CN113051741A - Method and device for solving reliability parameters of elements of high-voltage direct-current power transmission system - Google Patents

Method and device for solving reliability parameters of elements of high-voltage direct-current power transmission system Download PDF

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CN113051741A
CN113051741A CN202110290680.5A CN202110290680A CN113051741A CN 113051741 A CN113051741 A CN 113051741A CN 202110290680 A CN202110290680 A CN 202110290680A CN 113051741 A CN113051741 A CN 113051741A
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李凌飞
侯婷
罗炜
姬煜轲
钱海
辛清明
黄莹
喇元
李岩
杨煜
李欢
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Research Institute of Southern Power Grid Co Ltd
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Abstract

The invention provides a method and a device for solving reliability parameters of elements of a high-voltage direct-current power transmission system, wherein the method comprises the following steps: obtaining reliability parameters of elements to be solved of the high-voltage direct-current power transmission system; inputting the reliability parameters of the elements to be solved into a preset reliability evaluation model of the high-voltage direct-current power transmission system, and calculating the reliability index of the high-voltage direct-current power transmission system by adopting a state transition sampling method in a time sequence Monte Carlo; the reliability evaluation model of the high-voltage direct-current power transmission system is constructed by adopting an analytic method; inputting the reliability index into a preset equation set model of the reliability index of the element to be solved; and solving an equation set model of the reliability index related to the element reliability parameter to be solved by adopting an interval algorithm combining interval dichotomy and a Krawczyk-Hansen operator. The method can accurately solve and obtain the reliability parameters of the main elements of the high-voltage direct-current transmission system, thereby providing more reliable basis for reliable and safe operation or planning of the high-voltage direct-current transmission system.

Description

Method and device for solving reliability parameters of elements of high-voltage direct-current power transmission system
Technical Field
The invention relates to the technical field of high-voltage direct-current transmission, in particular to a method and a device for correcting reliability parameters of elements of a high-voltage direct-current transmission system.
Background
The reliability evaluation of the high-voltage direct-current transmission system refers to the capacity of the high-voltage direct-current transmission system for transmitting electric energy in a certain period. The transmission capacity of the high-voltage direct-current transmission system is large, and once a fault occurs, huge loss is caused, so that the method has great practical significance in accurately quantifying the reliability of the high-voltage direct-current transmission system.
During planning of the direct-current transmission project, the reliability of a planning scheme generally needs to be calculated to evaluate whether the scheme meets a preset reliability requirement, and then extension or reinforcement measures are selected. In general, reliability evaluation estimates system reliability indicators based on topology, component reliability parameters (failure rate and repair time), and the like. However, the reliability parameters of the components are usually obtained from historical failure statistics data, and therefore, the data are often influenced by various uncertainties, which are mainly reflected in the following aspects: 1) massive statistical data are involved in the power system, and invalid records or missing exist inevitably; 2) the reliability parameters of the elements change along with the aging of the equipment, and if the data is not updated timely, the reliability parameters are inaccurate; 3) in some cases, the reliability parameters are manually input, but the reliability parameters are inaccurate due to different personnel qualities.
Therefore, for the high-voltage direct-current transmission system, the selection of the element reliability parameters directly influences the accuracy of reliability evaluation of the high-voltage direct-current transmission system, and even influences the reliable and safe operation of the planned direct-current transmission system. In addition, for the grid company, the false reliability evaluation result may also mislead the bid of the dc transmission equipment. Therefore, obtaining accurate device reliability parameters is a key issue for reliability evaluation.
Therefore, how to obtain accurate device reliability parameters and improve the accuracy of reliability evaluation is a technical problem to be solved urgently by those skilled in the art.
Disclosure of Invention
In view of this, the present invention provides a method and an apparatus for solving reliability parameters of components of a high voltage direct current transmission system, aiming at solving the problem that the reliability parameters of components in an actual direct current transmission project are inaccurate, so as to accurately solve the reliability parameters of main components of the high voltage direct current transmission system, thereby providing a more reliable basis for reliable and safe operation or planning of the high voltage direct current transmission system.
In order to solve the above technical problem, an embodiment of the present invention provides a method for solving reliability parameters of an element of a high voltage direct current transmission system, including:
obtaining reliability parameters of elements to be solved of the high-voltage direct-current power transmission system;
inputting the reliability parameters of the elements to be solved into a preset reliability evaluation model of the high-voltage direct-current power transmission system, and calculating the reliability index of the high-voltage direct-current power transmission system by adopting a state transition sampling method in a time sequence Monte Carlo; the reliability evaluation model of the high-voltage direct-current power transmission system is constructed by adopting an analytic method;
inputting the reliability index into a preset equation set model of the reliability index of the element to be solved;
and solving an equation set model of the reliability index related to the element reliability parameter to be solved by adopting an interval algorithm combining interval dichotomy and a Krawczyk-Hansen operator.
Further, the equation set model construction method of the reliability index about the reliability parameter of the element to be solved comprises the following steps:
constructing a reliability evaluation model of the high-voltage direct-current power transmission system by adopting an analytic method;
acquiring reliability parameters of all elements of the high-voltage direct-current transmission system;
inputting the reliability parameters of all the elements into a reliability evaluation model of the high-voltage direct-current power transmission system, and calculating the reliability index of the high-voltage direct-current power transmission system by adopting a state transition sampling method in a time sequence Monte Carlo;
according to the reliability parameters of all the elements and the reliability indexes, an analytic model of the reliability indexes of the high-voltage direct-current power transmission system about the element reliability parameters is constructed by adopting a full probability formula;
and constructing an equation set model of the reliability index of the element to be solved according to the analytic model of the reliability index of the high-voltage direct-current power transmission system on the element reliability parameter.
Further, if the high-voltage dc transmission system is a double 12-pulse high-voltage dc transmission system, the element reliability parameters include an element failure rate and an element repair rate, and the reliability indexes of the high-voltage dc transmission system include an energy unavailability rate, a unipolar forced outage number, and a bipolar forced outage number, the calculating the reliability index of the high-voltage dc transmission system by using a state transition sampling method in a time sequence monte carlo specifically includes:
step 3.1, assuming that the component state duration follows exponential distribution, and the components are all normal at the initial moment;
step 3.2, calculating the system state duration T according to the formula (1)kIn the formula (1), m is the total number of outward transition conditions of the current state, and U is [0,1 ]]Random number of between, lambdaiFor the state transition rate of the element i, i.e. the reliability parameter, τiThe state transition rate of the element i is equal to τiIs the component failure rate or component repair rate;
Figure BDA0002982456970000031
step 3.3, calculating the state transition probability P of the element j according to the following formula (2)jAnd obtaining the cumulative transition probability P of the element according to the formula (3)i；
Figure BDA0002982456970000032
Figure BDA0002982456970000041
Step 3.4, carrying out element state transition positioning according to the formula (4), if ChIf 1, the state of the element is transferred, otherwise, the state of the element remains unchanged.
Ch＝find(Pi＞rand(1)) (4)；
Wherein, ChWhether the recording state is transferred or not is indicated, namely whether the element is transferred from the normal state to the fault state or not is seen;
step 3.5, after obtaining a certain number of system states, calculating the system state SState；
Step 3.6, updating the reliability index according to the formulas (5), (6) and (7), and counting the times of forced shutdown of the single pole and the double pole;
Figure BDA0002982456970000042
Figure BDA0002982456970000043
EOT(i)＝Ti(1-available capacity during outage ÷ PS) (7)；
In the formula, EU is the energy unavailability rate, and T is the time scale; TEOT is total equivalent outage time in T; EOT (i) is the ith equal outage time in the year; n is the total outage times; ti represents the ith actual fault outage time, and Ps represents the rated capacity of the system;
and 3.7, calculating a variance coefficient n, as shown in formula (8), if n is smaller than a preset constant, stopping iterative calculation, and outputting a corresponding reliability index, otherwise, repeating the steps 3.2-3.4 to generate a new system state.
Figure BDA0002982456970000044
Wherein T is a time scale.
Further, if the hvdc transmission system is a double 12-pulse hvdc transmission system, the element reliability parameters include an element failure rate and an element repair rate, and the reliability indexes of the hvdc transmission system include an energy unavailability rate, a unipolar forced outage frequency and a bipolar forced outage frequency, then obtaining an analytic model of the reliability indexes of the hvdc transmission system with respect to the element reliability parameters by using a full probability formula according to the reliability parameters of all the elements and the reliability indexes, specifically including:
the failure rate lambda of the element 1 is determined by knowing the energy unavailability rate EU, the monopolar forced shutdown frequency MFOT and the bipolar forced shutdown frequency BFOT1And rate of repair mu1Are unknown, failure rate λ of element 22Unknown, repair Rate mu of component 33Unknown, since the number of elements whose parameters are unknown is 3, the combination of the states of these elements has a total of 23In 8 cases, the unknown parameter vector λ of the elements 1,2,3 is denoted by X1,μ1,λ2,μ3]Then, the analytic model of the energy unavailability EU, the analytic model of the unipolar forced outage times MFOT, and the analytic model of the bipolar forced outage times BFOT are respectively:
(1) the analytic model of the energy unavailability EU is
Figure BDA0002982456970000051
In the above formula (9), Ai、Ui(i ═ 1,2,3) represents the steady-state availability and the steady-state unavailability, ai＝μi/(λi+μi)， Ui＝λi/(λi+μi)，
Figure BDA0002982456970000054
Expressed as:
Figure BDA0002982456970000052
in the above formula (10), B _ EUjA set of system outage events representing 3 elements under study in a jth combined state; phibIndicating the normal operating conditions of the system in each case excluding the conditions already listed above for the above formula;
Figure BDA0002982456970000053
is phibThe complement of (1); c represents correspondencePer unit value of capacity state in state;
(2) and the analytic model of the single-pole forced outage frequency MFOT is as follows:
Figure BDA0002982456970000061
in the above-mentioned formula (11),
Figure BDA0002982456970000066
expressed as:
Figure BDA0002982456970000062
in the formula (12), B _ MFOTjA set of system unipolar forced outage events representing 3 elements under study in a jth combined state;
(3) the analytic model of the bipolar forced outage times BFOT is as follows:
Figure BDA0002982456970000063
in the above-mentioned formula (13),
Figure BDA0002982456970000067
expressed as:
Figure BDA0002982456970000064
in formula (14), B _ BFOTjA set of system bipolar forced outage events representing 3 elements under study in the jth combination state.
Further, the equation set model of the reliability index with respect to the reliability parameter of the element to be solved specifically includes:
Figure BDA0002982456970000065
wherein, EU0、MFOT0、BFOT0Respectively representing given values of an energy unavailability rate EU, a monopolar forced outage frequency MFOT and a bipolar forced outage frequency BFOT; f. ofEU(X)、fMFOT(X) and fBFOTAnd (X) are nonlinear equations of the energy unavailability rate EU, the unipolar forced outage times MFOT and the bipolar forced outage times BFOT respectively.
Further, the solving of the equation set model of the reliability index about the element reliability parameter to be solved by using an interval algorithm combining interval dichotomy and a Krawczyk-Hansen operator specifically comprises:
step 6.1: let [ X ]]＝[X]0∈I(Rn) Initializing a table binary interval table B and solving an interval table T; initializing a binary variable number b as 1, a binary interval table length l as 1, giving convergence precision epsilon and xi of a solution interval, and initializing an interval width coefficient alpha;
step 6.2: calculation of H (X) and Z ═ X ≠ H (X) according to the Krawczyk-Hansen operator
Figure BDA0002982456970000071
H'＝H(y,X)∩X
Figure BDA0002982456970000072
m(X)＝(m(X1),m(X2),...m(Xn))T
Wherein X is an interval vector; h (X) is Krawczyk-Hansen operator; y is the midpoint of the interval solution X; m (X) is the midpoint of the interval vector X; i is an n-order identity matrix; y is an n-order nonsingular matrix; l (X) and U (X) are interval matrixes [ I-YF' (X)]Lower triangular matrix and upper triangular matrix X1And
Figure BDA0002982456970000074
respectively representing the upper and lower bounds of the first component of the interval solution X; xnIs the nth component of the interval solution X.
Step 6.3: judging the existence and uniqueness of the solution according to the inclusion relationship between Z and X; if it is
Figure BDA0002982456970000073
Turning to step 6.6; if W (X) belongs to X, then there is a solution on X, go to step 6.4; if W (Z)<α w (X), then X ═ Z, go to step 6.2; otherwise, turning to step 6.5; (ii) a Wherein W (X) is the width of the interval X, and W (Z) is the width of the interval Z;
step 6.4: taking m (X) as an initial value, and performing iterative calculation by using a point Newton method to obtain a solution X of the equation set, and storing the solution X in a table T;
step 6.5: if W (X)<ξ, then X is stored in T, and step 6.6 is carried out. Halving the component Xb of the interval vector X to obtain
Figure BDA0002982456970000081
Will 2 bX,m(Xb)]Store into interval table B, order
Figure BDA0002982456970000082
B +1, turning to step 6.2;
step 6.6: if l is 0, go to step 6.7. Taking out the interval arranged at the head from the interval table B, assigning X to l-1, and going to step 6.2;
step 6.7: outputting all solution intervals in the table T; if T is an empty set, the system of equations is unsolved.
In a second aspect, an embodiment of the present invention provides an apparatus for solving reliability parameters of components of a high-voltage direct-current power transmission system, including:
the acquiring unit is used for acquiring reliability parameters of elements to be solved of the high-voltage direct-current power transmission system;
the first input unit is used for inputting the reliability parameters of the elements to be solved into a preset reliability evaluation model of the high-voltage direct-current power transmission system and calculating the reliability index of the high-voltage direct-current power transmission system by adopting a state transition sampling method in time sequence Monte Carlo; the reliability evaluation model of the high-voltage direct-current power transmission system is constructed by adopting an analytic method;
the second input unit is used for inputting the reliability index into a preset equation set model of the reliability index of the element to be solved;
and the solving unit is used for solving an equation set model of the reliability index related to the element reliability parameters to be solved by adopting an interval algorithm combining interval dichotomy and a Krawczyk-Hansen operator.
Further, the equation set model construction method of the reliability index about the reliability parameter of the element to be solved comprises the following steps:
constructing a reliability evaluation model of the high-voltage direct-current power transmission system by adopting an analytic method;
acquiring reliability parameters of all elements of the high-voltage direct-current transmission system;
inputting the reliability parameters of all the elements into a reliability evaluation model of the high-voltage direct-current power transmission system, and calculating the reliability index of the high-voltage direct-current power transmission system by adopting a state transition sampling method in a time sequence Monte Carlo;
according to the reliability parameters of all the elements and the reliability indexes, an analytic model of the reliability indexes of the high-voltage direct-current power transmission system about the element reliability parameters is constructed by adopting a full probability formula;
and constructing an equation set model of the reliability index of the element to be solved according to the analytic model of the reliability index of the high-voltage direct-current power transmission system on the element reliability parameter.
In a third aspect, an embodiment of the present invention provides an apparatus for solving reliability parameters of components of an hvdc power transmission system, including a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein the processor, when executing the computer program, implements a method for solving reliability parameters of components of an hvdc power transmission system as described in any one of the above.
In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium, which includes a stored computer program, where the computer program, when executed, controls an apparatus where the computer-readable storage medium is located to perform a method for solving a reliability parameter of an element of an hvdc power transmission system according to any one of the above claims.
The invention provides a method for solving element reliability parameters of a high-voltage direct-current power transmission system, which comprises the following steps of firstly, obtaining element reliability parameters to be solved of the high-voltage direct-current power transmission system; inputting the reliability parameters of the elements to be solved into a preset reliability evaluation model of the high-voltage direct-current power transmission system, and calculating the reliability index of the high-voltage direct-current power transmission system by adopting a state transition sampling method in a time sequence Monte Carlo; the reliability evaluation model of the high-voltage direct-current power transmission system is constructed by adopting an analytic method; inputting the reliability index into a preset equation set model of the reliability index of the element to be solved; and solving an equation set model of the reliability index related to the element reliability parameter to be solved by adopting an interval algorithm combining interval dichotomy and a Krawczyk-Hansen operator. Through the design, the reliability parameters of the main elements of the high-voltage direct-current transmission system can be accurately solved, so that a more reliable basis can be provided for reliable and safe operation or planning of the high-voltage direct-current transmission system.
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In order to more clearly illustrate the technical solution of the present invention, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic flow chart of a method for solving reliability parameters of components of a high-voltage direct-current power transmission system according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a subsystem division of a dual 12-pulse wire HVDC system;
fig. 3 is a schematic diagram of an ac filter subsystem in a dual 12-pulse wire-connection hvdc transmission system.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be understood that the step numbers used herein are for convenience of description only and are not intended as limitations on the order in which the steps are performed.
It is to be understood that the terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in the specification of the present invention and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.
The terms "comprises" and "comprising" indicate the presence of the described features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
The term "and/or" refers to and includes any and all possible combinations of one or more of the associated listed items.
Example 1:
the embodiment of the invention provides a method for correcting element reliability parameters of a high-voltage direct-current power transmission system, which comprises the following steps of S1-S4:
and S1, obtaining reliability parameters of the elements to be solved of the high-voltage direct-current power transmission system.
Specifically, the component reliability parameters include a component failure rate and a component repair rate.
S2, inputting the reliability parameters of the elements to be solved into a preset reliability evaluation model of the high-voltage direct-current power transmission system, and calculating the reliability index of the high-voltage direct-current power transmission system by adopting a state transition sampling method in a time sequence Monte Carlo; the reliability evaluation model of the high-voltage direct-current power transmission system is constructed by adopting an analytic method.
Specifically, the reliability index of the high-voltage direct-current transmission system comprises an energy unavailability rate, a unipolar forced outage frequency and a bipolar forced outage frequency, and the preset reliability evaluation model of the high-voltage direct-current transmission system is not a preset reliability evaluation model of the double-12-pulse high-voltage direct-current transmission system.
And S3, inputting the reliability index into a preset equation set model of the reliability index of the element to be solved.
And S4, solving an equation set model of the reliability index related to the element reliability parameters to be solved by adopting an interval algorithm combining interval dichotomy and a Krawczyk-Hansen operator.
The invention provides a method for solving element reliability parameters of a high-voltage direct-current power transmission system, which comprises the following steps of firstly, obtaining element reliability parameters to be solved of the high-voltage direct-current power transmission system; inputting the reliability parameters of the elements to be solved into a preset reliability evaluation model of the high-voltage direct-current power transmission system, and calculating the reliability index of the high-voltage direct-current power transmission system by adopting a state transition sampling method in a time sequence Monte Carlo; the reliability evaluation model of the high-voltage direct-current power transmission system is constructed by adopting an analytic method; inputting the reliability index into a preset equation set model of the reliability index of the element to be solved; and solving an equation set model of the reliability index related to the element reliability parameter to be solved by adopting an interval algorithm combining interval dichotomy and a Krawczyk-Hansen operator. Through the design, the reliability parameters of the main elements of the high-voltage direct-current transmission system can be accurately solved, so that a more reliable basis can be provided for reliable and safe operation or planning of the high-voltage direct-current transmission system.
As an example of the embodiment of the present invention, the method for constructing the equation set model of the reliability index with respect to the reliability parameter of the element to be solved includes:
s31, constructing a reliability evaluation model of the high-voltage direct-current power transmission system by adopting an analytic method;
it should be noted that the high-voltage direct-current transmission system includes a plurality of subsystems, and when the high-voltage direct-current transmission system is evaluated, the whole high-voltage direct-current transmission system is often divided into a plurality of subsystems, as shown in fig. 2, the high-voltage direct-current transmission system is schematically divided into two 12-pulse-wave high-voltage direct-current transmission system subsystems, including a converter transformer subsystem, an alternating-current filter subsystem, a direct-current transmission line subsystem, a valve bank subsystem, and a direct-current. The reliability model of the high-voltage direct-current transmission system can be obtained by constructing a reliability evaluation model of each subsystem of the high-voltage direct-current transmission system. The specific process of establishing the reliability evaluation model of each subsystem of the double 12-pulse high-voltage direct-current transmission system is as follows:
(1) converter transformer subsystem
In fig. 2, the a-module represents the converter transformer subsystem. The module a can know that:
each pole of the converter transformer subsystem is provided with 12 converter transformers, wherein 6 converter transformers are respectively connected with Y/Y and Y/delta;
each converter valve is connected with converter transformers with different wiring, wherein, 3 sets of Y/Y and Y/delta wiring are respectively connected;
therefore, the typical component group is shut down to 6 converter transformers corresponding to a single 12-pulse converter valve, the converter transformer subsystem cannot be directly equivalent to a multi-state component for reliability evaluation, and the method adopts a simplified equivalence method to solve the problem, namely 3Y/Y corresponding to each converter valve and 3Y/delta-connected converter transformers are respectively equivalent to 1 component. According to the module a, 3Y/Y corresponding to each converter valve and 3 converter transformers of Y/delta connection are in a series structure, and according to the equivalent formula of the fault rate and the repair rate of the series structure, the equivalent element fault rate and the equivalent repair rate can be obtained and are respectively shown in the following formulas.
Figure BDA0002982456970000131
Figure BDA0002982456970000132
In the formula, n is the number of elements, and is 6; con is a converter transformer wiring mode, Y/Y type or Y/delta type; lambda [ alpha ]i_conAnd mui_conThe fault rate and the repair rate of the ith Y/Y or Y/delta type wiring converter transformer are respectively set; lambda [ alpha ]s_conAnd mus_conThe equivalent failure rate and the repair rate of the converter transformer corresponding to one converter valve are respectively.
(2) AC filter subsystem
In fig. 2, the b block represents the ac filter subsystem, which is structured as shown in fig. 3. As can be seen from fig. 3: the alternating current filter subsystem has more elements and mainly comprises a main bus, a small bus, a circuit breaker and an alternating current filter; the structure is relatively complex, but the alternating current filter and the circuit breaker connected with the alternating current filter, the small bus and the circuit breaker connected with the small bus are in series connection, so that the alternating current filter can be equivalent to 3 types of elements of the main bus, the small bus and the alternating current filter according to the calculation formula of the fault rate and the repair time. However, in actual engineering, different types and models of ac filters are often used, and therefore, a certain way is needed to determine the capacity state of the ac filter subsystem, and the present invention adopts a capacity state table, which is introduced as follows:
assuming class 4 AC filters, respectively F1、F2、F3、F4Represents; the number of each category is recorded as N1、 N2、N3、N4. The invention defines the commissioning equivalence to be expressed as: seq＝(N1*1000+N2*100+N3*10+ N41), the commissioning equivalence and the capacity state are in one-to-one correspondence, and the capacity state in each commissioning situation can be determined through the commissioning equivalence. Such as F1After the type AC filter fails, the equivalent system operation value Seq1＝SeqAnd 1000, determining the system capacity state according to the commissioning equivalence table.
(3) DC transmission line subsystem
In fig. 2, the c-block represents a dc transmission line subsystem, in which the components are primarily hvdc transmission lines, and thus can be directly equivalent to two-state components.
(4) Valve group subsystem
In fig. 2, the d-block represents a valve group subsystem, which includes two 12-pulse converter valve groups of the same polarity, wherein each 12-pulse converter valve group is connected in series by two 6-pulse valves. Therefore, each 12-pulse valve set can be equivalent to a two-state element according to the above calculation formula of the failure rate and the repair time. The two 12-pulse valve groups are in a parallel relationship in reliability, that is, the failure of any valve group only causes the corresponding pole to lose 50% of capacity.
(5) DC field subsystem
In fig. 2, the e-block represents a dc field subsystem, in which the main components are a dc filter and a smoothing reactor, and a failure of either component will cause the electrode to be out of operation, so that the two components are in a series relationship, and can be equivalent to a two-state component according to the above calculation formula of failure rate and repair time.
And S32, acquiring reliability parameters of all elements of the high-voltage direct-current power transmission system.
Specifically, the component reliability parameters include a component failure rate and a component repair rate.
And S33, inputting the reliability parameters of all the elements into a reliability evaluation model of the high-voltage direct-current power transmission system, and calculating the reliability index of the high-voltage direct-current power transmission system by adopting a state transition sampling method in a time sequence Monte Carlo.
In the embodiment of the invention, the system state transition sampling method is a sequential Monte Carlo method for sampling the state transition of the whole system, and the key point is to determine the duration of the current state of the system and the next state and duration of the system. And finally, calculating to obtain the system reliability index through a large number of samples. The reliability indexes of the double 12-pulse high-voltage direct-current transmission system comprise: energy unavailability EU, unipolar forced outage times MFOT and bipolar forced outage times BFOT. The definitions of the energy unavailability rate EU, the unipolar forced shutdown times MFOT and the bipolar forced shutdown times BFOT are as follows:
(1) rate of energy unavailability
Figure BDA0002982456970000151
Figure BDA0002982456970000152
EOT(i)＝Ti(1-available capacity during outage ÷ PS)
Wherein T is a time scale; TEOT is total equivalent outage time in T; EOT (i) is the ith equal outage time in the year; and N is the total shutdown number.
(2) Number of monopole forced outages
The MFOT index is defined as the number of times a monopolar forced outage occurs in a high voltage direct current transmission system (HVDC) during ttime.
(3) Number of bipolar forced outages
The BFOT indicator is defined as the number of bipolar forced outages of a high voltage direct current transmission system (HVDC) during time T.
Specifically, if the high-voltage dc transmission system is a double 12-pulse high-voltage dc transmission system, the element reliability parameters include an element failure rate and an element repair rate, and the reliability indexes of the high-voltage dc transmission system include an energy unavailability rate, a unipolar forced outage number, and a bipolar forced outage number, the calculating the reliability index of the high-voltage dc transmission system by using a state transition sampling method in a time sequence monte carlo specifically includes:
step 331, assuming that the component state duration follows exponential distribution, and the components are all normal at the initial moment;
step 332, calculating the system state duration T according to the formula (1)kIn the formula (1), m is the total number of outward transition conditions of the current state, and U is [0,1 ]]Random number of between, lambdaiAs the state transition rate of element i
Figure BDA0002982456970000161
Step 333 of calculating the state transition probability P of the element j according to the following expression (2)jAnd obtaining the cumulative transition probability P of the element according to the formula (3)i；
Figure BDA0002982456970000162
Figure BDA0002982456970000163
Step 334, element state transition positioning is carried out according to the formula (4), if ChIf 1, the state of the element is transferred, otherwise, the state of the element remains unchanged.
Ch＝find(Pi＞rand(1)) (4)；
Wherein, ChWhether the recording state is transferred or not is indicated, namely whether the element is transferred from the normal state to the fault state or not is seen;
step 335, after obtaining a certain number of system states, calculating a system state SState；
Step 336, updating the reliability index according to the formulas (5), (6) and (7), and counting the forced shutdown times of the single pole and the double pole;
Figure BDA0002982456970000164
Figure BDA0002982456970000165
EOT(i)＝Ti(1-available capacity during outage ÷ PS) (7)；
In the formula, EU is the energy unavailability rate, and T is the time scale; TEOT is total equivalent outage time in T; EOT (i) is the ith equal outage time in the year; n is the total outage times; ti represents the ith actual fault outage time, and Ps represents the rated capacity of the system;
337, calculating a variance coefficient n, as shown in formula (8), if n is smaller than a preset constant, stopping iterative calculation, and outputting a corresponding reliability index, otherwise, repeating 332 and 334 to generate a new system state.
Figure BDA0002982456970000171
Wherein T is a time scale.
And S34, constructing an analytic model of the reliability index of the high-voltage direct-current power transmission system relative to the element reliability parameters by adopting a full probability formula according to the reliability parameters of all the elements and the reliability indexes.
In the embodiment of the invention, the analytic model of the reliability index of the high-voltage direct-current power transmission system relative to the element reliability parameter is an analytic expression of the reliability index of the high-voltage direct-current power transmission system relative to the element reliability parameter.
Specifically, according to the reliability parameters and the reliability indexes, an analytic model of the energy unavailability rate EU, the monopolar forced outage times MFOT and the bipolar forced outage times BFOT of the double-12-pulse-wave high-voltage direct-current power transmission system can be constructed by using a total probability formula.
Assuming that the energy unavailability rate EU and the number of unipolar forced outages MFOT and the number of bipolar forced outages BFOT are known, the failure rate λ of the element 1 is1And rate of repair mu1Are unknown, failure rate λ of element 22Unknown, repair Rate mu of component 33Unknown, so as to derive a component reliability parameter solution model. The number of elements whose parameters are unknown is 3, the combination of the states of these elements has a total of 23In 8 cases, the embodiment of the present invention uses X to denote the unknown parameter vector λ of elements 1,2,31,μ1,λ2,μ3]Then, the analytic model of the energy unavailability EU and the analytic model of the monopole forced outage number MFOT are respectively as follows:
(1) the analytic model of the energy unavailability EU is as follows:
Figure BDA0002982456970000181
in the above formula, Ai、Ui(i ═ 1,2,3) represents the steady-state availability and the steady-state unavailability, ai＝μi/(λi+μi)，Ui＝λi/(λi+μi)，
Figure BDA0002982456970000188
Expressed as:
Figure BDA0002982456970000182
in the above formula, B _ EUjA set of system outage events representing 3 elements under study in a jth combined state; phibIndicating the normal operating conditions of the system in each case excluding the conditions already listed above for the above formula;
Figure BDA0002982456970000186
is phibThe complement of (1); c represents a capacity state per unit value in the corresponding state.
(2) And the analytic model of the single-pole forced outage frequency MFOT is as follows:
Figure BDA0002982456970000183
in the above formula, the first and second carbon atoms are,
Figure BDA0002982456970000187
expressed as:
Figure BDA0002982456970000184
in the formula, B _ MFOTjA set of system unipolar forced outage events representing 3 elements under study in the jth combination state.
(3) The analytic model of the bipolar forced outage times BFOT is as follows:
Figure BDA0002982456970000185
in the above formula, the first and second carbon atoms are,
Figure BDA0002982456970000193
expressed as:
Figure BDA0002982456970000191
in the formula, B _ BFOTjA set of system bipolar forced outage events representing 3 elements under study in the jth combination state.
And S35, constructing an equation set model of the reliability index of the element to be solved according to the analytic model of the reliability index of the high-voltage direct-current power transmission system on the element reliability parameter.
In the embodiment of the present invention, it should be understood that the equation set model of the reliability index with respect to the reliability parameter of the component to be solved is an equation set of the reliability index with respect to the reliability parameter of the component to be solved.
The reliability index is an equation set model of the reliability parameter of the element to be solved, and specifically comprises the following steps:
Figure BDA0002982456970000192
wherein, EU0、MFOT0、BFOT0Respectively representing given values of an energy unavailability rate EU, a monopolar forced outage frequency MFOT and a bipolar forced outage frequency BFOT; f. ofEU(X)、fMFOT(X) and fBFOTAnd (X) are nonlinear equations of the energy unavailability rate EU, the unipolar forced outage times MFOT and the bipolar forced outage times BFOT respectively.
The equation in the above equation is expressed as the following equation:
F(X)＝0。
and S5, solving a nonlinear equation set model of the reliability index related to the element reliability parameter to be solved by adopting an interval algorithm combining interval dichotomy and a Krawczyk-Hansen operator.
Specifically, the specific step of solving the nonlinear equation set to obtain the element reliability parameter interval of the double-12-pulse-wave high-voltage direct-current power transmission system comprises the following steps:
step 6.1: let [ X ]]＝[X]0∈I(Rn) Initializing the table, dividing the interval table B, and solving the interval table T. Initializing a binary variable number b as 1, a binary interval table length l as 1, giving convergence precision epsilon and xi of a solution interval, and initializing an interval width coefficient alpha; wherein, [ X ]]0Represents a given value;
step 6.2: h (X) and Z ═ X ≠ h (X) are calculated according to the Krawczyk-Hansen operator.
H(y,X)＝y-Yf(y)+L(X)(H'-y) +U(X)(X-y)，y∈X
H'＝H(y,X)∩X
Figure BDA0002982456970000201
m(X)＝(m(X1),m(X2),...m(Xn))T
Wherein X is an interval vector; h (X) is Krawczyk-Hansen operator, y is the midpoint m of the interval solution X (X) is the midpoint of the interval vector X; i is an n-order identity matrix; y is an n-order nonsingular matrix; l (X) and U (X) are interval matrixes [ I-YF' (X)]A lower triangular matrix and an upper triangular matrix of,X 1and
Figure BDA0002982456970000202
respectively representing the upper and lower bounds of the first component of the interval solution X; xnIs the nth component of the interval solution X.
Step 6.3: and judging the existence and uniqueness of the solution according to the inclusion relationship between Z and X. If it is
Figure BDA0002982456970000203
Turning to step 6.6; if W (X) belongs to X, then there is a solution on X, go to step 6.4; if W (Z)<α w (X), then X ═ Z, go to step 6.2; otherwise, turning to step 6.5; wherein W (X) is the width of the interval X, and W (Z) is the width of the interval Z.
Step 6.4: taking m (X) as an initial value, and performing iterative calculation by using a point Newton method to obtain a solution X of the equation set, and storing the solution X in a table T;
step 6.5: if W (X)<ξ, then X is stored in T, and step 6.6 is carried out. Halving the component Xb of the interval vector X to obtain
Figure BDA0002982456970000204
Will 2 bX,m(Xb)]Store into interval table B, order
Figure BDA0002982456970000205
And (5) switching to step 6.2 when the bisection number b is equal to b + 1.
Step 6.6: if l is 0, go to step 6.7. The first-ranked segment is taken from the segment table B and given X, l equals l-1, and the process goes to step 6.2.
Step 6.7: and outputting all solution intervals in the table T. If T is an empty set, the system of equations is unsolved.
In order to verify whether the method can accurately solve and obtain the reliability parameters of the main elements of the high-voltage direct-current transmission system, the method for solving the reliability parameters of the elements of the high-voltage direct-current transmission system provided by the invention is applied to an actual high-voltage direct-current transmission system, and the specific implementation process is as follows:
firstly, obtaining element reliability parameters of the double-12-pulse-wave-connection high-voltage direct-current power transmission system, including element failure rate and element repair time. The schematic diagram of the high-voltage direct-current transmission engineering with double 12-pulse connection is shown in fig. 2. The inverter side and the rectifier side have 24 converter transformers, 4 groups of valve banks and also comprise smoothing reactors, alternating current filters and the like, wherein the smoothing reactors have three types. The original parameters of each element are shown in table 1.
TABLE 1 Dual 12-pulse wiring reliability parameters of ultra-high voltage DC power transmission system
Figure BDA0002982456970000211
And secondly, calculating the reliability index energy unavailability rate EU, the monopolar forced outage times MFOT and the bipolar forced outage times BFOT by using a state transition sampling method in the time sequence Monte Carlo.
The method adopts a state transition sampling method to calculate the state outage capacity of the double-12-pulse-wave-connection high-voltage direct-current power transmission system, and is shown in a table 2, wherein the state probability and the frequency index of each fault capacity state are respectively given in the table. The calculation results of the reliability indexes of the double-12-pulse-wave-connection high-voltage direct-current transmission system are shown in table 3.
TABLE 2 probability and frequency calculation results corresponding to capacity state of double-12-pulse-wave-connection HVDC system
Figure BDA0002982456970000221
TABLE 3 evaluation results of main reliability indexes of double-12-pulse-wave-connection high-voltage direct-current transmission system
Figure BDA0002982456970000222
And thirdly, inputting the reliability index obtained in the second step into an equation set model of the reliability index related to the reliability parameters of the element to be obtained, and solving the equation set model of the reliability index related to the reliability parameters of the element to be obtained by adopting an interval algorithm combining interval dichotomy and a Krawczyk-Hansen operator.
Fourthly, when only one of 3 reliability indexes of the forced energy unavailability rate, the unipolar forced outage rate and the bipolar forced outage rate is known, solving any one element reliability parameter in the failure rate and the repair rate of the elements 1,2 and 3, namely lambda1、λ2、λ3、μ1、μ2、μ3The reliability parameter of any one of the elements and the solution result are shown in table 4.
Fifthly, when any two of 3 reliability indexes of forced energy unavailability, unipolar forced outage rate and bipolar forced outage rate are known, lambda is obtained1、λ2、λ3、μ1、μ2、μ3The results of solving the partial results of the combination of any two reliability parameters of the elements are shown in Table 5Shown in the figure.
Sixthly, when 3 reliability indexes of the forced energy unavailability rate, the unipolar forced outage rate and the bipolar forced outage rate are known, calculating lambda1、λ2、λ3、μ1、μ2、μ3The results of solving for any three combinations of reliability parameters of the elements are shown in table 6.
TABLE 4 parameter solving calculation results
Figure BDA0002982456970000231
Figure BDA0002982456970000241
TABLE 5 parameter solving calculation results
Figure BDA0002982456970000242
TABLE 6 parameter solving calculation results
Figure BDA0002982456970000243
The calculation result shows that the accurate interval solution of the element reliability parameters can be found in a larger initial parameter value interval, namely the reliability parameters of the main elements of the HVDC system can be accurately solved, and a more reliable basis is provided for reliable and safe operation or planning of the direct current transmission system.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention.
Example 2:
the embodiment of the invention provides a device for correcting the reliability parameters of elements of a high-voltage direct-current transmission system, which comprises:
the system comprises a construction unit, a data processing unit and a data processing unit, wherein the construction unit is used for constructing a reliability evaluation model of the high-voltage direct-current power transmission system by adopting an analytic method;
the acquiring unit is used for acquiring reliability parameters of all elements of the high-voltage direct-current transmission system;
the reliability index calculation unit is used for inputting the reliability parameters of all the elements into a reliability evaluation model of the high-voltage direct-current transmission system and calculating the reliability index of the high-voltage direct-current transmission system by adopting a state transition sampling method in a time sequence Monte Carlo;
the establishing unit is used for obtaining an analytic expression of the reliability index of the high-voltage direct-current power transmission system relative to the element reliability parameter by adopting a full probability formula according to the reliability parameters of all the elements and the reliability index, and establishing an equation set of the reliability index relative to the element reliability parameter to be solved according to the analytic expression of the reliability index of the high-voltage direct-current power transmission system relative to the element reliability parameter;
and the correcting unit is used for solving an equation set of the reliability index about the element reliability parameter to be solved by adopting an interval algorithm combining interval dichotomy and a Krawczyk-Hansen operator to obtain the corrected reliability parameter.
Example 3:
in a third aspect, an embodiment of the present invention provides an apparatus for solving reliability parameters of components of an hvdc power transmission system, including a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein the processor, when executing the computer program, implements a method for solving reliability parameters of components of an hvdc power transmission system as described in any of the embodiments above.
Example 4:
the invention further provides a computer-readable storage medium, which specifically includes a stored computer program, where when the computer program runs, the apparatus where the computer-readable storage medium is located is controlled to execute the method for solving the reliability parameter of the component of the high-voltage direct current power transmission system according to any of the above embodiments.
It should be noted that, all or part of the flow in the method according to the above embodiments of the present invention may also be implemented by a computer program instructing related hardware, where the computer program may be stored in a computer-readable storage medium, and when the computer program is executed by a processor, the steps of the above embodiments of the method may be implemented. Wherein the computer program comprises computer program code, which may be in the form of source code, object code, an executable file or some intermediate form, etc. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, usb disk, removable hard disk, magnetic disk, optical disk, computer Memory, Read-Only Memory (ROM), Random Access Memory (RAM), electrical carrier wave signals, telecommunications signals, software distribution medium, and the like. It should be further noted that the computer readable medium may contain content that is subject to appropriate increase or decrease as required by legislation and patent practice in jurisdictions, for example, in some jurisdictions, computer readable media does not include electrical carrier signals and telecommunications signals in accordance with legislation and patent practice.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention.

Claims (10)

1. A method for solving reliability parameters of elements of a high-voltage direct-current transmission system is characterized by comprising the following steps:
obtaining reliability parameters of elements to be solved of the high-voltage direct-current power transmission system;
inputting the reliability parameters of the elements to be solved into a preset reliability evaluation model of the high-voltage direct-current power transmission system, and calculating the reliability index of the high-voltage direct-current power transmission system by adopting a state transition sampling method in a time sequence Monte Carlo; the reliability evaluation model of the high-voltage direct-current power transmission system is constructed by adopting an analytic method;
inputting the reliability index into a preset equation set model of the reliability index of the element to be solved;
and solving an equation set model of the reliability index related to the element reliability parameter to be solved by adopting an interval algorithm combining interval dichotomy and a Krawczyk-Hansen operator.
2. The method of solving for a reliability parameter of an HVDC transmission system component of claim 1,
the method for constructing the equation set model of the reliability index about the reliability parameter of the element to be solved comprises the following steps:
constructing a reliability evaluation model of the high-voltage direct-current power transmission system by adopting an analytic method;
acquiring reliability parameters of all elements of the high-voltage direct-current transmission system;
inputting the reliability parameters of all the elements into a reliability evaluation model of the high-voltage direct-current power transmission system, and calculating the reliability index of the high-voltage direct-current power transmission system by adopting a state transition sampling method in a time sequence Monte Carlo;
according to the reliability parameters of all the elements and the reliability indexes, an analytic model of the reliability indexes of the high-voltage direct-current power transmission system about the element reliability parameters is constructed by adopting a full probability formula;
and constructing an equation set model of the reliability index of the element to be solved according to the analytic model of the reliability index of the high-voltage direct-current power transmission system on the element reliability parameter.
3. The method according to claim 2, wherein if the hvdc transmission system is a double 12-pulse hvdc transmission system, the element reliability parameters include an element failure rate and an element repair rate, and the reliability indexes of the hvdc transmission system include an energy unavailability rate, a unipolar forced outage frequency and a bipolar forced outage frequency, the calculating the reliability index of the hvdc transmission system by using a state transition sampling method in time-series monte carlo specifically includes:
step 3.1, assuming that the component state duration follows exponential distribution, and the components are all normal at the initial moment;
step 3.2, calculating the system state duration T according to the formula (1)kIn the formula (1), m is the total number of outward transition conditions of the current state, and U is [0,1 ]]Random number of between, tauiFor the state transition rate of the element i, i.e. the reliability parameter, τiThe state transition rate of the element i is equal to τiIs the component failure rate or component repair rate;
Figure FDA0002982456960000021
step 3.3, calculating the state transition probability P of the element j according to the following formula (2)jAnd obtaining the cumulative transition probability P of the element according to the formula (3)i；
Figure FDA0002982456960000022
Figure FDA0002982456960000023
Step 3.4, carrying out element state transition positioning according to the formula (4), if ChIf 1, the state of the element is transferred, otherwise, the state of the element remains unchanged.
Ch＝find(Pi＞rand(1)) (4)；
Wherein, ChWhether the recording state is transferred or not is indicated, namely whether the element is transferred from the normal state to the fault state or not is seen;
step 3.5, after obtaining a certain number of system states, calculating the system state SState；
Step 3.6, updating the reliability index according to the formulas (5), (6) and (7), and counting the times of forced shutdown of the single pole and the double pole;
Figure FDA0002982456960000031
Figure FDA0002982456960000032
EOT(i)＝Ti(1-available capacity during outage ÷ PS) (7)；
In the formula, EU is the energy unavailability rate, and T is the time scale; TEOT is total equivalent outage time in T; EOT (i) is the ith equal outage time in the year; n is the total outage times, Ti represents the actual failure outage time of the ith time, and Ps represents the rated capacity of the system;
step 3.7, calculating a variance coefficient n, as shown in formula (8), if n is smaller than a preset constant, stopping iterative calculation, and outputting a corresponding reliability index, otherwise, repeating the step 3.2-3.4 to generate a new system state;
Figure FDA0002982456960000033
wherein T is a time scale.
4. The method according to claim 3, wherein if the HVDC transmission system is a double 12-pulse HVDC transmission system, the element reliability parameters include an element failure rate and an element repair rate, and the reliability indexes of the HVDC transmission system include an energy unavailability rate, a unipolar forced outage frequency and a bipolar forced outage frequency, the obtaining an analytic model of the reliability indexes of the HVDC transmission system about the element reliability parameters by using a full probability formula according to the reliability parameters and the reliability indexes of all the elements specifically comprises:
the failure rate lambda of the element 1 is determined by knowing the energy unavailability rate EU, the monopolar forced shutdown frequency MFOT and the bipolar forced shutdown frequency BFOT1And rate of repair mu1Are unknown, failure rate λ of element 22Unknown, repair Rate mu of component 33Unknown, since the number of elements whose parameters are unknown is 3, the combination of the states of these elements has a total of 23In 8 cases, the unknown parameter vector λ of the elements 1,2,3 is denoted by X1,μ1,λ2,μ3]Then, the analytic model of the energy unavailability EU, the analytic model of the unipolar forced outage times MFOT, and the analytic model of the bipolar forced outage times BFOT are respectively:
(1) the analytic model of the energy unavailability EU is
Figure FDA0002982456960000041
In the above formula (9), Ai、Ui(i ═ 1,2,3) represents the steady-state availability and the steady-state unavailability, ai＝μi/(λi+μi)，Ui＝λi/(λi+μi)，Wj EUExpressed as:
Figure FDA0002982456960000042
in the above formula (10), B _ EUjA set of system outage events representing 3 elements under study in a jth combined state; phibIndicating the normal operating conditions of the system in each case excluding the conditions already listed above for the above formula;
Figure FDA0002982456960000043
is phibThe complement of (1); c represents the per unit value of the capacity state in the corresponding state;
(2) and the analytic model of the single-pole forced outage frequency MFOT is as follows:
Figure FDA0002982456960000044
in the above formula (11), Wi MFOTExpressed as:
Figure FDA0002982456960000051
in the formula (12), B _ MFOTjA set of system unipolar forced outage events representing 3 elements under study in a jth combined state;
(3) the analytic model of the bipolar forced outage times BFOT is as follows:
Figure FDA0002982456960000052
in the above formula (13), Wi BFOTExpressed as:
Figure FDA0002982456960000053
in formula (14), B _ BFOTjA set of system bipolar forced outage events representing 3 elements under study in the jth combination state.
5. The method according to claim 4, wherein the reliability index is based on an equation set model of the reliability parameter of the component to be determined, and specifically comprises:
Figure FDA0002982456960000054
wherein, EU0、MFOT0、BFOT0Respectively representing given values of an energy unavailability rate EU, a monopolar forced outage frequency MFOT and a bipolar forced outage frequency BFOT; f. ofEU(X)、fMFOT(X) and fBFOTAnd (X) are nonlinear equations of the energy unavailability rate EU, the unipolar forced outage times MFOT and the bipolar forced outage times BFOT respectively.
6. The method for correcting the reliability parameters of the HVDC transmission system components according to claim 5, wherein the solving of the equation set model of the reliability index with respect to the reliability parameters of the components to be solved by using an interval algorithm combining interval dichotomy and Krawczyk-Hansen operator specifically comprises:
step 6.1: let [ X ]]＝[X]0∈I(Rn) Initializing a table binary interval table B and solving an interval table T; initializing a binary variable number b as 1, a binary interval table length l as 1, giving convergence precision epsilon and xi of a solution interval, and initializing an interval width coefficient alpha;
step 6.2: calculation of H (X) and Z ═ X ≠ H (X) according to the Krawczyk-Hansen operator
Figure FDA0002982456960000061
Figure FDA0002982456960000062
Wherein X is an interval vector; h (X) is Krawczyk-Hansen operator; y is the midpoint of the interval solution X; m (X) is the midpoint of the interval vector X; i is an n-order identity matrix; y is an n-order nonsingular matrix; l (X) and U (X) are interval matrixes [ I-YF' (X)]A lower triangular matrix and an upper triangular matrix of,X 1and
Figure FDA0002982456960000064
respectively representing the upper and lower bounds of the first component of the interval solution X; xnIs the nth component of the interval solution X.
Step 6.3: judging the existence and uniqueness of the solution according to the inclusion relationship between Z and X; if it is
Figure FDA0002982456960000063
Turning to step 6.6; if W (X) belongs to X, then there is a solution on X, go to step 6.4; if W (Z)<α w (X), then X ═ Z, go to step 6.2; otherwiseTurning to step 6.5; wherein W (X) is the width of the interval X, and W (Z) is the width of the interval Z;
step 6.4: taking m (X) as an initial value, and performing iterative calculation by using a point Newton method to obtain a solution X of the equation set, and storing the solution X in a table T;
step 6.5: if W (X)<ξ, then X is stored in T, and step 6.6 is carried out. Halving the component Xb of the interval vector X to obtain
Figure FDA0002982456960000071
Will 2 bX,m(Xb)]Store into interval table B, order
Figure FDA0002982456960000072
B +1, turning to step 6.2;
step 6.6: if l is 0, go to step 6.7. Taking out the interval arranged at the head from the interval table B, assigning X to l-1, and going to step 6.2;
step 6.7: outputting all solution intervals in the table T; if T is an empty set, the system of equations is unsolved.
7. A device for solving reliability parameters of elements of a high-voltage direct-current power transmission system is characterized by comprising:
the acquiring unit is used for acquiring reliability parameters of elements to be solved of the high-voltage direct-current power transmission system;
the first input unit is used for inputting the reliability parameters of the elements to be solved into a preset reliability evaluation model of the high-voltage direct-current power transmission system and calculating the reliability index of the high-voltage direct-current power transmission system by adopting a state transition sampling method in time sequence Monte Carlo; the reliability evaluation model of the high-voltage direct-current power transmission system is constructed by adopting an analytic method;
the second input unit is used for inputting the reliability index into a preset equation set model of the reliability index of the element to be solved;
and the solving unit is used for solving an equation set model of the reliability index related to the element reliability parameters to be solved by adopting an interval algorithm combining interval dichotomy and a Krawczyk-Hansen operator.
8. The device for solving the reliability parameter of the HVDC transmission system component according to claim 7, wherein the method for constructing the equation set model of the reliability index with respect to the reliability parameter of the component to be solved comprises:
constructing a reliability evaluation model of the high-voltage direct-current power transmission system by adopting an analytic method;
acquiring reliability parameters of all elements of the high-voltage direct-current transmission system;
inputting the reliability parameters of all the elements into a reliability evaluation model of the high-voltage direct-current power transmission system, and calculating the reliability index of the high-voltage direct-current power transmission system by adopting a state transition sampling method in a time sequence Monte Carlo;
according to the reliability parameters of all the elements and the reliability indexes, an analytic model of the reliability indexes of the high-voltage direct-current power transmission system about the element reliability parameters is constructed by adopting a full probability formula;
and constructing an equation set model of the reliability index of the element to be solved according to the analytic model of the reliability index of the high-voltage direct-current power transmission system on the element reliability parameter.
9. An hvdc power transmission system component reliability parameter solving apparatus comprising a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, the processor implementing the method of solving for a reliability parameter of an hvdc power transmission system component as claimed in any of claims 1 to 6 when executing the computer program.
10. A computer-readable storage medium, comprising a stored computer program, wherein the computer program, when executed, controls an apparatus in which the computer-readable storage medium is located to perform a method for solving reliability parameters of components of an hvdc power transmission system according to any of claims 1-6.
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