OPTIMAL POWER FLOW WITH TCSC
USING GENETIC ALGORITHM
K.Sreenivasulu
M.Tech (PSE)
Roll No. 061721
Under the guidance of
Prof. D.M. Vinod Kumar
Objective of the thesis





To solve OPF with fuel cost minimization as objective
function.
To solve OPF with active power loss minimization as
objective function.
To solve OPF with fuel cost and active power loss
minimization as objective function.
To solve OPF with FACTS devices i.e. TCSC.
All the above cases are studied using Genetic Algorithm.
Results obtained using IEEE 30 bus and 75 bus Indian
system are presented
Contents
1.
2.
3.
4.
5.
6.
7.
8.
Introduction
Optimal power flow
Genetic Algorithm(GA) Based optimal power flow
Modeling of thyristor control series capacitor (TCSC)
Optimal power flow with TCSC using GA
Case studies
Conclusions
References
Introduction





Optimal Power Flow (OPF) is a useful tool in modern
Energy Management System.
Optimal power flow plays an important role in power
system planning and operation.
The OPF optimizes the Power System operating
objective function while satisfying a set of equality and
inequality constraints.
Conventional optimization methods that make use of
derivatives and gradients are in general not able to
locate or identify the global optimum.
To over come the drawbacks of conventional
optimization methods, we use genetic algorithm (GA)
Optimal power flow

Problem formulation

OPF problem is to minimize the steady state performance of the
power system in terms of the objective function while satisfying
several equality and in equality constraints.
minimize J ( x, u )
subject to g ( x, u )  0
h ( x, u )  0
u :vector of problem control variables
x :vector of system state variables
J ( x, u ) : objective function to be minimized

Control variables
u is a vector of control variables consisting of generator voltages,
generator active power out puts, transformer tap settings and shunt
VAR compensation
uT  [VG1 ...VGNG , PG2 ...PGNG , T1...TNT , QC1 ...QCNC ]

State variables
These are the set of variables, which describe any unique state of
the system. the set of state variables are voltage magnitude of all
buses and voltage angle of all the buses.
xT  [ ,V ]

Equality constraints

Real power balance equation

0  Pi  Vi  V j Gij cosij  Bij sin ij
jNi
i  NB 1


Reactive power balance equation

0  Qi  Vi  V j Gij sin ij  Bij cos ij
jNi
iN

PQ
Inequality constraints
min  P  P max
Pgi
i  Ng
gi
gi
min  Q  Q max
Qgi
i  Ng
gi
gi
S  S max
k  NE
k
k
Vimin  Vi  Vimax
i  NB

Application of GA to OPF:




GA is used to solve the OPF problem.
The control variables modeled are generator active power outputs,
voltage magnitudes, shunt devices, and transformer taps.
Each chromosome represents a set of control variables namely
continuous control variables and discrete control variables. The
continuous control variables include generator active power outputs,
generator voltage magnitudes, and discrete control variables include
transformer tap settings and switchable shunt devices.
GA-OPF approaches overcome the limitations of the conventional
approaches in the modeling of nonconvex cost functions and
discrete control variables.
Genetic Algorithm solution to optimal
power flow
1.Encoding Chromosome is formed as
2.Decoding of chromosome to the problem physical
variables is performed as follows


 Nui 
min
max
min
ui  ui  ui  ui  k /  2  1


Algorithm for OPF using GA
1. (a) Read line data, system data
(b) Read a,b,c constants for generators
(c) Read GA parameters
(d) Read maximum line flow limits and load bus voltage limits
(e) Calculate Psp(i) and Qsp(i) for i=1 to n
2. Form Y-bus by sparsity
3. Generate initial population of chromosomes
4. Set generation and chromosome count.
5. Decode the chromosomes and calculate the actual values.
6. Calculate Psp(i) with new values of active power outputs
7. Run usual NR power flow.
8. Calculate line flows and bus powers.
Algorithm for OPF using GA
9. Check limits of load bus voltage magnitudes, active bus
powers and reactive powers of all generators,line flows.
10. Calculate fitness function.
11. Calculate fitness=100/minf of all chromosomes
12. Repeat the procedure from step5 until chromosome
count is greater than population size.
13. Arrange chromosomes in descending order of their
fitness values .
14. Copy elitism probability of chromosomes to next
generation and perform roulette wheel reproduction
technique for parent selection.
Algorithm for OPF using GA
15. If (r<Pc), perform uniform cross over to obtain children
of next generation, where r is a randomly generated number
between 0 and 1 and Pc is the cross over probability.
16. Perform mutation.
17. Replace old population with new population.
18. Increment generation count. If generation count <max
iteration, go for next iteration , else print “problem not
converged in maximum number of iterations”.
19. Print optimized values of active power outputs of generators,
voltage magnitudes and line flows and also optimal operating cost
Simulation Results
Solution of OPF is evaluated for IEEE 30 bus system using
GA. The IEEE 30-bus, 41-branch system has control
variables as follows: 5 Active power outputs of generators,
4 transformer tap settings and 6 generator-bus voltage
magnitudes.
GA parameters are:
Population size = 40
Maximum number of generations = 100
Elitism probability = 0.15
Cross over probability = 0.95
Mutation probability = 0.001
a, b, c constants for generators :
Pgmax and Pgmin for generators :
Generator
No
a
b
c
Generato
r bus no
Pgmin
Pgmax
1
0
2
0.00375
1
0.5
2.0
2
0
1.75
0.0175
2
0.2
0.8
5
0.15
0.5
3
0
1
0.0625
8
0.1
0.35
4
0
3.25
0.002075
11
0.1
0.3
5
0
3
0.025
13
0.2
0.8
6
0
3
0.025
Solution of GA OPF under base case
Fuel cost minimization
Generator
bus number
Active power
outputs(MW)
Voltage
magnitudes(p.u)
Fuel cost
($/hr)
1
110.26
1.0180
266.10
2
42.81
1.0350
106.98
5
34.7
0.9910
109.95
8
29.98
1.0227
99.30
11
15.66
1.0098
53.11
13
50.66
1.0467
216.14
Total cost($/hr)
=849.41
Active power loss (M.W) =6.3834
Variation of fitness with number generations
Variation of best Fitness with number of generations
0.12
fitness value
0.1
0.08
0.06
Series1
0.04
0.02
0
1
4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64
number os generations
Solution of GA OPF under base case
Active power loss minimization
Generator
bus number
Active power
outputs(MW)
Voltage
magnitudes (p.u)
Fuel cost
($/hr)
1
68.41
1.0643
154.36
2
49.65
1.0625
130.02
5
34.92
1.0209
111.13
8
29.52
1.0408
97.74
11
37.47
1.0525
147.51
13
90.25
1.0631
474.37
Total cost($/hr)
=1064.7
Active power loss (M.W) =4.3285
Variation of fitness with number generations
30
25
fitness value
20
15
Series1
10
5
0
1
4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67
mumber of generations
Solution of GA OPF under base case
Fuel cost and Active power loss minimization
Generator
bus number
Active power
outputs(MW)
Voltage
magnitudes (p.u)
Fuel cost
($/hr)
1
108.62
1.0906
261.48
2
48.26
1.0736
125.21
5
34.91
1.015
111.07
8
29.37
1.0654
97.24
11
15.36
1.0754
52.44
13
52.45
1.0227
226.12
Total cost($/hr)
=872.667
Active power loss (M.W) =5.7255
fitness value
Variation of fitness with number generations
0.115
0.11
0.105
0.1
0.095
0.09
0.085
0.08
0.075
0.07
0.065
Series1
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52
number of generations
GA solution to OPF:IEEE 30 bus system
Objective function
Fuel cost($/hr)
Losses (MW)
Fuel cost
minimization
849.41
6.3834
Active power loss
minimization
1064.7
4.3285
Fuel cost and
active power loss
minimization
872.667
5.7255
GA solution to OPF:75 bus Indian system
Objective function
Fuel cost ($/hr)
Losses (MW)
Fuel cost
minimization
7986.9
172.43
Active power loss
minimization
8037.3
141.73
Fuel cost and
active power loss
minimization
8044.8
176.07
Modeling of TCSC

Transmission lines are represented by lumped π
equivalent parameters. The series compensator TCSC is
simply a static capacitor/reactor with impedance jxc. Fig.
shows a transmission line incorporating a TCSC.

Where Xij is the reactance of the line, Rij is the
resistance of the line, Bio and Bjo are the half-line
charging susceptance of the line at bus-i and bus-j.
Modeling of TCSC

The difference between the line admittance before and after the
addition of TCSC can be expressed as:
yij  yij'  yij  ( gij'  jbij' )  ( gij  jbij )
g ij 
g 'ij 

rij
bij  
rij  xij2
2
rij
rij  ( xij  xc )
2
b 'ij  
2
xij
rij2  xij2
xij  xc
rij2  ( xij  xc ) 2
After adding TCSC on the line between bus i and bus j of a general
power system, the new system admittance matrix Y’bus can be
updated as:
0
0 ... 0
0
0
0
 0 y
0 ... 0  yij
ij

0
0
0 ... 0
0

'
Ybus  Ybus  ...
...
... ... 0
...
0
0
0 ... 0
0

 0  yij 0 ... 0 yij
0
0
0 ... 0
0

col  i
col  j
0 row  i
0

0
0

0 row  j
0
Genetic Algorithm solution to optimal
power flow
1.Encoding Chromosome is formed as
2.Decoding of chromosome to the problem physical variables is
performed as follows


 Nui 
min
max
min
ui  ui  ui  ui  k /  2  1


Algorithm for OPF with TCSC using GA
1.(a) Read line data, system data
(b) Read a,b,c constants for generators
(c) Read GA parameters
(d) Read no. of control variables i.e. TCSC location and reactance
(d) Read maximum line flow limits and load bus voltage limits
(e) Calculate Psp(i) and Qsp(i) for i=1 to n
2. Form Y-bus by sparsity.
3. Generate initial population of chromosomes
4. Set generation and chromosome count
5. Using the line no. and reactance information modify Y-bus.
6. Decode the chromosomes and calculate the actual values.
7. Calculate Psp(i) with new values of active power outputs.
Algorithm for OPF with TCSC using GA
8.Run usual NR power flow
9.Calculate line flows and bus powers
10.Check limits of load bus voltage magnitudes, active bus
powers and reactive powers of all generators, line flows
11.Calculate fitness function
12.Calculate fitness=100/minf of all chromosomes
13.Repeat the procedure from step5 until chromosome count is greater
than population size.
14.Arrange chromosomes in descending order of their fitness values
15.Copy elitism probability of chromosomes to next generation and
perform roulette wheel reproduction technique for parent selection.
Algorithm for OPF with TCSC using GA
16. If (r<Pc), perform uniform cross over to obtain children of next
generation, where r is a randomly generated number between 0 and
1 and Pc is the cross over probability.
17. Perform mutation.
18. Replace old population with new population.
19. Increment generation count. If generation count <max iteration, go
for next iteration , else print “problem not converged in maximum
number of iterations”.
20. Print optimized values of active power outputs of generators,
voltage magnitudes and line flows and also optimal operating cost
and TCSC location and compensation level.
Simulation Results
Solution of OPF is evaluated for IEEE 30 bus system using
GA. The IEEE 30-bus, 41-branch system has control
variables as follows:5 Active power outputs of generators,
4 transformer tap settings and 6 generator-bus voltage
magnitudes.
GA parameters are:
Population size = 40
Maximum number of generations = 100
Elitism probability = 0.15
Cross over probability = 0.95
Mutation probability = 0.001
Solution of GA OPF using TCSC
Fuel cost minimization
Generator Active power Voltage
bus number outputs(MW) magnitudes
(p.u)
Fuel cost
($/hr)
1
88.51
1.0180
206.39
2
45.97
1.0350
117.42
5
33.43
0.9910
103.27
8
29.75
1.0227
98.52
11
13.04
1.0098
43.37
13
50.00
1.0467
212.5
Total cost($/hr)
=828.332
Active power loss (M.W) =5.9707
Variation of fitness with generations
0.14
0.12
fitness value
0.1
0.08
Series1
0.06
0.04
0.02
0
1
5
9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77
number of generations
Solution of GA OPF using TCSC
active power loss minimization
Generator Active power Voltage
Fuel cost
bus number outputs(MW) magnitudes (p.u) ($/hr)
1
51.96
1.0643
114.04
2
49.53
1.0625
129.60
5
33.33
1.0209
102.76
8
28.88
1.0408
95.59
11
33.38
1.0525
127.99
13
75.45
1.0631
368.66
Total cost($/hr)
=955.8482
Active power loss (M.W) =3.4925
Variation of fitness with generations
30
25
fitness value
20
15
Series1
10
5
0
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70
number of generations
Solution of GA OPF under base case
Fuel cost and Active power loss minimization
Generator
bus number
Active power
outputs(MW)
Voltage magnitudes
(p.u)
Fuel cost
($/hr)
1
92.23
1.0145
216.35
2
46.94
1.035
120.70
5
34.84
1.0174
110.702
8
27.46
1.0467
90.80
11
16.51
1.0766
56.34
13
50.18
1.0719
213.49
Total cost($/hr)
=829.40
Active power loss (M.W) =5.422
Variation of fitness with generations
0.12
0.115
0.11
0.105
0.1
Series1
0.095
0.09
0.085
0.08
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81
Comparison between base case OPF and OPF using TCSC:
objective: fuel cost minimization
Generator bus Active power
number
outputs (MW)
(base case)
Active power
outputs (MW)
(using TCSC)
Fuel cost
($/hr)
(base case)
Fuel cost
($/hr)
Using (TCSC)
1
110.26
88.51
266.10
206.39
2
42.81
45.97
106.98
117.42
5
34.7
33.43
109.95
103.27
8
29.98
29.75
99.30
98.52
11
15.66
13.04
53.11
43.37
13
50.66
50.00
216.14
212.5
Total cost($/hr) (base case) = 849.41
Total cost($/hr) (using TCSC) = 828.332
Comparison between base case OPF and OPF using
TCSC:
objective: active power loss minimization
Generator bus
number
Active power
outputs (MW)
(base case)
Active power
outputs (MW)
(using TCSC)
Fuel cost
($/hr)
(base case)
Fuel cost
($/hr)
Using (TCSC)
1
68.41
51.96
154.36
114.04
2
49.65
49.53
130.02
129.60
5
34.92
33.33
111.13
102.76
8
29.52
28.88
97.74
95.59
11
37.47
33.38
147.51
127.99
13
90.25
75.45
474.37
368.66
Active power loss (M.W) (base case) =4.3285
Active power loss (M.W) (using TCSC) =3.4925
Comparison between base case OPF and OPF using TCSC:
objective: fuel cost and active power loss minimization
Generator bus Active power
number
outputs (MW)
(base case)
Active power
outputs (MW)
(using TCSC)
Fuel cost
($/hr)
(base case)
Fuel cost
($/hr)
Using (TCSC)
1
108.62
92.23
261.48
216.35
2
48.26
46.94
125.21
120.70
5
34.91
34.84
111.07
110.702
8
29.37
27.46
97.24
90.80
11
15.36
16.51
52.44
56.34
13
52.45
50.18
226.12
213.49
Total cost($/hr) =872.667 ;Active power loss (M.W) =5.7255
Total cost($/hr) = 829.40 ;Active power loss (M.W) =5.422
GA solution to OPF with TCSC:75 bus Indian
system
GA solution to OPF with TCSC:75 bus Indian
system
GA solution to OPF with TCSC:75 bus Indian
system
Objective function
Fuel cost ($/hr)
Losses (MW)
Fuel cost
minimization
7947.7
167.16
Active power loss
minimization
7996.5
141.16
Fuel cost and
active power loss
minimization
7896.7
155.97
Comparison between base case OPF and OPF using
TCSC:75 bus Indian system

Objective: fuel cost minimization
Total cost($/hr) (with out TCSC)
Total cost($/hr) (with TCSC)

= 7986.9
= 7947.7
Objective: active power loss minimization
Active power losses( with out TCSC)
Active power losses (with TCSC)

= 141.73
= 141.16
Objective: fuel cost and active power loss minimization
Total cost($/hr) (with out TCSC)
=8044.8; Active power loss (M.W) =176.07
Active power loss (M.W) (with TCSC)=7896.7; Active power loss (M.W) =155.97
conclusions

Optimal power flow (OPF) has been solved using genetic algorithm
(GA) to obtain the optimal fuel cost and active power losses.

Optimal power flow (OPF) has been solved with FACTS devices i.e.
TCSC. By incorporating TCSC in the system fuel cost and active
power losses are reduced when compared to base case OPF .

Analysis for OPF is carried out on IEEE 30 bus system and it can be
extended to 75 bus Indian practical system.
References

Alberto Berrizzi, Maurizio Delfanti, Paolo Marannino, Marco savino
pasquadibisceglie, andrea Silvestri, Enhanced security-constrained OPF with
FACTS devices, IEEEtrans.on power systems, vol.20 no.3, august 2005

M.S.Osman, M.A.Abo-sinna, A.A.Mousa, ``A solution to the optimal power flow
using genetic algorithm”, Appl.math.comput.2003.

William D.Rosehart, Claudio A canizares,` `Multi objective optimal power flows to
evaluate voltage security costs in power net works” ,IEEE trans. On power
systems, vol.18,no2 ,may2003

Anastasios G. Bakirtzis, Pandel N. Biskas, Christoforos E. Zoumas, Vasilios
Petridis, ”Optimal Power Flow by Enhanced Genetic Algorithm”, IEEE
Transactions On Power Systems, Vol. 17, no. 2, pp 229-236, May 2002.

X.-P. Zhang and E. Handschin, “Optimal power flow control by converter based
facts controllers,” in Proc. 7th Int. Conf. AC-DC Power Transm., London, U.K., pp
28–30, Nov 2001.

Geraldo Leite Torres, Victor Hugo Quintana, “An Interior-Point Method For
Nonlinear Optimal Power Flow Using Voltage Rectangular Coordinates”, IEEE
Transactions on Power Systems, Vol. 13, No. 4, November 1998.

L. L. Lai, J. T. Ma, R. Yokoyama, and M. Zhao, “Improved genetic algorithms for
optimal power flow under both normal and contingent operation states,” Elec.
Power Energy Syst., Vol. 19, no. 5, pp. 287–292, 1997.

M.Noroozian, G.Anderson, “Power Flow Control by Use of Controllable Series
Components”, IEEE Transactions on Power Delivery, VO1.8, No.3, July 1993,
1420-1428.
Allocation of TCSC to optimize total transmission capacity in a competitive
power market, Wang feng student member IEEE, G.B.Shrestha senior member,
IEEE.


Optimal choice and allocation of FACTS devices using genetic algorithms. L.j.cai,
student member IEEE and Erlich, member IEEE.

Optimal location and settings of FACTS for optimal power flow problem using a
hybrid/PSO algorithm.M.A. Abido, M.M.Al-Hulail.