REAL POWER LOSS REDUCTION BY BASKETBALL LEAGUE ALGORITHM Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

UDC 519.6

EDN: RGSEIK

REAL POWER LOSS REDUCTION BY BASKETBALL LEAGUE ALGORITHM

L. Kanagasabai

gklenin@gmail.com

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

In this paper Basketball League (BL) algorithm is ap- Optimization, power, transmis-plied to solve the power loss lessening problem. sion loss, Basketball league BL algorithm has been modelled based on the actions algorithm of BL squad. Basketball League game characteristically entails of 4 quarters and each one is ten minutes. Subsequently double quarters the squads shift sides on the courtyard. The squad with extra points at the conclusion of the 4 quarters triumphs the competition. If the total is tied at the conclusion of ruling time, the play will be preceded to additional time period. A bellicose competitor can possess the ball stirring round the court by drooling or fleeting the basketball to a co-player. In a ball drool, a competitor requests to rebound the basketball counter to the base incessantly practice single hand in a period. Using the both hands concurrently drool the basketball two times previously it rebounds on one occasion establishes a twofold drool defilement, which finishes in relinquishing control to the rival squad. Basketball team possess 12 players, with 5 players on the courtyard with Limitless replacements are permissible. Players in BL are alienated into consistently fragmented squads grounded upon age, capability, and proficiency. Elucidation has been generated grounded on the squad, players, trainer, and replacement approach. Principally fitness utility for every solution will be calculated and the consequence of competition amongst any two squads playing in BL is anonymous; some squad can triumph at the conclusion. Obviously when squad "i" win over squad "j" it's owed to the influence of the winning squad correspondingly it will be pathetic point for the dropping squad. Initial solution of the problem is engendered and squads are initialized contingent on the creation of the squad with strategies. Initial

Abstract

Keywords

solution of the problem is engendered and squads are initialized contingent on the creation of the squad with strategies. Trainers are playing principal part in providing effective contribution to the squad. Correspondingly trainers modify the strategies throughout the competition in the direction of competition wining. Rendering to the performance in the specific period elevation and relegation of the squads will be present. Supremely accomplished squads will be endorsed to eldest competition and deprived performed squad will be downgraded to junior division league. Legitimacy of BL algorithm is corroborated in IEEE 30 bus system and IEEE 14, 30, 57, 118, 300 bus test systems without considering the power constancy index. True power loss lessening, voltage divergence curtailing, and voltage constancy index augmentation has been attained

Received 19.10.2021 Accepted 30.12.2021 © Author(s), 2024

Introduction. Optimal reactive power dispatch is envisaged as one of the remarkable circumstances for safe and fiscal operation of 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. Zhu et al [1] solved the optimal reactive power control using modified interior point method. Quintana et al [2] did reactive-power dispatch by successive quadratic programming. Jan et al [3] did application of the fast Newton — Raphson economic dispatch and reactive power/voltage dispatch by sensitivity factors to optimal power flow. Terra et al. [4] did security-constrained reactive power dispatch. Grudinin [5] did Reactive power optimization using successive quadratic programming method. Ebeed et al [6] did the optimal reactive power dispatch using marine predators algorithm considering the uncertainties in load and wind-solar generation systems. Sahli et al [7] did reactive power dispatch optimization with voltage profile improvement using an efficient hybrid algorithm. Davoodi et al [8] did a novel fast semidefinite programming-based approach for optimal reactive power dispatch. Bingane et al [9] applied tight-and-cheap conic relaxation for the optimal reactive power dispatch problem. 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 en-

hanced pseudo-gradient pursuit particle swarm optimization. Thanh et al [16] solved the problem by an operative metaheuristic procedure. Adolph et al [17] had done research on the golden age of amateur basketball: the AAU Tournament. Brown et al [18] did a study on a basketball. Forrest et al [19] did a research on basketball. 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. 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. In this paper Basketball League (BL) algorithm is applied to solve the real power loss lessening problem. In this paper BL algorithm has been modelled based on the actions of BL squad. The beginning of basketball is in 1891. Basketball is a squad game between two teams. The fundamental aim of the game is to notch points by positioning the ball inside the loop and to prevent the opposite squad to score the points. Basketball play starts at the middle of the courtyard once the ball is flung tall up by the umpire and single player from every team contending to increase control. The League team that clasps the ball is called the attacking squad whereas the side not on the ball is the apologetic squad. Basketball League game characteristically entails of 4 quarters and quarter duration is ten minutes. Subsequently double quarters the squads shift sides on the courtyard. The squad with extra points at the conclusion of the 4 quarters triumphs the competition. If the total is tied at the conclusion of ruling time, the play will be preceded to additional time period. A bellicose competitor can possess the ball stirring round the court by drooling or fleeting the basketball to a co-player. In a ball drool, a competitor requests to rebound the basketball counter to the base incessantly practice single hand in a period. Using the both hands concurrently drool the basketball two times previously it rebounds on one occasion establishes a twofold drool defilement, which finishes in relinquishing control to the rival

squad. Basketball team possess 12 players, with 5 players on the courtyard with limitless replacements are permissible. Players in BL are alienated into consistently fragmented squads grounded upon age, capability, and proficiency. Elucidation has been generated grounded on the squad, players, trainer, and replacement approach. Principally fitness utility for every solution will be calculated and the consequence of competition amongst any two squads playing in BL is anonymous; some squad can triumph at the conclusion. Obviously when squad "i" win over squad "j" it's owed to the influence of the winning squad correspondingly it will be pathetic point for the dropping squad. Initial solution of the problem is engendered and squads are initialized contingent on the creation of the squad with strategies. Trainers are playing principal part in providing effective contribution to the squad. Correspondingly trainers modify the strategies throughout the competition in the direction of competition wining. Rendering to the performance in the specific period elevation and relegation of the squads will be present. Supremely accomplished squads will be endorsed to eldest competition and deprived performed squad will be downgraded to junior division league. Legitimacy of the BL 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 i^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,

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

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

d = [VLG1,..., VLGNg; QQ,..., QCnc; Ti,..., Tnt ] ;

e = [ PGslack ; VL1, ••• , VLNLoad ; QG1, ••• , QGNg ; SLb ••• , SLNT ]•

Fl = Pmin = min

m

F2 = min

F3 = min Lmax,

where NTL is number of transmission line; 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; QKGlim is reactive power limitation; NLB , Ng are number load and generating units; Lmax = max [ Lj ], j =

= 1, -, Nlb ,

1 -[7! [Y2

NPV V. 1

Lj = 1 - X FjiTT, Fji =-[Y1 ] Y ]; Lmax = max i = 1 Vj

Parity constraints:

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

j e NB

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

j e NB

Disparity constraints:

PGmank * PGslack < PGmk; QGtmin < QGi < QGimax, i E Ng, VLmin < VLi < VLmax, i e NL, Tmin < T < Tmax, i e NT, QCmin < QC < QCmax, i e NC, | SLi | < SLmax, i e NTL, VGmin < VGi < VGmax, i e Ng. Multi objective fitness function:

MOF = F + nF2 + uF3 =

V

= Fl +

NL Г .-|2 г

[VLi - VL™in ] + [QGi - QGf i = 1 i = 1

+ TfFi,

u is dependent variables;

. \VLfax, VLi > VLfax; . |QGmax, QGi > QGmax;

VLmm I ^ i i QGmm = JV i i ^ i

i [ VLmin, VLi < VLm in, i [ QGmin, QGi < QGmin.

Basketball league algorithm. In this paper BL algorithm has been modelled based on the actions of BL squad. Basketball is a squad game between two teams. The fundamental aim of the game is to notch points by positioning the ball inside the loop and to prevent the opposite squad to score the points. Basketball play starts at the middle of the courtyard once the ball is flung tall up by the umpire and single player from every team contending to increase

Fig. 1. An image of basketball court

control. The league team that clasps the ball is called the attacking squad whereas the side not on the ball is the apologetic squad.

Basketball league game characteristically entails of 4 quarters and quarter duration is ten minutes. Subsequently double quarters the squads shift sides on the courtyard. The squad with extra points at the conclusion of the 4 quarters triumphs the competition. If the total is tied at the conclusion of ruling time, the play will be preceded to additional time period. Figure 1 shows the image of basketball court1.

A bellicose competitor can possess the ball stirring round the court by drooling or fleeting the basketball to a co-player. In a ball drool, a competitor requests to rebound the basketball counter to the base incessantly practice single hand in a period. Using the both hands concurrently drool the basketball two times previously it rebounds on one occasion establishes a twofold drool defilement, which finishes in relinquishing control to the rival squad. Basketball team possess 12 players, with 5 players on the courtyard with limitless replacements are permissible. Players in BL are alienated into consistently fragmented squads grounded upon age, capability, and proficiency. Elucidation has been generated grounded on the squad, players, trainer, and replacement approach. Principally fitness utility for every solution will be calculated and the consequence of competition amongst any two squads playing in BL is anonymous; some squad can triumph at the conclusion. Obviously when squad "i" win over squad "j" it's owed to the influence of the winning squad correspondingly it will be pathetic point for the dropping squad. Initial solution of the problem is engendered and squads are initialized contingent on the creation of the squad with strategies.

At that time the initial squad is represented as Basketball squad0 with the populace of number of squads. Initial period Bc, Bs of the j-th variable is demarcated by:

Bc = min j + R ( ) (max j - min j ) ; Bs = min j + R ( ) (max j - min j ).

Here Bc, Bs are squad creation and substitution; R is random; min, max indicate lower and upper limits.

1 Available at: https://www.istockphoto.com/illustrations/basketball-hoop-from-above (accessed: 08.10.2021).

At that point the creation and substitution formation is represented in the form of matrix

" Bf,1 • " Bc»j" " Kl ■ " B5» j"

c = ; 5 =

_ Bf1 • ■■ yf, j _ _ B/,1 • ■■ B5, j _

Customarily there will be a game with respect to fixture and every squad "i" creation demarcated as Bf and the forte file is defined as:

Hi ) =

fi (Bf)

Total fi Total fi =nfi(Bf),

(1) (2)

i = 1

where fi specify the fitness value.

Once 2 squads; j and l are playing a competition with creations Bf and Bf then the forte file rate of the squads will be calculated as:

M j ) =

fi (BC)

Hi ) =

fi (BC )

Total fi Total fi

Possibility for the squad "j" to triumph the competition is defined as:

^^j l '-jta • Possibility of the competition between the squads "l" and "j" is defined as:

M j)

РУ(j»l) + РУ (j) = 1.0; py (l, j) = 1.0-

M j )+s(i )■

Then the competition between squad "j" and "l" procedure is:

a. F. competition (j, l)

b. Calculate j)

c. Compute Total fi

d. Formula (1)

e. Formula (2)

f. if py < r; then

g. Squad "j" will be the champion and squad "l" will be the loser of the competition

h. Or else

i. Squad "l" will be the champion and team "j" will be the loser of the competition

j. End if

k. Employ the captivating scheme for the champion

l. Employ the trailing scheme for the failed squad m. End

Trainers are playing principal part in providing effective contribution to the squad. Correspondingly trainers modify the strategies throughout the competition in the direction of competition wining and it defined as:

Bc (t +1) = Bc (t) + R1lf (max j - min j); (3)

Bs (t +1 ) = Bs (t) + r{ks (max j - min j). (4)

Strategies given to the squad is defined as:

NStrategies = [ Sum of posmons ( j ) 5strategies ] .

Strategies sharing technique is defined as:

a. For k = 1: Nstrategies

b. Elect capriciously a location

c. Creation of location — modernization of "j"

d. Formula (3)

e. Substitution of position — modernization of "j"

f. Formula (4)

g. End for

h. End

In a squad transposition of the players in the competition is applied to elevate the performance:

NTransposition = [ sum of positions ( j ) 5Transposition ] .

Successively after selecting two possible location i and j then dual variables U and V with two ways of creation and substitution is defined as:

Uc = BC ; (5)

Us = BS ; (6)

= Bc ; (7)

Vs = Bs. (8)

At that moment:

BC = Vc; (9)

Bs = Vs; (10)

Bc = Uc; (11)

Bs = Us. (12) Then then transposition is defined as:

a. For k = 1: NTransposition

b. Locations "i" and "j" are capriciously selected

c. Formula (5)

d. Formula (6)

e. Formula (7)

f. Formula (8)

g. Location "i" and "j" are retreated by

h. Formula (9)

i. Formula (10) j. Formula (11) k. Formula (12)

l. End

There will be replacement in squads after each competition:

Ns =[ R position ( j )]. (13)

The substitution process is defined as:

a. Calculate the quantity of substitution

b. Formula (13)

c. Designate the collections

d. For k = 1: Ns

e. BS n= s (notion)

h (notion) v '

f. Bs,, .. n= c(notion)

h(notion J v '

g. End

Triumphant squad will notice the location within the examination space and it demarcated scientifically by comprising inertia weight ra:

Bc (t +1 ) = Bc (t) + R1 (rac)(bc (t)* -Bc (t));

Bs (t +1 ) = Bs (t) + R1 (cos)i^Bs (t)* -Bs (t)).

In any squad erudition segment is significant and it significantly progress the performance: s = eaR1 - g; h = eR2; g = P~(t((3 /tmax)), then

p с+1 ), =К с >14h № с й-к с ))

в

Uppermost 3 squads in the points table will own the virtuous superiority of erudition

BC

BC

BC

(t+1 )i =(Bj (t))1 "s(lh(Bj (t))1 ~(Bcj (t))|); (14)

С (t+1 )2 =(Bj (t ))2-z(\h (BCj (t ))2-(Bj (t ))|); (15)

(t +1 )з =(BCj (t))3-e^h(Bj (t))3-(Bj (t))|). (16)

With orientation to the premium squad assets the present solution upgrading is done:

B

B

B

(t +1)1 ={Bs (t ))1 -s(|h (Bs (t ))1 -(Bs (t ))|); s (t +1 )2 =(BS (t »2-e(|h (B* (t »2-(BS (t ))|);

S (t + 1)з =(BSj (t))з-e(|h fà (t))з ~^BSj (t))|);

BS (t +1) = '

B) (t+1 )i + B) (t+1 )2 + y) (t+1 )3

-jV-v- 3 •

Players are moved to various squads and it defined as:

N)t = [ N % of squads take part in cyclical transference ].

The cyclic transfer is defined as:

a. For k = 1: N Cyclic transfer

b. Ct = {select rand index i from \i ^ Ct]

c. End for

d. For k = 1 to N _ (Ct)

e. For j = 1 to j

f. if rand > 0.5

g. ctf (notion)= qc

(17)

(18)

(19)

(20)

h. cts (notion )= qs

i. q = select arbitrarily for current squads j. End if

k. End for

l. cf (notion) = fi (Bc (notion)) m. End for n. End

Rendering to the performance in the specific period elevation and relegation of the squads will be present. Supremely accomplished squads will be endorsed to eldest competition and deprived performed squad will be downgraded to junior division league:

NSquads move ~ [ sum of squads 5Squads moved to alternative league ]•

Elevation and relegation procedure is defined as:

a. Eradicate poorest squads NSquads move

b. Define the creation and substitution

c. For k = 1: N Squads move

a. For j = 1 to j

d. Nsquadsc (notion) = Zc

e. Nsquadss (notion) = Zs

f. End for

g. cf (notion) = f (Nsquadsc (notion) )

h. End for

i. Add number of teams to the league j. End

The overall procedure of the BL algorithm as follows:

a. Start

b. Initialize the variables

c. Identify the premium Basketball squad period

d. Nperiod = Nperiod +1, i = 1

e. Stimulate the league schedule

f. Competition amongst squads

i. F. Competition (j, l)

ii. Calculate j)

iii. Compute total fi

iv. Formula (1)

v. Formula (2)

vi. if py < r;then

vii. Squad "j" will be the champion and squad "l" will be the loser of the competition

viii. Or else

ix. Squad "l" will be the champion and team "j" will be the loser of the competition

x. End if

xi. Employ the captivating scheme for the champion

xii. Employ the trailing scheme for the failed squad

xiii. End

g. Strategies sharing technique

i. For k = 1 : N Strategies

ii. Elect capriciously a location

iii. Creation of location — modernization of "j"

iv. Formula (3)

v. Substitution of position — modernization of "j"

vi. Formula (4)

vii. End for

viii. End

h. Forte index calculated for squads

i. Apply transposition procedure

i. For k = 1 : NTransposition

ii. Locations "i" and "j" are capriciously selected

iii. Formula (5)

iv. Formula (6)

v. Formula (7)

vi. Formula (8)

vii. Location "i" and "j" are retreated by

viii. Formula (9)

ix. Formula (10)

x. Formula (11)

xi. Formula (12)

xii. End

j. The Substitution process is defined as

i. Calculate the quantity of substitution

ii. Formula (13)

iii. Designate the collections

iv. For k = 1: Ns

v. Bcu .. )(notion)

h[notton j v '

vi. Bw .. N= c (notion)

h [notion j V '

vii. End

k. Champion and loser are defined

l. Uppermost 3 squads in the points table will own the virtuous superiority of erudition

i. Formula (14)

ii. Formula (15)

iii. Formula (16)

m. With orientation to the premium squad assets the present solution upgrading is done

i. Formula (17)

ii. Formula (18)

iii. Formula (19)

iv. Formula (20)

n. Smearing altered strategies

o. Renewal of premium squad

p. Erudition segment will be employed

q. If max No. of week = N weeks

r. Yes, then erase the poorly performed squads

s. Or else go to step e

t. Include fresh squad to the BL

u. Smear the transferal procedure

L For k = 1: NCyclic transfer

ii. Ct = {select rand index i from |i ^ Ct]

iii. End for

iv. k = 1 to N _ (Ct)

v. For j = 1 to j

vi. if rand > 0.5

vii. c^ (notion)= qc

viii. ctS) (notion)= qS)

ix. q = select arbitrarily for current squads xi. End if

xii. End for

xiii. cf ( notion ) = fi ( Bc ( notion ) )

xiv. End for

xv. End

v. Transformation of the preeminent squad w. max N period = N period x. Yes, then define the premium solution y. Or else go to step d z. End

The offline inaccuracy is computed by

Offline inaccuracy =

1 Maximum iteration

X Present inaccuracyt.

Maximum iteration t = 1

The computation complexity is a metric key for BL algorithm to comprehend its running time. It is influenced by the quantity of maximum iterations, summation of variables, and addition of other parameters in iterations. By reason of quicksort algorithm is realized, the sort's computation complication of O (nlogn) and O [n2) in the finest and least case respectively. The generalized total calculation of complexity is apportioned as follows:

O (nlogn ) = O (T (O (s ) + O (p )));

O (n2 ) = O (t (n2 + nd)) = O (tn2 + tnd).

Simulation results and discussion. Projected BL algorithm is corroborated in IEEE 30 bus system [20]. Table 1 shows the real loss appraisal, Table 2 shows the voltage aberration evaluation and Table 3 gives the voltage constancy assessment. Figure 2 give the graphical appraisal between the methods. BL abridged the power loss efficiently. Appraisal of loss has been done with particle swarm optimization (PSO), adapted PSO, enriched PSO, comprehensive learning PSO, adaptive genetic algorithm (GA), canonical GA, enhanced GA, hybrid PSO-Tabu search (PSOTS), ant lion approach (ALO), quasi-oppositional teaching learning based algorithm (QOTLBO), enriched stochastic fractal search optimization algorithm, harmony search, advanced pseudo-gradient search PSO 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 B-PSO [13] 4.9239

B-TS [10] 4.6862 Hybrid-AS [13] 4.9059

S-PSO [10] 4.6862 B-FS [14] 4.5777

B-ALO [11] 4.5900 Hybrid-ISFS [14] 4.5142

Hybrid-QOTLBO [12] 4.5594 B-FS [16] 4.5275

B-TLBO [12] 4.5629 BL 4.4012

S-GA [13] 4.9408

Table 2 Comparison of voltage deviancy

Algorithm Voltage deviancy, PU Algorithm Voltage deviancy, PU

Hybrid-PSOTVIW [15] 0.1038 Hybrid-MPGPSO [15] 0.0892

Hybrid-PSOTVAC [15] 0.2064 Hybrid-QOTLBO [12] 0.0856

Hybrid-PSOTVAC [15] 0.1354 B-TLBO [12] 0.0913

Hybrid-PSOCF [15] 0.1287 B-FS [14] 0.1220

Hybrid-PGPSO [15] 0.1202 Hybrid-ISFS [14] 0.0890

Hybrid-SWTPSO [15] 0.1614 B-FS [16] 0.0877

Hybrid-PGSWTPSO [15] 0.1539 BL 0.0824

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 BL 0.1001

Standard PSOTS

S-FS

ISFS

S-FS

S-PSO

ALO

QOTLBO

TLBO

S-GA

0.25

£

^ 0.20

I 0.15 >

1 0.10 gp

15 0.05 £

/¿Ш&Я/Рs * ' *

Сy i^ ч

ля ля ля # # Ж Ж сГ

cf

D 0.16

Оч

СГ

<г

ъ

ы> £ 0.14 S а

£

S 0.12

я

В 0.10

Л л

/ V V ч V л-

N Ч

^ X X A cO ¿0 ¿O ¿O -O -O O X aO A A

cfcfc^ * * c

Fig. 2. Assessment of real power loss (a), appraisal of voltage deviancy (b) and assessment of voltage constancy index (c)

Then the BL 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, 5. Figures 3, 4 give graphical comparison between the approaches with orientation to power loss. Proposed algorithms are compared with adapted PSO, PSO, evolutionary programming, self-adaptive real coded GA, canonical GA, adaptive GA, enhanced PSO, comprehensive learning PSO, enhanced GA, faster evolutionary algorithm (EA) and cuckoo search optimization (CSO) algorithm.

Table 4

Assessment of results

Algorithm True power loss, MW Ratio of loss diminution

Base case [24] IEEE 14 bus system 13.550 0

Improved PSO [24] 12.293 9.200

B-PSO [23] 12.315 9.100

B-EP [23] 13.346 1.500

Hybrid-SARGA [22] 13.216 2.500

BL 10.019 26.059

Base case [24] IEEE 57 bus system 27.8 0

Improved PSO [24] 23.51 15.400

B-PSO [23] 23.86 14.100

Canonical-GA[22] 25.24 9.200

Adaptive-GA [22] 24.56 11.600

BL 21.016 24.4028

Base case [24] IEEE 118 bus system 132.800 0

Improved PSO [24] 117.190 11.700

B-PSO [23] 119.340 10.100

B-EPSO [21] 131.990 0.6000

B-CLPSO [21] 130.960 1.3000

BL 112.002 15.6611

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 7.4000

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

BL 14.0180 20.1253

Base case

Base case

bl

sarga

Adapted pso

JAYA

pso depso

Base case 3C

aga

Adapted pso bl

pso clpso

Amended pso

s-pso

s-ep

Adapted pso

pso

cga epso

c d

Fig. 3. Power loss appraisal:

a) IEEE 14 bus system ( »true power loss; ratio of loss diminution); b) IEEE 30 bus system (♦ true power loss; proportion of lessening in power loss);

c) IEEE 57 bus system (♦ true power loss; ratio of loss diminution);

d) IEEE 118 bus system (♦ true power loss; ratio of loss diminution)

True power loss, MW, appraisal (IEEE 300 bus system):

Adaptive-GA [31] ........................................ 646.299800

Faster-EA [31] .............................................. 650.602700

B-CSO [32] ................................................... 635.894200

BL algorithm ................................................ 625.090877

The convergence characteristics of BL algorithm for IEEE 30 bus system show bellow:

Actual loss with / without power reliability, MW.................. 4.4012 / 14.018

Time with / without power reliability, s ................................. 26.13 / 23.91

Number of iterations with / without power reliability ......... 27 / 22

BL

FEA

cso

Fig. 4. True power loss, MW, appraisal (IEEE 300 bus system)

In IEEE 30 bus BL algorithm been evaluated as multiobjective and single objective mode. Figure 5 shows the graphical representation of the characteristics.

30

0

■■ö 25 •с

<D

1 20

Ü л

о <0 U

S

й> <0

à 5

о

U

о

15

10

BL

Fig. 5. Convergence characteristics:

actual power loss with (□) or without (□) voltage constancy; time with (□) or without (□) voltage constancy; number of iterations with (□) or without (□) voltage constancy

Conclusion. Basketball League algorithm reduced the genuine power loss competently. Proposed 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. Basketball League game characteristically entails of 4 quarters and quarter duration is ten minutes. Subsequently double quarters the squads shift sides on the courtyard. The squad with extra points at the conclusion of the 4 quarters triumphs the competition. If the total is tied at the conclusion of ruling time, the play will be preceded to additional time period. A bellicose competitor can possess the ball stirring round the court by drooling or fleeting the basketball to a co-player. In a ball drool, a competitor requests to rebound the basketball counter to the base incessantly practice single hand in a period. Using the both hands concurrently drool the basketball two times previously it rebounds on one occasion establishes a twofold drool defilement, which finishes in relinquishing control to the rival squad. Basketball League algorithm creditably condensed the power loss and proportion of Actual power loss lessening has been elevated. Trainers are playing principal part in providing effective contribution to the squad. Correspondingly trainers modify the strategies throughout the competition in the direction of competition wining. Rendering to the performance in the specific period elevation and relegation of the squads will be present. Supremely accomplished squads will be endorsed to eldest competition and deprived performed squad will be downgraded to junior division league. Convergence characteristics show the better performance of the proposed BL algorithm. Valuation of power loss has been done with other customary reported algorithms.

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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 Basketball League algorithm. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2024, no. 3 (114), pp. 92-114. EDN: RGSEIK