# 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) + | Ã— sin{ Ã— (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 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)

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 Ã— 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.

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