Abstract
In this paper, a robust method for quantifying the impact of short-circuit faults on microgrids is proposed. Microgrids can operate in both islanded (grid-forming) and grid-connected (grid-following) modes, and the ownership and responsibility for the microgrid operation can vary significantly from distribution system operators (DSOs) to third-party microgrid operators. This necessitates the development of a robust short-circuit calculation (SCC) method that can provide accurate results for all the possible microgrid topologies, operational modes, and ownership models. Unlike previously developed SCC methods for microgrids, the SCC method proposed in this paper provides highly accurate results for all possible microgrid topologies: islanded microgrid, grid-connected microgrid, and utility microgrid as a part of a larger distribution grid. In addition, the proposed SCC method solves the short-circuit faults of any complexity, with the same simplicity. The proposed SCC method is tested on a complete model of a real-life microgrid on the Case Western Reserve University campus, operating in both islanded and grid-connected modes. The computational results show the advantages of the proposed SCC method in comparison to the previous ones for microgrids, regarding the robustness (ability to solve complex short-circuit faults with an arbitrary number of faulted buses and phases that affect a microgrid of any topology), as well as the accuracy of the results.
THE objective of this paper is to develop a robust and accurate short-circuit calculation (SCC) method applied to microgrids, which may be affected by any types of complex short-circuit faults, regardless of their operational state, topology, and ownership. A complex short circuit, in the context of this paper, is defined as any type of single or simultaneous short circuit, solid short circuit, or short circuit through impedances, with an arbitrary number of faulted buses and phases [
SCC methods are well-established for transmission grids and have been successfully applied in the last several decades [
For microgrids, which are the focus of this paper, it is essential to consider several important and unique features of the topology and structure. First, microgrids can operate in distinct modes, and the fault currents inside the microgrid may differ significantly depending on the operational mode [
This section presents a comprehensive overview of the current state-of-the-art in SCC methods across various parts of a power system. This analysis, coupled with identified gaps in existing literature, forms the basis for defining the motivation, objectives, and key contributions of this paper.
SCC methods for distribution grids are predominantly branch-oriented [
The state-of-the-art SCC methods for microgrids are much less developed than those for transmission and distribution grids as previously described. In [
To the best of our knowledge, the only two SCC methods developed to date that do not require predefining the fault conditions for each of different fault types are in [
The motivation for this paper is the lack of robust methods capable of performing SCCs in faulted microgrids, regardless of their operational mode, topology, and ownership, without the need to predefine boundary conditions for short-circuit faults of any complexity. The main objectives are as follows.
1) Improve the modeling of complex short-circuit faults from [
2) Develop an admittance matrix based SCC method that can be applied to microgrids in the grid-connected and islanded modes, as well as those integrated into larger distribution grids.
3) Integrate accurate models for DERs, including traditional and electronically-coupled DERs, into the proposed SCC method for microgrids.
Following these objectives, a robust and efficient SCC method for faulted microgrids is developed in this paper. The contributions of the proposed SCC method are as follows.
1) The proposed SCC method can be applied to faulted microgrids, regardless of their operational mode, ownership, or topology.
2) The proposed SCC method does not require a network root, and thus overcomes the issues of traditional SCC methods when a microgrid is operating in the islanded mode.
3) The proposed SCC method solves all types of complex short-circuit faults without requiring a complicated derivation of boundary conditions for each of different fault types, and thus it can be readily integrated into industrial software tools for performing SCCs.
4) The proposed SCC method is computationally efficient and suitable for online calculations in real-life systems and can also be implemented in advanced applications such as adaptive relay protection and FLISR.
The proposed SCC method is tested on a model of a real-life microgrid on the Case Western Reserve University (CWRU) campus, with different short-circuit faults simulated in various nodes. Both islanded and grid-connected modes are considered. To further study the applicability of the proposed SCC method, it is also tested on a utility microgrid as a part of a larger distribution grid. The computational results of these experiments are provided and clearly demonstrate the advantages of the proposed SCC method in comparison to previous ones.
The remainder of this paper is organized as follows. In Section III, different microgrid topologies are discussed and DER modeling for SCC purposes is presented. In Section IV, the complex short-circuit faults are discussed and their mathematical models are derived. In Section V, a microgrid affected by complex short-circuit faults is discussed and modeled. The proposed SCC method is presented in Section VI, while the numerical results are presented and discussed in Section VII. This paper is concluded in Section VIII.
According to the definition by the US Department of Energy, a microgrid is “A group of interconnected loads and DERs with clearly defined electrical boundaries that acts as a single controllable entity with respect to the grid and can connect and disconnect from the grid to enable it to operate in both grid-connected or islanded modes” [
A microgrid should be able to operate as an autonomous system, i.e., in islanded mode without connection to the utility grid, as well as in the grid-connected mode, where the utility grid maintains the stability of the entire system. The characteristics of the fault current flows are very different in these two operational modes [
1) Case 1: islanded microgrid.
2) Case 2: grid-connected microgrid, owned and controlled by a third-party operator.
3) Case 3: utility microgrid, owned and operated by a DSO.
The three cases are depicted in

Fig. 1 Structure of cases 1-3. (a) Cases 1 and 2. (b) Case 3.
Finally, if it is a utility microgrid as part of a larger distribution grid (case 3), the matrix consists of the entire grid including the microgrid. The equation that connects the voltages and injected currents through the admittance matrix of the modeled (micro)grid is expressed as:
(1) |
where is the admittance matrix; is the vector of nodal voltages; and is the vector of injected currents.
For the SCC, DERs can be divided into those directly connect to the grid (traditional synchronous and induction machines) and those that are electronically-coupled inverter-based DERs (IBDERs) including PVs, WTs, ES, etc. [
The excess current of IBDER is calculated as:
(2) |
where l and are the index and set of nodes where IBDERs are connected to the grid, respectively; is the fault current of IBDER; and is the pre-fault current obtained from power flow or state estimation.
To calculate , the modeling procedure from [
Any type of a complex short-circuit fault can be accurately modeled with one or several fault modules associated with the pre-fault model of microgrid [
As illustrated in

Fig. 2 Fault module and its Δ-circuit. (a) Fault module. (b) Δ-circuit.
1) Five nodes: phase nodes a, b, and c, neutral node n, and a ground node G. Nodes a, b, and c are the connection points between the fault module and the microgrid.
2) Four branches with impedances , where j is the index of fault module, and six ideal voltage sources with the pre-fault phase voltages of bus k and . On each branch, the two ideal voltage sources have the same magnitudes but opposite polarity.
The state of a fault module is represented through a set of seven elements:
(3) |
The arbitrarily-selected complex short-circuit faults can be described by a set of N1 appropriately selected fault modules as:
(4) |
To model the connection between the fault modules and a microgrid, a 3N×3N1 incidence matrix T is introduced. The matrix T is of block type, with the 3×3 block defined as:
(5) |
where ; N is the number of buses in the modeled microgrid; and I and 0 are the identity and zero matrices, respectively.
The model of faulted microgrid consists of all its elements (including traditional machines as well as IBDERs), with the associated fault modules described in Section III. In this paper, the faulted microgrid is analyzed by decomposing its state to the pre-fault state and generalized -circuit state [
In the pre-fault state, all ideal voltage sources of the traditional machines and the voltage sources of the fault modules with positive polarity oriented toward the faulted buses are retained. They are nulled in the generalized -circuit. The ideal current sources of IBDERs with their pre-fault currents are also retained.
In the generalized -circuit, the active elements are the ideal voltage sources of the fault modules oriented from the faulted buses to the ground, as shown in
(6) |
If the fault module j is associated with bus k (
The mathematical model of the generalized -circuit for the fault module j associated with bus k in the phase domain can be derived as [
(7) |
The parameters in (7) are defined as:
(8) |
(9) |
(10) |
(11) |
(12) |
(13) |
where the subscript i corresponds to the three phases a, b, and c.
The mathematical model for the generalized -circuit of the fault module in the sequence domain can be easily derived based on the model in (7), by multiplying the corresponding vectors and matrices with the transformation matrices and :
(14) |
The transformation matrix is defined as:
(15) |
Now, (14) can be written as:
(16) |
where the symbol “” corresponds to the element in the sequence domain.
The generalized -circuit of the faulted microgrid can be modeled as:
(17) |
where is the admittance matrix of microgrid in the sequence domain; and are the vectors corresponding to the injected sequence currents and sequence voltages of all buses in the generalized -circuit, respectively; is the vector corresponding to currents of all fault modules; and T is the 3N×3N1 incidence matrix.
As explained in Section II-B, due to the presence of IBDERs in the microgrid and the dependence of their fault currents on estimated voltages at their connection points at the moment of the fault occurrence, the proposed SCC method consists of two steps: ① pre-iteration step, in which the fault voltages at the connection points of all IBDERs are estimated; and ② calculation of the faulted state of microgrid. For both steps, the same SCC procedure is used, but with IBDERs modeled differently in each step, as explained in the following.
By combining (16) and (17), the mathematical model of the generalized -circuit of the faulted microgrid is represented as (18) or in a more compact form as (19).
(18) |
(19) |
The block of matrix is defined as:
(20) |
The diagonal matrix is defined as:
(21) |
where is the set of indices of faulted buses.
The matrices and are defined as:
(22) |
The diagonal matrix is defined as:
(23) |
The vector is defined as:
(24) |
The vector is defined as:
(25) |
In the first step, the aim is to estimate the voltages at the connection points of IBDERs at the moment of the fault occurrence, and it is assumed that all IBDERs inject their pre-fault currents. After the decomposition of the faulted state of microgrid to a pre-fault state and a generalized -circuit state, the values of all IBDER currents in the generalized -circuit state are null. Thus, the vector in (18) is the zero vector, and the entire vector is known.
The vector of unknown variables in (19), which includes the short-circuit currents at the fault locations and the voltages of the faulted buses in the generalized -circuit, is calculated as:
(26) |
Note that in (26), the factorization of the matrix is used.
Once the vector is known, all the voltages in the faulted microgrid including the voltages at the connection points of IBDERs are calculated by superposition of the voltages in the generalized -circuit state and the known pre-fault state. Finally, with the voltages at the connection points of IBDERs known, the excess currents of IBDERs are calculated following the procedure in [
When the excess currents of all IBDERs are known, the vector is populated with their respective values at the connection points of IBDERs. The remaining elements in the vector are null. In this step, the vector is not a zero vector, but its values are known, and therefore vector is known as well.
The vector of unknown variables is calculated in (26) and contains values of all the voltages in the generalized -circuit. The faulted state of microgrid is then calculated by superposition of the calculated generalized -circuit state and the known pre-fault state. This concludes the SCC procedure and all the necessary variables for the faulted microgrid that have been calculated. The proposed SCC method is able to accurately calculate the state within both balanced (three-phase) and unbalanced (multi-phase) microgrids with complex faults. The flowchart of the proposed SCC method is presented in

Fig. 3 Flowchart of proposed SCC method.
The proposed SCC method is initially tested on a fully modeled microgrid on the CWRU campus, as shown in

Fig. 4 Topology of microgrid on CWRU.
The rated power of WT is 60 kVA, and the rated power of ES and PV is 40 kVA. The impedances of lines 1, 2, 9, 10, 11, and 12 are the same and equal to /km. Lines 1, 2, 9, and 10 are 45.72 m, and lines 11 and 12 are 60.96 m. Lines 13, 14, 21, 22, 23, 24, 25, 26, and 27 have the same impedances equal to /km and all of them are 121.92 m.
The parameters for transformers TG, T1, and T2 are given in
Transformer | Connection type | Transformer ratio | Impedance voltage (%) | Rated capacity | X/R |
---|---|---|---|---|---|
TG | Y/Y |
11.2 kV/ 0.48 kV | 5.75 | 2.0 | 6 |
T1 | Y/Y |
11.2 kV/ 0.48 kV | 5.75 | 0.5 | 6 |
T2 | Y/Y |
0.48 kV/ 0.207 kV | 5.75 | 0.5 | 3 |
To validate the accuracy of the proposed SCC method, the microgrid on CWRU campus is modeled using in-house developed software solution, coded in FORTRAN 2015, as well as a state-of-the-art hardware-in-the-loop (HIL) setup with connected (physical) inverter controller, implemented at the Smart Grid Laboratory, at the Faculty of Technical Sciences, University of Novi Sad [

Fig. 5 Inverter controller and HIL device.
Five standard solid short-circuit faults, i.e., single-line-to-ground (SLG), two-line-to-ground (2LG), two-line (2L), three-line-to-ground (3LG), and three-line (3L) faults, are simulated at bus 11.
Fault current | Phase a | Phase b | Phase c | |||
---|---|---|---|---|---|---|
Magnitude (A) | Angle (°) | Magnitude (A) | Angle (°) | Magnitude (A) | Angle (°) | |
I1 | 10.23 | 179.54 | 10.23 | 59.54 | 10.23 | -60.46 |
I2 | 338.29 | -67.07 | 338.29 | 172.93 | 338.29 | 52.93 |
I3 | 10.46 | 178.54 | 10.46 | 58.53 | 10.46 | -61.46 |
I4 | 1.86 | -175.31 | 1.86 | 64.69 | 1.86 | -55.31 |
I5 | 2.05 | -0.43 | 2.05 | -120.43 | 2.05 | -121.52 |
I6 | 341.35 | -65.90 | 341.35 | 174.10 | 341.35 | 54.10 |
I7 | 2.81 | -4.55 | 2.81 | -124.55 | 2.81 | 115.46 |
I8 | 10.45 | 178.43 | 10.45 | 58.42 | 10.45 | -61.57 |
I9 | 43.36 | -175.31 | 43.36 | 64.69 | 43.36 | -55.31 |
I10 | 47.72 | -0.43 | 47.72 | -120.43 | 47.72 | 119.57 |
I11 | 7964.93 | -65.90 | 7964.93 | 174.10 | 7964.93 | 54.10 |
I12 | 65.52 | -4.55 | 65.52 | -124.55 | 65.52 | -115.45 |
I13 | 108.98 | 179.92 | 108.98 | 59.92 | 108.98 | -60.08 |
I14 | 72.45 | -179.91 | 72.45 | 60.08 | 72.45 | -59.91 |
I15 | 69.14 | -1.49 | 69.14 | -121.49 | 69.14 | 118.51 |
I16 | 69.14 | -1.49 | 69.14 | -121.49 | 69.14 | 118.51 |
I17 | 0 | 0 | 0 | 0 | 0 | 0 |
I18 | 0 | 0 | 0 | 0 | 0 | 0 |
I19 | 68.74 | -2.20 | 68.74 | -122.20 | 68.74 | 117.80 |
I20 | 68.74 | -2.20 | 68.74 | -122.20 | 68.74 | 117.80 |
I21 | 72.07 | 179.94 | 72.07 | 59.94 | 72.07 | -60.06 |
I22 | 160.32 | -1.49 | 160.32 | -121.49 | 160.32 | 118.51 |
I23 | 160.32 | -1.49 | 160.32 | -121.49 | 160.32 | 118.51 |
I24 | 0 | 0 | 0 | 0 | 0 | 0 |
I25 | 0 | 0 | 0 | 0 | 0 | 0 |
I26 | 159.41 | -2.20 | 159.41 | -122.20 | 159.41 | 117.80 |
I27 | 159.41 | -2.20 | 159.41 | -122.20 | 159.41 | 117.80 |

Fig. 6 Root mean square (RMS) values of currents on lines 1-27 under 3LG fault in HIL setup when microgrid is in grid-connected mode.

Fig. 7 Time-domain currents on lines 1-27 under 3LG fault in HIL setup when microgrid is in grid-connected mode
The RMS values in
The microgrid is then switched to islanded mode, and the same fault is applied to bus 11. During the simulations, the islanded microgrid is in the droop-controlled operating mode. The results in the HIL setup are given in Figs.

Fig. 8 RMS values of currents on lines 1-27 under 3LG fault in HIL setup when microgrid is in islanded mode.

Fig. 9 Time-domain currents on lines 1-27 under 3LG fault in HIL setup when microgrid is in islanded mode.
Fault current | Phase a | Phase b | Phase c | |||
---|---|---|---|---|---|---|
Magnitude (A) | Angle (°) | Magnitude (A) | Angle (°) | Magnitude (A) | Angle (°) | |
I1 | 42.12 | 115.21 | 42.12 | -4.79 | 42.12 | -124.79 |
I2 | 42.12 | -76.46 | 42.12 | 163.54 | 42.12 | 43.54 |
I3 | 35.42 | 111.30 | 35.42 | -8.70 | 35.42 | -128.70 |
I4 | 10.88 | -88.86 | 10.88 | 151.14 | 10.88 | 31.14 |
I5 | 0.72 | -24.95 | 0.72 | -144.95 | 0.72 | 95.05 |
I6 | 78.01 | -71.50 | 78.01 | 168.50 | 78.01 | 48.50 |
I7 | 1.65 | -85.05 | 1.65 | 154.95 | 1.65 | 34.95 |
I8 | 35.22 | 111.29 | 35.22 | -8.71 | 35.22 | -128.70 |
I9 | 248.64 | -88.86 | 248.64 | 151.14 | 248.64 | 31.14 |
I10 | 11.10 | -24.96 | 11.10 | -144.96 | 11.10 | 95.04 |
I11 | 1815.09 | -71.50 | 1815.09 | 168.50 | 1815.09 | 48.50 |
I12 | 35.52 | -85.05 | 35.52 | 154.95 | 35.52 | 34.95 |
I13 | 229.23 | -93.19 | 229.23 | 146.81 | 229.23 | 26.81 |
I14 | 68.51 | -93.98 | 68.51 | 146.02 | 68.51 | 26.02 |
I15 | 21.12 | -50.32 | 21.12 | -170.32 | 21.12 | 69.69 |
I16 | 21.12 | -50.32 | 21.12 | -170.32 | 21.12 | 69.69 |
I17 | 0 | 0 | 0 | 0 | 0 | 0 |
I18 | 0 | 0 | 0 | 0 | 0 | 0 |
I19 | 17.88 | -52.36 | 17.88 | -172.36 | 17.88 | 67.64 |
I20 | 17.88 | -52.36 | 17.88 | -172.36 | 17.88 | 67.64 |
I21 | 52.95 | -96.24 | 52.95 | 143.76 | 52.95 | 23.76 |
I22 | 46.95 | -50.32 | 46.95 | -170.32 | 46.95 | 69.68 |
I23 | 46.95 | -50.32 | 46.95 | -170.32 | 46.95 | 69.68 |
I24 | 0 | 0 | 0 | 0 | 0 | 0 |
I25 | 0 | 0 | 0 | 0 | 0 | 0 |
I26 | 40.72 | -52.36 | 40.72 | -172.36 | 40.72 | 67.64 |
I27 | 40.72 | -52.36 | 40.72 | -172.36 | 40.72 | 67.64 |
The CPU time needed for SCC execution is 0.225 s in real-life example that implies the microgrid connected to the 186-bus feeder. The location of fault does not affect the CPU time needed.
Furthermore, the proposed SCC method is applied to the 9-bus microgrid from [

Fig. 10 Structure of 9-bus microgrid.
Location | Method | Fault current under SLG (A) | Fault current under 3LG (A) | The maximum difference (%) | ||||
---|---|---|---|---|---|---|---|---|
Phase a | Phase b | Phase c | Phase a | Phase b | Phase c | |||
Bus 8 |
[ | 527.0 | 0 | 0 | 539.0 | 539.0 | 539.0 | 1.15 |
Proposed | 531.2 | 0 | 0 | 545.2 | 545.2 | 545.2 | ||
DG1 |
[ | 182.7 | 21.5 | 22.3 | 186.1 | 186.1 | 186.1 | 0.93 |
Proposed | 179.5 | 21.3 | 22.1 | 185.3 | 185.3 | 185.3 | ||
DG2 |
[ | 187.5 | 24.6 | 22.8 | 195.2 | 195.2 | 195.2 | 2.03 |
Proposed | 186.6 | 24.1 | 22.4 | 193.5 | 193.5 | 193.5 | ||
DG3 |
[ | 182.7 | 21.5 | 22.3 | 186.1 | 186.1 | 186.1 | 0.93 |
Proposed | 179.5 | 21.3 | 22.1 | 185.3 | 185.3 | 185.3 |
Ultimately, the results obtained by the proposed SCC method under the following two conditions of complex short-circuit faults in the microgrid on CWRU campus are presented in
Fault current | Phase a | Phase b | Phase c | |||
---|---|---|---|---|---|---|
Magnitude (A) | Angle (°) | Magnitude (A) | Angle (°) | Magnitude (A) | Angle (°) | |
I1 | 359.94 | -70.70 | 442.24 | 157.93 | 442.17 | 37.92 |
I2 | 1.84 | -170.95 | 1.67 | 62.85 | 1.77 | -59.05 |
I5 | 364.27 | -68.87 | 444.34 | 159.48 | 444.34 | 39.49 |
I10 | 8499.56 | -68.87 | 0 | 0 | 0 | 0 |
Fault current | Phase a | Phase b | Phase c | |||
---|---|---|---|---|---|---|
Magnitude (A) | Angle (°) | Magnitude (A) | Angle (°) | Magnitude (A) | Angle (°) | |
I1 | 310.31 | -56.22 | 359.40 | 169.32 | 9.95 | -59.68 |
I2 | 1.71 | -176.19 | 1.90 | 62.27 | 1.59 | -34.81 |
I5 | 317.73 | -54.44 | 364.26 | 171.13 | 2.06 | 119.71 |
I10 | 7413.61 | -54.44 | 8499.44 | 171.13 | 48.02 | 119.71 |
Condition 1: simultaneous LL-G fault (phases bc) at bus 5 and L-G fault (phase a) at bus 10. The microgrid is in the grid-connected mode.
Condition 2: simultaneous L-G fault (phase a) with fault impedance 0.01 at bus 10 and L-G fault (phase b) at bus 10. The microgrid is in the grid-connected mode.
From the aforementioned results, the following conclusion can be obtained.
1) It can be observed from
2) It can be observed from
3) It is obvious from
4) The results from Tables
Finally, as presented on a real-life example of a 186-bus feeder with a connected microgrid, besides islanded and grid-connected microgrids owned and operated by third-party aggregators, the proposed SCC method is able to efficiently calculate faulted microgrids as parts of utility grids and thus, it offers DSOs a reliable and efficient tool for implementation in advanced applications such as adaptive relay protection and FLISR.
In this paper, a robust and highly accurate SCC method for microgrids is proposed, regardless of their operational state, topology, and ownership, affected by any kind of complex short-circuit faults.
The proposed SCC method is efficient for microgrids in both islanded and grid-connected modes as well as utility microgrids as part of a larger distribution grid, with the same simplicity. As the proposed SCC method is based on the admittance matrix of the faulted system, it does not need a stiff slack bus (network root), and thus overcomes the limitations of BFS methods.
Further, the proposed SCC method solves all types of complex short-circuit faults with the same simplicity, without the need to predefine fault conditions for each of different fault types. This differentiates the proposed method from other SCC methods for microgrids.
Finally, the robustness and efficiency of the proposed SCC method make it particularly useful for advanced applications in industrial software tools for grid management, such as ADMS, DERMS, and MMS [
References
L. Strezoski, M. Prica, and K. A. Loparo, “Sequence domain calculation of active unbalanced distribution systems affected by complex short circuits,” IEEE Transactions on Power Systems, vol. 33, no. 2, pp. 1891-1902, Mar. 2018. [Baidu Scholar]
P. M. Anderson, Analysis of Faulted Power Systems. New York: IEEE Press, 1995. [Baidu Scholar]
R. Bergen and V. Vittal, Power System Analysis. New Jersey: Prentice Hall, 2000. [Baidu Scholar]
V. C. Strezoski and D. D. Bekut, “A canonical model for the study of faults in power systems,” IEEE Transactions on Power Systems, vol. 6, no. 4, pp. 1493-1499, Nov. 1991. [Baidu Scholar]
X. Zhang, F. Soudi, D. Shirmohammadi et al., “A distribution short circuit analysis approach using hybrid compensation method,” IEEE Transactions on Power Systems, vol. 10, no. 4, pp. 2053-2059, Nov. 1995. [Baidu Scholar]
W. Lin and T. Ou, “Unbalanced distribution network fault analysis with hybrid compensation,” IET Generation, Transmission & Distribution, vol. 5, no. 1, p. 92, Dec. 2011. [Baidu Scholar]
J. Teng, “Systematic short-circuit-analysis method for unbalanced distribution systems,” IEE Proceedings: Generation, Transmission and Distribution, vol. 152, no. 4, p. 549, Jul. 2005. [Baidu Scholar]
J. Teng, “Unsymmetrical short-circuit fault analysis for weakly meshed distribution systems,” IEEE Transactions on Power Systems, vol. 25, no. 1, pp. 96-105, Feb. 2010. [Baidu Scholar]
L. Strezoski, M. Prica, and K. A. Loparo, “Generalized Δ-circuit concept for integration of distributed generators in online short-circuit calculations,” IEEE Transactions on Power Systems, vol. 32, no. 4, pp. 3237-3245, Jul. 2017. [Baidu Scholar]
R. A. Jabr and I. Džafić, “A fortescue approach for real-time short circuit computation in multiphase distribution networks,” IEEE Transactions on Power Systems, vol. 30, no. 6, pp. 3276-3285, Nov. 2015. [Baidu Scholar]
M. Ghanaatian and S. Lotfifard, “Sparsity-based short-circuit analysis of power distribution systems with inverter interfaced distributed generators,” IEEE Transactions on Power Systems, vol. 34, no. 6, pp. 4857-4868, Nov. 2019. [Baidu Scholar]
I. Kim, “Short-circuit analysis models for unbalanced inverter-based distributed generation sources and loads,” IEEE Transactions on Power Systems, vol. 34, no. 5, pp. 3515-3526, Sept. 2019. [Baidu Scholar]
N. Simic, L. Strezoski, and B. Dumnic, “Short-circuit analysis of DER-based microgrids in connected and islanded modes of operation,” Energies, vol. 14, no. 19, p. 6372, Oct. 2021. [Baidu Scholar]
T. C. Mosetlhe, O. M. Babatunde, T. R. Ayodele et al., “Fault analysis in a grid-tied microgrid system,” in Proceedings of 2022 30th Southern African Universities Power Engineering Conference, Durban, South Africa, Jan. 2022, pp. 1-4. [Baidu Scholar]
S. Ghosh, C. K. Chanda, and J. K. Das, “Performance analysis of a grid connected microgrid system under fault condition,” Microsystem Technologies, vol. 28, no. 12, pp. 2689-2696, Apr. 2022. [Baidu Scholar]
T. Ghanbari and E. Farjah, “Unidirectional fault current limiter: an efficient interface between the microgrid and main network,” IEEE Transactions on Power Systems, vol. 28, no. 2, pp. 1591-1598, May 2013. [Baidu Scholar]
U.S. Department of Energy Office of Scientific and Technical Information. (2017, May). Fault analysis and detection in microgrids with high PV penetration. [Online]. Available: https://doi.org/10.2172/1367437 [Baidu Scholar]
Z. Wang, L. Mu, Y. Xu et al., (2021, Apr.). The fault analysis method of islanded microgrid based on the U/f and PQ control strategy. [Online]. Available: https://doi.org/10.1002/2050-7038.12919 [Baidu Scholar]
L. Strezoski, “Distributed energy resource management systems – DERMS: state of the art and how to move forward,” WIREs Energy and Environment, vol. 12, no. 1, pp. 1-21, Jan. 2023. [Baidu Scholar]
L. V. Strezoski, B. Dumnic, B. Popadic et al., “Novel fault models for electronically coupled distributed energy resources and their laboratory validation,” IEEE Transactions on Power Systems, vol. 35, no. 2, pp. 1209-1217, Mar. 2020. [Baidu Scholar]
M. Patel, “Opportunities for standardizing response, modeling and analysis of inverter-based resources for short circuit studies,” IEEE Transactions on Power Delivery, vol. 36, no. 4, pp. 2408-2415, Aug. 2021. [Baidu Scholar]
A. Haddadi, E. Farantatos, M. Patel et al., “Need for load modeling in short circuit analysis of an inverter-based resource-dominated power system,” IEEE Transactions on Power Delivery, vol. 38, no. 3, pp. 1882-1890, Jun. 2023. [Baidu Scholar]
E. E. Pompodakis, L. Strezoski, N. Simic et al., “Short-circuit calculation of droop-controlled islanded AC microgrids with virtual impedance current limiters,” Electric Power Systems Research, vol. 218, p. 109184, May 2023. [Baidu Scholar]
L. Strezoski, I. Stefani, and D. Bekut, “Novel method for adaptive relay protection in distribution systems with electronically-coupled DERs,” International Journal of Electrical Power & Energy Systems, vol. 116, p. 105551, Mar. 2020. [Baidu Scholar]
S. Parhizi, H. Lotfi, A. Khodaei et al., “State of the art in research on microgrids: a review,” IEEE Access, vol. 3, pp. 890-925, Jun. 2015. [Baidu Scholar]
M. Hong. (2014, Jul.). The Case Western Reserve University campus microgrid. [Online]. Available: https://www.energy.gov/sites/prod/files/2014/07/f18/CaseWesternReserveUniversityCampusGrid.pdf [Baidu Scholar]
N. Simić, L. Strezoski, and R. Milićević, “Relay protection in microgrids: settings and sensitivity in presence of IBDERs,” in Proceedings of 2022 IEEE PES Innovative Smart Grid Technologies Conference Europe, Novi Sad, Serbia, Oct. 2022, pp. 1-5. [Baidu Scholar]
L. Strezoski, H. Padullaparti, F. Ding et al., “Integration of utility distributed energy resource management system and aggregators for evolving distribution system operators,” Journal of Modern Power Systems and Clean Energy, vol. 10, no. 2, pp. 277-285, Mar. 2022. [Baidu Scholar]
L. Strezoski, I. Stefani, and B. Brbaklic, “Active management of distribution systems with high penetration of distributed energy resources,” in Proceedings of IEEE EUROCON 2019 – 18th International Conference on Smart Technologies, Novi Sad, Serbia, Jul. 2019, pp. 1-5. [Baidu Scholar]
L. V. Strezoski, N. R. Vojnovic, V. C. Strezoski et al., “Modeling challenges and potential solutions for integration of emerging DERs in DMS applications: power flow and short-circuit analysis,” Journal of Modern Power Systems and Clean Energy, vol. 7, no. 6, pp. 1365-1384, Nov. 2019. [Baidu Scholar]