A Multi-Objective Approach for Voltage Stability Enhancement and Loss Reduction Under PQV and P Buses Through Reconfiguration and Distributed Generation Allocation

This paper proposes a novel approach of voltage stability enhancement and power loss minimization in addition to maintenance of good voltage profile in radial distribution networks through optimally placed distributed generation, network reconfiguration and voltage control of PQV bus through variable reactive power source at P bus. A multi-objective function has been proposed that considers maximum system loadability enhancement and network loss minimization. Optimization of proposed multi-objective function, under distributed generation and network reconfiguration with presence of PQV and P buses in the system have been done using grey wolf optimization technique. Case studies performed on IEEE 33-bus radial distribution system shows that presence of PQV and P buses in the system yields significant enhancement in voltage stability margin under optimal placement of distributed generations and network reconfiguration.


I. INTRODUCTION
The continuously increasing demand in transmission as well as distribution network has rendered many planning and operational challenges such as maintaining voltage stability, network loss reduction and voltage profile improvement. Voltage stability is the ability of system to maintain bus voltages within permissible limits. According to IEEE/CIGRE joint task force, ''Voltage stability is defined as the ability of a power system to maintain steady voltages at all buses in the system after being subjected to a disturbance from a given initial operating condition'' [1]. The increased load of the distribution network and other disturbances creates risk to voltage instability of the network due to deterioration of voltage profile in significant part of the network. A system with fairly good voltage profile having nearly same voltage magnitude at all the buses at the base case operating point may also face voltage instability under severe contingencies. Thus it is important to maintain sufficient voltage stability margin (the distance between the base case operating point The associate editor coordinating the review of this manuscript and approving it for publication was Jamshid Aghaei . and voltage stability limit). A continuously increasing load increases the chance of voltage collapse within the system. When voltage instability occurs, voltages at some buses may progressively fall or rise that may ultimately lead to voltage collapse. The main factor causing this problem is the inability of the power system to meet the reactive power demand as it is difficult to transmit reactive power under heavily loaded conditions. Voltage stability is a key issue in radial distribution networks as increase in demand may deteriorate voltage at remote buses to unacceptable limits leading to partial/complete blackout [2]. Voltage stability can be examined in terms of maximum loadability (λ max ) of the system. Several methods have been reported in literature to evaluate maximum loadability [3]- [6]. Remote end buses of radial distribution networks undergo very low voltages that poses threat of voltage instability as system may reach maximum loadability limit under contingencies [7]. Therefore, proper strategy is required to enhance maximum loadability of these networks in order to improve voltage stability. Optimal placement of distributed generations (DGs) seems to be a viable solution for voltage stability enhancement of radial distribution networks. Fast Voltage Stability Index under varying load growth and penetration of wind and photo-voltaic have been reported for a practical Japanese distribution system to study its voltage stability enhancement [2]. Optimal placement of DGs based on Particle Swarm Optimization (PSO) has been considered for enhancement of maximum system loadability [8]. An ε-constraints based teaching and learning algorithm has been proposed to maximize system loadability and minimize losses under reconfiguration and DGs placement [9]. A probabilistic nature of renewable DG and load modeling has been studied to decide optimal location and size of DGs for voltage stability enhancement [10]. A new multi-objective index based optimization considering active and reactive power loss minimization in presence of DG unit has been proposed to enhance system loadability [11]. A voltage stability index driven optimal location of DG under increasing load has been reported for voltage stability improvement [12]. The hybrid differential evolutionary and particle swarm optimization approach has been reported to enhance the system loadability [13]. An analytical power stability index based DG placement algorithm has been proposed to realize the DG influence on loadability, network losses, and voltage magnitude [14]. An effective swarm-based optimization for DG placement has been reported to enhance voltage stability and reduce network losses [15], [16]. Placement of permanently connected capacitor wind-operated squirrel cage induction based dispersed generator has been performed to enhance voltage stability [17].
Network reconfiguration is another important strategy that is being utilized for performance enhancement of distribution networks through closing and opening the sectionalizers and/or tie lines. In general, distribution system constitutes a mix of residential, commercial, industrial types of loads. The feeder of these systems may experience variable load patterns at different time frame with changing days and seasons. At some point of time the system is loaded heavily while at another time it is lightly loaded. In such a scenario, load scheduling by reconfiguration may lead to optimal performances with regard to system losses and voltage stability. Reconfiguration of radial network smoothens peak demands that improves the voltage profile, and maximum loadability thus making the network quite reliable [18]. Optimal reconfiguration with different optimization techniques have been reported to enhance the system loadability [19]- [23]. A fuzzy genetic rule-based optimization for reconfiguration is studied to enhance voltage stability [24]. A discrete artificial bee colony approach is adopted based on Continuation Power Flow algorithm to enhance maximum loadability of system [25], [26]. A two-stage algorithm for reactive power loss minimization to enhance voltage stability and loadability enhancement through network reconfiguration has been proposed [27]. A two stage hierarchical optimization approach has been presented to tradeoff between enhanced maximum loadability and reduced network losses under reconfigurable [28] and integrable DG environment [29], [30]. The matroid theory based reconfiguration was carried out with the help of graph theory [31].
In traditional transmission and distribution systems, presence of PV and PQ buses is very common. Static voltage stability analysis has been carried out by introducing novel bus type referred as bus AQ with known reactive power demand and bus voltage angle [32]. Thus, voltage magnitude and real power at AQ bus remain unknown. In recent publications, the concept of voltage control at PQV buses by remotely located P buses has been introduced. The dedicated P bus having pre-defined real power injection has variable reactive power source that controls the voltage of PQV bus [33]- [35]. A PQV bus is defined as the bus with pre-specified quantities of active power, reactive power and voltage magnitude. Only the voltage angle of this bus is unknown. A P bus is defined as a reactive power generator bus which is maintaining the voltage magnitude at PQV bus constant at the required value [33]. For a P bus, the quantity of active power is pre-specified. The quantities reactive power, voltage magnitude and voltage angle at this bus remain unknown and hence need to be calculated. Injection of regulated reactive power at generator bus P results in maintaining the desired value of the voltage magnitude of PQV bus located remotely [34]. The PQV bus thus has pre-defined voltage magnitude in addition to predefined real and reactive power injections. Loss minimization under reconfigurable and optimally integrated DG environment has been performed in a system employed with remotely located PQV bus with its voltage magnitude being maintained by variation of reactive power injection at the selected P bus [36], [37]. The bus with minimum voltage magnitude has been chosen as PQV bus while P bus was selected by choosing the bus which gives least power loss in the network.
Literature review reveals that loadability enhancement of distribution system has been studied so far by various authors under presence of PQ buses in the system. Maintenance of voltage at a remote PQV bus through variation of reactive power injection at P bus may be quite helpful in enhancing maximum loadability of the system. Optimal placement of DGs and network reconfiguration under presence of PQV and P buses may further enhance voltage stability margin. No effort seems to be made in study of loadability enhancement through network reconfiguration and DG placement under presence of PQV and P buses. In order to overcome this research gap, this paper proposes a multiobjective fitness function to enhance maximum loadability and reduce network losses by reconfiguration and DG unit allocation under presence of P and PQV buses in the system. The fitness function has been optimized through Grey Wolf Optimization (GWO) technique. Maximum loadability obtained by proposed approach has been compared with existing approaches to establish its effectiveness.

II. PROBLEM FORMULATION: OBJECTIVE FUNCTION AND CONSTRAINTS
In this work network reconfiguration and DG allocation has been performed for a certain designed set of objective functions. To achieve the optimum solution space with the optimum objective, the Grey Wolf Optimization tool has been implemented. Real power loss minimization is the main factor that distribution companies want to perform since this objective is not only economically favorable to distribution companies worldwide but also it enhances the operational constraints of the distribution system. Apart from this increasing load demand restricts the distribution system planners to operate it within the stable region, beyond a particular load the network does not remain stable and becomes unstable. To accomplish the increased load demand and stable system operation voltage stability or loadability limit of the system must be incorporated in the objective problem formulation and hence a distribution system voltage stability index has been formulated.
The Objective Functions are where sw i is the status of i th branch, sw i =0 if the switch is open and sw i =1, if it is closed, P loss is total network real power loss i.e. sum of losses in all closed branches, I i is current flowing in i th branch and R i is the resistance of i th branch, and b represents total number of closed branches.
where, [21] (3) DVSI system represents voltage stability index of whole distribution system. Determination of VSI i is explained by means of a simple distribution network shown in Figure 1. In Figure 1, P ei and Q ei represents effective real and reactive power demand at i th bus in two bus equivalent network [21], X i represents reactance of i th closed branch and nb represents total number of buses present in the system.  The effective load P ei (Q ei ) at i th bus can be evaluated by addition of all real (reactive) demands at i th bus and all other buses beyond i th bus and the addition of real (reactive) losses incurred across all the branches beyond i th bus.
Minimization of a multi-objective problem formulation has been proposed in this work that considers minimization of network losses and maximization of voltage stability. The proposed multi-objective function is given as: where, w 1 and w 2 represents weightage assigned to f 1 and f 2 , respectively. To convert the maximization optimization formulation into minimization negative sign has been assigned to the objective function, f 2 . The constraints are: Power balance constraints: where, P s grid = Real power injected through grid to the radial distribution network Q s grid = Reactive power injected through grid to the radial distribution network P DG,i = real power injected to the network through DG placed at bus-i Q DG,i = reactive power injected to the network through DG placed at bus-i Q sh,i = reactive power injected to the network through shunt capacitor placed at bus-i NDG = total number of DGs placed in the system P load,i = real power demand at bus-i Q load,i = reactive power demand at bus-i P loss,i = real power loss in closed branch i Q loss,i = reactive power loss in closed branch i DG Size constraint: The bus voltages should be within permissible limits: where, V i is i th bus voltage magnitude, V L,max and V L,min represents maximum and minimum voltage limits. In this work V L,max and V L,min has been taken as 1.05 pu and 0.95 pu respectively, considering beyond ±5% voltage variation as large voltage variations. Current in each branch should be within the permissible limit where, I k,max represents maximum permissible current in branch k. To operate the system radially, equality constraint required is as below:

III. REFORMULATION OF NRLF EQUATION UNDER PQV AND P BUSES
Existence of pair of PQV and P buses in network may be solved by redefining the Jacobian matrix. A P bus is introduced as a reactive power source with unknown reactive power output [33]. Since the P bus with unspecified reactive source injection Q controls the voltage magnitude of remotely located PQV bus, hence this unknown quantity Q becomes the state variable, while real power generation at P bus is set to zero. A PQV bus has the characteristics of a PQ bus with known voltage magnitude in addition to real and reactive power injections [33]. By injecting the appropriate amount of reactive power at P bus, the desired magnitude of voltage at PQV bus is achieved. The detailed explanation regarding concept of PQV and P buses has been illustrated by means of a simple 5 bus system shown in Figure 2. In Figure 2, bus 1 is set to be a reference bus, buses 2 and 4 are assigned as PQ bus while buses 3 and 5 have been designated as P and PQV bus, respectively. To incorporate the concept of the P bus (bus 3) to keep the magnitude of voltage of the PQV bus (bus 5) constant, set of equations augmented are given by (12) and (13) as below: With the above modification, equation augmented relating to power mismatch with respect to the mismatch in the phase angle and voltage magnitudes for the Newton-Raphson algorithm takes the form as below: where, and J , as shown at the bottom of the next page.
With the above modification in the power balance equation, the Newton Raphson load flow method solves the network for unknown reactive injection (Q 3 ) at bus P and other state variables. To keep the voltage of PQV bus constant, different voltage controlling devices given in [34] may be utilized. In this work the desired PQV bus voltage is achieved by assuming a shunt capacitor placed at P bus due to its low cost as compared to other voltage controlling devices. In Figure 2, Q SC3 represents the amount of reactive power injection by the shunt capacitor Placed at P bus 3 to maintain voltage of PQV bus 5 constant. Once the net reactive power injection Q 3 at bus 3 is obtained using (14) in load flow, the value of reactive power Q SC3 requisite at P bus 3 to keep the voltage magnitude constant at PQV bus 5 is computed using the formula (15), given below: where, Q 3 = net reactive power injection at bus 3. Q SC3 = reactive power injection by shunt capacitor at bus 3. Q L3 = specified reactive power load at bus 3.

IV. SOLUTION METHOD FOR THE RECONFIGURATION
In this section concept of network reconfiguration as a decision variable has been explained.

A. RECONFIGURATION USING FUNDAMENTAL LOOPS METHOD AND ITS DEMERITS
In a radial distribution system (RDS),there are certain number of initially opened tie-switches and normally closed branches, in general. These normally closed branches are equipped with sectionalizer switches. Closing these tie-switches creates many numbers of loops in the system. To reconfigure the distribution system, associated sectionalizer switches of a set of particular branches in association with the available tie-switches must be opened and closed. Selection of these switches to alter the topology of network is a tedious and cumbersome job as there are huge number of possible combinations of switches. Generally, a random selection of these switches is done. To generate the random initial population meta-heuristic methods have been proposed. Thus, a random selection of these switches in decision variable population creates large number of network configurations many of which, may violate radial topology constraints as well as load bus disconnection while dealing with distribution network reconfiguration problem leading to infeasibility. Fundamental loop (FL) analysis is a viable and suggested solution to reduce this tedious job with a certain extent [38]. Selection of random switches in decision variable is now made only with associated fundamental loop. Fundamental loop analysis using graph theory, not only ascertains the reduction in search space of network configuration but also elimination of many infeasible population generations. Total number of fundamental loops (nFL) present in a RDS is obtained using (16) given below: Total number of FLs in a RDS is same as the number of available tie-switches, NTie. Each FL has constituent branches and tie-switches associated with it. To determine the constituent/members of FLs, each loop-forming branch has been selected including tie-switch closed to form the loop.
The incidence matrix 'A', is generated using the graphical method representation of RDS [39]. The size of matrix 'A' is b × nb. The element A ij in matrix 'A' is obtained using expression (17): To obtain the first FL, an open branch containing the first tie-switch is inserted into the incidence matrix 'A'. The sum of the absolute value of each element in each column of matrix 'A' is evaluated. Buses which have the sum equals to 1 are identified. Branches connected to these buses are removed. The procedure is repeated until the sum result in no longer equal to 1. A vector is formed to store the remaining branches in matrix 'A' representing first FL. The remaining FLs are determined using the same procedure as the first FL [40].
For a system having NTie tie-switches, the required length of the decision vector becomes equal to NTie as each switch is selected from each fundamental loop. Hence, the decision where, TS i is the branch/tie-switch to be opened in the i th fundamental loop created by closing the tie switch associated with the loop. To illustrate this, Figure 3 with schematic of the IEEE 33-bus distribution system is shown. In Figure 3, the digits 1, 2, 3, etc., represent the bus numbers, while the branches (switches) are numbered as b1, b2, b3, . . . etc. Total five number of tie switches represented as b33, b34, b35, b36, and b37, forming five fundamental loops are present in this system. Details of these loops are also presented in Table 2. However, selection of switches from each fundamental loop has its own demerits. Certain combinations of selected switches from each fundamental loop may isolate one or more system buses in radial distribution system. For simple understanding, consider the IEEE 33-bus distribution network shown in Figure 3. Let us suppose decision variable [b6 b14 b21 b7 b22] generated with the selection of one switch from each fundamental loop. If this decision variable is selected, then load bus 6 will be isolated as both b6 and b7 belongs to fundamental loops 1 and 4. Both these branches are common to fundamental loops 1 and 4 and hence participation of such common branches between two loops must be restricted to only one in either loop. There are many more such combinations that exist between any two loops. Let us take another combination of switches [b6 b34 b8 b25 b5] selected from each fundamental loop. Opening of these switches isolate the load bus 6 from the distribution system. This is because of bus 6, which is common to fundamental loops 1, 4 and 5 and branches b6, b25 and b5 common between two loops participating simultaneously. To overcome these demerits, each combination of decision variable for reconfiguration must adhere to a set of rules designed. And hence, the concept of switch selection from each fundamental loop needs to be modified based on certain rules.

B. RULE BASED DECISION VARIABLES MODIFICATION
Each decision variable must have NTie number of elements, representing the number of switches to be opened to operate system in a radial manner. To incorporate the demerits of fundamental loops reported in previous sub-section the set of rules defined are as below: Rule-1 : At least one element must be chosen from each fundamental loop. TS i ∈ FL i . Rule-2 : If a common branch vector participates while creating a decision variable, it must be ensured that at most a single element is chosen. Rule-3 : While creating a decision variable it must be ensured that all the vectors with common branches of any restricted group must avoid the simultaneous participation. To form the feasible decision variables, algorithm are explained as below [41]: Step 1 : Create fundamental loop vectors, having the set of switches in each fundamental loop, as shown in Table 2.
Step 2 : Obtain the decision variable such that TS i belonging to FL i following the 1 st Rule.
Step 3 : Obtain vectors of common branches, CB jk , having the set of switches common between two loops FL j and FL k .
Step 4 : Obtain vectors of restricted group RG i , cluster of common branch vectors incident at the i th common bus(es) of the distribution network.
Step 5 : Check and modify the decision variable to satisfy the feasibility based on the 1 st , 2 nd and 3 rd rules designed. The first rule ensures the selection of switches to be opened from each fundamental loop and prevention of any load bus disconnection at the exterior of the network, while 2 nd and 3 rd rules prevent the disconnection of the load buses at the interior of the network. Hence, these rules ensure the generation of feasible decision variables with radiality of the network as well as prevention of any bus disconnection. In this work, GWO is adapted using basics of graph theory to populate the decision variables. The GWO guided by set of rules defined above modifies the infeasible decision variable into feasible one during iteration process. This algorithm bypasses the hectic mesh check and overcomes the deficiency of the reconfiguration method by [38]- [40] to create feasible decision variables. To understand the algorithm for reconfiguration, let us consider the IEEE 33-bus network, shown in the Figure 3.  The list of vectors of common branches between two fundamental loops, obtained from Figure 3, are presented in Table 3. The restricted group vectors and the associated common buses that may be disconnected, if all the common branch vector participate in decision variable creation for the system are obtained from Figure 3, as shown in Table 4. For the distribution system shown in Figure 3, The decision variable constitutes total five switches selected from each fundamental loop according to 1 st Rule. Suppose the decision variable [b20 b13 b35 b26 b25] is populated at any instant of iteration. It can be observed that this decision variable is violating the 2 nd rule as both b26 and b25 switches belong to CB 45 . If this decision variable is selected, then load bus 26 will be isolated. Let us Consider another infeasible decision variable [b7 b34 b8 b25 b4], violating the 3 rd Rule, since switches b7, b25, b4 belong to vector of common branches CB 14 , CB 45 and CB 15 respectively, which falls under the vectors of restricted group RG 6 = [CB 14 CB 15 CB 45 ] isolating common bus 6. Selecting switches for reconfiguration creates many more infeasible decision variables which can be converted into feasible ones in accordance with 1 st , 2 nd and 3 rd Rules. To demonstrate the modification of infeasible decision variable into the feasible decision variable under the guidance of vectors of common branches and restricted groups are shown in Figure 4 through an example. As shown in Figure 4 decision variable [b20 b13 b35 b26 b25] populated at any stage of iteration, violates the 2 nd Rule. According to 2 nd Rule switches [b25 b26 vb27 b28], which belong to CB 45 and hence only one switch has to participate either in 4 th or 5 th fundamental loop from this vector. Therefore, 4 th loop switch is modified under the guidance of 1 st , 2 nd and 3 rd Rules replacing the switch b25 by b29 creating a feasible decision variable [b20 b13 b35 b29 b25].

V. GREY WOLF OPTIMIZATION SEARCH ALGORITHM: AN OVERVIEW
Like other evolutionary ones, this algorithm model the hunting behavior of grey wolves and starts with an initial population of these hunting wolfs. Population individuals called wolf are subdivided into alpha beta, delta, and omega wolf. These wolves attack the prey based on their location and distance from the prey. Encircling, hunting, and attacking the prey are the three important steps for prey hunting [42].

A. ENCIRCLING
Encircling of the prey by the grey wolf is modeled as; where, − → D is the distance between grey wolf and prey, − → A and − → C are coefficient vectors, − → P prey is the position vector of the prey, and − → P wolf indicates the position vector of a grey wolf. The coefficient vectors − → A and − → C are given by; where, coefficient of acceleration − → a is decreased linearly from 2 to 0 throughout the iterations. − → r 1 and − → r 2 are random VOLUME 10, 2022 vectors in [0 1]. During the encircling the prey changes its position and try to get away from the wolves, vectors − → A and − → C updates the position of a wolf according to that of changing the position of the prey [42] and brings the position of the wolf closer to prey.

B. HUNTING
The alpha wolf is superior to the entire wolves and leads the hunting of prey in association with beta and delta wolves. The beta and delta wolf follows the alpha wolf in hunting. To represent the hunting phenomena during the iteration process, the best candidates considered first as solutions are alpha, beta, and delta wolves. The fourth search agent i.e. omega wolves update their positions in association with and according to the best search solution obtained from alpha, beta, and delta wolves. Mathematically this can be modeled as:

C. ATTACKING
In this phase, the wolves take the position of prey without letting the prey to change its position and assault it. The vector coefficient − → A in mathematical modeling depicts the approach of the victim and plays a key role and its vacillation range gradually reduces by acceleration coefficient vector − → a as the wolf moves closer to the prey. In general, vector − → A changes its value in the interval [-a a] randomly, and is governed by decreasing the value of the vector − → a from 2 to 0 linearly throughout the iterative process. During the attack modeling the position of a solution candidate, the succeeding location/position of a candidate solution/wolf will be somewhere in between its current location and the location of prey, if the random value of the vector − → A lies in the range[- 1 1]. The absolute value of the vector − → A ensures the convergence of the solution candidate if it satisfies (26); otherwise, there is no solution as the candidate diverges away from the prey if the absolute value follows (27), and definitely, an optimally best prey will be evolved as a final solution with this algorithm.

D. ACCELERATION COEFFICIENT
The acceleration coefficient vector a controls the exploration and exploitation process and balances it with adequate value. A larger surface area for exploration results in sluggishness and the increased chance of stagnation to be trapped in local optima, and hence an enhanced rate of exploration can be achieved by decreasing the acceleration coefficient vector linearly with increasing iterations, where the acceleration coefficient is varied adaptively throughout the iterations and is given as; where, t and T are current and maximum iterations count respectively, during the optimization process adopted.

VI. PROPOSED GWO BASED ALGORITHM FOR MULTI-OBJECTIVE FUNCTION
The illustration of the GWO algorithm application for the reconfiguration of the distribution system by closing/opening of branch/tie switches to evaluate the objective function is presented in this section. In this work, a number of cases that consist of reconfiguration with and without simultaneous allocation of single DG injecting only real power are taken to minimize the objective function using GWO. To reconfigure the distribution system, variables of decision vector DV R are same as the total number of loops (represented by a discrete variable) present in the system as below:  (30) For better understanding, further the variables either for switches, location and size will be denoted as U x (x = 1, 2, 3, . . . , N ). This notation will be used for optimal switches, location and size of DG positions to evaluate the fitness function.
In the start, GWO optimization parameters are assigned and a DVPM is created. Every row of DVPM is denoted by a decision vector. The elements of the DV R (U x ) is generated using (31) as shown below: The population matrix of decision vectors is generated using (31) as shown below: In GWO the decision vector represents the grey wolf. Corresponding to grey wolf evaluated fitness function given by (4) represents the position of prey. The flowchart for proposed GWO based stability enhancement approach under optimal DG placement, network reconfiguration and presence of PQV and P buses is shown in Figure 5. As per this flowchart maximum loadability of the system is computed under optimal fitness function and decision variables, where decision variables consist of open status of tie switches and DG location and size.

A. MAXIMUM LOADABILITY CALCULATION
In voltage stability analysis, one of the most significant part is the determination of maximum system loadability. Considering a load case, a successive load flow utilizes the network solution to evaluate the minimum voltage magnitude till the collapse point (i.e., where the load flow solution diverges) to evaluate the voltage stability margin [5] and to draw the loadability curve. The voltage stability margin is calculated in terms of maximum loadability. The voltage stability margin is termed as the extent from an operating point to a voltage collapse point until the load increment can be served without fail. In the successive procedure, the active and reactive load power at each bus in the system is increased repeatedly by a loading factor λ given by: where, P 0 and Q 0 are the active and reactive power loads at initial operating point, and P new and Q new are new active and reactive power demand at loading factor λ which is increased at a rate of 1%.
Voltage stability margin has been defined as the distance between initial operating point (loading factor λ = 0) to maximum loadability point having loading factor as λ max . Maximum loadability point has been obtained based on the divergence of load flow. Voltage stability margin has been shown in Figure 6 representing loading factor, λ Vs. voltage magnitude curve for the system. The flow chart in Figure 7 presents the algorithm to calculate the maximum loadability. The following six cases have been studied to examine impact of DG allocation, network reconfiguration and presence of PQV and P buses in voltage stability margin (maximum loadability) enhancement.
Case 1 : It is a case study of base-case without considering reconfiguration and PQV and P buses. Case 2 : It is an application of only network reconfiguration without consideration of PQV and P buses. Case 3 : It is the case study for simultaneous reconfiguration and DG allocation without PQV and P buses. Case 4 : It is a case study when PQV and P buses have been considered for base case. Case 5 : It is a case study when PQV and P buses have been considered for reconfiguration only.  Case 6 : It is the case for simultaneous reconfiguration and DG allocation with consideration of PQV and P buses.

VII. INDICES TO EXAMINE SYSTEM PERFORMANCE
To analyze the effects of reconfiguration and/or DG placement, different performance indices [9] have been evaluated. These indices are defined as below:

1) NUMBER OF VOLTAGE LIMIT VIOLATING BUSES (NVVB)
NVVB signifies the number of buses violating the permissible voltage limits in the system considered.

2) VOLTAGE DEVIATION INDEX (VDI)
In order to specify the measure of violation of limits imposed on voltage magnitudes at buses in an nb bus system, the voltage deviation index (VDI ) is defined as: where, i belong to set of buses violating upper or lower voltage limit. V i = voltage magnitude at bus i. V i,limit = upper or lower voltage limit at bus i. nb = total number of buses present in the system. During reconfiguration and DG placement, VDI signifies the amount of voltage fluctuation at buses violating voltage limits. It is desired to have zero voltage deviation index (VDI ),i.e. voltage at all buses should be within permissible limits.

3) VOLTAGE PROFILE IMPROVEMENT INDEX (VPI)
In a radial distribution system at base load condition, the voltage at source to remote buses falls much below the desired 1 pu value, due to voltage drops in lines. With the incorporation of distributed generation and/ or tie-switch allocation the voltage at each bus changes to different operating value. Incorporation of these devices in system leads to further rise or drop in voltages leading to improvement or deterioration in voltages at a specific or set of buses in the network. Hence, voltage profile improvement index (VPI ) signifies the appropriate selection of these devices (Reconfiguration and DG placement considered in our work) for enhancement of the voltage profile of the network.

4) QUALIFIED LOAD INDEX (QLI)
Qualified load index is defined as: where, V i = voltage at bus i. P base L,i = real power drawn by load at bus i at the base case operating point.
A higher value of QLI represents higher distance of base case operating point from the maximum loadability point as bus voltages is high. Thus, QLI is an index helpful in assessing voltage stability margin (The distance between the base case operating point and maximum loadability point). QLI may be enhanced by optimal DG placement/network reconfiguration. Modified QLI after DG placement/network reconfiguration is given by: where, QLI m = modified network reconfiguration/DG placement. V REC/DG i = Voltage at bus i after network reconfiguration/ DG placement. It is apparent that by improving QLI by network reconfiguration and DG placement, voltage stability of radial distribution system may be enhanced.

5) ACTIVE POWER LOSS REDUCTION (%APLR )
APLR represents percent reduction in active power loss and is given by: where, APL old = active power loss in the radial distribution system without DG and/ or reconfiguration. APL new = active power loss in the radial distribution system with DG and/ or reconfiguration.

6) REACTIVE POWER LOSS REDUCTION (%QPLR)
QPLR represents percent reduction in reactive power loss and is given by: where, QPL old = reactive power loss in the radial distribution system without DG and/ or reconfiguration QPL new = reactive power loss in the radial distribution system with DG and/ or reconfiguration All the indices defined in this section have been summarized in Table 5.

VIII. RESULTS AND DISCUSSION
Numerical simulation is accomplished on IEEE 33-bus, 37 branch distribution system [43]. It has 33 buses, 32 generally closed branches and 5 tie switches generally kept open with 3 laterals. The total load demand on substation bus of this RDS constitutes 3.715 MW of real and 3.715 MVAr reactive power. The simulation study is performed using code developed on MATLAB on a system having Intel(R) Core(TM) i7-8700 CPU @ 3.20 GHz processor.
A. WITHOUT CONSIDERING PQV AND P BUSES Table 6, displays the optimal load flow outcome of IEEE 33-bus distribution system for the different cases under study. It can be realized that only considering PQ buses, 202.68 kW of real power losses incurred in the system at base case. The maximum loadability of the base case system without reconfiguration is found to be 2.63. The farthest bus 18 possesses the lowest voltage of 0.9131 pu in the system. Table 6, also presents the outcome of reconfiguration with and without DG allocation of the IEEE 33-bus RDS without considering PQV and P buses.
The paper reveals the efficacy of the proposed method to enhance/improve the maximum loadability by simultaneously allocating the DG and reconfiguring the RDS. The system performance enhancements are realized based on the performance indices defined in Table 5. The different results and their comparison with the work in existing literature are accessible in Table 6, Table 7 and Table 8. The consequences of results are analyzed as below:   i.
From A noteworthy enhancement in the maximum loadability corresponding to Case 3 has been observed with λ max = 5.29. iv.
The simultaneous application of optimal DG allocation and reconfiguration enhances the maximum loadability of the RDS without violating the bus voltage limits. v.
From Table 7, It can be noticed that proposed algorithms give the marginally better result than [27] and much better result than [44] and [45] in terms of enhancing the maximum system loadability for Case 2 considering reconfiguration only. vi. Figure 9 presents the voltage profile of the RDS for cases under study. From Table 6 it is noticed that there are 21 and 8 buses in the RDS which violates the permissible voltage limits for Case 1 and Case 2, respectively. Nevertheless, Case 3 implies a significant enhancement in the RDS voltage magnitude with all the buses voltage lying within the permissible voltage limit. vii.
With the application of reconfiguration and DG injection it is found that Case 3 gives much better results than [27] in terms of maximum loadability as shown in Table 8. Voltage at all the buses lie within the permissible limits.

B. CONSIDERING PQV AND P BUSES
The efficacy of the method proposed is explained with IEEE 33-bus RDS and associated data are available in [43]. As the primary objective in the presented work is to enhance the maximum loadability of the RDS and to lower the active losses, hence, a suitable designation of 'P' bus should be accomplished.  Table 9 shows the maximum loadability, minimum voltage stability indices, as well as real losses of the RDS to maintain fixed magnitude of voltage at PQV bus corresponding to different sizes of shunt capacitor injecting reactive power at all buses on main feeder. In Table 9, verify that designating 6 th bus as P bus, offers the higher maximum loadability, higher voltage stability index, and lowest real power loss for the RDS. Except 6 th bus, the characteristics for the P bus selection criterion worsen drastically for other buses when they are designated as P type bus, as shown in Table 9.
Consequently, bus-6 of IEEE 33-bus RDS is designated as the P bus. With load flow of system consisting of PQV and P pair of buses, establishes that shunt capacitor injection of value 1.75353 MVAr at 6 th bus leads to enhanced maximum system loadability, highest minimum voltage stability index, and least real power loss of 3.78, 0.7580 pu, and 154.44 kW respectively. Table 9 clearly depicts that the reactive power required by the shunt capacitor to keep the PQV bus voltage constant at desired set value is lesser when the bus P remains near the PQV bus, though at the cost of higher real power loss and lower loadability and lower voltage stability index. Hence in this work, bus-6 has been selected as a P bus as it gives better system performance in terms of maximum system loadability, improved voltage stability index, and reduced real power losses. Table 10 demonstrates the active power loss, loadability, maximum and minimum voltage of the test system before and after the selection of PQV and P bus in the 33 bus system.  2) RESULTS FOR VARIOUS CASES CONSIDERING PQV AND P BUSES Table 11 demonstrates the outcomes of the IEEE 33-bus RDS for the various cases studied with incorporation of the PQV and P buses by proposed algorithm. Some key points of the results are discussed as below: i.
From Table 11 for Case 6, it is perceived that λ increases while APL and QPL decreases reconfiguration and simultaneous application of reconfiguration and DG allocation. The maximum enhancement in λ max is found to be 112.54% for Case 6 (w.r.t. Case 1). The Reductions of 60.857% and 58.947% in APL and QPL are noticed, with respect to base case. The improvement at minimum voltage of the system is achieved as 0.98495 p.u with Case 6. ii.
The maximum value of QLI takes place in Case 6 when DG is placed simultaneously with network reconfiguration optimally. The maximum enhancement in QLI is 3.1727% with simultaneously optimal DG allocation and reconfiguration considering PQV and P buses (w.r.t. Case 1). iii.
A noteworthy enhancement in the VDI is witnessed. The VDI is reduced to zero whereas the index VPI is improved to 0.098197 for Case 6 from zero. iv.
From Table 11, It is noticed that Case 5 does not converge for any solution within the voltage limit. Hence, the lower limit on voltage magnitude is diluted further for convergence. v. Figure 11, presents the voltage profile of RDS for cases under study. From Table 11 it is noticed that Case 4 and 5 experiences voltage constraint violation at 14 and 3 number of buses in RDS, respectively while Case 6 ensures there is no voltage limit violation witnessed. vi.
The simultaneous reconfiguration with DG enhances the maximum system loadability of the RDS without voltage limit violation. It is witnessed that proposed algorithm with PQV and P buses provides much better results in terms of maximum loadability, VPI, VDI, NVVB, QLI, APL and QPL of the system. vii.
For Case 6, Table 11 ensures that with proposed multi-objective approach optimal allocation of DG and reconfiguration results in substantial enhancements in Maximum loadability (λ = 5.59), QLI (3.774452), and VPI (0.098197) while the real and reactive losses dropped by 65.857 and 58.947%, respectively. Consequently, Case 6 awards a considerable enhancement in the performance indices and harvests best maximum VOLUME 10, 2022 loadability. The proposed multi-objective algorithm for enhancement of maximum system loadability increases the network loadability with reduction in active power, with all buses within the specified voltage limits.

IX. CONCLUSION
This paper proposes the computational challenges of network reconfiguration problem for enhancement of loadability in distribution system with the simultaneous Distributed generation allocation. Multi-objective meta-heuristic method is used to simultaneously obtain the objectives of loss minimization and voltage stability enhancement. The method uses GWO optimization algorithm to attain the aforesaid objective for loadability enhancement both without and with novel set of PQV and P buses to enhance the loadability of the system and reduce active power losses.