CN114460445B - Transformer aging unavailability evaluation method considering aging threshold and service life - Google Patents
Transformer aging unavailability evaluation method considering aging threshold and service life Download PDFInfo
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- 230000032683 aging Effects 0.000 title claims abstract description 178
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- 238000013210 evaluation model Methods 0.000 claims abstract description 9
- 238000005314 correlation function Methods 0.000 claims description 32
- 238000007476 Maximum Likelihood Methods 0.000 claims description 18
- 238000006731 degradation reaction Methods 0.000 claims description 14
- 238000004458 analytical method Methods 0.000 claims description 13
- 230000015556 catabolic process Effects 0.000 claims description 11
- 238000006116 polymerization reaction Methods 0.000 claims description 11
- 238000004804 winding Methods 0.000 claims description 11
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- 238000012614 Monte-Carlo sampling Methods 0.000 claims description 7
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- 238000012549 training Methods 0.000 claims description 7
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- 229910052760 oxygen Inorganic materials 0.000 claims description 6
- 238000000342 Monte Carlo simulation Methods 0.000 claims description 4
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- 238000012886 linear function Methods 0.000 claims description 3
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- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/50—Testing of electric apparatus, lines, cables or components for short-circuits, continuity, leakage current or incorrect line connections
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- Y04S10/00—Systems supporting electrical power generation, transmission or distribution
- Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications
Abstract
The invention relates to the technical field of transformer unavailability evaluation, in particular to a transformer aging unavailability evaluation method considering an aging threshold value and service life, which comprises the following steps: establishing a transformer evaluation model for acquiring an aging threshold value and a service life value of an individual transformer, and correspondingly acquiring the aging threshold value and the service life value of the individual transformer; establishing a three-parameter Weibull distribution probability density function, then calculating the mapping relation between Weibull distribution parameters and the aging threshold and life value, and generating a three-parameter Weibull model which simultaneously considers the aging threshold and the life value; calculating an unavailability mathematical expression of the corresponding individual transformer based on a three-parameter Weibull model; the aged unavailability of an individual transformer is evaluated based on its unavailability mathematical expression. According to the transformer aging unavailability rate assessment method, the aging threshold value and the service life value can be simultaneously considered in the individual transformer Weibull model modeling, so that the accuracy of individual transformer aging unavailability rate assessment can be improved.
Description
Technical Field
The invention relates to the technical field of transformer unavailability evaluation, in particular to a transformer aging unavailability evaluation method considering an aging threshold value and service life.
Background
Reliability assessment of electrical power systems has a wide range of applications, which play a vital role in the operation, investment and maintenance of electrical power systems. The reliability parameters of the components of the power system determine the accuracy of reliability assessment and subsequent maintenance, planning and decision making. Oil-immersed power transformers are key devices in power transmission systems, and therefore it is important to obtain their reliability parameters as accurately as possible. Where unavailability is an important reliability parameter of a power element that represents the probability that a certain element will be unavailable due to failure within a certain period of time in the future.
Faults of power transformers can be divided into two categories: random faults and irreparable aged faults can be repaired. Modeling the unavailability due to random faults is relatively easy because it can be assumed to be a constant independent of run time. The unavailability caused by aging failure is time-varying and can be influenced by various factors such as the running condition and environmental condition of the transformer. In general, a two-parameter weibull model is used to model the aging unavailability rate of an individual transformer, for example, chinese patent publication No. CN107330286a discloses a dynamic correction method for evaluating reliability of a large oil-immersed power transformer, and uses a transformer oil paper insulation system as an evaluation object, which is divided into two processes: in the first process, a transformer aging fault model based on HST is established by taking the calculated hot spot temperature as a core and combining Weibull distribution and Alternet reaction law, the winding HST is calculated, and the fault rate of a transformer oil paper insulation system is solved. In the second process, the gray target correction is analyzed by using dissolved gas in oil as a core, the relation between the health state of the transformer and the life expectancy of the transformer is established by using a gray theory, an equivalent HST value is obtained, the dynamic correction of a basic model in the first process is realized, and the evaluation value can be well tracked and reflect the actual reliability level of the transformer.
The dynamic correction method for the transformer reliability evaluation in the prior art is also a transformer aging unavailability evaluation method, and adopts a structure of a basic model and a dynamic correction model, so that the whole reliability evaluation model can be adjusted according to the running state of an evaluation object. In the existing scheme, the Weibull model generally selects the service life as the characteristic for describing the degradation process of the differential performance of the transformer, and the shorter the service life of the transformer, the faster the aging speed of the transformer is, the smaller the corresponding Weibull scale parameter is, and the steeper the aging unavailability curve changes. However, for transformers with the same life, the performance degradation process will also vary significantly if their aging thresholds (the onset of aging period for the transformer) are different. In other words, the performance degradation process of the individual transformer can be accurately described only by considering the aging threshold and the service life at the same time, namely, the aging unavailability rate of the individual transformer can be accurately estimated and predicted only by considering the aging threshold and the service life characteristic at the same time in the Weibull model modeling. Therefore, how to design a method that can consider the aging threshold and the lifetime value in the modeling of the individual transformer weibull model is a technical problem that needs to be solved.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to solve the technical problems that: how to provide a transformer aging unavailability evaluation method considering an aging threshold and service life, so that the aging threshold and service life value can be considered in the modeling of an individual transformer Weibull model, and the accuracy of the individual transformer aging unavailability evaluation can be improved.
In order to solve the technical problems, the invention adopts the following technical scheme:
the transformer aging unavailability evaluation method considering the aging threshold and the service life comprises the following steps:
s1: establishing a transformer evaluation model for acquiring an aging threshold value and a service life value of an individual transformer, and correspondingly acquiring the aging threshold value and the service life value of the individual transformer;
s2: establishing a three-parameter Weibull distribution probability density function, then calculating the mapping relation between Weibull distribution parameters and the aging threshold and life value, and generating a three-parameter Weibull model which simultaneously considers the aging threshold and the life value;
s3: calculating an unavailability mathematical expression of the corresponding individual transformer based on a three-parameter Weibull model;
s4: the aged unavailability of an individual transformer is evaluated based on its unavailability mathematical expression.
Preferably, in step S1, a corresponding transformer evaluation model is established based on the polymerization degree analysis and the monte carlo sampling method.
Preferably, in step S1, the method specifically includes the following steps:
s101: calculating a polymerization degree analysis value, namely a DP value, of the transformer based on the temperature data of the hot spot of the transformer, the water content and the oxygen content in combination with the following formula:
wherein: t represents the run time; τ represents the iteration stage; t represents the hottest spot temperature of the transformer winding; a represents an influence factor of the environment where the transformer is located; ea represents the activation energy of the aging reaction; r represents a molar gas constant;
s102: predicting future load, ambient temperature and relative humidity of the transformer by a Monte Carlo method, and further simulating the running condition and the ambient condition of the transformer in the future to generate a corresponding DP degradation sequence;
s103: and matching the DP degradation sequence with the set corresponding criterion to generate an aging threshold value and service life of the corresponding transformer.
Preferably, in step S101, the hottest spot temperature T and the influence factor a are calculated by the following formula:
T τ ＝Θ H,τ ＝Θ Ae,τ +ΔΘ TU,τ +ΔΘ H,τ ；
wherein: theta (theta) Ae,τ 、ΔΘ TU,τ And DeltaΘ H,τ Respectively representing the increment of the environment temperature, the top oil temperature and the ambient temperature in the tau-th iteration and the increment of the hot spot temperature and the top oil temperature;
wherein: ulti, init represent the end time and start time of the τ -th iteration; k (K) τ Representing a load factor; upsilon (v) TU 、υ H Representing the thermal time constant of the oil, windings; m represents the exponent power of the total loss relative to the rise of the top oil temperature of the oil tank; n represents an exponential power of the current with respect to the rise in winding temperature; r represents the ratio of load loss to no-load loss at rated current;
wherein: γ1, γ2, γ3 and γ4 are determined by the oxygen content and the paper type; omega τ,paper Represents the moisture content of the insulating paper;
Θ TU,τ ＝Θ Ae,τ +ΔΘ TU,τ ；
wherein:Θ TU,τ and RH (relative humidity) τ Respectively representing the moisture content in the transformer insulating oil, the transformer top oil temperature and the environment relative humidity in the tau-th iteration; kappa (kappa) 1 、κ 2 、κ 3 、κ 4 、κ 5 、κ 6 All represent constant coefficient terms fitted based on historical experimental data.
Preferably, in step S103, the time for decreasing the DP value to 450 and 200, respectively, is used as the aging threshold and lifetime value of the corresponding transformer based on the DP degradation sequence.
Preferably, in step S2, the method specifically includes the following steps:
s201: the following three-parameter weibull distribution probability density function was constructed:
wherein: alpha n 、β、η n Respectively representing a Weibull scale parameter, a shape parameter and a threshold parameter; t represents the run time;
s202: assigning a threshold parameter of the transformer based on a Weibull threshold parameter setting rule;
s203: aging threshold y based on transformer n And lifetime value z n Build variable X n ＝y n -z n The method comprises the steps of carrying out a first treatment on the surface of the Then for variable X n And weibull scale parameter α n Modeling the positive correlation relationship to obtain alpha n ＝g(X n ；S)；
S204: select a typical positive correlation function pair g (X n The method comprises the steps of carrying out a first treatment on the surface of the S) carrying out characterization;
s205: statistical-based transformer population aging threshold and life data set, and determining optimal positive correlation function characterization X by combining maximum likelihood estimation method n And alpha is n And generating a three-parameter Weibull model which simultaneously considers the aging threshold and the service life value by combining the mapping relation.
Preferably, in step S204, typical positive correlation functions include, but are not limited to, linear functions, quadratic functions, exponential functions, sigmoid functions, and power functions.
Preferably, in step S205, the method specifically includes the following steps:
s2051: the following maximum likelihood function is constructed based on the maximum likelihood principle:
wherein: g v Representing an alternative positive correlation function; s is S v G represents g v Unknown coefficients of (a) are determined;the representation is based on a positive correlation function g v Established transformer T n Probability density function of aging failure of (a)A number; n (N) training Representing the number of transformers used as the training dataset; />And->Representing a transformer T n Sampling the aging threshold value and the service life value obtained by the kth sampling; wherein, variable X constructed based on aging threshold and life value of transformer n Marked +.>
S2052: Λ is taken based on maximum likelihood function (S v ) Is calculated as follows:
s2053: the maximization solution problem is constructed as follows to determine the maximization In (Λ (S v ) Set of optimal coefficients)
S2054: solving a maximized solving problem by adopting a particle swarm algorithm to obtain the optimal coefficient of each alternative positive correlation function;
s2055: checking each alternative positive correlation function on the test data set, and selecting the positive correlation function with the minimum normalized root mean square error index to represent X n And alpha is n The positive correlation relationship between the Weibull distribution parameters and the aging threshold and life value.
Preferably, in step S2055, the normalized root mean square error indicator NRMSE is calculated by the following formula:
wherein:representing a transformer T n In the presence of an alternative positive correlation function g v Cumulative probability distribution values under a three-parameter weibull model; f (F) sd,n,k Representing a transformer T n Cumulative probability distribution values at; n (N) testing The number of transformers used as the test set is indicated.
Preferably, in step S3, the method specifically includes the following steps:
s301: for the transformer T n Assuming that it has been operating for Q years, the probability of it experiencing an aging failure during the subsequent x-period can be expressed as:
wherein:representing a transformer T n At the aging threshold and the life are respectively y n And z n The probability density function of the corresponding three-parameter Weibull model;
s302: in the investigation period q, if the transformer has aging failure fault at the moment x, the unavailable duration of the transformer in the period q is (q-x), and the average aging failure probability of the transformer in the period q can be characterized as follows:
wherein: u (U) ag,n (. Cndot.) shows that the transformer T has been operated for Q years n Average aging failure probability in the subsequent period q;
s303: repeating step S301 and step S302The transformer T is calculated as follows n Mathematical expression of expected average aging unavailability over the q period:
wherein: k represents the total sampling times;representing a transformer T n Aging threshold and lifetime values at the kth sample.
Compared with the prior art, the transformer aging unavailability rate evaluation method has the following beneficial effects:
firstly, obtaining estimated aging threshold values and service life values of individual transformers based on a polymerization degree analysis and a Monte Carlo sampling method; thirdly, deriving a mapping relation between the Weibull distribution parameters and the aging threshold and life values based on maximum likelihood estimation and a particle swarm solution algorithm, and establishing a three-parameter Weibull distribution analysis expression which simultaneously considers the aging threshold and the life values; and then deducing a mathematical expression of the unavailability of the individual transformer from the established three-parameter Weibull model based on an integral method, and evaluating the unavailability of the aging of the individual transformer, so that the aging threshold and the life value can be simultaneously considered in the modeling of the Weibull model of the individual transformer, the accuracy of evaluating the unavailability of the aging of the individual transformer can be improved, and more reliable basis can be provided for evaluating the reliability of the electric power system, maintaining, planning and deciding.
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For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings, in which:
FIG. 1 is a logic block diagram of a transformer aging unavailability assessment method considering aging threshold and lifetime;
FIGS. 2 (a) and (b) are transformers T, respectively 1 、T 2 Probability distribution of corresponding aging threshold and lifetime;
FIG. 3 shows a press T 2 Unavailability change curve.
Detailed Description
The following is a further detailed description of the embodiments:
examples:
the embodiment discloses a transformer aging unavailability evaluation method considering an aging threshold value and service life.
As shown in fig. 1, the transformer aging unavailability evaluation method considering the aging threshold and the lifetime includes the following steps:
s1: establishing a transformer evaluation model for acquiring an aging threshold value and a service life value of an individual transformer, and correspondingly acquiring the aging threshold value and the service life value of the individual transformer;
s2: establishing a three-parameter Weibull distribution probability density function, then calculating the mapping relation between Weibull distribution parameters and the aging threshold and life value, and generating a three-parameter Weibull model which simultaneously considers the aging threshold and the life value;
s3: calculating an unavailability mathematical expression of the corresponding individual transformer based on a three-parameter Weibull model;
s4: the aged unavailability of an individual transformer is evaluated based on its unavailability mathematical expression.
Firstly, obtaining estimated aging threshold values and service life values of individual transformers based on a polymerization degree analysis and a Monte Carlo sampling method; thirdly, deriving a mapping relation between the Weibull distribution parameters and the aging threshold and life values based on maximum likelihood estimation and a particle swarm solution algorithm, and establishing a three-parameter Weibull distribution analysis expression which simultaneously considers the aging threshold and the life values; and then deducing a mathematical expression of the unavailability of the individual transformer from the established three-parameter Weibull model based on an integral method, and evaluating the unavailability of the aging of the individual transformer, so that the aging threshold and the life value can be simultaneously considered in the modeling of the Weibull model of the individual transformer, the accuracy of evaluating the unavailability of the aging of the individual transformer can be improved, and more reliable basis can be provided for evaluating the reliability of the electric power system, maintaining, planning and deciding.
In a specific implementation process, a corresponding transformer evaluation model is established based on polymerization degree analysis (degree of polymerization, DP) and a Monte Carlo sampling method.
The step S1 specifically comprises the following steps:
s101: calculating a polymerization degree analysis value, namely a DP value, of the transformer based on the temperature data of the hot spot of the transformer, the water content and the oxygen content in combination with the following formula:
the aging of the power transformer is mainly due to the irreversible degradation of its paper insulation system, and the aging threshold and lifetime of the transformer can be defined as the time for which the DP value of its insulation paper falls to 450 and 300, respectively. However, it is not practical to directly measure the DP value in actual engineering, because such operation requires an invasive destruction operation of the transformer winding system. Based on the method, the invention provides a transformer DP estimation method based on calculation to realize non-invasive indirect estimation of the transformer time-varying DP value.
The specific calculation formula is as follows:
wherein: k is the aging rate; DP (DP) 0 The DP value of the transformer operation; DP (DP) t Is the DP value at time t.
In order to calculate the transformer time-varying DP value more accurately, the recursive form of the above is adopted:
wherein: t represents the run time; τ represents the iteration stage; a represents an influence factor of the environment where the transformer is located; t represents the hottest spot temperature of the transformer winding; ea represents the activation energy of the aging reaction; r represents a molar gas constant;
s102: predicting future load, ambient temperature and relative humidity of the transformer by a Monte Carlo method, and further simulating the running condition and the ambient condition of the transformer in the future to generate a corresponding DP degradation sequence;
considering that some in-service transformers do not enter the aging period, the calculated current DP sequence value is larger than 450, and the aging threshold and the service life cannot be estimated directly. Therefore, the invention proposes to artificially generate future load, ambient temperature, relative humidity and other data of the transformer by using the Monte Carlo method to simulate the running and environmental conditions of the future transformer, thereby generating a future DP degradation sequence.
The data generation method is described below by taking the generation of transformer load data as an example, and the specific steps are as follows:
1) Establishing an average daily load curve of the transformer according to load data of the transformer for 5 years per hour:
2) Collecting an expected annual load growth rate ψ of a transformer from an electric company;
ψ＝[ψ 1 ,ψ 2 ,…,ψ θ-1 ,ψ θ ]；
3) Generate [0,1 ]]Random number vectors within a range. The vector contains 24 elements, corresponding to 24 hours of the day. For any one of the i th year, 24 normal distribution random variables are generated, and the average value isStandard deviation of->
4) And (3) repeating the steps 2-3, so that load data of the future theta years can be generated.
Future ambient temperature and relative humidity data for the transformer may also be generated in accordance with the above-described methods. It is noted that it is necessary to generate sets of future data for the transformer, taking into account the inherent uncertainties (i.e., random nature) associated with future operating and environmental conditions. Thus, in practice, the resulting transformer aging threshold and lifetime estimate are a probability distribution rather than a deterministic value.
S103: the DP degeneration sequence is matched with the set corresponding criteria (450 and 200) to generate an aging threshold and lifetime for the corresponding transformer. The time to drop the DP value to 450 and 200, respectively, based on the DP degeneration sequence is taken as the aging threshold and lifetime value of the corresponding transformer.
Specifically, the influence factor a and the hottest spot temperature T are calculated by the following formula:
wherein: γ1, γ2, γ3 and γ4 are determined by the oxygen content and the paper type; omega τ,paper Represents the moisture content of the insulating paper; in practical engineering, it is not desirable to collect the moisture content of the insulating paper in an invasive manner, based on which the present invention calculates the moisture content of the insulating paper using the equation set provided by ABB corporation:
Θ TU,τ ＝Θ Ae, +ΔΘ TU,τ ；
wherein:Θ TU,τ and RH (relative humidity) τ Respectively representing the moisture content in the transformer insulating oil, the transformer top oil temperature and the environment relative humidity in the tau-th iteration; kappa (kappa) 1 、κ 2 、κ 3 、κ 4 、κ 5 、κ 6 Are all based on historical experimental dataFitting the obtained constant coefficient term.
Calculating the DP sequence is a time sequence that requires the acquisition of a transformer historical T value (hot spot temperature). In actual engineering, the temperature at the hot spot of the insulating paper cannot be directly sampled in real time. Based on the above, the invention utilizes the dynamic thermal model proposed by IEEE std.C57.91-2011 to acquire the T value sequence. In this model, the ambient temperature and load are inputs, and the T value is an output, specifically:
T τ ＝Θ H,τ ＝Θ Ae,τ +ΔΘ TU,τ +ΔΘ H,τ ；
wherein: theta (theta) Ae,τ 、ΔΘ TU,τ And DeltaΘ H,τ Respectively representing the increment of the environment temperature, the top oil temperature and the ambient temperature in the tau-th iteration and the increment of the hot spot temperature and the top oil temperature;
wherein: ulti, init represent the end time and start time of the τ -th iteration; k (K) τ Representing a load factor; upsilon (v) TU 、υ H R, m and n are operational characteristics of the transformer, depending on the cooling system and type of transformer; wherein v TU 、υ H Representing the thermal time constant of the oil, windings; m represents the exponent power of the total loss relative to the rise of the top oil temperature of the oil tank; n represents an exponential power of the current with respect to the rise in winding temperature; r represents the ratio of the load loss to the no-load loss at rated current.
According to the invention, the corresponding transformer evaluation model is established through the polymerization degree analysis and the Monte Carlo sampling method, so that the non-invasive indirect estimation of the aging threshold value and the service life value of the transformer can be realized, a three-parameter Weibull model which simultaneously considers the aging threshold value and the service life value can be constructed in an auxiliary manner, and damage to the transformer can be avoided.
The step S2 specifically includes the following steps:
s201: the following three-parameter weibull distribution probability density function was constructed:
considering that the probability of aging failure is extremely low (0 can be assumed in engineering practice) before the transformer reaches the aging threshold, the invention introduces a new threshold parameter, expands the traditional two-parameter Weibull model into a three-parameter Weibull model containing a new threshold parameter, and the corresponding three-parameter Weibull distribution probability density function is specifically expressed as follows:
wherein: alpha n 、β、η n Respectively representing a Weibull scale parameter, a shape parameter and a threshold parameter; alpha n The degradation rate for an individual transformer depends on the aging threshold and the lifetime. η (eta) n Can ensure that when t is less than eta n And no aging failure fault occurs. The weibull shape parameter β is a performance quality parameter, and may be uniformly set to a constant value for a transformer population.
S202: assigning a threshold parameter of the transformer based on a Weibull threshold parameter setting rule; i.e. eta n Should be the ageing threshold of the transformerValue of η at this time n ＝y n The method comprises the steps of carrying out a first treatment on the surface of the Wherein y is n For individual transformers T n Is used for the aging threshold of (a).
S203: aging threshold y based on transformer n And lifetime value z n Build variable X n ＝y n -z n The method comprises the steps of carrying out a first treatment on the surface of the Then for variable X n And weibull scale parameter α n Modeling the positive correlation relationship to obtain alpha n ＝g(X n ；S)；
In the Weibull scale parameter determination process, the aging threshold and the service life are required to be considered simultaneously so as to accurately reflect the heterogeneity of the transformer group. However, it is difficult to directly establish the relationship between the Weibull scale parameter and the aging threshold, and the lifetime value, for this reason, the present invention is implemented by introducing a new variable X n The indirect modeling is carried out, and the specific steps are as follows:
1) Based on the longer the operation time of the transformer in the aging period, the slower the performance degradation of the transformer, the corresponding Weibull scale parameter alpha n The larger this basis, the invention gives X first n ＝y n -z n Wherein y is n And z n Transformer T n Aging threshold and lifetime of (1) at which point X n Is a transformer T n Run time during aging.
(2) For X n And alpha is n The positive correlation between the two can be marked as alpha by modeling n ＝g(X n ；S)。
Then for a certain body transformer T n The aging failure probability density function can be expressed as:
s204: select a typical positive correlation function pair g (X n The method comprises the steps of carrying out a first treatment on the surface of the S) carrying out characterization; the invention selects 5 typical and common monotonically increasing functions as selected functions of the positive correlation function, wherein the functions are respectively linear functions, quadratic functions, exponential functions, sigmoid functions and power functions, and the specific table 1 is as follows:
TABLE 1 typical positive correlation function
S205: statistical-based transformer population aging threshold and life data set, and determining optimal positive correlation function characterization X by combining maximum likelihood estimation method n And alpha is n And generating a three-parameter Weibull model which simultaneously considers the aging threshold and the service life value by combining the mapping relation.
In step S205, an optimal positive correlation function form is determined using a maximum likelihood estimation method based on the aging threshold and the lifetime data set of the counted transformer population. The general steps of maximum likelihood estimation are: the likelihood function is written out-collating the likelihood function-Jie Shiran equation (the estimate maximizes the likelihood function value). The method specifically comprises the following steps:
s2051: the following maximum likelihood function is constructed based on the maximum likelihood principle:
wherein: g v Representing an alternative positive correlation function; s is S v G represents g v Unknown coefficients of (a) are determined;the representation is based on a positive correlation function g v Established transformer T n Is a function of the aging failure probability density; n (N) training Representing the number of transformers used as the training dataset; it should be noted that since the aging threshold and lifetime of each transformer are probability distributions rather than deterministic values, K samples of the aging threshold and lifetime of each transformer are needed,/for each transformer>And->Representing a transformer T n Sampling the aging threshold value and the service life value obtained by the kth sampling; wherein, variable X constructed based on aging threshold and life value of transformer n Marked +.>
S2052: in most cases Λ (S v ) Is a very small value and can be inconvenient to calculate. For ease of calculation, Λ is taken based on a maximum likelihood function (S v ) Is calculated as follows:
s2053: the maximization solution problem is constructed as follows to determine the maximization In (Λ (S v ) Set of optimal coefficients)
The present invention assumes that the quality level of individual transformers does not deviate from the quality level of the transformer population. For each transformer T n (n is not less than 1 and not more than Ntracking), its shape parameter beta n The constraint s.t needs to be satisfied.In (1) the->The Weibull shape parameter values estimated for the unified three-parameter Weibull model are used to reflect the quality level of the transformer population.
S2054: solving a maximized solving problem by adopting a particle swarm algorithm to obtain the optimal coefficient of each alternative positive correlation function;
s2055: checking each alternative positive correlation function on the test data set, and selecting the positive correlation function with the minimum normalized root mean square error index to represent X n And alpha is n The positive correlation relationship between the Weibull distribution parameters and the aging threshold and life value.
The normalized root mean square error indicator NRMSE is calculated by the following formula:
wherein:representing a transformer T n In the presence of an alternative positive correlation function g v Cumulative probability distribution values under a three-parameter weibull model; f (F) sd,n,k Representing a transformer T n Cumulative probability distribution values at; n (N) testing The number of transformers used as the test set is indicated.
The invention derives the mapping relation between the Weibull distribution parameter, the aging threshold and the life value through the maximum likelihood estimation and the particle swarm solving algorithm, establishes the three-parameter Weibull distribution analysis expression which simultaneously considers the aging threshold and the life value, and enables the aging threshold and the life value to be simultaneously considered in the modeling of the Weibull model of the individual transformer, thereby improving the accuracy of the evaluation of the aging unavailability rate of the individual transformer
The step S3 specifically includes the following steps:
s301: for the transformer T n Assuming that it has been operating for Q years, the probability of it experiencing an aging failure during the subsequent x-period can be expressed as:
wherein:representation ofTransformer T n At the aging threshold and the life are respectively y n And z n The probability density function of the corresponding three-parameter Weibull model;
s302: in the investigation period q, if the transformer has aging failure fault at the moment x, the unavailable duration of the transformer in the period q is (q-x), and since x can be any point between [0, q ], the average aging failure probability of the transformer in the period q can be characterized as follows:
wherein: u (U) ag,n (. Cndot.) shows that the transformer T has been operated for Q years n Average aging failure probability in the subsequent period q;
s303: the estimated aging threshold and lifetime of the in-service transformer are a joint distribution, not a fixed value. In view of this uncertainty, the present invention proposes to repeat the above calculation randomly a sufficient number of times to calculate the transformer T n Is expected to average aging unavailability over the q period.
Repeating step S301 and step S302, and calculating to obtain the following transformer T n Mathematical expression of expected average aging unavailability over the q period:
wherein: k represents the total sampling times;representing a transformer T n Aging threshold and lifetime values at the kth sample.
According to the invention, the mathematical expression of the unavailability of the individual transformer is deduced from the established three-parameter Weibull model by an integral method, so that the aging unavailability of the individual transformer can be accurately and effectively estimated.
To better illustrate the method for evaluating the aging unavailability of the transformer in the present invention, the following experiment is disclosed in this example.
The transformer aging unavailability evaluation method considering the aging threshold and the service life, which is provided by the invention, is applied to a certain type of actual transformer group of the southwest power grid in China, and is used for evaluating the unavailability of an individual transformer, and the specific implementation process is as follows:
in the first step, 73 power transformers with the model SFPSZ9-12000/220kV are collected to form a transformer group, wherein the transformer group comprises 29 scrapped transformers and 43 in-use transformers. Asset management data, operation condition data and environmental weather data of the transformer group are respectively derived from a transformer ledger management system, a local weather center and other platforms.
And secondly, determining the joint probability distribution of the aging threshold and the service life of each in-service transformer by using the provided transformer aging threshold and service life estimation method based on polymerization degree analysis and Monte Carlo sampling. With two transformers T in service 1 T and T 2 For example, the results of the estimation are shown in the following sub-graphs 2 (a) and (b), respectively:
thirdly, adopting the statistical aging threshold values and the service lives of 58 power transformers as training data sets, evaluating and selecting an optimal positive correlation function, and modeling the relationship among the calibrated Weibull scale parameters, the personalized aging threshold values and the service lives. The data of the remaining 14 power transformers are used to form a test data set. The result of the optimal solution based on the maximum likelihood estimation and the particle swarm is as follows:
table 2 various positive correlation function performance comparisons
In table 2, the subscript n denotes the transformer Tn. yn and zn represent the estimated aging threshold and lifetime of the transformer Tn.
It can be seen from table 2 that the NRMSE value of the power function decreases most significantly compared to other established positive correlation functions. Therefore, the invention selects a power function to model the error relation among the Weibull scale parameter, the personalized aging threshold and the service life.
Fourth step, using transformer T 2 For example, based on the proposed individual transformer unavailability evaluation method, its time-varying aging unavailability is calculated from an established three-parameter weibull model. For ease of comparison, the present method assumes a random unavailability of 0.007.
As shown in fig. 3, when the transformer T2 is in service for more than 35 years (enters the aging period), the unavailability caused by the aging fault is gradually greater than the unavailability caused by the random fault. The results indicate that aging failure is a major factor in the unreliability of the aged transformer. Thus, if the utility company still ignores the aging fault as before, the reliability level of the transformer during aging is highly likely to be overestimated. In this case, the accuracy of the subsequent system reliability assessment and planning decisions will not be guaranteed.
Finally, it should be noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the technical solution, and those skilled in the art should understand that modifications and equivalents may be made to the technical solution of the present invention without departing from the spirit and scope of the present invention, and all such modifications and equivalents are included in the scope of the claims.
Claims (8)
1. The transformer aging unavailability evaluation method considering the aging threshold and the service life is characterized by comprising the following steps:
s1: establishing a transformer evaluation model for acquiring an aging threshold value and a service life value of an individual transformer, and correspondingly acquiring the aging threshold value and the service life value of the individual transformer;
s2: establishing a three-parameter Weibull distribution probability density function, then calculating the mapping relation between Weibull distribution parameters and the aging threshold and life value, and generating a three-parameter Weibull model which simultaneously considers the aging threshold and the life value;
the step S2 specifically includes the following steps:
s201: the following three-parameter weibull distribution probability density function was constructed:
wherein: alpha n 、β、η n Respectively representing a Weibull scale parameter, a shape parameter and a threshold parameter; t represents the run time;
s202: assigning a threshold parameter of the transformer based on a Weibull threshold parameter setting rule;
s203: aging threshold y based on transformer n And lifetime value z n Build variable X n ＝y n -z n The method comprises the steps of carrying out a first treatment on the surface of the Then for variable X n And weibull scale parameter α n Modeling the positive correlation relationship to obtain alpha n ＝g(X n ；S)；
S204: select a typical positive correlation function pair g (X n The method comprises the steps of carrying out a first treatment on the surface of the S) carrying out characterization;
s205: statistical-based transformer population aging threshold and life data set, and determining optimal positive correlation function characterization X by combining maximum likelihood estimation method n And alpha is n The positive correlation relation between the Weibull distribution parameters, the aging threshold and the life value is a mapping relation between the Weibull distribution parameters and the aging threshold and the life value, and then a three-parameter Weibull model which simultaneously considers the aging threshold and the life value is generated by combining the mapping relation;
s3: calculating an unavailability mathematical expression of the corresponding individual transformer based on a three-parameter Weibull model;
the step S3 specifically includes the following steps:
s301: for the transformer T n Assuming that it has been operating for Q years, the probability of it experiencing an aging failure during the subsequent x-period can be expressed as:
wherein:representing a transformer T n In the oldThe threshold value and the service life are respectively y n And z n The probability density function of the corresponding three-parameter Weibull model;
s302: in the investigation period q, if the transformer has aging failure fault at the moment x, the unavailable duration of the transformer in the period q is (q-x), and the average aging failure probability of the transformer in the period q can be characterized as follows:
wherein: u (U) ag,n (. Cndot.) shows that the transformer T has been operated for Q years n Average aging failure probability in the subsequent period q;
s303: repeating step S301 and step S302, and calculating to obtain the following transformer T n Mathematical expression of expected average aging unavailability over the q period:
wherein: k represents the total sampling times;and->An aging threshold value and a life value of the transformer Tn at the kth sampling are represented;
s4: the aged unavailability of an individual transformer is evaluated based on its unavailability mathematical expression.
2. The transformer aging unavailability assessment method considering aging threshold and lifetime as claimed in claim 1, wherein: in step S1, a corresponding transformer evaluation model is established based on the polymerization degree analysis and the monte carlo sampling method.
3. The transformer aging unavailability assessment method considering the aging threshold and the lifetime of claim 2, wherein: the step S1 specifically comprises the following steps:
s101: calculating a polymerization degree analysis value, namely a DP value, of the transformer based on the temperature data of the hot spot of the transformer, the water content and the oxygen content in combination with the following formula:
wherein: t represents the run time; τ represents the iteration stage; t represents the hottest spot temperature of the transformer winding; a represents an influence factor of the environment where the transformer is located; ea represents the activation energy of the aging reaction; r represents a molar gas constant;
s102: predicting future load, ambient temperature and relative humidity of the transformer by a Monte Carlo method, and further simulating the running condition and the ambient condition of the transformer in the future to generate a corresponding DP degradation sequence;
s103: and matching the DP degradation sequence with the set corresponding criterion to generate an aging threshold value and service life of the corresponding transformer.
4. A transformer aging unavailability assessment method considering an aging threshold and lifetime as claimed in claim 3, wherein: in step S101, the hottest spot temperature T and the influence factor a are calculated by the following formula:
T τ ＝Θ H,τ ＝Θ Ae,τ +ΔΘ TU,τ +ΔΘ H,τ ；
wherein: theta (theta) Ae,τ 、ΔΘ TU,τ And DeltaΘ H,τ Respectively representing the increment of the environment temperature, the top oil temperature and the ambient temperature in the tau-th iteration and the increment of the hot spot temperature and the top oil temperature;
wherein: ulti, init represent the end time and start time of the τ -th iteration; k (K) τ Representing a load factor; upsilon (v) TU 、υ H Representing the thermal time constant of the oil, windings; m represents the exponent power of the total loss relative to the rise of the top oil temperature of the oil tank; n represents an exponential power of the current with respect to the rise in winding temperature; r represents the ratio of load loss to no-load loss at rated current;
wherein: γ1, γ2, γ3 and γ4 are determined by the oxygen content and the paper type; omega τ,paper Represents the moisture content of the insulating paper;
Θ TU,τ ＝Θ Ae,τ +ΔΘ TU,τ ；
wherein:Θ TU,τ and RH (relative humidity) τ Respectively representing the moisture content in the transformer insulating oil, the transformer top oil temperature and the environment relative humidity in the tau-th iteration; kappa (kappa) 1 、κ 2 、κ 3 、κ 4 、κ 5 、κ 6 All represent constant coefficient terms fitted based on historical experimental data.
5. A transformer aging unavailability assessment method considering an aging threshold and lifetime as claimed in claim 3, wherein: in step S103, the times at which the DP values are reduced to 450 and 200, respectively, are taken as the aging threshold and lifetime values of the corresponding transformer based on the DP degradation sequence.
6. The transformer aging unavailability assessment method considering aging threshold and lifetime as claimed in claim 1, wherein: in step S204, typical positive correlation functions include, but are not limited to, linear functions, quadratic functions, exponential functions, sigmoid functions, and power functions.
7. The transformer aging unavailability assessment method considering aging threshold and lifetime as claimed in claim 1, wherein: in step S205, the method specifically includes the following steps:
s2051: the following maximum likelihood function is constructed based on the maximum likelihood principle:
wherein: g v Representing an alternative positive correlation function; s is S v G represents g v Unknown coefficients of (a) are determined;the representation is based on a positive correlation function g v Established transformer T n Is a function of the aging failure probability density; n (N) training Representing the number of transformers used as the training dataset; />And->Representing a transformer T n Sampling the aging threshold value and the service life value obtained by the kth sampling; wherein, variable X constructed based on aging threshold and life value of transformer n Marked +.>
S2052: Λ is taken based on maximum likelihood function (S v ) Is calculated as follows:
s2053: the maximization solution problem is constructed as follows to determine the maximization In (Λ (S v ) Set of optimal coefficients)
S2054: solving a maximized solving problem by adopting a particle swarm algorithm to obtain the optimal coefficient of each alternative positive correlation function;
s2055: checking each alternative positive correlation function on the test data set, and selecting the positive correlation function with the minimum normalized root mean square error index to represent X n And alpha is n The positive correlation relationship between the Weibull distribution parameters and the aging threshold and life value.
8. The transformer aging unavailability assessment method considering the aging threshold and the lifetime of claim 7, wherein: in step S2055, the normalized root mean square error indicator NRMSE is calculated by the following formula:
wherein:representing a transformer T n In the presence of an alternative positive correlation function g v Cumulative probability distribution values under a three-parameter weibull model; f (F) sd,n,k Representing a transformer T n Cumulative probability distribution values at; n (N) testing The number of transformers used as the test set is indicated.
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