REAL POWER LOSS REDUCTION BY EXTREME LEARNING MACHINE BASED DRONGOS SEARCH ALGORITHM Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

UDC 519.6

EDN: FIMVMC

REAL POWER LOSS REDUCTION BY EXTREME LEARNING MACHINE BASED DRONGOS SEARCH ALGORITHM

L. Kanagasabai gklenin@gmail.com

Prasad V. Potluri Siddhartha Institute of Technology, Kanuru, Vijayawada, India

Abstract

In this paper the Extreme learning machine (ELM) based Drongos search (DS) algorithm — ELMDS algorithm — is applied to solve the power loss lessening problem. Extreme learning machine is applied and learning speed of feed-forward neural networks is composed of input, hidden and output layer. Drongos search algorithm is a modern algorithm which is inspired on the elegance performance of Drongos. In expedition to control obscured place a Drongos j pursuit Drongos i. Formerly Drongos i do not sentient of the existence of the added Drongos, as a consequence to the cause of Drongos j is to accomplish. And in Fiddling "Drongos" i differentiate about the presence of Drongos j and it protector its nourishment, Drongos i calculatingly take an impulsive way to sentinel its nourishment. This show is replicated by employing an unpredictable evolution. Then care possibility is replaced by a vibrant care possibility for enrichment, which is adapted by the aptness supremacy of every contender solution. Levy flights are employed as a substitute of unswerving illogical activities to duplicate the dodging performance. In ELMDS algorithm input weight rate and concealed layer inception in ELM are logically optimized by the DS algorithm. Legitimacy of ELMDS algorithm is corroborated in IEEE 30 bus system and IEEE 14, 30, 57, 118, 300 bus test systems without considering the voltage constancy index. True power loss lessening, voltage divergence curtailing, and voltage constancy index augmentation has been attained

Keywords

Optimal reactive power, Transmission loss, Extreme Learning Machine, Drongos

Received 04.10.2021 Accepted 27.12.2021 © Author(s), 2024

Introduction. Optimal reactive power dispatch is envisaged as one of the remarkable circumstances for safe and fiscal operation of a system. It is consummate by appropriate organization of the edifice apparatus used to cope up the power flow with the goal of diminishing the true power losses and

progress the voltage outline of the structure. Lee et al. [1] had done a united approach to optimal real and reactive power dispatch. Dommel et al. [2] did optimal power flow solutions. Medani et al. [3] solved whale optimization algorithm based optimal reactive power dispatch: A case study of the Algerian power system. Taha et al. [4] did optimal reactive power resources sizing for power system operations enhancement based on improved grey wolf optimizer. Sakr et al. [5] had done adaptive differential evolution algorithm for efficient reactive power management. Heidari et al. [6] applied Gaussian barebones water cycle algorithm for optimal reactive power dispatch in electrical power systems. Keerio et al. [7] had done multi-objective optimal reactive power dispatch considering probabilistic load demand along with wind and solar power integration. Roy et al. [8] did optimal reactive power dispatch for voltage security using JAYA algorithm. Mugemanyi et al. [9] had done optimal reactive power dispatch using chaotic bat algorithm. Sahli et al. [10] applied hybridized PSO-Tabu exploration for the problem. Mouassa et al. [11] applied Ant lion algorithm for solving the problem. Mandal et al. [12] solved the problem by using quasi-oppositional teaching. Khazali et al. [13] solved the problem by harmony search procedure. Tran et al. [14] solved problem by innovative enhanced stochastic fractal search procedure. Polprasert et al. [15] solved the problem by using enhanced pseudo-gradient pursuit particle swarm optimization. Thanh et al. [16] solved the problem by an operative metaheuristic procedure. Raghuwanshi et al. [17] did class imbalance learning using under bagging based kernelized extreme learning machine. Yu X. et al. [18] had done dual-weighted kernel extreme learning machine for hyperspectral imagery classification. Han et al. [19] did hyperspectral image classification based on multiple reduced kernel extreme learning machine. From Illinois Center [20] for a Smarter Electric Grid (ICSEG) IEEE 30 bus system data obtained. Dai et al. [21] used seeker optimization procedure for solving the problem. Subbaraj et al. [22] used self-adaptive real coded genetic procedure to solve the problem. Pandya et al. [23] applied particle swarm optimization to solve the problem. Ali Nasser Hussain et al. [24] applied amended particle swarm optimization to solve the problem. Vishnu et al. [25] applied an enhanced particle swarm optimization to solve the problem. Omelchenko I.N. et al. [26] did development of a design algorithm for the logistics system of product distribution of the mechanical engineering enterprise. Omelchenko I.N. et al. [27] did the work on organization of logistic systems of scientific productions. Omelchenko I.N. et al. [28] solved the problems and organizational and technical solutions of processing management problems of material and technical resources in

a design-oriented organization. Khunkitti et al. [29] solved multi-objective optimal power flow problems based on slime mould algorithm. Diab et al. [30] solved multi-objective optimal power flow control of electrical transmission networks using intelligent meta-heuristic optimization techniques. Reddy [31] solved optimal reactive power scheduling using Cuckoo search algorithm. Reddy [32] did faster evolutionary algorithm based optimal power flow using incremental variables. In this paper Extreme learning machine (ELM) based Drongos search (DS) algorithm — ELMDS algorithm — is applied to solve the real power loss lessening problem. Extreme learning machine is applied and learning speed of feed-forward neural networks is composed of input, hidden and output layer. Drongos search algorithm is a modern algorithm which is inspired on the elegance performance of Drongos. In expedition to control obscured place a Drongos j pursuit Drongos i. Formerly Drongos i do not sentient of the existence of the added Drongos, as a consequence to the cause of Drongos j is to accomplish. In Fiddling Drongos i differentiate about the presence of Drongos j and it protector its nourishment, Drongos i calculatingly take an impulsive way to sentinel its nourishment. This show is replicated by employing an unpredictable evolution. Each Drongos i performance is pronounced by a care possibility cp. Consequently, an unpredictable value ri consistently disseminated between 0 and 1. If ri is improved than or equivalent to cp, show 1 is applied, if not state 2 is designated. Then cp, is replaced by a vibrant care possibility vcp for enrichment, which is adapted by the aptness supremacy of every contender solution. Levy flights are employed as a substitute of unswerving illogical activities to duplicate the dodging performance. Accordingly, a novel capricious location Zit k+1 is produced, in addition to the current location Zi>j from calculated Levy flight Lf. Through Mantegna procedure, the main segment is to evaluate the stage size Si. In ELMDS algorithm input weight rate and concealed layer inception in ELM are logically optimized by the DS algorithm. Legitimacy of the ELMDS algorithm is corroborated in IEEE 30 bus system and IEEE 14, 30, 57, 118, 300 bus test systems without considering the voltage constancy index. True power loss lessening, voltage divergence curtailing, and voltage constancy index augmentation has been attained.

Problem formulation. Power loss minimization is defined by min F (d, e), where min is minimization of power loss. Subject to the constraints A (d, e) = 0; B ( d, ~e ) = 0, d, e are control and dependent variables,

d = [VLG\,..., VLGNg; QQ,..., QCnc; T\, —, Tnt ];

[ PGslack; VLb •••, VLNLoad; QGb ••• , QGNg; SLl, ... , ].

Here QC is reactive power compensators; T is tap setting of transformers; PGsiack is slack generator; VLg is level of the voltage; QG is generation unit's reactive power; SL is apparent power.

The fitness function (¿1, F2, F3) is designed for power loss (MW) lessening, voltage deviancy, voltage constancy index (L-index) is defined by:

where NTL is number of transmission line; NLB , Ng are number load and generating units; VLk is load voltage in k-th load bus; VLdkesired is voltage desired at the k-th load bus; QGK is reactive power generated at k-th load bus generators; QKGm is reactive power limitation; Lmax = max [Lj ], j = 1,..., Nlb ,

F3 = min L

Lj -1 X Fji лг , i=1 Vj

Fji = -[Yf [ Y2 ];

Lmax = max 1 -[Y1 ]_1 [Y2]V- .

mv v.

max

Parity constraints:

0 = PGi - PDi - Vi X Vj [ Gij cos [ 0i - 0j ] + Bij sin [ 0i - 0j ] ] ;

j e NB

0 = QGi - QDi - Vi X Vj [Gj sin [0t - 0j ] + Bj cos [0t - 0j ]] .

QCmin < QC < QCmax, i e NC, \ SL \ < SLmax, i e NTL,

VGmin < VGi < VGmax, i e Ng. Multi objective fitness function:

MOF = F + riF2 + uF3 =

= F +

NL Г .-|2 г • П2

Xxv [vLi- - VLmin ] +Zrg [QG. - QGm1" i = 1 i = 1

+ r/F,

where u is dependent variables;

VLmax, VLi > VLmax; ^ [QGmax, QG. > QGmax;

VLmin _ j г ' г QG min = J i

1 ' VLmin, VLi < VLmin, i 1 QGmin, QGi < QGmin.

Extreme learning machine. Extreme learning machine is applied and learning speed of feed-forward neural networks is composed of input, hidden and output layer [17-19]. Remarkably, the learning speed of ELM can be thousands of times quicker than customary feed forward network learning procedures. When equated with orthodox learning algorithms, ELM not only incline to grasp the smallest training error nevertheless it obtains the minimum standard of weights. Extreme learning machine assurances the noble performance, and significantly progresses the learning speed of the forward neural networks, and evades many of the problems of gradient descent training approaches epitomized by BP neural networks, like easiness of being stuck into local optimum, more number of iterations, and so on.

The linking neurons weight matrix of input to hidden layer is demarcated

as:

Wt\\ ••• wtin WtL1 ••• WtLn _

Neurons weight matrix of input to hidden layer (nwtp) is defined as:

nwtPn ••• nwtPin nwt^Ll ••■ nwt&Ln

Wt =

wtT

wd

wt.

nwtß =

nwtßT nwtß2

nwtßT

Neurons hidden layer bias vector (bvr ):

bvr =

bvr1 bvr2

bvrL

L x 1

For N impulsive ( щ, Hi); щ = [ m, щ2,..., Uidn ]E e VU = [Иц, Hi2,..., Hidn ] eVUdn,

dn

(H ) =

hT H

H11 ••• H1n HL1 HLn

N

I

i = 1

Y^nwtfiikn {&iUj + ai) = Hj, j = 1,..., N;

Hi =

(X )(nwtp) = H; X («1, ..., ul ; ©1, ..., WL ; fl1, •••, a/ ) = kn (ro1w1 + a1) ••• kn (&Lu1 + aL)

kn (co1uN + a1) ••• kn (&LuN + aL) nwtfi = X _1h.

Procedure of the ELM is as defined as follows:

a. Begin

b. Input the data

c. Conjoint data test and training sets are created

d. With alignment to the training set — control the amount of (X)

e. (1)

f. Regulate the output rate of weight

g. (2)

h. With alignment to the test set — appraise the rate of (V)

i. (1)

(1)

(2)

j. Assess the actual rate through nwtp and V

k. Computation of error degree

l. Valuation of actual value with possible rate

m. Return the error rate

n. End

Drongos search algorithm. Drongos search algorithm is a modern algorithm which is inspired by elegance performance of Drongos. Magnitude of Drongos is recognized by N entities and the position Z(tk of the Drongos i in a fixed iteration k is demarcated as:

Zi,k = [_ z1,k, z*k,..., znikk ], i = 1,2,..., N, k = 1,2,..., max. iter.

Every Drongos is supposed to have the probability of remembering the premium visited position Hi, k to conceal nourishment up until the contemporary iteration specified as: Hi,k = [h* k, h?,k, ..., hf^k ].

Expedition: To control obscured place a Drongos j pursuit Drongos i. Formerly Drongos i do not sentient of the existence of the added Drongos, as a consequence to the cause of Drongos j is to accomplish.

Fiddling: Drongos i differentiate about the presence of Drongos j and it protector its nourishment, Drongos i calculatingly take an impulsive way to sentinel its nourishment. This show is replicated by employing an unpredictable evolution.

Each Drongos i performance is pronounced by a care possibility cp. Consequently, an unpredictable value ri consistently disseminated between 0 and 1. If ri is improved than or equivalent to care possibility, show 1 is applied, if not state 2 is designated:

Z _ | Zi,k + rifii,k (Hi,k - Zi,k )r, >cp; (3)

Rand or else,

where f ,k is elect the gauge of development from Drongos Z\kk in the way of premium place Hj,k of Drongos j; the ri is a whimsical amount with vague dissemination in the sort of [0, 1]. Once the Drongos are personalized, at that moment their position is assessed and memory vector is streamlined:

_f F (Zi,k +1) F (Zi, k +1 )< F (Hit k );

Hi, k +1 ] u 1

Hitk or else.

Then care possibility is replaced by a vibrant care possibility vcp for enrichment, which is adapted by the aptness supremacy of every contender solution:

vcpi, k = 0

F (Zik ) .90—LJiLi + 0.1.

шУ

(4)

Levy flights are employed as a substitute of unswerving illogical activities to duplicate the dodging performance. Accordingly, a novel capricious location Za+1 is produced, in addition to the current location Zi, j from calculated Levy flight Lf. Through Mantegna procedure, the main segment is to evaluate the stage size Si as follows:

Si =■

b

1/p

a - N (0,G2a ), b - N (0,o2 ),

О a =

r(1 + ß)sin (7Tß/2 )

G b = 1.

(5)

T[(1 + p)/2 ]p2(P"1)/2

Factor Lf is calculated by Lf = 0.01 - Sj e ( Z,, k - Zb ). Novel location Zi, k+1 is given by

Zi, k +1 = Zi, k + Lf.

Crusade and swiftness of the swarm by using particle swarm optimization is integrated in the procedure:

vlj+1 = wvj + c1 r (pbi - z\) + c2r (g - z\ )

zt. +1 = zt{ + vlt+1; Dr + D2r2

(6) (7)

Dm + D2T2 > 0;

-ю< 0.1; ю<1; 0 < D1 +D2 < 4.0;

D1 + D2 -1 <®< 1,then +1 = Kwt^ 2

Mutation probability is defined as:

M pi = 0.5 x

Fmax Fi _ Fmax _ Favg _

if Fi > Fa

avg j

M pi =

Favg Fi Fmax _ Favg

if Fi < Fa

avg :

i1,t+1 ) _ (U)

=z)

-(ri - 0.5 ) Ai, A i = 0.5 x (max zi - min zi ); Ai =(0.03-0.08)xavg z{.

a

2

Afterward the places are rationalized then the mid particle mp is included in the population:

N -1

X zt, j

m,] = r~N _ 1 , j=1,2, -,d. (8)

By time wavering swiftness fluctuations is organized by

Vlm

Г1J iter ^g ^

^ V itermax )

Vmax0, Vmax 0 — ( zmax zmin ) ;

F

Pryi =N-; (9)

X Fi

i = 1

zt+l = i 1 > j ^

zt,j iff (zij)< f [ztj);

zf"1;1, otherwise.

(10)

Algorithm

a. Start

b. Initialization of agents

c. Mid particle mp is included in the population

d. (8)

e. Particle's location and drive are calculated

f. (6)

g. (7)

h. Quixotically stimulate the Drongos location

i. Memory has been weighed down with orientation to initial position j. For each place fitness point has been calculated

k. Vibrant care possibility vcp is computed

l. (4)

m. Engender the whimsical value ri for each Drongos i n. r > vcp; If "Yes" then compute fresh location

o. (3)

p. If "No" calculate fresh location

q. (5)

r. Prospect of the fresh location has to be set up

s. Fresh locations fitness rate has to be calculated

t. Streamline the memory when development in fitness rate u. Local operative is smeared v. (10) w. (9)

x. Once termination condition is not met then go to step "c" y. Return the preeminent solution z. End

ELMDS algorithm. Input weight rate and concealed layer inception in ELM are logically optimized by DS algorithm. Fig. 1 shows the schematic diagram of ELMDS algorithm:

a. Begin

b. Input the data

c. Conjoint data test and training set are created

d. With alignment to the training set — control the amount of (X)

e. (1)

f. Regulate the output rate of weight

g. (2)

h. With alignment to the test set — appraise the rate of (V)

i. (1)

j. Assess the actual rate through nwtp and V k. Calculation of error degree l. Assessment of real value with probable rate m. Return the error rate n. Apply the DS algorithm

i. Start

ii. Initialization of agents

iii. Mid particle mp is included in the population

iv. (8)

v. Particle's location and drive are calculated

vi. (6)

vii. (7)

viii. Quixotically stimulate the Drongos location

ix. Memory has been weighed down with orientation to initial position

x. For each place fitness point has been calculated

xi. Vibrant care possibility vcp is computed

xii. (4)

xiii. Engender the whimsical value ri for each Drongos i

xiv. r > vcp; If "Yes" then compute fresh location

xv. (3)

xvi. If "No" calculate fresh location

xvii. (5)

xviii. Prospect of the fresh location has to be set up

xix. Fresh locations fitness rate has to be calculated

xx. Streamline the memory when development in fitness rate

xxi. Local operative is smeared

xxii. (10)

xxiii. (9)

xxiv. Once termination condition is not met then go to step "c"

xxv. Return the preeminent solution

xxvi. End

o. Computing the output error p. Parameters values are verified q. Update the data r. End while

s. Return the optimal solution t. End

Extreme learning machine process encompasses double steps, training authentication and test segment. The dataset is arbitrarily segregated into dual non-overlapped sets, in order to create the input training authentication matrix and test single. Input matrix is possessing load demand (real and reactive power (PD), (QD)) bus voltage magnitude (V-). The goal matrix is enclosing power generation (real and reactive power (PG), (Qg )) and system losses (real and reactive (Pj), (Qj)). ELM training time 0.0469, training performance is 3.564e-25 and testing performance is 8.218e-27.

Computation complexit. To compute the fitness value the time is required and the time complication is defined as O(z1 + N(nz2 + f (n))) = = O (n + f (n)). Then the time required for the iterative update and the time complication is demarcated as O(N(nz3 + f (n)) + z4 + z5 + z6) = = O(n + f (n)). The loop fragment time complication is

O (N (nz3 + f (n)) + z4 + z5 + z6 + N (z2 + z3) + z1) = O (n + f (n)).

Sequentially the entire time complication is defined as

Time (n) = O (n + f (n )) + (n + f (n)) = O (n + f (n)).

Fig. 1. Schematic diagram of ELMDS algorithm

Simulation results and discussion. Projected ELMDS algorithm is corroborated in IEEE 30 bus system [20]. In Table 1 shows the loss appraisal, Table 2 shows the voltage aberration evaluation and Table 3 gives the voltage constancy assessment. Figures 2, 3 gives the graphical appraisal between the methods. ELMDS abridged the power loss efficiently. Appraisal of loss has been done with particle swarm optimization, adapted particle swarm optimization, enriched particle swarm optimization, comprehensive learning particle swarm optimization, adaptive genetic algorithm, canonical genetic algorithm, enhanced genetic algorithm, hybrid particle swarm optimization — Tabu search, Ant lion approach, quasi-oppositional teaching learning based algorithm, enriched stochastic fractal search optimization algorithm, harmony search, advanced pseudo-gradient search particle swarm optimization and cuckoo search algorithm. Power loss abridged competently and proportion of the power loss lessening has been enhanced. Predominantly voltage constancy augmentation attained with minimized voltage deviancy.

Table 1

Assessment of real power loss

Algorithm Power loss, MW Algorithm Power loss, MW

Hybrid-PSOTS [10] 4.5213 S-GA [13] 4.9408

B-TS [10] 4.6862 B-PSO [13] 4.9239

S-PSO [10] 4.6862 Hybrid-AS [13] 4.9059

B-ALO [11] 4.5900 B-FS [14] / B-FS [16] 4.5777 / 4.5275

Hybrid QOTLBO [12] 4.5594 Hybrid-ISFS [14] 4.5142

B-TLBO [12] 4.5629 ELMDS 4.4019

Table 2

Comparison of voltage deviancy

Algorithm Voltage deviancy, PU Algorithm Voltage deviancy, PU

Hybrid-PSOTVIW [15] 0.1038 Hybrid-QOTLBO [12] 0.0856

Hybrid-PSOTVAC [15] 0.2064 B-TLBO [12] 0.0913

Hybrid-PSOTVAC [15] 0.1354 B-FS [14] 0.1220

Hybrid-PSOCF [15] 0.1287 Hybrid-ISFS [14] 0.0890

Hybrid-PGPSO [15] 0.1202 B-FS [16] 0.0877

Hybrid-SWTPSO [15] 0.1614 CLO 0.0849

Hybrid-PGSWTPSO [15] 0.1539 BO 0.0840

Hybrid-MPGPSO [15] 0.0892 ELMDS 0.0828

Table 3

Appraisal of voltage constancy

Algorithm Voltage constancy (L-index), PU Algorithm Voltage constancy (L-index), PU

Hybrid-PSOTVIW [15] 0.1258 B-TLBO [12] 0.1180

Hybrid-PSOTVAC [15] 0.1499 B-ALO [11] 0.1161

Hybrid-PSOTVAC [15] 0.1271 B-ABC [11] 0.1161

Hybrid-PSOCF [15] 0.1261 B-GWO [11] 0.1242

Hybrid-PGPSO [15] 0.1264 B-BA [11] 0.1252

Hybrid-SWTPSO [15] 0.1488 B-FS [14] 0.1252

Hybrid-PGSWTPSO [15] 0.1394 Hybrid-ISFS [14] 0.1245

Hybrid-MPGPSO [15] 0.1241 B-FS [16] 0.1007

Hybrid-QOTLBO [12] 0.1191 ELMDS 0.1002

S-PSO TS

0.25

0.20

0.15

§

1

и

•8

a> o.io

то

3

> 0.05

ISFS

S-FS

ALO

QOTLBO

TLBO

S-PSO S-GA

Fig. 2. Assessment of actual power loss, MW

i XJ X Л i? Л ¿О .О -О -О ф ф Û, Û,

//VV / ^ ^ a

# & # ^ c^

x 0.16

•g 0.14

* 0.12

I 0.10

^ ^ Л cP cP cP cP .О .О , О -С aO ^ A ^

^ ^ ^ Я'"

Fig. 3. Appraisal of voltage aberration (a), and assessment of voltage constancy

index (b)

Then the ELMDS algorithm is substantiated in IEEE 14, 30, 57, 118 and 300 bus test systems deprived of voltage constancy. Loss appraisal is shown in Tables 4 to 8. Figure 4, 5 gives graphical comparison between the approaches with orientation to power loss. Proposed algorithms are compared with adapted particle swarm optimization, particle swarm optimization, evolutionary programming, self-adaptive real coded genetic algorithm, canonical genetic algorithm, adaptive genetic algorithm, enhanced particle swarm optimization, comprehensive learning particle swarm optimization, enhanced genetic algorithm, faster evolutionary algorithm and cuckoo search optimization algorithm.

Table 4

Assessment of results (IEEE 14 bus system)

Algorithm True loss, MW Ratio of loss diminution

Base case [24] 13.550 0

Improved PSO [24] 12.293 9.20

B-PSO [23] 12.315 9.10

B-EP [23] 13.346 1.50

Hybrid-SARGA [22] 13.216 2.50

ELMDS 10.069 25.69

Table 5

Appraisal of loss (IEEE 30 bus system)

Algorithm Actual power loss, MW Proportion of lessening in power loss

Base case value [24] 17.5500 0

Improved PSO[24] 16.0700 8.40000

B-PSO [23] 16.2500 7.40000

B-EP [21] 16.3800 6.60000

B-GA [22] 16.0900 8.30000

S-PSO [25] 17.5246 0.14472

Improved DEPSO [25] 17.5200 0.17094

B-JAYA [25] 17.5360 0.07977

ELMDS 14.0320 20.0455

Table 6

Assessment of parameters (IEEE 57 bus system)

Algorithm True loss, MW Ratio of loss diminution

Base case [24] 27.8 0

Improved PSO [24] 23.51 15.4000

B-PSO [23] 23.86 14.1000

Canonical-GA[22] 25.24 9.2000

Adaptive-GA [22] 24.56 11.6000

ELMDS 21.062 24.2374

Table 7 Assessment of results (IEEE 118 bus system)

Algorithm True loss, MW Ratio of loss diminution

Base case [24] 132.8 0

Improved PSO [24] 117.19 11.700

B-PSO [23] 119.34 10.100

B-EPSO [21] 131.99 0.6000

B-CLPSO [21] 130.96 1.3000

ELMDS 112.012 15.6536

Table 8

Power loss appraisal (IEEE 300 bus system)

Algorithm True loss, MW

Adaptive-GA [32] 646.299800

Faster-EA [32] 650.602700

B-CSO [31] 635.894200

ELMDS 625.106428

Table 9 shows the convergence characteristics of projected ELMDS algorithm for IEEE 30 bus system. In IEEE 30 bus projected ELMDS algorithm has been evaluated as multi objective and single objective mode. Figure 6 shows the graphical representation of the characteristics.

ELMDS

JAYA

DEPSO

Base case 30

ELMDS

Hybrid-SARGA

Base case value

Amended PSO

ELMDS

S-PSO

S-EP

AGA

B-PSO

S-GA

b

Improved PSO

B-PSO

Base case

30/

Adapted PSO

PSO

Fig. 4. Power loss appraisal:

a) IEEE 14 bus system; b) IEEE 30 bus system; c) IEEE 57 bus system; true loss (-),

proportion of lessening in power loss (-); ratio of loss diminution ( )

Power loss

Power loss

FEA CSO ELMDS

>5 я

Fig. 5. Power loss appraisal:

a) IEEE 118 bus system; b) IEEE 300 bus system; ratio of loss diminution (

), true loss ( )

Table 9

Convergence characteristics of ELMDS algorithm

Actual loss with / without power reliability, MW Time with / without power reliability, s Number of iteration with / without power reliability

4.4019 / 14.032 28.29 / 24.98 29 / 20

Fig. 6. Convergence characteristics:

actual loss with (■) or without (■) voltage constancy; actual loss with (■) or without (■) voltage constancy;

number of iteration with (■) or without (■) voltage constancy

ELMDS

Conclusion. ELMDS algorithm reduced the genuine power loss competently. Proposed algorithms is corroborated in IEEE 30 bus system and IEEE 14, 30, 57, 118, 300 bus test systems without considering the voltage constancy index. True power loss lessening, voltage divergence curtailing, and voltage constancy index augmentation has been attained. ELMDS algorithm creditably condensed the power loss and proportion of Actual power loss lessening has been elevated. Extreme learning machine is applied and learning speed of feed-forward neural networks is composed of input, hidden and output layer. Drongos search algorithm is a modern algorithm which is inspired on the elegance performance of Drongos. In expedition to control obscured place a Drongos j pursuit Drongos i. Formerly Drongos i do not sentient of the existence of the added Drongos, as a consequence to the cause of Drongos j is to accomplish. In Fiddling Drongos i differentiate about the presence of Drongos j and it protector its nourishment, Drongos i calculatingly take an impulsive way to sentinel its nourishment. This show is replicated by employing an unpredictable evolution. Each Drongos i performance is pronounced by a care possibility. Consequently, an unpredictable value consistently disseminated between 0 and 1. If ri is improved than or equivalent to care possibility, show 1 is applied, if not state 2 is designated. Then care possibility is replaced by a vibrant care possibility for enrichment, which is adapted by the aptness supremacy of every contender solution. Levy flights are employed as a substitute of unswerving illogical activities to duplicate the dodging performance. Accordingly, a novel capricious location Zit k+1

is produced, in addition to the current location Z[, j from calculated Lévy flight Lf. Through Mantegna procedure, the main segment is to evaluate the stage size Si. In ELMDS algorithm input weight rate and concealed layer inception in ELM are logically optimized by the DS algorithm. Convergence characteristics show the better performance of the proposed ELMDS algorithm. Valuation of power loss has been done with other customary reported algorithms.

REFERENCES

[1] Lee K.Y., Park Y.M., Ortiz J.L. A united approach to optimal real and reactive power dispatch. Trans. Power App. Syst., 1985, vol. PAS-104, iss. 5, pp. 1147-1153.

DOI: https://doi.org/10.1109/TPAS.1985.323466

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Kanagasabai Lenin — Dr. Sc. (Full), Professor, Department of Electrical and Electronics Engineering, Prasad V. Potluri Siddhartha Institute of Technology (Kanuru, Vijayawada, Andhra Pradesh, 520007 India).

Please cite this article as:

Kanagasabai L. Real power loss reduction by extreme learning machine based Drongos search algorithm. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2024, no. 1 (112), pp. 41-62. EDN: FIMVMC