Cost-Effective Outage Management in Smart Grid under Single, Multiple, and Critical Fault Conditions through Teaching–Learning Algorithm ^†

Abstract

A distribution system becomes the most essential part of a power system as it links the utility and utility customers. Under abnormal conditions of the system, a definitive goal of the utility is to provide continuous power supply to the customers. This demands a fast restoration process and provision of optimal solutions without violating the power system operational constraints. The main objective of the proposed work is to reduce the service restoration cost (SRC) along with the elimination of the out-of-service loads. In addition, this work concentrates on the minimal usage and finding of optimal locations for additional equipment, such as capacitor placement (CP) and distributed generators (DGs). This paper proposes a two-stage strategy, namely, the service restoration phase and optimization phase. The first phase ensures the restoration of the system from the fault condition, and the second phase identifies the optimal solution with reconfiguration, CP, and DG placement. The optimization phase uses the teaching–learning algorithm (TLA) for optimal restructuring and optimal capacitor and DG placement. The robustness of the algorithm is validated by addressing the test cases under different fault conditions, such as single, multiple, and critical. The effectiveness of the proposed strategy is exhibited with the implementation to IEEE 33-bus radial distribution system (RDS) and 83-bus Taiwan Power Distribution Company (TPDC) System.

1. Introduction

A distribution system plays a key role in transmitting power from the utility to the utility customer. Its reconfiguration has been widely used to improve the power delivery performance of the system through the loss reduction of transmission lines for the past several decades. The initial contribution for distribution system loss reduction was attempted by the authors [1] using conventional approaches. In order to minimize the complexity involved in the optimal reconfiguration process, recent optimization techniques and heuristic approaches are practiced for reconfiguration [2,3,4,5,6]. Further, the analyses on the distribution system under abnormal operating conditions were initiated by the researchers, where the performance of the system was studied at prefault and postfault conditions. It has been realized that service restoration is the essential task to be carried out immediately after the fault in order to avoid the out-of-service loads. In [7], the programmed optimal load allocation was proposed for the effective service restoration during postfault. The reconfiguration methodology suitable for reconfiguration and service restoration was proposed in [8]. After realizing the implementation feasibility of the optimal placement of distributed generators (DGs) in the distribution system, the DGs were utilized for service restoration. DGs’ placement through smart control functions was developed in [9]. The approach based on a spanning tree was proposed in [10] for service restoration. Additionally, a method for minimizing the switching loss cost along with the service restoration was proposed in [11]. Service restoration through a multiagent approach for the allocation of DGs was proposed in [12]. The investigation on the applicability of the vehicle-to-grid (V2G) facility of the electric vehicles (EVs) for service restoration with the presence of DGs was studied in [13].

Service restoration for large-scale unbalanced distribution through multistage modified adaptive K-means method was proposed in [14]. The optimal DGs’ placement based on spanning tree search strategy for service restoration was proposed in [15]. The authors of [16] proposed a four-stage service restoration approach based on island matching, distributed generators, network reconfiguration, and minimization of out-of-service loads. The solution through local search algorithm and optimal switching plans suitable under the emergency circumstances of the distribution system was presented in [17]. A sequential search strategy [18] with control actions to coordinate switches, DGs, and detachable loads was proposed to solve service restoration problem. A multistage service restoration through service restoration index (SRI) was proposed in [19], where the main objective is to maximize the service restoration index based on the switching operations and priority of the restored loads.

In [20], a two-stage approach for repair and optimization under fault conditions was proposed. The first stage works for the repairing task in the cluster environment by measuring the distance between the fault location and the utility. The second stage focuses on the optimization through reconfiguration and optimal DG placement. A dynamic programming based on a stochastic approach [21] was implemented to solve a distribution system restoration (DSR) problem, which positions different technologies of DGs and energy storage systems to improve the performance of the optimal searching. Service restoration under single and multiple faults through an integrated classical spanning tree search strategy was proposed in [22], where the critical loads could be served by the reconfiguration with the reduced number of switching, reduction in power loss, and out-of-service loads.

In [23], service restoration was achieved through self-healing actions at the de-energized nodes of the system. The problem has been formulated as an analytical approach based on mixed-integer second-order cone programming (MISOCP). Fault location identification and service restoration were attempted with the support of wireless sensors and smart meters with an advanced metering infrastructure located at the edge of the grids in [24]. This scheme addressed the complexities of bidirectional power flow with the integration of PhotoVoltaic based DGs. A comparison based on the scalability, robustness, cost-effectiveness, complexity, and service restoration cost of the proposed techniques in the literature is shown in

Table 1. Comparison of the literatures.

References	Techniques Adapted	Scalability			Robustness			SRC	Optimization	Complexity
		Small	Medium	Large	SFC	MFC	CFC
[11]	Reconfiguration	C	C	C	C	NC	NC	C	NC	Less
[12]	Reconfiguration + DG	C	NC	NC	C	NC	C	NC	NC	Moderate
[13]	DG + V2G	C	C	C	NC	NC	C	NC	NC	Moderate
[16]	Reconfiguration + DG	C	C	NC	C	C	NC	NC	NC	Moderate
[17]	Reconfiguration	C	C	C	C	C	NC	C	NC	Large
[19]	DG	C	C	C	C	C	C	NC	NC	Less
[20]	Reconfiguration + DG	C	C	C	C	C	C	NC	NC	Large
Proposed	Reconfiguration + CP + DG	C	C	C	C	C	C	C	C	Less

In the above table, “C” refers to “considered” and “NC” refers to “not considered.”

.

In Table 1, it is observed that in the research work addressed in [19,20], the service restoration cost (SRC) has not been considered. Furthermore, in [11], multiple and critical fault conditions were not addressed. In [12,13,16], the effectiveness of the associated techniques was not validated for scalability and robustness along with the SRC. Regarding the complexity of the literature, factors such as the mathematical modeling of the problem, the proposed strategy for restoration, and the assumptions applied in the strategy are used to classify the complexity of the literature under less, moderate, and large. For the research works addressed in [12,13,16,17,20], the authors assumed the critical load conditions along with the fault conditions, which leads to further increase in the complexity of the problem.

In addition, many of the methods presented for service restoration are self-healing-based approaches. However, a well-defined strategy suitable to handle any uncertainties of the system with minimized switching and unserved loads is still required. A better strategy should possess the following properties:

• Well-defined control mechanism in each control agent (CA)
• Smart communicating equipment for coordination among CA
• Robust optimal restoration procedure with good scalability index
• Efficient handling of internal and external equipment constraints

Considering this reality, the minimization of SRC has been considered as the main objective of this research work in order to optimally restore the system through the teaching–learning algorithm (TLA) [25,26]. It works absolutely by considering regular controlling parameters and has no algorithm-specific parameters. By keeping the upside of TLA, in this research work, postfault ideal restructuring, optimal capacitor, and DG placement have been proposed. The strength of the proposed algorithm is validated with two test cases, IEEE 33-bus radial distribution system (RDS) and 83 Taiwan Power Distribution Company (TPDC). Furthermore, the test cases are assumed under different fault conditions, such as single, multiple, and critical, and tried for cost-effective restoration by TLA. The obtained results are compared with the results from proposed works in the literature.

The rest of the paper is organized as follows. The mathematical modeling of the restoration problem is described in Section 2. The idea and usage of the proposed algorithm is dealt with in Section 3 and Section 4, respectively. In Section 5, the acquired outcomes from two test cases under different fault conditions are examined. The conclusion and the primary commitment of the proposed look into the work are outlined in Section 6.

2. Problem Formulation

2.1. Objective Function

This research work solves the service restoration problem with the effective implementation of reconfiguration, optimal capacitor, and DG placement. The total cost utilized for the optimal service restoration is considered as the main objective of the problem, which has been expressed as Equation (1),

Minimize

SRC = f (ELC, CC, DGC)

(1)

where

$$\begin{gathered} ELC=P_{loss}+K_p \\ CC=C_{q,fixed}+C_i^{annual}\times Q_i \\ DG{C}_i=a_i+b_i\times P_{Gi}+c_i\times P_{Gi}^2 \end{gathered}$$

The transmission line losses are calculated through radial load flow. The formation of the load flow equations is described through a sample radial distribution system as shown in Figure 1.

From Figure 1, the load flow equations can be derived as

$${\mathrm{P}}_{\mathrm{i}+1}={\mathrm{P}}_{\mathrm{i}}-{\mathrm{P}}_{\mathrm{L},\mathrm{i}+1-}{\mathrm{R}}_{\mathrm{i},\mathrm{i}+1}\frac{{\mathrm{P}}_{\mathrm{i}}^2+{\mathrm{Q}}_{\mathrm{i}}^2}{{\left|V_i\right|}^2}$$

(2)

$${\mathrm{Q}}_{\mathrm{i}+1}={\mathrm{Q}}_{\mathrm{i}}-{\mathrm{Q}}_{\mathrm{L},\mathrm{i}+1-}{\mathrm{X}}_{\mathrm{i},\mathrm{i}+1}\frac{{\mathrm{P}}_{\mathrm{i}}^2+{\mathrm{Q}}_{\mathrm{i}}^2}{{\left|V_i\right|}^2}$$

(3)

$${\mathrm{V}}_{i+1}^2={\mathrm{V}}_i^2-2\left({\mathrm{R}}_{\mathrm{i},\mathrm{i}+1}{\mathrm{P}}_{\mathrm{i}}+{\mathrm{X}}_{\mathrm{i},\mathrm{i}+1}{\mathrm{Q}}_{\mathrm{i}}\right)+\left({\mathrm{R}}_{i,i+1}^2+{\mathrm{X}}_{i,i+1}^2\right) \frac{{\mathrm{P}}_{\mathrm{i}}^2+{\mathrm{Q}}_{\mathrm{i}}^2}{{\left|V_i\right|}^2}$$

(4)

$$P_{loss}={\displaystyle \sum }_{j=1}^{nl}{R}_j\frac{P_j^2+Q_j^2}{|V_j{|}^2}$$

(5)

The percentage saving of the SRC has been calculated using the following equation:

$$\% \mathrm{saving}=\frac{\mathrm{SRC} \mathrm{before} \mathrm{optimization}-\mathrm{SRC} \mathrm{after} \mathrm{optimization}}{\mathrm{SRC} \mathrm{before} \mathrm{optimization}}$$

(6)

2.2. Constraints

2.2.1. Radiality Constraint

Distribution network should be maintained with the radial structure.

2.2.2. Power Balance Constraint

This constraint ensures that no loads are unserved after restoration in the radial distribution system.

$$P_G-{\displaystyle \sum }_{i=1}^{nb}{P}_{D,i}-{\displaystyle \sum }_{j=1}^{nl}{P}_{j,loss}=0$$

(7)

2.2.3. Power Flow Constraints

Bus voltage and branch currents should be maintained within the limit.

$$\left.\begin{array}{c}\left|{\mathrm{V}}_{\min }\right|<\left|{\mathrm{V}}_{\mathrm{i}}\right|<\left|{\mathrm{V}}_{\max }\right|\\ \left|{\mathrm{I}}_{\max },\mathrm{j}\right|>\left|{\mathrm{I}}_{\mathrm{j}}\right| \end{array}\right\}$$

(8)

2.2.4. Capacitors’ Capacity Constraints

Capacitors’ capacity limits should not be violated. The commercially available capacitor and its cost in $/kVAR-year are given in [26]. The constant C_q,fixed is assumed as 1000 $.

150 kVAR < Qcapacitor < 4050 kVAR

2.2.5. DGs Capacity Constraints

The total restored power by DGs should not exceed the DG power limit.

• Total real and reactive power demand should not exceed the total generation by the DGs

  $$\begin{gathered} {{\displaystyle \sum }}_{d=1}^{N_L}{P}_D\le {{\displaystyle \sum }}_{j=1}^{N_G}{P}_{Gj} \& \\ {\displaystyle \sum }_{d=1}^{N_L}{Q}_D\le {\displaystyle \sum }_{j=1}^{N_G}{Q}_{Gj} \end{gathered}$$

  (9)
• Individual DGs’ maximum real and reactive power should not be violated.

  $$\begin{gathered} 0\le P_{Gj}\le P_{Gj,max} \& \\ 0\le Q_{Gj}\le Q_{Gj,max} \end{gathered}$$

  (10)

2.2.6. Frequency Constraint

Frequency limits should be maintained within the limit, which is expressed as,

$$f_{min}\le f_l\le f_{max}$$

(11)

3. Conception of Active Zones

It is well known that the radial distribution system is presented with tie switches for restructuring. Restructuring is usually carried out for two purposes, namely, optimization and service restoration. In this work, service restoration is attempted with restructuring by grouping switches into separate zones. The zones are numbered based on the number of tie switches present in the system. The IEEE 33 Bus RDS shown in Figure 2 is considered for the demonstration of identification of zones.

As shown in Figure 2, 5 tie switches are present in the system, which creates 5 active zones. Figure 3 shown below provides the zonewise splitting of switches.

The number of switches present in each zone is significantly diminished when independent zones are taken as choice factors described in [3]. However, it can’t stay away from the unfeasible arrangements in the iterative system. Furthermore, the switches are portrayed into four states, such as open, closed, permanently closed, and temporarily closed, in order to lessen the odds of an unfeasible solution in the iterative method, which also additionally enhances the effectiveness of the estimation. The final set of switches in each zone is given in

Table 2. Set of switches in each zone.

Zone (Z)	Normally Closed Switches (NCs)	Normally Open Switches (NOs)
1	S4, S5, S6, S7, S19, S20	S33
2	S12, S13, S14	S34
3	S8, S9, S10, S11, S21	S35
4	S15, S16, S17, S29, S30, S31, S32	S36
5	S23, S24, S25, S26, S27, S28	S37

.

4. Optimization Strategy

This research work follows optimization with two different phases in a sequence, which are restoration phase and optimization phase.

4.1. Restoration Phase

Among the two phases of the proposed strategy, service restoration phase is the most essential as it ensures the isolation of the faulty section and eliminates out-of-service loads at postfault conditions. This phase must be carried out at the substation level when a fault occurs. It is assumed that the distribution system is equipped with the Type 1 fast messages servicing devices for faster communication between the protection devices [25]. If a fault is detected by the protection devices, then it spurts Type 1A generic object-oriented substation event (GOOSE) messages for faster service restoration. The service restoration process under three different fault conditions, such as single-fault case, multiple-fault at multiple zone case, and multiple-fault at single zone case is shown in Figure 4.

4.2. Optimization Phase

The restored system can be brought into the prefault configuration after the repair or replacement of faulted system devices, which usually may take several hours depending on the fault case. The delivery performance and lifetime of the other major components in the system under the varying load conditions become a major threat if the distribution system is continuously operated for a few hours in this restorative state. Therefore, it is indispensable to bring the distribution system into an optimal configuration after immediate restoration.

• Unfaulted zone: which is unaffected by a fault
• Faulted zone: which is affected by a fault
• Critical zone: which is affected by multiple faults

Per this phase, the zones of the distribution system are categorized as follows:

The critical fault condition (CFC) condition occurs when any of the zones is affected by more than a single fault. At this condition, the proposed algorithm handles with reconfiguration, capacitor placement, and DG placement simultaneously. CFC results in the islanding of loads or disconnection of supply from the feeder to the loads at the fault affected zone. The primary task must provide a specific service to the disconnected loads, which will be done with the support of DGs at the associated zone by the DG agents. For convenience, it is assumed that each zone is equipped with the DG of required size. The size of the DG is determined according to the loads connected at each zone. The steps involved in the optimal restoration of the system from the critical condition is given below:

Step 1:

Identify the critical zone.

Step 2:

Restore the unserved loads by DG associated to the zone by the DG agent.

Step 3:

Ensure all the constraints are not violated.

Step 4:

The line and load data of the distribution system are updated at the load dispatch center.

Step 5:

Load dispatch center (LDC) initiates the optimization phase if no further faults are identified in the system.

Step 6:

Find the optimal location for DG placement along with reconfiguration and capacitor placement.

Step 7:

Relocate the DG for optimal solution.

Step 8:

Terminate the process.

4.3. Teaching Learning Algorithm for the Optimization Process

In this paper, the optimal configuration of the restored system was achieved through the teaching–learning algorithm [27,28]. This algorithm is one of the population-based algorithms that use a population of solutions to proceed to the global solution. Unlike the other population-based algorithms, such as GA, ABC, PSO, HS, DE, hybrid-PSO, the TLA doesn’t require any algorithm-specific parameters for searching which works on the effect of inspiration of a teacher on learners. More specifically, the success rate of the algorithm in bringing the global optimal solution is more compared with the other algorithms for the problem of different levels.

The whole process is divided into two parts, namely, teacher phase and learner phase.

• Teacher phase: The best learner becomes the teacher in each iteration, where the teacher is the most experienced, knowledgeable, and highly learned person in the community.
• Learner phase: The learners learn the course according to the quality of the teacher and the quality of the learners in the class for each course. The learners get the course input from the teacher and the interaction between the colearners of the class.

The step-by-step procedure involved in TLA is given below:

Step 1:

Initialize total courses offered (C), total learners (L), maximum iteration (MIT), and k = 0.

Step 2:

Create the initial population G(C,L).

Step 3:

Find the mean of each course, M_j = Mean_j(G(C)), j ε C.

Step 4:

Identify the best learner that becomes teacher, T^k = Min(f(G)).

Step 5:

Create the new population per teacher, Gplus(C,L) = G(C,L) + random() * (T^k − TF*M_j).

Step 6:

Produce the best learners’ population, G(C,L) = min(G,Gplus).

Step 7:

In interaction between learners, m and n refer to integers (<C) and m ≠ n

• if(f(f_learners(m,L)) > f(f_learners(n,L)))
• G(m,L) = f_learners(m,L) + random()*(f_learners(m,L) - f_learners(n,L))
• else
• G(m,L) = f_learners(m,L) + random()*(f_learners(n,L) - f_learners(m,L))

Step 8:

If k < MIT, update k = k + 1 and go to step 3; else, go to step 9.

Step 9:

Print the best solution and terminate the program.

The selection of courses for the TLA was identified from the categorized zones. With the effective implementation of TLA, the optimal restructuring, optimal capacitor placement (CP), and DG placement are carried out in unfaulted, faulted, and critical zones, respectively. Figure 5 shows the complete process involved in the optimization phase according to the fault condition.

5. Results and Discussions

The effectiveness of the proposed algorithm is validated with two benchmark test cases under different fault conditions. It is assumed that the capacitor banks with a maximum range of 4050 kVAR are available at the zones. Further, it assumes that each zone is equipped with the DG of the required size. The size of the DG is determined according to the loads connected at each zone. The proposed algorithm is programmed in Java servlet and executed in an Intel Core i5 processor with 2.9 GHz.

5.1. Test Case 1

The first test case is a 33-bus balanced radial distribution system with the base of 12.66 kV, which is shown through the single-line diagram in Figure 2. The total real and reactive power demands of the system are 3715 kW and 2300 kVAR, respectively. The characteristic data of the system are taken from [3]. The bus voltage minimum limit is assumed to be 0.9 pu, and the branch current capacity of each line is assumed to be 300 A except the lines connected near to the feeder. The real power loss of the system under normal operating conditions is 202.66 kW. This test case has five active zones, which are shown in Table 1 with their associated switches. For TLA, the total number of learners (population) and maximum iteration are initialized as 50.

5.1.1. Single Fault Condition (SFC)

The analysis is performed by assuming that one of the transmission lines is affected by a three-phase fault. For validation purposes, the line connecting buses 15 and 16 at zone 5 is considered as faulted. Based on the proposed strategy, the optimization phase is activated once the service restoration phase ensures there are no other faults in the system to be restored. By the service restoration phase, the open switch corresponding to zone 4 (S₃₆) is closed, followed by the opening of a faulted branch switch (S₁₆) as indicated in Figure 6a,b.

The optimization phase is performed to enhance the power delivery performance of the distribution system. Per the present status, it is realized that the system has four unaffected zones and one fault zone. The number of unfaulted zones is considered as the number of courses offered for restructuring, and the number of faults decides the number of courses offered for optimal capacitor placement for TLA implementation. The optimal structure and optimal capacitor locations are identified after the successful implementation of the proposed algorithm. The resultant configuration real power loss is verified as 114.59 kW. The obtained configuration bus voltage is compared with the other configurations, which are shown in Figure 7, which reveals that the new configuration voltage has a better voltage profile compared with other configurations. The speed of convergence of the TLA is compared with the other algorithms in bringing the global optimal solution, which is shown in Figure 8. All the algorithms considered for comparison have been executed for 50 iterations by assuming suitable values of the associated algorithm-specific parameters. The proposed algorithm reaches the optimal solution at 23rd iteration, which is lesser than the other algorithms. Moreover, the algorithms such as GA, ABC, and PSO, failed to produce the optimal solution. The performance by the hybrid PSO algorithm is comparatively better than those of the other algorithms and consumed little more load flow executions than the teaching–learning algorithm. However, PSO can bring the optimal solution by the proper identification of its own algorithm-specific parameters, such as learning factors, variation of weight, and maximum value of velocity. Mostly, the values are identified based on trial and error, which sometimes will not be suitable for other systems of different scale. Furthermore, hybrid PSO adds few more algorithm-specific parameters in addition to PSO’s.

Next, the robustness of the algorithm is validated by assuming that a single fault has occurred at different zones. The summary of results after implementing the proposed algorithm is shown in

Table 3. Summary of results for test case 1 under SFC at different zones.

Faulted Zone	Faulted Switch	Normally Open Switches	Optimal Location of Capacitor	Q in kVAR	Postfault before Optimization		Postfault after Optimization		% Saving
					Minimum Bus Voltage in pu	Energy Loss Cost in $	Minimum Bus Voltage in pu	SRC in $
1	S5	S5, S10, S28, S34, S36	5	450	0.8378	57,969.54	0.9389	27,030.26	53.37
2	S12	S7, S9, S12, S32, S37	14	300	0.9167	33,152.44	0.9379	24,250.46	26.85
3	S8	S8, S14, S28, S32, S33	11	700	0.9297	25,786.38	0.9406	24,888.02	3.48
4	S26	S7, S9, S14, S26, S32	23	300	0.9300	30,246.10	0.9410	24,050.27	20.48
5	S16	S7, S9, S14, S16, S37	29	900	0.9090	34,273.78	0.9501	19,321.30	43.63

. It is clear from Table 3 that the proposed algorithm provides optimal solutions irrespective of the fault location with a minimum saving of 3.48% and a maximum saving of 53.37%.

5.1.2. Multiple Fault Condition (MFC)

The multiple fault condition (MFC) is created by assuming two lines, S₅ (zone 1) and S₁₀ (zone 3), of the test case as faulted. The normally open switches (NOs) corresponding to zone 1 (S₃₃) and zone 3 (S₃₅) are closed after immediate isolation of the faulted branches (S₅) and (S₁₀), which ensures none of the loads are unserved and retain the radial structure. The restored system is handled properly for optimization through TLA. With the successful adoption of the proposed algorithm, the real power loss of the system is reduced from 285.93 to 155.63 kW. The bus voltage under different configurations of the system is shown in Figure 9, which shows that the resultant configuration bus voltages are maintained above the minimum of 0.9 pu. The robustness of the algorithm is validated by implementing the algorithm under different fault conditions. The obtained results are shown in

Table 4. Summary of results for test case 1 under MFC at different zones.

Faulted Zone	Faulted Switches	Normally Open Switches	Optimal Location of Capacitor	Q in kVAR	Postfault before Optimization		Postfault after Optimization		% Saving
					Minimum Bus Voltage in pu	Energy Loss Cost in $	Minimum Bus Voltage in pu	SRC in $
1 & 3	S5 & S10	S5, S10, S28, S34, S36	5,11	450 750	0.8528	48,036.70	0.9579	27,467.61	42.82
2 & 5	S14 & S31	S7, S9, S14, S31, S37	14,29	300 900	0.9051	33,742.64	0.9681	18,715.66	44.53
1,2 & 4	S6, S14 & S24	S6, S9, S14, S24, S32	14, 19, 27	900,600 1800	0.9213	32,175.71	0.9762	26,968.99	16.18

, which shows that the proposed algorithm identifies the optimal structure and optimal capacitor locations under a different MFC.

5.1.3. Critical Fault Condition (CFC)

The critical fault condition (CFC) is created for the test case by assuming that the lines shown in

Table 5. Assumed faulted lines of test case 1.

Sl. No.	Line Number	Affected Zone	Fault Category
1	13	Z2	Faulted zone
2	16	Z4	Critical zone
3	24	Z5	Faulted zone
4	31	Z4	Critical zone

are affected by a sequence of faults for validation purpose. The zones are categorized as faulted and critical zones with reference to Section 4.2. Service restoration for zones 2 and 5 does not require any external equipment as they are affected by a single fault. Therefore, a simple restoration practice can be done for these zones by modifying the open/close status of the switches associated to the faulted zone. Zone 4 is considered to be a critical zone as it has more than one faulted line. As a result of opening the faulted lines to restore the system, the loads connected at buses 16, 17, 31, and 32 associated to zone 4 get isolated from the feeder. It makes few of the loads connected to the system as out of service.

With the proposed algorithm, in the critical zone, the optimal location of DG is identified. In this research work, the cost coefficients a, b, and c of DG are assumed to be 6 $/hr, 0.012 $/kW-hr, and 0.00085 $/kW²-hr, respectively. And then the bus voltage and branch currents are compared with different configurations through Figure 10 and Figure 11, respectively. From these figures, it is understood that the voltage stability index of the final configuration is better compared with the postfault condition, and also, the branch currents are kept within the specified limit. The summary of results is shown in

Table 6. Summary of results for test case 1 under CFC.

Before Restoration	After Restoration
Unserved Loads	Unserved Loads	CP Location	DG Location	SRC in $
16, 17, 31 and 32	-	14 & 27	16	34,652.02

, where it is evident that the solution through the proposed algorithm assures that all loads are served, power flow constraints are not violated, and it obviously provides an optimal solution.

5.2. Test Case 2

The next test case for performance validation is an 83-bus balanced three-phase system [3] with a base of 11.4 kV served from 11 feeders. The system has 83 normally closed switches (NCs) and 13 normally open switches (NOs) for effective operation and control. The current carrying capacity of the transmission lines is assumed to be 600 A, and the bus voltage limits are assumed to be V_min = 0.9 pu and V_max = 1.0 pu. The effectiveness of the proposed algorithm has been evaluated on the test case with single, multiple, and critical fault conditions.

5.2.1. Single Fault Condition

The performance analysis of the proposed algorithm under a single fault condition is conducted by considering a three-phase single fault happening at the line connecting buses 3 and 4 (zone 2). According to the first stage of the algorithm, service restoration has been performed by opening the faulted line followed by the closing of NO associated to the zone. The first stage ensures no out-of-service loads after isolation of the faulty section from the system. The second stage is initiated after the fault clearing to bring the system on the way to the optimal configuration. Per the second stage, the restructuring is done for the unfaulted zones, and optimal CP is done for the faulted zone by TLA. The implementation of the proposed algorithm results in the optimal configuration with a transmission loss reduction of 371.72 kW from 568.19 kW. The identified NOs for the optimal configuration are S₄, S₁₃, S₃₄, S₃₉, S₄₂, S₆₁, S₇₂, S₈₃, S₈₄, S₈₆, S₈₉, S₉₀, and S₉₂. The bus voltages at the initial configuration and after optimal restoration are compared in Figure 12, which indicates that none of the bus voltages have been violated and maintain a minimum voltage of 0.9274 pu at bus 4. The convergence characteristics of the proposed algorithm is compared with those of the other algorithms, which is shown in Figure 13, where the proposed algorithm reaches to the optimal solution at the 58th iteration.

5.2.2. Multiple Fault Condition

The validation of the proposed algorithm under multiple fault conditions is performed by assuming that the three-phase fault occurs at the lines connecting buses (31–32) and (38–39). Per the restoration phase, the faulty sections are isolated from the service, and the out-of-service loads are eliminated by closing the NOs of the associated zones. The optimization phase is initiated at the load dispatch center with the updated system structure after confirming that there are no further faults recorded in the distribution system. The TLA identifies the optimal configuration and the optimal locations for capacitors. The identified NOs for the optimal configuration are S₇, S₁₃, S₃₂, S₃₉, S₄₂, S₅₅, S₆₂, S₇₂, S₈₃, S₈₆, S₈₉, S₉₀, and S₉₂, and the optimal capacitor locations are buses 36 and 46. The real power loss of the resultant configuration is verified as 366.82 kW, which conserves 8.73% of the transmission line loss from its initial configuration loss. The bus voltage profiles for the different system configurations are shown in Figure 14, and it is clear from the figure that the optimal configuration has a healthy voltage profile compared with the other configurations with a minimum voltage of 0.9531 pu.

The

Table 7. Summary of results for test case 2 under different fault conditions at different zones.

Fault Conditions	Faulted Zone	Faulted Switch	Optimal Location of Capacitor + DG	Value Q in kVAR	Postfault before Optimization		Postfault after Optimization		% Saving
					Minimum Bus Voltage in Pu	Energy Loss Cost in $	Minimum Bus Voltage in Pu	SRC in $
SFC	Z2	4	57	900	0.8928	110,958.84	0.9274	91,244.70	17.77
	Z7	37	29	1850	0.9285	89,483.27	0.9531	78,882.78	11.85
	Z5	20	78	3150	0.9175	97,377.49	0.9520	80,813.86	17.01
MFC	Z8 Z7	32 39	46 36	450 1350	0.9285	87,027.61	0.9531	79,426.26	8.73
	Z1 Z2	54 6	51 57	1650 3300	0.9096	99,263.97	0.9531	77,659.92	21.76
	Z1 Z5 Z9	42 53 82	42 53 78	600 300 2100	0.9014	106,541.56	0.9383	87,788.26	17.60

details the optimal configuration identified through the proposed algorithm under different fault conditions of the system. A minimum of 11.85% and a maximum of 17.77% and a minimum of 8.73% and a maximum of 21.76% savings are recorded under single fault and multiple fault conditions, respectively. The feeder loadings of the optimal configuration under the different fault conditions are shown in Figure 15, which shows that none of the feeders are heavily loaded, and effective sharing of loads has been made to the feeders.

5.2.3. Critical Fault Condition

Normally, a zone affected by more than one single fault brings the system to the CFC, which results in the isolation of few loads from the feeder service. Importantly, this test case has been identified with two critical zones under a single fault condition. The details regarding the two zones and connected loads are shown in

Table 8. Critical zones and critical lines.

Zone	Critical Lines	Loads Connected
Zone 8	20–21, 21–22, 21–23, and 23–24	21, 22, 23, and 24
Zone 13	7–8,7–9, and 7–10	8, 9, and 10

. It is clear from Table 8 that a fault on any of the lines results in out of service to a few of the loads. Therefore, it is recommended to have DGs at these zones irrespective of the system condition to avoid out-of-service loads. The effectiveness of the algorithm is validated considering another possible critical fault condition. The critical fault condition is created by assuming that the lines shown in

Table 9. Assumed faulted lines of test case 2.

Sl. No.	Start Bus	End Bus	Affected Zone	Fault Category
1	36	37	10	Faulted zone
2	48	49	1	Critical zone
3	52	53	1	Critical zone
4	81	82	5	Faulted zone

are affected by a sequence of faults.

The proposed algorithm is implemented with the above information from the load dispatch center. The TLA algorithm identifies the optimal location for DG at the critical zone, the optimal location for CP at the faulted zone, and the restructuring at unfaulted zones. The final configuration bus voltage and branch currents compared with postfault configuration are shown in Figure 16 and Figure 17, respectively. The figures reveal that both the bus voltages and branch currents are maintained within the limits specified. The result summary is given in

Table 10. Summary of results for test case 2 under CFC.

Before Restoration	After Restoration
Unserved Loads	Unserved Loads	CP Location	DG Location	SRC in $
50, 51 and 52	-	37 & 78	50	125,401.95

to validate the effectiveness of the proposed algorithm. It is noted from Table 10 that the resultant configuration identifies the optimal location for capacitors and DGs and ensures zero unserved loads in the system.

The total number of selected learners, the maximum number of iterations considered, the number of iterations, and the execution time taken to reach the optimal solution with the implementation of TLA for the test cases under different fault conditions are shown in

Table 11. Set parameter values of TLA and iterations conceded under different fault conditions.

Test Case	Fault Condition	Number of Learners Considered	Maximum Number of Iterations Considered	Number of Iterations Taken to Reach Optimal Solution		Execution Time in Msec.
				Minimum	Maximum	Minimum	Maximum
1	SFC	25	50	23	28	482.69	559.29
	MFC	50	50	26	34	864.94	890.45
	CFC	50	50	31	39	988.40	1003.05
2	SFC	75	100	58	72	31,498.32	31,717.51
	MFC	100	100	64	78	42,039.26	42,066.82
	CFC	100	100	73	84	42,268.46	43,172.34

. It is clear from the table that for test case 1, a minimum of 23 and a maximum of 39 iterations are taken to reach the optimal solution under different fault conditions. Similarly, for test case 2, a minimum of 58 and a maximum of 84 iterations are taken to reach the optimal solution.

6. Conclusions and Future Work

This research work considered the minimization of service restoration cost as the main objective, including the energy loss cost, capacitor cost, and DG cost. The proposed search strategy adopts a two-stage process, namely, the service restoration phase and the optimization phase. The service restoration phase ensures the elimination of out-of-service loads, whereas the optimization phase identifies the optimal configuration and optimal locations for capacitors and DGs. The optimization phase works according to the fault locations and the category of a fault condition. The TLA is used for the optimization process to search for the optimal configuration in the given boundary conditions. The validation of the proposed strategy for optimal service restoration is performed on the two standard distribution systems under different fault conditions, such as single, multiple, and critical. With the effective implementation of the algorithm, the optimal solution has been achieved, which is well demonstrated through the obtained results. Finally, the competency of the proposed technique is validated by comparing the proposed work with other algorithms. This work can be further extended by considering the unbalanced system under unbalanced system fault conditions.