 Open Access
 Total Downloads : 221
 Authors : Yun Tonce Kusuma Priyanto, Muhammad Robith
 Paper ID : IJERTV6IS010302
 Volume & Issue : Volume 06, Issue 01 (January 2017)
 Published (First Online): 30012017
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Economic Dispatch and Losses Minimization using MultiVerse Optimizer on 150 kV Mahakam Transmission System
Yun Tonce Kusuma Priyanto Electrical Engineering Department Kalimantan Institute of Technology Balikpapan, Indonesia
Muhammad Robith Electrical Engineering Department Kalimantan Institute of Technology
Balikpapan, Indonesia
AbstractOn this paper, MultiVerse Optimizer (MVO) is proposed to solve multiobjective optimal power flow. This algorithm inspired from interaction of universes using black holes, white holes, and wormholes. This algorithm is used to solve multiobjective optimal power flow on 150 kV Mahakam transmission system on East Kalimantan. As comparison, PSO and FA would be used to solve the same problem. As seen on discussion section, each algorithm provide really competitive result at economic dispatch, losses minimization, and both. On the first case, MVO successfully solve the problem with most plausible result, reaching 442552.19 point. MVO also succeed solve the latter case and overcome another algorithms with 4.42 MW. On last case, MVO still solve the problem with the best result with 279499.774 point. From this results, MVO can be used to solve multiobjective optimal power flow.
KeywordsEconomic Dispatch, Losses Minimization; Multiobjective Optimization; Optimal Power Flow; Multi Verse Algorithm; Power Generation, Capacitors

INTRODUCTION
Population growth and technological advances are some

MULTIOBJECTIVE OPTIMAL POWER FLOW FORMULATION
Generally, every optimization problem can be represented using this following model:
minimize/maximize ()
subject to () = 0 (1)
() 0
On (1), f(x) is the objective function, where x is a vector containing all variables that can be controlled. g(x) and b(x) are constraints in equality or inequality forms, respectively. On this paper, cost and losses function are used as objective function. Objective function and constraints used here will explained on next section [8].

Power Losses Function
Power losses represented on this equation:
P Nl g t V 2 V2 2t V V cos
causes that increases demand of electrical energy [13]. This demand increases faster than number of electrical energy resource discovered. To solve this problem, electrical energy
loss
k k i
k1
j k i j i j
(2)
must be managed optimally. Optimality of this management can be seen on many factors, two of them are their cost and power losses that happens on system. This problem categorized as Optimal Power Flow (OPF), where the aiming for the best combination of some variables like generated power and Static VAR Compensators (SVC). OPF problems are really flexible and complex problems [1]. This means that
OPF problems may have many objectives to deal with, and these objectives may conflict each other. Until now, there are
On (2), Vi and Vj are voltage magnitude on bus i and bus
j respectively; Nl is total branches; gk is conductance of branch k; tk is transformer tap ratio installed on branch k; i and j are voltage angle on bus i and bus j respectively.

Cost Function
Operational cost of a thermal generators modeled as a cost function based on real power generated by that generator. Mathematical model used is quadratic function as
some methods proposed to solve this problem, from classical differentiationbased methods like NewtonRaphson method [2,3,4,6,8] to metaheuristic methods like Particle Swarm Optimization (PSO) [5,7]. However, first mentioned methods
below:
Ng
Fe Pg i
i1

P2
(3)
i i gi
sometimes trapped on local optima. On the other hand, metaheuristic methods successfully overcome this problem. On this paper, new algorithm is proposed to OPF problems, called MultiVerse Optimizer (MVO) [14,15]. This algorithm inspired from universes interaction mechanism. This algorithm will be tested on 150 kV Mahakam transmission system on East Kalimantan, and will be compared with two wellknown algorithms, PSO and Firefly Algorithm (FA) [9 12].
On (3), , , and are cost characteristic coefficients. Pgi
is real power supplied by generator i and Ng is total generators.


Real and Reactive Power Balance
On power flow, (4) and (5) must hold, where P and Q are real and reactive power respectively. Gi, load, and losses indexes are tags to mark any variables above to generator i, load, and losses respectively.
M
PGi Pload Plosses i1
M
QGi Qload Qlosses i1

Constraints
(4)
(5)

MultiVerse Optimizer
MultiVerse Optimizer (MVO) founded by Seyedali Mirjalili on 2015 [14]. MVO is a new algorithm that inspired by interaction between universes with a mechanism known as black holes, white holes, and wormholes. There are some theories that explain universes origin, one of them is Multi Verse Theory. This theory states that there are other universes outside the universe that mankind live, where each universes interact each other. When interaction occurs, they interact using some mechanism known as black holes and white
These following inequalities are constraints used in this
paper:
holes. These holes connect two different universes where an object enters black hole and come out through white hole. In addition to these holes, there are wormholes that connects
P P P
min max
Gi Gi Gi
Q Q Q
min max
Gi Gi Gi
Qmin Q Qmax
(6)
(7)
(8)
two point on the same universe. MVO is created using these interaction described above. To convert this to a mathematical model, we apply these approachs:

A galaxy is assumed as a combination of some objects

shunt i
shunt i
shunt i
(or variables) to be optimized. This algorithm search
t min t t max
(9)
for a galaxy with the best objective value through
i i i
On (6) to (9), Pgi is real power supplied by generator i, Qgi is real power supplied by generator i, Qshunti is capacity of capacitor banks installed on bus i, and ti is transformer tap ratio installed on branch i. min and max indexes are tags to mark any variables above to maximum and minimum values respectively. Inequality (6) represent real power constraint; inequality (7) represent reactive power constraint; inequality
(8) represent capacity constraint on installed capacitor; and inequality (9) is transformer tap ratio constraint.


METHODOLOGY

Weighted Sum Method
Optimal solutions of multiobjective function are solutions from some objective functions simultaneously. To simplified those functions, weighted sum method is proposed. This methods combine all objective functions into a single objective function. For multiobjective optimal power flow in this paper, this method formulated as follow:
some mechanisms.

Probability of black holes or white holes existence on a galaxy determined from its objective value. White holes probability is higher whenever its objective value is far from optimum, and vice versa.

Every objects has chances to moving randomly in the same galaxy.

Flowchart of this algorithm for multiobjective power flow is given in fig. 1. First operation executed is black and white holes mechanism. First, each galaxy are sorted based on their objective values, then normalied them. For each variable, we assign a variable form a galaxy randomly (not nessecary different). Randomly selected galaxy are chosen by roulette wheel method. This method chosen for provide variables from the best galaxy to others. This mechanism works like GAs crossover, but GA exchange their gen with others. Pseudocode of this mechanism is given at fig. 2.
Second operation executed is wormholes mechanism. On this mechanism, each variable may move randomly. There are two parameters used for this mechanism,
F w1f1 w2f2
Nl
fref max
PLosses Max k1
(10)
(11)
Wormhole Existence Probability (WEP) and Travelling Distance Rate (TDR). WEP determine each variable move or not, and TDR determine how far they move. This movement following one of these equations:
, = , + TDR Ã— (3 Ã— ( ) + ) (14)
, = , TDR Ã— (3 Ã— ( ) + ) (15)
Ng
fref max

P
(12)
Where Xi,j is the best variable reached so far, ub and lb
i i i1
2
i gi
are upper and lower bound of that variable respectively. Constant value may be assigned for WEP and TDR, but these
w1 w2 1
(13)
values may be vary following these equation:
On (10), f1(x) and f2(x) will be subtituted with (2) and (3). and are penalty factor. w1 and w2 are weighting factors,
WEP = min + Ã— max min
1/
(16)
where w 1 and satisfy (13) [10].
TDR = 1 ( )
(17)
Fig. 1. Multiverse optimizer flowchart for this paper
SG = sorted_galaxy
NF = normalized_fitness for each galaxy indexed by i
black_hole_index = i
for each variable indexed by j r1 = random(0,1)
if r1 < NF(xi)
white_hole_index = roulette_wheel(NF) G(i,j) = SG(white_hole_index,j)
end if end for
end for

SIMULATION AND DISCUSSION
Input data, test cases, and algorithms used as comparison algorithm will be summarized before simulations started. Transmission system that would be used on this paper is 150 kV Mahakam transmission system on East Kalimantan. Single line diagram of this system given in fig.3. There are three test cases to be examined. They are economic dispatch, losses minimization, and both. Algorithms used as comparison algorithm on this paper are PSO and Firefly Algorithm (FA). On this paper, each algorithm using 20 search agents that searching for best combination for 10000 iterations, performed 10 times on 64bit Intel Core i76700 computer with 16 GB RAM. Parameters used by all algorithms and cost characteristic functions of all generators shown in tables below.
apply (16) and (17)
for each galaxy indexed by i
for each variable indexed by j r2 = random(0,1)
if r2 < WEP
r3 = random(0,1) r4 = random(0,1) if r4 < 0.5
apply (14)
else apply (15) end
end if end for
end for
Fig. 3. Wormhole mechanism
Fig. 2. Black and white hole mechanism
Generator
Cost characteristic function
Minimum
Power
Maximum
Power
Generator 1
2 + 2288,5P
C1 = 16,873 P1 1
1524,5
41
100
Generator 2
C2 = 1658,7P2
20
80
Generator 3
C3 = 2213,2P3
11
190
Generator 4
C4 = 2628,8P4
1.74
50
On (16) and (17), min and max are manimum and maximum values assigned for WEP. On this paper min = 0.2 and max = 1 are assigned. p describe algorithms exploitation ability, where 6 is assigned on this paper. l and L are ongoing and maximum iteration respectively. Pseudocode of this mechanism given on fig. 3.
Fig. 4. 150 kV Mahakam transmission system single line diagram TABLE 1. GENERATORS COST CHARACTERISTIC FUNCTION
TABLE 2. LOAD DATA FOR EACH BUS
Bus
Number
Bus
Code
Real Power Load
(MW)
Reactive Power
Load (MW)
1
0
56.164
18.396
2
0
60.925
19.374
3
2
0
0
4
0
49.622
11.519
5
2
23.264
4.385
6
0
77.442
32.866
7
1
57.116
8.033
8
0
18.747
4.790
9
0
18.331
6.368
10
0
11.179
2.785
11
0
23.439
9.759
12
2
15.452
4.541
TABLE 3. LINE IMPEDANCE DATA FOR EACH BUS
Bus Number
Resistance (p.u.)
Impedance (p.u.)
Supceptance (p.u.)
From
To
1
2
0.058135
0.167716
0.002392
2
3
0.016497
0.048836
0.000825
3
4
0.016497
0.048836
0.000825
4
5
0.185652
0.549582
0.009285
5
6
0.020436
0.060498
0.001022
5
9
0.032907
0.094933
0.001354
6
7
0.038903
0.115164
0.001946
7
8
0.056216
0.162178
0.002313
9
10
0.017728
0.052480
0.000887
10
11
0.110800
0.328000
0.005541
10
12
0.221600
0.656000
0.011083
TABLE 4. MVO PARAMETERS
Parameter
Value
min
0.2
max
1
p
6
TABLE 5. PSO PARAMETERS
Parameter
Value
w
0.9
c1
0.1
c2
0.1
TABLE 6. FA PARAMETERS
Parameter
Value
beta
1
gamma
0.5

Test Case 1: Economic Dispatch
On the first case, each algorithms perform economic dispatch on 150 kV Mahakam transmission system. Table 5 and 6 shows simulation result of this case. From table 9, MVO and PSO provide adjacent power generation, while FA provide a little different result power generation 3 and 4. However, even each algorithms provide variative capacitor result, these algorithms provides competitive itness values. MVO successfully overcome other algorithms, as seen on table 6. To obtain each algorithms characteristic, fig. 5 provide the best fitness value reached each iterations from any randomly selected data, where MVO represented on blue curve, PSO on red curve, and FA on yellow curve. It can be seen that MVO actually can overcome all other algorithms near 1000th iterations and converge even at the start at process.
TABLE 5. OBTAINED VARIABLES FROM EACH ALGORITHM FROM TEST CASE 1
Variable
MVO
PSO
FA
Generation Power 1 (MW)
99.999
99.973
99.977
Generation Power 2 (MW)
79.910
78.672
79.428
Generation Power 3 (MW)
110.92
112.570
101.19
Generation Power 4 (MW)
2.2490
1.996
11.847
SVC 1 (MVAR)
28.302
19.858
38.092
SVC 2 (MVAR)
18.310
48.716
35.159
SVC 3 (MVAR)
19.266
10.283
27.068
SVC 4 (MVAR)
39.385
21.040
42.041
SVC 5 (MVAR)
27.372
27.964
20.575
TABLE 6. TEST CASE 1 SIMULATION RESULT
Method used
Best Fitness
MVO
442552.19
PSO
443506,526
FA
445471.413
Fig. 5. Total cost convergence curve

Test Case 2: Losses Minimization
On the second case, each algorithms perform losses minimization on 150 kV Mahakam transmission system. Table 7 and 8 shows simulation result of this case. From these tables, each algorithm give adjacent result on all generation power, but slightly different SVC results. However, each algortihm provides really competitive fitness value. MVO successfully overcome other algorithms, as seen on table 8. To obtain each algorithms characteristic, fig. 6 provide the best fitness value reached each iterations from any randomly selected data, where MVO represented on blue curve, PSO on red curve, and FA on yellow curve. It can be seen that MVO sometimes get another best fitness value, different than other algorithms that can converge at the start of iteration.
Variable
MVO
PSO
FA
Generation Power 1 (MW)
99,999
99,828
99,883
Generation Power 2 (MW)
79,985
79,565
79,260
Generation Power 3 (MW)
93,196
89,957
91,512
Generation Power 4 (MW)
18,839
22,809
21,457
SVC 1 (MVAR)
24,090
27,151
29,034
SVC 2 (MVAR)
23,013
32,392
20,631
SVC 3 (MVAR)
10,209
22,313
13,298
SVC 4 (MVAR)
35,921
48,418
49,444
SVC 5 (MVAR)
24,295
13,703
47,066
TABLE 7. OBTAINED VARIABLES FROM EACH ALGORITHM FROM TEST CASE 2
TABLE 8: TEST CASE 1 SIMULATION RESULT
Method used
Best Fitness
MVO
4.42
PSO
4.513
FA
4.56

Test Case 3: Economic Dispatch and Losses Minimization
As the last test case, all algorithms would be used to solve multiobjective optimal power flow on same transmission system, where both Economic Dispatch and Losses Minimization melted into a single objective function by weight sum method. Table 9 and 10 shows simulation result of this case. From table 9, one can see that these results has almost the same characteristic with results on test case 1. MVO gives the minimum fitness value than others, as seen on table 10. To obtain each algorithms characteristic, fig. 7 provide the best fitness value reached each iterations from any randomly selected data, where MVO represented on blue curve, PSO on red curve, and FA on yellow curve. It can be seen that result of this case is almost the same with previous case.
Fig. 6. Total losses convergence curve
TABLE 9: OBTAINED VARIABLES FROM EACH ALGORITHM FROM TEST CASE 3
Variable
MVO
PSO
FA
Generation Power 1 (MW)
100
99,846
99.978
Generation Power 2 (MW)
80
79,319
79.622
Generation Power 3 (MW)
95.689
96,224
94.283
Generation Power 4 (MW)
22.335
16,683
18.225
SVC 1 (MVAR)
2.869
23,956
22.203
SVC 2 (MVAR)
32.728
21,581
40.113
SVC 3 (MVAR)
8.948
4,767
29.834
SVC 4 (MVAR)
38.725
23,425
45.350
SVC 5 (MVAR)
31.029
12,323
26.731
TABLE 10: TEST CASE 3 SIMULATION RESULT
Method used
Best Fitness
Total Cost
Power Losses
(MW)
MVO
279499.774
448513.690
4.470
PSO
280474.940
447149.492
4.472
FA
280982.273
447265.95
4.507
Fig. 6. Test case 3 convergence curve


CONCLUSION
On this paper, a new algorithm is proposed to solve multiobjective optimal power flow. This algorithm called MultiVerse Optimizer (MVO). This algorithm inspired from interaction of universes using black holes, white holes, and wormholes. This algorithm is used to solve multiobjective optimal power flow on 150 kV Mahakam transmission system. As comparison, PSO and FA would be used to solve the same problem. As seen on discussion section, each algorithm provide really competitive result at economic dispatch, losses minimization, and both. Each algorithms provide almost the same result on generation power on each generator, but really different SVC values, that proves non linearity of each cases. MVO successfully overcome other algorithms on each cases. This makes MVO as a option to solve any multiobjective optimal power flow.
REFERENCES

Dommel, H.W., Tinney, W.F. (1968). Optimal power flow solution, IEEE Transactions on Power Apparatus and Systems, PAS87(10), 18661876.

Sun, D.I., Ashley, B., Brewer, B., Hughes, A., Tinney, W.F. (1984). Optimal power flow by Newton approach. IEEE Transactions on Power Apparatus and Systems, PAS103(10), 28642880.

Santos A, da costa GR. (1995). Optimal power flow by Newtons method applied to an augmented lanrangian function. IEE Proc Gener Transm Distrib, 3336

Wood, A.J., Wollenberg, B.F. (1996). Power generation operation and control, NJ: John Wiley & Sons Ltd.

Abido, M.A (2002), Optimal power flow using particle swarm optimization, International Journal of Electrical Power and Energy System, 24(7), 563571.

Saadat, H. (2004). Power system analysis (2nd edition), NY: McGraw Hill

Roy. R., Ghoshal, S.P. (2008). A novel crazy swarm optimized economic load dispatch for various types of cost function, Electrical Power and Energy Systems 30(4), 242253.

Zhu, J. (2009). Optimization of power system, NJ: John Wiley & Sons

Yang, X.S. (2009). Firefly algorithms for multimodal optimization, in:
Stocasthic Algorithms: Foundations and Applications, 5792, 169178

Yang, X.S. (2010). Engineering optimization: An introduction with metaheuristic applications, NJ: John Wiley & Sons

Yang, X.S. (2010). Firefly algorithm, Levy flights and global optimization, in: Research and development in intellegent systems, 209218

Yang, X.S. (2010). Firefly algorithm, stochastic test function, and design optimization, Int. J. BioInspired Computation, 2(2), 7884

Priyanto, Y.T.K., Hendarwin, L. (2015). Multi objective optimal power flow to minimize losses and carbon emission using wolf algorithm, International Seminar on Intelligent Technology and Its Applications.

Mirjalili, S., Mirjalili S.M., Hatamlou, A. (2015). MultiVerse Optimizer: a natureinspired algorithm for global optimization. Neural Comput. & Applic. http://dx.doi.org/ 10.1007/s0052101518707

Jangir, P., Parmar, S.A., Trivedi, I.N., Bhesdadiya, R.H. (2016). A novel hybrid Particle Swarm Optimizer with multi verse optimizer for global numerical optimization and Optimal Reactive Power Dispatch problem. Eng. Sci. Tech., Int. J. http://dx.doi.org/10.1016/j.jestch.2016.10.007