HEURISTIC BASED OPTIMAL PMU ROUTING IN KPTCL POWER GRID

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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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