Optimization of maintenance management of trees in power distribution systems

We propose a data-analysis-based methodology for maintaining trees that affect power distribution networks. From the information captured in (cid:12)X(cid:8)(cid:7) (cid:16)(cid:8)(cid:4)(cid:5)(cid:21)(cid:7) (cid:131)(cid:8)(cid:7) (cid:25)(cid:6)(cid:8)(cid:7) (cid:24)(cid:25)(cid:132)(cid:132)(cid:27)(cid:18)(cid:4)(cid:17)(cid:20)(cid:13)(cid:9)(cid:18)(cid:22)(cid:3)(cid:6)(cid:8)(cid:5)(cid:7)

Optimization of maintenance management of trees in power distribution systems JOSÉ ALEXANDER MARTÍNEZ / FREDY HERNÁN MARTÍNEZ S.

INTRODUCTION
The electricity distribution aerial networks may be affected by temporary or permanent contact with trees, at the expense of service quality.This is the reason why distribution companies of electricity in Colombia include forest care in maintenance programs, which entails a large investment.
On behalf of the Colombian government, the Energy Regulatory and Gas Commission (CREG) with resolution 097 of 2008 [1] established the methodology and quality indices ITAD (Grouped Quarterly Index of Discontinuity), IAAD (Grouped Annual Index of Discontinuity), and IRAD (Grouped Benchmark Index of Discontinuity) to which it applies the new scheme of incentives and compensation to users, allowing network operator (OP) increase or decrease their usage charges of connected assets to Local Distribution System (SDL).The aim of this new regulation is to standardize the quality of service around the average quality, i.e. reduce the dispersion of quality improving the indices for the worst users served.The issue of trees takes center stage because the new regulatory philosophy requires improving quality indices in rural areas.
To manage the ITAD part involving the maintenance of networks, i.e., the NTG (Quarterly Level of Discontinuity by Quality Group) component (the part not manageable in maintenance is corresponding to Energy Sales VT, this component is inversely proportional to the ITAD and its management is of commercial nature), we propose an analysis involving only the interruptions caused by trees.In this way, we think that we can identify the circuits with higher energy not supplied and most users affected, parameters that directly affect the ITAD.
Our ideas for the projection of tree maintenance DUH VWURQJO\ LQÀXHQFHG E\ UHVHDUFK RQ PDLQWHQDQce services priority in electrical feeders [2]- [7].According to these researches, there is a strong relationship between system parameters such as reliability and power quality and environmental parameters such as the vegetation presence, seasonal loading and even vandalism.
7R SULRULWL]H WKH FLUFXLWV ZH DUH ¿UVW LQVSLUHG E\ the power of abstraction used in fuzzy systems [4], [8]- [10].As is common in many approaches, we use the experience of experts to establish the growth of trees as high impact variable in the failure of circuits in the city of Bogota D.C. (Colombia).Subsequently, we perform a graphical analysis of the hierarchy obtained in order to perform a technical analysis to validate the results.
2XU UHVHDUFK DOVR ZDQWV WR ¿QG DQVZHUV WR TXHVtions that arise once we have found the critical circuits: What trees should I intervene?When should I intervene and how much maintenance costs?These problems have been addressed from different perspectives.One option uses the philosophy of Reliability Centered Maintenance (RCM), based on four principles: best pruning techniques, documentation of the work, training and competence requirements, quality control and auditing [11].
Another approach documented, which is also related to our work, uses a mathematical model based RQ $UWL¿FLDO 1HXUDO 1HWZRUN $11 >@ ZKLFK relates the failure rates of the feeders with variables that affect the nature of vegetation as the ambient temperature, the rain and the time elapsed since the last pruning.A variation of the latter model uses a JHQHWLF DOJRULWKP *$ >@ LQYROYLQJ YDULDEOHV such as the feeder length, height and growth rates of trees by species, and time of year, giving costs associated with maintenance and estimated ENS.Our research also estimates the optimum time for pruning through a genetic algorithm, which uses models of growth of native trees.
The paper is organized as follows.Section 2 presents preliminary concepts and problem formu-ODWLRQ 6HFWLRQV LOOXVWUDWHV WKH PHWKRGRORJ\ RI work, details of the prioritization of the circuits and the optimal pruning cycle.Section 4 presents the behavior of the methodology developed and Section 5 concludes the paper.

METHODOLOGY
7KH ¿UVW SDUW RI WKH DQDO\VLV HVWDEOLVKHV D PDLQWHnance priority for each network circuit of medium voltage, from a "measure" of criticality due to forestry events.The second part of the analysis is WKDW RQFH DUH LGHQWL¿HG WKH PRVW FULWLFDO FLUFXLWV we analyze the characteristic of them in order to GH¿QH D SHULRG RI SUXQLQJ D TXDQWLW\ RI SUXQLQJ and a stable budget for each feeder.

Prioritization of Circuits
The prioritization of the circuit begins with downloading and debugging information from WKH XQL¿HG V\VWHP LQIRUPDWLRQ UHJLVWU\ IURP WKH network operator (OR).We only retrieve information related to forestry events, taking into account the events for transitory faults, permanent faults, circuits associated with events, duration of interruptions, customers affected by transformer and transformer energy demand (Figure 1).
With the downloaded information, we implement a forestry database to calculate the indicators EPNS (not included in the Equation 5 the load factor) and the NU.These are the input data that feed the fuzzy logic systems, system which is responsible for prioritizing the circuits.This calculation should be performed by transformer, circuit and period.
(316 YDULDEOH LV GH¿QHG DV WKH DYHUDJH HQHUgy not supplied due to the interruption i, for the transformer j, circuit k, in the period l.This variable is calculated as: (5) Where: T i,j,k,l is the duration in minutes of interruption and DEP j,k,l is the average energy demand.
Similarly we calculate the sum of users affected NU, as the number of users affected by interruption i, transformer j, circuit k, in period l.
Both the system output variable, priority P, as input variables EPNS and NU, are associated with OLQJXLVWLF YDULDEOHV GH¿QHV IX]]\ VHWV $Q RYHUview of rules that govern the inference engine is illustrated in Table 1.
The prioritization performed by the fuzzy logic V\VWHP FDQ EH YLVXDOL]HG DV D ' VXUIDFH ZKHUH X and Y axes correspond to the inputs and the Z Source: own work axis to the output.We evaluate the prioritization using both Mamdani as Takagi-Sugeno inference, using different sets of rules.In Figure 5 we show the result of four of these exercises.
The fuzzy logic system provides the possibility of periodic monitoring of indicators of critical circuits on which it is applied preventive and corrective measures.Graphically speaking, we expect that all circuits tend to come together at the lower part of the surface with the majority of the population.

Optimal Pruning Cycle
At this stage we process the information collected LQ WKH ¿HOG ZKLFK FRUUHVSRQGV WR IRUHVW LQYHQtories conducted for each feeder.The inventory information is entered into a genetic algorithm (GA), and so we get a curve that describes the optimal pruning cycle (CPO) and the budget.
Among the most important data that contains an inventory are: location of tree, species, physical condition, health, geographical coordinates, height, diameter at breast height (DAP), plate LGHQWL¿FDWLRQ LQWHUYHQWLRQ SHUIRUPHG SUXQLQJ RU felling) and a photographic record for each individual.From this database, in our research, we use for the optimization process the following data: LGHQWL¿FDWLRQ SODWH KHLJKW VSHFLHV DQG WUHHQHWwork distance (distance between the medium vol-tage network and the nearest point of the tree).
The time between pruning done at the same tree is called pruning cycle (CP).The optimal pruning cycle is then the optimal time that should elapse between forest maintenance performed on a circuit, in order to minimize the possibility of contact between the trees and the medium voltage network and thus minimize service interruptions.
The analysis methodology is summarized in Figure 2.The inventory information is encoded in  a matrix.This matrix is composed of n rows representing the number of trees, and four columns that correspond to the parameters: Tree ID, Cost code, Species code, and Di.
The ID LGHQWL¿HV D XQLTXH WUHH 7KH Cost code is the cost of pruning the tree according to his height.We assign to this parameter three possible values: 0, 1 and 2. Thus, 0 corresponds to a height of less than 7 m, 1 is to a height between 7 m and 15 m, and 2 correspond to greater heights.
The species are coded with values from 0 to 18. Finally, Di is the initial tree-network distance in cm.
We handle a total of 19 native species to the savannah of Bogota.The growth curves for these species were determined by previous research [14].
That research describes the cumulative growth of trees after having been subjected to pruning.With this information, we can simulate the implementation of forest maintenance, and in this way, we can make the performance evaluation of the genetic algorithm.
We build the objective function to minimize from two elements: the tree-network distance coming from the inventory, and growth models by species Ɣ Pruning threshold.Is the distance that serves as a criterion to discriminate between trees should be pruned and which should not be pruned.
The optimum distance for an individual tree is GH¿QHG DV WKH GLVWDQFH GLIIHUHQFH EHWZHHQ LQLtial and cumulative growth.Thus, Equation 6DWWHPSWV WR ¿QG WKH PD[LPXP WLPH t to wait for pruning, i.e., the time at which the distance D is equal to or approaching zero.Negative values of D in Eq. ( 6) (when y(t)>Di) are produced by the growth of a tree which is already higher than the desired value, that is, greater than the tree-network distance found in the inventory.Accordingly, the optimal distance should not have negative values, therefore: 'Lí\W Equation 8 is the constraint equation to optimize D without getting negative values.
Since along an air electricity network there are a certain number of trees of different species and KHLJKWV LW LV QHFHVVDU\ ¿QG QRW WKH F\FOH RI SUXning each tree but the best pruning cycle which can perform general maintenance.For a number n of trees, the objective function )2 LV GH¿QHG as the sum of distances D for all trees in the inventory, namely: Likewise, for a number n RI WUHHV ZH GH¿QH n constraint equations as follows: The simulation of maintenance is shown in Figu-UH )URP WKLV ¿JXUH LW FDQ DQDO\]H WKH EHKDYLRU by individual or species according to the cumulative growth.The process happens at each step corresponds to: 1. We recorded the distance Di in the inventory DV IRXQG LQ WKH ¿HOG ,Q WKH ¿UVW 3& WKH JURZWK y(t) is calculated and subtracted to Di (Equation 9).Then it is estimated that trees are within the threshold of pruning, i.  hold, D(t) is the same as calculated above, i.e.: 4. Then we repeat the three previous steps as the number of cycles to simulate, according to a SUHYLRXVO\ GH¿QHG YDOXH Finally, we obtain curves that describe the CP characteristic of the circuit and the amount of pruning performed in each cycle.On these graphs, we analyze the execution time of maintenance and the number of individuals to intervene.The cost of maintenance in each CP value is calculated according with the pruning of costs according to the Cost Codeassociated with each tree.Note that this budget is the minimum required in each Source: own work CP to minimize the possibility that some trees generated outages.The methodology concludes with an analysis of the data obtained from the simulation and proposals for solution in accordance with the analysis.

RESULTS AND PERFORMANCE
:H SULRULWL]H WKH FLUFXLWV ¿UVW LQWURGXFLQJ WR WKH fuzzy logic system the historic events for the year 2009 for all unplanned events caused by trees, in the medium-voltage circuits, in the area of in-ÀXHQFH RI %RJRWD DQG WKH QHLJKERULQJ PXQLFLSDlities of the savannah.In the upper surface of Figure 5 are the most critical circuits, and is a clear priority among them.By contrast, in the bottom RI WKH ¿JXUH LV WKH PDMRULW\ RI WKH SRSXODWLRQ ,W LV REYLRXV WKDW WKH PRGL¿FDWLRQ RI UXOHV DQG fuzzy sets directly affects the way the system prioritizes the circuits, but this becomes visible when comparing the four graphs.We work the two Mamdani systems with three fuzzy sets in the output.The design difference between them is that it has changed the core and the boundary of the input fuzzy sets, and the scale priority.With these changes the output is a bit more uniform and hierarchy between priority circuits is more visible.We also changed some rules to give more priority to circuits with a very high rate relative to the other; the effect of this is seen in Table 2.
Mamdani's 2 ranking is achieved include circuits that were not previously but which deserved more priority characteristics, this is the case of circuits 68 08' DQG 7% %\ DQDO\]LQJ WKHLU LQdicators, we can observe that they have industrial FXVWRPHU SUR¿OH LH KLJK FRQVXPSWLRQ DQG ORZ users, or otherwise, many users and low consumption.Both cases are of concern, both for the SUR¿OH DQG E\ &RORPELDQ UHJXODWRU\ IUDPHZRUN Importantly, if sales of energy are low in proportion to the number of users, the ITAD increases.
,Q WKH ¿JXUH WKHVH FXVWRPHUV WHQG WRZDUG WKH ends, which is very useful because it displayed sectors in that are grouped circuits with special characteristics.Another example of this is in the bottom-right edge of the surface, where they have EHHQ ORFDWHG VRPH N9 FLUFXLWV VXI¿[ 5 These circuits are also very important because although they have few users, the service of substations or industrial customers depends on them, hence the EPNS is high.While some of them are not included in the ranking, view them may be XVHIXO DV D ZDUQLQJ ÀDJ  UDQJH ,Q WKH ¿UVW FDVH DQ RI WKH GDWD ZHUH UDQNHG FRPSOHWHO\ ZKLOH LQ WKH VHFRQG DQ As in the previous comparison, the second case has a change in the rules to give some importance to circuits with extreme indicators; however, this is not visible in the ranking of the most important because in the high hierarchy not there were differences.
To evaluate the optimal pruning cycle, we use a forest inventory of 2009, of the circuit CY12 code, which contains 27 trees distributed in six species: Acacia Melanoxylum, FicusAndicola, PrunusSerotina, CupressusLusitanica, Eucalyptus Globulus and Salix Humboldtiana.According to information processing detailed in Fig. 2we coded the information with the following parameters: threshold = 200 cm, Di = 400 cm, CP = 10.The results are shown in Table 4.
$FFRUGLQJ WR WKH VLPXODWLRQ WKH ¿UVW PDLQWHQDQce is performed in the very short term, but this time gradually increased until a point of stability.
In the same way it happened with the amount of pruning, stabilizing between 25 and 26 pruning per CP.
To simulate the maintenance cost, we assume values to the type of pruning: Code 0 costs 0.9, Code 1 costs 1, and Code 2 costs 1.4.By optimizing the amount of pruning is also optimized the budget (Figure 6).
Figure 7 shows the behavior of the trees along the VLPXODWLRQ ,Q WKLV ¿JXUH KLJKOLJKWV WZR LQGLYLduals whose growth contrasts, the growth curve of the Salix Humboldtiana, is faster than the curve of Acacia Melanoxylum.The red stripe passes the threshold in all cycles of pruning, so the tree should be pruned in all cycles of pruning.On the other hand, the yellow stripe passes the threshold LQ RQO\ ¿YH WLPHV 7KLV ODVW LQGLYLGXDO QHYHU UHDches the maximum point.The pruning cycle period depends on the individual faster.
To verify the performance of the algorithm with more data is entered TI21 circuit inventory, which is among the most critical, according to initial   ZHLJKWLQJ 7KH H[HUFLVH LV SHUIRUPHG ZLWK LQdividuals, which are divided into eleven species.
The results are shown in Table 5 and Figure 8.In this case, the number of trees was not inconve-QLHQW WR ¿QG D SRLQW RI VWDELOLW\ The last methodological block is the approach to solutions.For this it is necessary to propose alternatives that emerge as the analysis of the simulated results, as a technical analysis of the design conditions of the medium voltage network, geography, and individual trees.Some possible solutions found are: Ɣ Identify the optimum time of pruning, when the best solution is to simply perform pruning along the circuit.
Ɣ By combining the analysis of CP with the location of individual trees along the network, we can identify sectors in which take technical measures to mitigate the indicators and/or extend the CP.
Ɣ It is possible to identify individuals whose management tree is not expensive or complicated, in exchange for extending the CP, such as cuttings, transportation network, replacement of species, and the other coming from each particular case.Source: own work

CONCLUSIONS AND FUTURE WORK
In this paper we apply fuzzy logic techniques to design a tool that would guide the management of trees in medium voltage networks globally.This tool also allows grouping, view and track FLUFXLWV DFFRUGLQJ WR WKH OLQJXLVWLF TXDOL¿HUV WKDW denote key technical criteria in the management of maintenance, additionally considering the quality indicators established by the regulator.From D VSHFL¿F SRLQW RI YLHZ ZH ¿QG WKDW WKHUH LV D VWDble pruning time for all trees that affect a circuit, despite the diversity of species and the uneven growth of these.
The methodologies proposed, but from real data, are purely theoretical and the nature of the problem require monitoring for at least the medium term.The prioritization of circuits must be a periodic process that evidences the effectiveness of the maintenance performed, and the projection of the indicators of the circuits.Similarly, analysis of the optimal CP requires monitoring and feedback both growth curves used and the pruning to be done.For the application of the integrated methodology we propose: Ɣ Pilot tests should be performed for implementing and monitoring of maintenance, allowing for adjustment of the growth curves either by mistake or in the model including environmental factors such as humidity, temperature, soil conditions, time of year and in general any other factor affecting the growth of trees.
Here we take into account the follow any technical measure applied and its impact to the CP.
Ɣ Should be continued the work in [14], developing the cumulative growth curves for species that have not yet.
Ɣ Should be design and implement a fuzzy logic system as proposed in this research, but allows prioritizing circuits using all possible causes of failure.
:[k]ĺ; to be the valuation of cost of maintenance that is obtained from by applying genetic search for a given circuit k.

Figure 1 .
Figure 1.Flow diagram of information management for prioritization of circuits.

Figure 2 .
Figure 2. Flow diagram of information management to determine the optimal pruning cycle.Source: own work )LJXUH :H GH¿QH WKUHH GLVWDQFHV Ɣ D(t)= Distance to optimize [cm].Ɣ Di= Initial distance [cm].It's the same treenetwork distance.Ɣ y(t)= Cumulative growth [cm] of the tree in time t [days] This depends on the growth function of each species.

Figure 3 .
Figure 3. Distances that form the objective function.Source: own work WKDW QHFHVVDU\ SUXQLQJ DUH performed by assigning a new value of Di (for WKLV H[DPSOH RI FP IRU WKRVH WUHHV ZKRVH cumulative growth is within the threshold, according to the value previously set.The new value of Di for trees that are not within thres-

Figure 4 .
Figure 4. Simulation of carrying out forest maintenance.Source: own work

Figure 5 (
Figure5(c) and 5(d) correspond to two Takagi-Sugeno systems with four fuzzy sets in the output.The most obvious difference compared to Mamdani systems is that the surface is uniform, i.e., the prioritization is more uniform.The organization along the z axis is more vertical; consequently, there is a better distribution of the data
WԹ be the closure of a contractible open set in the line that has a connected open interior.
information matrix for n trees in a given circuit encoding: the tree ID, the cost code, the species code and the Di, which is the open subset of M. Let KԹ be the closure of a contractible open set in the line that has a connected open interior.Let NCK be the circuits to be considered for forest maintenance, which is the open subset of K.The optimization model depicted in Figure 2 is obtained by an optimization mapping of the form: h: XĺC Optimization of maintenance management of trees in power distribution systems JOSÉ ALEXANDER MARTÍNEZ / FREDY HERNÁN MARTÍNEZ S.

Table 1 .
Set of fuzzy rules for prioritizing circuits.

Table 4 .
Simulation of forest maintenance.Circuit CY12