This document presents a multi-objective fuzzy-genetic algorithm approach for optimal placement and sizing of shunt Flexible AC Transmission System (FACTS) controllers. The objectives are to maximize the distance to voltage instability, minimize voltage deviations, and minimize the size of the FACTS controller. Membership functions are developed for each objective and a fitness function is defined based on the membership functions. The approach is tested on the IEEE 14-bus system and results show that placing a STATCOM at bus 9 provides the best improvement in voltage stability and profile.

1. -:Prepared by:-
Divyangkumar R Soni.
(160410707008)
Optimal Placement of FACTS Controller
-:Guided By:-
Dr. P. R. Gandhi
Ph.D(Electrical)
(Asst.prof.)
Electrical Engg. Dept.

2. PAPERS
Multi-objective Fuzzy-GA Formulation for Optimal Placement and Sizing
of Shunt FACTS Controller
AUTHORS
A. R. Phadke*, Manoj Fozdar**, K. R. Niazi***
3/31/20172

3. OUTLINE
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 Abstract
 Introduction
 Fuzzy Membership Functions
 GA Implementation
 Simulation And Results
 References

4. ABSTRACT
 The location and sizing of FACTS controllers for voltage
stability enhancement is an important consideration for practical
power systems.
 A strategy for placement and sizing of shunt FACTS controller
using Fuzzy logic and Real Coded Genetic Algorithm is
proposed.
 A fuzzy performance index based on distance to saddle-node
bifurcation, voltage profile and capacity of shunt FACTS
controller is proposed.
 The proposed technique can be used to find the most effective
location and optimal size of the shunt FACTS devices.
 The proposed approach has been applied on IEEE 14-bus test
system.
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5. INTRODUCTION
 The continual increase in demand for electric power has forced
utility companies to operate their systems closer to the limits of
instability.
 One of the major problems that may associate with such a
stressed system is voltage instability or voltage collapse.
 Under stressed condition, one way to save the system from
voltage collapse is to provide reactive power support with shunt
FACTS controllers at appropriate locations.
 The techniques used for optimal placement of FACTS devices
can be broadly classified into :
1. Index based methods
2. Optimization based methods
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6. MULTI-OBJECTIVE FORMULATION FOR
PLACEMENT AND SIZING OF SHUNT FACTS
CONTROLLER
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 Shunt FACTS controller like SVC or STATCOM connected at
the appropriate location results in prevention of voltage collapse
and better voltage profile.
 Placing of shunt FACTS controller can be formulated as a multi-
objective problem with the following objectives and constraints.
1. Maximum distance to saddle-node bifurcation
2. Minimum voltage deviation
3. Minimum size of the shunt FACTS device

7. Maximum distance to saddle-node
bifurcation
 Saddle-node bifurcation point give the information loading
margin.
 Loading margin is defined as the distance between the current
operating point and the saddle-node bifurcation or voltage
collapse point.
 Saddle-node bifurcation is identified by a zero eigenvalue
associated with system Jacobian.
 the first objective can be expressed as:
Max f1 = min(eig(J)) . . . . . (1)
 Where,
min(eig(J)) = the minimum eigen value of the system
Jacobian.
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8. Minimum voltage deviation
 The Excessively low voltages can lead to an unacceptable service
quality and can create voltage instability problems.
 Shunt FACTS devices connected at the appropriate location play a
leading role in improving voltage profile and avoiding the voltage
collapse in the power system.
 the second objective can be expressed as :
Min f2 = ⅀ | v mref - vm | . . . . .(2)
(m=1 to k)
Where ,
Vm = the voltage magnitude at bus m.
Vmref = the nominal voltage of bus m and k is the number of
buses for which bus voltage limit is violated.
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9. Minimum size of shut FACTS device
 Due to the high installation cost of FACTS controllers, these controllers
should be optimally sized.
 Thus, third important objective is to have minimum possible size of the
shunt FACTS devices.
 This objective can be expressed as :
min f3 = ⅀ ci . . . . . (3)
(i=1 to sf)
Where,
Ci = the capacity of the ith shunt FACTS device in p.u.
sf = the total number of shunt FACTS devices.
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10. During normal operation, power system is required to
satisfy some constraints.
 Load constraint: The load constraints are the active and reactive
power balance equations .
 It can be expressed in a compact form as :
g(x,u) = 0. . . . . (4)
Where , g = the equality constraint
 Operational constraint :
 These constraints can be represented in a compact form as :
h(x,u) <= 0. . . . . (5)
Where, h = the system operating constraint
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11.  Considering the objectives and constraints the problem of
optimal placement and sizing of shunt compensation can be
mathematically formulated as a non linear constrained multi
objective optimization problem as follows :
 The multi-objective optimization problem (6) is converted into a
single objective optimization problem using fuzzy framework.
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12. FUZZY MEMBERSHIP
FUNCTIONS
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 Membership Function for maximum distance to saddle-node bifurcation
( μ λi )
 Membership Function for Minimum Bus Voltage Deviation (μ VPi)

13. 3/31/201713
 Membership function for capacity of minimum possible size of the
shunt FACTS devices.
 The installation cost/MVA of FACTS devices is inversely
proportional to its capacity.
 Cmin = 50 MVA
 Cmax = 200 MVA

14. GA implementation for determination of optimal
location and size of shunt FACTS controller
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STAR
T
Read system data and initialize
GA parameter
Gen >Max
gen?
Run Power Flow
Compute Fitness
function
Apply GA operators: Selection,
Crossover and Mutation
STOP
ye
s
no
F = μ λi * μ Vpi * μ ci
Read system data and initialize
GA parameter
Gen >Max
gen?
Run Power Flow
Compute Fitness
function

15. SIMULATION AND RESULTS
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 The applicability of the proposed method has been tested on IEEE 14-
bus system.
 Optimal location and size of the shunt FACTS controller was
determined by applying the proposed fuzzy-GA approach.
 Which accurately represents the active and reactive power flows to and
from the voltage source converter of the STATCOM.
 The voltage at the STATCOM bus is given by :
V= Vref + IX SL . . . . . (7)
V= Vref - IX SL . . . . . (8)
where ,
XSL = the controller droop.
Vref = reference voltage.

16. SIL Of IEEE 14 Bus System
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 There are 20 branches and 14 buses with 11 loads totaling 259
MW and 77.4 MVAR at base case.

17. 3/31/201717
 The fitness function F was computed at a loading factor close to
the voltage collapse condition in order to consider generator
reactive power limits and nonlinearity.
 The application results of the proposed method are shown in
below Table I.

18. Table I. Maximum Value Of Fitness Function And Corresponding
Membership Functions With STATCOM At Candidate Buses In
IEEE 14-bus Test System
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Bus no. μ λi μ Vpi μ ci F
4 0.984603 0.961974 0.425632 0.403142
5 0.967506 0.859246 0.45114 0.375855
9 0.869041 0.812158 0.860714 0.607491
10 0.789196 0.694504 0.906888 0.497065
11 0.71103 0.353176 0.969483 0.243455
12 0.603024 0.00 0.611662 0.00
13 0.724371 0.365386 0.959321 0.253908
14 0.680108 0.601062 0.943261 0.385593
F = μ λi * μ Vpi * μ ci
F= 0.869041 * 0.812158 * 0.860714
F=0.607491

19. Figure 3. Evolution of the fitness function with respect to
number of generations for bus no. 9 in IEEE 14 bus
system.
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Best Fitness Value
Is Achieved In About
25 Generation For
STATCOM

20. Figure 4. The PV Curves Of The System Without STATCOM,
And With STATCOM At Bus No. 9 And Bus No. 14.
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 The loading margin of the system increases from 0.69381 to 0.87848
and 0.88570 for the STATCOM connected at bus 14 and 9 respectively

21. Figure 5. Voltage Profile Of IEEE 14-bus System Without
STATCOM And With STATCOM At Bus 9 And 14 At a Loading
Factor Of λ= 0.4
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 It may be observed that STATCOM connected at bus no. 9
provides the best improvement in voltage profile.

22. CONCLUSIONS
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 The proposed method determines a bus which is strongly tied with the
number of weak buses. Placement of shunt FACTS controller at this bus
results in optimal reactive power reinforcement for voltage stability
enhancement as compared to the shunt FACTS controller connected at the
weakest bus or in weak area.
The Weak
Zone
Strongly
Tied With
The Number
Of Weak
Buses

23. REFERENCES
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 C. A. Canizares, M. Pozzi, S. Corsi and E. Uzunovic,
“STATCOM modeling for voltage and angle stability studies,”
Elect. Power and Energy Syst., vol. 25, pp. 431–441, 2003.
 B. Gao, G.K. Morison and P. Kundur, “Voltage stability
evaluation using modal analysis,” IEEE Trans. on Power Syst.,
vol. 7, No. 4, pp. 1529-1542, 1992.
 N. K. Sharma, A. Ghosh and R. K. Varma, “A novel placement
strategy for FACTS controllers,” IEEE Trans. on Power Syst.,
vol. 18, pp. 982 – 987, 2003.

24. Thank you
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