HEURISTIC BASED OPTIMAL PMU ROUTING IN KPTCL POWER...

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International Journal of Electrical Engineering & Technology (IJEET)

Volume 7, Issue 1, Jan-Feb, 2016, pp.01-16, Article ID: IJEET_07_01_001

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HEURISTIC BASED OPTIMAL PMU

ROUTING IN KPTCL POWER GRID

V.Girish and A.V. Anitha

Karnataka Power Transmission Corporation Limited, Shimoga, India

Dr. T. Ananthapadmanabha

Department of Electrical Engineering,

National Institute of Engineering, Mysore, India

ABSTRACT

Power system monitoring is an important process in an efficient smart

grid. The control centers used in smart grid requires restructuring. State

measurements rather than state estimationare pre-requisite for the modern

control center. The Phasor Measurement Unit (PMU) measures the

synchronized voltage and current parameters. Placement of minimum number

of PMUs in a bus system such that the wholes system becomes observable is

considered as Optimal PMU Placement (OPP) problem. In this paper, Hybrid

Distance Optimization (HDO) algorithm is proposed to reduce the number of

PMUs for complete observability along with the minimum length of fiber optic

cable required for interconnecting the PMU nodes. Since Fiber optic is

invariably used for communication of PMU data, shortest distance for

interconnecting PMU nodes will result in minimum cost for creating an

efficient communication infrastructure, thereby reducing the cost for

establishing Wide Area Monitoring System (WAMS). The HDO algorithm

combines the three algorithms. Initially, Depth First Search (DFA) algorithm

finds the minimum number of nodes, where PMU needs to be placed, such that

the bus system becomes completely observable. Then, Dijkstra’s algorithm

calculates the shortest distance between the PMU nodes. Finally, Prim’s

algorithm constructs the minimum spanning tree that includes all PMU nodes,

wherein each PMU node can be reached from other with minimum distance

and this is the distance where fiber optic cable can be laid for effective

communication. This paper also considers the cost optimization problem in

two ways a) Finding the minimum length of fiber infrastructure required,

assuming no communication exists. b) Finding the minimum length of fiber

infrastructure required, considering already existing fiber optic connectivity

in the system. The proposed approach effectively optimizes the distance

between the PMU nodes there by decreasing the overall cost for establishing

WAMS. The OPP problem and their solution process tested on IEEE-6, IEEE-

V. Girish, A. V. Anitha and Dr. T. Ananthapadmanabha


7, IEEE 8, IEEE-9, IEEE-14, IEEE 24, IEEE-30, IEEE 39, IEEE 57, IEEE 118

bus systems and KPTCL power maps for 28, 127 and 155 bus systems by using

C language. The comparative analysis of distance measurement without and

with Fiber Optic (FO) cable confirms the effective optimization in distance

forstate measurement in smart grid system.

Index Terms: Dijkstra’s Algorithm, IEEE Bus system, Karnataka Power

Transmission Corporation Limited (KPTCL), Optimal PMU placement,

Particle Swarm Optimization (PSO), Phasor Measurement Unit (PMU), Prim’s

Algorithm, Wide Area Monitoring Systems (WAMS).

Cite this Article: V. Girish, A. V. Anitha and Dr. T. Ananthapadmanabha,

Heuristic Based Optimal PMU Routing In KPTCL Power Grid. International

Journal of Electrical Engineering & Technology, 7(1), 2016, pp. 01-16.

http://www.iaeme.com/IJEET/issues.asp?JType=IJEET&VType=7&IType=1

1. INTRODUCTION

Monitoring of power systems is an important process for secure performance. State

estimation in control centers provides an estimate of the electrical and network

parameters of the system and reduces the topology errors. Restructuring of systems is

a key function to design the control center in Modern Energy Management Systems

(EMS). The State Estimation (SE) is the necessary process in restructuring process.

The state estimators in the conventional method requires bus voltages, real and

reactive power flow and injections to measure the bus phasor in the system. The

Phasor Measurement Units (PMUs) determines the status of the system such as

system instability, disconnected lines converges with high accuracy.

PMUs measures the synchronized voltage and current parameters in real time

through the observability process. There are two types of observability such as

numerical and topological. The measurement of Jacobian is in full rank for numerical

observable. The iterative procedure of matrix operations in Jacobian calculation leads

to computational complexity. The interconnections of buses and the network

observability rules governs the topological observability of the power system. The

PMU measures the current phasors and provides the measurement for voltage phasors

to adjacent buses. Hence, PMU placement is not done for all the buses. The placement

problem denotes the enough measurements to reach the observable system. The

challenging task considers the optimum number of PMUs and configurations is

termed as Optimal PMU Placement (OPP) problem.

Several optimization methods are used to analyze the OPP problem

conventionally. They are Linear Programming (LP), dynamic programming or

combinatorial optimization and Non-Linear Programming (NLP). Various problems

are introduced in conventional optimization techniques like difficulties introduced in

trapping of local minima, constraint handling and numerical analysis. Hence,

combination of heuristic algorithms and meta-heuristic algorithms termed as

advanced heuristic algorithms are introduced to overcome the problems occurred in

conventional optimization techniques. The advanced approaches also considers the

branch outage, lack of communication in substation constraint, critical measurements

and fault observability.

Various heuristic approaches attacks the OPP problem. Chemical Reaction

Optimization (CRO) is one such Heuristic approach which yields the optimal

solutions for PMU placement. Simplified CRO reduces the execution time of process.

Heuristic Based Optimal PMU Routing In KPTCL Power Grid


The placement of PMU requires the identification of suitable location for PMU.

Based on graph theoretical approach, the decomposition technique identifies the

possible locations of PMU. The Artificial Bee Colony (ABC) algorithm achieves the

minimum number of PMUs. The error affects the optimal placement problem. The

Posterior Cramer Rao Bound (PCRB) reduces the error for effective placement. The

reliability of the system based on PMU placement is low in traditional approaches.

The multi-objective based optimization produces the improved reliability model of

PMU placement using Genetic Algorithm (GA).

The PMU measurement is the necessary task in Wide Area Network Monitoring

Systems (WAMS). The effective design of smart grid involves the WAMS to involve

the fast gathering of information and processing. The SE process enhances the

performance of WAMS. Research works provides Distributed approach for SE in

large area monitoring systems. More number of PMU placement in the network leads

to delay in communication due to maximum traffic. The communication delay

significantly affects the performance of WAMS system. Hence, minimum number of

optimal PMU requires to reduce the communication delay and increases the

performance of the system with maximum observability.

This paper considers the OPP problem and identifies the minimum number of

PMUs and minimum distance with maximum network observability by implementing

Hybrid Distance Optimization (HDO) algorithm in C language. Initially, the proposed

method searches the node with single connectivity. The PMU is placed at the node

adjacent to single connectivity node. Then, nodes with maximum connectivity are

selected for PMU placement in each iteration, until all nodes are obseravble. Then the

minimum distance between the PMU nodes is measured using a combination of

Dijkstra’s algorithm and Prim’s algorithm for two different cases.

Assuming no FO infrastructure exists in the bus system.

Considering the existence of FO infrastructure in the system

Finally, the number of PMU requires for network observability, distance between

the connected nodes are measured without and with fiber placement. The comparative

analysis between the distance measurement without and with Fiber Optic (FO) cable

shows that the optimization in distance. The optimal PMU placement proposed in this

paper applied to various bus systems such as on IEEE-6, IEEE-7, IEEE 8, IEEE-9,

IEEE-14, IEEE 24, IEEE-30, IEEE 39, IEEE 57, IEEE 118 bus systems and KPTCL

power maps for 28 bus, 127 bus and 155 bus systems. The contribution of proposed

work is to minimize the distance, number of optimal PMUs and cost with maximum

observability.

The paper organized as follows: The detailed description about the related works

on the requirement of optimal PMU problem and heuristic approaches to handle the

OPP problem in section 2. The implementation process of Hybrid Distance

Optimization (HDO) in section 3. The performance analysis on parameters such as

number of PMU required, location for PMU and the distance between them without

and with Fiber Optic (FO) cable in section 4. Finally, the conclusions about the

application of heuristic approaches on optimal PMU placement presented in section 5.

2. RELATED WORK

This section presents the detailed description about the traditional research works on

Optimal PMU Placement (OPP) problem and various heuristic approaches to find the

solution of OPP. Computerized power system applications contains the General



Processing Systems (GPS) with the sampled data led to the development of Phasor

Measurement Unit (PMU). Manousakis et al presented the detailed literal review of

Optimal PMU Placement (OPP) problem and the various heuristic and meta-heuristic

approaches [1, 2]. They categorized the solution methodologies of OPP problem into

three such as mathematical, heuristic and meta-heuristic algorithms. The objective of

OPP problem is to provide the minimal set of PMUs were used with maximum

observability. Design of high informative PMU was an important task in the Energy

Management Systems (EMS). Li et al presented the information theoretic approach,

which used Mutual Information (MI) between the PMU measurements and states of

power systems. The MI criterion optimized the PMU placement to ensure the high

informative PMU [3]. Three parametric computations were necessary in power

system state estimation. They were Convergence, Observability and Performance

(COP). Li et al presented the frame work for the placement of PMU and enhanced the

hybrid state estimation. They formularized OPP problem as a Semi Definite

Programming (SDP) and solved by using the constraints that guarantee the

observability [4]. The reliability of electrical power system ensured by two processes

such as wide area monitoring and observability of state variables. The optimal PMU

placement is an important requirement to carry out the monitoring and observability

process with considerable cost. Mousavian et alproposed the Integer Linear

Programming (ILP) model for optimal PMU placement in two phases. PMUs installed

to achieve the full observability in one phase and N-1 observability in second

phase[5].

The contingencies introduced in power system affects the observability

performance. Azizi et al used the ILP based framework to efficiently reduce the

number of PMUs with conventional measurements. They also provided the smooth

transition from Supervised Control and Data Acquisition (SCADA) to PMU based

Wide Area Monitoring Systems (WAMS)[6]. PMUs were the important unit in Wide

area systems to acquire the high accuracy and time synchronized process in smart

grid. Miles et al and monitoring the Phasor Data Concentrators (PDC) installed in

power systems. The PDC used in power system were expensive in order to build the

high bandwidth WAMS network [7, 8]. The robustness to the missing data improved

in traditional approaches. He et al used online Dynamic Security Assessment (DSA)

to mitigate the impact of missing data. They used the random sub-space method to

train the multiple small Decision Tree (DT) [9]. The reliability of communication

network maximized with the suitable selection of relative locations of Phasor

Measurement Unit (PMU) and Phasor Data Concentrators (PDC). Fesharaki et al

developed an organized method for partitioning WAMS and used a new algorithm for

optimal placement of PMU and PDC [10].

Numerical optimal guarantee is an important criterion for PMU placement.

Kekotas et al presented the convex based relaxation approach to improve the

guarantee of optimal placemen. On the basis of state estimation used in grid

monitoring, they optimized PMU placement by estimation theoretic approach [11,

12]. The hierarchical based methods suffered by several factors such as local

observability of all control areas required, same communication topology as physical

topology and coordinator was required for state estimation. Xie et al presented the

fully distributed state estimation methods[13] for WAMS. They utilized information

sharing approach among the neighboring nodes to achieve the unbiased state estimate

of power system. Hence, the proposed fully distributed method reduces the factors of

hierarchical methods. Wide Area Monitoring, Protection and Control (WAMPC)

counteract the local disturbances before propagating. Fadiran et al presented the multi



criteria ILP, which accommodated three categories of applications like fault analysis,

voltage control and state estimation. An optimal PMU placement using multi criteria

ILP was achieved [14]. Xu et al used the novel meta-heuristic technique such as

Chemical Reaction Optimization (CRO) to analyze the problem of size of PMU and

their placement. They proposed Simplified CRO (SCRO) for OPP problem. They

tested the observability of the network using SCRO and traditional CRO [15].

Research works shifted to consideration of OPP problem in order to minimize the

number of PMUs with maximum number of observable nodes.

Liao et al presented the hybrid two phase methods for OPP problem. The possible

locations of PMU were identified by decomposition technique based on graph-

theoretic approach in the first phase and reduced the number of PMUs by novel

optimization technique Artificial Bee Colony (ABC) algorithm [16, 17]. The power

system state estimation required synchronization between linear measurements. The

synchronization was not perfect in practical systems. Yang et al derived the Cramer

Rao bound on estimation error to provide the synchronization. They also used the

Greedy algorithm for PMU placement based on bound values. The objective functions

for PMU placement problem sub modular to provide the guarantee the optimal

placement [18, 19]. The two conflicting objectives for PMU placement were

maximization of reliability and observability and minimization of number of PMU.

Khiabani et al formulate the multi-objective problem as a non-linear optimization

problem and solved the large scale bus systems by using the Genetic Algorithm (GA).

The application of GA based approaches to the optimal PMU placement reduced the

reliability of the electric power system [20].

The coordinated attacks on power readings were not detected by the data detection

algorithm used state estimation algorithm. Giani et al used an efficient data detection

algorithm and the unobservable attacks were detected. The neutralization of cyber-

attacks carried out by using the detection algorithm [21]. The assumption in OPP

problem was that the PMU units measured the all voltage and current phasors. But, in

practical, the placed PMU was not measured all current phasors of the line due to

limited number of channels availability. Abiri et al investigated the effect of channel

capacity of optimal placed PMU. They extended the conventional formulation of OPP

problem for complete observability on single PMU loss [22]. The realistic assumption

restricted to the channel capacity against simple infinite models. Fan et al considered

various optimization models and considered the realistic assumptions for OPP

problem. The relationship between three problems such as PMU Placement Problem

(PPP), classic combinatorial problem and Set Cover Problem (SCP) were identified

[23]. The dependence between WAMS systems and high performance systems

specified with the help of characteristics of communication delays for multiple PMUs.

Chenine et al included the Phasor Data Concentrator (PDC) that collected and

arranged the data from PMU in hierarchial order. The configuration of central nodes

were optimized on the basis of collected data [24]. The vision of smart grid contained

many standardized wired and wireless communication. But the wireless technologies

offered various benefits included the low installation cost, mobility and suitability in

remote applications. Parikh et al presented the various wireless applications and the

challenges were discussed [25].

The real time data delivery provided and security issues were handled by fast

communication infrastructure. The design of smart grid significantly depended on fast

communication infrastructure. The placement of PMU in everywhere of smart grid

leads to more critical issues. Kansal and Bose presented the simulation approaches to



various critical security issues. They considered latency and bandwidth among the

security issues and the communication requirements for power grid applications such

as design, simulation were formulated [26, 27].Huang et al presented the model that

contained set of binary decision variables for PMU to utilize the communication links.

The decision variables were solved and the expected cost minimized. Initially, the

decision variables were chosen according to the solution of PMU placement such that

whether at a bus or between two buses. Then, the solution of decision variables in

PMU placement were derived [28]. The optimized Phasor Measurement System

(PMS) required to minimize the cost by using the optimized Phasor Data

Concentrators (PDC). Rincon et al considered different scenarios in minimizing the

cost of PMU such as length and number of PDUs required to construct the optimized

model [29]. The enhanced design of WAMS provided the intelligent monitoring,

control and protection of power grid. Mohammadi et al presented the new method for

optimization of cost of optimal PMU placement. They also used the Dijkstra’s single

source shortest path algorithmto obtain the minimum Communication Infrastructure

(CI) cost [30]. Janamala et al relieved the congestion in power system devices

discussed with the utilization of FACTS devices such as Unified Power Quality

Conditioners (UPFC) in suitable locations [31]. The voltage regulation and power loss

in power systems required the optimized location and size of Dispersed Generation

(DG) by the heuristic two step method [32]. The contributions of this proposed

method are minimization of distance between the connected and cost. For that, the

traditional distance measurement (Depth First Search, Dijkstra’s algorithm, Prim’s

algorithm) grouped by Hybrid Distance Optimization (HDO) in this paper.

3. HYBRID DISTANCE OPTIMIZATION

This section presents the detailed description for proposed Hybrid Distance

Optimization (HDO) algorithm implementation for Optimal PMU Placement (OPP)

problem. The block diagram of proposed system as shown in fig. 1.

Figure 1 Block diagram of HDO



The implementation of proposed optimal PMU placement consists of three

processes namely,

Location of PMU node

PMU node selection

Minimum distance estimation

Initially, the location of nodes for optimal PMU placement is predicted by using

the Depth First Search (DFS) algorithm. The DFS algorithm chooses a node adjacent

to single connectivity node and later, from among nodes it chooses the node having

maximum connectivity. The step is iterated until the complete bus system becomes

observable. Then, the minimum distance between PMU nodes are estimated through

Dijkstra’s algorithm. Finally, the Prim’s algorithm extracts the PMU nodes in order to

connect all the PMU nodes, so that FO cable can be laid in this minimum path. The

comparison between distance with and without fiber optic placement yields the

minimum length of fiber optic cable required, considering the existence and non-

existence of FO cable in the network. The maximum distance leads to increase in the

length of FO cable required and hence the cost. The proposed algorithm effectively

reduces the distance between PMU nodes. Hence, the optimal placed PMU with minimum distance between each other leads to reduction of cost and also the time for

data communication. The flow diagram for proposed Hybrid Distance Optimization

(HDO) for optimal PMU placement with fiber optic cable is shown in fig. 2.

The proposed Hybrid Distance Optimization (HDO) performs three heuristic

algorithms sequentially to determine the Optimal PMU Placement (OPP) and

minimum FO cable infrastructure required as follows:

Depth First Search (DFS)

Dijkstra’s Algorithm

Prim’s Algorithm

The proposed algorithms applied on the grid consists of following Karnataka

Power Transmission Corporation Limited (KPTCL) bus system as follows:

KPTCL-28 Bus system (28 nodes of 400 & 765kV network of Karnataka state)

KPTCL-127 Bus system (127 nodes of 220kV network of Karnataka state)

KPTCL-155 Bus system (155 nodes of combined 220kV, 400kV & 765kV network

of Karnataka state).

3.1. Hybrid Distance Optimization Algorithm

The distance measurement between the nodes is a necessary process in the state

estimation process. The Hybrid Distance Optimization (HDO) algorithm proposed in

this paper finds the optimal placement for PMU. The nodes and the connections are

given as the input to the HDO. The implementation proposed HDO algorithm is

shown as follows:

Step 1: Selection of node with minimum connectivity min_c by using Depth First

Search (DFS) algorithm

Step 2: Place of PMU on the node adjacent to min_c node.

Step 3: Check the connection between PMU node PMU_node and other nodes.

Step 4: If connection is exists, then the nodes regarded as observable nodes

(Obs).Otherwise, repeat step 3.



Step 5: The distance between PMU node and other nodes are listed in distance matrix

by using Dijkstra’s algorithm.

Step 6: From the coefficients of distance matrix, the minimum spanning tree refers

the distance for Fiber Optic (FO) estimated by using Prim’s algorithm.

The cost matrix is computed on the basis of existence and non-existence of fiber

optic cable by using the results from depth first search algorithm. The distance

between the PMU nodes to other nodes in the bus system for fiber optic cable stored

as a coefficients of cost matrix. The final minimal distance recognized as required

output distance for optimal PMU placement with maximum observability.

3.2. Location of PMU nodes

One of the tree search method used to find the location of PMU nodes is Depth First

Search (DFS) algorithm. The searching process involves three rules as follows:

For Depth First Search (DFS) algorithm the connections between the nodes are

tabulated in binary matrix. The algorithm predicts the node with single connectivity.

Figure 2 Flow diagram of HDO algorithm

The adjacent node to single connectivity node is the required node for PMU

placement. Then, the nodes with maximum connectivity are considered for PMU

placement. The chronological selection is made if more than one bus contains same

number of maximum connections. The connections from PMU nodes are identified

and the corresponding nodes are recognized as observable nodes. The binary table

gets updated correspondingly in each iteration until all the nodes are observable. The

DFS method expands the PMU placement to pseudo measurement voltage and current

measurement. The expanded nodes create the metric tree that contains the observable

nodes. Hence, topology observability is achieved. The algorithm for DFS as shown in

fig. 3.



Figure 3 Depth First Search

3.3. PMU node selection

The shortest path between the PMU nodes to other nodes is calculated by using

Dijkstra’s algorithm. Initially, the distance corresponding to link assigned as infinity.

This implies that the link is not visited. The current link denotes the distance between

the PMU node and the node available on the link considers as zero in first iteration.

The sum of distance between the unvisited links to current link is calculated and

update the distance of the node connected to it. Then, the unvisited link is labelled

with the new calculated distance value and compare the distance with current value in

order to choose the minimum distance. The unvisited link is relabeled with the

shortest distance continuously until the destination is reached. The shortest path is

computed when the destination is reached. The flow chart for Dijkstra’s algorithm is

shown in fig. 4.

Figure 4 Dijkstra’s algorithm

3.4. Minimum distance estimation

The distance between the PMU nodes to other nodes need to be optimized to reduce

the cost with high observability. The fiber optic cable is used to make the connection

between the nodes. Hence, the distance between the PMU connected nodes minimized

by using the minimum spanning tree. The sub-graph of the graph, which contains all



nodes termed as spanning tree. The minimum weight of edges required to construct

the minimum spanning tree. Prim’s algorithm is used for construction of minimum

spanning tree to identify the nodes which can be connected using FO.

Initially, the number of PMU connected nodes generates the N minimum spanning

trees. The PMU nodes in the tree replaced with fiber optic connected PMU buses. The

observability is checked for each PMU connected buses. Finally, the minimum

distance corresponds to maximum observability with fiber optic placement is stored

as the required distance. Hence, the proposed algorithm efficiently considered the

Optimal PMU Placement (OPP) problem and reduction of distance leads to cost

reduction in power system. The flow chart for prim’s algorithm as shown in fig5.

Figure 5 Prim’s algorithm

The bus system considered for optimal PMU placement is IEEE 14 bus system is

shown in fig.6

Figure 6 IEEE 14 bus system



The optimal PMU placement for IEEE 14 bus system is shown in fig. 7. The

dotted lines represents the existing connections between the buses and the arrow lines

represents the respective buses are observable by PMU. The number of PMU requires

for an IEEE bus system are 4 and they are placed in 2, 6, 7, and 9. The total number of

nodes are observable are 14.

Figure 7 Optimal PMU placement in IEEE 14 bus system

The optimal PMU placement for KPTCL 765kV/400kV 28 bus system is shown

in fig. 8. The dotted lines represents the existing FO connections between buses. The

number of PMU requires for a KPTCL 765kV/400kV 28 bus system are 7 and they

are placed in 2, 7, 10, 11, 17, 18, and 25. The total number of nodes are observable

are 28.

Figure 8 Optimal PMU placement in KPTCL 765kV/400kV 28 bus system.

4. PERFORMANCE ANALYSIS

The algorithms proposed in this paper to obtain the optimal PMU placement for IEEE

and Karnataka Power Transmission and Corporation Limited (KPTCL) and analysis

the parameters such as distance for two cases such as without considering fiber optic



cable and with fiber optic cable. The location and number of PMUs are listed by using

DFS shown in table I.

Table I Location of PMU

Bus system No. of PMUs Location of PMUs

IEEE 6 2 2,5

IEEE 7 2 2,4

IEEE 8 2 2,4

IEEE 9 3 4,8,6

IEEE 14 4 2,6,7,9

IEEE 24 8 1, 2, 8, 9, 11, 15, 17, 20

IEEE 30 10 1, 2, 6, 9, 10, 12, 15, 18, 25, 27

IEEE 39 12 12, 16, 19, 20, 22, 23, 25, 29, 30 31, 34, 37

IEEE 57 18 1, 4, 9, 11, 15, 20, 24, 25, 26, 29, 32, 34, 37, 38,

46, 50, 53, 56

IEEE 118 36

2, 5, 9, 11, 12, 17, 20, 23, 25, 27, 28, 32, 34, 37,

40, 45, 49, 50, 51, 52, 59, 61, 62, 68, 71, 75, 77,

80, 85, 86, 89, 92, 94, 100, 105, 110

KPTCL 28 7 2, 7, 10, 11, 17, 18, 25

KPTCL 127 38

1, 4, 6, 9, 11, 15, 17, 21, 24, 27, 30, 33, 36, 38,

44, 46, 52, 54, 56, 58, 61, 64, 67, 68, 79, 80, 84,

86, 90, 93, 97, 99, 101, 103, 105, 109, 115, 123

KPTCL 155 47

1, 4, 6, 9, 11, 15, 17, 21, 24, 27, 30, 33, 36, 38,

44, 46, 50, 52, 54, 56, 58, 61, 64, 67, 68, 70, 78,

79, 80, 84, 86, 90, 93, 97, 99, 101, 103, 105,

109, 115, 123, 129, 134, 138, 144, 145, 152

The distance between the nodes of KPTCL bus system are available. Hence, the

analysis considered KPTCL bus system since the distance between nodes in IEEE bus

system are not available in real time. The selected path between PMU nodes to other

PMU nodes without fiber optic cable for KPTCL 28 bus system is shown in table II.

Table II Minimum distance between PMU nodes with other PMU nodes (without FO cable)

Edges Nodes Selected path

1 (2, 25) 2->24->25

2 (2, 7) 2->1->7

3 (7, 11) 7->8->11

4 (11, 17) 11->14->17

5 (17, 18) 17->18

6 (11, 10) 11->10

Table II describes the path between the PMU nodes (2, 7, 10, 11, 17, 18, and 25)

for KPTCL 28 bus system. Dijkstra’s algorithm initially forms the matrix that

contains the distances between the each PMU node to other nodes. Then, the matrix

coefficients are updated and identified the distance between the each PMU nodes to

other PMU nodes. The laying of cables to cover the distance of each path as shown in

the table. The total distance to connect all PMU nodes is 953 km for KPTCL 28 bus

system. Hence, the cost of laying cables between the nodes are maximum. The

distance between PMU nodes are further minimized to reduce the cost.

Further the nodes with existing Fiber Optic (FO) cable requires the additional

connection. The input for corresponding connected nodes are set as zero in the Prim’s

algorithm. Then, this algorithm constructs the minimum spanning tree for optimal



PMU placement. The minimum distance between PMU nodes to other PMU nodes

with fiber optic cable for KPTCL 28 bus system is shown in table III.

Table III Minimum distance between PMU nodes with other PMU nodes (with FO cable)

Edges Nodes Selected path

1 (2, 7) 2->1->7

2 (2, 10) 2->1->7->8->10

3 (2,11) 2->1->7->8->11

4 (2, 17) 2->1->7->8->11->14->17

5 (2, 18) 2->1->7->8->11->15->16-

>18

6 (2, 25) 2->24->25

Table- III describes the distance between each PMU node to other PMU nodes.

The existence of fiber optic cable denoted as zero in the input matrix of Prim’s

algorithm. The algorithm computes the minimum spanning tree, which contains the

nodes with minimum distance. For example, the path between the nodes 2 and 7 be

(2->1->7). The fiber optic cable connects the 2->1 and 1-> 7. Hence, the distance

value treated as zero. The overall minimum distance between PMU nodes are

effectively reduces to zero there by reducing the cost and the time for communication.

The proposed algorithms are also applied for other KPTCL 127 and 155 bus system

using similar procedure and the distance are calculated.

The comparative analysis between the measured distance for without and with

fiber optic cable in KPTCL 28, 127 and 155 bus system listed in table IV.

Table IV Comparative analysis

Network Without FO cable (km) With FO cable (km)

KPTCL 28 bus system 953 0



The comparative analysis between the distance between PMU nodes without and

with Fiber Optic (FO) cable is depicted in fig. 9.

Figure 9 Comparative analysis

Fig. 9 provides the comparison between the distance between PMU nodes for

KPTCL 28, 127 and 155 bus system. The proposed algorithms effectively reduces the

distance with by laying of Fiber Optic (FO) cable. The reduction in distance reduces

the cost of installation and the time for communication between PMU nodes and other



nodes. Hence, the Optimal PMU Placement (OPP) problem solved and minimum

number of PMU placed with maximum observability of the system. The state

estimation process of smart grid simplified by using proposed algorithms.

5. CONCLUSION

In this paper, Hybrid Distance Optimization (HDO) proposed to reduce the distance

and number of PMU with high observabilty. Initially, Depth First Search (DFA)

algorithm detected the location of PMU nodes in bus system. Then, Dijkstra’s

algorithm calculated the shortest distance between the nodes and selected the path

corresponds to distance. Finally, Prim’s algorithm constructed the minimum spanning

tree that contains the PMU nodes with minimum distance. This paper also considered

the OPP problem in two ways such as without optical fiber and with fiber. The

proposed approach effectively optimized the distance between the PMU nodes there

by decreased the cost of PMU placement. The OPP problem and their solution process

tested on IEEE-6, IEEE-7, IEEE 8, IEEE-9, IEEE-14, IEEE 24, IEEE-30, IEEE 39,

IEEE 57, IEEE 118 bus systems and KPTCL power maps for 28 bus, 127 bus and 155

bus systems. The comparative analysis between the proposed PMU placements

confirmed the effective optimization in state estimation for smart grid system.

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