CC BY
1УДК 621.317
Aliyev T.E.
Lecturer, Department of Electrical Power Engineering, Azerbaijan State University of Oil and Industry (Baku, Azerbaijan)
UTILIZING FUY LOGIC FOR ASSESSING TECHNICAL CONDITIONS OF DISTRIBUTION TRANSFORMERS
Аннотация: distribution transformers represent vital components within distribution networks due to their prevalence and widespread distribution. Failures in these transformers incur significant economic losses, impacting both the transformer itself and the cost of unfulfilled energy demand. The technical state of distribution transformers is influenced by various external factors, which contribute to their diminished lifespan. Therefore, a comprehensive understanding of these factors is essential for accurate diagnosis. This study presents a method employing fuy logic for diagnosing distribution transformers, aligning with international operational regulations. The methodology was implemented utilizing the fuy toolbox within MATLABprogramming tools version 9.8 (R2020a).
Ключевые слова: transformer, losses, faults, MATLAB program, diagnostics, methods.
Introduction. Putting a distribution transformer out of service poses a significant challenge for electricity distribution companies, particularly when it leads to service interruptions in sectors with social or economic importance. The situation exacerbates when untimely equipment failures cause interruptions, adding the cost of repairing or replacing the transformer to the aforementioned inconveniences. Hence, monitoring the technical status of distribution transformers within a network is paramount. Transformer diagnostic methods continue to evolve, often focusing on analyzing chemical indicators in oil, such as methanol (MeOH) and 2-furfural (2FAL), as aging indicators [1-3]. Additionally, research has explored partial discharge (PD) pulse identification and analysis [4, 5], with techniques like Fourier transform and
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frequency response analysis (FRA) gaining prominence. FRA, in particular, has demonstrated reliability in diagnosing transformer conditions, including mechanical vibrations, by comparing the transformer's initial and current response across frequency sub-bands. Artificial intelligence (AI) techniques, including neural networks, text mining with machine learning, fuy logic, and neurofuy networks, have been leveraged to develop fault detection approaches for transformers. For instance, a fuy model based primarily on the thermal behavior of distribution transformers is proposed in this study for diagnosing their technical condition.
Methods. The proposed fuy model enhances the characterization of distribution transformer states by employing an interpretation methodology derived from international standards and distribution companies' failure records.
Moreover, these conditions must concurrently meet, with implication rules connected by the AND operator.
The inference process engine comprises implication rules of the IF-THEN format. Given the inherent imprecision, a consequent may be inferred even if the antecedents incompletely verify it. The resultant consequent aligns more closely with Formal Logic as antecedents are better satisfied. For practical maintenance application, the consequent doesn't require numerical values but rather fuy responses like:
The primary challenge lies in appropriately defining acceptable intervals for input variables and expressing their acceptability levels through corresponding fuy set membership functions. "Low," "medium," and "high" status scales are employed to denote membership levels of different input variables. The program output presents users with the degrof maintenance intervention necessity for the analyzed transformer and facilitates observation of partial indicator behaviors through accompanying graphs [6-8].
"Fuification" of Input and Output Variables. During the fuification process, crisp inputs within the domain undergo transformation into fuy inputs utilizing membership functions. These input variables are then compared with the
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membership functions in the antecedent part of fuy rules to derive membership values
for each linguistic label.
The "fuification" of the first variable, "operation time of the transformers," is
delineated through thrtriangular membership functions, the equations for which are
provided below.
(-2x/TEXPalobal + 1 if 0 < x < TEXPave TEXP Low^ / x ^TExp>ave ™ (1)
TEXP Mediurni 2 7 J^^+T -У tIII^T^ tf (2) {-2x/TEXPglobal + 1 if TEXPave <x< TEmax
(2x/TEXPqlobal - 1 if TEXPave <x< TEXPqlobal TEXP High] giobai ' g (3)
I 1 IJ X > LtXFglobal
where: TEXPgiobai: Average global operating time of transformers installed in the distribution network (years), TEXPave: Average operating time of failed transformers (years), TEXPmin: Average operating time of failed transformers minus thrtimes the standard deviation (years), TEXPmax: Average operating time of failed transformers plus thrtimes the standard deviation (years).
The triangular membership function comprises thrparameters, essentially representing a linear approximation of bell curves. These parameters are derived through control charts, as illustrated in Figure 1, leveraging historical data from distribution companies on transformer failures. Specifically, the average operating time of failed transformers and the standard deviation are utilized to determine these parameters. Figure 2 depicts the graphical representation of the thrmembership functions corresponding to the exploitation time variable.The variable representing the temperature of the hottest point during the period of maximum demand is characterized by thrtrapezoidal functions. This function type delineates sets where the degrof membership remains constant at one for points near the central value, indicating a saturation zone.
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Figure 1 illustrates an example of a control chart derived from historical data on transformer failures within a distribution circuit.
Figure 2 depicts the graphical representation of the fuification process for the exploitation time variable.
This behavior aligns with the temperature characteristics observed in transformer operation, as described in . The expressions for these trapezoidal functions are as follows:
T Low
1 if HST < 110° С
TMedium
(130°с - hst)/(130 - 110) if hst e (110°с,130°с)
(5)
(4)
0 if (HST < 120°C or HST > 180°C) (HST - 140°C)/(140°C - 120°C) if HST e (120°C, 140°C) 1 if hst e (140°c, 160°c) (180°C - HST)/(180°C - 160°C) if HST e (160°C, 180°C)
THigh
0 si HST < 160°C
(HST - 180°C)/(180°C - 160°C) si HST e (160°C,180°C) (6)
1 si HST > 180°C
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where: HST: Maximum temperature calculated during a 24-hour load cycle, determined using the calculation method outlined in annex G of the standard I.E.E.E. C57.91 of 2011.
Figure 3 depicts the graphical representation of the thrmembership functions corresponding to the variable temperature of the hottest point.
0 20 ¿10 60 eo 100 120 140 160 180 200 input variable "T*
Figure 3 illustrates the graphical representation of the fuification process for the variable temperature of the hottest point
LULP: Loss of life percentage calculated over a 24-hour load cycle. The limits of the trapezoidal functions were determined according to Section 5.3 of the I.E.E.E. C57.91 standard of 2011. Figure 4 illustrates the graphical representation of the thrmembership functions corresponding to the variable percentage of loss of useful life.
Membership function plots
Low Medium High
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 input variable "LULP"
Figure 4 Graphical depiction of the fuification process for the variable percentage of loss of useful life
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Transformer parameters, such as hottest point temperature and percentage of loss of useful life, are computed using expressions outlined in the I.E.E.E.
C57.91
standard. These calculations rely on characteristic data of the transformer, load profile, and monthly billing information. The load profile is obtained from the type of customer served by the transformer, recorded in the utility's network management system (SIGERE). Detailed calculation methodologies are elaborated in [9-13].
Inference System. The inference system comprises 81 implication rules governing the determination of the distribution transformer's technical status. These rules establish relationships between the antecedent variables (operation time of the transformers, temperature of the hottest point during peak demand, percentage of loss of useful life, failure rate of circuit transformers) and the consequent variable (technical state of the transformer) (Figure 5.).
Membership Tunctlcn plots '
Good.
1
XI
0.5
0 20 40 SO SO 100 120 14(1
oulput variable "Technical jondition"
Figure 5. Graphical depiction of the variable representing the consequent, namely "technical condition of the transformer."
When applying any of the aforementioned implication rules, a result is obtained that can be challenging to apply in practice: a value of the antecedent infers a fuy set of values for the consequent. This is demonstrated in Figure 6, which provides an example of a rule in the rule editor. The figure displays the rule editor, where each of the 81 rules relating each antecedent variable to the consequent variable is written using the AND connective [14-17].
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Results and discussion. The method was implemented on a random sample comprising 8 distribution transformers situated across 3 distribution circuits. Once the temperature of the hottest point of the transformer is considered, several parameters are calculated, including the aging acceleration factor per hour, aging factor over a period of time, and the percentage of useful life loss relative to a useful life of 180,000 hours. It's important to note that while temperature significantly influences insulation, it's not the sole determinant, as transformers with insulation well below the minimum have been in service for extended periods [19,20].
Figure 6. The surface plot depicting the behavior of the consequent variable is generated based on variations in the antecedent variables "temperature of the hottest point" and "operation time of the transformers" within the Mamdani inference system.
As evident from the results, there is alignment with the specifications outlined in the I.E.E.E. C57.91 standard of 2011. Among the analyzed transformers, those with a temperature of the hottest point close to or exceeding 110°C are identified as being at risk, which coincides with the maximum permissible temperature for continuous operation as per the standard. Additionally, the loss of annual useful life determined through fuy logic slightly exceeds that obtained conventionally, attributed to the influence of other factors such as the operating time of the transformers under study and the failure rate of the circuit transformers. Despite the temperature of the hottest point during a load cycle in the transformers at risk being below the limit set by the I.E.E.E. C57.91 standard of 2011, the protection devices of these transformers were triggered at least once during the year.
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Conclusions.
The proposed fuy model facilitates working with standardized variables in accordance with the I.E.E.E. C57.91-2011 standard, encompassing technical and construction characteristics across various transformer types. These variables include nominal power, nominal losses, element weight, monthly invoicing, and service type. While the temperature of the hottest point correlates directly with the loss of useful life, this percentage is also influenced by factors such as oil characteristics, humidity, external faults, and overvoltage, all of which impact insulation condition. The loss of useful life is not solely determined by temperature value but also by the duration the transformer operates at that temperature. Thus, the decision to incorporate the percentage of loss of useful life as an independent input variable in the fuy model was made.The implementation of this method yields significant benefits, notably the efficient utilization of resources. By leveraging updated distribution circuit databases, the need for resources like fuel, wages, and measurement tools such as thermographic cameras is minimized. Additionally, early diagnosis helps prevent the costly damage associated with failing transformers.
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