# Economic Dispatch and Losses Minimization using Multi-Verse Optimizer on 150 kV Mahakam Transmission System

DOI : 10.17577/IJERTV6IS010302

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#### Economic Dispatch and Losses Minimization using Multi-Verse 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

Abstract-On this paper, Multi-Verse 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.

Keywords-Economic Dispatch, Losses Minimization; Multiobjective Optimization; Optimal Power Flow; Multi Verse Algorithm; Power Generation, Capacitors

1. INTRODUCTION

Population growth and technological advances are some

2. 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].

1. 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.

2. 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 differentiation-based methods like Newton-Raphson 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 Multi-Verse 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 well-known 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.

3. 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

M

4. Constraints

(4)

(5)

1. Multi-Verse Optimizer

Multi-Verse 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, Qshunt-i 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.

3. METHODOLOGY

1. 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. Multi-verse 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

1. 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 64-bit Intel Core i7-6700 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 on-going 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
1. 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

2. 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
3. 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

2. CONCLUSION

On this paper, a new algorithm is proposed to solve multiobjective optimal power flow. This algorithm called Multi-Verse 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.

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