CN106447530A - Imprecise condition estimation method for outage probability of power equipment - Google Patents
Imprecise condition estimation method for outage probability of power equipment Download PDFInfo
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Abstract
The invention discloses an imprecise condition estimation method for an outage probability of power equipment. The method comprises the steps of taking related running condition factors, which influence a running state of the power equipment, as sub-nodes, taking the running state of the power equipment as a father node, and constructing a reliability network of equipment outage probability estimation; calculating prior probabilities of the power equipment in different running states and a condition reliability set corresponding to the sub-nodes according to related running condition history data of the power equipment; and implementing probabilistic reasoning based on the prior probabilities and the condition reliability set corresponding to the sub-nodes in the reliability network according to equipment running conditions given in a target time segment of estimation, and finally obtaining an imprecise condition estimation result of the outage probability of the power equipment under the running conditions given in the target time segment of estimation. According to the method disclosed by the invention, an important basic parameter estimation means can be provided for assessing the running reliability of a power system lack of historical statistic data; and the method has wide application potential.
Description
Technical field
The invention belongs to power equipment reliability evaluation areas, more particularly to a kind of non-precision of power equipment stoppage in transit probability
Condition method of estimation, the method is applied to exposed type equipment.
Background technology
Probability and its generation that Power System Operating Reliability Evaluation technology can occur to following set period forecast accident
Consequence estimated, with quantization system operational reliability level, the significance of crime prevention system operation risk.Power equipment
Used as the basic element that power system is constituted, analysis causes the factor which is stopped transport, predicts its stoppage in transit probability, be Operation of Electric Systems
The top priority that reliability assessment job demand is completed.
In actual motion, the factor for causing power equipment to stop transport has a lot, is broadly divided into four classes：(1) equipment itself
Factor, such as ageing equipment, production defect etc.；(2) influence factor of external environment, such as strong wind, heavy rain, bird pest etc.；(3) at system
In the relay protection action that abnormal operational conditions cause；(4) other factorses.Wherein, due to equipment components such as transmission lines of electricity
Main function components are externally exposed in natural environment, and its running status is affected significantly by external conditions such as weather, such as big
Under the severe weather conditions such as wind, thunderstorm, the probability that this kind equipment occurs random failure will be greatly increased.Now, impact equipment fortune
The factor of row reliability level is also run with outside weather conditions, equipment load level etc. in addition to the degree of aging of its own
Operating mode is closely related.As can be seen here, the estimation to exposed type power equipment stoppage in transit probability level, substantially can be summarized as to shape
The forecasting problem of state Condition of Discrete Random Variables probability mass function.
Traditionally power equipment stoppage in transit probability level is generally substituted with counting the plateau probability for obtaining, main application
In fields such as medium-term and long-term Electric Power Network Planning, scheduled overhauls.However, for the short-term stoppage in transit risk of equipment, during due to which with assessment
The section inside and outside portion's service condition of equipment is closely related, and the change according to operating condition is changed, constant average probability index
It is difficult to describe impact of the operating condition change to equipment short-term stoppage in transit risk.
Thus, many scholars have carried out fruitful research to the stoppage in transit probability Estimation problem of equipment time-varying.Article " electricity
Element time-varying outage model analysis in Force system operation risk assessment " is positioned at the stochastic process modeling of equipment stoppage in transit, demonstrates
The condition of equipment time-varying outage model is set up using Markov process, operating condition change is to exposing using the process analysis
The impact of type equipment stoppage in transit probability；Article " Power System Operating Reliability Evaluation based on real-time running state " is constructed and is based on
The equipment short-term outage model of the real-time operating conditions such as Line Flow, busbar voltage, system frequency, analyzes above-mentioned service condition
Impact of the change to equipment stoppage in transit probability；On its basis, article " the interdependent power transmission and transforming equipment short term reliability model of condition "
Establish by the ageing failure model according to temperature, the overload protection action model according to current-carrying situation and according to weather conditions
The interdependent power transmission and transforming equipment short term reliability assessment models of condition that constitute of 3 part of random failure model, calculate different fortune
The stoppage in transit probability of power equipment under the conditions of row.The above-mentioned research that estimates for the interdependent dependability parameter of appointed condition, with reference
Meaning, however, for the service condition for limiting, its available stoppage in transit sample is relative to be lacked, and the estimation to dependability parameter is difficult to
Accurately, above-mentioned work does not have the how probabilistic problem of quantitative analysiss equipment operational reliability parameter estimation of embodying.
On the other hand, " statistical sample is few, measurement period length " is always the difficulty for perplexing power equipment reliability parameter estimation
Point problem, and the great majority research of existing method of estimation is all positioned at the modeling of equipment longtime running reliability level, not
Embody equipment in a short time to stop transport according to its operating condition change and the feature of time-varying；And when sample size is very few, it is difficult to obtain
Reliable estimated result.
Content of the invention
In order to solve the shortcoming of prior art, the present invention provides a kind of non-precision condition of power equipment stoppage in transit probability and estimates
Method, the stoppage in transit probability level interdependent to equipment operation conditional is implemented non-precision condition and is estimated, estimated result is general with non-precision
The form of rate embodies.The present invention can either embodiment device stoppage in transit probability level according to equipment operating condition change and the feature of time-varying,
The uncertainty of the estimated result for causing because of Finite Samples can be embodied again, so as to can for Operation of Electric Systems decision-making offer more
Add standby equipment dependability information.
For achieving the above object, the present invention is employed the following technical solutions：
A kind of non-precision condition method of estimation of power equipment stoppage in transit probability, including：
Using the related operating condition factor of impact power equipment running status as belief network child node, power equipment
Running status is used as father node, and then constructs the belief network model of equipment stoppage in transit probability Estimation；
According to the related operating condition historical data of power equipment, priori of the power equipment in different running statuses is calculated
Probability and the corresponding condition reliability collection of child node；
The equipment operating condition given according to objective time interval is estimated, in the belief network model of equipment stoppage in transit probability Estimation
In, probability inference is implemented based on prior probability and the corresponding condition reliability collection of child node, is finally given and estimating objective time interval
The non-precision condition evaluation results of power equipment stoppage in transit probability under given operating condition.
The related operating condition factor of impact power equipment running status includes：Ice and snow, wind speed, ambient temperature, rainfall, thunder
Electricity and load level.
The running status of power equipment includes the stoppage in transit state of power equipment and state of not stopping transport.
The number of times that the corresponding condition reliability collection of child node comes across various operating condition conditions when equipment is stopped transport by statistics is obtained
Arrive.
In the belief network model of equipment stoppage in transit probability Estimation, based on prior probability and the corresponding condition reliability of child node
Collection, implements probability inference using Accurate Reasoning algorithm.
In the belief network model of equipment stoppage in transit probability Estimation, based on prior probability and the corresponding condition reliability of child node
Collection, implements probability inference using approximate resoning algorithm.
Using outer approximate and interior approximate approximate resoning algorithm is included, in the belief network model of equipment stoppage in transit probability Estimation
Middle enforcement probability inference.
Implement probability inference to set up in classical Bayesian network based on prior probability and the corresponding condition reliability collection of child node
On the basis of network probability inference.
Under the conditions of equipment difference running status, the statistics acquisition methods of non-precision probability adopt IDM method.
IDM method is eliminated under condition of small sample, and priori arranges the unreasonable unfavorable shadow to event occurrence rate estimation
Ring.
The reasoning target of the belief network model of equipment stoppage in transit probability Estimation is：Estimating the given operating condition of objective time interval
The stoppage in transit probability interval of equipment under condition electric power.
The belief network model of the equipment stoppage in transit probability Estimation meets strong Markov condition.
Stoppage in transit probability level describes equipment and is shifted by the state of normal operating condition to stoppage in transit state in set period
Probability.In practice, as the running status of exposed type equipment is closely related with operating condition, thus, the stoppage in transit of this kind equipment
Probability is not the fixed value of a stable state, and which is identical with outage rate index, with significant time-varying characteristics.The present invention is positioned at
The non-precision condition of exposed type equipment time-varying stoppage in transit probability level is estimated, carries out non-precision bar with to exposed type equipment stoppage in transit event
Part probability Estimation is same implication, is style of writing unification, and the present invention is using the former form of presentation.
Beneficial effects of the present invention are：
(1) due to asking for the equipment operational reliability index according to operating condition time-varying under Small Sample Size for power train
System safe operation is significant, and therefore, the present invention proposes a kind of non-precision condition estimation side of power equipment stoppage in transit probability
Method, combines IDM and belief network model, and demonstrates the effectiveness of method by sample calculation analysis, and the present invention can either embody
Equipment stoppage in transit probability level changes and the feature of time-varying according to equipment operating condition, and can embody the estimation for causing because of Finite Samples
As a result uncertainty, so as to providing more complete equipment dependability information for Operation of Electric Systems decision-making.
(2) the method is stopped transport based on equipment historical statistical data and the operating condition data of estimation objective time interval, build
Process the belief network of non-precision conditional probability inference problems, and non-precision Di Li Cray mould using multimode stochastic variable
Type, obtain equipment stoppage in transit sample lack under the conditions of belief network node non-precision conditional probability, so as to, estimate obtain to
Determine the interval range of equipment stoppage in transit probability under service condition.Method embodies power equipment stoppage in transit probability according to its operating condition change
And the feature of time-varying, it is to solve the problems, such as that the power equipment operation reliability evaluation under the conditions of stoppage in transit sample shortage provides new think of
Road.
(3) present invention proposition method can be important for lacking the Power System Operating Reliability Evaluation offer of historical statistical data
Underlying parameter estimate means, have a wide range of applications potentiality.
Description of the drawings
Fig. 1 is a kind of non-precision condition method of estimation schematic flow sheet of power equipment stoppage in transit probability of the present invention；
Fig. 2 is three node beliefs schematic network structure；
Fig. 3 is the geometric representation schematic diagram of reliability collection；
Fig. 4 is power equipment stoppage in transit probability Estimation belief network structural representation；
Fig. 5 is transmission line of electricity stoppage in transit probability non-precision/single-valued conditions estimated result schematic diagram in continuous time；
Fig. 6 (a) is the equipment stoppage in transit probability Estimation result plausibility check result upper limit curve figure based on analog systemss；
Fig. 6 (b) is the equipment stoppage in transit probability Estimation result plausibility check result lower limit curve figure based on analog systemss.
Specific embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete
Site preparation is described.The reliability for referring in the embodiment of the present invention refers to the probability of equipment normal operation in time t, i.e., in time t
There is no the probability that stops transport in interior equipment.Wherein, t is nonnegative number.If continuous random variabless T (T >=0) represent the continuous normal work of equipment
Time before making to stoppage in transit, then Reliability Function can be expressed as
R (t)=P (T >=t) (1)
Corresponding with Reliability Function R (t), failure distribution function F (t) description equipment stopped before t arrival
The size of the fortune probability of happening, is clear to, and which with the relation of Reliability Function F (t) is
F (t)=P (T ＜ t)=1-R (t) (2)
Outage rate (fault rate, risk) λ (t) is conventional reliability index, and its statistics is described as in the unit interval
The ratio that equipment is stopped transport, is defined by formula (1), formula (2), and its λ (t) probability description is
If the running status of equipment is considered as 2 state stochastic variable X, 0 represents normal operation, and 1 represents equipment stoppage in transit, then stop
The definition of fortune probability is equipment in t0Moment is normally run, and the probability for occurring within the subsequent delta t time to stop transport.Stoppage in transit probability
P0-1(t0, Δ t) is represented by
It is clear to, stoppage in transit probability level describes equipment state by normal operating condition to stoppage in transit state in the set period
Transition probability.Stoppage in transit probability is associated by formula (4) with outage rate.In practice, due to running status and the fortune of exposed type equipment
Row operating mode is closely related, thus, the stoppage in transit probability of this kind equipment is not the fixed value of a stable state, itself and outage rate index phase
With with significant time-varying characteristics.
Present invention research is positioned at the non-precision condition of exposed type equipment time-varying stoppage in transit probability level and estimates, and to exposed type
Equipment stoppage in transit event carries out non-precision conditional probability and is estimated as same implication, is style of writing unification, and the present invention is using the former side of statement
Formula.
Be otherwise known as non-precision probability (imprecise probability, IP) interval probability.In the nineties in 20th century,
As Walley et al. is to the perfect of non-precision probability theory basis, the theory has obtained extensive concern and application.Non-precision
The core concept of probability theory the statistical law of stochastic variable is described in the form of the probability distribution collection, it is thus possible to
The probability interval of random event generation is obtained to substitute accurate monodrome probability.The expression-form of non-precision probability is
In formula：Pim(A) represent the non-precision probability of event A generation；P(A) it is non-precision probability lower bound,For non-precision
The probability upper bound, it is clear thatP(A) withMeetConstraint.
As can be seen that for the non-precision probability shown in formula (5), ifThen non-precision probability will deteriorate to essence
True monodrome probability, the probability of this explanation event A generation will be accurate.On the other hand, ifP(A)=0,Then represent
The non-precision probability may be got by the arbitrary value in 0 to 1 interval, illustrate that the probabilistic information of event A lacks, by existing information
It is difficult to provide valuable probability statistics result.As can be seen here, non-precision probability is the natural extending of exact probability, and event is sent out
Raw probability has more comprehensive, flexible ability to express.
Due to the effective sample limited amount that power equipment is stopped transport, thus, the condition that the law of large numbers is set up is difficult in reality
To meet.In the case, accurate monodrome probability Estimation result is just difficult to reflection equipment and really stops transport probability.Phase therewith
Corresponding, non-precision probability is the effective ways of probability Estimation in the case of process sample information deficiency, and which can adopt data statisticss
Mode is obtained.Wherein, IDM is a kind of effective non-precision Probabilistic estimation.
The extension of IDM being to determine property Dirichlet model, it is adaptable to which the non-precision for obeying multinomial distribution stochastic variable is general
Rate statistical estimate.If the stochastic variable for obeying multinomial distribution has the state that n kind is likely to occur, the probability that its each state occurs
With θ=(θ1,θ2,…,θn) represent；Wherein, θiRepresent the probability that i-th kind of state being likely to occur occurs, i=1,2 ..., n；n
It is the positive integer more than or equal to 1.
Definitiveness Dirichlet model regards unknown parameter θ as stochastic variable by Bayesian statistic principle, and using such as
Dirichlet shown in formula (6) is distributed as its priori probability density function.
In formula：Γ () represents Gamma function；riFor hyper parameter, 0≤r is meti≤ 1 and and for 1 constraint, which represent θi
Average；S is setup parameter, which determines influence degree of the prior information for statistical result, and the value of s is bigger, it is necessary to
More samples eliminating impact of the prior information for statistical result, thus, s is often interpreted the prudent journey to fresh information again
Degree, its value generally between [1,2].
Further, under conditions of sample observations M is got, priori Dirichlet probability density function is through Bayes's mistake
Cheng Gengxin, forms posteriority Dirichlet probability density function, as shown in formula (7).
In formula：M={ m1,m2,…,mnObserve for sample；miRepresent the number of times that stochastic variable state i occurs；M is sample
Sum, i.e. M=m1+m2+…+mn, the meaning of other symbols is identical with formula (6)；N is positive integer.
Obviously, after obtaining the Posterior distrbutionp shown in formula (7), parameter θiJust expect using the Posterior distrbutionp shown in formula (8)
Value is estimated, i.e.,
E(θi)=(mi+s·ri)/(s+M) (8)
In formula：s·riRepresent θiThe weights of prior information, meet s r1+s·r2+…+s·rn=s, for convenience of description,
Use parameter betaiReplace s ri.
Shown in analysis mode (8), the estimated result of definitiveness Dirichlet model, is clear to, when sample observation is not yet obtained,
The probability Estimation occurred by each state of random event is by its priori weights βiDetermine, i.e. E (θi)=βi/(β1+β2+…+βn).Cause
And, it is readily appreciated that, it is the drawbacks of using definitiveness Dirichlet Probabilistic estimation, for sample present event, the method is received
The impact of its prior distribution is notable, and when prior information arranges unreasonable, be easy to get insecure estimated result.
The drawbacks of in order to avoid definitiveness Dirichlet method, IDM is not entered to θ using single probability density function
Row is estimated, but using priori probability density function set being estimated, the set is by all of under given s Parameter Conditions
Dirichlet distribution is constituted, i.e., after fixing s value in formula (7), make r traversal whole [0,1] interval.Further, can be according to pattra leaves
This principle, the priori probability density function set of θ is updated to posterior probability density function set, so as to obtain taking for probability θ
Value is interval, and (the interval up-and-down boundary is respectively in hyper parameter riObtain for value at 0 and 1), as shown in formula (9).
Thus, it is possible to according to Small Sample Database, easily estimate to obtain that stochastic variable state under specified criteria occurs is non-
Exact probability.It is clear to, IDM statistical method is eliminated under condition of small sample, priori setting is unreasonable to be estimated to event occurrence rate
The adverse effect of meter.
The ultimate principle of belief network is：
Belief network is that a kind of expression uncertainty knowledge for being proposed by Cozman and the non-precision for carrying out causal reasoning are general
Rate graph model[28].Substantially, belief network is the expansion of classical Bayesian network, and which is by graph model and non-precision probability theory
In conjunction with expression more typically uncertain problem and the ability for carrying out uncertain inference.With classical Bayesian network not
It is with part, in belief network, node it is not absolutely required to express with accurate probability with arc, but can be with non-
The expression-form that exact probability is estimated, which relaxes the modeling requirement of classical Bayesian network.If belief network meets each
Non- descendants of the node variable under given his father's node condition independently of it, non-father node, then claim the network to meet strong Ma Erke
Husband's condition, most reasoning problems include the belief network corresponding to the estimation problem of power equipment stoppage in transit probability of the present invention
Meet strong Markov condition.
Fig. 2 gives the schematic diagram of a simple three node beliefs network.In figure, father node X0And its child node X1、X2All
For 2 state stochastic variables；x0、x1、And x2、Illustrate the state of stochastic variable；[P ()] and [P (|)] difference
It is the marginal probability and conditional probability for occurring with the state that interval represents.In fig. 2, child node is general with the non-precision condition of variable
Rate is distributed as：
[P(x0)]=[0.3,0.4]
Root node with the non-precision marginal probability distribution of variable is：
Root node takes
Root node takes
In order to the expression-form of compatible node stochastic variable non-precision probability, belief network is based on reliability collection
(credal set) implements probability inference.Have between the non-precision probability that reliability collection is occurred with each state of stochastic variable close
Contact.Mathematically, stochastic variable XiReliability collection K (Xi) be defined as by XiAll possible probability mass function P (Xi) constitute
Closed convex set, i.e.,
In formula：P1(Xi),P2(Xi),…,PL(Xi) it is reliability collection K (Xi) in L apex probability mass function, its
In, L is the positive integer more than 0；Its corresponding αkFor reliability collection K (Xi) in k apex probability mass function weight.
Fig. 3 gives 2 state stochastic variable X in Fig. 20Reliability collection.From the figure 3, it may be seen that stochastic variable X0There is x0State
Probability interval is [0.3,0.4], occursThe probability interval of state is [0.6,0.7], therefore by state x0Probability of happening and stateIn the two-dimensional coordinate system that probability of happening is constituted, tetragon a-b-c-d is represented and is met x0WithThe region of probability interval.However,
Consider and for 1 standardization constrain, actually only line segment ac is only stochastic variable X0Probability mass function P (X0) may deposit
Scope.While being clear to, line segment ac is represented by α1P1(X0)+α2P2(X0), α1+α2=1,0≤α1,α2≤ 1 form, i.e.,
Illustrate that line segment ac is the closed convex set on this two dimensional surface.It follows that line segment ac is X0Reliability collection K (X0), P1(X0) and P2
(X0) be reliability collection two summits, be expressed as ext [K (X0)]={ (0.3,0.7), (0.4,0.6) }.
In actual applications, reliability collection summit can meet specification by searching each state probability of occurrence interval of stochastic variable
Property constraint end points combination directly asking for.
The reasoning process of belief network is：
The probability inference of belief network is set up on classical Bayesian network probability inference basis, for calculate node with
The probability interval that each state of machine variable occurs under the conditions of known association relation with evidence, inference method includes Accurate Reasoning algorithm
With approximate resoning algorithm.
For the belief network with N number of node, the joint probability mass function of the corresponding N number of stochastic variable of node is not
Determine that set is referred to as the extension of belief network.For the belief network for meeting strong Markov condition, strong extension (strong
Extension) it is its corresponding extended mode, which is defined as all joint probability mass functions of stochastic variable in belief network
Convex closure, the summit of the convex closure can be obtained by way of the combination of each local reliability collection summit is multiplied.That is, for the strong expansion of belief network
One summit j, the N-dimensional random vector X=(X which correspond to of exhibition1,X2,…,XN) one group of state x=(x1,x2,…,xN)
Joint probability, can be calculated by formula (11).
In formula：X is one group of state of N-dimensional random vector X；xiIt is stochastic variable XiState；πiIt is XiThe shape of father node
State；Pj(Xi|πi)∈ext[K(Xi|πi)], show Pj(xi|πi) should be from the general of i-th stochastic variable condition reliability collection vertex correspondence
Value on rate mass function；N is the positive integer more than or equal to 1.
The Accurate Reasoning algorithm of belief network is by traveling through the joint probability matter that belief network reliability collection summit combines
Flow function, using conventional Bayesian Network Inference means, calculates unknown variable XQState value xqIn evidence variable XEObserved value
xeLower probability of occurrence P (xq|xe) maximum, minimum boundary value, as shown in formula (12), formula (13).
In formula：V represents the number of vertex of strong extension in belief network, and V is the positive integer more than or equal to 1；XM1Become for node
Duration set { X1,X2,…,XN}\{XQ,XE}；XM2For node variable set { X1,X2,…,XN}\{XE}；∑ represents to node variable
Set XM1、XM2The different conditions of middle variable carry out full probability computing.
Additionally, belief network can also implement probability inference using outer approximate and interior approximate approximate resoning algorithm is included.
As the cause effect relation that single power equipment is stopped transport not is especially complex, the present invention is stopped transport generally to which using Accurate Reasoning algorithm
Rate is implemented non-precision condition and is estimated.
It is emphasized that the non-precision probability of the belief network node of present invention structure is estimated to obtain by IDM.
Fig. 1 is that a kind of flow process of the non-precision condition method of estimation of power equipment stoppage in transit probability in the embodiment of the present invention is illustrated
The non-precision condition method of estimation for scheming the power equipment stoppage in transit probability in the present embodiment as shown in the figure can include：
S101, using the related operating condition factor of impact power equipment running status as child node, the fortune of power equipment
Row state is used as father node, and then constructs the belief network model of equipment stoppage in transit probability Estimation.
In specific implementation process, the exposed type equipment such as transmission line of electricity being set up in open-air atmosphere, its operational reliability
Parameter is closely related with the weather condition of its their location, and under severe weather conditions, the probability that equipment occurs random failure will show
Write and increase.Meanwhile, when equipment heavy service, when raising and then reach setting valve with its current-carrying capacity, relay protection will be caused to move
Its stoppage in transit is caused, thus, under the conditions of this, equipment stoppage in transit probability will also increase.Thus, the present invention is by above-mentioned appreciable impact equipment
The running status of the operating condition of operational reliability level and equipment builds Belief Network as the node evidence variable of belief network
Network, as shown in Figure 4.Further, since under identical operating condition, with the accumulation of military service duration, in operation, degree of aging is higher
Equipment stoppage in transit probability larger, thus, the present invention also will consideration impact of the military service duration to equipment operational reliability level, by which
The principal element of the equipment priori stoppage in transit probability of the long-term mean reliability level of equipment is represented as impact.
The factor of the related operating condition of impact power equipment and running status includes：Ice and snow, wind speed, ambient temperature, drop
Rain, thunder and lightning and load level.In belief network shown in Fig. 4, child node be represent 6 kinds of equipment operating condition condition random
(evidence) variable：Ambient temperature, wind speed, rainfall, thunder and lightning, load level, ice and snow, use E respectively1、E2、E3、E4、E5、E6To represent；
Father node is the 2 state stochastic variable H for representing equipment running status：Note equipment stoppage in transit state is H1, state of not stopping transport is H2.Right
In ambient temperature E1With wind friction velocity E2, which is 3 state stochastic variables：High temperature (temperature 26 DEG C and more than), low temperature (temperature
Below 4 DEG C) and room temperature (temperature 4 DEG C to 26 DEG C between), and strong wind (6 grades and above wind-force), mild wind (3 to strong breeze
Power) and calm (2 grades and with apparatus for lower wind).For equipment load level conditions E5, according to equipment protection seting value determining which
The division of two kinds of different conditions：It is load for equipment load heavy duty, remaining situation that current-carrying capacity exceedes the 80% of circuit rated capacity
Normally.The specific state demarcation situation of 6 kinds of evidence variables is as shown in table 1.
1 evidence variable states of table are divided
S102, according to the related operating condition historical data of power equipment, calculates power equipment in different running statuses
Prior probability and the corresponding condition reliability collection of child node.
In the belief network shown in Fig. 4, the non-precision condition to giving equipment stoppage in transit probability under operating condition to be realized
Estimate, need to know the probabilistic correlation relation between equipment running status prior probability and equipment running status and operating condition.Right
In the prior probability that equipment is stopped transport, can be substituted with the long-time statistical stoppage in transit probability of equipment.Equipment running status are transported with which
Probabilistic correlation between row operating mode, then using the corresponding condition reliability collection K (E of each evidence nodea|Hz),a∈{1,2,5},z∈{1,
2}、K(E3|Hz,E1,b1)、K(E4|Hz,E3,b3)、K(E6|Hz,E1,b1),b1∈{1,2,3},b3∈ { 1,2 }, z ∈ { 1,2 } carrys out table
Show.
Wherein, for K (Ea|H1), can pass through to coming across the number of times system that when equipment is stopped transport, various operating condition conditions occur
Meter is obtained.For example, it is intended to ask for the reliability collection K (E of equipment load situation under the conditions of equipment is stopped transport5|H1), formula (9) need to be first depending on
Shown IDM method, seeks out the non-precision conditional probability P of equipment load from historical dataim(E5,1|H1) and Pim(E5,2|
H1), i.e.,
In formula：M represents that equipment adds up stoppage in transit number of times；m5,1、m5,2It is illustrated respectively in its load working condition under the conditions of equipment is stopped transport
For heavily loaded, normal occurrence number；S is the setup parameter in IDM, value in [1,2].
Further, reliability collection K (E is obtained5|H1), i.e.,
In formula：Reliability collection K (E5|H1) in probability mass function P (E5,1|H1)、P(E5,2|H1) general in its corresponding non-precision
Value in the upper and lower bounds of rate, and which meets probability and the standardization constraint for 1.
Now, reliability collection K (E can be passed through5|H1) corresponding meet probability and for 1 standardization constraint non-precision probability on,
Summit ext [K (the E for combining to obtain reliability collection of lower boundary5|H1)], i.e.,
On the other hand, for K (Ea|H2), as time of the equipment in state of not stopping transport is much larger than its idle time, because
And, the sample size in the case of equipment is not stopped transport is enriched, and can adopt exact probability form to simplify calculating, i.e. for equipment not
The probability that during stoppage in transit, each operating condition occurs, the accumulation duration that can be occurred by each operating mode when not stopping transport and equipment are not stopped transport total duration
Ratio approximately obtaining.In the case, K (Ea|H2) P (E will be reduced toa|H2).For example, certain putting equipment in service 3 years, which does not stop
About 1080 days fortune time, in the time, equipment severe duty amounts to appearance about 205 days, then P (E5,1|H2)=205/1080=
0.1898≈0.19,P(E5,2|H2)=1-P (E5,1|H2).
It should be noted that due to evidence variable E in Fig. 43,E4,E6Guided into by multiple father nodes jointly respectively, thus,
Ask for count during condition reliability collection of each state of above-mentioned evidence variable under equipment difference running status and its all father nodes are each
The situation that state occurs.
S103, according to the equipment operating condition for estimating that objective time interval gives, in the belief network of equipment stoppage in transit probability Estimation
In model, probability inference is implemented based on prior probability and the corresponding condition reliability collection of child node, finally give and estimating target
Period gives the non-precision condition evaluation results of power equipment stoppage in transit probability under operating condition.
The reasoning target of belief network model of the present invention is：Equipment under the conditions of the given operating condition of objective time interval is estimated
Stoppage in transit probability interval.Which is estimated, can be considered a class in belief network, it is known that equipment state prior probability P (Hz), condition is believed
Degree collection K (Ea|Hz)、K(E3|Hz,E1,b1)、K(E4|Hz,E3,b3)、K(E6|Hz,E1,b1), and estimate objective time interval operating condition E
={ E1,E2,E3,E4,E5,E6, solve non-precision conditional probability Pim(H1| E), its reasoning formula is
In formula：Should be from reliability collection summit ext [K (Ea|H1)] place's selection, Also be in the same manner；And
Take the monodrome probability that statistics is obtained.
The equipment operating condition given according to objective time interval is estimated, implements probability in belief network using formula (17) and pushes away
Reason, finally gives the non-precision condition evaluation results of power equipment stoppage in transit probability under the given operating condition of objective time interval is estimated.
Below the inventive method is verified with real system test：
Selection puts into operation defeated in the typical exposure type equipment LGJ-300 type frame sky of Shandong Province somewhere high voltage distribution network on the spot
Electric line is used as object of study, and based on belief network as shown in Figure 4, probability which is stopped transport is implemented non-precision condition and estimated.Should
Area has 2, LGJ-300 molded line road, and its electric pressure is 110kV.Wherein, 1 active time of circuit is 5 years, and which puts into operation certainly
Since add up to stop transport for totally 12 times；2 active time of circuit is 10 years, has added up to stop transport totally 28 times.Within the phase of putting into operation, line outage
Reason mostly be wire end fault isolating switch, insulator breakdown, terminal contact loosely, wire fracture etc. short-circuit and breaking
Fault, field statistics shows, the generation of above-mentioned fault is all closely related with the operating condition of overhead transmission line.
The computing electric power line average stoppage in transit probability of nearly 3 years, as the priori stoppage in transit probability of circuit, embodies currently aging journey
Impact of the degree to equipment operational reliability level.Wherein, circuit 1, circuit 2 occurred to stop transport 7 times, 11 times in nearly 3 years respectively, meter
Calculate its average stoppage in transit probability and be respectively 0.000 27 and 0.000 42.
Being to contrast with non-precision condition method of estimation of the present invention, equipment is asked for using Deterministic Methods and stopping transport and do not stopping transport
The probability distribution that under state, each operating condition occurs.First, varying environment temperature work when occurring to stop transport using formula (8) statistics circuit
The conditional probability that condition occurs, as a result as shown in table 2.Temperature case probability in table 2, when equipment is not stopped transportAccording to
The belief network model of historical data and equipment stoppage in transit probability Estimation is counting acquisition.
2 ambient temperature conditions of table conditional probability distribution under equipment difference running status
2 result of table shows occur the operating mode of high temperature, low temperature ambient temperature when equipment is stopped transport more；And do not stop transport in equipment
Under state, ambient temperature conditions mostly are room temperature, and high temperature is close with probability that worst cold case occurs, this and the on-site gas of circuit
Time condition is consistent.
Similarly, the probability to wind speed, rainfall, thunder and lightning, equipment load and ice and snow operating mode under distinct device running status
Distribution is counted, as a result as shown in table 3 to table 7.
3 wind speed operating mode of table conditional probability distribution under equipment difference running status
4 rainfall operating mode of table conditional probability distribution under equipment difference running status
5 thunder and lightning operating mode of table conditional probability distribution under equipment difference running status
6 equipment load operating mode of table conditional probability distribution under equipment difference running status
7 ice and snow operating mode of table conditional probability distribution under equipment difference running status
As measurement circuit occurs the number of times that stops transport less in its service phase, above-mentioned statistical result lacks enough samples
Data supporting, therefore the deviation to line outage probability Estimation is easily caused based on statistical result shown in table 2 to table 7.In this regard, this
Bright using IDM, to equipment, the probabilistic correlation of various operating conditions under stoppage in transit state is counted, and is replaced with obtaining non-precision probability
For monodrome probability, as a result as shown in table 8.It should be noted that in IDM, s elects 1 as.
Operating condition non-precision conditional probability distribution under 8 equipment stoppage in transit state of table
Based on the above results, 4 kinds of scenes are simulated, under the conditions of giving operating condition, the stoppage in transit probability of circuit 1 and circuit 2
Estimated.
Scene 1：Circuit 1 is currently at normal operating condition, and thunderstorm, temperature occurs in weather forecast 1 hour this area of future
30 DEG C, 6 grades of wind-force, and 1 hour future circuit will be estimated in heavy condition through following 1 hour circuit 1 of short-term load forecasting
Stoppage in transit probability.
Scene 2：Circuit 1 is currently at normal operating condition, and weather forecast 1 hour this area's weather of future is fine, temperature 15
DEG C, 2 grades of wind-force, and normal through following 1 hour 1 load of circuit of short-term load forecasting, estimate that the stoppage in transit of following 1 hour circuit is general
Rate.
Scene 3：Circuit 2 is currently at normal operating condition, and working condition estimates 1 hour future circuit with scene 1
Stoppage in transit probability.
Scene 4：Circuit 2 is currently at normal operating condition, and thunderstorm, temperature occurs in weather forecast 1 hour this area of future
30 DEG C, it is 70% that wind-force reaches 6 grades of probability, and it is 30% that wind-force is 3 to 5 grades of probability, following 1 hour through short-term load forecasting
2 heavy duty of circuit, estimates the stoppage in transit probability of following 1 hour circuit.
Scene 1 and scene 2 simulate severe with the good equipment operating condition of two quasi-representatives respectively, and circuit 1 is stopped transport generally
The non-precision condition of rate and single-valued conditions estimated result are as shown in table 9, table 10.
9 scene of table, 1 circuit, 1 stoppage in transit probability non-precision/single-valued conditions estimated result
10 scene of table, 2 circuit, 1 stoppage in transit probability non-precision/single-valued conditions estimated result
1 result of calculation of scene shows, is compared to priori stoppage in transit probability, under 1 operating condition of given scenario, 1, circuit
The raw probability that stops transport is significantly increased, reason be to estimate objective time interval occur in that be unfavorable for equipment normally the thunderstorm of operation, high temperature,
Strong wind, the working condition of equipment heavy duty, embody adverse effect of the bad working environments to circuit operational reliability level；Meanwhile, base
The monodrome probability that estimates in definitiveness classics Bayesian network method is fallen in non-precision probable range, demonstrates the inventive method
The non-precision probability for obtaining can embody the estimation difference and uncertainty for causing because sample data is not enough.
2 result of calculation of scene shows, as the operating condition for estimating objective time interval circuit 1 is conducive to which normally to run, because
And, the stoppage in transit probability Estimation result under this scene is substantially reduced compared with priori stoppage in transit probability.Meanwhile, it is general that belief network reasoning is obtained
Rate is interval comprising the probit for being obtained based on classical Bayesian network, has further demonstrated that the inventive method objectively can be described
The fluctuation range of transmission line of electricity stoppage in transit probability.
Impact of the ageing equipment level to its operational reliability level with 3 relative analyses of scene of scene 1.Above-mentioned scene
Equipment operating condition is identical, but circuit 1 is different from the active time of circuit 2, and the longer circuit 2 of active time is due to degree of aging
Higher, its priori stoppage in transit probability is larger.In this scenario, using the inventive method and Deterministic Methods to 2 stoppage in transit probability of circuit
Estimated result as shown in table 11.
11 scene of table, 3 circuit, 2 stoppage in transit non-precision/single-valued conditions estimated result
Contrast scene 3 and the result of calculation of scene 1, when equipment occurs the prior probability that stops transport to increase, which is in identical operation
Under working condition, posteriority stoppage in transit probability Estimation result increases therewith, embodies active time increase, degree of aging and increases to equipment fortune
The adverse effect of row reliability.
Scene 4 is counted and equipment is in the uncertainty for estimating that objective time interval operating condition state occurs, and this is also that equipment can
By property assessment average case in practice.Understand according to total probability formula, the substantially equipment estimated by the scene is at two kinds
Different scenes { E1,1,E2,1,E3,1,E4,1,E5,1,E6,2}∪{E1,1,E2,2,E3,1,E4,1,E5,1,E6,2Under stoppage in transit probability weighting
With.Thus, according to the inventive method, this 2 stoppage in transit probability non-precision condition evaluation results of scene circuit is [0.020 49,0.026
46].
4 result of calculation of scene shows, as estimation objective time interval is likely to occur the situation of less wind-force, equipment under the scene
Stoppage in transit probability Estimation result has reduced compared with 3 result of scene, embodies belief network and has the appearance of compatible evidence variable states not
Deterministic ability.
Further, it is the situation of change of investigating the stoppage in transit probability in operation of circuit 2, the present invention is in fact in continuous time
Apply the estimation of non-precision condition.In following 6 hours, the situation of change of 2 operating condition state of circuit is as shown in table 12.According to the present invention
Method of estimation, the situation of change of stoppage in transit probability in the future time period of circuit 2 is as shown in Figure 5.
Can be clearly seen that by Fig. 5, in continuous time, the stoppage in transit probability of circuit 2 is not a fixed value, its
Each estimates the stoppage in transit probit difference of period, embodies equipment operational reliability level and operates therewith working conditions change and time-varying
Feature.Easy to understand, in Fig. 5, stoppage in transit probability upper bound curve is the estimation more conservative to equipment stoppage in transit probability, and stoppage in transit probability
Lower bound curve is the estimation more optimistic to equipment stoppage in transit probability.Meanwhile, the non-precision condition for being drawn using belief network reasoning
Probability results contain the accurate single-valued conditions probability Estimation result of classical Bayesian network, embody non-precision probability and have to setting
The feature that received shipment row reliability level is more fully described, can provide more complete probability letter to Operation of Electric Systems decision-making
Breath.
12 circuit of table, 2 continuous time working condition
For further inspection the present invention propose method effectiveness, the present invention by equipment operating condition be divided into severe with good
Two kinds of scenes.It is assumed that the probability that somewhere bad working environments occur is 0.3, i.e., the probability that good operating mode occurs is 0.7, meanwhile, should
Stoppage in transit probability of regional certain overhead transmission line (circuit 3) under severe, good working condition is respectively 0.005,0.0001.Base
In this, the present invention builds analog systemss and carries out following simulating, verifying test：According to above-mentioned parameter, analog systemss generate totally 50000
The sample of individual hour, operating condition information and equipment running status information of each sample packages containing the period.Further, based on sampling
Gained sample, is utilized respectively article " Fuzzy models of overhead power line weather-related
Application card side's location mode of proposition, article " Modeling weather-related failures of in outages "
Method in the application central limit theorem for proposing in overhead distribution lines " and the present invention is to severe
Under working condition, 3 stoppage in transit probability of circuit is estimated, as a result as shown in Fig. 6 (a) and Fig. 6 (b).
By Fig. 6 (a) and Fig. 6 (b) as can be seen that the stochastic sampling sample for being produced based on analog systemss, moving party of the present invention
Method is compared with proposition in article " Fuzzy models of overhead power line weather-related outages "
Application card side's location mode, article " Modeling weather-related failures of overhead
The application central limit theorem both approaches for proposing in distribution lines " have advantage, show：“Fuzzy
models of overhead power line weather-related outages”、“Modeling weather-
This 2 kinds of methods of related failures of overhead distribution lines " are to the severe operating condition in this area
The interval estimation scope of 3 stoppage in transit probability of lower circuit is larger, although its result can be truly stopped transport probability comprising equipment, but in sampling
When sample size is less, as method estimated result scope is excessive, Practical Project limited use.Can by Fig. 6 (a) and Fig. 6 (b)
See, the estimated result that the inventive method draws all the time significantly close to the actual value of equipment stoppage in transit probability, and with sampling samples
The increase of quantity, the stoppage in transit probability interval that the inventive method draws progressively reduces and converges on equipment truly stops transport probability, embodies
The reasonability of the inventive method estimated result.
Although the above-mentioned accompanying drawing that combines is described to the specific embodiment of the present invention, not model is protected to the present invention
The restriction that encloses, one of ordinary skill in the art are should be understood that on the basis of technical scheme, and those skilled in the art are not
The various modifications that makes by needing to pay creative work or deformation are still within protection scope of the present invention.
Claims (10)
1. the non-precision condition method of estimation of a kind of power equipment stoppage in transit probability, it is characterised in that include：
Using the related operating condition factor of impact power equipment running status as belief network child node, the operation of power equipment
State is used as father node, and then constructs the belief network model of equipment stoppage in transit probability Estimation；
According to the related operating condition historical data of power equipment, prior probability of the power equipment in different running statuses is calculated
And the corresponding condition reliability collection of child node；
The equipment operating condition given according to objective time interval is estimated, in the belief network model of equipment stoppage in transit probability Estimation, base
Implement probability inference in prior probability and the corresponding condition reliability collection of child node, finally give and estimating the given fortune of objective time interval
The non-precision condition evaluation results of power equipment stoppage in transit probability under row operating mode.
2. a kind of non-precision condition method of estimation of power equipment stoppage in transit probability as claimed in claim 1, it is characterised in that shadow
The factor of the related operating condition and running status that ring power equipment includes：Ice and snow, wind speed, ambient temperature, rainfall, thunder and lightning and load
Lotus level.
3. a kind of non-precision condition method of estimation of power equipment stoppage in transit probability as claimed in claim 1, it is characterised in that electricity
The running status of power equipment includes the stoppage in transit state of power equipment and state of not stopping transport.
4. a kind of non-precision condition method of estimation of power equipment stoppage in transit probability as claimed in claim 1, it is characterised in that son
The number of times that the corresponding condition reliability collection of node comes across various operating condition conditions when equipment is stopped transport by statistics is obtained.
5. the non-precision condition method of estimation of a kind of power equipment stoppage in transit probability as claimed in claim 1, it is characterised in that
In the belief network model of equipment stoppage in transit probability Estimation, based on prior probability and the corresponding condition reliability collection of child node, using essence
Really reasoning algorithm is implementing probability inference.
6. the non-precision condition method of estimation of a kind of power equipment stoppage in transit probability as claimed in claim 1, it is characterised in that
In the belief network model of equipment stoppage in transit probability Estimation, based on prior probability and the corresponding condition reliability collection of child node, using near
Implement probability inference like reasoning algorithm.
7. the non-precision condition method of estimation of a kind of power equipment stoppage in transit probability as claimed in claim 1, it is characterised in that adopt
With outer approximate and interior approximate approximate resoning algorithm is included, implement probability in the belief network model of equipment stoppage in transit probability Estimation
Reasoning.
8. a kind of non-precision condition method of estimation of power equipment stoppage in transit probability as claimed in claim 5, it is characterised in that base
Implement probability inference to set up in classical Bayesian network probability inference in prior probability and the corresponding condition reliability collection of child node
On the basis of.
9. the non-precision condition method of estimation of a kind of power equipment stoppage in transit probability as claimed in claim 1, it is characterised in that set
For the reasoning target of the belief network model of stoppage in transit probability Estimation it is：Under the given operating condition condition electric power of objective time interval is estimated
The stoppage in transit probability interval of equipment.
10. the non-precision condition method of estimation of a kind of power equipment stoppage in transit probability as claimed in claim 1, it is characterised in that
The belief network model of the equipment stoppage in transit probability Estimation meets strong Markov condition.
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| CN109783945A (en) * | 2019-01-21 | 2019-05-21 | 电子科技大学 | Based on the non-precision failure model construction method of gamma-generalized inverse Weibull distribution |
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