# A New Hybrid Nelder-Mead Particle Swarm Optimization for Coordination Optimization of Directional Overcurrent Relays

Authors: An Liu; Ming-Ta Yang
Journal: Mathematical Problems in Engineering
 (2012)

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## Abstract

Coordination optimization of directional overcurrent relays (DOCRs) is an important part of an efficient distribution system. This optimization problem involves obtaining the time dial setting (TDS) and pickup current (Ip) values of each DOCR. The optimal results should have the shortest primary relay operating time for all fault lines. Recently, the particle swarm optimization (PSO) algorithm has been considered an effective tool for linear/nonlinear optimization problems with application in the protection and coordination of power systems. With a limited runtime period, the conventional PSO considers the optimal solution as the final solution, and an early convergence of PSO results in decreased overall performance and an increase in the risk of mistaking local optima for global optima. Therefore, this study proposes a new hybrid Nelder-Mead simplex search method and particle swarm optimization (proposed NM-PSO) algorithm to solve the DOCR coordination optimization problem. PSO is the main optimizer, and the Nelder-Mead simplex search method is used to improve the efficiency of PSO due to its potential for rapid convergence. To validate the proposal, this study compared the performance of the proposed algorithm with that of PSO and original NM-PSO. The findings demonstrate the outstanding performance of the proposed NM-PSO in terms of computation speed, rate of convergence, and feasibility.


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## Body

## 1. Introduction

Transmission lines are exposed to the environment and stretch long distances, which increases the probability of failure far beyond that of other components of the network, including generators, transformers, and switchgear equipment.A transmission network is usually divided according to function: (1) transmission lines between various major substations forming the backbone of the network; (2) subtransmission lines connecting substations to load centers or major users; (3) distribution lines between load centers and end users.Lines from substations or load centers are often distributed in the form of radial feeders. Radial feeders only require the installation of relays and breakers at the ends of the various lines from which the power is sent. When a fault occurs in most radial feeders, the fault current will be greater than the load current with no reverse fault current. As a result, these types of radial feeders can be protected using nondirectional overcurrent relays.If the protected line is installed with power supplies at both ends, such as in the case of loop networks, the fault current may be fed from the left or right in the event of reverse external failure. In this case, relay malfunctions may occur only if nondirectional overcurrent relays are used for protection, as these relays cannot be coordinated. Directional overcurrent relay (DOCR) is a method to improve protection. DOCR is designed to function only in the event of a unidirectional fault current.The study of coordination problems in electrical power systems has become increasingly important in recent years. Economic considerations have propelled DOCR into widespread use as the primary protection for distribution systems and as the backup protection for transmission systems. When working with a DOCR system, operators must set time dial setting (TDS) and pick up current (Ip) values according to the coordination relationship of the primary/backup (P/B) pairs to fully secure protection for the entire system.In recent years, several optimization techniques have been proposed for the optimal coordination of DOCRs. Urdaneta et al. applied a minima optimization approach to determine the TDS values for presetIp values for fixed and multiple power system network configurations [1]. Abyaneh et al. obtained optimum coordination by considering linear and nonlinear models of relay characteristics and changes in network configuration [2]. Birla et al. demonstrated the simultaneous optimization of all DOCR settings with nonlinear relay characteristics using a sequential quadratic programming method [3]. In [4], a genetic algorithm was selected as the tool to solve the DOCR coordination problem, which included nonlinear constraints. The results of [5] reveal that the advantage of the proposed interval method for the DOCR coordination problem provides robust support against uncertainty in the topology of the network. Bedekar and Bhide used a genetic algorithm and nonlinear programming method to systematically determine initial and final values of the time multiplier and plug settings for optimal DOCR coordination [6].In general, PSO algorithms are not easily trapped in local optima; however, the convergence rate is slow, and optimization problems with constraints cannot be effectively solved. Zeineldin et al. proposed an approach using a modified particle swarm optimization (PSO) algorithm to calculate the optimal relay settings, formulating the coordination problem as a mixed-integer nonlinear programming problem [7]. In [8], the problem of setting the DOCR was formulated and solved as a linear programming problem; a modified PSO was also applied. The major goal of this study was to investigate the feasibility of applying a Nelder-Mead simplex search method and a particle swarm optimization (NM-PSO) methodology to address the coordination optimization of a DOCR distribution system.We have divided the remainder of this paper into three sections. The first provides an introduction to the theoretical foundations of the research, involving the modeling of DOCR coordination problems. The proposed optimization algorithm includes a constraint handling method, an NM simplex search method, a PSO algorithm, and an NM-PSO method. We utilized IEEE 8- and 14-bus test systems to verify the feasibility of the proposed algorithm. The results show that the proposed method, comprising a linear programming (LP) problem and a mixed-integer nonlinear programming (MINLP) problem, is capable of overcoming the relay coordination problem of a power system. The combined approach effectively increases the convergence rate of calculation and enhances the capability of the PSO when processing under constraints. Finally, we discuss the results and draw conclusions.


## 2. DOCR Coordination Problem

The main purpose of the DOCR coordination problem is to determine the TDS andIp values of each relay in a power system. The optimal operating times of the primary relays are then minimized, and coordination pairs of the P/B relays and coordination constraints are obtained. The DOCR coordination optimization problem in a power system can be described as follows:
(2.1)min⁡J=∑i=1nwitik,
where n is the number of relays in zone k of a power network, and wi is a coefficient indicating the probability of a fault occurring on the ith line in zone k of a power network. In general, the value of wi is either 1 or 0. The variable tik indicates the operating time of relay i for a close-in fault in zone k.The coordination constraints between the primary relayi and the backup relay(s) j are as follows:
(2.2)tjk-tik≥CTI,
where tjk reveals the operating time of relay j, and the relay is the backup relay of relay i. CTI is the minimum coordination time interval; its value ranges from 0.2 to 0.5 s. In this study, a CTI of 0.2 s was chosen.The function for the nonlinear relay characteristics is based on IEEE standard C37.112-1996 and is represented as follows:(2.3)ti=TDSi×(28.2(Ifi/Ipi)2-1+0.1217),
where TDSi and Ipi are the time dial setting and the pickup current setting of the ith relay, respectively. Ifi is the short-circuit fault current passing through the ith relay.The constants and exponent in (2.3) define the shape of the extremely inverse trip characteristics.The results of this research not only describe the methodology of DOCR coordination optimization but also demonstrate the feasibility of the TDS andIp settings of the relays. In general, DOCR allows for a continuous TDS value, but a discrete Ip setting. To satisfy this requirement, this study explored both linear and nonlinear programming for DOCR coordination optimization. The variable TDS is optimized according to a predefined Ip for each DOCR, and this optimization problem can be viewed as a linear programming (LP) problem. For the nonlinear programming (NLP) problem, variables TDS and Ip are optimized for each DOCR. In the LP or NLP problem of the DOCR coordination optimization, the TDS values can range continuously from 0.1000 to 1.1000, and the Ip values can range discretely between 10 and 1000 with a step size of 1, depending on the close-in fault current for each relay.


## 3. Proposed Optimization Algorithm

PSO is a random optimization technology developed by Eberhart and Kennedy in 1995 [9], who were inspired by simulating the intelligence of swarming bird flocks. PSO shares many similarities with evolutionary computation techniques such as genetic algorithms (GAs) [6]. The problem is initialized with a population of feasible random solutions; however, PSO contains no genetic operations, such as crossover or mutation.Another important feature of PSO is that each particle has memory. PSO’s information sharing mechanism differs greatly from that of GAs. In GAs, chromosomes mutually share information, and therefore, the movement of the population as it approaches the best area is relatively even. In PSO, the possible individual elements of PSO algorithms are called particles. The global best particle gives information to other particles and updates the movement direction and speed of each particle.Based on the PSO method, we propose the NM-PSO method for solving the constrained optimization problem. The following section introduces the basic principles of NM-PSO, including constraint-handling methods, Nelder-Mead (NM) simplex search, and PSO.


### 3.1. Constraint-Handling Methods

Constraint handling is a major concern when applying PSO algorithms to solve constrained optimization problems. This is because the traditional search operators of PSO algorithms are blind to constraints. Thus far, the most commonly used constraint handling methods for PSO are the penalty and repair methods.The gradient-based repair method was addressed by [10, 11]. This method adopts gradient information derived from the constraint set to gradually repair an infeasible solution by directing the infeasible solution toward a feasible area. Because the constraints of the DOCR coordination optimization are not complicated, this method is highly suitable. Furthermore, because DOCR coordination optimization has no equality constraints,equality constraint equations can be ignored. This method is described below.(1)
For a random solution, determine the degree of constraint violationΔV using the following equation:
(3.1)V=[g]m×1⇒ΔV=[-gj(x)]k×1whengj(x)>0,j=1,…,m,
where V is the vector of inequality constraints (g), and k is the degree of constraint violation ΔV.(2)
ComputeΔxg, where Δxg are the derivatives of these constraints with respect to the solution vector (n decision variables)
(3.2)ΔxV=[Δxg]k×n,x=1,…,k.(3)
The relationship between changes in the constraint violationΔVand the solution vector Δx is expressed as
(3.3)ΔV=ΔxV×Δx⟹Δx=ΔxV-1×ΔV.(4)
Compute the pseudoinverseΔxV-1.(5)
Update the solution vector by(3.4)xt+1=xt+Δx=xt+ΔxV-1×ΔV.The degree of constraint violation is adjusted according to the above procedure. In this algorithm, a “repair method” rapidly revises infeasible solutions to move them toward a feasible region. The number of constraint violations decreases and quickly vanishes with each iteration. Finally, a solution in the feasible region will be obtained.


### 3.2. The Nelder-Mead Simplex Search Method

When the search space isn-dimensional, the simplex consists of n+1 solutions [12]. As shown in Figure 1(a), in a two-dimensional search plane, a simplex is a triangle. The fitness of each solution is considered at each step of the Nelder-Mead method, and the worst solution Pworst is identified. The centroid, Pcent, of the remaining n points is computed, and the reflection of Pworst is determined. This reflection yields a new solution, Prefl, which replaces Pworst, as shown in Figure 1(b). If the solution Prefl  produced by this reflection has a higher fitness than any other solution in the simplex, the simplex is further expanded in the direction of Prefl, and Pworst is replaced with Pexp, as shown in Figure 1(c).Illustration of the Nelder-Mead simplex method.
(a)
(b)
(c)
(d)
(e)
(f)On the other hand, ifPrefl has a comparatively low fitness, the simplex is contracted. Contraction can either be outward or inward, depending upon whether Prefl is better or worse than Pworst, respectively. The contraction operations (i.e., Pworst is replaced with Pcont) are shown in Figures 1(d) and 1(e). If neither contraction improves the worst solution in the simplex, the best point in the simplex is computed, and a shrinkage is then performed; all the points of the simplex are moved a little closer towards the best solution (Pbest), as shown in Figure 1(f).


### 3.3. Particle Swarm Optimization

In the past several years, PSO has been successfully applied in many fields [13, 14]. It has been demonstrated that the results of PSO are superior to other methods. The PSO procedure is reviewed below.(1)
Initialization. It randomly generates a swarm of potential solutions called “particles” and assigns a random velocity to each.(2)
Velocity Update. The particles are then “flown” through hyperspace by updating their own velocity. The velocity update of a particle is dynamically adjusted, subject to its own past flight and those of its companions. The velocity and position of the particles are updated by the following equations:
(3.5)Vidnew(t+1)=co×Vidold(t)+c1×rand()×(pid(t)-xidold(t))+c2×rand()×(pgd(t)-xgdold(t)),(3.6)xidnew(t+1)=xidold(t)+Vidnew(t+1),(3.7)co=0.5+rand()3,where c1 and c2 are two positive constants; c0 is an inertia weight, and rand( ) is a random value between (0, 1). Zahara and Hu suggested c1 = c2 = 2 and c0 = [0.5 + (rand( )/2)] [15]. However, many experiments have shown that using c0 = [0.5 + (rand( )/3)] provides better results. Equation (3.5) illustrates the calculation of a new velocity for each individual. The velocity of each particle is updated according to its previous velocity (Vid), the particle’s previous best location (pid), and the global best location (pgd). Particle velocities for each dimension are clamped to a maximum velocity Vmax. Equation (3.6) shows how each particle’s position is updated in the search space.


### 3.4. NM-PSO Method

The NM-PSO optimization method [16] integrates the constraint-handling methods, the Nelder-Mead simplex search method (traditional algorithm), and the PSO algorithm (evolutionary algorithm) [17]. The PSO optimal method resists easily falling into the local best solution, but it requires many particles in an optimal process, which reduces the speed of computation. The Nelder-Mead simplex search method improves the efficiency of PSO due to its capacity for rapid convergence. However, the drawback of this method is that it easily falls into a local best solution. This drawback is improved by integrating the two algorithms. Combining the two algorithms and the gradient-based repair methods enables feasible optimal solutions to be found that satisfy the constraint conditions [18].Using the advantages mentioned above, the NM-PSO method clearly overcomes the drawbacks of low convergence speed, the need for more particles, and the inability to deal with constraint conditions to accurately find optimal solutions.


### 3.5. Implementation of Proposed Method

The following section introduces the NM-PSO algorithm procedure. Assume the problem to be solved isn-dimensional. First produce N(N≧2n+1) particles to form a swarm. For every particle that violates the constraints, use the gradient repair method to direct the infeasible solution toward the feasible region. In most cases, the repair method does move the solution to the feasible region. Arrange the results of the objective function in order of good to bad and divide the N particles into n particles, the (n+1)th particle, and N-(n+1) particles and then create three groups. First calculate the top n particles and the (n+1)th particle using the NM simplex method. The updated best particle is obtained and the result saved. The PSO method adjusts the N particles by taking into account the position of the (n+1) best particle. Through the calculation of a simple NM algorithm, the probability of finding the optimal solution was increased. This procedure for adjusting the N particles involves selection of the global best particle, the selection of the neighboring best particles, and finally the velocity updates. The global best particle of the population is determined according to the sorted fitness values.Unlike the original PSO calculation method proposed by [15], which updates the remaining particles (N-(n+1)), we use the PSO algorithm to update all of the N particles. These two PSO algorithms combination NM methods are referred to in this paper as the original NM-PSO method and the proposed NM-PSO method, respectively. Repeat the entire NM-PSO optimization process until the condition is fulfilled. Figure 2 depicts the schematic representation of the proposed NM-PSO. Algorithm 1 shows the pseudocode of the NM-PSO algorithm embedded within the constraint-handling methods.Algorithm 1:Pseudocode of the proposed hybrid NM-PSO algorithm.
1.Initialization. Generate a population of size N(N > (n + 1)).
Repeat
2.Constraint handling method
2.1The Gradient Repair Method.Repair particles that violate the constraints by
directing the infeasible solution toward the feasible region.
2.2 Identify solutions (that fulfill the constraint conditions) and arrange them in the
order of good to bad.
3.Nelder-Mead Method. Apply NM operator to the top n+ 1 particles and update the
(n + 1)th particle.
4.PSO Method. Apply PSO operator for updating the N particles.
4.1Selection.Select the global best particle and the neighborhood best particle from
the population.
4.2Velocity Update.Apply velocity updates to the N particles
until the condition is fulfilled.Figure 2
Flow chart of the proposed NM-PSO algorithm.


## 3.1. Constraint-Handling Methods

Constraint handling is a major concern when applying PSO algorithms to solve constrained optimization problems. This is because the traditional search operators of PSO algorithms are blind to constraints. Thus far, the most commonly used constraint handling methods for PSO are the penalty and repair methods.The gradient-based repair method was addressed by [10, 11]. This method adopts gradient information derived from the constraint set to gradually repair an infeasible solution by directing the infeasible solution toward a feasible area. Because the constraints of the DOCR coordination optimization are not complicated, this method is highly suitable. Furthermore, because DOCR coordination optimization has no equality constraints,equality constraint equations can be ignored. This method is described below.(1)
For a random solution, determine the degree of constraint violationΔV using the following equation:
(3.1)V=[g]m×1⇒ΔV=[-gj(x)]k×1whengj(x)>0,j=1,…,m,
where V is the vector of inequality constraints (g), and k is the degree of constraint violation ΔV.(2)
ComputeΔxg, where Δxg are the derivatives of these constraints with respect to the solution vector (n decision variables)
(3.2)ΔxV=[Δxg]k×n,x=1,…,k.(3)
The relationship between changes in the constraint violationΔVand the solution vector Δx is expressed as
(3.3)ΔV=ΔxV×Δx⟹Δx=ΔxV-1×ΔV.(4)
Compute the pseudoinverseΔxV-1.(5)
Update the solution vector by(3.4)xt+1=xt+Δx=xt+ΔxV-1×ΔV.The degree of constraint violation is adjusted according to the above procedure. In this algorithm, a “repair method” rapidly revises infeasible solutions to move them toward a feasible region. The number of constraint violations decreases and quickly vanishes with each iteration. Finally, a solution in the feasible region will be obtained.


## 3.2. The Nelder-Mead Simplex Search Method

When the search space isn-dimensional, the simplex consists of n+1 solutions [12]. As shown in Figure 1(a), in a two-dimensional search plane, a simplex is a triangle. The fitness of each solution is considered at each step of the Nelder-Mead method, and the worst solution Pworst is identified. The centroid, Pcent, of the remaining n points is computed, and the reflection of Pworst is determined. This reflection yields a new solution, Prefl, which replaces Pworst, as shown in Figure 1(b). If the solution Prefl  produced by this reflection has a higher fitness than any other solution in the simplex, the simplex is further expanded in the direction of Prefl, and Pworst is replaced with Pexp, as shown in Figure 1(c).Illustration of the Nelder-Mead simplex method.
(a)
(b)
(c)
(d)
(e)
(f)On the other hand, ifPrefl has a comparatively low fitness, the simplex is contracted. Contraction can either be outward or inward, depending upon whether Prefl is better or worse than Pworst, respectively. The contraction operations (i.e., Pworst is replaced with Pcont) are shown in Figures 1(d) and 1(e). If neither contraction improves the worst solution in the simplex, the best point in the simplex is computed, and a shrinkage is then performed; all the points of the simplex are moved a little closer towards the best solution (Pbest), as shown in Figure 1(f).


## 3.3. Particle Swarm Optimization

In the past several years, PSO has been successfully applied in many fields [13, 14]. It has been demonstrated that the results of PSO are superior to other methods. The PSO procedure is reviewed below.(1)
Initialization. It randomly generates a swarm of potential solutions called “particles” and assigns a random velocity to each.(2)
Velocity Update. The particles are then “flown” through hyperspace by updating their own velocity. The velocity update of a particle is dynamically adjusted, subject to its own past flight and those of its companions. The velocity and position of the particles are updated by the following equations:
(3.5)Vidnew(t+1)=co×Vidold(t)+c1×rand()×(pid(t)-xidold(t))+c2×rand()×(pgd(t)-xgdold(t)),(3.6)xidnew(t+1)=xidold(t)+Vidnew(t+1),(3.7)co=0.5+rand()3,where c1 and c2 are two positive constants; c0 is an inertia weight, and rand( ) is a random value between (0, 1). Zahara and Hu suggested c1 = c2 = 2 and c0 = [0.5 + (rand( )/2)] [15]. However, many experiments have shown that using c0 = [0.5 + (rand( )/3)] provides better results. Equation (3.5) illustrates the calculation of a new velocity for each individual. The velocity of each particle is updated according to its previous velocity (Vid), the particle’s previous best location (pid), and the global best location (pgd). Particle velocities for each dimension are clamped to a maximum velocity Vmax. Equation (3.6) shows how each particle’s position is updated in the search space.


## 3.4. NM-PSO Method

The NM-PSO optimization method [16] integrates the constraint-handling methods, the Nelder-Mead simplex search method (traditional algorithm), and the PSO algorithm (evolutionary algorithm) [17]. The PSO optimal method resists easily falling into the local best solution, but it requires many particles in an optimal process, which reduces the speed of computation. The Nelder-Mead simplex search method improves the efficiency of PSO due to its capacity for rapid convergence. However, the drawback of this method is that it easily falls into a local best solution. This drawback is improved by integrating the two algorithms. Combining the two algorithms and the gradient-based repair methods enables feasible optimal solutions to be found that satisfy the constraint conditions [18].Using the advantages mentioned above, the NM-PSO method clearly overcomes the drawbacks of low convergence speed, the need for more particles, and the inability to deal with constraint conditions to accurately find optimal solutions.


## 3.5. Implementation of Proposed Method

The following section introduces the NM-PSO algorithm procedure. Assume the problem to be solved isn-dimensional. First produce N(N≧2n+1) particles to form a swarm. For every particle that violates the constraints, use the gradient repair method to direct the infeasible solution toward the feasible region. In most cases, the repair method does move the solution to the feasible region. Arrange the results of the objective function in order of good to bad and divide the N particles into n particles, the (n+1)th particle, and N-(n+1) particles and then create three groups. First calculate the top n particles and the (n+1)th particle using the NM simplex method. The updated best particle is obtained and the result saved. The PSO method adjusts the N particles by taking into account the position of the (n+1) best particle. Through the calculation of a simple NM algorithm, the probability of finding the optimal solution was increased. This procedure for adjusting the N particles involves selection of the global best particle, the selection of the neighboring best particles, and finally the velocity updates. The global best particle of the population is determined according to the sorted fitness values.Unlike the original PSO calculation method proposed by [15], which updates the remaining particles (N-(n+1)), we use the PSO algorithm to update all of the N particles. These two PSO algorithms combination NM methods are referred to in this paper as the original NM-PSO method and the proposed NM-PSO method, respectively. Repeat the entire NM-PSO optimization process until the condition is fulfilled. Figure 2 depicts the schematic representation of the proposed NM-PSO. Algorithm 1 shows the pseudocode of the NM-PSO algorithm embedded within the constraint-handling methods.Algorithm 1:Pseudocode of the proposed hybrid NM-PSO algorithm.
1.Initialization. Generate a population of size N(N > (n + 1)).
Repeat
2.Constraint handling method
2.1The Gradient Repair Method.Repair particles that violate the constraints by
directing the infeasible solution toward the feasible region.
2.2 Identify solutions (that fulfill the constraint conditions) and arrange them in the
order of good to bad.
3.Nelder-Mead Method. Apply NM operator to the top n+ 1 particles and update the
(n + 1)th particle.
4.PSO Method. Apply PSO operator for updating the N particles.
4.1Selection.Select the global best particle and the neighborhood best particle from
the population.
4.2Velocity Update.Apply velocity updates to the N particles
until the condition is fulfilled.Figure 2
Flow chart of the proposed NM-PSO algorithm.


## 4. Case Study

The appearance and parameters of the relevant line equipment of two typical test systems are introduced. We discuss the fault current and the corresponding DOCR relationship of the coordination pairs of P/B when a close-in three-phase short fault occurs in transmission lines.Taking the above two test systems as examples, this study validated the feasibility of the proposed NM-PSO optimization algorithm to solve the DOCR optimal coordination problem. The results were compared with PSO and original NM-PSO algorithm. The results of the comparison demonstrate that the proposed NM-PSO algorithm is clearly better than PSO and original NM-PSO in terms of the objective function, the rate of convergence, and computation speed.In this study, the multiples2×n+1, 5×n+1, 10×n+1, and 20×n+1 were adopted as the number of populations to demonstrate the influence of the number of particles on the proposed algorithm. To observe the process and changes of convergence in the objective function, the number of iterations was set at 300, to highlight the superior performance of the proposed system.


### 4.1. IEEE 8-Bus Test System

As shown in Figure3, the 8-bus test system consists of 9 lines, 2 transformers, and 14 DOCRs. All the DOCRs have the IEEE standard inverse-time characteristics mentioned in (2.3) above. The system parameters are the same as in [6]. At bus 4, there is a link to another network modeled by a short-circuit capacity of 400 MVA. The DOCR coordination problem can be formulated as an LP problem or an MINLP problem. Additionally, there are 20 inequality constraints corresponding to each relay pair.Figure 3
One-line diagram for an IEEE 8-bus test system.Table1 illustrates the fault currents of the DOCR coordination pairs of P/B of each phase in the event of a close-in three-phase short fault of the system. If a DOCR coordination optimization problem with known Ip values is assumed to be an LP problem, the results obtained using PSO, original NM-PSO, and proposed NM-PSO for the case of 300 iterations and a population size of 141 (10 × n + 1, where n is the number of variables TDS of the 14 relays) are illustrated in Table 2. The results are also compared to those of Linprog (linear programming) obtained using the MATLAB optimization toolbox.Table 1
P/B relays and the close-in fault currents for an IEEE 8-bus test system.
Primary relay
Backup relay
No.
Current
No.
Current
1
3230
6
3230
8
6080
9
1160
8
6080
7
1880
2
5910
1
993
9
2480
10
2480
2
5910
7
1880
3
3550
2
3550
10
3880
11
2340
6
6100
5
1200
6
6100
14
1870
13
2980
8
2980
14
5190
9
1160
7
5210
5
1200
14
5190
1
993
7
5210
13
985
4
3780
3
2240
11
3700
12
3700
5
2400
4
2400
12
5890
13
985
12
5890
14
1870Table 2
Optimal settings of the relays for an IEEE 8-bus test system (LP problem).
Algorithm
Linprog
PSO
Original NM-PSO
Proposed NM-PSO
Relay
I
p
TDS
TDS
TDS
TDS
1
600
0.1007
0.1000
0.1000
0.1000
2
800
0.2485
0.2191
0.2260
0.2178
3
500
0.2294
0.2272
0.2369
0.2240
4
800
0.1115
0.1104
0.1234
0.1097
5
600
0.1003
0.1000
0.1075
0.1000
6
500
0.3858
0.3844
0.3882
0.3850
7
600
0.1103
0.1030
0.1233
0.1028
8
500
0.3575
0.3645
0.3587
0.3537
9
600
0.1001
0.1000
0.1007
0.1000
10
500
0.2947
0.3476
0.2963
0.2943
11
600
0.1794
0.2102
0.1958
0.1786
12
500
0.5591
0.6000
0.6194
0.5954
13
600
0.1007
0.1000
0.1000
0.1000
14
800
0.1094
0.1000
0.1030
0.1000
Obj-Fun
1.9640
2.0468
2.0278
1.9783To validate the feasibility of the proposed method, the obtained TDS values and knownIp values were entered as constraints to obtain the results shown in Table 3. Since the proposed method satisfies all constraints (i.e., CTI ≧ 0.2), the best coordination setting for DOCR can be efficiently completed.Table 3
Operating time of P/B relays for an IEEE 8-bus test system (LP problem).
Proposed NM-PSO method
Backup relay
Primary relay
Constraint value
No.
Operating time
No.
Operating time
6
0.3134
1
0.1130
0.2004
9
1.0422
8
0.1110
0.9312
7
0.3413
8
0.1110
0.2303
1
1.6338
2
0.1412
1.4926
10
0.3875
9
0.1875
0.2000
7
0.3413
2
0.1412
0.2001
2
0.3551
3
0.1551
0.2000
11
0.3762
10
0.1760
0.2002
5
0.9522
6
0.1203
0.8319
14
0.6439
6
0.1203
0.5236
8
0.3320
13
0.1313
0.2007
9
1.0422
14
0.0808
0.9614
5
0.9522
7
0.0515
0.9007
1
1.6338
14
0.0808
1.5530
13
1.6758
7
0.0515
1.6243
3
0.3585
4
0.1584
0.2001
12
0.3848
11
0.1578
0.2270
4
0.4000
5
0.2000
0.2000
13
1.6758
12
0.1943
1.4815
14
0.6439
12
0.1943
0.4496As expected, the proposed NM-PSO yields better objective function results than PSO and original NM-PSO. Figure4 shows that proposed NM-PSO nearly reached the global optimum after 189 iterations. The results of this proposed NM-PSO algorithm reveal better convergence.Figure 4
Convergence of PSO, original NM-PSO, and proposed NM-PSO to the optimal solution for an IEEE 8-bus test system (LP problem).To analyze the convergence consistency of the proposed NM-PSO algorithm when solving the LP problem in the case of different initial values, this study randomly performed the proposed method five times. As seen in Figure5, the proposed NM-PSO algorithm can reduce the objective function to the same value after nearly 200 iterations. The convergence of the proposed NM-PSO is evidently not affected by different initial values.Figure 5
Convergence of the NM-PSO for five different random initial populations for an IEEE 8-bus test system (LP problem).


### 4.2. IEEE 14-Bus Test System

The IEEE 14-bus test system consists of 5 generators, 2 power transformers, 20 transmission lines, and 40 DOCRs, as shown in Figure6. The system parameters are given in [19]. The voltage level and the power base of this system are 138 kV and 100 MVA, respectively.Figure 6
One-line diagram for an IEEE 14-bus test system.It is assumed that the DOCRs all have the standard IEEE inverse-time characteristics as an IEEE 8-bus test system. Table4 reveals the P/B relay pairs and the corresponding fault currents passing through them for a close-in fault in this network. There are 92 inequality constraints corresponding to each relay pair.Table 4
P/B relays and the close-in fault currents for an IEEE 14-bus test system.
Primary relay
Backup relay
Primary relay
Backup relay
Primary relay
Backup relay
No.
Current
No.
Current
No.
Current
No.
Current
No.
Current
No.
Current
1
11650
6
654
8
3880
30
188
19
955
17
955
5
12400
2
1980
29
4720
7
1220
18
725
20
725
2
4260
4
750
29
4720
9
1990
22
1930
29
499
2
4260
12
875
29
4720
13
1070
22
1930
24
1160
2
4260
8
723
29
4720
25
449
22
1930
32
280
3
7310
1
3920
6
3830
3
1280
23
1200
21
434
3
7310
12
848
6
3830
10
1990
23
1200
29
499
3
7310
8
689
6
3830
16
560
23
1200
32
281
11
7180
4
725
4
3920
5
1370
30
1810
21
424
11
7180
1
3920
4
3920
16
562
30
1810
24
1130
11
7180
8
695
4
3920
10
1990
30
1810
32
275
7
7330
1
3920
15
4610
5
1360
31
2060
21
428
7
7330
4
716
15
4610
3
1280
31
2060
24
1150
7
7330
12
845
15
4610
10
1970
31
2060
29
494
13
3280
11
1380
9
3260
5
1390
27
2030
26
1230
12
3130
14
1250
9
3260
3
1310
27
2030
23
808
26
4640
9
2080
9
3260
16
569
25
1430
28
633
26
4640
13
1120
16
1490
40
201
25
1430
23
806
26
4640
7
1270
16
1490
18
388
24
1870
26
1230
26
4640
30
179
16
1490
37
51
24
1870
28
634
10
3110
13
1140
17
2210
15
1110
37
572
35
572
10
3110
7
1290
17
2210
37
51
36
781
38
781
10
3110
25
495
17
2210
40
199
35
1480
33
368
10
3110
30
190
39
2400
15
1120
35
1480
39
1110
14
4030
9
2090
39
2400
18
389
34
1390
36
284
14
4030
7
1270
39
2400
37
47
34
1390
39
1110
14
4030
25
489
38
2530
15
1110
40
654
36
285
14
4030
30
188
38
2530
40
191
40
654
33
370
8
3880
9
2090
38
2530
18
386
32
547
34
547
8
3880
25
489
21
564
19
564
33
783
31
783
8
3880
13
1120
20
1310
22
1310
x
x
x
xThis study also used PSO, original NM-PSO, and proposed NM-PSO to solve the DOCR coordination optimization of the MINLP problem, which required obtaining the TDS andIp values of each DOCR. The results after 300 iterations with a population size of 1601 (20 × n + 1, where n is the number of TDS and Ip variables of the 40 relays) are shown in Table 5. The integer Ip can be directly applied in the current intelligent electronic device (IED) settings.Table 5
Optimal settings of the relays for an IEEE 14-bus test system (MINLP problem).
Algorithm
PSO
Original NM-PSO
Proposed NM-PSO
relay
I
p
TDS
I
p
TDS
I
p
TDS
1
881
0.1746
807
0.2024
736
0.3038
2
579
0.1000
515
0.1729
540
0.1211
3
408
0.2746
422
0.2108
437
0.1418
4
216
0.1239
261
0.1574
237
0.1184
5
758
0.1059
700
0.1860
700
0.1184
6
296
0.1607
227
0.2694
200
0.1020
7
532
0.2192
435
0.1187
419
0.1718
8
226
0.1335
206
0.1605
270
0.1452
9
444
0.1812
504
0.1454
537
0.1258
10
488
0.3347
528
0.1154
450
0.1523
11
477
0.1717
516
0.2881
550
0.1006
12
352
0.1015
295
0.2357
220
0.1414
13
394
0.1546
355
0.2212
350
0.1307
14
418
0.1000
362
0.2003
358
0.1250
15
333
0.1342
316
0.2404
359
0.1872
16
149
0.1451
126
0.2268
117
0.2302
17
216
0.3880
268
0.2414
177
0.3258
18
110
0.1172
101
0.1418
100
0.1301
19
164
0.2737
168
0.1379
108
0.3402
20
151
0.2322
170
0.1708
211
0.1057
21
100
0.3998
121
0.1308
115
0.1534
22
174
0.6243
339
0.1427
326
0.1473
23
119
0.5556
193
0.1457
150
0.2554
24
147
0.7269
307
0.1543
315
0.1437
25
133
0.2076
127
0.1483
102
0.3358
26
260
0.3107
351
0.1631
399
0.2024
27
150
0.1005
150
0.2364
150
0.1641
28
204
0.1230
127
0.3070
154
0.1779
29
245
0.2288
200
0.2564
200
0.2033
30
150
0.1000
100
0.2557
100
0.2124
31
241
0.1776
247
0.1765
164
0.2053
32
100
0.1066
100
0.1000
100
0.1001
33
177
0.1000
108
0.2252
100
0.1511
34
123
0.2518
100
0.2858
112
0.2285
35
100
0.3861
100
0.2349
100
0.3681
36
146
0.1132
121
0.1311
100
0.1300
37
36
0.1000
10
0.2869
11
0.3143
38
238
0.2182
245
0.1527
249
0.1892
39
268
0.2090
269
0.1850
266
0.1596
40
113
0.1000
100
0.2529
100
0.1485
Obj-Fun
4.2233
3.6362
3.1829Figure7 shows the results of the comparison demonstrate that the proposed NM-PSO algorithm is clearly better than PSO and original NM-PSO in terms of the objective function, the rate of convergence, and computation speed.Figure 7
Convergence of PSO, original NM-PSO, and proposed NM-PSO to the optimal solution for an IEEE 14-bus test system (MINLP problem).To analyze the consistency in convergence of the proposed NM-PSO when solving MINLP problems, this study randomly executed the proposed method five times. As seen from Figure8, the proposed NM-PSO can reduce the objective function to almost the same value after approximately 220 iterations. Results show that the convergence of the proposed NM-PSO is not seriously influenced by optimization problems of high complexity.Figure 8
Convergence of the proposed NM-PSO for five different random initial populations for an IEEE 14-bus test system (MINLP problem).In addition to convergence rate, we investigated the final convergence values of the objective function (Obj-Fun). Figures9(a) and 9(b) show the results of LP coordination problems, for the same number of iterations (300) and for four different populations 2 × n + 1, 5 × n + 1, 10 × n + 1, and 20 × n +1.Objective function values by PSO, original NM-PSO, and proposed NM-PSO algorithms for the LP problem withn=40 for four different populations.
(a)
IEEE 8-bus test system (LP problem)
(b)
IEEE 14-bus test system (LP problem)It can clearly be seen that the proposed NM-PSO method results in better Obj-Fun values than the PSO and original NM-PSO algorithm. For the more complicated MINLP problem shown in Figures10(a) and 10(b), the proposed NM-PSO after 300 iterations results in even better Obj-Fun values in the case of particles 2 × n + 1 than the Obj-Fun values of PSO algorithm in the case of particles 20 × n + 1. Hence, the proposed method produces better results than the PSO algorithm using fewer particles (less computation time).Objective function values by PSO, original NM-PSO, and proposed NM-PSO algorithms for the MINLP problem withn=80 for four different populations.
(a)
IEEE 8-bus test system (MINLP problem)
(b)
IEEE 14-bus test system (MINLP problem)


## 4.1. IEEE 8-Bus Test System

As shown in Figure3, the 8-bus test system consists of 9 lines, 2 transformers, and 14 DOCRs. All the DOCRs have the IEEE standard inverse-time characteristics mentioned in (2.3) above. The system parameters are the same as in [6]. At bus 4, there is a link to another network modeled by a short-circuit capacity of 400 MVA. The DOCR coordination problem can be formulated as an LP problem or an MINLP problem. Additionally, there are 20 inequality constraints corresponding to each relay pair.Figure 3
One-line diagram for an IEEE 8-bus test system.Table1 illustrates the fault currents of the DOCR coordination pairs of P/B of each phase in the event of a close-in three-phase short fault of the system. If a DOCR coordination optimization problem with known Ip values is assumed to be an LP problem, the results obtained using PSO, original NM-PSO, and proposed NM-PSO for the case of 300 iterations and a population size of 141 (10 × n + 1, where n is the number of variables TDS of the 14 relays) are illustrated in Table 2. The results are also compared to those of Linprog (linear programming) obtained using the MATLAB optimization toolbox.Table 1
P/B relays and the close-in fault currents for an IEEE 8-bus test system.
Primary relay
Backup relay
No.
Current
No.
Current
1
3230
6
3230
8
6080
9
1160
8
6080
7
1880
2
5910
1
993
9
2480
10
2480
2
5910
7
1880
3
3550
2
3550
10
3880
11
2340
6
6100
5
1200
6
6100
14
1870
13
2980
8
2980
14
5190
9
1160
7
5210
5
1200
14
5190
1
993
7
5210
13
985
4
3780
3
2240
11
3700
12
3700
5
2400
4
2400
12
5890
13
985
12
5890
14
1870Table 2
Optimal settings of the relays for an IEEE 8-bus test system (LP problem).
Algorithm
Linprog
PSO
Original NM-PSO
Proposed NM-PSO
Relay
I
p
TDS
TDS
TDS
TDS
1
600
0.1007
0.1000
0.1000
0.1000
2
800
0.2485
0.2191
0.2260
0.2178
3
500
0.2294
0.2272
0.2369
0.2240
4
800
0.1115
0.1104
0.1234
0.1097
5
600
0.1003
0.1000
0.1075
0.1000
6
500
0.3858
0.3844
0.3882
0.3850
7
600
0.1103
0.1030
0.1233
0.1028
8
500
0.3575
0.3645
0.3587
0.3537
9
600
0.1001
0.1000
0.1007
0.1000
10
500
0.2947
0.3476
0.2963
0.2943
11
600
0.1794
0.2102
0.1958
0.1786
12
500
0.5591
0.6000
0.6194
0.5954
13
600
0.1007
0.1000
0.1000
0.1000
14
800
0.1094
0.1000
0.1030
0.1000
Obj-Fun
1.9640
2.0468
2.0278
1.9783To validate the feasibility of the proposed method, the obtained TDS values and knownIp values were entered as constraints to obtain the results shown in Table 3. Since the proposed method satisfies all constraints (i.e., CTI ≧ 0.2), the best coordination setting for DOCR can be efficiently completed.Table 3
Operating time of P/B relays for an IEEE 8-bus test system (LP problem).
Proposed NM-PSO method
Backup relay
Primary relay
Constraint value
No.
Operating time
No.
Operating time
6
0.3134
1
0.1130
0.2004
9
1.0422
8
0.1110
0.9312
7
0.3413
8
0.1110
0.2303
1
1.6338
2
0.1412
1.4926
10
0.3875
9
0.1875
0.2000
7
0.3413
2
0.1412
0.2001
2
0.3551
3
0.1551
0.2000
11
0.3762
10
0.1760
0.2002
5
0.9522
6
0.1203
0.8319
14
0.6439
6
0.1203
0.5236
8
0.3320
13
0.1313
0.2007
9
1.0422
14
0.0808
0.9614
5
0.9522
7
0.0515
0.9007
1
1.6338
14
0.0808
1.5530
13
1.6758
7
0.0515
1.6243
3
0.3585
4
0.1584
0.2001
12
0.3848
11
0.1578
0.2270
4
0.4000
5
0.2000
0.2000
13
1.6758
12
0.1943
1.4815
14
0.6439
12
0.1943
0.4496As expected, the proposed NM-PSO yields better objective function results than PSO and original NM-PSO. Figure4 shows that proposed NM-PSO nearly reached the global optimum after 189 iterations. The results of this proposed NM-PSO algorithm reveal better convergence.Figure 4
Convergence of PSO, original NM-PSO, and proposed NM-PSO to the optimal solution for an IEEE 8-bus test system (LP problem).To analyze the convergence consistency of the proposed NM-PSO algorithm when solving the LP problem in the case of different initial values, this study randomly performed the proposed method five times. As seen in Figure5, the proposed NM-PSO algorithm can reduce the objective function to the same value after nearly 200 iterations. The convergence of the proposed NM-PSO is evidently not affected by different initial values.Figure 5
Convergence of the NM-PSO for five different random initial populations for an IEEE 8-bus test system (LP problem).


## 4.2. IEEE 14-Bus Test System

The IEEE 14-bus test system consists of 5 generators, 2 power transformers, 20 transmission lines, and 40 DOCRs, as shown in Figure6. The system parameters are given in [19]. The voltage level and the power base of this system are 138 kV and 100 MVA, respectively.Figure 6
One-line diagram for an IEEE 14-bus test system.It is assumed that the DOCRs all have the standard IEEE inverse-time characteristics as an IEEE 8-bus test system. Table4 reveals the P/B relay pairs and the corresponding fault currents passing through them for a close-in fault in this network. There are 92 inequality constraints corresponding to each relay pair.Table 4
P/B relays and the close-in fault currents for an IEEE 14-bus test system.
Primary relay
Backup relay
Primary relay
Backup relay
Primary relay
Backup relay
No.
Current
No.
Current
No.
Current
No.
Current
No.
Current
No.
Current
1
11650
6
654
8
3880
30
188
19
955
17
955
5
12400
2
1980
29
4720
7
1220
18
725
20
725
2
4260
4
750
29
4720
9
1990
22
1930
29
499
2
4260
12
875
29
4720
13
1070
22
1930
24
1160
2
4260
8
723
29
4720
25
449
22
1930
32
280
3
7310
1
3920
6
3830
3
1280
23
1200
21
434
3
7310
12
848
6
3830
10
1990
23
1200
29
499
3
7310
8
689
6
3830
16
560
23
1200
32
281
11
7180
4
725
4
3920
5
1370
30
1810
21
424
11
7180
1
3920
4
3920
16
562
30
1810
24
1130
11
7180
8
695
4
3920
10
1990
30
1810
32
275
7
7330
1
3920
15
4610
5
1360
31
2060
21
428
7
7330
4
716
15
4610
3
1280
31
2060
24
1150
7
7330
12
845
15
4610
10
1970
31
2060
29
494
13
3280
11
1380
9
3260
5
1390
27
2030
26
1230
12
3130
14
1250
9
3260
3
1310
27
2030
23
808
26
4640
9
2080
9
3260
16
569
25
1430
28
633
26
4640
13
1120
16
1490
40
201
25
1430
23
806
26
4640
7
1270
16
1490
18
388
24
1870
26
1230
26
4640
30
179
16
1490
37
51
24
1870
28
634
10
3110
13
1140
17
2210
15
1110
37
572
35
572
10
3110
7
1290
17
2210
37
51
36
781
38
781
10
3110
25
495
17
2210
40
199
35
1480
33
368
10
3110
30
190
39
2400
15
1120
35
1480
39
1110
14
4030
9
2090
39
2400
18
389
34
1390
36
284
14
4030
7
1270
39
2400
37
47
34
1390
39
1110
14
4030
25
489
38
2530
15
1110
40
654
36
285
14
4030
30
188
38
2530
40
191
40
654
33
370
8
3880
9
2090
38
2530
18
386
32
547
34
547
8
3880
25
489
21
564
19
564
33
783
31
783
8
3880
13
1120
20
1310
22
1310
x
x
x
xThis study also used PSO, original NM-PSO, and proposed NM-PSO to solve the DOCR coordination optimization of the MINLP problem, which required obtaining the TDS andIp values of each DOCR. The results after 300 iterations with a population size of 1601 (20 × n + 1, where n is the number of TDS and Ip variables of the 40 relays) are shown in Table 5. The integer Ip can be directly applied in the current intelligent electronic device (IED) settings.Table 5
Optimal settings of the relays for an IEEE 14-bus test system (MINLP problem).
Algorithm
PSO
Original NM-PSO
Proposed NM-PSO
relay
I
p
TDS
I
p
TDS
I
p
TDS
1
881
0.1746
807
0.2024
736
0.3038
2
579
0.1000
515
0.1729
540
0.1211
3
408
0.2746
422
0.2108
437
0.1418
4
216
0.1239
261
0.1574
237
0.1184
5
758
0.1059
700
0.1860
700
0.1184
6
296
0.1607
227
0.2694
200
0.1020
7
532
0.2192
435
0.1187
419
0.1718
8
226
0.1335
206
0.1605
270
0.1452
9
444
0.1812
504
0.1454
537
0.1258
10
488
0.3347
528
0.1154
450
0.1523
11
477
0.1717
516
0.2881
550
0.1006
12
352
0.1015
295
0.2357
220
0.1414
13
394
0.1546
355
0.2212
350
0.1307
14
418
0.1000
362
0.2003
358
0.1250
15
333
0.1342
316
0.2404
359
0.1872
16
149
0.1451
126
0.2268
117
0.2302
17
216
0.3880
268
0.2414
177
0.3258
18
110
0.1172
101
0.1418
100
0.1301
19
164
0.2737
168
0.1379
108
0.3402
20
151
0.2322
170
0.1708
211
0.1057
21
100
0.3998
121
0.1308
115
0.1534
22
174
0.6243
339
0.1427
326
0.1473
23
119
0.5556
193
0.1457
150
0.2554
24
147
0.7269
307
0.1543
315
0.1437
25
133
0.2076
127
0.1483
102
0.3358
26
260
0.3107
351
0.1631
399
0.2024
27
150
0.1005
150
0.2364
150
0.1641
28
204
0.1230
127
0.3070
154
0.1779
29
245
0.2288
200
0.2564
200
0.2033
30
150
0.1000
100
0.2557
100
0.2124
31
241
0.1776
247
0.1765
164
0.2053
32
100
0.1066
100
0.1000
100
0.1001
33
177
0.1000
108
0.2252
100
0.1511
34
123
0.2518
100
0.2858
112
0.2285
35
100
0.3861
100
0.2349
100
0.3681
36
146
0.1132
121
0.1311
100
0.1300
37
36
0.1000
10
0.2869
11
0.3143
38
238
0.2182
245
0.1527
249
0.1892
39
268
0.2090
269
0.1850
266
0.1596
40
113
0.1000
100
0.2529
100
0.1485
Obj-Fun
4.2233
3.6362
3.1829Figure7 shows the results of the comparison demonstrate that the proposed NM-PSO algorithm is clearly better than PSO and original NM-PSO in terms of the objective function, the rate of convergence, and computation speed.Figure 7
Convergence of PSO, original NM-PSO, and proposed NM-PSO to the optimal solution for an IEEE 14-bus test system (MINLP problem).To analyze the consistency in convergence of the proposed NM-PSO when solving MINLP problems, this study randomly executed the proposed method five times. As seen from Figure8, the proposed NM-PSO can reduce the objective function to almost the same value after approximately 220 iterations. Results show that the convergence of the proposed NM-PSO is not seriously influenced by optimization problems of high complexity.Figure 8
Convergence of the proposed NM-PSO for five different random initial populations for an IEEE 14-bus test system (MINLP problem).In addition to convergence rate, we investigated the final convergence values of the objective function (Obj-Fun). Figures9(a) and 9(b) show the results of LP coordination problems, for the same number of iterations (300) and for four different populations 2 × n + 1, 5 × n + 1, 10 × n + 1, and 20 × n +1.Objective function values by PSO, original NM-PSO, and proposed NM-PSO algorithms for the LP problem withn=40 for four different populations.
(a)
IEEE 8-bus test system (LP problem)
(b)
IEEE 14-bus test system (LP problem)It can clearly be seen that the proposed NM-PSO method results in better Obj-Fun values than the PSO and original NM-PSO algorithm. For the more complicated MINLP problem shown in Figures10(a) and 10(b), the proposed NM-PSO after 300 iterations results in even better Obj-Fun values in the case of particles 2 × n + 1 than the Obj-Fun values of PSO algorithm in the case of particles 20 × n + 1. Hence, the proposed method produces better results than the PSO algorithm using fewer particles (less computation time).Objective function values by PSO, original NM-PSO, and proposed NM-PSO algorithms for the MINLP problem withn=80 for four different populations.
(a)
IEEE 8-bus test system (MINLP problem)
(b)
IEEE 14-bus test system (MINLP problem)


## 5. Conclusions

In this paper, the DOCR coordination problem is formulated as a constrained optimization problem. It can be concluded that the proposed NM-PSO optimization algorithm is applicable to the DOCR coordination optimization of a distribution system. In contrast to other methods in the literature that only find TDS, the algorithm proposed in this study obtainsIp and TDS values simultaneously, and the Ip values can be represented by integers for applications in the IED setting to complete a more comprehensive coordination optimization. The proposed method makes use of the advantages of both the NM and PSO methods, while overcoming the drawbacks associated with these methods. Regardless of whether LP or MINLP is used to solve a coordination optimization problem, we have demonstrated that the proposed algorithm performs better than PSO and original NM-PSO algorithm in terms of computation speed, rate of convergence, and objective function value. The reduction in the DOCR operating time in our results demonstrates that the proposed method can be adopted for determining the optimum settings of DOCRs.



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*Source: 456047-2012-08-15.xml*