Automatic restoration of large-scale distribution networks with distributed generators, voltage control devices and heating loads

Electric Power Systems Research 176 (2019) 105925

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Automatic restoration of large-scale distribution networks with distributed generators, voltage control devices and heating loads

T

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Renzo Amilcar Vargas Peralta, Jonatas Boás Leite , José Roberto Sanches Mantovani Electrical Engineering Department, UNESP, Ilha Solteira, SP, Brazil

A R T I C LE I N FO

A B S T R A C T

Keywords: Network restoration Power distribution Cold load pickup Distributed generation Voltage control Metaheuristic

Energy supply interruption by permanent faults causes economic and social problems, dissatisfaction of customers and penalization to electrical power distribution companies. In the procedure to restore distribution networks, power interruption damages must be minimized by energizing the largest possible number of customer loads in the shortest time interval. The restoration problem of distribution networks can be mathematically formulated as a mixed integer nonlinear programming problem that is non-convex of type NP-complete. The existence of heating loads causes the cold load pickup condition in the distribution network that requires the step-by-step procedure increasing the complexity of the restoration problem. In this work, therefore, it is proposed a methodology to solve the restoration problem of large-scale distribution networks with heating loads where the mathematical model is subjected to intentional islanding of distributed generation and voltage control through optimized adjustments on capacitor banks and voltage regulators. The outcomes are achieved under a testing distribution system with 53 nodes and a real system with 7052 nodes.

1. Introduction The continuous energy supplying to consumers in an electrical network is the most important function of the energy power system. Permanent faults, due to human, environment or technical factors, cause unplanned disconnection of loads in overhead and radial electrical power distribution networks. The interrupted loads within faulted section must remain disconnected from the main power grid until the finalization of corrective maintenance services, whereas interrupted safe loads at adjacent sections must be restored. The plan for restoring the distribution network using switching operations must be able to restore the largest number of loads, or energy consumers, in the shortest time interval. In this way, power distribution company (DISCO) reduces, or even avoids, the consumers’ dissatisfaction and financial losses, that are consequences of regulatory authority rules by penalizing the nonconformity of quality and reliability indexes. Heating loads demand large amount of power from distribution network, in comparison to other types of electrical loads, due to their intermittent behavior on the start of re-energization [1]. The heating/ cooling loads comprise thermostatically controlled electrical appliances, or regulating process devices, like air conditioner, water/air heater and thermal pumps, require great amount of power demand in the distribution network. In normal operation condition, the

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thermostatic cycle is maintained by alternating between non- and working periods but, this behavior is not detected in the load curve analysis since the load diversity is preserved (heating loads do not operate simultaneously) and the non-thermostatic loads are also connected in the power grid contributing to shape the load curve. However, in an energy supply interruption due to a permanent fault, the thermostatic cycle is also interrupted and, after the power restoration, many heating loads must demand power simultaneously. The procedure to restore a power grid after a significant period of supply interruption by taking into account this behavior of heating loads is known as cold load pickup (CLPU). Under the CLPU condition the load diversity is lost resulting in initial demand excessively high where the feeder current can exceeding its rating causing, as consequence, large voltage drops and possible service re-interruption. Emerging technologies, new devices and communication protocols have enhanced the power system normal operation and improved the response of the network against a permanent fault condition. In normal condition, daily operation costs [2] and power losses [3] has been tackled as needed improvements as economical and power quality supply issues. Moreover, the presence of distributed generation (DG) offers benefits to the distribution network. DG optimal placement [4] can decrease failure feeder`s rate and, after a permanent fault, DG units can be used in the energization of local load groups by forming

Corresponding author. E-mail address: [email protected] (J.B. Leite).

https://doi.org/10.1016/j.epsr.2019.105925 Received 21 January 2019; Received in revised form 7 June 2019; Accepted 20 June 2019 Available online 01 August 2019 0378-7796/ © 2019 Elsevier B.V. All rights reserved.

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Fig. 1. Function diagram and information flow of the restoration method.

In the traditional power distribution systems, the voltage control is performed through the local signal sampling on load tap changer (OLTC), voltage regulator (VR) and capacitor bank (CB). The tap controller of OLTC and VR is associated to the voltage magnitude from a pre-established remote node while the tap controller of CB has a horary characteristic or is associated to the voltage magnitude from a local node. With the DG in the electrical network injecting a significant amount of active power, the power flow can change its direction in some power distribution lines and, in particular operating scenarios, it can generate atypical behavior on VRs, like the condition of reverse power tap changer runaway [19], which is defined in the specialized literature as the VRs’ trying and failure to determine the final tap position where extremes positions, inferior or superior, are achieved. The use of centralized Volt/VAr control based on information and communication technologies provides the optimal operation of equipments to control voltage and reactive power in distribution systems [20]. In Ref. [21], it is proposed a real-time Volt/VAr control technique for smart grids using a two-way communication system. In the most recent literature works, the local controller of the Volt/VAr control devices is replaced by a supervised controller based on communication system [20,22]. In this work, it is proposed the association of the traditional service restoration (i.e. the load reenergization through the network reconfiguration) with the Volt/VAr control devices using the centralized architecture to improve the system response in the restorative state. The increased reliability is achieved by forming microgrids with dispatchable DG in power consumption regions subjected to load shedding. The heating loads are also considered using the condition of cold load pickup. The chosen technique to solve the distribution system with heating loads is the step-by-step restoration where the electrical network is restored using multiple steps in different time intervals [23]. A heuristic to obtain the switching sequence for each step, as part of DMS output as seen in Fig. 1, is described as well. In Fig. 1, real-time measurements, instantaneous loading, voltage profile and current flow in the distribution network are processed by the DMS functionalities, as well as topological information and electric parameters values that are

microgrids [5–7], and aid to maintain the diversity of heating loads reducing the additional power demand in the CLPU condition [8]. The additional power demand also can be reduced through an effective charging management applied to plug-in electric vehicles’ fleet that has high potential for congestion management [9]. Modern devices, such as automatic switches, make rapid the procedures of fault isolation and system reconfiguration by aiding in the formation and delimitation of microgrids with dispatchable DG. Real-time measurements with smart meters allow for getting high quality measures to distribution system state estimators. Through the improved system observability, the distribution management system (DMS) can achieve information of operating conditions and initial states that are required by the demand response management (DRM), Volt/VAr control (VVC), fault location, isolation and service restoration (FLISR), and many other applications. The service restoration in power systems has been studied by many works in the literature [10–15,5,6], but there yet are unsolved issues related to solution techniques for large-scale distribution networks. In the recent literature, it is emphasized the solution of the restoration problem using techniques based on classical mathematical optimization [16,5]. Two main limitations can be found in the most part of the works that solve the restoration problem through classical optimization: (i) the reduced scalability of algorithms that should be employed in realtime applications able to process distribution systems with thousands of nodes; (ii) in the restoration procedure, the network reconfiguration and load reenergization in neighbor feeders are not considered whereas just the formation of microgrids is considered. On the other hand, metaheuristic techniques allow the use of complete mathematical models for restoring the large-scale distribution networks without approximating or linearizing the mathematical model. The problem solution is done in short time interval which permits its implementation into real-time applications. In Ref. [11], modern heuristic techniques are evaluated in the solution of restoration problem where the tabu search metaheuristic-based techniques present better performances [17,18]. In this work, it is described a new version of the metaheuristic tabu search (TS), which is the reactive variable neighborhood tabu search (RVNTS), for solving the service restoration problem. 2

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in (2) and (3);

stored in the database. After the processing of these data, it is obtained, for instance, the switching sequence plan through the restoration network algorithm and, then, all control parameters, such as switching plan, DG operating parameters and tap positions of VRs and CBs, should be sent to a data concentrator unit able to distribute this information to the control devices in the electric network. The main contributions of this work are as following:

PkG − PkD = Vk ∑ Vm (Gkmcosθkm + Bkmsinθkm) mεK

QkG − QkD = Vk ∑ Vm (Gkmsinθkm − Bkmcosθkm) mεK

• Propose a robust, rapid and efficient algorithm to solve the re•

•

•

where:PkD :

th

(2)

(3)

node;QkD :

demand of active power at k demand of reactive power at kth node;PkG : active power generated at kth node;QkG : reactive power generated at kth node;Vk : voltage magnitude in kth node;Vm : voltage magnitude in mth node;Gkm : conductance between the kth and mth nodes.Bkm : susceptance between the kth and mth nodes.θkm : difference in voltage angle between the kth and mth nodes.The power flow balance is then supported through a forward/ backward method to distribution power flow calculation. Since the NDE arranges the network buses by layers, it makes possible the forward-sweeping method to solve the branch current while the backward-sweeping method to compute nodal voltages [25]. When the DG is connected in the distribution network a power compensation method is needed as given in Ref. [26]. 3) Every VR has a predefined number of tap positions that control the voltage steps (Δtapa). The regulation ratio is given as in (4);

storation problem to large-scale distribution networks with DGs, VRs, CBs and heating loads; Employ the centralized Volt/VAr control available at the distribution management system and data from the state estimation to operate the DG and change the tap position of VRs and CBs during the restoration procedures in distribution networks. According to the diagram in Fig. 1, in the DMS and after a permanent fault, the proposed algorithm must, for each step of the restoration procedure of distribution networks, provide the final switching plan and adjustment parameters of control to DGs, VRs and CBs; Solve the restoration problem using a dedicated metaheuristic that is known as reactive variable neighborhood tabu search and show the achieved outcomes under a real and large-scale distribution network. In the RVNTS algorithm, it is proposed the use of a specialized neighborhood structure by employing operators from nodedepth encoding (NDE) [24] which allow for exploring the search space with more efficiency and lower computational cost; Use the geographical information system (GIS) as a tool of graphical analysis to visualize the interrupted feeder sections, localization and operating conditions (opened or closed) of automatic and manual maneuver switches, reducing the restoration procedure time by sending maintenance crews to faulted areas

RRa = 1 − tapa*Δtapa tapa ∈ {tapmin, a, …, tapmax , a}

(4)

4) The switched CBs have a maximal number of steps (nswmax , b ) that control the total individual capacity (ΔCb ). The reactive power injection for each operating condition (Cbsw ) is given as in (5);

Cbsw = nswb*ΔCb nswb ∈ {0,1, 2, …, nswmax , b}

This work is arranged as following. In Section 2, it is introduced the hypothesis to build the mathematical formulation of the restoration problem. Section 3 depicts the development of RVNTS algorithm to solve the restoration problem through the NDE as well as a heuristic to obtain the switching sequence. In Section 4, issues involving the voltage control devices, distributed generation and CLPU condition on restoration problem are discussed and analyzed. Section 5 shows the results of performed tests with their correspondent analysis and, finally, the concluding remarks are exposed in Section 6.

(5)

5) Limits of active and reactive power generation, (6) and (8), GD power factor, (7), node voltage magnitude, branch current flow and substation transformer power flow, (9), (10) and (11), respectively.

0 ≤ PkG ≤ PkG, max

(6)

− φk, min ≤φk ≤ φk, max

(7)

2. Mathematical modeling of the restoration problem

− PkG * tan(φk, max ) ≤ QkG ≤ PkG * tan(φk, max )

(8)

In this section, the mathematical model of the restoration problem is described. The objective function must minimize the number of customers with interrupted power supply and the number of switching operations that is necessary to restore the distribution network, as given in (1).

Vk, min ≤ Vk ≤ Vk, max

(9)

minF = α∑ Li + β iεL

∑ jεSW

SWj

|Ikm| ≤ Ikm, max

(10)

|Sjn| ≤ Sjn, max

(11)

where: PkG, max : maximum generation capacity of DG at the kth node; φk : power factor angle of DG at the kth node; φk, min , φk, max : minimum and maximum power factor angles of DG at the kth node, respectively; Vk, min, Vk, max : minimum and maximum voltage magnitude in the kth node; |Ikm|: current magnitude between the kth and mth nodes; Ikm, max : maximum capacity of current flow through the conductor between the kth and mth nodes; |Sjn|: magnitude of apparent power through the jth transformer in the nth substation; Sjn, max : maximum capacity of apparent power through the jth transformer in the nth substation; Ramp constraints, due to the CLPU condition, have detailed description in Section 4.

(1)

where: Li : energy supply status, normal (0) or interrupted (1), of the ith customer in the distribution network; SWj: switching operation, none (0) or open/close (1), of the jth switch in the distribution network; α, β : weighted factors of variables in objective function where α + β = 1. Constraints of the restoration problem are as following: 1) The distribution network is represented by the NDE that guarantees the network radiality through the employment of its operators for exploring the search space in the restoration algorithm, as is exposed in the Section 3.1; 2) Power flow balance equations for radial networks with DG is given 3

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Fig. 2. Graph representation of the operators: PAO, CAO and CUT.

3. Solution technique

Subsequently, a new set of neighbor solutions is generated from the current solution and a new best neighbor solution is then selected. If the best neighbor solution has not attributes into the TL or complies the AC, it becomes the new current solution. This iterative process continues until the achievement of the stopping criteria, which is typically defined as the maximum number of iterations. The performance of the RVNTS algorithm is enhanced as consequence of its reaction feature when the best neighbor solution has attributes into the TL, i.e., the algorithm begins with an initial neighborhood structure (NS-1) and, subsequently, this structure is changed to another final neighborhood structure (NS-2). The NS-1 neighborhood structure uses initially the PAO and CAO operators and, at the ith iteration, the neighborhood structure undergoes a change by including the CUT operator (NS-2), since it is not possible to restore all interrupted loads satisfying the constraints of the mathematical model after this iteration. With the check of all feasible neighbors using NS-1, the CUT operator is then included into neighborhood structure that is now named NS-2 and allows the load cut and islanding operation of DG. In the TL is stored the identifications of the sectionalizing switches that has its status (open/closed) modified to generate the best configuration in the analyzed neighborhood. The AC is the value of the best incumbent solution, i.e. a candidate configuration is not more a tabu configuration whether the value of its objective function is better than the value of the incumbent solution. The RVNTS algorithm to solve the restoration problem of distribution network has two stages:

3.1. Representation of the radial distribution network The NDE representation together with its operators PAO (preserve ancestral operator) and CAO (change ancestral operator) are used in the development of the RVNTS algorithm to solve the restoration problem in large-scale distribution networks. In addition to these two classical operators, it is used a new operator that is known as CUT [23] that performs the load shedding in conditions where is impossible to restore all interrupted loads. In Fig. 2, it is illustrated the use of operator: PAO; CAO; and CUT, under a distribution system with two radial feeders. Each feeder has three load sections where one section is defined as a group of distribution system elements that is limited by switches. In Fig. 2, the solid lines are normally closed switches while dashed lines are opened switches. Before the PAO operation, one pruning node, p, is chosen as a connection point to an adjacent node, a, at the neighbor feeder for yielding the final network configuration after the PAO operation. In the CAO operation, one pruning node, p, is selected as the disconnection point while a root node, r, is chosen as the connection point to one adjacent node, a, at the neighbor feeder yielding the final network configuration after the CAO operation. Before the CUT operation, one pruning node, p, is selected as the disconnection point for performing the load shedding after the CUT operation. In the restoration problem, the use of PAO, CAO and CUT operators depends on the localization of maneuver switches and interconnection branches among feeders. Differently from Refs. [27] and [28] where a pre-established percent of neighbors is randomly generated by PAO, CAO and CUT operators, in this work is generated a specialized neighborhood structure from current configuration by applying all possible operators, PAO, CAO and CUT, to explore all neighbor configurations of the electrical distribution network. In this way, the new proposed method, that employs these operators as specialized neighborhood structure of RVNTS algorithm, permits to explore the search space of the restoration problem with more efficiency and lower computational cost.

3.2.1. Initialization stage Build an initial solution, x0, through the following procedures: (a) isolate the faulted feeder section by opening their adjacent sectionalizing switches; and (b) connect all interrupted safe feeder sections to the nearest energized feeder sections considering the radiality constraint of the mathematical model. Do LT = ∅; 3.2.2. Main stage i) Use the initial solution equals to the current solution and employ the NS-1 neighborhood structure; ii) If one stopping criteria is satisfied, then go to the step vii, otherwise follow to the step iii; iii) Apply the NS-1 neighborhood structure on the current solution. Check the objective function and the constraints of the mathematical model for each generated neighbor. Select the best generated neighbor and compare its attributes to those stored in the TL. If the best neighbor has not prohibitive attributes or complies the aspiration criteria, then do the current solution equals to the best neighbor, update the TL and return to the step ii. Otherwise, follow to the step iv; iv) Change the neighborhood structure to NS-2;

3.2. Reactive variable neighborhood tabu search (RVNTS) RVNTS algorithm to solve the restoration problem is a modified version of the classic tabu search algorithm and uses its main functions such as neighborhood structure (NS), tabu list (TL) and aspiration criterion (AC) [17,18]. The classic TS algorithm begins the search process using an initial solution and an empty TL. A set of neighbor solutions is generated from the initial solution using the NS. The best neighbor solution, i.e. the neighbor solution with better value of adaptation function (objective function that is penalized by values of exceeded problem constraints), is selected as new current solution and its attributes are stored into the TL. 4

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new sectionalizing switches pair with combinations of types 7 and 2, and do it until the exhaustion of all possible combinations of these types. Go to the stage 3.

v) If one stopping criteria is satisfied, then go to the step vii, otherwise, follow to the step vi; vi) Idem the step iii but now it must apply the NS-2 neighborhood structure and return to the step v; vii) Finalize the algorithm execution.

3.3.3. Stage 3: restoration of de-energized area i) Put all sectionalizing switches in the operating state of the IC. Go to the step ii ; ii) Select a sectionalizing switches pair that is composed of one sectionalizing switch with combination of type 7 and another of type 2. Open the sectionalizing switch of type 7, close the sectionalizing switch of type 2. Verify that no new feeder section is isolated and no loop is created. Then consider opening of the sectionalizing switch of type 7 and the closing of the sectionalizing switch of type 2 under analysis and store the numeration of these sectionalizing switches that are not in the RSS vector. Otherwise, look for a new sectionalizing switches pair that complies these conditions until the exhaustion of all possible sectionalizing switches with combination of types 7 and 2. Go to the step iii ; iii) Idem the step ii but select one sectionalizing switches pair of types 3 and 2. If no new feeder section is isolated and no loop is created, then store the closing of sectionalizing switch with combination of type 2 if it is absent in RSS vector. Otherwise, look for a new pair of sectionalizing switches until the exhaustion of all possible sectionalizing switches with combination of types 3 and 2. Go to the step iv ; iv) Store the sectionalizing switches with combination of type 4 into RSS vector and provide the switching sequence to restore the distribution network.

The basic premise of this algorithm is the solution of the restoration problem through the search of feasible solutions that can primarily energize as many customers as possible localized in restorable feeder sections without operating problems, i.e., in feeder sections with feasible operating conditions. 3.3. Switching sequence heuristic In the heuristic algorithm to obtain the sectionalizing switching sequence, it is used the states of every sectionalizing switches in the configurations of post fault (PFC), initial (IC) and incumbent, or final, (FC) solutions generated by RVNTS algorithm. The sectionalizing switches’ states are classified in 1 (closed) and 0 (opened). Thus, the operating states for each switch in PFC/IC/FC topologies are classified using eight combinations: type 1 (0/0/0), type 2 (0/0/1), type 3 (0/1/ 0), type 4 (0/1/1), type 5 (1/0/0), type 6 (1/0/1), type 7 (1/1/0) and type 8 (1/1/1). The sectionalizing switch combinations of types 1 and 8 do not provide information about the switching sequence to restore the distribution network, since they do not change their operating state during the execution of the RVNTS algorithm. The sectionalizing switch combinations of types 5 and 6 are not considered in the problem solution because no sectionalizing switch must be opened in the generation of IC. In this way, the achievement process of sectionalizing switching sequence just needs to analyze the combinations of types 2, 3, 4 and 7. The sectionalizing switches with combination of type 4 were closed to generate the IC, remained in this operating state in the FC and, hence, provide useful information to determine the sectionalizing switching sequence. The sectionalizing switches with combination of type 2, together to sectionalizing switches with combination of type 3 and 7, are analyzed in pairs (2–3 and 2–7), because the operating states of the sectionalizing switches with these types of combination are opposite in IC and FC. The sequential execution of three stages and sub steps of the heuristic algorithm to obtain the switching sequence yields the restoration switching sequence (RSS) vector with the set of sectionalizing switches that must be operated by the restoration application in the DMS.

4. Voltage control devices, distributed generation and cold load pickup issues 4.1. Voltage control devices In distribution systems, devices, such as OLTC, VRs and CBs are utilized to maintain the voltage magnitudes under the acceptable bounds that are pre-established by regulatory standards. In this work, it is proposed the centralized control of tap position as part of the restoration process. In this way, the final tap positions are determined using the operating requirements of the distribution system for each restoration step. The prevention of unnecessary power flow calculations during the execution of the RVNTS algorithm is performed by a previous analysis of tap positions on OLTCs and VRs and steps on CBs for each candidate topology with exceeded voltage limits. In distribution feeders with voltage control devices, the analysis procedure is as following:

3.3.1. Stage 1: load cut and islanding operation i) Do RSS = ∅ and go to the step ii ; ii) Select sectionalizing switches with combination of type 7 to integrate the switching sequence whether only one of its poles is energized in the loop that is built from the switch to the substation in the final configuration. Go to the step iii; iii) Store the numeration of these sectionalizing switches into RSS vector. Go to the stage 2.

4.1.1. Stage 1:adjustment of tap position on voltage control devices i) If the lower voltage limit in any feeder node is exceeded, then the tap position of voltage control devices is adjusted in the maximum position. Go to stage 2.

3.3.2. Stage 2: reconfiguration of adjacent feeder sections 4.1.2. Stage 2: checking of lower and upper volt- age limits in the analyzed feeder

i) Put all sectionalizing switches in operating state of PFC. Go to the step ii ; ii) Select a sectionalizing switches pair that is composed of one sectionalizing switch with combination of type 7 and another of type 2 with external nodes out from faulted area. Open the sectionalizing switch of type 7, close the sectionalizing switch of type 2. Verify that no new feeder section is isolated and no loop is created. Select the opening of the sectionalizing switch with combination of type 7 and the closing of the sectionalizing switch with combination of type 2 to integrate the switching sequence and store the numeration of these sectionalizing switches into RSS vector. Otherwise, look for a

i) Check whether the lower voltage limit in all feeder nodes is satisfied and, then, go to step ii. Otherwise, the candidate solution is dismissed and the algorithm execution is finalized; ii) Check whether the upper voltage limit in all feeder nodes is satisfied and, then, go to stage 5. Otherwise, go to stage 3. 4.1.3. Stage 3: finding tap of VR in the analyzed feeder i) Find the VR in the analyzed feeder and go to step ii. Otherwise, go 5

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order of depth. If another DG is found, consider it as a negative load. Go to step i and select a different DG not yet used. iv) End of the procedure.

Table 1 RVNTS algorithm and CLPU condition parameters. Parameter

Value

Maximum number of iterations Iterations without the improvement of the incumbent solution α β Tabu list size Aspiration criteria

200 15

4.3. Cold load pickup issues

0.8 0.2 4 Improve the incumbent solution 2.5. p.u. 1.0 p.u. 1 h−1 0.5 h

In the restoration of distribution networks with overload due to CLPU condition, the step-by-step restoration has been the most used method [23], where the distribution network is split in small areas that are sequentially restored in specific time intervals. In the literature, different mathematical models have been used in the estimation of the restoration performance of distribution networks with high penetration of heating loads: CLPU curves [29]; physical models [30]; delayed exponential models [31] and probabilistic models [32]. In this work, it is used a model of delayed exponential function for determining the peak value and duration of the aggregated non-diversified load. Additionally, the restoration algorithm uses the step-bystep process where a particular switching sequence is provided by the algorithm for each step. The final topology, which is obtained after the realization of the switching sequence to one restoration step, is dealt as the initial topology to the subsequent restoration step. Eq. (12) [33] states the apparent power variation to a set of heating loads after an unplanned interruption.

SU SD γ ti – Ri

to stage 4; ii) Check whether the voltage at the VR reference node exceeds the upper limit. If the upper voltage limit is exceeded then, reduce one tap position systematically until the voltage at the VR reference node achieves the suitable voltage profile. In cases with two or more VRs, the procedure begins with the closest VR to the root node of analyzed feeder. Go to step iii ; iii) Verify whether lower and upper voltage magnitude limits are achieved in every feeder node. Go to stage 5. If the lower voltage magnitude limit is exceeded, dismiss the candidate solution and finalize the algorithm execution. In case only the upper voltage magnitude limit is exceeded, go to stage 4.

S(t)= [SD + (SU − SD ) e−γ (t − ti ) ] u (t − ti ) + SU [1 − u (t − ti )] u (t − Ri ) (12) 5. Numerical results

4.1.4. Stage 4: finding the step number of CB in the analyzed feeder

In this work, two test systems are used to demonstrate the robustness and the efficiency of the proposed methodology. The first one is a 53 nodes test system with data found in Ref. [16]. The second one is a real large-scale distribution system from Brazilian coast. The proposed algorithm to distribution network restoration is implemented using the C++ programming language, and the simulations are done under a computer with Intel I7 processor. The calibration parameters of RVNTS algorithm are presented in Table 1, and they are the same for all performed tests.

i) Find the switched CB in the analyzed feeder and go to step ii. Otherwise, go to stage 5; ii) Check whether the voltage magnitude at the node with switched CB installed exceeds the upper limit. If the upper limit is exceeded then, reduce one tap position systematically until the voltage magnitude at the node with switched CB achieves the suitable voltage magnitude profile. In cases with two or more CBs, the procedure begins with the closest CB to the root node of analyzed feeder. Go to stage 5.

5.1. Results to 53 nodes testing system

4.1.5. Stage 5: checking the operating voltage magnitude limits in the analyzed feeder

The first analyzed system has 53 nodes, 3 substations, 61 switches, 45.6 MW of active and 22.1 MVAr of reactive power demand. The nominal voltage is 13.8 kV with inferior and superior voltage limits of 0.95 and 1.05 p.u., respectively. Fig. 3 shows the schematic of this testing system where every node represents a feeder section and each branch represents a switch.

i) Check whether the magnitude limits of voltage, current and power are satisfied in the analyzed feeder and store the candidate solution. Otherwise, dismiss the candidate solution. End of the analysis procedure. 4.2. Distributed generation In the proposed restoration algorithm is considered that DGs have the black start functionality by permitting the islanding operation for a group of loads. The demanded power of this load group must not overcome 50% of the maximum generation capacity of DGs at the instant of fault occurrence in order to guarantee the safety margin to avoid power oscillations. Feeder sections that are supplied by the DG on islanding operation are selected as following: i) Select the DG with more capability in regions that are defined as load shedding by the RVNTS algorithm, go to step ii. Otherwise, go to step iv ; ii) Using the selected DG section as new root and unsupplied feeder sections as elements, organize these feeder sections using NDE. Go to step iii. iii) Select feeder sections that will be supplied by the selected DG in

Fig. 3. Schematic of 53 nodes test system. 6

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described test system. In scenarios with faults on the feeder sections 1 and 30, the possibility of islanding operation from installed DG allows for increasing the number of restored loads. In the scenario with simultaneous faults on feeder sections 1, 21 and 14, the control of DG, VR and CB can increase to 75.50% the amount of restored load. Test #3: In this test, the restoration procedure is step-by-step performed due to heating loads that are distributed along the entire nodes of the testing system. In the Table 5, the results for each restoration step are presented where just automatic maneuver switches are used in the restoration process. In the scenario with a simple fault on feeder sections 3, 21 or 30, it is obtained the same percentage of restored load in the steps 1, 2 and 3 because of current, voltage and power restrictions. In simple and simultaneous faults in other feeder sections, the number of loads that can be restored increases through the steps because the restored loads retrieve the diversity factor of the system along the time thus, the influence of heating loads in restoration process is diminished. Test #4: Table 6 shows the results to the system with CLPU condition plus GD, VR and CB as is described in the Test #2. The operation of DG in the test system allows for improving the results quality because loads in feeder sections with DG do not loss their diversity when operating in islanded mode. Computational cost analysis for the restoration algorithm: In the Table 7, it is presented the processing time of the performed tests to the 53 nodes system. Performed tests with two or more devices, such as voltage control devices and GD, require large processing time in order to determine the final solution. This algorithm behavior is expected because the computational cost depends on the number of analyzed solutions and control variables in the determination of the best solutions.

Table 2 Switching sequence to a fault in node 3 of the 53 nodes system. Order

Maneuver

Switch

Non-restored feeder sections

Re-connected customers

1 2 3 4 5 6 7 8 9

Open Open Open Close Open Close Open Close Close

5–4 26–27 28–6 35–40 34–33 28–27 27–8 28–50 8–33

4,5,6,7,8,26,27,28 4,5,6,7,8,26,27,28 4,5,6,7,8,26,27,28 4,5,6,7,8,26,27,28 4,5,6,7,8,26,27,28 4,5,6,7,8,26,27,28 4,5,6,7,8,26,27,28 4,5,6,7,8,26 5,6,26

0% 0% 0% 0% 0% 0% 0% 20.56 %

The restoration algorithm is evaluated using the outcomes from four performed tests that are described as following: Test #1 comprises simple contingencies with daily loading curve of transformers, without the installation of DG and CLPU condition, using only automatic switches to restore the distribution network; Test #2 has the same conditions of Test #1, plus the optimized adjustments of DGs and voltage control devices; Test #3 has the same conditions of Test #1 with addition of the CLPU condition; and Test #4 consists of Test #2 and CLPU conditions. In all tests, the following nomenclatures are used in the analysis of results: N is the switching number; R is the percentage of re-connected customers; and I is the number of feeder sections in islanding operation Test #1: One permanent fault in the node 3 is simulated. The fault is isolated by opening the switches between nodes 3–101 and 3–4. The algorithm obtains a solution where 57.94% of all active power is restored. The computational cost necessary to obtain this solution is equal to 27 ms. After this fault, the switching sequence to restore the testing distribution network is presented in Table 2. In the presented results of Table 3, the reactive feature of the RVNTS algorithm is activated in scenarios where the load cut is required. Analogously, in restoration scenario with only restorative loads, the best solution is determined without the activation of the reactive feature. In scenarios including the feeder sections 1 and 30, the restoration of all restorative loads is infeasible with just switching operations because the re-connection of sections 2 and 29 is impossible. The obtained results considering permanent faults in the sections 3 and 11 are the same ones found using the classical optimization, as proposed in Ref. [16], which allows proving the precision and robustness of proposed methodology. Test #2: CBs of 600 kVAr with 6 steps of 100 kVAr are installed into nodes 16 and 24, and a VR is installed between sections 38 and 39 with the capability to regulate +/- 10% of input voltage and, consequently, the tap variation is equals to 0.00625 p.u., minimum tap is -16 and maximum tap is +16. The control adjustments of CBs and VRs, and simultaneous adjustments of these devices are done separately. Additionally, two DGs with black start, active power generation capability of 2.1 MW and capacitive/inductive power factor limit of 0.9 are connected in the feeder sections 2 and 29 at voltage-controlled nodes. In the Table 4, it is demonstrated the restoration results to the

5.2. Results to the real system with 7052 nodes The second system is real and has 7052 nodes, 708 automatic switches, 2 VRs and 9 fixed CBs with capability of 900 kVAr, 700 kVAr, 600 kVAr, 2000 kVAr, 600 kVAr, 1000 kVAr, 600 kVAr, 600 kVAr and 600 kVAr that are distributed among 9 feeders. The distribution network has 46.1 MW of active power and 15.3 MVAr of reactive power demand. The nominal voltage of the system is 13.6 kV and the voltage limits are defined in Ref. [34]. In the tests #1 and #2, permanent faults are simulated in different feeder sections by considering the control of VRs and CBs. The penetration of heating loads, which are superior to 30% in distribution feeders, requires the insertion of the CLPU condition on the restoration procedure [35]. In this work, the simulated tests #3 and #4 analyze scenarios where the penetration of heating loads is equals to 100%. Test #1: In the Table 8, it is presented results to faults in the substation node for every feeder with just switching operations without taking account the adjustments of voltage control devices. In the most part of fault scenarios, the load totality can be restored using around one to five switching operations, which highlights the correct system planning. In the scenario with simulated fault on feeder 9, the determined restoration solution defines a load cut of 1.57 MW permitting, thus, to restore 78.90% of its active power load. Test #2: In addition to voltage control devices in the original system, the fixed power CBs are replaced by switched CBs, with their maximum capacity divided in ten power steps, and three DGs are installed at nodes 5, 6 and 9 with black start and reactive control features, active power limits of 200 kW, 800 kW and 700 kW, respectively, and inductive/capacitive power factor equals to 0.9. Table 9 shows the results to simulated faults at the beginning of every feeder of the system. In the scenario with fault on feeder 2, the DG control induces the reduction of switching number from 5 to 3 and, when controlling voltage with VRs and CBs, this switching number can be reduced to 1. In the scenario with fault on feeder 9, the islanding operation of a feeder section with DG allows for increasing the restoration percentage from

Table 3 Main results to the 53 nodes system. Faulted feeder section

N

R (%)

Non-restored active power (kW)

03 11 14 01 21 30 01, 21 01, 14, 21

9 7 5 3 1 3 6 11

57.94 100 40.17 84.69 100 78.79 88.64 65.86

3118.50 0 4851.00 1039.50 0 970.20 1039.50 5890.50

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Table 4 Results to 53 nodes system by considering GD, VR and CB. Faulted feeder section

System with DG

03 11 14 01 21 30 01, 21 01, 14, 21

System with DG and CB

System with DG and VR

N

R(%)

I

N

R (%)

I

N

R (%)

I

N

R (%)

I

9 7 5 4 1 4 7 12

57.94 100 40.17 100 100 100 100 71.89

0 0 0 1 0 1 1 1

9 7 5 4 1 4 7 12

57.94 100 40.17 100 100 100 100 71.89

0 0 0 1 0 1 1 1

9 7 8 4 1 4 7 15

57.94 100 47.86 100 100 100 100 75.50

0 0 0 1 0 1 1 1

9 7 6 4 1 4 7 13

57.94 100 47.86 100 100 100 100 75.50

0 0 0 1 0 1 1 1

78.90% to 83.35% and, with voltage control of VRs and CBs, this percentage increases to 85.26%. Test #3: In the Table 10, it is shown the results to testing system with CLPU condition and faults happening at the beginning of the feeders that have only automatic switches. In scenarios with fault on feeders 1, 4 and 5, 100% of loads are restored in the step 1 using around five to fifteen switching operations. On feeder 3, it is necessary two restoration steps and, on feeder 8, 100% of loads are restored after the third step. In scenarios with fault on feeders 2, 6, 7 and 9, the entire restoration of interrupted loads is impossible. In the most part of obtained solution, the switching number in the first restoration step is the biggest because in the system topology there are groups of feeder sections that are connected to only one feeder section requiring a major switching number in order to avoid the load cut when just one remains connected. Test #4: The results to testing system with CLPU plus GD and voltage control devices are presented in Table 11. In the scenario with fault at the beginning of feeder 2, the enhancement on switching number and restored load percentage is notable in the restoration steps 2 and 3 in comparison to results in Table 10. In scenarios with fault on feeders 3 and 4, the interrupted load is restored in step 2 by reducing two switching operations. In the feeder 6, there is an improvement on restored load percentage and switching number along four restoration steps. Finally, in the feeder 9, 4.46% of restorative loads operate in islanded mode after the fault isolation, which avoids the loss of load diversity increasing the restored load percentage in the next three restoration steps, in comparison to results in the Table 10. Computational cost analysis: In Table 12, it is presented the values of minimum and maximum processing time for each performed test on feeder 9 of the 7052 nodes system. Ten simulations per test are performed. The switching operations and processing time increase proportionally to number of variables control analyzed in the determination of the best solutions. When the heating loads are inserted in the restoration problem, the proposed algorithm spends more time in the determination of a feasible solution due to the high initial loading of the system. Furthermore, the increased complexity of the analyzed system, the severity level of the simulated fault and the huge number of control variables involving the restoration problem indicate that the computational cost is in concordance with expected limits to restore real largescale distribution networks. Energy not supplied (ENS): the distribution network restoration problem must be solved as fast as possible in response the interruption emergency state providing a switching sequence. The performance of a restoration algorithm can be evaluated by using reliability index like the ENS that can be defined as the amount of energy not consumed by the customers due to the energy supply interruption. The ENS value is equivalent to the area under the curve of not restored load along the time, i.e. from the start of interruption until the time when the fault is repaired. In the Table 13, it is presented the processing time and the ENS by solving the restoration problem through TS and RVNTS considering a fault repair time of three hours and automatic switch operation time of one minute. The time and ENS gains indicate how much

Table 5 Results to 53 nodes system with CLPU condition. Faulted feeder section

Step 1

03 11 14 01 21 30 01, 21 01, 14, 21

Step 2

Step 3

N

R (%)

N

R (%)

N

R (%)

2 12 2 5 2 4 5 8

6.54 42.75 11.11 44.90 35.29 27.27 33.33 20.08

0 1 0 3 0 0 0 1

6.54 45.04 11.11 55.10 35.29 27.27 33.33 24.10

0 3 4 0 0 0 3 5

6.54 60.31 17.95 55.10 35.29 27.27 50.00 30.12

Table 6 Results to 53 nodes system with CLPU condition plus GD, VR and CB. Faulted feeder section

03 11 14 01 21 30 01, 21 01, 14, 21

Step 1

Step2

N

R (%)

N

0 0 0 1 0 1 1 1

0 0 0 15.31 0 21.21 11.36 6.02

2 11 2 5 2 4 5 8

Step 3

Step 4

R (%)

N

R (%)

N

R (%)

6.54 45.04 11.11 60.20 35.29 48.48 44.70 26.10

5 0 0 3 0 0 0 1

24.30 45.04 11.11 70.41 35.29 48.48 44.70 30.12

0 3 4 0 0 0 3 5

24.30 60.31 17.95 70.41 35.29 48.48 61.36 36.14

Table 7 Minimum and maximum processing time for 53 nodes system. Test

Step

Minimum time (s)

Maximum time (s)

Average time (s)

#1 #2 #3

1 1 1 2 3 1 2 3

0.002 0.004 0.015 0.021 0.016 0.033 0.035 0.035

0.044 0.096 0.033 0.047 0.032 0.079 0.131 0.084

0.028 0.059 0.026 0.029 0.023 0.057 0.069 0.055

#4

System with GD, VR and CB

Table 8 Results simulation for 7052 nodes system. Faulted feeder

N

R (%)

Non-restored active power (kW)

1, 3, 4, 5 or 7 02 6 or 8 09

1 5 3 14

100 100 100 78.90

0 0 0 1568.62

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Table 9 Results to 7052 nodes system by considering DG, VR and CB. Faulted feeder

1, 3, 4, 5 or 7 2 6or 8 09

System with DG

System with GD and CB

System with DG and VR

N

R(%)

I

N

R (%)

I

N

R(%)

I

N

R (%)

I

1 3 3 14

100 100 100 83.35

– – – 4

1 1 3 13

100 100 100 85.26

– – – 3

1 3 3 14

100 100 100 83.35

– – – 4

1 1 3 13

100 100 100 85.26

– – – 3

Table 10 Results to 7052 nodes system with CLPU condition. Faulted feeder

Step 1

1 2 3 4 5 6 7 8 9

Table 13 Performance comparison of TS with RVNTS using ENS.

Step 2

N

R (%)

5 15 15 11 15 24 12 21 16

100 56.22 95.50 100 100 73.27 80.48 86.63 43.33

N

Step 3 R (%)

N

Faulted feeder

1 or 7 2 3 or 4 5 6 8 9

Step 1

3 2

65.51 100

2

72.37

4 10 8 4

86.48 87.96 98.10 48.97

2 6 2 7

99.25 96.45 100 55.79

Step2

Step3

N

R (%)

N

R (%)

0 0 0 0 0 0 1

0 0 0 0 0 0 4.46

3 14 7 9 21 15 14

100 58.89 100 100 74.39 88.91 48.51

1 2 3 4 5 6 7 8 9

RVNTS

Time Gain (s)

ENS Gain (kWh)

Step4

N

R (%)

N

R (%)

2

67.99

2

72.37

5 6 6

87.91 100 54.15

3

100

4

60.61

Test

Step

Minimum time (s)

Maximum time (s)

Average time (s)

#1 #2 #3

1 1 1 2 3 1 2 3

39.47 151.47 33.25 19.66 22.48 123.14 323.24 102.66

40.48 153.95 33.41 19.72 22.59 126.33 341.30 109.64

39.98 153.15 33.33 19.70 22.56 124.42 335.81 107.48

Time (s)

ENS (kWh)

Time (s)

ENS (kWh)

4.24 34.15 7.24 4.95 8.03 6.05 0.24 17.42 21.23

76.81 223.24 76.81 76.81 76.81 437.36 12.39 280.05 6194.23

1.2 8.72 2.76 2.15 4.19 4.85 0.23 12.74 172.32

76.81 196.38 76.81 76.81 76.81 437.36 12.39 280.05 5725.73

3.04 25.43 4.48 2.8 3.84 1.2 0.01 4.68 −151.09

0 26.86 0 0 0 0 0 0 468.5

restoration function in the DMS uses the proposed algorithm. Therefore, in a permanent fault scenario and after the fault localization, the GIS application [36] permits the operator to visualize the distribution feeder sections that are damaged, without energy supply, by supervising all steps of the restoration procedure as is shown in Fig. 4. For example, in (a), the distribution network georeferenced topology indicates the lines’ status immediately after the fault location when the restoration level is 0% and the decision matrix provides the required operating actions. With the isolation of faulted feeder section and closing the substation circuit breaker, the monitored restoration level increases to 53% as is shown in (b) that also displays the energized lines and operated switches.

Table 12 Minimum and maximum processing time for the performed tests in the feeder 9 of the 7052 nodes system.

#4

TS

R (%)

Table 11 Results to 7052 nodes system with CLPU condition plus DG, VR and CB. Faulted feeder

System with DG, CB and VR

6. Concluding remarks This work describes a scalable method to perform the automatic restoration of large-scale distribution networks in CLPU condition, which results in excessive initial loads to be reconnected in scenarios with high penetration of heating loads. Due to the complexity of this problem, distribution companies around the world are constantly looking for new approaches able to minimize the effects of permanent faults in the electrical network. In this way, a centralized approach based on the reactive variable neighborhood tabu search (RVNTS) is proposed by taking into account the optimized control of DGs, VRs and CBs, as well. The results demonstrate the improvement in the quality of solutions when these controls are considered in the mathematical model, with or without appearance of the CLPU condition in the distribution network. The DG also increases the quality of solutions during the steps of the restoration procedure by avoiding the diversity loss of heating loads. Regarding to the computational cost, the proposed methodology is robust and determines solutions with good quality in sufficient processing time that guarantees its use to restore real large-scale distribution networks. It can be implemented as a resource of DMS from power distribution companies to obtain the switching sequence in secure and efficient way in the network operating.

the performance of the proposed method is better. The RVNTS provides the same or better results than TS with time gain, except in the case of fault in the feeder 9. This increased time comes from the delay in the activation of the algorithm reactive feature that includes the CUT operator in the neighbor structure allowing for the load cut and the formation of microgrid with dispatchable GD. On the other hand, in cases of fault in the feeders 1 to 8, the TS algorithm needs more processing time because the TS just provides feasible solutions with load cut ignoring that good solutions using only PAO and CAO operators. Visualization of restoration procedures using GIS: Fig. 4 displays the results of restoration procedures that are obtained using the restoration function for a simulated fault on feeder 4. The implementation of the

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Fig. 4. Visualization of restoration procedures (a) feeder disconnected by the substation circuit breaker; (b) partial feeder restoration.

Conflict of interest [5]

None. Acknowledgements

[6]

This work was fully supported by the Capes, FAPESP (grant: 2015/ 17757-2) and CNPq (grant: 3053182016-0).

[7] [8]

References [9] [1] J.E. McDonald, A.M. Bruning, W.R. Mahieu, Cold load pickup, IEEE Trans. Power App. Syst. PAS- 98 (4) (1979) 1384–1386. [2] M. Rahmani-Andebili, Dynamic and adaptive reconfiguration of electrical distribution system including renewables applying stochastic model predictive control, IET Gener. Transm. Distrib. 11 (2017) 3912–3921. [3] M. Jegadeesan, C.K. Babulal, V. Subathra, Simultaneous placement of multi-DG and capacitor in distribution system using hybrid optimization method, 2017 International Conference on Innovations in Green Energy and Healthcare Technologies, IEEE, 2017, pp. 1–7. [4] M. Rahmani-Andebili, Distributed generation placement planning modeling feeder’s

[10]

[11] [12] [13]

10

failure rate and customer’s load type, IEEE Trans. Ind. Electron. 63 (3) (2016) 1598–1606. B. Chen, C. Chen, J. Wang, K.L. Butler-Purry, Se- quential service restoration for unbalanced distribution systems and microgrids, IEEE Trans. Power Syst. 33 (2) (2018) 1507–1520. A. Sharma, D. Srinivasan, A. Trivedi, A decentralized multiagent system approach for service restoration using DG islanding, IEEE Trans. Smart Grid 6 (6) (2015) 2784–2793. A. Arif, Z. Wang, Networked microgrids for service restoration in resilient distribution systems, IET Gener. Transm. Distrib. 11 (14) (2017) 3612–3619. V. Kumar, H.C.R. Kumar, I. Gupta, H.O. Gupta, DG integrated approach for service restoration under cold load pickup, IEEE Trans. Power Deliv. 25 (1) (2010) 398–406. M. Rahmani-Andebili, M. Fotuhi-Firuzabad, An adaptive approach for PEVs charging management and reconfiguration of electrical distribution system penetrated by renewables, IEEE Trans. Ind. Informat. 14 (5) (2018) 2001–2010. S.J. Lee, S.I. Lim, B.S. Ahn, Service restoration of primary distribution systems based on fuzzy evaluation of multi-criteria, IEEE Trans. Power Syst. 13 (1) (1998) 1156–1163. S. Toune, et al., Comparative study of modern heuristic algorithms to service restoration in distribution systems, IEEE Trans. Power Deliv. 17 (1) (2002) 173–181. A.L. Morelato, A. Monticelli, Heuristic search approach to distribution system restoration, IEEE Trans. Power Deliv. 4 (4) (1989) 2235–2241. D. Shirmohammadi, Service restoration in distribution networks via network

Electric Power Systems Research 176 (2019) 105925

R.A.V. Peralta, et al.

IEEE Trans. Power Syst. 3 (2) (1988) 753–762. [26] S. Khushalani, J.M. Solanki, N.N. Schulz, Development of three-phase unbalanced power flow using PV and PQ models for distributed generation and study of the impact of DG models, IEEE Trans. Power Syst. 22 (3) (2007) 1019–1025. [27] W.P. Mathias-Neto, J.R.S. Mantovani, A node- depth encoding-based tabu search algorithm for power distribution system restoration, J Control Autom. Electr. Syst. 27 (3) (2016) 317–327. [28] R. Vargas, et al., Automatic restoration of active distribution networks based on tabu search specialized algorithm, Proc. Innovative Smart Grid Technologies Latin America (ISGT, in: Innovative Smart Grid Technologies Latin America (ISGT LATAM), (2015), pp. 411–416. [29] O.H. Mirza, Usage of CLPU curve to deal with the cold load pickup problem, IEEE Trans. Power Deliv. 12 (2) (1997) 660–667. [30] S. Ihara, F.C. Schweppe, Physically based modeling of cold load pickup, IEEE Power Eng. Rev. PER-1 (9) (1981) 27–28. [31] W.W. Lang, M.D. Anderson, D.R. Fannin, An analytical method for quantifying the electrical space heating component of a cold load pick up, IEEE Trans. Power App. Syst. PAS-101 (4) (1982) 924–932. [32] R.E. Mortensen, K.P. Haggerty, A stochastic computer model for heating and cooling loads, IEEE Trans. Power Syst. 3 (3) (1988) 1213–1219. [33] V. Gupta, A. Pahwa, A voltage drop-based approach to include cold load pickup in design of distribution systems, IEEE Trans. Power Syst. 19 (2) (2004) 957–963. [34] A. N. de Energia Elétrica (ANEEL), Procedimentos da Distribuição — Módulo 8, in Portuguese (2010). URL http://www.aneel.gov.br. [35] K.P. Schneider, et al., Evaluating the magnitude and duration of cold load pick-up on residential distribution using multi-state load models, IEEE Trans. Power Syst. 31 (5) (2016) 3765–3774. [36] J.B. Leite, J.R.S. Mantovani, Development of a smart grid simulation environment, part II: implementation of the advanced distribution management system, J. Control Autom. Electr. Syst. 26 (1) (2016) 96–104.

reconfiguration, IEEE Trans. Power Deliv. 7 (2) (1992) 952–958. [14] K. Miu, H.D. Chiang, R.J. McNulty, Multi-tier service restoration through network reconfiguration and capacitor control for large-scale radial distribution networks, IEEE Trans. Power Syst. 15 (3) (2000) 1001–1007. [15] A.C. Santos, et al., Node-depth encoding and multiobjective evolutionary algorithm applied to large-scale distribution system reconfiguration, IEEE Trans. Power Syst. 25 (3) (2010) 1254–1265. [16] R. Romero, et al., A new mathematical model for the restoration problem in balanced radial distribution systems, IEEE Trans. Power Syst. 31 (2) (2016) 1259–1268. [17] F. Glover, Tabu search: part I, ORSA J. Comput. 1 (3) (1989) 190–206. [18] F. Glover, Tabu search: part II, ORSA J. Comput. 2 (1) (1990) 4–32. [19] Y.P. Agalgaonkar, B.C. Pal, R.A. Jabr, Distribution voltage control considering the impact of PV generation on tap changers and autonomous regulators, IEEE Trans. Power Syst. 29 (1) (2014) 182–192. [20] A. Majumdar, Y.P. Agalgaonkar, B.C. Pal, R. Gottschalg, Centralized volt–var optimization strategy considering malicious attack on distributed energy resources control, IEEE Trans. Sustain. Energy 9 (1) (2018) 148–156. [21] R.W. Uluski, VVC in the smart grid era, IEEE Power Energy Society General Meeting, Providence, IR, USA, 2010, pp. 1–7. [22] T. Senjyu, Y. Miyazato, A. Yona, N. Urasaki, T. Funabashi, Optimal distribution voltage control and co- ordination with distributed generation, IEEE Trans. Power Deliv. 23 (2) (2008) 1236–1242. [23] C. Ucak, A. Pahwa, An analytical approach for step-by-step restoration of distribution systems following extended outages, IEEE Trans. Power Deliv. 9 (3) (1994) 1717. [24] A.C.B. Delbem, et al., Node-depth encoding for evolutionary algorithms applied to network design, 6th Genetic and Evolutionary Computation Conf.—GECCO, (2004), pp. 678–687. [25] D. Shirmohammadi, H.W. Hong, A. Semlyen, G.X. Luo, A compensation-based power flow method for weakly meshed distribution and transmission networks,

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