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

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.