1. OPTIMAL POWER FLOW WITH TCSC USING GENETIC ALGORITHM
Under the guidance of
Prof. D.M. Vinod Kumar
K.Sreenivasulu
M.Tech (PSE)
Roll No

2. 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

3. Contents 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

4. 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)

5. 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
subject to
u :vector of problem control variables
x :vector of system state variables
: objective function to be minimized

6. Control variables State variables
u is a vector of control variables consisting of generator voltages, generator active power out puts, transformer tap settings and shunt VAR compensation
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.

7. Inequality constraints
Real power balance equation
Reactive power balance equation
Inequality constraints

8. 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.

9. 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

10. 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.

11. 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.

12. 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

13. 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

14. a, b, c constants for generators : Pgmax and Pgmin for generators :
Generator No a b c 1 2
1.75
0.0175 3
0.0625 4
3.25 5
0.025 6
Generator bus no
Pgmin
Pgmax 1
0.5
2.0 2
0.2
0.8 5
0.15 8
0.1
0.35 11
0.3 13

15. 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

16. Variation of fitness with number generations

17. 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

18. Variation of fitness with number generations

19. 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) =
Active power loss (M.W) =5.7255

20. Variation of fitness with number generations

21. 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
5.7255

22. 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

23. 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.

24. Modeling of TCSC
The difference between the line admittance before and after the addition of TCSC can be expressed as:
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:

25. 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

26. 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.

27. 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.

28. 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.

29. 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

30. Solution of GA OPF using TCSC Fuel cost minimization
Generator bus number
Active power outputs(MW)
Voltage 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) =
Active power loss (M.W) =5.9707

31. Variation of fitness with generations

32. Solution of GA OPF using TCSC active power loss minimization
Generator bus number
Active power outputs(MW)
Voltage magnitudes (p.u)
Fuel cost
($/hr) 1
51.96
1.0643
114.04 2
49.53
1.0625
129.60 5
33.33
1.0209
102.76 8
28.88
1.0408
95.59 11
33.38
1.0525
127.99 13
75.45
1.0631
368.66
Total cost($/hr) =
Active power loss (M.W) =3.4925

33. Variation of fitness with generations

34. 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
($/hr) 1
92.23
1.0145
216.35 2
46.94
1.035
120.70 5
34.84
1.0174 8
27.46
1.0467
90.80 11
16.51
1.0766
56.34 13
50.18
1.0719
213.49
Total cost($/hr) =829.40
Active power loss (M.W) =5.422

35. Variation of fitness with generations

36. Active power outputs (MW)
Comparison between base case OPF and OPF using TCSC: objective: fuel cost minimization
Generator bus number
Active power outputs (MW)
(base case)
(using TCSC)
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) =
Total cost($/hr) (using TCSC) =

37. Active power outputs (MW)
Comparison between base case OPF and OPF using TCSC: objective: active power loss minimization
Generator bus number
Active power outputs (MW)
(base case)
(using TCSC)
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

38. Comparison between base case OPF and OPF using TCSC: objective: fuel cost and active power loss minimization
Generator bus number
Active power outputs (MW)
(base case)
(using TCSC)
Fuel cost
($/hr)
Using (TCSC) 1
108.62
92.23
261.48
216.35 2
48.26
46.94
125.21
120.70 5
34.91
34.84
111.07 8
29.37
27.46
97.24
90.80 11
15.36
16.51
52.44
56.34 13
52.45
50.18
226.12
213.49
Total cost($/hr) = ;Active power loss (M.W) =5.7255
Total cost($/hr) = ;Active power loss (M.W) =5.422

39. GA solution to OPF with TCSC:75 bus Indian system

40. GA solution to OPF with TCSC:75 bus Indian system

41. 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

42. Comparison between base case OPF and OPF using TCSC:75 bus Indian system
Objective: fuel cost minimization
Objective: active power loss minimization
Objective: fuel cost and active power loss minimization
Total cost($/hr) (with out TCSC) =
Total cost($/hr) (with TCSC) =
Active power losses( with out TCSC) =
Active power losses (with TCSC) =
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

43. 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.

44. 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 , 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.

45. 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,
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.