Harris Hawks Optimization for Solving Optimum Load Dispatch Problem in Power System

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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)

      1. Institute of Engg. and Tech. Jalandhar

        Abstract-Optimum 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

        1. 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) + | × sin{ × (Pmin Pgi)}|

          i gi

          i=1

          Where fuel-cost coefficients of the ith unit are ai, bi, and ci, and di & ei are with the valve-point effects [5]. The total fuel cost has to be decreased with the following restraints:

          1. 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)

          2. Generator limit restraint

            The particular lower operating limits and upper operating limits are controlled each generators real power generation.

            i=1,2,…,ng (4)

        2. 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..

            1. 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.

            2. 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 (1-t/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.

            3. 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.

          1. 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.

          2. 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)

          3. 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 LF-based patterns used by following rule:

            Z = Y + S × LF(D) (11)

            Levy flight function is LF and S is an arbitrary size 1 × 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)

          4. 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 × LF (D) (15)

        3. RESULTS& DISCUSSIONS

            1. 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

            2. 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

          EP-SQP [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

          PSO-SQP [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 40-Unit system

        4. 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:

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

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

  3. Chiang, Chao-Lung. "Improved genetic algorithm for power economic dispatch of units with valve-point effects and multiple fuels." Power Systems, IEEE Transactions on 20, no. 4 (2005): 1690-1699.

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

  5. Nidul Sinha, R. Chakrabarti, and P. K. Chattopadhyay. Evolutionary programming techniques for economic load dispatch. IEEE Transactions on Evolution Computation. 2003; 7: 83-94.

  6. N. Noman and H. Iba. Differential evolution for economic load dispatch problems. Electric Power Systems Research. 2008; 78: 1322-31.

  7. J. Park, K. Lee and J. Shin. A particle swarm optimization for economic dispatch with non-smooth cost functions. IEEE Transactions on Power Systems. 2005; 20: 34-42.

  8. T. Aruldoss Albert Victoire and A. Ebenezer Jeyakumar. Hybrid PSO-SQP for economic dispatch with valve-point effect. Electric Power Systems Research. 2004; 71: 51-9.

  9. L. D. S. Coelho, V. C. Mariani, Particle swarm approach based on quantum mechanics and harmonic oscillator potential well for economic load dispatch with valve-point effects, EnergyConversion and Management, vol. 49, 2008, pp. 3080-3085.

  10. Niu, Qun, Xiaohai Wang, and ZhuoZhoua. "An Efficient Cultural Particle Swarm Optimization for Economic Load Dispatch with Valve-point Effect." Procedia Engineering 23 (2011): 828-834.

  11. Duman, S., U. Güvenç, and N. Yörükeren. "Gravitational search algorithm for economic dispatch with valve-point effects." International Review of Electrical Engineering 5, no. 6 (2010): 2890-2895.

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

  13. 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): 26-42.

  14. Reddy, K. Sudhakara, and M. Damodar Reddy. "Economic load dispatch using firefly algorithm." International journal of engineering research and applications 2, no. 4 (2012): 2325-2330.

  15. 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): 60-72.

  16. Wang, Ling, and Ling-po Li. "An effective differential harmony search algorithm for the solving non-convex economic load dispatch problems." International Journal of Electrical Power & Energy Systems 44, no. 1 (2013): 832-843.

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

  18. Roy, Priyanka, Pritam Roy, and Abhijit Chakrabarti. "Modified shuffled frog leaping algorithm with genetic algorithm crossover for solving economic load dispatch problem with valve-point effect." Applied Soft Computing 13, no. 11 (2013): 4244-4252.

  19. Kherfane, R. L., M. Younes, N. Kherfane, and F. Khodja. "Solving Economic Dispatch Problem Using Hybrid GA-MGA." Energy Procedia 50 (2014): 937-944.

  20. Bestha, Mallikrjuna, K. Harinath Reddy, and O. Hemakeshavulu. "Economic Load Dispatch Downside with Valve-Point Result Employing a Binary Bat Formula." International Journal of Electrical and Computer Engineering (IJECE) 4, no. 1 (2014): 101-107.

  21. 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.

  22. N. Chopra and S. Mehta, "Multi-objective optimum generation scheduling using Ant Lion Optimization," 2015 Annual IEEE India Conference (INDICON), New Delhi, 2015, pp. 1-6.doi: 10.1109/INDICON.2015.7443839

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

  24. 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.

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

  26. Pereira-Neto 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.

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

  28. Chiang CL. Genetic-based algorithm for economic load dispatch. IET GenerTransmDistrib 2007;1(2):2619.

  29. Wang SK, Chiou JP, Liu CW. Non-smooth/non-convex economic dispatch by a novel hybrid differential evolution algorithm. IET GenerTransmDistrib 2007;1(5):793803.

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

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

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

  33. Sa-ngiamvibool W, Pothiya S, Ngamro I. Multiple tabu search algorithm for economic dispatch problem considering valve-point effects. Electr Power Energy Syst 2011;33:84654.

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

  35. Alsumait JS, Sykulski JK, Al-Othman AK. A hybrid GAPSSQP method to solve power system valve-point economicdispatch problems. Appl Energy 2010;87:177381.

  36. 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.

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

  38. Niknam T. A new fuzzy adaptive hybrid particle swarm optimization algorithm for non-linear, non-smooth and non-convex economic dispatchproblem. Appl Energy 2010;87:32739.

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

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

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

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

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