CN104992377A - Method for analyzing reliability of transformer based on service year and load level - Google Patents

Abstract

The present invention discloses a method for analyzing reliability of a transformer based on service year and load level, comprising the following steps: (1) determining load levels of transformers; (2) determining load values of the transformers in an original state; (3) obtaining hot-spot temperatures of the transformers; (4) obtaining insulation lives of the transformers according to the hot-spot temperatures of the transformers; (5) obtaining a failure probability cumulative distribution function of the transformers; (6) obtaining an average failure rate index of the transformers in the original state and an average failure rate index of the transformers in a failure state; (7) obtaining a cascading failure starting probability index Pic and a cascading failure weak link indicatrix Pvc, and identifying the transformers in a critical state in a system by sorting of the Pic and the Pvc. The method provided by the present invention improves accuracy of analysis for the reliability of the transformers in the case of cascading failure by combining influences of self structures, functions, service years of the transformers and a coupling relation between the transformers in a regional power grid on equipment reliability.

Description

A kind of transformer analysis method for reliability based on enlistment age and load level

Technical field

The invention belongs to power transmission and transforming equipment technical field, more specifically, relate to a kind of transformer analysis method for reliability based on enlistment age and load level.

Background technology

Power transformer is as the hub device of electric system, and its running status directly has influence on stability and the reliability of electrical network.For a long time, be all by routine test and diagnostic test to the judgement of transformer reliability state both at home and abroad, realize in conjunction with prophylactic repair simultaneously, with relevant criterion and expert and operating experience for benchmark, static evaluation is carried out to it.Although prophylactic repair generally can in maintenance process discovering device exist defect, the safety and economic operation of power transformer is played an important role, but the situation such as " maintenance is superfluous " and " maintenance is not enough " may be there is, not only can cause the waste of man power and material, and add potential faults, reduce power supply reliability.Along with the iterative method of China's power engineering, net capacity increases day by day, and transformer is once break down and will produce serious influence to society, economy.Therefore, carry out fail-safe analysis for power transformer, determine the weak link in network, assist the turnaround plan of arrangement equipment, the stability tool of reduction maintenance cost, raising electric system is of great significance.

The fail-safe analysis of transformer is based on the running status of equipment, by recording system condition and other information, classify and integrate, to do well characteristic information carry out objective analysis from extracting data such as load level, diagnostic test result, device history record of examinations, complete the calculating of reliability index, and grading for reliability is carried out to transformer, and then the scheduling decision of auxiliary electrical network and the arrangement of Plant maintenance plan.

At present, China is still in the starting stage about the research of transformer fail-safe analysis, for the reliability assessment of converting equipment, mainly completes relevant reliability index according to operating statistic data and calculates; Application number is the patent of invention disclosed " power system weak link identification method based on risk assessment " of CN201310303983.1, propose the weak identifying index based on risk indicator and weak link characteristic quantity, pass through multiple repairing weld, statistics generator and power transmission and transforming equipment fault signature, the failure risk of system is obtained in conjunction with electric system failure state, and the weak identifying index of computing element, eventually through the sequence to index, find out the weak link of power transmission and transforming equipment in system; Coupled relation in the non-coupling system of said method in the factor such as transformer structure itself, function, operation age and fault mode and regional power grid between transformer is on the impact of equipment dependability.

Summary of the invention

For above defect or the Improvement requirement of prior art, the invention provides a kind of transformer analysis method for reliability based on enlistment age and load level, its object is to be sorted to transformer by probability level, to identify in system the transformer being in critical conditions, transformer fail-safe analysis accuracy under raising cascading failure sight thus.

For achieving the above object, according to one aspect of the present invention, provide a kind of transformer analysis method for reliability based on enlistment age and load level, specific as follows:

(1) transformer load grade is divided according to transformer load curve;

(2) for the transformer in each load level, tidal current analysis is carried out to obtain i-th transformer load value in an initial condition; Wherein, i indication transformer is numbered, i ∈ [1, N]; N is total number of units of transformer in electric power system;

Wherein, original state refers to the situation that in electric power system, all transformers normally work;

(3) transformer i hot(test)-spot temperature Θ corresponding with its load is in an initial condition obtained _iHST, and according to the relation between hot(test)-spot temperature and transformer insulated life-span, obtain the quantification life-span L of transformer i _i(Θ _hST);

(3) i-th transformer hot(test)-spot temperature Θ corresponding with its load is in an initial condition obtained _iHST; And according to the relation between hot(test)-spot temperature and transformer insulated life-span, obtain the quantification life-span L of i-th transformer _i(Θ _hST);

And quantize life-span L in conjunction with transformer _i(Θ _hST), adopt the probability of malfunction Cumulative Distribution Function of Weibull distributed acquisition transformer $P_f\left(t\right)=1-e^{(-{\left(\frac{t}{L_i\left({\mathrm{\Θ}}_{HST}\right)}\right)}^{\mathrm{\β}})};$

Wherein, transformer quantizes life-span L _i(Θ _hST) for Weibull distribution scale parameter; β is the form parameter of Weibull distribution, and t refers to the enlistment age of transformer;

(4) adopt the Markov model (Markov model) of process posteriority conditional probability, based on the enlistment age of transformer, obtain transformer based in the reliability index D of its enlistment age _f, $D_f=\frac{1}{t}\underset{j=1}{\overset{s}{\Σ}}{P}_j\×\[t-\frac{(2j-1)\·\mathrm{\Δ}t}{2}\];$

Wherein, P _jfor the probability of malfunction in a jth sub-range,

Wherein, s is the number in the equal sub-range divided by the enlistment age t of transformer, j ∈ [1, s]; Δ t is the time step in described sub-range, and as the case may be, Δ t can hour, minute be unit;

Equipment non-fault within the time period assessed from putting into operation to is referred to because equipment is in normal operating condition, for posteriority conditional probability event, the Markov model (Markov model) of process posteriority conditional probability is therefore adopted to analyze the impact of transformer enlistment age on transformer reliability; Above-mentioned reliability index D _fcharacterize the complexity that transformer breaks down, its numerical value is higher shows that equipment more easily breaks down, and reliability is lower;

(5) make i=i+1, and repeat step (2) ~ (4), until i=N, to obtain N platform transformer reliability index in an initial condition in electric power system;

(6) according to transformer reliability index in an initial condition, the cascading failure obtaining transformer starts probability level P _ic(Probability of Initiation of a Cascading Failure), and start probability level P according to cascading failure _icidentify the transformer the most easily causing cascading failure in electric power system;

Cascading failure starts probability level P _icto stop transport the effect that other transformers be in system under different enlistment age and load level are caused for characterizing certain transformer in electric power system; Its value is larger, shows that the interference of this transformer to other equipment is more serious, more easily causes cascading failure.

Preferably, above-mentioned transformer analysis method for reliability, also comprises the steps:

(7) load value of other each transformers in n-th transformer stoppage in transit situation is obtained, and make n=n+1, repeat step (3) ~ (4), until n=N, to obtain the reliability index of N platform transformer in n-th transformer stoppage in transit situation in electric power system; Wherein, n indication transformer is numbered, n ∈ [1, N];

Because n-th transformer will redistribute because of trend in electric power system when fault is stopped transport, therefore need again to carry out Load flow calculation to electric power system, determine the load value of each transformer;

(8) according to the reliability index of described transformer in certain transformer stoppage in transit situation, the fragile link indicatrix P of cascading failure of transformer is obtained _vc(Probability of Vulnerability toConsequent Failure), and according to the fragile link indicatrix P of described cascading failure _vcidentify the transformer the most easily by disturbing influence in electric power system;

The fragile link indicatrix P of cascading failure _vcunder being characterized in certain enlistment age and load level, when in electric power system, certain transformer is stopped transport, the probability of other transformer generation cascading failures; Its value is larger, shows that this transformer is more easily subject to the impact of other transformer faults, causes secondary cascading failure.

Preferably, the cascading failure described in step (6) starts probability level P _icspecific as follows:

$P_{ic}=D_{n,b}\×\underset{i=1}{\overset{N}{\Σ}}(D_{i,n}-D_{i,b})$

Wherein, D _n,bit is n-th transformer reliability in an initial condition; D _i,bit is i-th transformer reliability in an initial condition; D _i,nthe reliability of i-th transformer when n-th transformer is stopped transport.

Preferably, the fragile link indicatrix P of the cascading failure described in step (8) _vcspecific as follows:

$P_{vc}=\underset{i=1}{\overset{N}{\Σ}}\[(D_{n,i}-D_{n,b})\×D_{i,b}\]$

Wherein, D _n,ithe reliability of n-th transformer when i-th transformer is stopped transport; D _n,bn-th transformer reliability in an initial condition, D _i,bit is i-th transformer reliability in an initial condition.

Preferably, the process dividing transformer load grade in step (1) is specific as follows:

(1.1) according to the transformer load situation on transformer yearly load curve, in units of week, the transformer load level of the whole year is divided into m grade; Wherein, load level difference is drawn in same grade in week within ± 3%;

(1.2) load level of the transformer in same grade is averaged, using described mean value as the load level of this grade; M is positive integer, and 5≤m≤10.

Preferably, in step (3), according to the load value under original state, adopt hot(test)-spot temperature model Θ _hST=Θ _a+ Δ Θ _tO+ Δ Θ _w, obtain transformer hot(test)-spot temperature Θ in an initial condition _hST;

Wherein, Θ _afor environment temperature, Δ Θ _tOfor top-oil temperature liter, Δ Θ _wfor hot(test)-spot temperature relatively and the difference of top-oil temperature; The situation of sudden load change when stopping transport in conjunction with transformer fault, according to increased step-like, the production decline law of load, obtains Δ Θ _tOwith Δ Θ _w;

When load increases progressively:

${\mathrm{\Δ\Θ}}_{TO}={\mathrm{\Δ\Θ}}_{TO,in}+\[{\mathrm{\Δ\Θ}}_{TO,R}\×{\left(\frac{1+R\×k^2}{1+R}\right)}^x-{\mathrm{\Δ\Θ}}_{TO,in}\]\×f_1\left(t\right)$

ΔΘ _w＝[Hg _rk ^y-ΔΘ _w,in]×f ₂(t)

When load successively decreases:

${\mathrm{\Δ\Θ}}_{TO}={\mathrm{\Δ\Θ}}_{TO,R}\×{\left(\frac{1+R\×k^2}{1+R}\right)}^x+\[{\mathrm{\Δ\Θ}}_{TO,in}-{\mathrm{\Δ\Θ}}_{\mathrm{TO},R}\×{\left(\frac{1+R\×k^2}{1+R}\right)}^x\]\×f_3\left(t\right)$

ΔΘ _w＝Hg _rk ^y

Wherein, f ₁(t)=1-exp (-t/ (k ₁₁× τ _o)),

f ₂(t)＝k ₂₁×(1-exp(-t/(k ₂₂×τ _w)))-(k ₂₁-1)×(1-exp(-t/(τ _o/k ₂₂)))，

f ₃(t)＝exp(-t/(k ₁₁×τ _o))，

Wherein, Δ Θ _{tO, in}for the top-oil temperature of initial time, Δ Θ _{tO, R}for the nominal loss that top-oil temperature under stable situation rises, Δ Θ _{w, in}for initial time hot(test)-spot temperature is relative to the gradient of top-oil temperature, R is the load loss rate in unloaded rated current situation; K is stressor, is obtained by load current/rated current; X is the index coefficient of transformer oil, and H is hot spot factor, g _rfor the winding medial temperature under rated current is relative to the gradient of average oil temperature, y is winding index coefficient, and t is the enlistment age of transformer, k ₁₁, k ₂₁and k ₂₂for hot(test)-spot temperature model constants, τ _ofor transformer oil averaging time constant, unit is minute; τ _wfor winding time constant, unit is minute;

Wherein, the characteristic parameter in hot(test)-spot temperature model is the inherent characteristic of transformer, and the load loss rate R in unloaded rated current situation, the index coefficient x of transformer oil, hot spot factor H, winding index coefficient y etc. all can adopt the recommended parameter in IEC directive/guide.

Preferably, in step (3), according to the load value under original state, the hot(test)-spot temperature model of oil-immersed power transformer is adopted to obtain transformer hot(test)-spot temperature Θ in an initial condition _hST, specific as follows:

A, for the transformer that Natural Oil Circulation Power (ON) cools, the hot(test)-spot temperature Θ under any load _hSTfor environment temperature, top-oil temperature rise and temperature difference three summation between focus and top layer oil:

Hot(test)-spot temperature ${\mathrm{\Θ}}_{HST}={\mathrm{\Θ}}_a+{\mathrm{\Δ\Θ}}_{or}{\[\frac{1+{\mathrm{RK}}^2}{1+R}\]}^x+{\mathrm{Hg}}_r{K}^y;$

Wherein: Θ _hSTfor hot(test)-spot temperature; Θ _afor environment temperature, obtain by measuring; Δ Θ _orfor top-oil temperature liter; R is loss ratio; K is load factor, is obtained by load current/rated current; Hg _rfor focus is to the temperature difference of winding top oil; X is oil temperature coefficient; Y is winding temperature coefficient;

B, the transformer for forced oil-circulation (OF) cools: the hot(test)-spot temperature Θ under any load _hSTthe difference risen for environment temperature, bottom oil temperature liter, winding top oil liter and bottom oil temperature and the temperature difference summation between hot spot temperature of winding and top layer oil:

Hot(test)-spot temperature ${\mathrm{\Θ}}_{HST}={\mathrm{\Θ}}_a+{\mathrm{\Δ\Θ}}_{or}{\[\frac{1+{\mathrm{RK}}^2}{1+R}\]}^x+2\[{\mathrm{\Δ\Θ}}_{imr}-{\mathrm{\Δ\Θ}}_{br}\]K^y+{\mathrm{Hg}}_r{K}^y;$

Wherein, Θ _hSTfor hot(test)-spot temperature; Θ _afor environment temperature, obtain by measuring; Δ Θ _orfor top-oil temperature liter; Δ Θ _imrfor oily average temperature rising; Δ Θ _brfor bottom oil temperature liter; R is loss ratio; X is oil temperature coefficient; Y is winding temperature coefficient; K is load factor, is obtained by load current/rated current; Hg _rfor focus is to the temperature difference of winding top oil;

C, the transformer for forced oil-circulation guiding (OD) cools: its hot(test)-spot temperature obtain manner is similar to the OF type of cooling, but need to consider that conductor resistance along with the change of temperature, can add correction factor:

Θ _HST＝Θ _HST'+0.15(Θ _HST-Θ _hr)，K＞1；

Wherein, Θ _hST' for not considering hot(test)-spot temperature value when conductor resistance affects, Θ _hrfor hot(test)-spot temperature when ageing rate is 1.

Preferably, in step (3), between hot(test)-spot temperature and transformer insulated life-span, meet Arrhenius formula relationship, obtain the quantification life-span of transformer according to hot(test)-spot temperature

Wherein, A and B is constant, provides recommendation: A=9.8 × 10 by IEEE C57.91 standard " oil-immersed power transformer load directive/guide " directive/guide ^-18, B=15000.

In general, the above technical scheme conceived by the present invention compared with prior art, can obtain following beneficial effect:

(1) a kind of transformer analysis method for reliability based on enlistment age and load level of proposing of the present invention, in conjunction with hot(test)-spot temperature, the quantification life-span of transformer is obtained by Arrhenius formula, only analysis of Reliability is carried out according to history run statistics with existing transformer analysis method for reliability, and do not consider that the method for equipment self operating mode is compared, enhance the accuracy of assessment result;

(2) problem of the coupled relation between transformer cannot be reflected for the reliability index of prior art, transformer analysis method for reliability provided by the invention, based on Markov model (MarkovModel) and Weibull distribution, adopt " cascading failure startup probability " P _icidentify the transformer the most easily causing cascading failure to occur; Adopt " the fragile link indicatrix of cascading failure " P _vcidentify the transformer being subject to disturbing influence most;

And at " cascading failure startup probability " P _icwith " the fragile link indicatrix of cascading failure " P _vcacquisition in, combine coupled relation in the factors such as transformer structure itself in system, function, enlistment age and load level and regional power grid between transformer to the impact of equipment dependability, the reliability of electric power system is analyzed, to reflect under cascading failure influencing each other of transformer in electric power system, match with practical application, further increase the accuracy of Transformer Faults Analysis.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the transformer analysis method for reliability based on enlistment age and load level of the embodiment of the present invention;

Fig. 2 is the schematic diagram of the test macro adopted in embodiment.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.In addition, if below in described each embodiment of the present invention involved technical characteristic do not form conflict each other and just can mutually combine.

Embodiment is 500kV to an electric pressure, test macro containing 154 transformers carries out transformer fail-safe analysis, as shown in Figure 2, due to feature size restriction, the transformer having 126 capacity less does not mark out the wiring diagram of test macro in the drawings; Network shown in Fig. 2 contains 8 equivalent generator buses (numbering 1 ~ 8) and 24 charge circuit (numbering 10,12 ~ 20,23 ~ 28,30 ~ 31,34 ~ 36,38,53 ~ 54), and each loaded line represents a transformer station containing step-down transformer group, cable, isolating switch and disconnector; In Fig. 2, the node of other numberings is contact node, and the electric pressure in network comprises 132kV, 66kV and 33kV; T1-T28 in Fig. 2 is 28 transformers containing hospital bus bar, and rated voltage is 400/275k.

According to the enlistment age of transformer and the size of load level, obtain " cascading failure startup probability " P of each transformer in this test macro _ic" the fragile link indicatrix of cascading failure " P _vc;

According to " cascading failure startup probability " P _ic" the fragile link indicatrix of cascading failure " P _vcrank is carried out to the reliability of each transformer, specific as follows:

(1) load condition in its annual 52 week is obtained according to the yearly load curve of test macro, load level difference is drawn in a grade in several weeks within 3%, and calculate the arithmetic average of its load level, as the load level of this grade; Determine electric power system the whole year six grades load level, the load level division result of test macro is as shown in the table;

Table 1 test macro load level divides

(2) for the load condition of each grade, tidal current analysis is carried out to test macro, to determine each transformer load value in an initial condition;

The present embodiment processes for load level 1, and as shown in Table 1, the rate of load condensate of first order load level is 98.9%, has 9 week to be in this load level in the whole year, and its probability occurred is in the present embodiment, the transformer B20-1 extracted on No. 20 buses analyzes, and the load value obtained under its original state by Load flow calculation is 0.95;

(3) load value under B20-1 transformer original state is 0.95, corresponding environment temperature Θ _a=25.8 DEG C; Adopt the hot(test)-spot temperature model Θ provided in IEC-60076-7 directive/guide _hST=Θ _a+ Δ Θ _tO+ Δ Θ _w, obtain the hot(test)-spot temperature in initial load situation;

Wherein Θ _hSTfor hot(test)-spot temperature, Θ _afor environment temperature, Δ Θ _tOfor top-oil temperature liter, Δ Θ _wfor hot(test)-spot temperature relatively and the difference of top-oil temperature; The situation of sudden load change when considering that transformer fault is stopped transport, according to increased step-like, the production decline law of load, completes Δ Θ _tOwith Δ Θ _wcorrelation computations;

When load increases progressively:

${\mathrm{\Δ\Θ}}_{TO}={\mathrm{\Δ\Θ}}_{TO,in}+\[{\mathrm{\Δ\Θ}}_{TO,R}\×{\left(\frac{1+R\×k^2}{1+R}\right)}^x-{\mathrm{\Δ\Θ}}_{TO,in}\]\×f_1\left(t\right)---\left(1\right)$

ΔΘ _w＝[Hg _rk ^y-ΔΘ _w,in]×f ₂(t) (2)

When load successively decreases:

${\mathrm{\Δ\Θ}}_{TO}={\mathrm{\Δ\Θ}}_{TO,R}\×{\left(\frac{1+R\×k^2}{1+R}\right)}^x+\[{\mathrm{\Δ\Θ}}_{TO,in}-{\mathrm{\Δ\Θ}}_{TO,R}\×{\left(\frac{1+R\×k^2}{1+R}\right)}^x\]\×f_3\left(t\right)---\left(3\right)$

ΔΘ _w＝Hg _rk ^y(4)

Wherein: f ₁(t)=1-exp (-t/ (k ₁₁× τ _o));

f ₂(t)＝k ₂₁×(1-exp(-t/(k ₂₂×τ _w)))-(k ₂₁-1)×(1-exp(-t/(τ _o/k ₂₂)))；

f ₃(t)＝exp(-t/(k ₁₁×τ _o))；

Wherein, Δ Θ _{tO, in}for the top-oil temperature of initial time, Δ Θ _{tO, R}for the nominal loss that top-oil temperature under stable situation rises, Δ Θ _{w, in}for initial time hot(test)-spot temperature is relative to the gradient of top-oil temperature, R is the load loss rate in unloaded rated current situation, and k is stressor (load current/rated current), and x is the index coefficient of transformer oil, and H is hot spot factor, g _rfor the winding medial temperature under rated current is relative to the gradient of average oil temperature, y is winding index coefficient, and t is the time (minute), k ₁₁, k ₂₁and k ₂₂for hot(test)-spot temperature model constants, τ _ofor transformer oil averaging time constant (minute), τ _wfor winding time constant (minute); Characteristic constant in hot(test)-spot temperature model is the inherent characteristic of transformer, must be obtained, otherwise measurement data is by invalid by transformer temperature rise experiment;

For hot(test)-spot temperature parameter model, Δ Θ in the present embodiment _{tO, R}=47.7K, H=2.1, g _r=11.2, R=1.6, other parameters all adopt recommended parameter corresponding in IEC;

Obtain temperature rise of hot spot Δ Θ _tO=35.438K, the hot(test)-spot temperature Θ of transformer B20-1 _hST=364.8648K;

(4) according to the hot(test)-spot temperature obtained in step (3), utilize Arrhenius-Eyring model, insulation life assessment carried out to transformer:

$L\left({\mathrm{\Θ}}_{HST}\right)=A\·e^{(B/{\mathrm{\Θ}}_{HST})}---\left(5\right)$

Wherein L (Θ _hST) be the transformer quantification life-span, Θ _hSTfor hot(test)-spot temperature (K).

The present embodiment based on following two pre-conditioned: 1. under normal running conditions, the hot(test)-spot temperature of transformer is relevant with historical load level; 2. as hot(test)-spot temperature Θ _hST=80 DEG C, the characteristics life of transformer is 40 years; Obtain corresponding parameter value thus: A=0.56, B=1500;

Corresponding transformer quantizes life-span L (Θ _hST)=0.56 × e ^{(1500/364.8648)}=34.17 (6)

(5) transformer is utilized to quantize life-span L (Θ _hST), the probability of malfunction Cumulative Distribution Function P of transformer equipment is obtained based on Weibull distribution _f:

$P_f\left(t\right)=1-e^{(-{\left(\frac{t}{L\left({\mathrm{\Θ}}_{HST}\right)}\right)}^{\mathrm{\β}})}---\left(7\right)$

Wherein β is P _fform parameter, β=5 in embodiment, according to the L (Θ obtained in step (4) _hST)=34.17 and formula (7), obtain the probability of malfunction Cumulative Distribution Function P of transformer B20-1 _f:

$P_f\left(t\right)==1-e^{-{\left(\frac{t}{34.17}\right)}^5}---\left(8\right)$

(6) impact of transformer enlistment age on its reliability is analyzed according to Markov model (Markov model); Based on the enlistment age of transformer, obtain the reliability index D of each transformer _f, adopt reliability index D _fcharacterize the number of times that transformer breaks down within the unit interval:

$D_f=\frac{1}{t}\underset{j=1}{\overset{s}{\Σ}}{P}_j\×\[t-\frac{(2j-1)\·\mathrm{\Δ}t}{2}\]---\left(9\right)$

T becomes the working time referring to transformer, i.e. enlistment age, and in embodiment, the enlistment age of transformer B20-1 is 20 years, corresponding t=175200h;

Transformer t working time is divided into the individual equal sub-range of s, Δ t is the time step in each sub-range, Δ t=1h in the present embodiment; The prerequisite occurred due to fault be transformer from put into operation s, before fault occur, be in the normal state run always, therefore adopt posteriority condition probability formula, the probability of malfunction P in an acquisition jth sub-range _j:

$P_j=\frac{{\∫}_0^{j\mathrm{\Δ}t}{P}_f\left(t\right)dt-{\∫}_0^{(j-1\mathrm{\Δ})}{P}_f\left(t\right)dt}{{\∫}_0^{\mathrm{\∞}}{P}_f\left(t\right)dt}---\left(10\right)$

Further, the P obtained in integrating step (5) _ft () and formula (9), obtain P _j:

$P_j=\frac{{\∫}_0^{j\mathrm{\Δ}t}{1}^{-{\left(\frac{t}{34.17}\right)}^5}dt-{\∫}_0^{(j-1)\mathrm{\Δ}t}{1-e}^{-{\left(\frac{t}{34.17}\right)}^5}dt}{{\∫}_0^{j\mathrm{\Δ}t}{1-e}^{-{\left(\frac{t}{34.17}\right)}^5}dt}---\left(11\right)$

To sum up, transformer B20-1 reliability index D is in an initial condition obtained _{1, b};

(7) repeat step (4) ~ (6), other transformers in network are analyzed, obtain all transformers reliability index D in an initial condition in network _i,b; D _i,bfor the reliability of lower i-th transformer of initial situation;

(8) suppose transformer 2 because of fault cause stop transport, in network, trend will redistribute, and again carry out Load flow calculation to electric power system, obtain the load value of other transformers when transformer 2 is stopped transport;

(9) for transformers all in network, repeat step (4) ~ (6), obtain the reliability index D of all transformers under transformer 2 stoppage in transit situation in network _{i, 2}; D _{i, 2}for the reliability of transformer i when transformer 2 is stopped transport;

(10) obtain cascading failure and start probability level P _ic, and according to P _icprobability level identifies the transformer the most easily causing cascading failure in voltage transformer system; Wherein the cascading failure startup probability of transformer 2 is:

$P_{ic,2}=D_{2,b}\×\underset{i=1}{\overset{N}{\Σ}}(D_{i,2}-D_{i,b})---\left(12\right)$

Wherein, D _{2, b}for the reliability of transformer under initial situation 2; D _i,bfor the reliability of transformer i under initial situation; D _{i, 2}for the reliability of transformer i when transformer n stops transport;

(11) the fragile link indicatrix P of cascading failure is obtained _vc, and according to P _vcidentify the transformer the most easily by disturbing influence in electric power system; Wherein the fragile link indicatrix of the cascading failure of transformer 2 is:

$P_{vc,2}=\underset{i=1}{\overset{N}{\Σ}}\[(D_{2,i}-D_{2,b})\×D_{i,b}\]---\left(13\right)$

Wherein, D _{2, i}for the reliability of transformer 2 when transformer i stops transport; D _{2, b}for the reliability of transformer n under initial situation; D _i,bfor the reliability of transformer i under initial situation; I ∈ [1, N], N are total number of units of transformer in network;

(12) repeat step (10) ~ (11), obtain the P of transformers all in electric power system _icindex and P _vcindex;

(13) by all transformers respectively according to P _icindex and P _vcindex, sorts according to rule from big to small; P _icthe most forward transformer of index rank is the link the most easily causing cascading failure to occur; P _vcthe most forward transformer of index rank is the transformer being subject to disturbing influence most;

Table 2 be classified as the P of test macro under first order load level in embodiment _ic, P _vcindex ranking:

Table 2 test macro reliability index result of calculation rank

As can be seen from Table 2, the P of the transformer B20-1 on No. 20 buses is positioned at _icvalue ranks the first, and what show that this transformer causes system has the greatest impact, and the most easily causes cascading failure; The P of the transformer B20-3 on No. 20 buses _vcvalue ranks the first, and shows to deposit in case in disturbance, and this transformer is the most easily affected and stops transport, and is the link of most fragile in system.

In an embodiment, cascading failure is adopted to start probability P _icidentify in electric power system the link the most easily causing cascading failure to occur, adopt the fragile link indicatrix P of lock fault _vcidentify the fragile link the most easily by disturbing influence in electric power system; Probability P is started at acquisition cascading failure _iclink indicatrix P fragile with lock fault _vcprocess, fully combine coupled relation in the factors such as transformer structure itself in electric power system, function, operation age and fault mode and regional power grid between transformer to the impact of equipment dependability, taken into full account the practical situations of electric power system, the maintenance of fail-safe analysis result to reality provided has better directive significance.

Those skilled in the art will readily understand; the foregoing is only preferred embodiment of the present invention; not in order to limit the present invention, all any amendments done within the spirit and principles in the present invention, equivalent replacement and improvement etc., all should be included within protection scope of the present invention.

Claims (8)

1., based on a transformer analysis method for reliability for enlistment age and load level, it is characterized in that, described transformer analysis method for reliability specifically comprises the steps:

(1) transformer load grade is divided according to transformer load curve;

(2) for the transformer of each load level, tidal current analysis is carried out to obtain i-th transformer load value in an initial condition; Wherein, i indication transformer is numbered, i ∈ [1, N]; N is total number of units of transformer in electric power system;

(3) i-th transformer hot(test)-spot temperature Θ corresponding with its load is in an initial condition obtained _iHST; And according to the relation between hot(test)-spot temperature and transformer insulated life-span, obtain the quantification life-span L of i-th transformer _i(Θ _hST);

Life-span L is quantized in conjunction with described transformer _i(Θ _hST), obtain the probability of malfunction Cumulative Distribution Function P of transformer _f: $P_f\left(t\right)=1-e^{(-{\left(\frac{t}{L_i\left({\mathrm{\Θ}}_{HST}\right)}\right)}^{\mathrm{\β}})};$

Wherein, transformer quantizes life-span L _i(Θ _hST) be function P _fscale parameter; β is function P _fform parameter, t refers to the enlistment age of transformer;

(4) based on the enlistment age of transformer, the reliability index D of transformer is obtained _f, $D_f=\frac{1}{t}\underset{j=1}{\overset{s}{\Σ}}{P}_j\×\[t-\frac{(2j-1)\·\mathrm{\Δ}t}{2}\];$

Wherein, s is the number in the equal sub-range divided by the enlistment age t of transformer, j ∈ [1, s]; Δ t is the time step in described sub-range; P _jfor the probability of malfunction in a jth sub-range, $P_j=\frac{{\∫}_0^{j\mathrm{\Δ}t}{P}_f\left(t\right)dt-{\∫}_0^{(j-1)\mathrm{\Δ}t}{P}_f\left(t\right)dt}{{\∫}_0^{\mathrm{\∞}}{P}_f\left(t\right)dt};$

(5) make i=i+1, and repeat step (2) ~ (4), until i=N, to obtain N platform transformer reliability index in an initial condition in electric power system;

(6) according to transformer reliability index in an initial condition, the cascading failure obtaining transformer starts probability level P _ic, and start probability level P according to cascading failure _icidentify the transformer the most easily causing cascading failure in electric power system; Described P _icbe worth larger transformer reliability poorer, more easily cause cascading failure.

2. transformer analysis method for reliability as claimed in claim 1, is characterized in that, also comprise the steps:

(7) load value of other each transformers in n-th transformer stoppage in transit situation is obtained, and make n=n+1, repeat step (3) ~ (4), until n=N, to obtain the reliability index of N platform transformer in n-th transformer stoppage in transit situation in electric power system; Wherein, n indication transformer is numbered, n ∈ [1, N];

(8) according to the reliability index of described transformer in n-th transformer stoppage in transit situation, the fragile link indicatrix P of cascading failure of transformer is obtained _vc, and according to the fragile link indicatrix P of described cascading failure _vcidentify the transformer the most easily by disturbing influence in electric power system; Described P _vcbe worth larger transformer reliability poorer, be more subject to disturbing influence.

3. transformer analysis method for reliability as claimed in claim 1 or 2, is characterized in that, the cascading failure described in step (6) starts probability level P _icspecific as follows:

$P_{ic}=D_{n,b}\×\underset{i=1}{\overset{N}{\Σ}}(D_{i,n}-D_{i,b})$

Wherein, D _n,bit is n-th transformer reliability in an initial condition; D _i,bit is i-th transformer reliability in an initial condition; D _i,nthe reliability of i-th transformer when n-th transformer is stopped transport.

4. transformer analysis method for reliability as claimed in claim 2, is characterized in that, the fragile link indicatrix P of the cascading failure described in step (8) _vcspecific as follows:

$P_{vc}=\underset{i=1}{\overset{N}{\Σ}}\[(D_{n,i}-D_{n,b})\×D_{i,b}\]$

Wherein, D _n,ithe reliability of n-th transformer when i-th transformer is stopped transport; D _n,bit is n-th transformer reliability in an initial condition.

5. transformer analysis method for reliability as claimed in claim 1, it is characterized in that, described step (1) is specific as follows:

(1.1) according to the transformer load situation on transformer yearly load curve, in units of week, the transformer load level of the whole year is divided into m grade; Wherein, load level difference is drawn in same grade in week within ± 3%;

(1.2) load level of the transformer in same grade is averaged, using described mean value as the load level of this grade; M is positive integer, and 5≤m≤10.

6. transformer analysis method for reliability as claimed in claim 1 or 2, is characterized in that, in described step (3), according to the load value under original state, adopts hot(test)-spot temperature model Θ _hST=Θ _a+ Δ Θ _tO+ Δ, obtains transformer hot(test)-spot temperature Θ in an initial condition _hST;

Wherein, Θ _afor environment temperature, Δ Θ _tOfor top-oil temperature liter, Δ Θ _wfor hot(test)-spot temperature relatively and the difference of top-oil temperature;

When load increases progressively:

${\mathrm{\Δ\Θ}}_{TO}={\mathrm{\Δ\Θ}}_{TO,in}+\[{\mathrm{\Δ\Θ}}_{TO,R}\×{\left(\frac{1+R\×k^2}{1+R}\right)}^x-{\mathrm{\Δ\Θ}}_{TO,in}\]\×f_1\left(t\right)$

ΔΘ _w＝[Hg _rk ^y-ΔΘ _w,in]×f ₂(t)

When load successively decreases:

${\mathrm{\Δ\Θ}}_{TO}={\mathrm{\Δ\Θ}}_{TO,R}\×{\left(\frac{1+R\×k^2}{1+R}\right)}^x+\[{\mathrm{\Δ\Θ}}_{TO,in}-{\mathrm{\Δ\Θ}}_{TO,R}\×{\left(\frac{1+R\×k^2}{1+R}\right)}^x\]\×f_3\left(t\right)$

ΔΘ _w＝Hg _rk ^y

Wherein: f ₁(t)=1-exp (-t/ (k ₁₁× τ _o)),

f ₂(t)＝k ₂₁×(1-exp(-t/(k ₂₂×τ _w)))-(k ₂₁-1)×(1-exp(-t/(τ _o/k ₂₂)))，

f ₃(t)＝exp(-t/(k ₁₁×τ _o))；

Wherein, Δ Θ _{tO, in}for the top-oil temperature of initial time, Δ Θ _{tO, R}for the nominal loss that top-oil temperature under stable situation rises, Δ Θ _{w, in}for initial time hot(test)-spot temperature is relative to the gradient of top-oil temperature, R is the load loss rate in unloaded rated current situation, and k is stressor, and x is the index coefficient of transformer oil, and H is hot spot factor, g _rfor the winding medial temperature under rated current is relative to the gradient of average oil temperature, y is winding index coefficient, and t is the enlistment age of transformer, k ₁₁, k ₂₁and k ₂₂for hot(test)-spot temperature model constants, τ _ofor transformer oil averaging time constant, τ _wfor winding time constant.

7. transformer analysis method for reliability as claimed in claim 1 or 2, it is characterized in that, in described step (3), according to the load value under original state, the hot(test)-spot temperature model of oil-immersed power transformer is adopted to obtain transformer hot(test)-spot temperature Θ in an initial condition _hST, specific as follows:

A, the transformer for Natural Oil Circulation Power cooling:

Hot(test)-spot temperature ${\mathrm{\Θ}}_{HST}={\mathrm{\Θ}}_a+{\mathrm{\Δ\Θ}}_{or}{\[\frac{1+{\mathrm{RK}}^2}{1+R}\]}^x+{\mathrm{Hg}}_r{K}^y;$

B, the transformer for forced oil-circulation cooling:

Hot(test)-spot temperature ${\mathrm{\Θ}}_{HST}={\mathrm{\Θ}}_a+{\mathrm{\Δ\Θ}}_{or}{\[\frac{1+{\mathrm{RK}}^2}{1+R}\]}^x+2\[{\mathrm{\Δ\Θ}}_{imr}-{\mathrm{\Δ\Θ}}_{br}\]K^y+{\mathrm{Hg}}_r{K}^y;$

C, the transformer for forced oil-circulation Directed cooling:

Hot(test)-spot temperature Θ _hST=Θ _hST'+0.15 (Θ _hST-Θ _hr), K > 1;

Wherein, Θ _hST' for not considering hot(test)-spot temperature value when conductor resistance affects, Θ _afor environment temperature, Δ Θ _orfor top-oil temperature liter, Δ Θ _imrfor oily average temperature rising, Δ Θ _brfor bottom oil temperature liter, R is loss ratio, and x is oil temperature coefficient, and y is winding temperature coefficient, and K is load factor, Hg _rfor focus is to the temperature difference of winding top oil; Θ _hrfor hot(test)-spot temperature when ageing rate is 1.

8. the transformer analysis method for reliability as described in any one of claims 1 to 3, it is characterized in that, in described step (3), Arrhenius formula is adopted to obtain hot(test)-spot temperature and the relation between the transformer insulated life-span, to obtain the quantification life-span of transformer wherein, A and B is constant.