# Resilience-oriented intentional islanding of reconfigurable distribution power systems

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## Abstract

Participation of distributed energy resources in the load restoration procedure, known as intentional islanding, can significantly improve the distribution system reliability. Distribution system reconfiguration can effectively alter islanding procedure and thus provide an opportunity to supply more demanded energy and reduce distribution system losses. In addition, high-impact events such as hurricanes and earthquake may complicate the procedure of load restoration, due to disconnection of the distribution system from the upstream grid or concurrent component outages. This paper presents a two-level method for intentional islanding of a reconfigurable distribution system, considering high impact events. In the first level, optimal islands are selected according to the graph model of the distribution system. In the second level, an optimal power flow (OPF) problem is solved to meet the operation constraints of the islands by reactive power control and demand side management. The proposed problem in the first level is solved by a combination of depth first search and particle swarm optimization methods. The OPF problem in the second level is solved in DIgSILENT software. The proposed method is implemented in the IEEE 69-bus test system, and the results show the validity and effectiveness of the proposed algorithm.

## Keywords

Intentional islanding Active distribution system Distributed energy resources Distribution system reconfiguration Distribution system resilience## 1 Introduction

The distribution system is the most vulnerable part of the power system, due to distributed structure, and low level of monitoring, controllability, and protections [1, 2, 3]. Hence, studies on effective methods for load restoration to improve the reliability of distribution systems have recently attracted more attention from scholars [1, 2, 3, 4, 5]. The load restoration has been considered as a network reconfiguration problem in the conventional distribution systems. Accordingly, once a fault occurs, the faulty section is isolated, and the tie-switches are closed to restore the out-of-service customers [6, 7]. However, in the case of disconnection of a distribution system and upstream grid, this restoration method does not work [4].

The development of smart automation devices, such as digital protective devices, automatic feeder switches, and advanced metering infrastructure (AMI), motivates electric distribution utilities to modernize the grid [8, 9, 10]. In addition, the increasing penetration of distributed energy resources (DERs) in the distribution systems has changed the face of distribution systems from passive to active distribution systems (ADSs). Modern ADS can provide new opportunities to restore critical loads and to reduce the outage time, which enhances the reliability of the power system [8, 9, 10, 11, 12, 13].

IEEE 1547 recommendation [14] encourages ADS to sectionalize the system into multiple networks, by participating DERs in the case of fault occurrence, which can improve load restoration. Accordingly, intentional islanding has been recently proposed and studied in [15, 16, 17, 18, 19, 20] to improve the reliability of distribution systems. Intentional islanding is the procedure of selecting self-sufficient areas, called islands to restore critical loads through local DERs after a fault occurrence [15, 16, 17, 18, 19, 20]. Feasible intentional islanding is characterized as high-priority load restoration, minimization of the number of switching operations, meeting the operation constraints, and maintaining the radial structure of islands [4]. Intentional islanding problem is a complex problem. Therefore, a decomposition strategy is usually used to split the problem into two sequential sub-problems [16, 17, 18, 19, 20]. In the first sub-problem, primary islands are selected by determining the on/off status of switches in each line of ADS, by solving a mixed integer linear programming (MILP). For example, in [16], graph theory is used to model the ADS structure, and the branch and bound algorithm is applied to select primary islands. In [17] and [18], shuffled frog leap algorithm and particle swarm optimization (PSO) are respectively used to determine optimal primary islands. The authors of [19] employ a species-based quantum PSO (SQPSO) algorithm to obtain the primary islands. In the second sub-problem, various optimal decisions are made to meet the operation constraints of the primary islands. For example, [19] solves an optimal power flow (OPF) to meet the operation constraints. In addition, in [20], the demand side management (DSM) is proposed to meet the operation constraints of the islands in the second level.

*N*− 1 contingency analysis. However, low-frequency high-impact events such as natural disaster may surpass the traditional consideration of reliability. For instance, hurricane Sandy, in 2012, caused concurrent 90 contingencies in the New York power distribution system [26]. This led to an economic loss of about $52 billion [3]. In this regard, the resilience concept is introduced to the power systems. IEEE task force [27] defines resilience as “the ability to withstand and reduce the magnitude or duration of disruptive events, which includes the capability to anticipate, absorb, adapt to, or rapidly recover from such an event”. Power system resilience can be classified into long-term and short-term analyses [28]. The long-term resilience refers to the flexibility of a critical network to changing conditions and new threats. The short-term resilience denotes the preventive and corrective measures carried out before, during, and after the natural disasters [28]. The resilience performance of a power system can be presented by a multi-phase resilience trapezoid curve, as shown in Fig. 1. This performance curve consists of 5 main sections: pre-disturbance resilient state, disturbance progress state, post-disturbance degraded state, restorative state, post-restoration state. The load restoration of ADS after extreme events can be considered in the context of the restorative state of the power system resilience. Accordingly, the predefined intentional islanding can be proposed as a prospective approach to increase the power system short-term resilience. For example, in [3, 8], a MILP problem is solved to determine the primary islanding after concurrent outages of various lines caused by an adverse weather event. However, the operation constraints of islands are not considered in these works to check if the islanding is possible in a real case.

In this paper, a two-level approach is proposed to maximize the load restoration by intentional islanding of a reconfigurable distribution system. In the first level, primary islands are determined considering high-impact low-frequency events, which may cause more than one contingency. Unlike previous works, the presence of tie-switches between different branches is also considered in the selection of primary islands. This may lead to meshed islands, which are not operationally accepted [4]. A modified MILP-based method is proposed to guarantee the radial structure of obtained islands in the first level. This is a kind of tree knapsack problem (TKP), which, in line with the [16], can be solved by heuristic algorithms. However, due to the random generation of the initial population in heuristic methods, many non-feasible solutions are produced that imposes a high computation burden to the solving procedure. This may cause heuristic methods to fail to perform in real large-scale systems. In this paper, a search method known as depth first search (DFS) is utilized to remove unfeasible solutions and limit the search space for the application of PSO method. In the second level, an OPF problem is solved to minimize the power losses in the islands, which considers the load management capability based on the load priorities (LPs).

In conclusion, the main contributions of the paper are as follows: ① proposing a restoration method to improve the resilience of ADS through the enhancement of the restorative state of the multi-phase resilience curve; ② proposing a two-level intentional islanding method in a reconfigurable distribution system to maximize the load restoration and minimize the islands’ energy losses; ③ introducing value of served energy (VOSE) to evaluate the resilience performance; ④ using the DFS method to limit the search space for the application of PSO method in the problem, which makes the application of the proposed method in large-scale systems possible.

The proposed method is examined in the IEEE 69-bus distribution system in different cases to show the effectiveness and validity of the proposed algorithm.

## 2 Problem formulation

### 2.1 Problem description

This section presents the two-level approach for intentional islanding in the case of fault occurrence in a distribution system. In the first level, the primary islands are obtained to maximize the value of load restoration. The presence of tie-lines is also considered in the island selection. The on/off status of the switches in the ADS lines is determined by solving an optimization problem, considering generation and demand balance and keeping the radial structure of the distribution system. It is worthwhile to mention that the radial structure of ADS may change to mesh structure in the case of switching the tie-lines on. Hence, the MILP proposed in [17] is modified, and considered as a TKP to find the radial primary island. The main reason for MILP application is the availability of various solvers that guarantee the convergence of the problem and are computationally effective [15, 29]. In the second level, an OPF is performed to minimize the power losses in primary islands, while operation constraints are also considered. The decision variables in the second level are the reactive power of DERs, the reactive power of reactive suppliers such as capacitor banks, and the active power of controllable loads. As a result, a feasible solution for the non-convex intentional islanding problem is found to restore high LPs and minimize power losses.

In the following, the detailed mathematical formulations of the first and second levels are presented.

### 2.2 First level: primary islanding

*n*is calculated as follows:

*P*

_{n}, \(t_{n}\), and \(LP_{n}\) are the active power, interruption duration, and amount of LP at node

*n*, respectively. The main idea in the first level is to select the loads with the highest VOSE for restoration by DER units. Hence, the objective function would be:

*n*, it is 1 when the node

*n*is served, otherwise, it is 0 and

*N*is the set of nodes. Following constraints should be met in each island:

*d*is the index of nodes connected to DERs;

*D*is the set of nodes connected to DERs in the island;

*i*is the index of nodes in the island;

*I*is the set of selected nodes in the island; \(P_{i}\) is the active power consumption in the island; \(P_{d}^{g}\) is the active power generated by connected DER to node

*d*in the island; and \(\lambda (a,b)\) is a binary variable, indicating the edge status of two adjacent nodes

*a*and

*b*, selected in the primary island. Regarding the graph model, when an edge for connecting nodes

*a*and

*b*is available, \(\lambda (a,b)\) is 1; otherwise, it is 0.

In (3), it is verified that the generation of DERs in an island should be more than the load consumption. In (4), the node connected to DER is selected as the root node, since DER supplies the selected loads. Therefore, the nodes connected to DERs should be available in the island. In (5), the radial structure of islands is verified so that a set of nodes in an island forms a unique path. In other words, in a radial structure, the graph connecting all nodes has a unique path between two nodes, and the number of the edges is equal to that of nodes minus one. It is worth mentioning that the presence of a tie-line may change the ADS structure from a radial to loop structure. Therefore, (5) is the proposed modification on the conventional MILP methods to verify the radial structure of the islands.

It is shown in [32] that for a graph containing *n* nodes, there are *2*^{n−1} possible islands, although, many of them are not acceptable because of failing to satisfy (3). Reducing the unacceptable solutions to increase computational speed plays a vital role in the application of such methods. To this end, a limited search method known as DFS is performed in this paper to find all possible islands, satisfying (3). DFS is an algorithm to search a graph data structures. Here, the root node to search an island is the node connected to DER. The search is continuing, node by node, until (3) is met. Detailed mathematical modeling of this method can be found in [32].

*k*is the index of DER and

*M*is the number of DERs. The possible islands determined by DFS are the candidates for primary island formation in the PSO problem. These islands are considered as particles in PSO in the form of input vectors to solve the optimization problem in (2)–(5). In details, for every particle vector, a binary decision variable is defined, and the results are obtained in a hierarchical procedure. First, the objective function (2) is calculated; then, the active power balance constraint in (3) is checked; and finally, the radial connectivity constraint in (5) is verified. It is worth mentioning that increasing the penetration levels of DERs in ADS may cause some nodes to be in more than one island. The solution is to combine these islands to obtain one island. To this end, when a primary island is obtained, the VOSE and the active power of the selected nodes are set to be zero for the evaluation of other islands. This process is named neutralizing, which can lead to a larger island by combining islands. In addition, the selected island is merged to reduce the search space for the other islands. When all primary islands are obtained, the neutralizing procedure is deactivated, and the main load and VOSE of nodes are reassigned. Finally, the optimal islands are determined. In order to separate the selected island from other sections, only the boundary lines, which connect the island to the neighboring nodes, are disconnected by the operation of switches. The number of the switch operation depends on the network structure. The procedure of the primary island selection is presented in Fig. 3.

### 2.3 Second level: OPF

*j*, respectively;

*J*is the set of primary islands; \(I_{j}\) is the set of selected nodes in the island

*j*;

*U*

_{a}and

*U*

_{b}are the voltage magnitudes of nodes

*a*and

*b*, respectively; \(\delta_{a}\) and \(\delta_{b}\) are the phases of nodes

*a*and

*b*, respectively; \(Q_{d}^{g}\) is the reactive power generated by connected DER to node

*d*in the island; \(\phi_{ab}\), \(B_{ab}\), \(G_{ab}\), and \(Y_{ab}\) are the magnitude, real part, imaginary part, and the phase of admittance between nodes

*a*and

*b*in the primary island, respectively; \(U_{n,\hbox{min} }\) and \(U_{n,\hbox{max} }\) are the minimum and maximum voltage limits, respectively; \(Q_{DER,\hbox{max} }^{{}}\) is the maximum reactive power injected by DER; \(Q_{c,\hbox{max} }^{{}}\) and \(S_{{a,b , {\text{max}}}}^{{}}\) are the maximum reactive power generated by capacitor banks, and the maximum capacity of the line connected between nodes

*a*and

*b*, respectively; and \(P_{DER}\) and \(P_{DER,\hbox{max} }^{{}}\) are the active power and maximum active power injected by DER, respectively.

In (7) and (8), the active and reactive power losses in island *j* are calculated. In (9) and (10), active and reactive power for node *n* are obtained, respectively. In (11) and (12), the active and reactive power balance between generation and load consumption is verified. Voltage constraint for nodes is represented in (13). It is assumed that DERs can provide or consume reactive power in an acceptable range. This is mathematically presented in (14). In (15), active power generation of DERs is capped to their capacity \(P_{DER,\hbox{max} }^{{}}\). In (16), the reactive power generation of capacitor banks is limited. Finally, the line capacity constraint is modelled in (17).

*n*, respectively, \(\alpha_{n} + \beta_{n} = 1\). In this paper, the proposed OPF is performed by DIgSILENT power factory software [34].

### 2.4 Application of proposed two-level method

### 2.5 Resilience metrics

*t*

_{1}and

*T*are the event hit time and the recovery end time, respectively. In this paper, VOSE is also proposed as the resilience performance index. The proposed islanding method in this paper has impacts on the restorative procedure in the resilience curve, and the resilience metrics are reported in the numerical studies.

## 3 Numerical studies

### 3.1 Assumptions and scenario definition

Characteristics of installed DERs

DER number | Node number | Capacity (kW) |
---|---|---|

1 | 5 | 35 |

2 | 19 | 200 |

3 | 32 | 40 |

4 | 42 | 120 |

5 | 52 | 400 |

6 | 65 | 100 |

7 | 36 | 160 |

Priority of loads [16]

Priority level | Priority ($/kWh) | Node number |
---|---|---|

1 | 100 | 6, 9, 12, 18, 35, 37, 42, 51, 57, 62 |

2 | 10 | Other nodes |

3 | 1 | 7, 10, 11, 13, 16, 22, 28, 38, 43–48, 60, 63 |

Load controllability of nodes

Node number | Load type | \(\alpha\) | \(\beta\) |
---|---|---|---|

24,26, 27, 34, 39–41, 43–44, 48, 53–56,58, 66–69 | 100% controllable | 1.0 | 0 |

11, 13,16, 21, 38 | 40% controllable | 0.4 | 0.6 |

Other nodes | Uncontrollable | 0 | 1.0 |

The proposed method is implemented in the test system, and the results are presented in this subsection. In order to demonstrate the performance of the proposed method for resilience studies, two scenarios are designed. In scenario 1, it is assumed that the connection of ADS and the upstream grid is lost as a high impact event, and the two-level method is implemented for load restoration. In scenario 2, it is assumed that more than one failure occur in the system due to a high impact event, while the distribution system and the upstream grid remain connected. These scenarios are supposed to be the consequences of high impact events. The proposed two-level load restoration method is implemented, and the results are reported in the following.

### 3.2 Results of scenario 1

Characteristics of islands with LPs

Island | Candidate node determined by DFS | Selected node determined by PSO | Restored load (kW) | VOSE ($/hour) | Number of switch operation |
---|---|---|---|---|---|

1 | 1–7, 28, 36, 59 | 1–6, 28 | 28.60 | 520 | / |

2 | 13–27 | 18–22 | 180.30 | 7155 | 2 |

3 | 29–35 | 31–35 | 39.50 | 935 | 1 |

4 | 8–10, 43–47 | 8, 9, 42 | 109.35 | 4185 | / |

5 | 18–27, 51–54 | 24–27, 51–54 | 379.00 | 13780 | 3 |

6 | 1–6, 14–15, 28–36, 59–69 | 61–68 | 94.40 | 4630 | 2 |

7 | Neutralized islands 1, 4, 6, nodes 7, 10, 29, 36, 37, 43–47, 59, 60, 69, | Neutralized islands 1, 4, nodes 7, 36, 37, 59 | 145.40 | 8564 | 6 |

Total | 976.55 | 39769 | 14 |

At the first stage, the tie-switches are closed, and primary islands are determined. For example, as presented in Table 4, the particle vector obtained by DFS for DER 2 at node 19 are nodes 13–27. Then, the modified MILP is solved by PSO, and nodes 18–22 are selected as the primary island 2. Two switches operate to separate the optimal island from other parts. Accordingly, the boundary lines connecting the nodes 17 and 18, and nodes 22 and 23 are opened. The effect of neutralization and merging can be found in island 7. Before selecting island 7, other islands are merged and neutralized. In island 7, the DFS selects nodes 7, 10, 29, 36, 37, 43–47, 59, 60, 69 as particles, including the primary neutralized islands 1 and 4. Then, by solving the optimization problem, nodes 7, 36, 37 and neutralized islands 1, 4 are selected as the optimal island. Then, the unmerging is performed and neutralization is deactivated. Finally, a larger island by combining islands 1, 4, and 7 is obtained. It is interesting to see that closing tie-switch 1 has made the formation of island 5 possible. Switching tie-switch 1 on, the DFS has selected nodes 18–27 besides nodes 51–54 as candidates. Finally, nodes 24–27 and 51–54 have been selected for the optimal formation of island 5. It is essential to mention that all DERs generate more than the selected island demand. Hence, it is possible that the maximum capacity of DERs is not utilized in the primary island formation. For example, in island 5, the generation capacity of DER 5 is 400 kW, while the demand is 379 kW. Thus, 21 kW of generation is curtailed in this island. The results presented in Table 4 also show that the total restored load and VOSE are 976.55 kW and 39769 $/hour, respectively.

Results of running OPF in second stage

Island number | Active power (kW) | Reactive power (kvar) | Power loss (kW) |
---|---|---|---|

1, 4, 7 | 282.6 | 238.0 | 0.5 |

2 | 182.6 | 119.7 | 0.1 |

3 | 39.6 | 28.0 | 0.1 |

5 | 379.0 | 275.5 | 1.0 |

6 | 94.5 | 65.6 | 0.1 |

Characteristics of islands without LPs

Island number | Candidate node | Selected node | Restored load (kW) |
---|---|---|---|

1 | 1–7, 28, 36, 59 | 1–6, 28 | 28.60 |

2 | 13–27 | 15–20 | 182.50 |

3 | 29–35 | 31–35 | 39.50 |

4 | 8–10, 43–47 | 8, 9, 42 | 109.35 |

5 | 18–27, 51–54 | 24–27, 51–54 | 379.00 |

6 | 1–6, 14–15, 28–36, 59–69 | 61–68 | 94.40 |

7 | Neutralized island 1, 4, 6, nodes 7,10, 29, 36, 37, 43–47, 59, 60, 69 | Neutralized islands 1, 6, nodes 36, 37, 59, 60 | 157.00 |

### 3.3 Results of scenario 2

- 1)
In the case of disconnection between the distribution system and the upstream grid, intentional islanding is a more effective procedure for load restoration, as demonstrated by the results of scenario 1.

- 2)
Both intentional islanding and reconfiguration cooperate in the load restoration when the ADS is connected to the upstream grid. For example, in scenario 2, where the connection between nodes 3 and 59 is interrupted, tie-switch 3 is closed, and reconfiguration enhances the resilience of the network. However, their quota of restorationdepends on the technical constraints such as the line capacity of the tie-line.

- 3)
Considering LP has an impact on the optimal island selection and the VOSE in the restoration procedure.

Power quality [38], stability, and protection coordination [39] are important to be discussed to realize resilience-oriented intentional islanding of reconfigurable ADS. These topics may be interesting to be addressed in future works.

## 4 Conclusion

In this paper, a two-level intentional islanding method for a reconfigurable distribution system is proposed, considering the restoration of islanded loads by local DERs. To this end, in the first level, a TKP problem is modeled and solved. In the second level, the feasibility of the islands’ operation is verified by solving an OPF problem. The results show that the operation of the primary islands can be optimized by controlling the reactive power generation of DERs and capacitor banks. In addition, the presence of tie-lines can improve the VOSE by 11.8% in comparison with the case without tie-lines. The application of the proposed method is also examined in the case of fault occurrences in different lines to show that the proposed method is valid in the resilience studies of the distribution systems. Considering the uncertainties of load and DER generation and severity of events is not in the scope of this paper. However, the authors are working on this issue, and the results will be reported upon accomplishment.

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