A reliability‐based optimal μ‐PMU placement scheme for efficient observability enhancement of smart distribution grids under various contingencies

Correspondence Navid Taghizadegan, 35 Km Tabriz-Maragheh Road, P.O.B: 53714-161, Tabriz, Iran Email: taghizadegan@azaruniv.ac.ir Abstract A reliability-based optimal μ-PMU (micro-phasor measurement unit) placement scheme is suggested for efficient observability enhancement of smart distribution grids at steady-state and contingencies conditions. This article introduces a unique method for the μ-PMU allocation in reconfigurable smart distribution grids in which communication system requirements and zero injection nodes (ZINs) are considered. The original objective function and limitations are proposed aiming at minimizing the capital cost, including communication links and installation costs of μ-PMU, optical power ground wire cost, power losses cost, and reliability cost as well as obtaining the maximum number of measurement redundancy constrained to full system observability in the presence of ZINs and tie switches. The suggested method is formulated as a mixed-integer linear programming problem applied to find optimal μ-PMU locations considering the cost of communication infrastructure and co-optimize the system switching plan simultaneously. In this regard, CPLEX—a high-performance mathematical solver—is used to solve the proposed mixed-integer linear optimization problem to reach the global optimality. The simulations are performed on 33, 69, and 85-bus radial distribution networks, and comprehensive simulation studies show the effectiveness of the suggested method.


Concepts and motivations
This Full observability of distribution systems is a suitable solution for long-term monitoring, contingency analysis, and model validation. For this purpose, state estimators in power systems are applied to monitor voltages magnitudes, injected currents, and real/reactive power flows to calculate voltage phasors. With the invention of the global positioning system (GPS), it has become possible to monitor the power system. Therefore, the role of μ-PMUs becomes more highlighted in the power systems [1][2][3][4]. In addition to the extensive study and application of PMU in the transmission systems, the invention of μ-PMU can have the same and even more advantages in the distribution systems [5].
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. With the development of electrical systems technology and the growth of consumption load, the structure of distribution systems has become larger and more complex. Widespread access to renewable energy sources and the rapid rise of flexible loads has changed the traditional distribution network into a smart distribution network with complex electrical quantities, inadequate measurement information, and inaccurate measurements. It is necessary to monitor and analyse the behaviour of distribution systems to adapt generation and consumption. Traditionally, the distribution network was monitored by supervisory control and data acquisition (SCADA) system, which their measurements were not accurate and coordinated, their sampling rate was longer, and they were not able to provide direct phase angle data. So, μ-PMUs introduces as the most effective and prominent measuring devices in monitoring, controlling, and protecting smart distribution systems [6].
Technically, μ-PMUs provides accurate, coordinated, reliable, and high-speed measurement data such as bus voltages and branch currents magnitude and phase angle with higher sample rates [7]. Distribution networks are more challenging than transmission networks in several aspects: (1) Distribution system measurements have a higher noise level, which makes it difficult to detect the exact angle signal; (2) from an economic point of view, the cost of μ-PMU setting up in the distribution grid must be less compared to the transmission system. Deployment of μ-PMU in the grid can make a kind of advantages including but not restricted to load and generation balance, fault detection and location, topology and disturbance detection, phase identification, state estimation, voltage stability analysis, and reverse power flow detection [8]. The principal developments in state estimation and related areas such as observability analysis, bad data processing, network topology processing, topology estimation, and parameter estimation are reviewed in ref. [9].

Literature review
The authors in [10] presented a comprehensive study on PMUs applications, data quality, and communication requirements in a modern distribution system in the presence of renewable energy sources. In paper [11], two different mathematical programming models, including mixed-integer linear programming (MILP) and nonlinear programming, are proposed to solve the optimal PMU allocating problem to reach the full observability of the power grid. Moreover, some technical constraints such as ZINs, single PMU outages, channel capacity, and communication infrastructure (CI) have been considered in this model. Ref. [12] introduces a centralized optimal PMU placement model, which considers the reliability of zero injection observation. To enhance the zero injection reliability, the depth of zero injection observation is limited as well as the utilization rate of zero injection is minimized. A computationally effective machine-learning method is introduced in [13] to generate weighted pseudo measurements to improve the quality of distribution system state estimation and enhance observability with advanced metering infrastructure against unobservable consumers and unknown data. A generalized optimal PMU placement problem is performed in [14], in which observability, delay time, reliability, and communication facilities constraints are considered in the objective function. In the paper [15], the author presents a power system state estimation based on the weighted least squares method incorporating a combination of SCADA technology and a widearea measurement system. Also, the measurement errors have been investigated in this work. A multi-objective MILP model is presented to solve the optimal PMU placement problem in [16]. The effect of PMU allocating is considered in different energy management system applications. Also, the installation cost of PMUs, system observability, and identification of gross errors are discussed in the proposed model. To optimally allocate PMUs based on the identifying of gross errors, the vulnerability index is applied to determine the amount of vulnerability of each element in the system. A data-driven learning-based distribution system state estimation is presented in [17], which designs a neural network that can provide several types of measurements as well as pseudo measurements. Harmonic sources placement and unbalanced three-phase distribution system state estimation are investigated in [18]. An approach for harmonic state estimation is developed in the presence of two kinds of measurement including smart meters and distribution PMU. The suggested method needs fewer D-PMUs than nodes, making it more suitable to existing distribution networks. A security-oriented optimal PMU placement with efficient observability redundancy of transmission networks considering zero injection bus has been performed in [19]. Moreover, new security notions for modelling channel failures, PMU losses, and branch outages are introduced to improve accuracy and applicability in the contingency statuses.
Ref. [20] provides a comprehensive method for the optimal PMU allocation and maximizes the measurement redundancy by using traditional meters that ensure the full observability of the network. An optimal aggregation of single and three-phase μ-PMU allocation with a radial asymmetrical topology is developed in [21] to maximize the observability index of the network. To obtain the advantage of ZINs features considering the full observability constraint, two types of ZINs have been introduced, including full and partial ZIN. In paper [22], the observation index is discussed and comparison in the presence of both topological and numerical observation methods. An innovative method is presented in ref. [23] for optimal placement of synchronized phasor measurement units to guarantee the full observability of the system considering ZIBs. The suggested method determines the minimum number and the optimal locations of μ-PMUs required to make the power system numerically observable. The problem is modelled as a binary semidefinite programming problem, with binary decision variables.
An innovative method to μ-PMU placement is presented in [24] in unbalanced distribution systems. The suggested problem is solved using integer linear programming, ensuring the optimality of results. Some practical constraints such as zero injection buses, modern smart meters, and multiple switch configurations are incorporated in this problem. Optimal placement of μ-PMU in a balanced three-phase distribution system integrated with distributed energy resources is implemented in ref. [25]. The hybrid depth search algorithm is employed to determine the minimum number of μ-PMUs for the full observability of the system. An optimal μ-PMUs placement technique in the various configuration of distribution networks is developed in [26] based on the integer linear programming framework to identify the optimized locations for the μ-PMUs. A customized optimal μ-PMU placement method is examined in ref. [27] for various configurations of distribution networks. The customized optimal μ-PMU placement technique used the radial structure of distribution networks to downsize the scale of the networks equivalently. This method is applied to identify the minimum number of μ-PMU in large-scale distribution networks.

Novelties and contribution
As declared in the prior section, some original works performed on the optimal μ-PMU placement method. However, still, there are lots of shortcomings in the previous research in the optimal μ-PMU placement. By ignoring the various configurations of smart distribution grids, it is not feasible to achieve optimal μ-PMU placement. The μ-PMUs created voltage and current phasors at placed buses and in their neighbouring lines, respectively. This notion can be changed under the influence of the network reconfiguration process. The μ-PMU placement without considering a change in distribution network topology is not an optimal strategy and is more money wasted because part of the network remains unobservable. Due to the notes mentioned earlier, this paper proposed a reconfiguration-based optimal μ-PMU placement for efficient observability enhancement in smart distribution grids considering CI costs. The proposed method is modelled as a MILP problem, including communication links and installation costs of μ-PMU, optical power ground wire cost, power losses cost, and customer interruption costs. The primary purpose of the optimal μ-PMU placement is to make the distribution system full observable with maximum possible redundancy. Moreover, to reach the maximum use of data and reduce the number of μ-PMUs as much as possible, the maximum available capacity of ZINs is used. In continue, incorporation of power losses cost and customer interruption costs are considered to solve the reconfiguration strategy. A new linear formulation of power flow is presented that does not require any binary variables in the linearization process. The proposed model is also extended for different power network contingency such as the measurement losses and single line outage for enhancing its flexibility. The novelty and contribution of this paper can be briefly expressed as below: • Developing a mathematical methodology based on MILP to solve the suggested optimal μ-PMU placement problem for efficient observability enhancement in reconfigurable-based smart distribution grids considering CIs costs. • Determine the optimal μ-PMU locations by considering different configurations of proposed smart distribution grids to minimize the installation and investment cost of μ-PMU, power losses cost, customer interruption cost, and optical power ground wire (OPGW) cost as well as maximize the observability level and measurement redundancy index, simultaneously. • Applying the ZIN properties to reduce the number of installed μ-PMUs in the distribution grid and making the system observable. • Taking into considering different contingency cases of distribution grids such as single μ-PMU failure or single line outage to ensure complete observability. • Formulation of the proposed method as a MILP problem and subsequently minimizing through the implementation of CPLEX solver to reach the best global optima. • Using large-scale and practical radial test systems such as 69 and 85-bus distribution systems.

Paper organization
The rest of this paper is formed as follows: Section 2 introduces the problem formulation of the suggested method; Optimal reconfiguration model for distribution network is presented in Section 3; Simulation results and discussion are demonstrated in Section 4, and Section 5 provides the conclusion.

PROBLEM FORMULATION
The theory of μ-PMU placement is to determine the minimum number of μ-PMUs in the most optimal places to ensure that the observability of the entire distribution network will be remain. However, the reconfiguration procedure can change the network structure so that the μ-PMUs location is no longer optimal and observability not achieved. To overcome this issue, a novel aggregated μ-PMU placement set based on the reconfiguration problem is proposed. Also, the reconfiguration process is used for mitigating the cost of the system in the form of power loss, reliability cost, or power supply cost. Meanwhile, reconfiguration methodology cause to improve the voltage magnitude in the buses with weak voltage. So, the aggregated cost function is developed aiming at minimizing the capital cost including installation cost of μ-PMU, cost of communication infrastructure, power losses cost, and reliability cost as well as obtaining the maximum number of measurement redundancy constrained to full observability enhancement in the presence of ZINs and tie switches. The proposed model is formulated as a MILP problem, which consists of variables, linear constraints on these variables, and an objective function that is to be minimized under these constraints. This cost objective function is formulated as below:

Cost of µ-PMU
In this section, a linear model proposed for μ-PMU placement to optimize the installation and communication infrastructure cost subjected to full observability enhancement and a linear term considered in the objective function to maximize the measurement redundancy index. Moreover, the impact of the ZIN constraint is taken into account in the optimal μ-PMU model. Finally, the implied model is examined in the presence of various contingencies, such as a line outage or measurement loss.

Without considering the effect of ZINs
The model as mentioned earlier for optimal μ-PMU placement is presented as follows.
The objective function of the optimal μ-PMU placement cost has been shown in Equation (2). The first term of the objective function (2) is used to minimize the installation, geographical location, and communication infrastructure cost of the μ-PMUs. The second term of Equation (2) is employed to maximize the measurement redundancy index. In inequality constraint (3), of i denotes the observability function, which must be larger than or equal to '1′ to ensure that all busses in the system are observable at least from one μ-PMU.

Considering the effect of ZINs
To evaluate the observability with ZINs impact, a common observability law according to Kirchhoff 's current law (KCL) explains that between a ZIN and its neighboring buses, if all buses are observable except one, the unobservable bus can be observed by employing KCL at ZIN. The impact of ZINs is considered in Equation (2) as the following equations. where Equations (7)-(10) express the inequality constraints of the proposed problem in the presence of ZINs. According to the KCL, constraint (8) declares that the bus i will be observable with the impact of ZIN j, only in a condition that all the adjoining buses of the bus j are observable. Constraints (8) and (9) present a linear expression of KCL at ZINs. The inequality constraint (10) was applied to observe at least one bus by the ZINs. Equation (11) indicates the observability function that includes an auxiliary variable added to ZIN. The first-term of Equation (11) suggests that the observability of a bus and its neighbouring buses achieved by locating at most one μ-PMU on the same bus. Furthermore, the second term of (11) means that a given bus is observed by the impact of at least one adjoining ZIN.

2.1.2
Linear framework for optimal μ-PMU placement under various contingencies Contingency analysis is described as the security investigation application in modern distribution system planning and operation. Its goal is to analyse the distribution system to diagnose the overload that leads to congestion and other problems that can happen due to a contingency. Various contingencies, including single line outage and single measurement losses, are studied in linear equations in the objective function (2). In the following subsections, the single contingencies are added to the model.

Single line outage
The impact of a single line outage is considered in the formulation using Equations (13)- (18). where Equations (13)- (17) are similar to Equations (7)-(11), respectively, while connectivity parameters, auxiliary variables, and observability functions are substituted with those indicating the line failure. According to Equation (18), the effect of the line ij related to the contingency on itself is ignored.

Single μ-PMU loss
In the proposed model, a single μ-PMU loss can be modelled by using a similar strategy of single line outage. For describing a single μ-PMU loss, the following equations have been reported.
In Equations (19)-(23), the index μp is applied to describe the variable that handles the allocating problem in the measurement failure condition.

Cost of optical power ground wire
In previous work, μ-PMU has been used to observe the system in the presence of several practical limitations. Whereas, the cost of CIs should be reflected in the proposed problem formulation. Commonly, Power system CI technologies are classified into two main groups: dependent and independent technologies. As can be understood from the title, the dependent media are part of power system components like OPGW. On the opposite, independent media do not depend on the power system components and are accessible to all users like wireless or satellite communication media [28]. So, the OPGW cost is considered and optimized as the dependent CI technology in the proposed problem. The OPGW cost is depicted as follows.

Cost of power loss
Numerous goals are suggested for the reconfiguration problem in [29][30][31]. There are promoting the use of the reconfiguration method to alleviating the reliability and power loss costs. So, an aggregation of both power losses and expected customer interruption costs are considered in the objective function. This cause provides a suitable equilibrium among the reliability and power loss costs. Equation (25) computes the real power loss cost.

Cost of reliability
Active distribution system reliability indicators are the source for the distribution system reliability measurement classified into two groups: system reliability indices and load point reliability indices.

Load point reliability indices
The average failure rate, average annual outage duration, and average outage time are the fundamental reliability indices applied to show the system reliability. The average failure rate λ is described as the probability of failure occurs at the individual load point for the definite period [32], presented by Equation (26).
The annual outage duration is described as the average supply unavailability of the load point for one year [32], which can be formulated as Equation (27).
The average outage time is obtained by dividing the average annual outage duration by the average failure rate according to Equation (28).

System reliability indices
With the help of the expected interruption cost (ECOST) index, network designers can calculate the level of reliability for consumers, detect weak spots in power distribution grids, promote proper maintenance planning. To compute the reliability worth indices like ECOST, the load point reliability indices are required. Accordingly, the ECOST of the jth bus is stated as Equation (29), and the network total expected customer interruption costs are calculated as Equation (30), which determines the expected losses cost of the consumption side based on power failure and is supposed to be remarkable information in the active distribution networks operation and planning.

OPTIMAL RECONFIGURATION MODEL FOR DISTRIBUTION NETWORK
The reconfiguration process in active distribution networks aims to determine a radial configuration that improves the system voltage profile and minimizes the system power losses. Distribution networks are operated as radial structures in which tie lines and sectionalizing switches play an essential role in specifying the network topology. Accordingly, the reconfiguration procedure is performed by modifying the feeder topological structure to efficiently manage the switching status of sectionalizing and tie-switches in the system under steady-state and contingency conditions. A full reconfiguration procedure formulation for the active distribution system with the different switching plans is explained in this section. A linear model is used for optimal distribution network reconfiguration based on the recursive method as presented in Figure 1.
To understand the accurate AC constraints in the system power flow, the active and reactive power balance equations are ensured by (31), (32). According to Equations (33) and (34), Kirchhoff 's voltage law has been used to determine the voltage drops in each line. In this section, the auxiliary variable (∆V jk ) is applied to indicate the switching condition, so that the ∆V jk is zero if the switch is closed. However, the ∆V jk is a positive or negative value if the switch is open.
Constraint (35) explains the permissible voltage range of each bus according to the technical limits. This constraint kept the voltage profile between the lower and upper amount of bus voltages. Also, constraint (36) shows the variable ∆V jk restricted to determining scope.
According to the thermal limits, constraint (37) shows the maximum limit of the current flow in each line. Constraints (38) and (39) guarantees the amount of power exchange between the upstream and distribution system does not exceed the maximum power capacity. Also, these constraints prevent possible congestion in the lines.
As discussed earlier, distribution systems commonly operate with a radial topology, so this constraint should be considered during the reconfiguration process. For this purpose, Equations (40)- (43) are applied to guarantee the radiality state of the distribution system as a strict constraint. It is necessary to mention that the variable w F i j exposes the line status in the distribution system. Moreover, a set of dummy current flows are defined to keep the grid topology as radial and at the same time avoid the formation of any islanded bus in the network.

Linearization process
The above expressions formulate the reconfiguration and optimal operation of active distribution systems. Due to the use of some nonlinear variables, the problem was developed as an MINLP problem. To ensure the optimal solution and reduce the problem's complexity, a linearization method is used to linearize the nonlinear part of the problem. Equations (31)-(36) make the problem nonlinear. For this purpose, some new variables are described as Equations (44), (45).
Equations (31)-(36) must be modified according to the newly defined variables.
, ∀jk ∈ N F (52) Now by using the above substitutions, the Equations (31)-(33) are linearized. Equation (49) is the single remained nonlinear term of this model that requires additional linearization. For this purpose, the left hand of Equation (49) as a bilinear term is approximated as below.
In the right-hand of Equation (49), a simple piecewise linearization method is used to linearize the quadratic expressions. The individual option of the suggested linearization formulation is it does not require any binary variable.
To clarify the suggested linearization method, the piecewiselinear approximation of the quadratic curve is presented in Figure 2. As can be seen, the distance between zero and VI F is first partitioned into K segments. Then, corresponding to each segment K, a line with the slope of A F and intercept of B F is assumed.

SIMULATION RESULTS AND DISCUSSION
The reliability-based optimal μ-PMU placement is modelled as a MILP problem. Many optimization algorithms and mathematical methods are proposed in the earlier literature to solve the optimal μ-PMU placement problem, which is mentioned in FIGURE 2 Piecewise-linear approximation of the quadratic curve the literature review section. In this paper, to provide a flexible, high-performance mathematical programming problem [33], the CPLEX optimizer is employed to solve the reliabilitybased optimal μ-PMU placement with complex constraints. This optimizer enables decision optimization for improving efficiency, reducing costs, and increasing profitability. It is suitable to solve large, real, and the speed required for today's interactive decision optimization applications. In this paper, the proposed problem is solved by IBM CPLEX optimizer in the MATLAB software environment [34]. CPLEX has evolved to adapt and become a leader in linear programming categories, such as integer programming, mixed integer programming, and quadratic programming. The simulations are performed on a Windows 10 laptop configured with Intel(R) Core(TM), CPU i5-4300 M, 2.60 GHz, and 8 GB of RAM.
In this part, the suggested method is examined on the 33, 69, and 85 bus test systems to show its efficiency to get all optimal placement schemes. The flowchart of the proposed reconfiguration-based optimal μ-PMU placement is demonstrated in Figure 3. To illustrate the impact of ZINs and different contingencies on the optimal μ-PMU placement problem, the results implemented under various scenarios:

Case study
The proposed optimal μ-PMU placement method is examined on the 33, 69, and 85-bus distribution networks. The IEEE 33-bus distribution network topology is demonstrated in Figure 4. The black lines show the sectionalizing switches, and the red lines show tie switches as S33-S37 [35]. Figure 5 shows the single line diagram of the IEEE 69-bus distribution system. The system base configuration is having S1-S68 sectionalize switches normally closed, and S69-S73 tie switches normally opened [36]. The single line diagram of the standard 85-bus radial distribution network is shown in Figure 6. This system consists of 85 buses with 84 branches, operating at 11 kV, and MVA base is 100. Also, the intended system consists of 5 microgrids with different applications that are connected with S85-S89 tie switches [37], [38]. The primary load point indices for all three systems are presented in Tables 1, 2, and 3, respectively [39]. The power loss cost coefficient is considered to be 0.4 ($/kW.hr). It is supposed that the μ-PMU are all of the same kind, so their cost will be the same. The cost of each μ-PMU device and its installation cost is estimated to be 10′000 $ in all test systems. The cost of OPGW and its installation cost for 1 km is assumed 1000 $.

Scenario I
The optimal number and location of μ-PMUs, the installation cost, and the achieved measurement redundancy index subjected to the complete observability of the distribution networks during normal operating conditions without considering ZINs presented in Table 4.

Scenario II
In the previous scenario, the optimal μ-PMU placement was tested in a normal operating condition without considering ZINs. In order to clarify the efficiency of the proposed method, Table 5 demonstrates the optimal μ-PMU placement problem results in a normal operating condition considering ZINs for three test cases. It can be intuitively seen that considering ZINs in the model effectively reduces the required number of the μ-PMUs and objective function value. According to the results, the measurement redundancy index reduces as the number of μ-PMUs reduces, which provides more measurement accuracy.

Scenario III
The optimal number and location of μ-PMUs, the installation cost, and the achieved measurement redundancy index subjected to the full observability of the distribution networks during a single line outage or single μ-PMU loss without considering ZINs depicted in Table 6. The μ-PMU installed on a particular bus can not only make that bus observable but also can make neighbouring buses indirectly observable. Therefore, with a single line outage or single μ-PMU loss, some buses or lines may be unobservable. To prevent this problem, an optimal μ-PMU   Single line diagram of the 85-bus distribution system placement method is implemented to find optimal locations to keep the whole system fully observable after any event. As can be seen from this table, with one or more events, the number of installed μ-PMUs in the network increases, so the cost function value significantly increases. For this reason, scenario III has no economic justification.

Scenario IV
The optimal number and location of μ-PMUs, the installation cost, and the achieved measurement redundancy index subjected to the full observability of the distribution networks during a single line outage or single μ-PMU loss after incorporating ZINs are illustrated in Table 7. As expected, to make a network observable under any single contingencies, more μ-PMUs should be installed. So, to make scenario III practical, reduce the number of μ-PMUs and objective function value, the ZINs must be considered. As can be seen, incorporating ZINs in the placement problem can effectively reduce the required number of μ-PMUs and objective function value in the system. Comparing scenarios III and IV, in the 33, 69, This part of the results concentrates on the suggested method's performance for optimizing the objective function based on the distribution system reconfiguration. The proposed MILP model is applied for three test systems in a reconfiguration problem to prove its efficiency. The optimal number of μ-PMU, measurement redundancy index, active power loss, optimal OPGW coverage, and the total cost function of the IEEE 33-bus test system are presented in Table 8 and compared in the different configurations to select the best network topology. The second column shows the switch status after reconfiguration. As can be seen from the third and fourth column, the number of installed μ-PMUs and the measurement redundancy index is different in various network configurations, so that a topology with the minimum number of μ-PMUs (11 units) and the maximum measurement redundancy index (index = 37) concerning the same number of installed μ-PMUs is selected.
Due to the results, the amount of power losses varies in different switch statuses. The reconfiguration strategy has reduced the power losses amount from the initial value of 202.67 (kW) to 139.55 (kW). Also, the optimal OPGW length determined by the CPLEX solver and depicted in this table. The OPGW length changed due to the distribution network topology, μ-PMUs location, and technical specifications. The best and optimal OPGW length is 25 Km related to the network's topology with S7, S9, S14, S32, S37 switch status. The total cost function is reduced to the optimal value of 135055.82 ($) after reconfiguration. The simulation results show that the proposed cost function can dramatically reduce the cost of μ-PMUs, communication infrastructure, power losses, and reliability indices simultaneously, which indicates the valuable role of reconfiguration strategy and its inevitable role in smart distribution grids. Table 9 shows the optimal number of μ-PMU, measurement redundancy index, active power loss, optimal OPGW coverage, and the total cost function for the IEEE 69-bus test system and compares them in the different configurations to select the best network topology. As can be seen from the third and fourth column, the number of installed μ-PMUs and the measurement redundancy index is different in various network configurations, so that a topology with the minimum number of μ-PMUs (24 units) and the maximum measurement redundancy index (index = 74) concerning the same number of installed μ-PMUs is selected. Due to the results, the amount of power losses varies in different switch statuses. The reconfiguration strategy has reduced the power losses amount from the initial value of 183.39 (kW) to 81.94 (kW). The best and optimal OPGW length is 53 km related to the network's topology with S12, S21, S40, S53, S70 switch status. The total cost function is reduced to the optimal value of 293032.77 ($) after reconfiguration. Table 10 exposes the optimal number of μ-PMU, measurement redundancy index, active power loss, optimal OPGW coverage, and the total cost function for the 85-bus practical system. It compares the given items in the different configurations to select the best network topology. A topology with the minimum number of μ-PMUs (29 units) and the maximum measurement redundancy index (index = 112) concerning the same number of installed μ-PMUs is selected. Due to the results, the amount of power losses varies in different switch statuses. The reconfiguration strategy has been able to reduce the power losses amount from the initial value of 249.90 (kW) to 231.35 (kW). The best and optimal OPGW length is 52 km, which is related to the network's topology with S11, S21, S35, S50, S83 switch status. The total cost function is reduced to the optimal value of 342092.54 ($) after reconfiguration. Figures 7,8,and 9 show the voltage profile of 33, 69, and 85-bus distribution systems for all configurations defined for the distribution system operator, respectively. The voltage profile of optimal network configuration found the minimum total cost function, displayed with a thick black line. According to this figure, the voltage profile of the structure (thick black line) is smoother than other configurations voltage profile. Finally, this figure proves that the proposed method not only reduces the costs of reliability, μ-PMU placement, OPGW coverage, and active power losses but also can improve the system voltage profile in the desired technical limitation.
To further evaluate the performance and effectiveness of the suggested method, the simulation results are compared with other related references in the mentioned test systems. The comparison results are presented in Table 11. Compared to other methods, the most optimal configuration is selected to install the minimum required number of μ-PMUs to achieve full observability.
(1) Monitor, control, and protect the distribution system against the spreading of disturbances and their negative consequences. In this condition, the customer interruption and outage costs have been reduced and minimized. (2) Increase distribution lines capacity and congestion management. By reducing the congestion, the distribution company (DISCO) can sell more power to the electricity market, which will lead to increase the profit of DISCO. (3) Improve distribution assets utilization by refining the planning, control, and protection process and models.

CONCLUSION
This paper presents a reliability-based method for efficient observability enhancement in smart distribution grids by applying high-speed μ-PMUs. The suggested problem is formulated as a mixed-integer linear programming model and solved employing a CPLEX solver. In this paper, the linearization process uses to linearize the nonlinear terms of the reconfiguration problem. The proposed linear function optimizes the minimal set of μ-PMUs in the presence of some practical considerations such as ZINs, different system switching schemes, and various contingency conditions. From the various contingency conditions, the single line outage and single μ-PMU failure accommodate in the model to make the system flexible and more reliable. Moreover, to ensure the network's full observability in the linear structure, the objective function was developed to maximize the measurement redundancy index. The results of simulations on IEEE 33, 69, and 85-bus systems confirm that the suggested method does not only determine the optimal μ-PMU locations for full observability of the system but can also improve the reliability, alleviating active power losses, and find the best OPGW coverage. Concluding from the outcomes obtained, significant total cost saving is efficaciously achieved.