Review on Energy Resilience

Applied Energy 199 (2017) 205–216

Contents lists available at ScienceDirect

Applied Energy

journal homepage: www.elsevier.com/locate/apenergy

A resilient microgrid formation strategy for load restoration considering master-slave distributed generators and topology reconfiguration

http://dx.doi.org/10.1016/j.apenergy.2017.05.012 0306-2619/� 2017 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. E-mail address: [email protected] (T. Ding).

Tao Ding a,⇑, Yanling Lin a, Zhaohong Bie a, Chen Chen b a State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University, Xi’an 710049, China b Energy Systems Division, Argonne National Laboratory, Lemont, IL 60439, USA

h i g h l i g h t s

� A resilient microgrid-forming model is set up considering master-slave DG operation. � The topology reconfiguration and microgrid-forming are coordinated in the model. � A mixed-integer second-order cone programming is employed to solve the model.

a r t i c l e i n f o

Article history: Received 6 February 2017 Received in revised form 10 April 2017 Accepted 2 May 2017 Available online 9 May 2017

Keywords: Resilient distribution network Topology reconfiguration Microgrid Master-slave control Mixed-integer second-order cone programming

a b s t r a c t

Recent severe power outages caused by extreme weather hazards have highlighted the importance and urgency of improving the resilience of electric distribution grids. Microgrids with various types of dis- tributed generators (DGs) have the potential to enhance the electricity supply continuity and thus facil- itate resilient distribution grids under natural disasters. In this paper, a novel load restoration optimization model is proposed to coordinate topology reconfiguration and microgrid formation while satisfying a variety of operational constraints. The proposed method exploits benefits of operational flex- ibility provided by grid modernization to enable more critical load pickup. Specifically, a mixed-integer second order cone programming is employed to reduce the computational complexity of the proposed optimization with optimality guaranteed. Finally, the effectiveness of the proposed method has been ver- ified on an IEEE 33-bus test case and a modified 615-bus test system.

� 2017 Elsevier Ltd. All rights reserved.

1. Introduction

Electrical power production is the large-scale conversion pro- cess of transforming different types of primary energy into easily transportable electrical energy. In particular, the distribution sys- tem is at the end of the whole power system, and directly affects the power supply quality and reliability seen by customers. Statis- tics from electric power companies show that more than 80% of power outages are caused by faults in the distribution network level [1]. Hence, load restoration from outages for resilient opera- tion is the core function of the distribution network, and it has great significance for serving customer demand and improving the reliability of the power supply [2]. With the development of information technology and distribution automation, remote con- trol enables fast switch operations, allowing the distribution sys- tem topology to adapt quickly to isolate faults and achieve

optimal operation. Reconfiguration has become a common feature in urban distribution systems, and has contributed greatly to enhancing power system reliability by redirecting faulted areas to alternative supply sources through sectionalizing switches within a feeder or tie switches between feeders [3–13].

In recent years, the world has witnessed several natural disas- ters and resulting severe power outages and blackout. For example, a hurricane hit Zhanjiang, China in October 2015, causing a loss of 4.24 million kW h of energy. In this scenario, the substations may be at fault so that the distribution system cannot be supplied by the main grids, or the damages to the distribution facilities may lead to several isolated areas without power. Thus, the traditional load restoration approaches (e.g., [3–13]), which rely entirely on reconfiguration, may not guarantee supply continuity of energy after natural disasters, and thus customers may experience extended outages [14].

Today’s power system is transiting from a centralized bulk sys- tem to smart grid, with the distribution system being smarter and more active by the integration of distributed generators (DGs) [15].

Nomenclature

Indices and sets i, j, s, k index of buses ij index of branch from bus i to bus j E set of lines in the network P set of DGs Eo set of lines in the open state V set of nodes in the network H set of master DGs d(j) set of all children of bus j p(j) set of all parents of bus j |E| the numbers of lines |V| the numbers of nodes |P| the number of DGs |H| the number of master DGs rij the resistance of branch ij xij the reactance of branch ij bs,j the charging capacitance connected to bus j P0L the active load demand under normal condition Q0L the reactive load demand under normal condition P0DG,j the j-th DG output under normal condition U0j the given voltage magnitude on master DG bus j SDG,j

max the maximum capacity of the DG j hj the maximum power factor angle of the j-th DG

Sij max the maximum capacity of the branch ij

Iij max the maximum branch current of the branch ij

N the number of substations R the number of load islands w weight of load M a big number aj the power factor angle of the j-th load demand

Decision variables yij binary variable for line ij. If the line is open, yij = 0;

otherwise, yij = 1 Hij the active power flow on distribution line ij Gij the reactive power flow on distribution line ij PDG,j the active power output of DG j QDG,j the reactive power output of DG j PL the active load demand under faulted condition QL the reactive load demand under faulted condition lij the square of branch current on line ij ui the voltage magnitude square on bus i Fij the fictional flow on the distribution line ij Wj the power supplied by the ‘‘source” buses in the ficti-

tious network

206 T. Ding et al. / Applied Energy 199 (2017) 205–216

DGs can make the distribution system more diverse, flexible, and secure. DGs are increasingly integrated in the distribution network due to their benefits such as loss reduction, voltage stability, sys- tem reliability enhancement and lowered global warming [16– 19]. In addition to their ability to satisfy the increasing energy demand, DG intentional islanding is gradually recognized as an essential capability in providing the load in contingency, which is further validated by IEEE 1547.4 [20]. It is found in many studies DGs can be used to enhance load restoration, providing an alterna- tive way to improve distribution network resilience [14]. The effi- cient way to manage a power system with significant level of DGs is to break the distribution system into small clusters or microgrids [21–23]. Thanks to the microgrids powered by the DGs, the supply to the customers can still be guaranteed, even for isolated areas [24–30].

On the basis of this idea, the concept of ‘‘resilience” in distribu- tion network was proposed in [31–35] to restore the system after natural disasters by use of microgrids. Ref. [31] built a model suit- able for re-configuration of a distribution system with microgrids. Once a fault occurs in a distribution system, some DG-based islands will be formed to guarantee the power supply of important customers. Ref. [32] studied multi-agent coordination for dis- tributed information discovery, but the restoration process did not consider the topology of the distribution network. Ref. [33] dis- cussed a spanning tree method for distribution network restora- tion with embedded microgrids to enhance the self-healing capability. However, this method only considered a single fault in the distribution network. When natural disasters occur, multiple faults could lead to several unsupplied, isolated islands. An opera- tional approach to restore loads after natural disasters was given in [14], where multiple microgrids were dynamically formed to con- tinue supplying critical loads. Ref. [34] reviewed the contribution of reconfiguration in reducing load shedding. Ref. [35] presented the reconfiguration scheme for minimal load shedding considering soft-open points.

The above references presented sound results and investigated the basic framework of resilience in distribution networks, but there are still two points that haven’t been addressed:

(i) Different types of control strategies for DGs may lead to dif- ferent operation rules for system restoration. Originally, droop-control-based methods were widely adopted for DGs in microgrid, which does not require communication among DGs for effective grid control. However, droop con- trol faces the problem of circulating current among DGs because it uses a voltage loop at each DG node [36]. Subse- quently, the master-slave control technique was deployed to solve the above problem; in this technique, the voltage and frequency of the system are controlled by only one gen- eration unit, which serves as the master unit, and the rest of the DGs work in current control mode and serve as the slave units. The master unit can be a diesel generator, storage device or DG with large capacity, etc. In contrast, DG units based on renewable energy, such as solar and wind, are usu- ally chosen as the slave units. However, the existing studies on service restoration haven’t considered the DG control strategies.

(ii) The network reconfiguration and the control strategy of the microgrids haven’t been coordinated in the previous works. The existing studies are based on either reconfiguration [1– 8] or microgrids [31–35]. To our best knowledge, how to coordinate the reconfiguration and microgrids should be investigated.

To address the above two shortcomings identified in the previ- ous research, this paper proposes a new resilient microgrid forma- tion strategy for load restoration with both topology reconfiguration and master-slave DG control framework. The main contributions can be summarized as follows:

(i) A resilient microgrid-forming model is formulated consider- ing master-slave DG operation, where there is only one mas- ter DG in each island to guarantee a self-adequate system.

(ii) The topology of the whole system can be reconfigured by sectionalizing and using tie switches, such that the load at one feeder can be transferred to another feeder in the microgrid-forming model to pick up more loads.

T. Ding et al. / Applied Energy 199 (2017) 205–216 207

(iii) A mixed-integer second-order cone programming (MISOCP) relaxation is employed to solve the proposed model.

The rest of the paper is organized as follows: Section 2 intro- duces the modeling of the restoration by microgrids with consider- ation of the master-slave control framework and network topology reconfiguration. Section 3 presents the simulation results of the proposed method on 33-bus and 615-bus test systems. Finally, conclusions are drawn in Section 4.

2. Modeling of restoration by microgrids

When multiple faults from natural disasters isolate parts of the distribution system into unsupplied islands, traditional distribu- tion system restoration approaches that only change system topol- ogy cannot guarantee restoration of the energy supply. However, a promising approach is to intentionally divide the distribution sys- tem into several microgrids by means of sectionalizing switches and DGs to continue supplying critical loads, while ensuring vari- ous constraints in each island. A DG-based microgrid is a localized grouping of small DG units and loads to guarantee a self-sufficient system. Moreover, it should be noted that for the master-slave con- trol framework, only one DG acts as the master unit that sets the voltage and frequency of the microgrid, while other DG units are slave units that follow the set voltage and frequency.

To meet the above requirements, the following constraints should be satisfied for forming microgrids in case of severe natural disasters:

(a) Distribution System Condition Constraints: The state of switches and the microgrid control mode should be consid- ered for each microgrid.

(b) Radiality with Network Topology Reconfiguration Constraints: The distribution system is operated radially, and the micro- grids should also adopt a radial topology. Moreover, the topology of microgrids can be further reconfigured by open- ing and closing sectionalizing switches

(c) Microgrid-forming Constraints: The distribution system should be split into several microgrids. For each microgrid, the power flow constraints should be satisfied.

(d) Power System Physical Constraints: DG generation limits, line capacity limits, and voltage magnitude restrictions should be met for each microgrid.

2.1. Modeling of the distribution system condition constraints

Let G = (V, E) be a connected and undirected graph with set of vertices and edges denoted by V and E respectively. After a natural disaster, some lines will be at fault and a substantial amount of time will be needed for repairs. Therefore, these lines should be in the open state. Let these lines be defined by the set EO, where EO � E. Let the binary decision variable yij represent the status of distribution line ij. If the line is open, yij = 0; otherwise, yij = 1. Therefore the constraints regarding the binary decision variables based on the actual conditions of the distribution system lines can be written as follows:

yij ¼ 0; 8ði; jÞ 2 EO: ð1Þ It is assumed that all lines that are in service (i.e., 8ði; jÞ 2 E n EO)

are equipped with a switch. Both the microgrid formation and topology reconfiguration will employ open/close operation of the switches.

In addition, the master-slave control mode in the microgrid suggests that only one DG is serving as a master control unit and the other DGs are serving as slave control units. Thus, the number

of microgrids is equal to the number of master control units. That means, |H| microgrids will be formed for restoration.

2.2. Modeling of the radiality with the network topology reconfiguration constraints

Traditionally, to guarantee radiality in the distribution reconfig- uration, graph-theory-based methods are proposed to eliminate unconnected buses and loops. For example, the branch exchange method was used in [37] to simultaneously open and close a pair of switches within one loop to maintain radiality; all switches were closed and then opened them one by one to form a radial network in [38]; and a spanning tree search algorithm was proposed in [39,40] to find the optimal radial topology.

Theoretically, a necessary and sufficient condition for radiality was proposed in [41], i.e., the graph is radial if and only if the fol- lowing two conditions are satisfied: (a) the number of closed branches equals the number of buses minus the number of sub- graphs, and (b) the connectivity of each sub-graph is guaranteed.

To achieve the first condition, the number of sub-graphs should be acquired at first. After a natural disaster, the faulted lines are opened which result in three isolated areas, as shown in Fig. 1. However, as shown in Figs. 2 and 3, with the consideration of the network reconfiguration and microgrids, the sub-graphs could be of three types—microgrids supplied by DGs, buses supplied by sub- stations, and unsupplied load islands—so condition (a) above will be represented by the following equality constraint:X ij2E

yij ¼ jVj � jHj � N � R; ð2Þ

It can be observed from Figs. 2 and 3 that N is actually a prede- termined parameter, but R is related to the locations of faulted lines, tie switches and DGs.

After a natural disaster, the system can pick up load through network reconfiguration and microgrids powered by DGs. As a result, the number of isolated load islands can be determined by closing all the tie lines to form a new mesh network where substa- tions and DGs are considered. For example, in Fig. 3, close all the tie lines and a new mesh network can be constructed, in which Area 1 is a load island and R = 1. Similarly, in Fig. 2, close all the tie lines and a new tree network will be constructed, in which there is no load island and R = 0.

Generally, finding the number of load islands in a graph (i.e., determining R) is equivalent to finding the number of connected components that only contain load buses. A connected component of an undirected graph is a connected sub-graph of the graph [42]. If an undirected graph is a connected graph, there is only one con- nected component. If there are multiple connected components, a traversal algorithm can be employed, either depth-first or breadth- first, to find connected components of an undirected graph. After a traversal starting from a vertex, all the vertices that can be reached from this vertex will be visited. If there are other connected com- ponents, there will still be unvisited vertices after the traversal is complete. Starting from one of those unvisited vertices, another connected component can be found. If continuing this procedure until all vertices are visited, all the connected components can be identified. Table 1 shows the flowchart of the algorithm finding all connected components of a graph.

According to Table 1, R can be determined and condition (a) can be satisfied by constraint (6) below. However, considering only condition (a) cannot sufficiently guarantee the radiality. As shown in Fig. 4, the microgrid after reconfiguration may be disconnected or meshed, or may contain several master units in one microgrid, so condition (b) to guarantee the network connectivity and the constraint of only one mater unit being in one microgrid should be satisfied, too.

Area 1

Area 2

Area 3

Master Control DG

Substation

Fig. 2. Network reconfiguration without the load island.

Area 1

Area 2

Area 3

Master Control DG

Substation

Fig. 1. Topology after natural disasters.

Area 1

Area 2

Area 3

Master Control DG

Substation

Fig. 3. Network reconfiguration with the load island.

Table 1 Algorithm for finding connected components.

Step 1 for i = 1: |V|

Step 2 visited[i] = false; compNum = 0; Step 3 for v = 1: |V| Step 4 if (!visit[V]) Step 5 compNum + + ; q = []; Step 6 q.enqueue(v); Step 7 visited[v] = true; Step 8 while (! q.isempty()) Step 9 w = q.dequeue(); Step 10 for each edge from w to vertex k Step 11 if (! visited [k]) Step 12 visited [k] = true; Step 13 q.enqueue(k); Step 14 end Step 15 end Step 16 end Step 17 end Step 18 end Step 19 end q.enqueue() adds an item to the queue. q.dequeue() removes an item from the queue and returns the value.

208 T. Ding et al. / Applied Energy 199 (2017) 205–216

In order to enforce the subgraph connectivity via mathematical programming formulations, the single commodity flow method [43] is employed in this paper. In essence, a fictitious network is constructed, where each microgrid has only one ‘‘source,” and all other buses are ‘‘sink” buses that have unit load demands (1.0 p. u.). Since each microgrid is only allowed to contain one master control unit, the master control unit should be chosen as the ‘‘source” bus. Then, the connectivity can be expressed by the fol- lowing constraints:X s2dðjÞ

Fjs � X i2pðjÞ

Fij ¼ �1; j 2 V n P ð3Þ

X s2dðjÞ

Fjs � X i2pðjÞ

Fij ¼ Wj; j 2 P ð4Þ

�Myij 6 Fij 6 Myij; 8ij 2 E ð5Þ

�Mð2 � yijÞ 6 Fij 6 Mð2 � yijÞ; 8ij 2 E ð6Þ

T. Ding et al. / Applied Energy 199 (2017) 205–216 209

Wj P 1; j 2 P ð7Þ Since the fictitious network has the same topology structure as

the original distribution network, they have the same connectivity. Thus, if the power balance constraint is guaranteed in the fictitious network, it suggests that for any sink bus, there exists at least one path from this sink to a source bus, so that each microgrid should be connected; otherwise, the microgrid will remain disconnected.

The connectivity constraints can be illustrated via an example in Fig. 5. The power in microgrid 1 can be balanced by satisfying those constraints, so microgrid 1 is connected. The load demand at buses #7–#10 in microgrid 2 cannot be satisfied, implying that there is no path between these buses and the source denoted by Source2.

2.3. Modeling of the microgrid-forming constraints

The microgrid-forming problem can be viewed as a graph parti- tion problem [44]. A split in G is a partition of V with several split sets. For instance, splitting G into Np sub-graphs Gi ¼ ðVi; EiÞ can be represented by G ¼ G1 [ G2 . . . [ GNp , and Gi \ Gj ¼ £ for 8i–j, which can also be expressed as V ¼ V1 [ V2 . . . [ VNp , Vi – £, and Vi \ Vj ¼ £ for 8i – j. Here, the cut set ðV1; V2; . . . ; VNp Þ is defined as a set of edges Eb # E with one end vertex in Vi and another end vertex in Vj, i – j [43].

For each microgrid, the power flow constraint should be satis- fied. It has been well recognized that a distribution network is often a radial network, and the power flow can be formed by a set of recursive equations, called branch flow formulation, which yields:

PDG;j � PL;j ¼ X k2dðjÞ

Hjk � X i2pðjÞ

ðHij � rijlijÞ; 8j 2 V

QDG;j � QL;j ¼ X k2dðjÞ

Gjk � X i2pðjÞ

ðGij � xijlijÞ þ bs;juj 8j 2 V

uj ¼ ui � 2ðrijHij þ xijGijÞ þ ðr2ij þ x2ijÞlij; 8ði; jÞ 2 E H2ij þ G2ij ¼ lijui; 8ði; jÞ 2 E

8>>>>>>>>< >>>>>>>>:

ð8Þ

Source1 Microgrid1

v1 v2

v3

v4

v6

v5

Fig. 5. Connectivity constraints

Master Control Unit

Fig. 4. Notional sys

Intuitively, if branch (i, j) is opened, the branch current and branch flow should be zero, such that Hij = 0, Gij = 0 and lij = 0; meanwhile, the voltage magnitudes between the two buses need not be restricted by the third equation in (8). The formation of microgrid primarily needs to find a cut set of the network. The edges belonging to the cut set should be open, and the other edges remain closed. Thus, the splitting constraints for the power flow equations of each microgrid can be given as:

PDG;j � PL;j ¼ X k2dðjÞ

Hjk � X i2pðjÞ

ðHij � rijlijÞ; 8j 2 V

QDG;j � QL;j ¼ X k2dðjÞ

Gjk � X i2pðjÞ

ðGij � xijlijÞ þ bs;juj 8j 2 V

8>>< >>: ð9Þ

uj � ui ¼ �2ðrijHij þ xijGijÞ þ ðr2ij þ x2ijÞlij if ði; jÞ 2 E \ yij ¼ 1 arbitrary otherwise

(

ð10Þ

Gij or Hij : 2 ½�Smaxij ; þSmaxij � if ði; jÞ 2 E \ yij ¼ 1 ¼ 0 otherwise

( ð11Þ

lij : 2 ½0; lmaxij � if ði; jÞ 2 E \ yij ¼ 1 ¼ 0 otherwise

( ð12Þ

However, constraints (10)–(12) are ‘‘if-else” type constraints, implying that only one constraint can hold. However, these con- straints can be equivalently transformed into a set of affine con- straints using the big-M approach [43,45] as follows:

�Mð1�yijÞ 6 uj �ui þ2ðrijHij þxijGijÞ�ðr2ij þx2ijÞlij 6 Mð1�yijÞ �Smaxij yij 6 Hij 6 Smaxij yij;�Smaxij yij 6 Gij 6 Smaxij yij 0 6 lij 6 ðImaxij Þ

2 yij

;

8>>< >>: 8ði;jÞ 2 E

ð13Þ

Source2 Microgrid2v7

v8 v9

v10

v11 v13

of the fictitious network.

tem topology.

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(c) non-reconfigurable (d) reconfigurable

Fig. 6. Comparison of different strategies (see Table 2) applied to IEEE 33-bus system.

210 T. Ding et al. / Applied Energy 199 (2017) 205–216

Table 2 Loads restored by different strategies depicted in Fig. 6.

Scenario Computational time (s) Gap (MW) Restored load (MW) Ratio (%)

(a) 0.0862 2.1681 � 10�5 2.3418 63.03 (b) 36.7805 2.4676 � 10�5 2.3692 63.78 (c) 0.0134 2.9157 � 10�5 2.1061 56.69 (d) 0.1989 2.4676 � 10�5 2.3692 63.78

T. Ding et al. / Applied Energy 199 (2017) 205–216 211

H2ij þ G2ij ¼ lijui; 8ði; jÞ 2 E; ð14Þ If yij = 1, the first constraints of (10)–(12) hold; otherwise, the last constraints hold.

2.4. Modeling of distribution system physical constraints

Distribution system physical constraints guarantee that the power generation of DGs, voltage magnitudes, and load shedding should be restricted within their physical limits:

ðPDG;j; QDG;jÞ jQDG;jj 6 PDG;jtanðcos�1hjÞ P2DG;j þ Q2DG;j 6 ðSmaxDG;jÞ

2

0 6 PDG;j 6 P0DG;j

��������

8>>< >>:

9>>= >>;; 8j 2 P ð15Þ

ðUminj Þ 2 6 uj 6 ðUmaxj Þ

2 ; 8j 2 V n H ð16Þ

uj ¼ ðU0j Þ 2 ; 8j 2 H ð17Þ

0 6 PL;j 6 P0L;j QL;j ¼ PL;jtanðcos�1ajÞ

( ; 8j 2 V ð18Þ

where constraint (15) describes the feasible region of each DG; con- straints (16) and (17) specify the voltage magnitude limit and con- straint (18) implies that the active and reactive power should be curtailed at the same time and the power factor of each load should be maintained.

Finally, let wj denote the priority weight associated with the load at bus j. Then, the proposed model can be explicitly formu- lated as (19) to maximize the total priority-weighted loads picked up, such that

max X j2V

wiPL;i ð19:aÞ

s:t: ð2Þ—ð7Þ; ð9Þ; ð13Þ—ð18Þ ð19:bÞ

2.5. Convex relaxation for solution methodology

The proposed model (19) is actually a mixed-integer nonlinear nonconvex programming (MINNP) problem, owing to the fact that the equality constraints (14) are nonlinear. Unlike the mixed- integer convex programming model, which can be generally solved by the branch-and-bound method, cutting plane, etc., the MINNP is very hard to handle, since the global optimality of the sub-problem obtained by relaxing the integrality constraints is challenged. To deal with this problem, convex relaxation approaches are widely utilized in optimal power flow problems to find a ‘‘good” approxi-

Table 3 Loads restored under different PV capacity.

Scenario PV capacity Restored Load (MW) Ratio (%)

(a) 1/2 of the original 2.1236 57.16 (b) 2 times of the original 2.8498 76.71 (c) 3 times of the original 3.2349 87.08 (d) 4 times of the original 3.5269 94.94

mate optimal solution, which can be obtained by reformulating the problem in terms of its continuous-variables convex second-order cone programming [46–50]. Thus, the whole problem can be for- mulated as a MISOCP.

Specifically, for the quadratic equalities (14), conic relaxation is performed by relaxing the quadratic equalities into inequalities. Thus, the relaxation yields

H2ij þ G2ij 6 lijui; 8ði; jÞ 2 E ð20Þ Furthermore, (14) can be reformulated as a standard second-

order cone formulation, such that

2Hij 2Gij lij � ui

������� ������� 2

6 lij þ ui; 8ði; jÞ 2 E ð21Þ

Then, the model can finally be reformulated as

max X j2V

wiPL;i ð22:aÞ

s:t: ð2Þ—ð7Þ; ð9Þ; ð13Þ; ð15Þ � ð18Þ; and ð21Þ ð22:bÞ

3. Numerical results

In this section, the proposed method is tested on a modified IEEE 33-bus system and a 615-bus test system composed of five IEEE 123-bus systems. The test is carried out on a personal com- puter with an Intel� CoreTM i5 Duo Processor T420 (2.50 GHz) and 4 GB of RAM (32-bit system) using CPLEX 12.5. In the simulation, a reasonable voltage magnitude is assumed to stay within the range [0.90, 1.10] p.u. The voltages of the master generators in island operation are kept at 1.0 p.u. and the priority weight of all load is chosen the same value.

3.1. IEEE 33-bus test system

The 12.66-kV 33-bus radial distribution test system is adopted from a standard IEEE 33-bus test system. Four master generators are installed at buses 13, 20, 23, and 29, respectively. The capacity of each generator is 0.5 MVA; 5 photovoltaic (PV) panels are installed at buses 9, 15, 18, 27, and 33, respectively. The individual capacity is 0.15 MVA. Two disaster scenarios are deployed for this test system, and each fault location is indicated with a red cross in Fig. 6: (1) a single fault occurs at the main transformer, and the optimal microgrid-forming solutions with/without reconfiguration are shown in Fig. 6(a) and (b); (2) multiple faults occur within the system, and the optimal solutions with/without reconfiguration are shown in Fig. 6(c) and (d). In this paper, non-reconfigurable system indicates that the system has no tie switches among feed- ers, while a configurable system retains the additional tie switches from the test system.

(A) Effect of reconfiguration on load restoration

In all the scenarios, the system is cut off from the main grid, and microgrids are formed by opening/closing line switches, each pow- ered by one master generator. The total DG installation capacity,

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Fig. 7. Comparison of DG islanding under different PV capacity in IEEE 33-bus system.

212 T. Ding et al. / Applied Energy 199 (2017) 205–216

including PVs, in the 33-bus system is 2.75 MVA, and the maxi- mum possible restored load is 74.02% of the total active load. A comparison of loads restored by different strategies is given in Table 2. For a single fault that occurs at the root bus, the microgrids can pick up 63.08% of the load, and with the help of topology reconfiguration, an additional 0.7% of the load will be restored. In contrast, for multiple faults, an additional 12.5% load is restored by coordinating topology reconfiguration with microgrid forma- tion. That is because the multiple faults that could result from

extreme disasters break the system into different parts, and those without a controllable DG will not be supplied. For example, a fault at line #30–#31 (i.e., S30) isolates loads without a controllable DG, and the load must be lost without reconfiguration, as seen in Fig. 6c. However, with a reconfigurable tie switch between bus 18 and 33 (Fig. 6d), isolated load buses can be reconnected to another island and supplied by the DG at bus 13.

On the other hand, it can be found from Table 2 that the pro- posed method that integrates topology reconfiguration and micro-

Substation 1 Substation 2

Fig. 8. 615-bus test system.

Table 5 Restoration of loads by different strategies.

Faults ① ② ③ ④

F1 69.63% 78.80% 81.81% 82.09% F1/F2 69.63% 78.37% 79.00% 81.02% F1/F2/F5 69.63% 77.94% 78.98% 80.65% F1 + internal 63.32% 73.07% 75.21% 81.23% F1/F2 + internal 62.46% 71.68% 72.79% 77.94% F1/F2/F5 + internal 61.89% 69.48% 71.79% 75.28%

Table 4 Resilience strategies for distribution system.

Strategy Sectionalizing Switches Tie switches

① – – ②

p –

③ – p

④ p p

T. Ding et al. / Applied Energy 199 (2017) 205–216 213

grid formation takes more computational time than the method without topology reconfiguration. This is because the feasible region will become larger when topology reconfiguration is considered.

To evaluate the accuracy of the SOCP relaxation, a gap (relax- ation error) is defined as

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jH2ij þ G2ij � lijuij ð23Þ

The maximum gap of conic relaxation on the test system is listed in the Gap column in Table 2; it is obvious that the gap on any test system is smaller than 10�4, which implies that the conic relaxation is actually an exact match to the original nonconvex model to guarantee the optimality.

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(B) Effect of DG capacity on load restoration

In this section, the DG capacity of the system is changed to investigate the effect of PV capacity on the final reconfiguration result. As indicated by Table 3, the restored load is increasing stea- dily as the capacity of the PV installation increases. In addition, the DG islanding schemes under scenarios of different PV capacity are sketched in the following figure. The fault is assumed to take place in line #1. The effect of the PV capacity is evident in the result. From (a) to (d) in Fig. 7, the most significant change is about the DG island supplied by DG at bus 2. It can be seen that the DG island

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formed by this DG is becoming smaller as PV capacity increases. In (a), this DG island supplies load at bus 18–19, 2–6, and 26–28. Due to limited capacity of the PV in this scenario, this island is formed to supply more loads, even though the long distance within the island may cause voltage problem. As the PV capacity increases, the load at bus 26–28 are then supplied by the controllable DG nearby. As can be seen, the increased PV capacity increase the flex- ibility of the DG islanding scheme.

3.2. 615-bus test system

The 615-bus test system (Fig. 8) is composed of five IEEE 123- bus systems, designated F1 through F5, each of which is described by the single line diagram shown in Fig. 9. The load of each feeder is 3.49 MW + 1.92 MVar. The capacities of substations 1 and 2 are set to be 15 MVA and 10 MVA, respectively. There are four addi- tional switches among the feeders, which could pick up loads after failures, as shown in Fig. 9. The total capacity of the installed DGs, including PVs, is 3.15 MVA, or 79% of the total active load. Therein, 8 DGs are set as the master control units and the others are PV units which are slave control units.

Six fault scenarios are considered where the faults occur either at the feeder bus only, or within internal feeders. For the faults at the feeder buses only, three scenarios are studied, with the faults occurring at Feeder 1, Feeders 1 & 2, and Feeder 1, 2, & 5, respec- tively. For the faults both at the feeder buses and within internal buses, another three scenarios are set up with faults occurring at the above feeder buses and within feeders (see Fig. 9).

With the help of topology reconfiguration, the strategies of DG formulation for 615-bus systems to deal with faults are manifold: when faults occur, the restoration can be implemented by inten- tional microgrid formation with master-slave control frameworks,

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and moreover, some parts of the lost load can be picked up by nearby feeders through the tie switches.

To compare the traditional intentional-microgrids method without reconfiguration, four resilience strategies, designated ① through ④, are described in Table 4. The strategies involving topol- ogy reconfiguration include both tie switches among feeders and sectionalizing switches within feeders. In Strategy ①, topology reconfiguration is not considered; in Strategy ②, only the section- alizing switches within feeders are considered; in Strategy ③, only the tie switches among feeders are considered; in Strategy ④, which is the method proposed in the present paper, both tie switches and sectionalizing switches are considered.

The ratios of restored load to the total lost load for all fault sce- narios under the different resilience strategies are summarized in Table 5. It can be observed that the picked-up loads are limited by the capacity of DGs, so the lost load cannot be 100% restored. However, in addition to microgrid, reconfiguration by both tie switches and sectionalizing switches can improve the performance of load restoration. Comparing ② with ①, the reconfiguration of sectionalizing switches increases the restored load from 11.93% to 15.40%, while comparing ③ with ①, the reconfiguration of tie switches increases the restored load from 13.43% to 18.78%.

These results show that reconfiguration by tie switches yields 3–4% more restored loads than reconfiguration by sectionalizing switches in the test cases. Moreover, the comparison between strategy ③ and ④ shows that for the faults at the feeder buses, the restored loads mainly come from the tie switches and micro- grids, and the effect of sectionalizing switches is slight (no more than 3%). This is because the lost loads are supplied mainly from the microgrids, and additional loads that cannot be supplied by the microgrid will be picked up by the nearby feeders from the tie switches.

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root buses of feeder 1 & feeder 2.

T. Ding et al. / Applied Energy 199 (2017) 205–216 215

However, for the faults within the feeder buses, the improve- ment due to sectionalizing switches becomes significant, at about 5% to 8%. This is because there will be several load islands when faults occur within the feeders. The capacity of the DGs is enough in some parts, but can be insufficient in other parts. If the section- alizing switches within the feeders are not taken into account, the load will be curtailed in the insufficient load islands to satisfy the power balance constraints. Therefore, the reconfiguration by sec- tionalizing switches can further increase the value of load picked up. Finally, it can be concluded that the restored load with micro- grid formulations by the proposed method ④ can pick up more critical load than the traditional method ③, i.e., more than 15%.

In Fig. 10, the voltage profiles of the 615-bus system corre- sponding to the four strategies are sketched. The buses in the five feeders are denoted as F1, F2, F3, F4, and F5. When faults occur at F1 and F2, the DG forms microgrids and the voltage at the master DG bus is kept at 1.0 p.u. For strategies ① and ②, there are no tie switches among feeders, so F1 and F2 are independent from F3, F4, and F5 and the voltage magnitudes in F1 and F2 are close to 1.0 p.u. In contrast, a noticeable voltage drop exists at bus #80 in both F1 and F2 under strategy ③ and ④, because DG microgrid formation and tie switches among feeders are applied as restoration strate- gies are coordinated. Meanwhile, the isolated buses are supplied by nearby feeders through tie switches instead of being supplied by DG, which lie at the end of the substations and have low voltage magnitude. However, owing to the voltage limit constraints, the voltage magnitudes always stay within the allowable feasible region.

4. Conclusions

In this paper, a new load restoration method is proposed to facilitate resilient distribution grids after natural disasters, Both the microgrid formulation and reconfiguration are considered and coordinated by sectionalizing the switches so that operational flexibility can be better exploited to enhance electricity supply continuity. The master-slave control technique is integrated in the optimization to coordinate multiple DGs in one microgrid. Fur- thermore, a mixed-integer second-order cone programming is employed to efficiently reduce the computational complexity of the proposed optimization model with optimality guaranteed. Two tests on an IEEE 33-bus test system and a modified 615-bus test system show that the proposed method can pick up more crit- ical load than the existing methods which do not coordinate the microgrid formulation and reconfiguration.

Acknowledgments

This work was supported by National Natural Science Founda- tion of China (Grant 51607137), National Key Basic Research Pro- gram of China (2016YFB0901904), China Postdoctoral Science Foundation (2015M580847), Natural Science Basis Research Plan in Shaanxi Province of China (2016JQ5015), and the project of State Key Laboratory of Electrical Insulation and Power Equipment in Xi’an Jiaotong University (EIPE16301).

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