 Open Access
 Total Downloads : 23
 Authors : Mrs. Shivani Mehta , Mr. Baljit Singh , Mr. Gagandeep
 Paper ID : IJERTV8IS060585
 Volume & Issue : Volume 08, Issue 06 (June 2019)
 Published (First Online): 28062019
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Harris Hawks Optimization for Solving Optimum Load Dispatch Problem in Power System
Mrs. Shivani Mehta (Assistant Professor)
Mr.Baljit Singh (Assistant Professor)
Mr.Gagandeep (Lecturer)

Institute of Engg. and Tech. Jalandhar
AbstractOptimum load dispatch problem (OLDP) is regular work in operative scheduling that needs to be optimized, in the power system. Here in the paper the problem on optimum load dispatch technique for Harris hawk optimization is effectually and consistently presented. The result indicates OLDP for various test system examining transmission losses and the valve point loading effect. The concluding results gained using HHO are compared with other algorithms and found to be encouraging.
Keywords Optimum load dispatch; HHO , transmission losses & valve point effects

INTRODUCTION
Optimum load dispatch problem (OLDP) is one of the main consequential affair of the power system, which is intent for the output power for each constant which generates electricity unit in an effort to decrease the cost of operation and simultaneously limits the matching power operation and load demand usually to satisfy system constraints the power system operation is grounded on reducing the cost of operation. This problem is periodically made easier by establishing the premises like even and exterior cost curve of generating units, which consequence quadratic cost functions for a generator. Literally, OLDPs intentive function has nondiffusiable points by reason of the valve point effect ascribed to that cost curves are nonlinear. Consequently in objective function, unsmooth cost function has to be involved. Intend conventional technique to solve OLDP contain the linear programming technique, incline technique, lambda repetition method and Newtons technique [1].
Long ago, numerous higher level approaches have been used to solve economic load dispatch such as Genetic algorithm [2,3], Tabu search [4],Evolutionary programming (EP) [5], Differential evolution [6] , particle swarm optimization (PSO) [7 10],gravitational search algorithm(GSA) [11], optimization on biogeography[12],Seeker optimization algorithm [13],Firefly algorithm [14],Simulated annealing (SA)[15],Harmony search[16,17],Shuffled frog leaping algorithm(SFLA) [18],Hybrid genetic algorithm(HGA) [19],Binary bat algorithm[20], Ant lion optimization[22], & multi verse optimization[23]etc.
Ali Asghar Heidariet.al. [21], suggest a new discover algorithm HHO inspired by chasing way of Harris hawks. In this report transmission losses for 3 and 6 generating unit systems solved economic load dispatch problem and HHO for 40 unit system solved the valve point effect. This section condenses the key steps to interpret the optimum load dispatch problem in HHO literature stated that the result acquired with the HHO algorithm was assessed and estimated with other methods.
PROBLEM PHRASING
For optimum load dispatch the objective function to be decreased, is given by:
=1
=1
() = (2 + + ) (1)
And after including the valve point loading effects the equation (1) is modified as below:
n
() = (aiP2 + biPi + ci) +  Ã— sin{ Ã— (Pmin Pgi)}
i gi
i=1
Where fuelcost coefficients of the ith unit are ai, bi, and ci, and di & ei are with the valvepoint effects [5]. The total fuel cost has to be decreased with the following restraints:

Power balance restraint
The power generation (Pgi) should be equal to the sum of power demand (Pd) and power loss ( ).
=1
(2)
=1
=1
The power loss Pl intended as:
=1
=1
=
=1
+
0 + 00
(3)

Generator limit restraint
The particular lower operating limits and upper operating limits are controlled each generators real power generation.
i=1,2,…,ng (4)


HARRIS HAWK OPTIMIZATION (HHO)
This section condenses the key steps to interpret the optimum load dispatch problem in Harris Hawk optimization (HHO). Ali Asghar Heidariet initiated the HHO. The Hunting activities of the Harris Hawks stimulated this algorithm. This predator demonstrates developed pioneering group pursuing ability in marking, enclosing, chasing ultimately assaulting the impending victim the Hawks in frequently will do a leaping movement right through the goal location and they reunite and how more than a few times to eagerly look for the sanctuary animal, that is mostly a rabbit. Surprise pounce is the major approach of Harris Hawks to imprison a victim that is also considered as Seven Skill technique.
With this prudent plan various agitators attempt to willingly assault from various directions and concurrently join to identify the escaped rabbit outside of the curve. In few seconds by imprisoning the surprising victim the assault may swiftly be finished but erratically concerning the escaping capabilities and action of the victim, many short length speedy dives close to the victim throughout various minutes, may contain in the in the Seven kills..

Exploration phase
Harris hawks mainly based upon two techniques roost randomly on some location and hang around to identify a victim. If we take a fair possibility q for every roosting policy. They roost according to other family members and rabbits position. That is shown in equation (5) for q < 0.5, or roost on fluky lanky trees, that shown in equation (5) for q 0.5 condition.
() 1 () 22() 0.5
( + 1) = [ ] (5)
() () 3( + 4( )) 0.5
Where in the next repetition t, X (t + 1) is upcoming repetition position sector of hawks. Rabbits position is X_rabbit (t), recent various quantity of hawks is X (t), r1, r2, r3, r4, and q were fluky numbers in (0, 1), which are updated repitedly, Lower and Upper bounds are shown as LB and UB of various variables bounds, from the recent population X_random (t) is arbitrarily chosen hawk, and X_m (t) is the hawks average positions current position.

Transformation from exploration to exploitation
Power of the sufferer diminishes unusually during escaping actions. Energy of the sufferer is imitated as shown in equation no. (6)
E=2E0 (1t/T) (6)
Here E is victim evading energy, T denoted the repetitions extreme number, and E0 is the preliminary position of power. E0 at every repetition usually converts in HHO, at every repetition in the interim (1, 1). E0 decreases from 0 to 1, rabbit is actually waning, that means strength of rabbit is increasing if the value of E0 expands from 0 to 1. In repetition Zestful escaping power E has a declining tendency. When E 1exploration occur, where E <1exploitation occur.

Exploitation phase
During this stage, Harris hawks carry out astonishment dive (seven kills) by attacking the proposed sufferer identified in the previous phase. Just as the busting manners of the sufferer and the pursuing tactics of Harris Hawks, there are four probable strategies to show the pounce stage in the HHO.
E parameters employed to allow HHO to toggle between soft and hard besiege procedure, to explore this approach. Considerably, when E 0.5, the soft besiege occurs, and when E <0.5, the hard besiege take place.

Soft besiege
Rabbit still has suffcient vigor When r 0.5 and E 0.5, by some arbitrary deceptive jumps rabbit has an attempt to flee but lastly it cannot., Harris hawks enclose easily throughout these attempts to make more worn out the rabbit then carry out the surprise pounce. Rules shown following by this behavior
X (t + 1) = X (t) E J Xrabbit(t) X (t) (7)
X (t) = Xrabbit (t) X (t) (8)
Where X (t) show the dissimilarity between the current position in iteration t, and vector of the rabbit, r5 is an arbitrary number in (0, 1), and J = 2(1 r5) shows the unsystematic dive power of rabbit all through the busting process. J alters usually in every repetition to replicate the motion character of rabbit.

Hard besiege
The sufferer is so worn out and it has a small escaping power when r 0.5 and E <0.5, then, the Harris hawks barely enclose the proposed victim to lastly carry out the astonishment dive. Additionally, the recent using eq. (9) updated in this situation.
X (t + 1) = Xrabbit (t) E X (t)
(9)

Soft besiege with progressive rapid dives
The rabbit has sufficient power to effectively escape When still E 0.5 but r<0.5 and still previously the astonishment dive a soft besiege is created. This process is cleverer than pretending case.
In the HHO algorithm the levy flight (LF) concept is implemented. To precisely replicate the escaping patterns of the victim and the leap frog movement.
From the rule in the equation (10) it is believed that the Hawks can decide their subsequent moves to perform a soft besiege. Y = Xrabbit (t) E J Xrabbit (t) X (t) (10)
They evaluate the probable outcome of preceding jump to perceive that whether it be good or not. They also begin to carry out uneven, abrupt, and brisk dives if it was not rational, when approaching the rabbit. It is thought that LFbased patterns used by following rule:
Z = Y + S Ã— LF(D) (11)
Levy flight function is LF and S is an arbitrary size 1 Ã— D and D is the dimension of problem. Eq. (10) can perform the Locations of hawks in the soft besiege phase.
X (t + 1) ={Y if F(Y) < F(X (t))
Z if F (Z) <F(X (t))} (12)

Hard besiege with progressive rapid dives
The rabbit has not adequate power to get away and hard besiege is done ahead of the astonishment dive to seize and kill the sufferer. When E <0.5 and r <0.5, the circumstances of victim side are alike the soft besiege, but at the time, the busting sufferer to minimize the average distance position of hawks. Accordingly, hard besiege condition shown in the following result: X (t + 1) ={Y if F(Y ) < F(X(t)); Z if F(Z) < F(X(t))} (13)
Where eq.(14) and (15) obtain Y and Z using new rules.
Y = Xrabbit (t) E J Xrabbit (t) Xm (t) (14)
Z = Y + S Ã— LF (D) (15)


RESULTS& DISCUSSIONS

Study system I: Three generating units
The loss coefficient matrix Bmn data and input data of study system I has taken from reference [14] with the help of HHO technique solved the study system I and compare with the other techniques.
Table 1.1: Results of study system I with the help of HHO technique
Sr.no.
Power Demand (MW)
P1(MW)
P2(MW)
P3(MW)
PLoss (MW)
Fuel Cost (Rs/hr)
1
500
105.8
212.62
193.5
11.91568
25465.47042
2
700
154.51
289.36
279.88
23.7679
35424.44203
Table 1.2: Comparison of study system I results to other techniques.
Sr.no.
Power demand (MW)
Fuel Cost (Rs/hr)
Lambda Iteration Method [14]
Fire Fly algorithm [14]
HHO
1
500
25495.2
25465.5
25465.469
2
700
35466.3
35424.4
35424.44203
25500
25495
25490
OPERATING COST
OPERATING COST
25485
25480
25475
25470
25465
25460
25455
25450
LI FFA HHO
500 MW demand
Figure 1: Comparison of fuel cost with other techniques
Figure 2: Convergence curve for 3 generators with 500 MW demand
Study system II: Six generating units
The loss coefficient matrix Bmn data and input data of study system II has taken from reference [14] with the help of HHO technique solved the study system II and compare with the other techniques
Table 1.3: Results of study system II with the help of HHO technique
Sr.no.
Power Demand (MW)
P1 (MW)
P2 (MW)
P3 (MW)
P4 (MW)
P5 (MW)
P6 (MW)
PLoss (MW)
Fuel Cost (Rs/hr)
1
700
28.29
10.00
119.23
118.51
230.66
212.72
19.428
36912.14
2
900
36.64
21.13
163.65
153.09
284.08
273.40
31.9911
47045.176
Table 1.4: Comparison of study system II results to other techniques.
Sr.No.
power demand (MW)
Fuel Cost
Lambda Iteration Method [14]
FireFly Algorithm [14]
HHO
1
700
36946.4
36912.2
36912.14
2
900
47118.2
47045.3
47045.176
47140
47120
OPERATING COST
OPERATING COST
47100
47080
47060
47040
LI FFA HHO
47020
47000
900 MW demand
Figure 3: Comparison of fuel cost with other techniques for900 MW demand
Figure 4: Convergence curve for 6 generators with 900MW demand

Study system III: Forty generating units
The 40 generating units data is adopted from [5]. In this case valve point effect has been considered while solving optimum load dispatch using HHO algorithm. The results obtained have been depicted below in tabular form and compared with other algorithms.
Table 1.5: OLDP using HHO for study system III with 10,500 MW load demand
Gen
Power Output
Gen
Power Output
Gen
Power Output
Gen
Power Output
Pg1
113.998
Pg11
98.3407
Pg21
527.208
Pg31
190
Pg2
113.660
Pg12
103.580
Pg22
523.685
Pg32
190
Pg3
100.205
Pg13
125.020
Pg23
523.692
Pg33
189.989
Pg4
180.880
Pg14
394.282
Pg24
524.641
Pg34
173.497
Pg5
88.490
Pg15
394.329
Pg25
523.454
Pg35
200
Pg6
139.994
Pg16
394.283
Pg26
523.268
Pg36
199.975
Pg7
300
Pg17
489.677
Pg27
10.681
Pg37
97.072
Pg8
284.970
Pg18
489.568
Pg28
10.252
Pg38
109.987
Pg9
289.585
Pg19
512.127
Pg29
10.544
Pg39
109.843
Pg10
130.113
Pg20
511.450
Pg30
96.373
Pg40
511.271
Total power generation (MW)
10500
Minimum Cost (Rs)
121731.6224
Table 1.6: comparison of OLDP results for study system III with other algorithms in literature.
Method
Minimum Cost ($/ h)
Average Cost ($/ h)
Maximum Cost ($/ h)
HGPSO [52]
124797.13
126855.70
NA
SPSO [52]
124350.40
126074.40
NA
PSO [18]
123930.45
124154.49
NA
CEP [47]
123488.29
124793.48
126902.89
HGAPSO [52]
122780.00
124575.70
NA
FEP [47]
122679.71
124119.37
127245.59
MFEP [47]
122647.57
123489.74
124356.47
IFEP [47]
122624.35
123382.00
125740.63
TM [53]
122477.78
123078.21
124693.81
EPSQP [18]
122323.97
122379.63
NA
MPSO [54]
122252.26
NA
NA
ESO [55]
122122.16
122524.07
123143.07
HPSOM [52]
122112.40
124350.87
NA
PSOSQP [18]
122094.67
122245.25
NA
GA_MU [57]
122000.2837
NA
NA
Improved GA [56]
121915.93
122811.41
123334.00
HPSOWM [52]
121915.30
122844.40
NA
IGAMU [57]
121819.25
NA
NA
HDE [58]
121813.26
122705.66
NA
PSO [21]
121735.4736
122513.9175
123467.40
HHO
121731.6224
122310.253
122954.09
Minimum Cost
125500
125000
124500
124000
123500
123000
122500
122000
121500
121000
120500
120000
Figure 5: Comparison of results for 40Unit system


CONCLUSION

HHO is latest higher level technique. In this report OLDP is solved with transmission losses and valve point effects using HHO for different test cases. In power system to solve optimum load dispatch the affect outcome unveil the potency of hardness of the HHO algorithm. The algorithm is used in MATLAB (R2009) Software. For solving optimum load dispatch problem the differentiation of the results with other methods unveil the accomplishment of HHO algorithm.
REFERENCES:

A.J Wood and B.F. Wollenberg, Power Generation, Operation, and Control, John Wiley and Sons, New York, 1984.

David C. Walters and Gerald B. Sheble. Genetic algorithm solution of economic dispatch with valve point loading. IEEE Transactions on Power Systems. 1993: 8.

Chiang, ChaoLung. "Improved genetic algorithm for power economic dispatch of units with valvepoint effects and multiple fuels." Power Systems, IEEE Transactions on 20, no. 4 (2005): 16901699.

S. Khamsawang, C. Boonseng and S. Pothiya. Solving the economic dispatch problem with Tabu search algorithm. IEEE Int Conf Ind Technol. 2002; 1: 2748.

Nidul Sinha, R. Chakrabarti, and P. K. Chattopadhyay. Evolutionary programming techniques for economic load dispatch. IEEE Transactions on Evolution Computation. 2003; 7: 8394.

N. Noman and H. Iba. Differential evolution for economic load dispatch problems. Electric Power Systems Research. 2008; 78: 132231.

J. Park, K. Lee and J. Shin. A particle swarm optimization for economic dispatch with nonsmooth cost functions. IEEE Transactions on Power Systems. 2005; 20: 3442.

T. Aruldoss Albert Victoire and A. Ebenezer Jeyakumar. Hybrid PSOSQP for economic dispatch with valvepoint effect. Electric Power Systems Research. 2004; 71: 519.

L. D. S. Coelho, V. C. Mariani, Particle swarm approach based on quantum mechanics and harmonic oscillator potential well for economic load dispatch with valvepoint effects, EnergyConversion and Management, vol. 49, 2008, pp. 30803085.

Niu, Qun, Xiaohai Wang, and ZhuoZhoua. "An Efficient Cultural Particle Swarm Optimization for Economic Load Dispatch with Valvepoint Effect." Procedia Engineering 23 (2011): 828834.

Duman, S., U. GÃ¼venÃ§, and N. YÃ¶rÃ¼keren. "Gravitational search algorithm for economic dispatch with valvepoint effects." International Review of Electrical Engineering 5, no. 6 (2010): 28902895.

Bhattacharya A, Chattopadhyay PK. Biogeographybased optimization for different economic load dispatch problems. IEEE Trans Power Syst 2010;25(2):106477.

Shaw, B., S. Ghoshal, V. Mukherjee, and S. P. Ghoshal. "Solution of Economic Load Dispatch Problems by a Novel Seeker Optimization Algorithm." International Journal on Electrical Engineering and Informatics 3, no. 1 (2011): 2642.

Reddy, K. Sudhakara, and M. Damodar Reddy. "Economic load dispatch using firefly algorithm." International journal of engineering research and applications 2, no. 4 (2012): 23252330.

Vishwakarma, Kamlesh Kumar, Hari Mohan Dubey, Manjaree Pandit, and B. K. Panigrahi. "Simulated annealing approach for solving economic load dispatch problems with valve point loading effects." International Journal of Enginering, Science and Technology 4, no. 4 (2013): 6072.

Wang, Ling, and Lingpo Li. "An effective differential harmony search algorithm for the solving nonconvex economic load dispatch problems." International Journal of Electrical Power & Energy Systems 44, no. 1 (2013): 832843.

Hatefi, A., and R. Kazemzadeh. "Intelligent tuned harmony search for solving economic dispatch problem with valvepoint effects and prohibited operating zones." Journal of Operation and Automation in Power Engineering 1, no. 2 (2013).

Roy, Priyanka, Pritam Roy, and Abhijit Chakrabarti. "Modified shuffled frog leaping algorithm with genetic algorithm crossover for solving economic load dispatch problem with valvepoint effect." Applied Soft Computing 13, no. 11 (2013): 42444252.

Kherfane, R. L., M. Younes, N. Kherfane, and F. Khodja. "Solving Economic Dispatch Problem Using Hybrid GAMGA." Energy Procedia 50 (2014): 937944.

Bestha, Mallikrjuna, K. Harinath Reddy, and O. Hemakeshavulu. "Economic Load Dispatch Downside with ValvePoint Result Employing a Binary Bat Formula." International Journal of Electrical and Computer Engineering (IJECE) 4, no. 1 (2014): 101107.

A.A. Heidari, S. Mirjalili, H. Faris et al., Harris hawks optimization: Algorithm and applications, Future Generation Computer Systems (2019),https://doi.org/10.1016/j.future.2019.02.028.

N. Chopra and S. Mehta, "Multiobjective optimum generation scheduling using Ant Lion Optimization," 2015 Annual IEEE India Conference (INDICON), New Delhi, 2015, pp. 16.doi: 10.1109/INDICON.2015.7443839

N. Chopra and J. Sharma, "Multiobjective optimum load dispatch using Multi Verse Optimization," 2016 Annual IEEE India Conference (PEICES), New Delhi, 2016

Ling SH, Lu HHC, Chan KY, Lam HK, Yeung BCW, Leung FH. Hybrid particle swarm optimization with wavelet mutation and its industrial applications. IEEE Trans Syst Man Cybern Part B: Cybern 2008;38(3):74363.

Liu D, Cai Y. Taguchi method for solving the economic dispatch problem with nonsmooth cost function. IEEE Trans Power Syst 2005;20(4):200614.

PereiraNeto A, Unsihuay C, Saavedra OR. Efficient evolutionary strategy optimization procedure to solve the nonconvex economic dispatch problem with generator constraints. IEE Proc GenerTransmDistrib2005;152(5):65360.

Ling SH, Leung FHF. An improved genetic algorithm with averagebound crossover and wavelet mutation operation. Soft Comput 2007;11(1):731.

Chiang CL. Geneticbased algorithm for economic load dispatch. IET GenerTransmDistrib 2007;1(2):2619.

Wang SK, Chiou JP, Liu CW. Nonsmooth/nonconvex economic dispatch by a novel hybrid differential evolution algorithm. IET GenerTransmDistrib 2007;1(5):793803.

Selvakumar AI, Thanushkodi K. Antipredatory particle swarm optimization: Solution to nonconvex economic dispatch problems. Electr Power Syst Res 2008;78:210.

Selvakumar L, Thanushkodi K. A new particle swarm optimization solution to nonconvex economic dispatch problems. IEEE Trans Power Syst 2007;22(1):4251.

Chaturvedi KT, Pandit M, Srivastava L. SelfOrganizing hierarchical particleswarm optimization for nonconvex economic dispatch. IEEE Trans Power Syst2008;23(3):107987.

Sangiamvibool W, Pothiya S, Ngamro I. Multiple tabu search algorithm for economic dispatch problem considering valvepoint effects. Electr Power Energy Syst 2011;33:84654.

Cai J, Li Q, Li L, Peng H, Yang Y. A hybrid CPSOSQP method for economic dispatch considering the valvepoint effects. Energy Convers Manage2012;53:17581.

Alsumait JS, Sykulski JK, AlOthman AK. A hybrid GAPSSQP method to solve power system valvepoint economicdispatch problems. Appl Energy 2010;87:177381.

Subbaraj P, Rengaraj R, Salivahanan S, Senthilkumar TR. Parallel particle swarm optimization with modified stochastic acceleration factors for solving large scale economic dispatch problem. Electr Power Energy Syst 2010;32:101423.

Bhattacharya A, Chattopadhyay PK. Hybrid differential evolution with biogeographybased optimization for solution of economic load dispatch.IEEE Trans Power Syst 2010;25(4):195564.

Niknam T. A new fuzzy adaptive hybrid particle swarm optimization algorithm for nonlinear, nonsmooth and nonconvex economic dispatchproblem. Appl Energy 2010;87:32739.

Dakuo H, Fuli W, Zhizhong M. A hybrid genetic algorithm approach based on differential evolution for economic dispatch with valvepoint effect. ElectrPower Energy Syst 2008;30:318.

Yang XS, Hosseini SSS, Gandomi AH. Firefly algorithm for solving nonconvex economic dispatch problems with valve loading effect. Appl Soft Comput2012;12:11806.

Amjady N, Sharifzadeh H. Solution of nonconvex economic dispatch problem considering valve loading effect by a new modified differential evolutionalgorithm. Electr Power Energy Syst 2010;32:893903.

MohammadiIvatloo B, Rabiee A, Soroudi A, Ehsan M. Iteration PSO with time varying acceleration coefficients for solving nonconvex economic dispatchproblems. Int J Electr Power Energy Syst 2012;42:50816.