Multiobjective Optimization of Maintenance Applied in Electric Power Distribution Systems

Luz, Thiago José da; Gapski, Anderson Luis; Unsihuay-Vila, Clodomiro

doi:10.1590/1678-4324-2024230894

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Article - Engineering, Technology and Techniques • Braz. arch. biol. technol. 67 • 2024 • https://doi.org/10.1590/1678-4324-2024230894 copy

Multiobjective Optimization of Maintenance Applied in Electric Power Distribution Systems

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Power distribution utilities effort to ensure the quality of energy to their consumers and the reliability of their power distribution system. It is necessary that maintenance activities are planned with the aim of maintaining or improving reliability indicators in supply to consumers. In this paper, a computational model based on integer nonlinear multiobjective programming is presented to improve the maintenance of equipment in the power distribution system. Since it is a reliability-centered approach, a probabilistic failure model is first used to obtain equipment reliability values at each time point through fuzzy inference. Three objective functions are optimized: i) minimizing maintenance cost, ii) minimizing failure frequency, and iii) maximizing equipment reliability. The optimization problem is also formed by three sets of constraints: i) individual and collective continuity indicators; ii) task execution time; and iii) maintenance limit for each type of equipment. Lichtenberg's algorithm is used to solve the model. A case study is performed for a feeder section consisting of twenty-eight distribution equipment. The results obtained using the Pareto constraints show scenarios that can help maintenance teams to make decisions and develop the preventive maintenance planning. Adding constraints on the duration and frequency of collective interruptions indicators improves the power quality of the distribution system; however, it requires an increase in investment by 36%.

Keywords:
Continuity Indicators; Fuzzy Inference; Lichtenberg Algorithm; Multiobjective Programming; Power Distribution Systems; Reliability-Centered Maintenance

HIGHLIGHTS

• Reliability-centered maintenance model for power distribution systems is presented.

• Fuzzy inference and integer nonlinear multiobjective programming is applied.

• A meta-heuristic called Lichtenberg's algorithm is used.

• The results can assist maintenance teams in decision making.

Technique Used	Proposed Model	[⁴4 Reis PA. [Reliability based optimization of maintenance schedules for electric power distribution systems] [Masters dissertation]. Campinas: Universidade Estadual de Campinas; 2007 [cited 2024 May 10]. 73 p. Available from: https://repositorio.unicamp.br/Busca/Download?codigoArquivo=469260 https://repositorio.unicamp.br/Busca/Dow... ]	[⁵5 Martin MP. [Optimal Strategies for the Maintenance on Power Distribution Networks] [Masters dissertation]. Campinas: Universidade Estadual de Campinas; 2016 [cited 2024 May 10]. 89 p. Available from: https://repositorio.unicamp.br/Busca/Download?codigoArquivo=468282 https://repositorio.unicamp.br/Busca/Dow... ]	[⁶6 Pereira FEL. [Determining Maintenance Scheduling of Transmission Systems Considering Penalties Associated With Unavailability] [Doctorate Thesis]. Rio de Janeiro: Pontifícia Universidade Católica do Rio de Janeiro; 2008 [cited 2024 May 10]. 212 p. Available from: https://www.maxwell.vrac.puc-rio.br/13371/13371_1.PDF https://www.maxwell.vrac.puc-rio.br/1337... ]	[⁷7 Neto JEA. [Optimization of maintenance programming of transmission assets of the Brazilian electric power system considering penalties for unavailability, systemic constraints and logistics technical teams] [Masters dissertation]. Campinas: Universidade Estadual de Campinas; 2011 [cited 2024 May 10]. 150 p. Available from: https://ime.unicamp.br/pos-graduacao/otimizacao-programacao-manutencao-ativos-transmissao-sistema-eletrico-brasileiro https://ime.unicamp.br/pos-graduacao/oti... ]	[⁸8 Piasson D. Otimização de planos de manutenções de componentes de sistemas de distribuição de energia elétrica centrados em confiabilidade [Optimization of maintenance plans for components of electric power distribution systems focused on reliability] [Doctorate Thesis]. Ilha Solteira: Universidade Estadual Paulista Júlio de Mesquita Filho; 2014 [cited 2024 May 10]. 266 p. Available from: http://hdl.handle.net/11449/110518 http://hdl.handle.net/11449/110518... ]	[⁹9 Rodriguez AM. [Reliability-centered maintenance task planning for electric power distribution systems] [Masters dissertation]. Ilha Solteira: Universidade Estadual Paulista; 2017 [cited 2024 May 10]. 164 p. Available from: http://hdl.handle.net/11449/151823 http://hdl.handle.net/11449/151823... ]	[¹⁰10 Carnero MC, Gómez A. Maintenance strategy selection in electric power distribution systems. Energy. 2017 Jun;129:255-72.]	[¹¹11 Moradi S, Vahidinasab V, Kia M, Dehghanian P. A mathematical framework for reliability-centered maintenance in microgrids. Int Trans Electr Energy Syst. 2019 Jan;29(1):1-21.]	[¹²12 Afzali P, Keynia F, Rashidinejad M. A new model for reliability-centered maintenance prioritisation of distribution feeders. Energy. 2019 Mar;171:701-9.]	[¹³13 Ferreira MIJ. [Maintenance Scheduling of Distribution Networks Based on Reliability Indices] [Masters dissertation]. Rio de Janeiro: Pontifícia Universidade Católica do Rio de Janeiro; 2019 [cited 2024 May 10]. 85 p. Available from: https://sucupira.capes.gov.br/sucupira/public/consultas/coleta/trabalhoConclusao/viewTrabalhoConclusao.jsf?popup=true&id_trabalho=7701959 https://sucupira.capes.gov.br/sucupira/p... ]	[¹⁴14 Yari AR, Shakarami MR, Namdari F, Cheshmehbeigi HM. A Practical Approach to Planning Reliability-Centered Maintenance in Distribution System Considering Economic Risk Function and Load Uncertainty. Int J Ind Electron Control Optim. 2019 Oct;2(4):319-30.]	[¹⁵15 Kong X, Liu C, Shen Y, Hu W, Ma T. Power supply reliability evaluation based on big data analysis for distribution networks considering uncertain factors. Sustain Cities Soc. 2020 Dec;63:102483.]	[¹⁶16 Catelani M, Ciani L, Galar D, Patrizi G. Optimizing Maintenance Policies for a Yaw System Using Reliability-Centered Maintenance and Data-Driven Condition Monitoring. IEEE Trans Instrum Meas. 2020 Jan;69(9):6241-9.]	[¹⁷17 Neto JEA. [Efficient scheduling of maintenance of transmission assets of the brazilian electricity sector] [Doctorate Thesis]. Campinas: Universidade Estadual de Campinas; 2020 [cited 2024 May 10]. 160 p. Available from: https://doi.org/10.47749/T/UNICAMP.2020.1157213 https://doi.org/10.47749/T/UNICAMP.2020.... ]
Mixed Integer Linear Programming
Markov model
Simulated Annealing
Fuzzy Inference & NSGAII
Risk Matrix
GRASP
GA - Genetic Algorithms
Dynamic Programming
MACBETH
FMEA
Lagrange multipliers
Weighted Importance
Big Data
IENN
FMECA
Objective function addition - collective continuity indicator
Continuity and Priority Constraints
Single Objective Optimization Methods
Multiobjective Optimization Methods
Lichtenberg's Algorithm
Proposed model		In the literature

	Algorithm 1: Main
1	Define objective functions and search space - $J_{i}$ upper and lower limits
2	Set the number of iterations and population - $N_{i t e r}, P o p$ (common for all optimizers)
3	Set LF refinement and switch parameters - $Re f, M$ (MOLA routine parameters)
4	Define LF parameters - $R_{c}, N_{p}, S$
5	if $M = 0,$ load LF, end if
6	if $M = 1,$ create LF, end if
7	while $(i t e r < N_{i t e r})$ Do
8	if $M = 2,$ create LF, end if
9	$X_{t r i g g e r} =$ space center search (first LF trigger point)
10	if $r e f = 0$
11	Applies to random scaling and rotation
12	Initialize the random population over the LF, $X_{i} (i = 1,2, \dots, P o p)$
13	copy the LF to create the second LF from the same *LF (Local)
14	Same random scaling and rotation applies to both
15	The random global population is initialized through the LF $X g l o b a l_{i} (i = 1,2, \dots,0.4 * P o p)$
16	Initialize the random local population through the LF $X l o c a l_{j} (j = 1,2, \dots,0.6 * P o p)$
17	$X_{i} = X g l o b a l_{i} + X l o c a l_{j}$
18	end if
19	Calculate $J_{i}$ for each one $X_{i}$ of the problem
20	Find the dominated and non-dominated solutions analyzed in $J_{i}$
21	Builds the current Pareto frontier with non-dominated solutions
22	Saves non-dominated solutions across iterations
23	$X_{t r i g g e r} = X_{N D}$
24	$I t e r = i t e r + 1$
25	End while
26	return Pareto border

	Algorithm 2: Creation of LF
1	An array $R_{c}$ is created - size zero
2	A unit particle is placed at the center
3	while $(i < N_{p})$ do
4	Randomly place a unit particle in the array
5	if the plotted unit particle t is close to another unit particle
6	if $r a n d < S$
7	This new unit particle is placed in the matrix
8	$i = i + 1$
9	If not
10	The plotted unit particle is eliminated
11	end if
12	end if
13	if the agglomerate of unit particles reaches $R_{c}$
14	The simulation is finished
15	end if
16	end while
17	$X =$ coordinates of all unit particles of cartesian space in the size of the search space

Equipment	Maintenance cost (R$)				Failure rate parameter multiplier				Failure rate (failures/year)
	m₀	m₁	m₂	m₃	m₀	m₁	m₂	m₃
TR	0	120	550	2500	1.04	0.8	0.5	0.01	0.2723
CP	0	350	1000	-	1.04	0.8	0.08	1.04	0.2723
RT	0	150	650	1200	1.03	0.8	0.5	0.01	0.4312
LN	0	80	170	-	1.04	0.8	0.08	1.04	0.4312
CS	0	30	70	-	1.01	0.8	0.01	1.01	0.2723
DJ	0	150	800	2000	1.04	0.8	0.5	0.01	0.4312

Equipment	AET				ATT				APT				ATL
	m₀	m₁	m₂	m₃	m₀	m₁	m₂	m₃	m₀	m₁	m₂	m₃
TR	0	120	150	180	0	60	80	100	0	20	30	60	30
CP	0	30	60	0	0	60	100	0	0	20	30	0	30
RT	0	120	150	180	0	60	80	100	0	20	30	60	30
LN	0	30	120	0	0	60	100	0	0	20	30	0	30
CS	0	30	60	0	0	60	100	0	0	20	30	0	30
DJ	0	60	120	0	0	60	100	0	0	20	30	0	30

Points	Unreliability	Cost (R$)	Quantity of Maintenance
$P 4$	0.1118	21,210.00	74	without (eq. 28)
$P 5$	0.09331	44,250.00	262
$P 6$	0.07624	115,500.00	672
$P 4 ’$	0.1118	34,750.00	189	with (eq. 4) and (eq. 28)
$P 5 ’$	0.09331	55,350.00	427
$P 6 ’$	0.07604	137,600.00	672

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[1] *Correspondence: thiagojluz@ufpr.br; Tel.: +55-41-33613622 (T.J.L.)