish a transient calculation model that considers the currents i cov , which are related to the effect of control systems in different converters.

III. TRANSIENT ANALYSIS OF FAULTY DC MICROGRID
The transient characteristic of converters is analyzed in this section. Firstly, the transient models of each converter are established. Secondly, to analyze the accuracy of the transient models of converters in a whole DC microgrid, the transient model of each converter is combined to achieve the transient model of the ring-type DC microgrid. VSC normally works as DC/AC converter to connect with AC grids or WFs in DC microgrids. The topology and control diagram of VSC is shown in Fig. 4. DC-link voltage control is used in VSC, which connects with AC grids, to stabilize DC-link voltage. While active power control is used in VSC, which connects with WFs, to regulate active power. Moreover, the double closed loop control with PI controllers is the commonly control method used in VSC.
The transient analysis of VSC is divided into three stages. The first stage is the establishment of the relationship between output (reference voltage of AC side, which defines as U * cd and U * cq ) and input (including DC-link voltage U dc , active power P ac , reactive power Q ac , current of AC side i s and voltage of AC side U s ) in control system. The second stage is the establishment of the relationship between output (modulation current of VSC, which defines as U cd and U cq ) and input (U * cd and U * cq ) in modulation. The third stage is the establishment of the relationship between output (P ac , Q ac , i s and injection current i cov ) and input (U cd and U cq ) in hardware circuit.
The first stage: the output U * cd and U * cq in difference form can be expressed as: where Kpα and τ iα are proportional coefficients and integral time constants of PI controller α, R stands for P ac in active power control, R stands for U dc in DC-link voltage control, c = 2/T s , T s is sample time, ω is AC frequency, L ac is inductance of AC lines.
The second stage: since the modulation of the VSC maybe saturate after fault, the output (U cd , U cq ) of modulation is not equal to input (U * cd , U * cq ) after U * c > U dc √ 3. Thus, in the second stage, the output U * cd and U * cq in difference form can be expressed as: The third stage: the expressions of P ac , Q ac , i d , i q and i cov can be expressed as (5) according to [28]: Through the iteration calculation of (1), (4) and (5), the changes of state variables in VSC before fault detection can be calculated.

1) PHOTOVOLTAICS AND ITS CONVERTERS
Boost circuit is normally worked as DC/DC converter in DC microgrid to connect with PVs. The topologies of boost circuit are shown in Fig. 5. To maximize PV power transmission, Incremental conductance method, which is a popular maximum power point tracking (MPPT) method, is used as the control strategy of boost circuit. The description of incremental conductance method can be found in [29]. The characteristic of PV can be expressed as: where I p is the short circuit current of PV, I 0 is the reverse saturation current of diode, R s and R sh are series and parallel internal resistances, q is elementary charge, A is the quality factor of diode, K is Boltzmann constant, T is temperature, N s and N p are the number of series and parallel photovoltaic cells. According to (6), the ratio of the rate of the change of current di pv and voltage dU pv can be expressed as: The DC-link voltage U dc decreases immediately after fault occurs. Because the transient characteristics of U dc changes rapidly, and the regulation of closed-loop of MTTP has hysteresis, U pv will drop along with U dc . According to the I-U curve of a single PV cell shown in Fig. 6, the working point of the PV system shifts to the left. Therefore, a constant current source is used to replace the output current of PV. Finally, i pv and U pv can be expressed as: where U dc is the DC-link voltage, g pv is the duty cycle of IGBT.
And the change of duty cycle g pv can be expressed as: where the constant value g pv is the rate of change in duty cycle. Because the step size of the change of duty cycle has little influence on efficiency [30], fixed step size is used for the change of duty cycle. Moreover, when the control system of boost circuit is saturated, g pv needs to be modified by: The expressions of variables in PV and its converters can be expressed as:

2) ENERGY STORAGE AND ITS CONVERTERS
The bidirectional chopper circuit is normally worked as DC/DC converter to connect with ESs in DC microgrids. The topology of bidirectional chopper circuit is shown as Fig. 7 a).
DC-link voltage control is normally used in bidirectional chopper circuit to stabilize DC-link voltage. And the control diagram is shown as Fig. 7 b). Batteries and super capacitors are two complementary ESs. The batteries have high energy density but have slow power regulation speed. In contrast, the super capacitors have fast power regulation speed but have low energy density.
Since the life of batteries decreases as the number of charges and discharges increases, the high frequency component of inputs is generally filtered out in the control system of batteries. Because the short circuit fault is a high frequency power fluctuation, the output of control system for battery is considered unchanged from fault occurrence to fault detection. Thus, the expression of i cov can be expressed as: where g bt is the output of control system, U bt is the voltage of battery, L bt is the inductance of DC line. The power regulation speed of super capacitors is fast. Once a fault occurs in DC microgrid, the super capacitor injects power immediately to suppress the dropping of DC-link voltage. The transient analysis of bidirectional chopper circuit for super capacitors is similar to the transient analysis of VSC and also can be divided into three stages.
The first stage is the establishment of the relationship between output g * s and input (U dc and i st ) in control system. The expression of g * s can be expressed as: where where Kpα and τ iα are proportional coefficients and integral time constants of PI controller α, c = 2/T s , T s is sample time.
The second stage is the establishment of the relationship between output g s and input g * s in modulation. The expression of g s can be expressed as: The third stage is establishment of the relationship between output (U sc , i sc and i cov ) and input g in hardware circuit. The expressions of those above variables can be expressed as:

3) DC LOAD AND ITS CONVERTERS
Buck circuit is normally worked as DC/DC converter in DC microgrid to connect with DC load. The topology and control diagram of buck circuit is shown in Fig. 8. DC-link voltage control is normally used to stabilize voltage U ld of DC load. Similar to the derivation of bidirectional chopper circuit for super capacitors, the transient analysis of buck circuit for DC loads can also be divided into three stages.
The first stage is the establishment of the relationship between output g * l and input (U dc and i st ) in control system. The expression of g * l can be expressed as: where where Kpα and τ iα are proportional coefficients and integral time constants of PI controller α, c = 2/T s , T s is sample time, U ld is the voltage of DC load, i ld is the current of DC load.
The second stage is the establishment of the relationship between output g l and input g * l in modulation. The expression of g can be expressed as: The third stage is the establishment of the relationship between output (U ld , i ld and i cov ) and input g l in hardware circuit. The expressions of those above variables can be expressed as:

C. TRANSIENT ANALYSIS OF FAULTY DC MICROGRID
According to [27], there are only two kinds of variables (nodes voltages and lines currents) in system structures of DC microgrids. And the difference expressions of nodes voltages and lines currents can be expressed as: where u i is the voltage of node i, i l is the current of line l, i ik is the current from node i to node k, i cov_i is the current from converter of node i, C i is the capacitance of node i, R l and L l are the resistance and inductance of line l. Taking pole-to-pole short circuit fault as an example and supposing a fault occurs on line p. The faulty line is shown in Fig. 9. A faulty node n and two DC lines p 1 , p 2 are denoted following the occurrence of the fault. The voltage of node n and currents of lines p 1 , p 2 can be expressed as (22). The difference expressions of other nodes voltages and lines currents still use (21).
150764 VOLUME 8, 2020 where u n , u m , u k are the voltages of node n, m, k; i p1 and i p2 are the currents of line p 1 and p 2 ; R fault is the fault resistance; R p1 , R p2 and L p1 , L p2 are the resistances and inductances of line p 1 and p 2 . T is the size of iteration step. Based on the above analysis, the transient analysis process of a ring-type DC microgrid is iterated by three parts: transient modeling of AC units and their converters; transient modeling of DC units and their converters; and transient modeling of variables in system structures of DC microgrids. Finally, the process of transient analysis of a DC microgrid is shown as Fig. 10.

IV. NUMERICAL ANALYSIS
The transient calculation models are coded as M-code in Matlab. And the faulty DC microgrid is run in Typhoon 602+ CHIL test system. The accuracy of the transient calculation models is validated by the comparison with the CHIL test system. In addition, to decouple the analysis of each converter's modeling, the converters are connected to the ideal DC grid respectively. To verify the accuracy of converters' models in a whole DC microgrid, the converters are connected through a ring-type DC microgrid.

A. CONTROL-HARDWARE-IN-LOOP TEST SYSTEM
The experiment platform based on CHIL is shown as Fig. 11. Firstly, the experiment scenarios of DC microgrid are designed in CHIL platform of Typhoon 602+. And the time step of Typhoon 602+ is 1µs. Meanwhile, the control systems of various converters are implemented in TMS32028335DSP+ Spartan 6XC6SLX16FPGA control board and the modulation frequency is 10kHz.

B. VALIDATION OF TRANSIENT MODELING OF CONVERTERS 1) STRUCTURE AND PARAMETERS OF TEST SYSTEM
The structure of test system of AC/DC and DC/DC converters are shown as Fig. 12. And the test system can be divided into four parts. Firstly, part 1 is the connected AC or DC units, including AC grid, WF, PV, ES (battery and super capacitor) and DC load. Secondly, part 2 is the converters corresponding to various units: AC grid uses VSC controlled by DC-link voltage control, and the voltage is set as 1000V; WF uses VSC controlled by active power control, and the output power is set as 100kW; PV uses boost circuit controlled by MPPT; ES uses bidirectional chopper circuit controlled by DC-link voltage control, and the voltage is set as 1000V; DC load uses buck circuit controlled by DC-link voltage control, and the voltage of DC load is set as 300V. Thirdly, part 3 includes the DC-link capacitor and DC line. The capacitance of capacitor is set as 8000µF. The length, resistance and inductance of DC line is set as 3km, 0.2 and 4mH. Finally, part 4 is a DC voltage source, which is used as an equivalent for the DC microgrid. And the voltage U sys is set as 960V.
It is assumed that pole-to-pole faults occur at midpoint of DC line. And to simulate different fault degrees, the fault resistance takes the values of 1µ , 1m , 0.1 , 0.2 and 0.4 . And transients characteristics of this test system are analyzed through CHIL test system, calculation model proposed in this paper and calculation model ignoring i cov . Moreover, the absolute error is used to compare the calculation results and CHIL results.
The errors of U dc and i dc are related to i cov . However, the currents i cov being injected from converters are ignored in previous researches [18]- [25]. Thus, the modeling method of ignoring the currents i cov is used for comparison. And the structure of test system using pervious researches' modeling method is shown as Fig. 13.

2) VALIDATION OF VSC CONNECTED WITH AC GIRD
Taking the fault resistance of 0.1 as an example, the waveform of DC-link voltage U dc , line current i dc and i cov (filtered through 500Hz) of the test system connected with AC grid are shown as Fig. 14. And the errors of the proposed calculation model and the calculation model ignoring i cov compared with the CHIL test system are shown in Fig. 15. It can be found that i cov obtained by calculation model is similar to i cov obtained by CHIL. The current i cov has the maximum error at the period from 3ms to 8ms. And the maximum error of i cov is less than 10A. Furthermore, since i cov is considered in the calculation of U dc and i dc , the maximum errors of U dc and i dc by calculation method and CHIL are 10.87V and 11.07A. Otherwise, the errors of U dc and i dc will reach 124.98V and 126.57A when i cov is not considered in calculation method.  Table 1. When i cov is not considered in calculation method, the maximum errors of U dc are greater than 107V and the average errors of U dc are greater than 59V. The maximum errors of i dc are greater than 112A, and the average errors of i dc are greater than 40A. On the contrary, when the transient characteristics of VSC and the corresponding injected current i cov are considered, the maximum errors of U dc are less than 18V and the average errors of U dc are less than 6V. The maximum errors of i dc are less than 13A, and the average errors of i dc are less than 5A.

3) VALIDATION OF VSC CONNECTED WITH WF
Taking the fault resistance of 0.1 as an example, the waveform of DC-link voltage U dc , line current i dc and i cov (filtered through 500Hz) of the test system connected with WF are shown as Fig. 16. And the errors of the proposed calculation model and the calculation model ignoring i cov compared with the CHIL test system are shown in Fig. 17. It can be found that the trend of i cov calculated by the proposed method is similar to that in CHIL test system. The error of i cov is less than 5A within 7ms from fault occurs. And the maximum error of i cov is less than 15A within 10ms from fault occurs. Furthermore, since i cov is considered in the calculation of U dc and i dc , the maximum errors of U dc and i dc are 27.78V and 14.39A. Otherwise, the errors of U dc and i dc will reach 167.98V and 138.91A when i cov is not considered in calculation method.
The more detailed error results under different fault resistances (1µ , 1m , 0.1 , 0.2 and 0.4 ) are shown in Table 2. When i cov is not considered in calculation method, the maximum errors of U dc are greater than 139V and the average errors of U dc are greater than 74V. The maximum errors of i dc are greater than 109A, and the average errors of i dc are greater than 40A. On the contrary, when the transient characteristics of VSC and the corresponding injected current i cov are considered, the maximum errors of U dc are less than 42V and the average errors of U dc are less than 19V.The maximum errors of i dc are less than 24A, and the average errors of i dc are less than 11A.

4) VALIDATION OF BOOST CIRCUIT CONNECTED WITH PV
Taking the fault resistance of 0.1 as an example, the waveform of DC-link voltage U dc , line current i dc and i cov (filtered through 500Hz) of the test system connected with PV are  shown as Fig. 18. And the errors of the proposed calculation model and the calculation model ignoring i cov compared with the CHIL test system are shown in Fig. 19. It can be found that ripples exist in i cov obtained by CHIL, and the frequency is 5kHz. This is because the duty cycle in control system varies by a fixed step size. Since the boost circuit is simplified by mean value model, the ripples are not reflected in the proposed calculation model. Despite the ripples, the error is less than 4A within 10ms after fault occurs. Furthermore, since i cov is considered in the calculation of U dc and i dc , the maximum errors of U dc and i dc are 5.40V and 7.62A. Otherwise, the errors of U dc and i dc will reach 85.72V and 101.58A when i cov is not considered in calculation method.
The detailed error results under different fault resistances (1µ , 1m , 0.1 , 0.2 and 0.4 ) are shown in Table 3. When i cov is not considered in calculation method, the maximum errors of U dc are greater than 85V and the average errors of U dc are greater than 50V. The maximum errors of i dc are greater than 88A, and the average errors of i dc are greater than 35A. On the contrary, when the transient characteristics of boost circuit and the corresponding injected current i cov are considered, the maximum errors of U dc are less than 13V

5) VALIDATION OF BIDIRECTIONAL CHOPPER CIRCUIT CONNECTED WITH ES
Taking the fault resistance of 0.1 as an example, the waveform of DC-link voltage U dc , line current i dc and i cov (filtered through 500Hz) of the test system connected with battery are shown as Fig. 20. And the errors of the proposed calculation model and the calculation model ignoring i cov compared with the CHIL test system are shown in Fig. 21. Because the life of batteries decreases as the number of charges and discharges increases, the high frequency component of inputs is generally filtered out in the control system of batteries. The short circuit fault is a high frequency power fluctuation. Therefore, in the proposed calculation model, the output of control system for battery is considered unchanged from fault occurrence to fault detection. Although the approximate processing of control system results in a monotonic increase of i cov 's error, the error is less than 10A within 10ms after  Table 4. When i cov is not considered in calculation method, the maximum errors of U dc are greater than 132V and the average errors of U dc are greater than 61V. The maximum errors of i dc are greater than 107A, and the average errors of i dc are greater than 40A. On the contrary, when the transient characteristics of bidirectional chopper circuit and the corresponding injected current i cov are considered, the maximum errors of U dc are less than 28V and the average errors of U dc are less than 8V.The maximum errors of i dc are less than 13A, and the average errors of i dc are less than 7A. Taking the fault resistance of 0.1 as an example, the waveform of DC-link voltage U dc , line current i dc and i cov (filtered through 500Hz) of the test system connected with SC are shown as Fig. 22. And the errors of the proposed calculation model and the calculation model ignoring i cov compared with the CHIL test system are shown in Fig. 23. It can be found that the trend of i cov calculated by the proposed method is similar to that in CHIL test system. The maximum  error of i cov occurs within 1ms after fault occurs, and the value is less than 5A. The error of i cov is reduced and maintained within 2A from 1ms to 10ms. Furthermore, since i cov is considered in the calculation of U dc and i dc , the maximum errors of U dc and i dc are 10.36V and 7.45A. Otherwise, the errors of U dc and i dc will reach 39.39V and 40.57A when i cov is not considered in calculation method.
The detailed error results under different fault resistances (1µ , 1m , 0.1 , 0.2 and 0.4 ) are shown in Table 5. When i cov is not considered in calculation method, the maximum errors of U dc are greater than 41V and the average errors of U dc are greater than 19V. The maximum errors of i dc are greater than 36A, and the average errors of i dc are greater than 13A. On the contrary, when the transient characteristics of bidirectional chopper circuit and the corresponding injected current i cov are considered, the maximum errors of U dc are less than 12V and the average errors of U dc are less than 4V. The maximum errors of i dc are less than 8A, and the average errors of i dc are less than 3A.

6) VALIDATION OF BUCK CIRCUIT CONNECTED WITH DC LOAD
Taking the fault resistance of 0.1 as an example, the waveform of DC-link voltage U dc , line current i dc and i cov (filtered through 500Hz) of the test system connected with DC load are   shown as Fig. 24. And the errors of the proposed calculation model and the calculation model ignoring i cov compared with the CHIL test system are shown in Fig. 25. It can be found that the trend of i cov calculated by the proposed method is similar to that in CHIL test system. The error of i cov is less than 5A within 8ms from fault occurs. And the maximum error of i cov is less than 15A within 10ms from fault occurs. Furthermore, since i cov is considered in the calculation of U dc and i dc , the maximum errors of U dc and i dc are 7.74V and 14.33A. Otherwise, the errors of U dc and i dc will reach 123.62V and 116.25A when i cov is not considered in calculation method.
The detailed error results under different fault resistances (1µ , 1m , 0.1 , 0.2 and 0.4 ) are shown in Table 6. When i cov is not considered in calculation method, the maximum errors of U dc are greater than 111V and the average errors of U dc are greater than 57V. The maximum errors of i dc are greater than 97A, and the average errors of i dc are greater than 34A. On the contrary, when the transient characteristics of buck circuit and the corresponding injected current i cov are considered, the maximum errors of U dc are less than 8V and the average errors of U dc are less than 5V.The maximum errors of i dc are less than 13A, and the average errors of i dc are less than 7A.

7) COMPARISON OF TRANSIENT MODEL OF DIFFERENT CONVERTERS
The errors of U dc and i dc are related to i cov . However, the currents i cov being injected from converters are ignored in previous researches [18]- [25]. And i cov is influenced by the control of converters. For example, the control target is DC-link voltage when converter connects to SC. To suppress the decrease of the DC-link voltage after fault occurs, the modulation ratio increases rapidly. This causes the drop of i cov . Thus, the average errors of U dc and i dc are only 21.04V and 14.80A even if i cov is ignored when converter connects to SC. On the contrary, the control target is selected as active power when converter connects to WF. The control reduces VSC's AC side voltage U c to increase active power delivery, and i cov increases continuously after the fault. As a result, the average errors of U dc and i dc reach 83.85V and 47.32A if i cov is ignored when converter connects to WF. Compared with the previous researches which ignores the control effect of converters and injected current i cov , the method proposed in this paper can always guarantee the calculation accuracy in the fault transient analysis.

C. VALIDATION OF TRANSIENT MODELING OF DC MICROGRID 1) PARAMETERS OF RING-TYPE DC MICROGRID
The ring-type DC microgrid shown in Fig. 1 is taken as the test system. The parameters and control targets of control systems in converters are the same as those in Part B, Section IV. In addition, both the bidirectional chopper circuits connect with ESs and the VSC connects with AC grid adopt DC-link voltage control. To prevent the conflicts of their control, the control systems in battery and SC only operate when the DC-link voltage is 50V away from 1000V (lower than 950V or higher than 1050V).
The circuit parameters of DC microgrid include DC-link capacitances, lines resistances and inductances. The DC-link capacitances of all converters are set as 8000µF. The resistances and inductances of lines are shown in Table 7. Moreover, the pole-to-pole faults are assumed to occur at midpoint of DC line. And the fault resistance is set as 0.1 .

2) CALCULATION ACCURACY
Taking the fault occurrence at the midpoint of line 3-6 as an example, the waveform of the currents i 36_left and i 36_right at fault line 3-6 are shown in Fig. 26. In addition, the currents calculated by the proposed method and currents calculated in the case of ignoring i cov are also shown in Fig. 26. And the errors of the proposed calculation model and the calculation model ignoring i cov compared with the CHIL test system are shown in Fig. 27.
It can be found that the trend of i 36_left and i 36_right calculated by the proposed method are the same as that in CHIL test system. And the maximum errors of i 36_left and i 36_right are  12.22A and 11.74A respectively. On the contrary, the errors of i 36_left and i 36_right will reach 97.30A and 95.47A when i cov is not considered.
The more detailed error results under different faulty conditions are shown in Table 8. It can be found that, after considering the i cov that changes with the control systems, the errors of calculated fault currents are reduced. The average error decreased from 76.56A to 6.77A.

3) CALCULATION EFFICIENCY
Referring to the analysis method in [21], the calculation efficiency of the proposed calculation method is analyzed. Using PC with Intel(R) core(TM) i7-8700 CPU @3.20 GHz as the experiment platform. The proposed calculation model for the six-terminal ring-type DC microgrid is coded as M-code in Matlab 2018b. The transient characteristics of variables are analyzed, and the time range is 10ms after fault occurs. The time spent under calculation model is 4.23ms. On the other hand, the DC microgrid is also simulated by Matlab/Simulink with 1µs time step. The short-circuit fault occurred at t = 1.0 s, and we observe the simulation results from 1.0s to 1.01s (time range is also 10ms). The time spent under simulation is 2.45s. The comparison shows that the transient model proposed in this paper is over 413 times faster than simulation. This validates the proposed method can analyze the faulty DC microgrid efficiently.

V. CONCLUSION
Through the analysis in this paper, it is proved that the control effect in converters has contributions on the fault transient characteristic of DC microgrid. Therefore, the influences of the control systems are being considered in the establishment of the transient calculation model in this paper. In detail, the transient characteristics of different converters (including voltage source converter, boost circuit, bidirectional chopper circuit and buck circuit) with different units (including AC grid, wind farm, photovoltaic, energy storage and DC load) are being analyzed. And then the transient model of ring-type DC microgrid, connecting with AC/DC units by different converters, is established. By comparison with the CHIL test system, the transient model proposed in paper improves the transient analysis accuracy significantly and enhances the computational efficiency.