Pmu's Placement in power System using AI algorithms

Approach for Placement of Phasor Measurement
Units in Power System Under Normal ,
Line Failure And Limited Channel Connectivity
Conditions
PRESENTED BY
AJAY PRAKASH SINGH
152603 pse -m .tech (2nd yr)
EEE NIT WARANGAL
Under the guidance of
Dr. B. Nagu
Assistant professor

 INTRODUCTION
 BRIEF HISTORY ABOUT BLACKOUT OCCURED IN 2012 ?
 WIDE AREA MONITORING.
 WHAT IS PMU ?
 WHY PMU ?
 PMU’S PLACEMENT BASED ON DIFFERENT CRITERIAN
 PMU’S PLACEMENT FORMULATION
 ALGORITHM USED
 RESULTS
 CONCLUSTION
 FUTURE WORK

 Regional Separation during Indian Blackout of 30th July
2012

 Sequence of events….
 System was weakened by several scheduled outages of
transmission lines connecting Western Region (WR) with
Northern Region (NR) boundary.
 Many of the NR utilities drew excessive power from the grid.
 Over loading on inter-tie link (Bina-Gwalior-Agra )
 Link was got tripped by zone-3 relay

 Expected Reasons…
 Improper Visualization of dynamic behavior
 System operation at its marginal limits
 Lack of adaptation
 Poor state determination
 Slower communication
 Poor security Vs. dependability relation

 Wide Area Monitoring(WAM)
 Wide Area Monitoring(WAM) is a premier approach in this
concept where entire grid will be under the surveillance of a
central control station
 Complements SCADA/EMS system
 Near real time monitoring of Power System
 Provides sub-second level sketch of Power System
 Synchronized measurements
 Direct measurement of absolute and relative Phase angle
 Realized integration of Phasor Measurement Units to Power
system

 Why phase angle…..?
 Angle is a measure of the grid stress.
 In AC, power flow is determined by phase angle differences
between two nodes.
 Provides a information about load variations of power system.
 Disturbances can be detected by monitoring the phase-angle
relations between strategically chosen nodes.

 Visualization of angular separation between two nodes
in the grid
 Angular difference is primarily a function of the voltage at the
two nodes; Impedance between the two nodes and the power
flow between the nodes.
𝛿 = 𝑠𝑖𝑛−1
{
𝑃.𝑋
𝑉1.𝑉2
}
δ = load angle , P = power flowing between two nodes
V1, V2 = voltages at individual node

 PMU Structure
Functional block diagram of Tipical P.M.U

 Time Synchronization
GPS Antenna
 Satellites have atomic clocks
 Provides coordinated universal time (UTC) which is international
atomic time compensated for leap seconds for slowing of earths
rotations
 1 PPS signal have a maximum time error of 1µs
 1µs time deviation corresponds to phase error of 0.018° for 50Hz
system and 0.022° for 60 Hz system
 Transmission of the GPS 1 pps signal from the receiver to the
PMU will be through IRIG-B or IEEE 1588 Precision timing
protocol (PTP) (mostly Ethernet)
GPS Receiver
1 PPS
NMEA / Proprietary
Messages

 Synchronized Measurements
.
Magnitude of the two phasors
can be determined
independently but phase angle
difference cannot be measured
without synchronization of
measurements
Phase angular difference
between the two can be
determined if the two local
clocks are synchronized.
Synchronizing pulses obtained
from GPS satellites.

 PMU Placement Formulation
 The problem can be formulated as follows.
minimize 𝑖=1
𝑛
𝑥 𝑞
subjected to 𝑠 𝑝 𝑥 ≥ 1 ∀𝑝 ∈ 𝑁
where 𝑠 𝑝 = 𝑞∈𝑁 𝐶 𝑝𝑞 𝑥 𝑞 ∀𝑝 ∈ 𝑁






otherwise,0
connectedareqp,busesif,1
q=pif,1
cpq

 To consider line outage, constraints will be rewritten as,
𝑆 𝑝
𝑙 ≥ 1 ∀𝑝 ∈ 𝑁 ∀𝑙 ∈ 𝐿
where 𝑆 𝑝
𝑙 = 𝑞∈𝑁 𝐶 𝑝𝑞
𝑙 𝑥 𝑞
 OPP considering only measurement failure
 OPP considering only line outage
𝑠 𝑝 ≥ 2 ∀𝑝 ∈ 𝑁

 OPP formulation considering line outage/PMU failure
This model derives the required constraints as follows,
𝑆 𝑝
𝑙 + 𝑆 𝑝 ≥ 2
OPP formulation considering channel limitations
The observability function becomes
𝑆 𝑝 = 𝑞∈𝑁 𝐶 𝑝𝑞 𝑚 𝑝𝑞 𝑥 𝑞
in addition with
𝑆 𝑝 = 𝑞∈𝑁 𝐶 𝑝𝑞 𝑚 𝑝𝑞 ≤ 𝑚 𝑞
𝑚𝑎𝑥
and 𝑚 𝑝𝑞 ≤ 𝑥 𝑞
∀𝑝 ∈ 𝑁 ∀𝑙 ∈ 𝐿

 Nomenclature
 𝑥 𝑞 = binary decision variable
 𝑠 𝑝 = vector of length N
 𝐶 𝑝𝑞 = connectivity matrix between two element
 𝑠 𝑝
𝑙
= vector representing line outage
 𝐶 𝑝𝑞
𝑙 = connectivity matrix between two nodes representing line
outage condition
 𝑚 𝑝𝑞 = channel limit connectivity element
 N = integer number
 P = no of P.M.U’s

 Genetic Algorithm
 A genetic algorithm (GA) is a method for solving both constrained
and unconstrained optimization problems based on a natural selection
process that portrays biological evolution.
 A population of candidate solutions(called individuals) to an
optimization problem is evolved toward better solutions.
 Genetic operators:
Selection
Crossover
Mutation
 Termination criteria:
no of iterations , cost

 G.A flow Chart
yes
no
start
Define fitness function
Set no of variable in the
functiion
Set stopping criteria
Define G.A parameters
Create initial population
stop
Set
iter =0
Is
iter ≥
itermax Display result
Sort according to fitnesss
Evaluate fitness
Select pairs and perform
crossover
Perform slection
Mutate the population Iter = iter +1
B
B

 Result for 14 bus system
Pmu placement optimization for 14 bus system

 Summaryof Results in normal condition
Bus System Location of PMU’S
For observability of normal system
No. of PMUs
IEEE 14 bus 2, 4, 8, 9 4
IEEE 30 bus 2, 4, 6, 10, 11, 12, 19, 24, 26, 29 10
IEEE 39 bus 2,6,9,14,16,22,23,24,29,32,34,37,38 13
IEEE 57 bus 1, 4, 9, 20, 24, 27, 29, 30, 32, 36, 38, 39, 41, 45, 46, 51, 17
IEEE 118 bus 2,5,9,12,13,17,21,23,26,29,34,37,42,45,49,53,56,62,64,71,7
5, 77,80,85,86,90,94,101,105,110,115,116
32

 Summary of Results
Bus System Location of PMU’S for observability
considering line outage/PMU failure
No. of PMUs
IEEE 14 bus 1,2,3,4,6,7,8,9,11,13 10
IEEE 30 bus 1,2,4,6,7,8,9,10,11,12,13,15,17,18,19,21,24,25,26, 29,30 21
IEEE 39 bus 2,3,6,8,10,11,13,14,16,17,19,20,21,22,25,28,29,30,31,32,
2,33,34,35,36,37,38,39
27
IEEE 57 bus 1,2,4,6,9,11,12,15,19,20,22,24,25,26,28,29,30,32,
33,35,36,38,39,41,45,46,47,50,51,53,54,56,57
33
IEEE 118 bus 1,3,5,7,9,10,11,12,15,17,19,21,22,24,26,27,28,30,31,32,3
,34,36,37,40,42,44,45,46,49,50,52,53,56,58,59,62,63
4,66,68,71,73,74,75,77,78,80,84,85,86,87,89,90,92,9
96,100,101,105,107,108,110,111,112,
114,116,117,118
68

 Summary of Results
Bus System Location of PMU’S for observablity
considering channel limit
No. of PMUs
IEEE 14 bus 6,7,9,14 4
IEEE 30 bus 1,2,6,9,12,16,19,20,26,29 10
IEEE 39 bus 2,9,10,13,14,15,19,20,22,23,29,32,37 13
IEEE 57 bus 1,4,9,13,14,19,26,29,30,32,33,35,36,43,46,50,52,54,
57
19
IEEE 118 bus 3,5,9,11,12,17,21,24,27,24,27,28,30,32,34,37,40,44,
46,49,51,53,56,59,68,71,77,80,86,91,92,
95,100,110
35

 Particle Swarm Optimization
 PSO has its roots in Artificial Life and social psychology, as well as
engineering and computer science.
 The particle swarms in some way are closely related to fish Schooling:
a) individual fish updates information in parallel
b) each new fish position value depends only on the old
 Individuals in a particle swarm can be defined as fish schooling whose
states changes in many dimensions simultaneously.

As described by the inventers
James Kennedy and Russell
Eberhart, “particle swarm algorithm
imitates human (or insects) social
behaviour. Individuals interact with
one another while learning from
their own experience, and gradually
the population members move into
better regions of the problem
space”.
Why named as “particle”, not “points”? Both Kennedy and Eberhart felt that velocities and
accelerations are more appropriately applied to particles.

As described by the inventers James
Kennedy and Russell Eberhart,
“particle swarm algorithm imitates
human (or insects) social behaviour.
Individuals interact with one another
while learning from their own
experience, and gradually the
population members move into better
regions of the problem space”.
Why named as “particle”, not “points”? Both Kennedy and Eberhart felt that velocities and
accelerations are more appropriately applied to particles.

 Original PSO
 𝑣𝑖 ← 𝑣𝑖 + 𝜑1 ∗ 𝑝𝑖 − 𝑥𝑖 ∗ 𝜑2 ∗ (𝑝 𝑔 − 𝑥𝑖)
 𝑥𝑖 ← 𝑣𝑖 +𝑥𝑖
 xi denotes the current position of the i–th particle in the swarm;
 vi denotes the velocity of the i-th particle;
 pi the best position found by the i-th particle so far, i.e., personal best;
 𝑝 𝑔 the best position found from the particle’s neighbourhood, i.e.,
global best;
 The symbol * denotes a point-wise vector multiplication
 𝜑1= 𝑟1 𝑐1 & 𝜑2= 𝑟2 𝑐2
 r1 and r2 are two vectors of random numbers uniformly chosen from [0, 1];
c1 and c2are acceleration coefficients.

 Original PSO
𝑣𝑖 ← 𝑣𝑖 + 𝜑1 ∗ 𝑝𝑖 − 𝑥𝑖 ∗ 𝜑2 ∗ 𝑝 𝑔 − 𝑥𝑖
𝑥𝑖 ← 𝑣𝑖 +𝑥𝑖
 Velocity vi (which denotes the amount of change) of the i-th particle is
determined by three components:
 momentum – previous velocity term to carry the particle in the direction it has
travelled so far;
 cognitive component – tendency to return to the best position visited so far;
 social component – tendency to be attracted towards the best position found in
its neighborhood.
momentum
cognitive
component
Social
component

 Pseudo-Code of a Basic PSO
Randomly generate an initial population
repeat
for i = 1 to population_size do
if f(𝑥𝑖 ) < f(𝑝𝑖 ) then 𝑝𝑖 = 𝑥𝑖 ;
𝑝 𝑔 = min( 𝑝 𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑢𝑟𝑠);
for d =1 to dimensions do
velocity_update();
position_update();
end
end
until termination criterion is met.

 Results PSO
Bus System Location of PMU’S
For observability of normal system
No. of PMUs
IEEE 14 bus 2, 4, 8, 9 4
IEEE 30 bus 2, 4, 6, 10, 11, 12, 19, 24, 26, 29 10
IEEE 39 bus
2,6,9,14,16,22,23,24,29,32,34,37,38
13
IEEE 57 bus 1, 4, 9, 20, 24, 27, 29, 30, 32, 36, 38, 39, 41,
45, 46, 51, 54
17
IEEE 118 bus 2,5,9,12,13,17,21,23,26,29,34,37,42,45,49,53,
56,62,64,71,75,77,80,85,86,90,94,101,
105,110,115,116
32

 Results PSO
Bus System Location of PMU’S for observability
Considering line outage/PMU failure
No. of PMUs
IEEE 14 bus 1,2,3,4,6,7,8,9,11,13 10
IEEE 30 bus 1,2,4,6,7,8,9,10,11,12,13,15,17,18,19,21,24,25,26,
29,30
21
IEEE 39 bus 2,3,6,8,10,11,13,14,16,17,19,20,21,22,25,28,29,30,31,3
,32,33,34,35,36,37,38,39
27
IEEE 57 bus 1,2,4,6,9,11,12,15,19,20,22,24,25,26,28,29,30,32,
33,35,36,38,39,41,45,46,47,50,51,53,54,56,57
33
IEEE 118 bus 1,3,5,7,9,10,11,12,15,17,19,21,22,24,26,27,28,30,31,32
32,34,36,37,40,42,44,45,46,49,50,52,53,56,58,59,6
63,64,66,68,71,73,74,75,77,78,80,84,85,86,87,89,9
92,94,96,100,101,105,107,108,110,111,112,114,116,117,1
117,118
68

 Results PSO
Bus System Location of PMU’S for observablity
Considering channel limit
No. of PMUs
IEEE 14 bus 6,7,9,14 4
IEEE 30 bus 1,2,6,9,12,16,19,20,26,29 10
IEEE 39 bus 13
IEEE 57 bus 1,4,9,13,14,19,26,29,30,32,33,35,
36,43,46,50,52,54,57
19
IEEE 118 bus 3,5,9,11,12,17,21,24,27,24,27,28,30,32,34,37
7,40,44,46,49,51,53,56,59,68,71,
77,80,86,91,92, 95,100,110
35

 Minimum Connectivity Based Reduction(MCBR)
Technique
The algorithm of the proposed technology:
 Step 1: Form the connectivity matrix
 Step 2: Arrange all the buses according to their connectivity in descending
order.
 Step 3: The set of buses with least connectivity are taken. The buses with
more connectivity and also incident to the above set of buses are chosen for
placing PMU. This will be repeated for all the buses in the set.
 Step 4: Repeat this for the next set of buses and so on.
 Step 5: This process will be continued until our whole system gets fully
observed.

 flow chart
The proposed methodology will be explained with
the help of IEEE-9 bus system below.
Sample IEEE-9 bus system

 MCBR Technique Problem Formation
minimize 𝑖=1
𝑛
𝑥 𝑞
subjected to 𝑠 𝑝 𝑥 ≥ 1 ∀𝑝 ∈ 𝑁
where 𝑠 𝑝 = 𝑞∈𝑁 𝐶 𝑝𝑞 𝑥 𝑞 ∀𝑝 ∈ 𝑁






otherwise,0
connectedareqp,busesif,1
q=pif,1
cpq

Minimum Connectivity Based Reduction(MCBR) Technique
𝐶 𝑝𝑞 =
1 0 0 1 0 0 0 0 0
0 1 0 0 0 0 0 1 0
0 0 1 0 0 1 0 0 0
1 0 0 1 1 0 0 0 0
0 0 0 1 1 1 0 0 0
0 0 1 0 1 1 1 0 0
0 0 0 0 0 1 1 1 0
0 1 0 0 0 0 1 1 1
0 0 0 1 0 0 0 1 1
connectivity matrix ( 𝐶 𝑝𝑞)
Bus numbers and their corresponding connected lines
Lines without
sorting
Bus no. Connectivity
1 8 3
1 6 3
1 4 3
3 9 2
2 7 2
3 5 2
2 3 1
3 2 1
2 1 1

 Minimum Connectivity Based Reduction(MCBR) Technique
Bus number Start of bus End of bus Set of buses
connected
Set of lines
connected
1 1 1 4 1
2 2 2 8 2
3 3 3 6 3
4 4 6 1,5,9 1,4,5
5 7 8 4,6 4,6
6 9 11 5,3,7 3,6,7
7 12 13 6,8 7,8
8 14 16 7,2,9 2,8,9
9 17 18 8,4 5,9

 Location of PMUs Using MCBR Technique
IEEE TEST SYSTEM LOCATIONS OF PMUs
9 bus system 4-8-6
14 bus system 7-2-9-6
30 bus system 9-12-25-2-4-6-10-15-18-27
57 bus system 1-4-9-15-20-24-26-29-31-34-36-38-
41-46-50-54-57
118 bus system 2-5-11-12-15-17-21-24-25-28-34-37-
40-45-49-52-56-62-63-68-73-75-77-
80-85-86-90-94-101-105-110-114

 Comparison of PMUs required based on different
algorithms
ALGORITHM 9 BUS 14 BUS 30 BUS 57 BUS 118BUS
GENETIC
ALGHORITHM
3 4 10 17 32
PARTICLE
SWARM
OPTIMIZATION
3 4 10 17 32
MCBR
TECHNIQUE
3 4 10 17 32

 Comparison of results
 Comparison of execution times
Methodology Time of execution
Proposed MCBR technique 0.6sec
PSO 3.9sec
GA 4.2 sec

 Future Work
 Clear road map for fulfilling long and short term goals:
I. Short term goals-enhanced visualization and post fault analysis
II. Long term goals-wide area monitoring, protection and control
 It should accommodate new communication devices like smart meters.
 It should be implemented in real time owing the absence of information
in the model of standard IEEE bus system.

 Reference
1. Approach for Placement of Phasor Measurement Units in Power sysem,V. Seshadri Sravan Kumar and D.
Thukaram, Senior Member IEEE, IEEE Trans. on power systems, Vol. 31, No. 4, July 2016.
2. Optimal Placement of PMU’s with limited number of channels, Z. Milzanic and I.Djurovic, IEEE Trans. on
power systems, Vol. 27, No. 14, May 2013.
3. Optimal PMU Placement Considering one line/ one PMU Outage Using genetic Algorithm ,Sudhir R. Bhide ,
Vijay S. Kale IEEE Transactions on Power Delivery, vol. 20, no. 2, april 2012
4. Rather, Z. H., Liu, C., Chen, Z., & Thogersen, P. (2013, November). Optimal PMU Placement by improved
particle swarm optimization. In Innovative Smart Grid Technologies-Asia (ISGT Asia), 2013 IEEE (pp. 1-6).
IEEE.
5. N V Phanendra Babu, Dr. P Suresh Babu, Prof. D V S S Siva Sarma, “Importance of Phasor Measurements In
Wide Area Protection of Power System: A Review”, National Conference On Power System Protection, pp 83-
89, February 2015.

 Publication Under Review
 A paper on “Minimum Connectivity Based Technique for PMUs
Placement in Power System” is communicated in 6th IEEE International
Conference on Computer Application in Electrical Engineering-Recent
Advances (CERA-2017)

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