Asset management of distribution systems is an important issue for smart grid. Maintenance scheduling, as an important part of asset management, affects the reliability of distribution equipment and power supply. This research focuses on longterm distribution system maintenance scheduling aided by available operation information, which is a prominent advantage of smart grid over conventional distribution systems. In this paper, the historical and future operation information in smart grid is taken into account through a decoupled timevarying reliability model of equipment. Based on distribution system reliability assessment, a maintenance scheduling model is proposed to determine the optimal implementation time of maintenance activities to minimize distribution systems’ total cost, while satisfying reliability requirements. A combined algorithm that consists of particle swarm optimization and tabu search is designed and applied to the optimization problem. Numerical result verifies that the proposed method can schedule longterm maintenance of distribution systems in smart grid economically and effectively.
As the most complex part in power networks, distribution systems play a fundamental role and their failures result in most interruptions of power supply. Maintenance of distribution equipment can extend equipment’s service life and reduce the duration of supply outage [
Distribution equipment maintenance can be generally divided into two types: preventive maintenance (PM) and corrective maintenance (CM). Preventive maintenance is conducted before equipment’s failure and can be scheduled, whereas corrective maintenance is performed after the occurrences of failures and it has very few optional schedules. According to different scheduling principles, preventive maintenance scheduling can be divided into several types: predetermined periodic maintenance, reliabilitycentred maintenance (RCM), and riskbased maintenance (RBM) [
Some research has proposed some models and algorithms for distribution maintenance scheduling. Mixedinteger programming is applied in [
For maintenance scheduling, the foremost and fundamental task is to form the equipment reliability model and obtain equipment’s failure rates. In conventional maintenance models, equipment’s condition is discretized into a few states [
The equipment monitoring devices in smart grid can record the continuously changing operation data. The smart grid framework may contain the prediction of future operation scenarios and even the preestablishment of future operation plans, but this information is rarely incorporated in current models. In this paper, operation information in smart grid is used to facilitate a more reasonable maintenance schedule for distribution systems. In the proposed method, the failure rate of distribution equipment is decoupled according to different failure mechanisms. This decoupled failure rate model is used to incorporate the information reflecting the timevarying operation conditions and environments, such as heavy load and adverse weather. Based on distribution system reliability assessment, a RBM scheduling model considering varying operation conditions is proposed to minimize distribution systems’ outage losses and maintenance cost over the scheduling horizon, while satisfying reliability requirements. Due to the fact that an accurate and complete method for distribution system reliability assessment is embedded in the maintenance model, it is difficult to solve this nonlinear combinational optimization problem through conventional mathematics programming methods. Therefore, a hybrid algorithm that combines particle swarm optimization (PSO) and tabu search (TS) is designed and applied to solve this optimization problem.
The remainder of this paper is organized as follows. In Section
In some reliability models of equipment [
In practice, equipment in distribution systems has various deterioration mechanisms [
An example of decoupled failure rate curves.
Meters and sensors in smart grids provide much system operation information. With this information, the condition of system components can be more accurately assessed. A frequently occurred operation condition, heavy load, is analyzed here as an example.
With the growth of load demand and the aggregated load such as simultaneously charging batteries of electrical vehicles, heavy load situations are not rare in distribution systems. Overload situations can be recorded and sometimes predicted by smart grid devices. Thus, their impacts on equipment reliability can be quantified. Generally, the heavy load will accelerate certain failure processes of electrical equipment, resulting in corresponding increase in failure rate components [
The impact of the heavy load on the insulation failure rate of transformers.
Maintenance tasks are often targeted at improving a certain part of equipment, such as vegetation pruning and conductor and pole refurbishment. Therefore, each maintenance activity only reduces one or several corresponding failure rate components and has little impact on other components. After maintenance, the corresponding failure rate of this deterioration type returns to a certain initial value instead of that of the brandnew state [
Aided by operation information in smart grids, the decoupled failure rate model accurately quantifies the impacts of operation conditions and maintenance activities on equipment reliability, serving as a basis for the distribution maintenance scheduling model presented below.
In system operation, both maintenance and failure may cause outages of equipment and reduce distribution system reliability. On one hand, equipment outages due to preventive maintenance may result in load shedding, thus decreasing systems’ reliability level in maintenance periods. On the other hand, maintenance can reduce equipment’s failure rates and improve the system reliability level in the following periods. To obtain the most economic preventive maintenance schedule, the influences of maintenance outages and failures should be comprehensively evaluated. Thus, the objective function is formulated as minimizing the total cost of the distribution system over the whole scheduling horizon [
where
Maintenance strategy constraints are the constraints of maintenance activities [
Maintenance time window constraint: the starting period of preventive maintenance must be within a specific interval:
For corrective maintenance, however, due to its high level of priority after a failure’s occurrence, there is no time window constraint for it.
Budget constraint: cost in each period should be within the following budget:
Labour constraint: the maximum number of staff for preventive and corrective maintenance is limited:
During maintenance, it is important to ensure a certain level of power supply reliability. The reliability indices—the System Average Interruption Frequency Index (SAIFI) and the System Average Interruption Duration Index (SAIDI), which, respectively, represent the frequency and duration of supply interruption, reflect the average level of power supply reliability in smart grid. In maintenance scheduling, system operation constraints are presented as follows.
SAIFI constraint: to guarantee a certain power supply reliability level, SAIFI in each period should not exceed its limit
where
SAIDI constraint: SAIDI in each period should not also exceed its limit
where
In smart grid, the values of
Distinguished from existing models that seldom consider various operation conditions, (
If the maintenance start time
Hybridized metaheuristic algorithms are considered to be effective and efficient in solving largescale optimization problems [
The solving flow chart through the PSOTS hybrid algorithm for maintenance scheduling.
Details of some steps are explained below.
A difference between the PSO part in this algorithm and PSO in current research [
The PSOTS hybrid algorithm inherits PSO’s advantage of fast optimization speed, while adopting the neighbourhood move and the tabu list of TS to escape from local cycle to enhance its global searching ability, thus facilitating fast and continuous improvement of the solution during the optimization process.
The distribution system formed by Feeder 1 and Feeder 2 on Bus 6 in IEEE RBTS [
Deterioration mechanisms data of 11 kV feeder distribution system.
Deterioration mechanism type  Coefficient  Line  Transformer  Breaker 

Type 1 (Tp1) 

11.47  11.47  11.47 

0.2651  0.2651  0.2651  

76.262  79.452  75.452  

4.4792  4.4792  4.2792  

0.00866  0.00866  0.00866  


Type 2 (Tp2) 

16.38  15.38  15.38 

0.3759  0.3559  0.3559  

98.045  92.045  87.045  

5.964  5.064  4.4792  

0.02673  0.02673  0.02673  


Type 3 (Tp3) 

25.64  25.64  25.64 

0.2873  0.2873  0.2873  

94.12  90.36  90.294  

5.954  5.028  5.028  

0.03512  0.03512  0.03512 
The preventive and corrective maintenance data of the test system are shown in Table
Maintenance data of different deterioration mechanism types and equipment.
Equipment  Duration (h)  Labour (ph)  Materials cost ($)  

Tp1  Tp2  Tp3  Tp1  Tp2  Tp3  Tp1  Tp2  Tp3  
Preventive maintenance  
Line (per km)  2  4  6  3  10  20  12.5  50  125 
Transformer  4  8  10  5  15  33  30  70  300 
Breaker  3  6  9  4  12  24  25  60  250 
Corrective maintenance  
Line (per km)  7  10  14  8  15  30  25  100  275 
Transformer  10  15  20  12  25  50  60  190  600 
Breaker  9  13  18  10  20  40  50  150  500 
Despite the fact that the proposed method is also capable of solving a largescale problem that considers all equipment’s maintenance and all their deterioration processes, not all equipment’s maintenance arrangements are considered in this case for simplicity. The maintenanceneeded equipment and constraints are shown in Tables
Preventive maintenance (PM) needed equipment.
Maintenance type  Equipment to be scheduled for preventive maintenance  

PM Tp1  Bus: B3  Line: L2, L3, L4, L5, L6, L8, L9, L10, 
Transformer: T7, T9, T11, 
PM Tp2  Bus: B4  Line: L7, L15, L20, L23  Transformer: T5, T23 
PM Tp3  Line: L1, L14, L19  Transformer: T13, T27, T33 
Maintenance and system operation constraints in one period.
Constraints  Limit value 

Budget constraints ($)  30,000 
Labour constraints (personhour)  85 
SAIFI (interruption·month^{−1})  1.75 
SAIDI (h·month^{−1})  10 
Based on historical operation data and equipment’s deterioration characteristics, the expected change of equipment’s reliability can be calculated. As an example, transformer T13’s timevarying failure rate curves are shown in Figure
Reliability model of the transformer T13.
The maintenance scheduling is optimized based on equipment’s reliability model in Section
Composition of the total cost in the iteration process.
It can be noted that in the early stage, the PSO algorithm has high search efficiency and the system total cost decreases rapidly. However, particles may immerse into the local nearoptimal solution cycles after several PSO iterations, and the accuracy of the solution cannot be further improved. For example, from the 12th to the 16th iteration step, a nearoptimal solution cycle emerges, in which the total cost of the distribution system is $307,025. From the 16th step, the algorithm turns to the TS mode and generates candidate solutions to expand the searching space through adding the local optimum to the tabu list. The neighbourhood move of TS helps to jump out of local optimum and find more accurate global optimum simultaneously. After the 17th iteration step (TS iteration), the solution gets rid of the local solution cycle and the total cost declines to $304,804. In the 29th iteration step, the objective value decreases to $281,929. This value remains unchanged during the next five PSO iterations and five TS iterations as shown in Figure
Maintenance scheduling result (
Number 

Number 

Number 

Number 

Number 

Number 


L1  4  L8  46  L15  35  L22  9  T9  17  T29  22 
L2  28  L9  27  L16  9  L23  15  T11  23  T31  43 
L3  39  L10  20  L17  46  L24  16  T13  22  T33  4 
L4  46  L11  44  L18  33  L25  33  T15  20  T35  27 
L5  9  L12  28  L19  15  L26  29  T23  3  B4  22 
L6  21  L13  29  L20  21  T5  27  T25  21  B3  40 
L7  44  L14  3  L21  11  T7  5  T27  3 
EENS of each period of the scheduling result.
Since this algorithm is a stochastic algorithm, 30 independent runs have been performed. The mean value of the result is $282,630 and the standard deviation is $853. The relative error is about 0.3%. The results indicate that the algorithm has good accuracy and can guarantee to obtain the optimal solution.
In smart grids, some future operation information is available through forecasting or presetting. Here, a future heavy load scenario is taken, for instance. It is assumed that the load on node 5 is 2.1 times of its original value during periods 12 and 13. Based on calculation through (
T13’s insulation failure rate change with heavy load and maintenance.
The optimal maintenance schedule considering future heavy load scenario is presented in Table
Maintenance scheduling result with future heavy load scenarios.
Number 

Number 

Number 

Number 

Number 

Number 


L1  10  L8  52  L15  27  L22  31  T9  27  T29  20 
L2  4  L9  27  L16  37  L23  5  T11  31  T31  22 
L3  1  L10  25  L17  41  L24  19 


T33  6 
L4  16  L11  7  L18  48  L25  50  T15  36  T35  13 
L5  17  L12  11  L19  9  L26  22  T23  15  B4  37 
L6  42  L13  30  L20  14  T5  15  T25  16  B3  39 
L7  17  L14  16  L21  47  T7  28  T27  2 
In Figure
System cost with different reliability requirements.
Cost  Ordinary constraints ($) 
Stricter constraints ($) 

Lost load penalty  257,278.0  268,927.0 
Corrective maintenance  22,495.7  23,531.1 
Preventive maintenance  2,156.0  2,137.5 


Total  281,929.7  294,595.6 
Reliability indices of each period with stricter reliability constraints.
As shown in Figure
This paper proposed a longterm distribution maintenance scheduling model for asset management in smart grid to minimize the total cost over the maintenance scheduling horizon. Based on data collected by smart meters and sensors in distribution systems, the decoupled failure rate model is more adaptable and accurate to represent the timevarying failure rates due to different deterioration mechanisms. It is proved that the incorporation of operation conditions into maintenance scheduling helps to make a more economic and reasonable schedule. The PSOTS hybrid algorithm used in this paper avoids the local optimum of PSO and low searching efficiency of TS, showing good applicability to the nonlinear integer programming problem. Numerical results show that the proposed model and algorithm have good potential for longterm distribution system maintenance scheduling in smart grid.
Maximum budget provided in period
The cost of one personhour in preventive maintenance type
The cost of one personhour in corrective maintenance type
The deterioration type index (i.e., preventive and corrective maintenance type index)
The number of deterioration types (i.e., number of preventive and corrective maintenance types)
Labour resources (in personhours) available in period
Labour resources (in personhours) required in preventive maintenance type
Labour resources (in personhours) required in corrective maintenance type
The number of maintenanceneeded equipment
The size of the particle swarm in PSO
The annual interest rate
The materials cost required in preventive maintenance type
The materials cost required in corrective maintenance type
The time horizon of maintenance scheduling
The earliest feasible starting period of preventive maintenance type
The latest feasible starting period of preventive maintenance type
The starting period of preventive maintenance type
The starting period of preventive maintenance type
The starting period of preventive maintenance type
The starting period of preventive maintenance type
A binary ancillary variable, which equals 1 if preventive maintenance type
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the National Natural Science Foundation of China (nos. 51277141 and 50807043).