A Framework for Placement Assessment of Synchrophasor [614962]

A Framework for Placement Assessment of Synchrophasor
Measurement in Practical Power Grid : A Case Study from Borneo

AHMED M. A. Haidara, HENG WEI Haub

aUniversiti Malaysia Sarawak, Department of Electrical and Electronic s, Faculty of Engineering, Malaysia
94300 Kota Samarahan, Sarawak, Malaysia , [anonimizat]
bUni-Kenyalang Engineering SDN. BHD, Malaysia
93350, Kuching, Sarawak, Malaysia
Abstract— Security control of electricity networks has
always been a key issue in the power industry development .
An important approach towards full observability of power
system is by means of using the phasor measurement u nit
(PMU) . The consideration when applying PMU in power
grid is the proper selection of its location . Therefore, an
optimal location has to be identified in order to minimize the
number of installed units, as it is not economically viable to
place PMU at each bus. Firstly, this paper reviews the
method s used for PMU placement. Further, the paper
proposes a framework to evaluate the optimal location s of
PMUs in a practical power grid consisting of 36 buses. The
power grid has been modeled by taking into account the
change in system configuration. Different o ptimal PMU
placement (OPP) methods have been utilized to determine
the best location with the lowest number of installed PMUs .
The implemented framework for solving a practical problem
using a classic al approach has proven to be ideal in terms of
ensuring the complete observability of the power system
under single and multiple transmission line outages .

Keywords: Phasor Measurement Unit , PMU placement
rules, Power grid observability , Single and multiple l ine
outage s.

I. INTRODUCTION

Phasor measurement u nit (PMU) is a synchrophasor
technology that is able to measure the magnitude and
phase angle of voltage and current as well as frequency
and the rate of its change. The use of PMU for effective
measurement becomes possible due to the advancement
in global positioning s ystem (GPS) technology in
addition to the development of digital signal processing.
Indeed, PMU is superior as compared to supervisory
control and data a cquisition (SCADA) in state
estimation for various aspects such as system
monitoring, security control and system protection
including detection of fault location, contingency
analysis, model validation, stability analysis, etc. This is
owing to the fact that SCADA can only perform
measuring the magnitude of voltage and current whereas
PMU can measure both magnitude and phase a ngle with
much higher sampling rate as compared to SCADA.
PMU is being widely used in many countries for
precise measurem ents of magnitude and phase angle
(voltage and current ) including the frequency and its rate
of change. The samples are time aligned by using GPS clock that allows accurate arrangement of data in the
control center of the power grid [1]. The use of
synchrophasor has been increasing since 2004
particularly, after the Northeast blackout s on 14th and
15th of August 2003 in the United States and Canada .
The investigation report states that blackouts occurred
due to the lack of awareness by grid operators about the
power system condition as it led to cascading outage [2].
The report recommended using effective synchrophasor
technologies to provide wide area monitoring in real
time for minimizing the blackouts.
Traditionally, SCADA plays a significant role in
planning , monitoring and control of power system .
SCA DA systems consist of numerous remote terminal
units ( RTU). These units are microprocessors controlled
devices used to control and collect data from sensors
situated at the remote site s and transfer the data back to
the central unit . Such functions include monitor ing and
control of transformer tap changer as well as circuit
breakers and re -closers. Since the 1960s, SCADA has
been used to monitor power grids. However, the growing
number of outages indicates that SCADA systems have
now reached their capability limits, as they are not able
to measure phase angles and can only obtain data once
every 4 –6 seconds. With such low data sample rate,
major power utilities have now shifted their focus on
deploying PMUs in power system .
The interfacing system of RTU with sensors is
unable to collect voltage and current phase angles in
power systems. These p hasor values are important in
determining the power flow, stability limits and resulting
load current. Furthermore , monitoring of transient
phenomena cannot be achieved using SCADA systems
operated based on quasi -steady -state power flow
analysis [3]. In other words, t he low sample rate of
SCADA with data obtained over few seconds may cause
an insufficient n umber of measurement s to be taken with
respect to time, resulting in both telemetr y errors and
measurement bias [4]. Therefore, i n modern power
systems, synchrophasor technologies have become the
main choice of measurement units for the power grid .
The supremacy of synchrophasor technologies over
SCADA systems lies in the capability of PMU to
synchronize voltage and current measurements within
microseconds because of the GPS availability as well as
the development of data processing techniques [5].

Nowadays, reliability has become more important
especially in the modern bulk transmission system. By
analyzing synchrophasor data, an early indication of
power system problems can be detected. This allows the
power grid operators to take preventive steps and
mitigation measures to minimize the duration and
severity of outages. In this case, the system restoration
can be achieved in a shorter time. With advanced
software applications , the full potential of synchrophasor
technologies can be realized in both online and offline
applications. PMU is also widely used for state
estimation, wide area monitoring, islanding and control
as well as for fault classification . State estimation is
important for various power system analysi s such as
optimal power flow, cont ingency analysis, stability
analysis, load forecasting [6], [7], [8]. The solvers of
state estimation in control centers of power grids provide
optimal estimates of real time operating state by using
sets of conventional measurements. These measurements
are traditionally obtained through SCADA system. As
the reliability of power system requires fast and accurate
estimation of the system condition, the measurements
can also be performed using PMU , as it is able to
provide synchronized data at high speed that definitely
improves the state estimation performance [9].
Certainly, the power system network can be said
observable if the condition of each part in the system is
recognizable either directly or indi rectly. It is possible to
make the system fully detectable by placing PMU in
each bus. However, installing the PMU s in all buses is
not economically viable, since the PMU is the most
expensive part in the protection system . On the same
note, PMU installation in some substation s may not be
possible due to the lack of communication devices ,
security and control facilities [10]. Therefore, it is
critical to identify the best location of PMU that mainly
depends on the configuration of the power system .
Numerous OPP methods have been developed since
the introduction of PMU . The notion of spanning tree
was extended in [3] to find through a dual search
algorithm the minimal PMU set. The concept of depth –
of-unobservability was applied in [11] to reduce the
required number of PMUs for achieving complete
observability. An integer quadratic pr ograming method
was proposed in [12] to maximize the redundancy of
measurement at the power grid bus. Authors in [13]
introduced stochastic simulated annealing for solving
optimal PMU placement. Unlike [13], the authors in [14]
proposed a two -stage PMU placement method. In this
approach, the first stage finds the minimum number of
units while the second stage check s if the identified
placemen t lead s to a full ranked measurement Jacobian.
In recent years, several research studies have been
carried out to develop methods for minimizing the
number of installed PMUs in the power system. For
instance, an adaptive scheme for wide area backup
protectio n has been proposed in [15] to limit the number
of synchronized phasor measurements . The schem e can
be realized if the grid is equipped with advance d
communication infrastructure . Authors in [16] used binary particle swarm optimization for the installations
of PMU s in a large -scale network . In this approach, a
practical solution has been implemented by minimizing
the number of substations in which the PMUs have to be
installed . To reduce the omission of optimization in a
large system , a hybrid i nteger linear progra ming -based
method was proposed in [17]. In this method , the system
is categorize d into three groups by considering three
constraints in the optimization problem such as the
number of PMUs , system observability and
measurement redundancy. An optimal PMU placement
approach was formulated in [18] for power system
dynamic state estimation using the empirical
observability Gramian. Authors in [19] proposed
selection rules to determine the best candidate bus that
involves a merging p rocedure of zero -injection bus with
its neighbors. A modified choice of the greedy algorithm
was proposed in [20] to solve the OPP problem . This
study also considered the realistic aspects affecting the
optimal location of PMU such as zero injection bus, the
presence of PMU channel limitation and conventional
measurements . The authors in [21] utilized intelligent
optimization techniques based on a genetic algorithm to
search the optimal set of PMUs . A formulation of
mixed -integer progra ming for dynamic state estimation
was proposed in [22]. This technique is based on PMU
measurements and can accelerate the estimation
execution. In practice, it is neither economical ly feasible
nor technically necessary to equip all buses with PMUs.
An imperialist competit ive algorithm was modified in
[23] for solving the OPP problem during normal and
abnormal conditions .
The literature review indicates that most of the
aforementioned studies have focused on the
development of intelligent methods for PMU placement,
while other s have used the topological approach es based
on assumptions and simple rules. The obtained outcomes
from these studies are found to be satisfied ; however, the
validation of these proposed methods on practical power
system s was not applied, and therefore, the methods may
have drawbacks when implemented on a dynamic
system. Furthermore, ensuring the complete power
system observability under various operating conditions
was not investigated . Note that the conducted study in
this paper only involves the location assessment of
PMUs for practical power grid using different classical
placement methods (d epth f irst, graph theoret ic, dual
search and recursive N –1 security algorithm ). The
SCADA measurements and fault location algorithm
using PMU -based wide area backup protection are out of
study scope. Motivated by the above review and
discussion, this paper aims to evaluate the current states
of the practical power system in Sarawak [24] in terms
of PMU s location s. The rest of the paper is organized as
follows, the basic concept of phasor estimation is
explained in Section II. The approaches implemented for
the search of optimal PMUs placement s are outlined in
Section III. The obtained results are discussed in Section
IV while the conclusion is given in Section V.

II. LINEAR MODEL FOR POWER SYSTEM WITH PMU S

The basic function of PMU technology is to provid e
real-time information of magnitude and phase angle .
Considering all v ariables in the same frequencies, t he
phasor representation of pure waveform given in (1) is
expressed by (2) [25]. The sinusoidal waveform and
phasor signals are depicted in Fig. 1 .

( ) ( ) (1)

( )
√ ( ) (2)

where is the magnitude of the waveform; denotes
signal frequency ; is the phase angle ;
√ is known as
the root mean squared value of waveform magnitude.
The conventional SCADA state estimation considers
the parameters of voltage magnitude , power flow and
power injection . With the incorporation of PMUs, the
state estimation performance can be improved due to
the utilization of voltage and current phasors [26]. This
yields linear model between measured and state
variables with N -number of buses as,
(3)
where consist s of voltage and current measurement
phasors; : designed ma trix of the system ( ); :
( ) addictive measurement error vector. Vector
of Eq. (3) can be split into vector voltage (
) and vector current ( ). Similarly, vector
is split into measured sub -vector ( ) and
non-measured sub -vector ( ). Eq. (4) is the
modified expression after splitting and vectors [27],
[28].
[
] [
][
] [
] (4)

where is the identity; matrix es and are series
and shunt admittances. Neglecting shunt elements , the
designed matrix of the system can be found using
(5). represents the measurement to branch
incidence matrix ( ). This matrix is associated
with the measurements of current ph asor. is the
( ) branch admittances diagonal matrix. is the
( ) measured bus to branch incidence sub -matrix
while is the ( ) calculated bus to branch
incidence sub -matrix .

[
] (5)

Fig. 1. Sinusoidal signal with its Phasor representation

III. SEARCH OF PMU LOCATION AND PLACEMENT RULES

Generally, the t opology methods of optimal location
of PMU are used to find the best location . In the real
power system, the strategically important buses in terms of their loads or located in the central area should be
identified as candidate locations. The OPP formulation s
[12] implemented by different topological methods are
defined using binary connectivit y matrix as in (6) and
the binary vector ( ) as in (7) [25]. Here, the
product of denotes the number of times the bus is
observed by the placement of the PMU set defined by .

( ) {

(6)

{

(7)

The rules of PMU placement were proposed in [29]
as the fundamental topological approach for OPP and
applied in [27]. The simple assumption and basic rules
are as follow:
1. The measurement of o ne vo ltage should be
assigned to the bus in which the PMU has been
placed. One measurement of current is also pla ced
for each branch that is conn ected to the said bus as
seen in Fig. 2 ( a).
2. A pseudo -measurement of one voltage is assigned
to buses that are reachable by buses that have been
placed with PMU.
3. A pseudo -measurement of the current is assigned
to each branch that is connected t o two buses with
known voltage as in Fig. 2 ( b).
4. If the balance of current at one bus is known,
apply Kirchhoff’s current law, one current pseudo –
measurement has to be assigned to each branch .
Here, the current can indirectly be calcula ted (see
Fig. 2 ( c)).

Based on the above mentioned rules, OPP was
carried out by placing a PMU in the bus that has the
most connected branches. Additional PMU is placed
one at a time in the unobservable bus until the whole
power system becomes observable.

Fig. 2. PMU pla cement : (a) rule “1”, (b) rule “2”, (c) rule “3”

IV. PMU PLACEMENT METHODS

This section presents the more topological
observability methods implemented for PMU placement
namely, depth first [11], [30]; graph theoretic p rocedure
[31]; dual s earch [3] and r ecursive N –1 security [32].

A. Depth First
The most fundamental method among other
traditional methods is the depth first search . It considers
the topology of the network and follows r ules from one
to three , as it does not take into account the zero
injection bus (also known as a pure transient node) [11]

(a)
(b)
(c)
Zero injection bus

Pure transit nodes

[27]. The basic principle when using this method,
firstly, the PMU has to be placed in the bus connected
to the highest number of branches. If the network
contain s more than one bus with the same number of
connected branche s, the PMU is placed randomly in one
of those buses. Then , the adjacent branches are
eliminated following the above mentioned rules ( Rule s
1 to 3 ). Accordingly, the PMUs are placed until all
buses in the power system are observed .

B. Graph Theoretic Procedure
The graph method is also based on system topology
and similar to the depth search but it takes into account
the pure transit nodes (see Fig. 2 (c)) [27], [31]. In other
words, it follows rules from one to four. Here, the OPP
is carried out as explained in the following steps:
Step ( 1): At the first stage, PMU is placed at the bus
connected to the highest number of incident branches in
the unobservable region.
Step (2): The region that can be observed after placing
PMU is determined .
Step (3): Stop when the whole system is observable;
otherwise go to Step 1.

C. Dual Search
This technique has been proposed in [3] specifically
for the applic ation of OPP. It is a combination of the
modified simulated a nnealing and bisecting search
method s. In this search strategy, t he former finds the
minimum number of PMU utilizing iterative search,
while the latter determine s the number of the
unobservable bus according to the former result s. Here,
the s imulated a nnealing works based on the objective
function “ ” which has to be minimized , while the
PMU p lacement set is randomly changed controlled by
a decreasing function . The placement decision is
considered accepted if the PMU placement set “ ” is
negative. Otherwise, it is accepted with the modified
probability of the Boltzmann function as given in (8) .

( ) ( )⁄ (8)

D. Recursive Security N Algorithm
This approach is a modification of the depth f irst
search method explained in (Section IV , A) . The
improvement in the proposed algorithm by [32] is
explained in three stages . Firstly, the algorithm
generates “ ” minimum spanning trees. The flowchart
in Fig. 3 shows that the algorithm performs repetitively
“ ” times using each node as a starting bus. The buses
number in the network is represented by . Secondly,
the searching stage of alternative patterns starts in order
to improve the results obtained in the first stage as
depicted in Fig. 4. As such, one at a time, each PMU of
each set generated by the first stage is replaced at the
buses with original PMU. The equivalent minimum sets
that should be taken into account are those having the
practical advantages for physical PMUs placements.
Thirdly, this stage involves the reduction of PMU
number in pure transit nodes as shown in Fig. 5 . Hence,
PMU is eliminated one at a time by considering pure transit nodes according to Kirchhoff’s current law ,
ensuring that the power system is fully observable .
In the aforesaid stages, t he algorithm of recursive
security ends at the second stage if the pure transient
nodes are not presented. Note that the recursive security
N–1 algorithm is furnished with a function of a single
line outage as this is one of the main advantage s when
using this algorithm compared to the other methods . In
this algorithm (N –1), a node is considered observable if
it me ets the following conditions [32]:
 The PMU is placed at the bus
 The bus is connected to at least two buses
equipped with PMU s.

Fig. 3. Recursive security N –1 algorithm (stage 1)

Fig. 4 . Alternative patterns search ( stage 2)

Fig. 5. PMU reduction due to pure transit nodes (stage 3)

V. RESULTS AND DISCUSSIO N

The case study is a local power system with 36
buses from Sarawak [24] as seen in Fig. 6 . This
practical power system was simulated using the power
system analysis t oolbox [27]. Four methods were used
to assess the optimal locations of PMUs as explained in
Section IV . The positions of the PMUs have been
evaluate d in the steady -state and when the system is
subjected to single or multiple line outages . Fig. 7
depicts the voltage and angle in each bus at the base
case (steady -state). On the same note, the locations and
number of PMUs have also been evaluated at the base
case as shown in Fig. 8. The implemented techniques
for OPP are the depth first, graph theoretic, dual search
and recursive (N –1) security methods . As seen from Fig.
8, the status “star 1” denotes the installed PMU at the
respective bus, while the status “star –1” means that no
PMU is installed in the associated bus. Similarly, the
status “circle 1” shows the optimal placement of PMU
using one of the above mentioned methods at the

Start
Place a PMU at N bus
Determine the connected buses according
to the current placement of PMU s
Determine the connected buses to the
buses found by the previous stage
Place PMUs at the nearer buses
N–1 criterion
satisfied?
End
No
Yes

A
B
C
D
A
B
C
D
A
B
C
D

Zero injection bus
Pure transit nodes
A
B
C
D
Zero injection bus
Pure transit nodes
A
B
C
D

respective bus, whereas the status “circle –1” means that
the PMU should not be installed in the associated bus.
Alternatively, if the status “star 1” and status “circle 1”
are found on the same bus, thi s indicates that the
selection by the search method confirms the installation
of PMU in that particular bus. Likewise, if the status
“star –1” and status “circle –1” are seen on the same bus,
this shows that the search method affirms that PMU is
installed on that bus.

Fig. 6. Case study of a 36 -bus practical test system

Fig. 7 . Steady -state of grid: (a) voltage profile; (b) angle

Fig. 8 . Optimal placements in relation to identified locations

The results obtained from four scenarios “known as
cases A – D” are discussed in this section for the power
system shown in Fig. 6. For instance, in the first scenario
(case A), an outage occurred in the line connecting buses
21 and 23. In the second scena rio (case B), an outage
occurred in the transformer between buses 21 and 15. In
the third scenario of case C, two outages occurred in the
line between buses 21 and 23, and the line between
buses 17 and 18. This scenario has shown notable
changes in the loc ation and the total number of PMUs to
achieve full observability. In the last scenario D, two outages occurred in the transformer located between
buses 12 and 15, and the line connecting buses 17 and
18. The results of case D are different compared to thos e
obtained from the previous cases (A –C). In case D, the
optimal locations of PMUs using recursive (N –1)
security algorithm for set (1) were found in buses (2, 4,
5, 7, 12, 14, 16, 20, 21, 23, 25, 27, 28, 29, 33, 34, 36),
while for set (2) in buses (2, 4, 5, 7, 12, 14, 16, 20, 21,
22, 24, 26, 27, 28, 29, 33, 34 ). For set (3), the locations
were identified in buses (1, 3, 4, 5, 7, 12, 14, 16, 20, 23,
25, 26, 30, 31, 33, 34, 36). Due to the reconfiguration of
power system caused by line outage (single or mult iple),
it is obvious that the previously determined optimal
locations as shown in Fig. 8 could be changed, which
may lead to the unobservability of some zones in power
system . It was observed that recursive (N –1) security
algorithm is the best approach to find the OPP. One of
the key advantages when using this method is the option
provided at the end of the simulation. The placement sets
as mentioned ab ove give alternatives if some of the
selected locations by the algorithm are practically not
suitable with regard to communication limitations,
security or control. Figure 9 compares the total number
of PMUs suggested by each method. While the l ocations
of the PMUs are changeable accordin g to the employed
method, the total number of the PMUs identified by each
approach is almost similar. According to the depth first
and graph t heoretic methods, the needed number of
PMUs was determined to be 17 fo r cases A and C
whereas B and D 16 units . Dual search method suggests
only 13 PMUs. These three methods are showing les s
number of PMUs as compared to the installed units in
the practical system. However, recursive (N –1) security
algorithm had the exact amount of PMUs similar to
those installed i n the practical power system. Therefore,
obtaining the minimum number of PMUs does not
guarantee the full coverage of measurements particularly
during system reconfiguration.

Fig. 9 . Comparison of placements based on all scenarios

VI. CONCLUSION

In the presented study, a practical power system has
been mode led to verify the current locations of PMUs ,
aiming to provide an insight to measure the level of
security in Sarawak power grid . The results show that
the loss of transmission lines may cause change s in the
optimal number of PMUs and their locations compared
to the base case . Even though some of the OPP methods
can provide the least number of the required PMU
placements, the system might become unobservable

12
33
11
13
36
35
22
20
23
24
18
19
17
16
21
15
14
27
6
9
26
25
7
8
3
10
5
2
31
34
4
28
1
29
30
32
PMU
PMU
PMU
PMU
PMU
PMU
PMU
PMU
PMU
PMU
PMU
PMU
PMU
PMU
PMU
PMU
PMU

during the line outage . Hence , it is importa nt to consider
single and double line outages while carrying out OPP.

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