CN117934210A - Power distribution network system restoring force evaluation method based on construction of multiple evaluation indexes - Google Patents
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Abstract
The invention provides a power distribution network system restoring force evaluation method based on construction of multiple evaluation indexes, and belongs to the technical field of power distribution network system restoring force evaluation; the technical problems to be solved are as follows: providing a power distribution network system restoring force evaluation method based on construction of multiple evaluation indexes; the technical scheme adopted for solving the technical problems is as follows: the load supply capacity of the power distribution network system under natural disasters is quantified through toughness evaluation, the processes of the early stage, the middle stage and the later stage of the fault are respectively evaluated, and elasticity evaluation indexes are established; in order to quantify a multi-element power distribution network and reduce power failure loss capacity in elasticity evaluation, an energy supply path model of each node dependent cell is established based on the relation between the power on and power off of the node cell and a specific line; analyzing fault probability events from two aspects of load outage time in an accident and load outage time after the accident, and establishing a probability event model; the method is applied to the recovery power evaluation of the power distribution network system.
Description
Technical Field
The invention provides a power distribution network system restoring force evaluation method based on construction of multiple evaluation indexes, and belongs to the technical field of power distribution network system restoring force evaluation.
Background
In recent years, large-scale power failure events caused by extreme weather frequently occur, so that the normal operation of a power equipment system is negatively influenced, and the improvement of the toughness and disaster resistance of a multi-element power distribution network is an effective means for coping with the events; the disaster resistance of the power distribution network can be improved by researching strategies and measures for enhancing the toughness of the power distribution network, the influence of natural disasters on a power supply system is reduced, corresponding countermeasures include reinforcing the wind resistance of the power distribution network, adopting toughness materials and designs, establishing standby power and redundant lines, improving the disaster prevention performance of power distribution equipment and the like, by means of the measures, the recovery capacity of the power distribution network when the natural disasters occur can be improved, the natural disasters possibly occurring in the future can be better dealt with, the toughness of the power distribution network system is enhanced to a certain extent, and the system can recover to be normal as soon as possible after the disaster influence is finished, so that the reliability and the stability of power supply are ensured; therefore, objective and correct assessment of the recovery power of the power distribution network system is a precondition for guaranteeing the planning quality of the power distribution network system and improving the recovery capacity after disaster.
However, the existing evaluation method has single standard, and the qualitative evaluation has inherent limitation defect due to the nature of low probability and high influence of natural disasters and multi-stage characteristics existing in a power distribution network system, so that the analysis expression aiming at evaluation indexes can not be realized, and the efficiency and the accuracy of the evaluation process are low.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and solves the technical problems that: the power distribution network system restoring force evaluation method based on construction of multiple evaluation indexes is provided.
In order to solve the technical problems, the invention adopts the following technical scheme: a power distribution network system restoring force evaluation method based on construction of multiple evaluation indexes comprises the following evaluation steps:
Step one: the load supply capacity of the power distribution network system under natural disasters is quantified through toughness evaluation, processes at the pre-fault, during-fault and post-fault stages are evaluated respectively, and elasticity level evaluation indexes of the system are established;
When evaluating the elasticity level of the system, the total loss of the system functions is adopted Characterization is performed, and the expression is:
；
Wherein SR is the system load supply capacity, SR 0 is the system load supply capacity when no fault occurs, T e、Ts is two time points, and [ T s,Td ] and [ T d,Te ] are defined as the duration of the fault in the disaster and the load recovery period after the disaster respectively;
Converting into expected values of system function loss considering all probability scenes by expanding deterministic elasticity indexes into probabilistic elasticity indexes E The expression is:
；
Wherein N is a node dependency cell set of the regional distribution network; τ d and τ e are load outage times during the in-disaster fault duration and post-disaster load recovery period, respectively; p d i,τd is the probability that the load outage time of the dependent cell i is tau d under the duration of the in-disaster fault; p e i,τe is the probability that the load outage time of the dependent cell i is tau e in the post-disaster load recovery period; f b D is the load power of node i; A node set in a node cell S;
step two: in order to quantify a multi-element power distribution network and reduce power failure loss capacity in elasticity evaluation, an energy supply path model of each node dependent cell is established based on the relation between the power on and power off of the node cell and a specific line, and the energy supply path is used for subsequent probability event construction and index analysis expression:
for a certain node cell S, the calculation formula of the objective function is as follows:
；
Wherein x s is marked as a 0-1 variable, if the variable is 1, the load of the node cell s can be recovered, otherwise, if the variable is 0, the load cannot be recovered; wherein Ω(s) is represented as a set of nodes in node cell s;
Analyzing the operation constraint of the node dependency cell energy supply path model, wherein a complete energy supply restoration path is required to start from a node cell comprising a transformer substation and end at a target node cell S, and the energy supply path is required to pass through a certain determined cell at most once, if at least one energy supply path passing through a node cell m exists, the node cell is restorable, and if the energy supply path passes through the node cell m, the power supply restoration can be realized for both a node i and a non-switching circuit (i, j) in the node cell;
The constraint expression adopting the topological state of the net rack is as follows:
；
Wherein x B m,n is a variable of 0 to 1, and if 1, the variable is expressed as an openable line passing between two node cells from cell m to cell n, and if not, the openable line passing between two node cells from cell m to cell n is expressed as 0;
x B n,m is a 0-1 variable, if 1, representing an openable line passing between two node cells from cell n to cell m, if not, marking the openable line passing between two node cells from cell n to cell m as 0;
n is a node cell set; NS is a collection of node cells comprising the substation;
；
Wherein x B n,s is a 0-1 variable representing an openable circuit passing between two node cells from cell n to cell s; x B s,n is a 0-1 variable representing an openable line from cell s to cell n passing between two node cells;
；
；
；
Wherein x B m,n is a variable of 0 to 1, and if 1, the variable is expressed as an openable line passing between two node cells from cell m to cell n, and if not, the openable line passing between two node cells from cell m to cell n is expressed as 0; NS is represented as a collection of node cells comprising the substation; i (M) represents a node set in node cell M;
wherein x m is a 0-l variable, if 1, it means that the energy supply path will pass through cell m, if not, it will be 0;
Wherein x B i,j is a 0-1 variable, which indicates whether the non-switching circuit (i, j) can be powered, if so, the power supply is restored, i, if not, the power supply is restored, 0;
Wherein B m is the set of non-switching lines in the node cell m;
Meanwhile, the safe operation constraint conditions of the load flow balance constraint and the capacity constraint are required to be met, and the expressions of the constraints are as follows:
；
；
Wherein: ，/> respectively representing node and line operation state variables, when corresponding equipment is powered, the value is 1, otherwise, the value is 0, and f l,fs,fu is respectively the energy flow of the line, the root node and the energy conversion equipment,/> 、/>、/>Energy flow upper limit of line, root node and energy conversion equipment respectively,/>,/>Is a head node-line, tail node-line association matrix,/>For node-energy production facility association matrix,/>The node-energy conversion equipment incidence matrix;
Obtaining an energy supply path leading to a cell S based on the solving of the energy supply path model, and obtaining all the needed energy supply paths by continuously carrying out loop iteration solving on each constraint expression model;
Step three: analyzing fault probability events from two aspects of load outage time in an accident and load outage time after the accident, and establishing a probability event model:
Step 3.1: for probabilistic events related to phase outage time in an accident:
In the accident middle stage of the multi-element power distribution network, positioning, isolating and repairing are carried out aiming at the equipment with faults or damages so as to recover the normal operation of the multi-element power distribution network, thereby defining that when the fault event meets the following event conditions, the load in the corresponding node dependent cell is stopped to supply to the disaster end:
Event 1: extreme faults occur inside the node dependent cells;
event 2: extreme faults occur in all possible energy supply paths of the node dependent cells;
expected value for loss based on probability of occurrence of event 1 and event 2 E The probability P d i,τd in the expression is expressed as:
；
Wherein, cell (i) is the index of the internal equipment of cell i; path (i, m i) provides a path index for cell i, where m i is the number of path entries for cell i; then A set of fault events representing a fault state within cell i at time t d -1,A set of fault events representing that the mth i energy supply paths of the cell i are in a fault state at time t d -1;
step 3.2: for probability events related to post-accident phase power failure time:
The system needs to be repaired and reconfigured after a fault event to ensure the reliability and stability of the power supply, thereby defining that the corresponding cells resume normal energy supply when the service measures meet the following event conditions:
event 3: repairing a fault element in the node dependency cell by using the overhaul resource;
Event 4: repairing one feasible energy supply path of the node dependent cell by using the overhaul resource;
Expected value for loss based on probability of occurrence of event 3 and event 4 E The probability P e i,τe in the expression is expressed as:
；
In the method, in the process of the invention, Indicates that the energy supply path of the cell is in a fault state at the time T d+τe +1, and the energy supply path of the cell is in a fault state at the time TThe node cell is in a fault state at the moment T d+τe, and B [ cell (i), tau e ] and B [ path (i, m i),τe ] respectively represent the time period/>A set of devices in the cell interior, energy supply path, greater than τ e, namely:
And
；
Step four: analyzing and expressing each elastic index, and specifically, analyzing and expressing event probability as a function of line fault probability based on a method of conditional probability, full probability and topology simplification:
step 4.1: establishing a power distribution network fault probability model:
based on normal distribution characteristics of tensile bending strength of the multi-element power distribution network frame, a mathematical model of the failure rate of the multi-element power distribution network under disasters is established, and the expression is as follows:
；
Wherein: σ l PDS is the failure rate of the first power line in the power distribution network, and x g is the stress which can be borne by the section of the first power line; x l is the tensile and bending strength of the first power line, and mu l and delta l are the tensile and bending strength mean value and standard deviation of the power line respectively;
Step 4.2: analyzing and expressing the power failure time in the accident stage:
When the corresponding device is in a non-fault state at time t d, then it must be in a non-fault state at time t d -1, i.e. conform to Therefore, satisfy/>；
When the corresponding device is in a fault state at the time t d -1, the corresponding device is in a fault state at the time t d, namely, the corresponding device accords withTherefore, it meets
；
Thereby converting the formula according to the full probabilityThe expression of probability P d i,τd based on the probability of occurrence of event 1 and event 2 is translated into:
；
The energy supply path based on the same monoblock has repeated cellular channels, so the transformed upper part still comprises the non-independent outage event intersection probability, namely There is also a need for a method based on the full probability transformation formula and the conditional probability transformation formula/>The following transformations were carried out:
；
In the method, in the process of the invention, Representing the probability that for the node dependent cell i, the first energy supply channel is not in a fault state at the time t d, and all other energy supply channels are in the fault state;
Defining an index Then the following is satisfied:
；
for convenience of description, further description will be made The second energy supply channel is decoupled from other energy supply channels in the conversion formula of (a), and an equivalent expression comprising three parts can be obtained:
the first part is related to the uncoupling path, and has the following expressions An item;
The second part is singly related to each energy supply path of decoupling, and has the following expression An item;
the third part is related to all decoupled energy supply paths, and is expressed by An item;
The expression is:
；
For the continuous application of the energy supply path simplification method based on the conditional probability, the complex non-independent fault event related to the energy supply path is decoupled, and the aim is achieved Equivalent formula after v-th decoupling of conversion formula, common/>The term, expression is:
；
The first category corresponds to energy supply path fault event probabilities for unassociated line removal (ω=0);
the second class corresponds to the energy supply path fault event probability of removing one associated line (ω=1);
the third class corresponds to the energy supply path failure event probability of removing two associated lines (ω=2);
And so on, for the node dependency cell i, after m i -1 decoupling, completely removing the complex non-independent fault event in the probability expression, and obtaining the non-simulation expression of the load outage event for representing the toughness in the energy system accident based on the general form, wherein the expression is as follows:
；
；
step 4.3: analyzing and expressing the power failure time at the post-accident stage:
when the corresponding equipment is overhauled at the moment T d+τe, the corresponding equipment is in a non-fault state at the moment T d+τe +1, namely, accords with Therefore, it meets
；
When the corresponding device is in a fault state at the moment T d+τe +1, the corresponding device is in a fault state at the moment T d+τe, namely the corresponding device accords withTherefore, it meets
；
Combining a full probability conversion formula, converting an expression of the probability P e i,τe based on the occurrence probability of the event 3 and the event 4 into:
；
continuously applying an energy supply path simplification method based on conditional probability to obtain a non-simulation expression of a load outage event for representing the toughness of an energy system after an accident, wherein the expression is as follows:
；
。
The specific method for recovering the normal operation of the multi-element power distribution network in the accident stage in the step 3.1 comprises the following steps:
fault detection and localization: the power distribution network operators receive fault alarms and then determine the position of the fault through fault detection and positioning technologies;
isolation and fault removal: after the fault position is determined, operators take necessary measures to isolate the fault equipment, so as to prevent the fault from continuing to spread or affecting other equipment;
Repair and replacement equipment: after isolating the fault, operators repair or replace the fault equipment, wherein the repair may comprise replacement of the fault element, repair of damaged cables or equipment, and replacement of new equipment is required if the equipment cannot be repaired;
Functional recovery and testing: after the repair or replacement of the fault equipment is finished, system testing and function recovery are carried out by power distribution network operators, so that the equipment can be ensured to normally operate;
And (5) power supply recovery: and after the fault equipment in the power distribution network is repaired and passes the test, the operators gradually recover the power supply, the affected node cells are reconnected to the power grid, and the power supply of the users is recovered.
Compared with the prior art, the invention has the following beneficial effects: dividing a multi-element power distribution network system into node cells, modeling energy supply path solutions of the node cells, establishing a related probability event of elastic index calculation on the basis, and finally expressing the probability event as a function of line fault probability based on conditional probability, full probability and topology simplification, and then solving to obtain a probabilistic elastic index of a system function loss expected value, thereby realizing elastic evaluation of the power distribution network system; the evaluation method is based on a non-sampling method to identify fault evolution, operation recovery and topology dynamics of equipment repair stages, and can remarkably improve evaluation efficiency and accuracy.
Drawings
The invention is further described below with reference to the accompanying drawings:
FIG. 1 is a diagram of the elastic functional effects of a multiple power distribution network system of the present invention at different time intervals;
FIG. 2 is a schematic diagram of an electrical-pneumatic area distribution network structure based on node-dependent cells according to the present invention;
FIG. 3 is a schematic diagram of the load distribution of each node cell according to the present invention.
Detailed Description
The invention provides a power distribution network system restoring force evaluation method based on construction of multiple evaluation indexes, which is based on quantification of dynamic performance of time-space variation of a power distribution network in different stages of fault occurrence, and the whole process of improving toughness of an elastic multiple power distribution network system is adopted, so that the inherent defects of qualitative evaluation are overcome and the restoring force of the power distribution network system is accurately evaluated, and two key aspects need to be considered:
On the one hand, the limitation of qualitative evaluation is overcome and more accurate recovery power evaluation is provided on the basis of the multistage dynamic performance of the system by constructing quantitative evaluation indexes based on the low-probability high-impact nature of natural disasters and the multistage characteristics of the power distribution network system, and on the other hand, an evaluation method for comprehensive calculation efficiency and precision is also required to be provided so as to realize the analytic expression of the evaluation indexes and ensure the high efficiency and accuracy of the evaluation process.
Based on the non-sampling mode, the method realizes the rapid evaluation of the multi-element power distribution network system, is beneficial to the planning and recovery research of the power distribution network system, enhances the toughness of the power distribution network system to a certain extent, and enables the system to recover to be normal as soon as possible after the disaster influence is over.
The method comprises the following specific steps:
firstly, establishing elasticity evaluation indexes:
the invention adopts a series of operation recovery measures through means such as grid reconstruction and the like to penetrate through the whole accident period and the two stages after the accident, namely the load supply capacity of the power distribution network system under natural disasters can be quantified through toughness evaluation, and the evaluation process penetrates through a plurality of stages before, during and after the fault.
As shown in FIG. 1, which shows the process of ductile evolution under natural disasters, the ordinate SR in the figure is the system load supply capacity, and [ T s,Td ] and [ T d,Te ] are the duration of the failure in the disaster and the recovery period of the load after the disaster, respectively, because FIG. 1 can reflect the dynamic behavior of the multi-stage energy system, the elasticity level of the system can be used as the total loss of the system functions in FIG. 1Characterization, the calculation formula is as follows:
（1）；
Wherein SR is the system load supply capacity, SR 0 is the system load supply capacity when no fault occurs, T e、Ts is two time points, and [ T s,Td ] and [ T d,Te ] are defined as the duration of the fault in the disaster and the load recovery period after the disaster respectively;
the natural disasters affect the electrical equipment in probability events at different time and place, so that the deterministic elastic index is further expanded into a probabilistic elastic index, namely, the probabilistic elastic index is converted into an expected value of system function loss considering all probability scenes E The calculation formula is as follows:
（2）；
Wherein N is a node dependency cell set of the regional distribution network; τ d and τ e are load outage times during the in-disaster fault duration and post-disaster load recovery period, respectively; p d i,τd is the probability that the load outage time of the dependent cell i is tau d under the duration of the in-disaster fault; p e i,τe is the probability that the load outage time of the dependent cell i is tau e in the post-disaster load recovery period; f b D is the load power of node i; Is a set of nodes in a node cell S.
(II) modeling node dependent energy supply paths:
The energy supply path model constructed by the invention is mainly used for reflecting the connection and disconnection of the node cells and the lines, and aims to quantify the multi-element power distribution network and reduce the power failure loss capacity in elasticity evaluation, so that the energy supply path model of each node dependent cell needs to be established before distribution network toughness analysis and evaluation research are carried out.
As shown in fig. 2, there are five power supply paths of the reflecting electric cell 2, specifically:
Cell 1→cell 2;
gas cell 1- & gt gas cell 2- & gt gas cell 3- & gt cross-energy flow cell 1- & gt electric cell 2;
Gas cell 1- & gt gas cell 3- & gt cross-energy flow cell 1- & gt electric cell 2;
gas cell 1- & gt gas cell 2- & gt cross-energy flow cell 2- & gt electric cell 3- & gt electric cell 2;
Gas cell 1- & gt gas cell 2- & gt cross-energy flow cell 2- & gt electric cell 3- & gt electric cell 4- & gt electric cell 2;
and the energy supply path obtained based on the above is used for the subsequent probability event construction and index analysis expression.
For a certain node cell S, the calculation formula of the objective function is as follows:
（3）；
Wherein x s is marked as a 0-1 variable, if the variable is 1, the load of the node cell s can be recovered, otherwise, if the variable is 0, the load cannot be recovered; where Ω(s) is represented as a set of nodes in node cell s.
For the operation constraint of the node dependency cell energy supply path model, including network frame topological state constraint formulas (4) to (8), a complete recoverable energy supply path should start from the node cell containing the transformer substation and end at the target node cell S, in addition, in order to ensure the normal operation of network radiation, for a certain determined cell, an energy supply path should pass at most once, and if at least one energy supply path passing through the node cell m exists, the node cell is recoverable, and if the energy supply path passes through the node cell m, the node i and the non-switching lines (i, j) in the node cell can be recovered from power supply; therefore, the 0-1 variable mixed integer model is consistent with x m, and the specific grid topological state constraint expression is as follows:
（4）；
Wherein x B m,n is a variable of 0 to 1, and if 1, the variable is expressed as an openable line passing between two node cells from cell m to cell n, and if not, the openable line passing between two node cells from cell m to cell n is expressed as 0;
x B n,m is a 0-1 variable, if 1, representing an openable line passing between two node cells from cell n to cell m, if not, marking the openable line passing between two node cells from cell n to cell m as 0;
n is a node cell set; NS is a collection of node cells comprising the substation;
（5）；
Wherein x B n,s is a 0-1 variable representing an openable circuit passing between two node cells from cell n to cell s; x B s,n is a 0-1 variable representing an openable line from cell s to cell n passing between two node cells;
（6）；
（7）；
（8）；
Wherein x B m,n is a 0-1 variable, if 1, then representing an openable line passing between two node cells from cell m to cell n, if not, then representing 0; NS is represented as a collection of node cells comprising the substation; i (M) represents a node set in node cell M;
wherein x m is a 0-l variable, if 1, it means that the energy supply path will pass through cell m, if not, it will be 0;
Wherein x B i,j is a 0-1 variable, which indicates whether the non-switching circuit (i, j) can be powered, if so, the power supply is restored, i, if not, the power supply is restored, 0;
Wherein B m is the set of non-switching lines within node cell m.
In addition, the precondition for ensuring energy supply should be to meet various safe operation constraint conditions, including a tide balance constraint (9) and a capacity constraint (10), and the expression is as follows:
（9）；
（10）；
Wherein: ，/> respectively representing node and line operation state variables, when corresponding equipment is powered, the value is 1, otherwise, the value is 0, and f l,fs,fu is respectively the energy flow of the line, the root node and the energy conversion equipment,/> 、/>、/>Energy flow upper limit of line, root node and energy conversion equipment respectively,/>,/>Is a head node-line, tail node-line association matrix,/>For node-energy production facility association matrix,/>And (5) associating the matrix for the node-energy conversion equipment.
However, the solution of the models (4) to (10) constructed above can only obtain one energy supply path leading to the cell S, and all the energy supply paths required can be obtained by continuously and iteratively solving the models (4) to (10) in a loop.
(III) probability event construction:
The analysis and research of the extreme fault probability event are respectively carried out from the two aspects of the load stop supply time in the disaster (in the fault) and the load stop supply time after the disaster (after the fault), and a probability model is built.
(1) For probabilistic events related to phase outage time in an accident:
in a multi-component power distribution network accident phase, in which a device that has failed or has been damaged needs to be located, isolated and repaired to restore normal operation of the multi-component power distribution network, the phase encompasses the entire process from the failure occurrence to the failure repair, the specific operating steps include:
fault detection and localization: the power distribution network operators receive fault alarms and then determine the position of the fault through fault detection and positioning technologies; this may be achieved by using fault indicators, fault recorders, telemechanical devices and the like.
Isolation and fault removal: once the fault location is determined, operators may take necessary steps to isolate the faulty device to prevent the fault from continuing to spread or affecting other devices; it may involve cutting off the power supply, opening a circuit breaker, operating a switch, etc.
Repair and replacement equipment: after isolating the fault, operators can repair or replace the fault equipment, wherein the repair can comprise the replacement of the fault element, the repair of damaged cables or equipment and the like; if the device cannot be repaired, it needs to be replaced with a new device.
Functional recovery and testing: once the fault equipment is repaired or replaced, system testing and function recovery can be carried out by power distribution network operators, so that the equipment can be ensured to normally operate; may involve performing functional tests, performing calibration and testing of the protection device, etc.
And (5) power supply recovery: and finally, after the fault equipment in the power distribution network is repaired and passes the test, operators gradually recover the power supply, and the affected node cells are reconnected to the power grid so as to recover the power supply of users.
The time length of the stage in the accident of the multi-element power distribution network depends on a plurality of factors including the fault type, the positioning and repairing difficulty of fault equipment, the response speed of maintenance personnel and the like, the fault is rapidly and accurately positioned and isolated, and the effective repairing and testing flow is of great importance to the time of the stage in the accident, so that the power failure time of a user can be reduced, and the economic loss can be reduced.
The power-off of the node cell m is caused by the following two conditions, one condition is satisfied, the power-off of the node cell m is caused, and the condition is continued until the end of the natural disaster:
1. The node cell m has faults and needs to be isolated to prevent the power supply of other nodes from being influenced;
2. All the power paths for node cell m fail.
The path-based method has important significance in the analysis of outage time at the stage of an accident: the analysis method can reflect the topological structure change, fault evolution and repair process of the multi-element power distribution network, evaluate reliability and recovery capability, can provide key indexes, and help to formulate emergency plans and recovery strategies so as to cope with natural disasters and faults, reduce power failure time and ensure power consumption requirements.
The load in the corresponding node dependent cell will therefore be shut down to the end of the disaster when the following event conditions are met for the event of extreme failure:
Event 1: extreme faults occur inside the node dependent cells; taking fig. 2 as an example, when an extreme fault event occurs between the non-reconfigurable lines E 6 and E 7, the reconfigurable line E 4,6、E7,9 needs to be disconnected and the operation of the electric switching device in the cross-energy flow cell is stopped to avoid the fault propagation, at this time, all loads in the cell 3 are stopped and the fault repair is waited for to restore the energy.
Event 2: extreme faults occur in all possible energy supply paths of the node dependent cells; still taking fig. 2 as an example, when an extreme N-k fault occurs simultaneously on the reconfigurable line E 4,6、E7,9、E8,6, all power paths of the cells 3 are interrupted and the load is disabled.
Thus, P d i,τd in equation (2) can be expressed based on the probability of occurrence of event 1 and event 2 to yield equation (11):
（11）；
Wherein, cell (i) is the index of the internal equipment of cell i; path (i, m i) provides a path index for cell i, where m i is the number of path entries for cell i; then A set of fault events representing a fault state within cell i at time t d -1,A set of fault events representing that the mth i power-up path of cell i is in a fault state at time t d -1.
(2) For probability events related to post-accident phase power failure time:
In the post-accident stage of the multi-element power distribution network, considering the related fault recovery and system operation, the post-accident stage refers to the fact that after a fault event occurs, the system needs to be repaired and reconfigured so as to ensure the reliability and stability of power supply; through effective fault recovery and system operation management, the power distribution network can quickly recover normal operation after an accident, power failure time is reduced, and power consumption requirements of users are guaranteed to the greatest extent; therefore, after an accident, a maintainer needs to repair the faulty original quickly so that the multi-power distribution network resumes normal operation, and in order to reduce the power outage time, it is necessary to find and repair preferentially one energy supply path with the shortest repair time to the target cell, so that the power outage time after the accident mainly depends on the shortest repair time among all energy supply paths leading to the power outage.
Thus, for the node-dependent cells that have been shut down, it is known that the corresponding cells can resume normal power supply when the service measure meets the following event conditions:
event 3: repairing a fault element in the node dependency cell by using the overhaul resource; taking the fault in the event 1 as an example, after the scheduled maintenance resource repairs the non-reconfigurable line E 6,7 after the accident, the reconfigurable line connected with the cell 3 can be closed and the cell energy supply can be recovered;
Event 4: repairing one feasible energy supply path of the node dependent cell by using the overhaul resource; taking the fault in the event 2 as an example, the repair of any reconfigurable circuit of E 4,6 and E 7,9 can restore the energy supply of the cell 3; it can be seen that the post-accident load recovery situation based on the energy supply path model is affected by the dynamic reconfiguration state of the network under the optimal overhaul resource scheduling.
Thus, P e i,τe in equation (2) can be expressed as equation (12) with the probability of event 3 and event 4 occurring:
（12）；
In the method, in the process of the invention, Indicates that the energy supply path of the cell is in a fault state at the time T d+τe +1, and the energy supply path of the cell is in a fault state at the time TThe node cell is in a fault state at the moment T d+τe, and B [ cell (i), tau e ] and B [ path (i, m i),τe ] respectively represent the time period/>A set of devices in the cell interior, energy supply path, greater than τ e, namely:
And
。
(IV) analysis expression of elastic index
Furthermore, various indexes are analyzed and expressed, and the event probability is analyzed and expressed as a function of the line fault probability based on the methods of conditional probability, full probability and topology simplification.
(1) Establishing a power distribution network fault probability model:
Based on normal distribution characteristics of tensile bending strength of the multi-element power distribution network frame, a mathematical model of the failure rate of the multi-element power distribution network in view of earthquake disasters is shown as a formula (13):
（13）；
Wherein: σ l PDS is the failure rate of the first power line in the power distribution network, and x g is the stress which can be borne by the section of the first power line; x l is the tensile and bending strength of the first power line, and mu l and delta l are the mean and standard deviation of the tensile and bending strength of the power line respectively.
(2) Aiming at the analysis expression of the power failure time in the stage of the accident:
firstly, when the corresponding equipment is in a non-fault state at the time t d, the corresponding equipment is in the non-fault state at the time t d -1, namely the corresponding equipment accords with Therefore, satisfy/>; Secondly, when the corresponding device is in a fault state at time t d -1, it must be in a fault state at time t d, i.e. conforming to/>Therefore, it meets
；
Thereby converting the formula according to the full probabilityFormula (11) can be converted to (14):
（14）；
Because the same cell may have a repeat cell path in its energy supply path, the transformed formula (14) still contains non-independent outage event intersection probabilities, i.e Based on the full probability transformation formula and the conditional probability transformation formula/>The following transformations were carried out:
（15）；
In the above formula (15) Representing the probability that for the node dependent cell i, the first energy supply channel is not in a fault state at the time t d, and all other energy supply channels are in the fault state;
Defining an index
The following steps are:
（16）；
For convenience of description, further decoupling the second energizing channel from the other energizing channels in formula (15) can yield formula (17) equivalent to formula (15), which can be divided into three parts:
the first part is related to the uncoupling path and is represented by formula (17) An item;
The second part is singly related to each energy supply path of decoupling, and is provided in the formula (17) An item;
the third part is related to all the decoupled energy supply paths, and is shown in the formula (17) An item;
The specific expression is:
（17）；/>
the continuous application of the energy supply path simplification method based on conditional probability can decouple complex non-independent fault events related to the energy supply path, and finally can obtain an equivalent formula after v-th decoupling of the formula (15), as shown in the formula (18), which is shared Item, expressed as formula (18):
（18）；
the first class of equation (18) corresponds to energy supply path fault event probabilities for unassociated line removal (ω=0);
the second class corresponds to the energy supply path fault event probability of removing one associated line (ω=1);
the third class corresponds to the energy supply path failure event probability of removing two associated lines (ω=2);
By analogy, for the node dependent cell i, after m i -1 decoupling, the complex non-independent fault event can be completely removed in the probability expression, and based on the general form of the formula (18), the non-simulation expression of the load outage event representing the toughness in the energy system accident is obtained, as shown in the formula (19) and the formula (20):
（19）；
（20）；
(3) Aiming at analysis expression of power failure time in the post-accident stage:
similarly, according to the characteristics of the load outage event after the accident, when the corresponding equipment is overhauled at the moment T d+τe, the corresponding equipment is in a non-fault state at the moment T d+τe +1, namely, accords with Therefore, it meets；
Secondly, when the corresponding equipment is in a fault state at the moment T d+τe +1, the corresponding equipment is in a fault state at the moment T d+τe, namely, the corresponding equipment accords withTherefore, the method satisfies the following conditions: /(I)
；
Then, in conjunction with the full probability transformation formula, equation (12) can be transformed into equation (21):
（21）；
continuously applying a conditional probability-based energy supply path simplification method similar to the previous section, a non-simulation expression of a load outage event representing the toughness after an energy system accident can be obtained, as shown in the formula (22) and the formula (23):
（22）；
（23）；
It should be noted that the evaluation method proposed by the present invention does not consider the switching action time, for the following reasons: the reason why the power distribution network system does not consider the switching time is mainly to simplify the model and improve the calculation efficiency; in the elasticity evaluation, the main concern is the power supply reliability and the recovery capability of the multi-element power distribution network, the switching time is often a relatively small factor, and considering the switching time introduces more variables and complexity, and the factors such as the operation speed, the response time and the coordination among the switches need to be considered, which all increase the complexity of a model, lead to the increase of the calculated amount and possibly lead to the instability of the calculated result; in addition, the switching time is generally related to the performance and technology of a specific device, and the switching time of different devices may be different, and in actual operation, the switching time may be affected by various factors, such as device conditions, operation maintenance, and the like, which cause variations and uncertainties in the switching time;
Therefore, in the evaluation of the multi-element power distribution network system, the switching time is generally regarded as a constant or a smaller fixed value, so that the model is simplified, the calculation complexity is reduced, and the power supply reliability, the recovery strategy and the overall elasticity level of the multi-element power distribution network can be more intensively studied, so that the disaster resistance and the emergency response capability of the multi-element power distribution network are more effectively improved.
In the embodiment of the invention, the effectiveness of the method is verified through the calculation and analysis, and particularly the effectiveness is verified through the rapid evaluation and the evaluation of the non-sampling method introduced above for the system formed by the IEEE10 node power distribution network and the 10 node natural gas network.
The IEEE10 node distribution network and the 10 node natural gas network system are used as shown in the figures, and it can be seen from fig. 3 that the electric-gas energy system is coupled through 1 distributed gas turbine and 1 electric conversion equipment, and all nodes are divided into 4 gas cells, 3 electric cells and 2 cross-energy flow cells.
Wherein the load of each node and each electric-gas cell and cross-energy flow cell in the electric-gas multi-cell distribution network system is shown in figure 3.
Setting a period T d =6 in natural disaster accidents, and setting a period T e =6 after the accidents, and obtaining the network frame fault probability and repair time according to a regional distribution network fault probability modeling method of the formula (13) as shown in the following table 1.
TABLE 1 probability of failure and repair time for grid rack in electric-air area distribution network
Cell energy supply paths accounting for the multi-energy support and network reconstruction are obtained based on the node dependent cell energy supply path model as shown in table 2 below.
TABLE 2 node dependency cell energy supply Path Table
After the energy supply path of each node dependent cell is obtained, the load outage event probability in an accident (table 3) and the load outage event probability after the accident (table 4) can be obtained based on the proposed extreme fault probability event model and the non-simulation expression method.
TABLE 3 probability of load outage event in an accident
TABLE 4 probability of post-accident load outage event
After obtaining the probability of failure time in and after all cell accidents, the value of the elasticity index is finally obtained by combining the loads of each node in (2) and fig. 3 E Therefore, the recovery power of the power distribution network is evaluated.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention.
Claims (2)
1. A power distribution network system restoring force evaluation method based on construction of multiple evaluation indexes is characterized by comprising the following steps of: the method comprises the following evaluation steps:
Step one: the load supply capacity of the power distribution network system under natural disasters is quantified through toughness evaluation, processes at the pre-fault, during-fault and post-fault stages are evaluated respectively, and elasticity level evaluation indexes of the system are established;
When evaluating the elasticity level of the system, the total loss of the system functions is adopted Characterization is performed, and the expression is:
；
Wherein SR is the system load supply capacity, SR 0 is the system load supply capacity when no fault occurs, T e、Ts is two time points, and [ T s,Td ] and [ T d,Te ] are defined as the duration of the fault in the disaster and the load recovery period after the disaster respectively;
Converting into expected values of system function loss considering all probability scenes by expanding deterministic elasticity indexes into probabilistic elasticity indexes E The expression is:
；
Wherein N is a node dependency cell set of the regional distribution network; τ d and τ e are load outage times during the in-disaster fault duration and post-disaster load recovery period, respectively; p d i,τd is the probability that the load outage time of the dependent cell i is tau d under the duration of the in-disaster fault; p e i,τe is the probability that the load outage time of the dependent cell i is tau e in the post-disaster load recovery period; f b D is the load power of node i; A node set in a node cell S;
step two: in order to quantify a multi-element power distribution network and reduce power failure loss capacity in elasticity evaluation, an energy supply path model of each node dependent cell is established based on the relation between the power on and power off of the node cell and a specific line, and the energy supply path is used for subsequent probability event construction and index analysis expression:
for a certain node cell S, the calculation formula of the objective function is as follows:
；
Wherein x s is marked as a 0-1 variable, if the variable is 1, the load of the node cell s can be recovered, otherwise, if the variable is 0, the load cannot be recovered; wherein Ω(s) is represented as a set of nodes in node cell s;
Analyzing the operation constraint of the node dependency cell energy supply path model, wherein a complete energy supply restoration path is required to start from a node cell comprising a transformer substation and end at a target node cell S, and the energy supply path is required to pass through a certain determined cell at most once, if at least one energy supply path passing through a node cell m exists, the node cell is restorable, and if the energy supply path passes through the node cell m, the power supply restoration can be realized for both a node i and a non-switching circuit (i, j) in the node cell;
The constraint expression adopting the topological state of the net rack is as follows:
；
Wherein x B m,n is a variable of 0 to 1, and if 1, the variable is expressed as an openable line passing between two node cells from cell m to cell n, and if not, the openable line passing between two node cells from cell m to cell n is expressed as 0;
x B n,m is a 0-1 variable, if 1, representing an openable line passing between two node cells from cell n to cell m, if not, marking the openable line passing between two node cells from cell n to cell m as 0;
n is a node cell set; NS is a collection of node cells comprising the substation;
；
Wherein x B n,s is a 0-1 variable representing an openable circuit passing between two node cells from cell n to cell s; x B s,n is a 0-1 variable representing an openable line from cell s to cell n passing between two node cells;
；
；
；
Wherein x B m,n is a variable of 0 to 1, and if 1, the variable is expressed as an openable line passing between two node cells from cell m to cell n, and if not, the openable line passing between two node cells from cell m to cell n is expressed as 0; NS is represented as a collection of node cells comprising the substation; i (M) represents a node set in node cell M;
wherein x m is a 0-l variable, if 1, it means that the energy supply path will pass through cell m, if not, it will be 0;
Wherein x B i,j is a 0-1 variable, which indicates whether the non-switching circuit (i, j) can be powered, if so, the power supply is restored, i, if not, the power supply is restored, 0;
Wherein B m is the set of non-switching lines in the node cell m;
Meanwhile, the safe operation constraint conditions of the load flow balance constraint and the capacity constraint are required to be met, and the expressions of the constraints are as follows:
；
；
Wherein: ，/> respectively representing node and line operation state variables, when corresponding equipment is powered, the value is 1, otherwise, the value is 0, and f l,fs,fu is respectively the energy flow of the line, the root node and the energy conversion equipment,/> 、/>、/>Energy flow upper limit of line, root node and energy conversion equipment respectively,/>,/>Is a head node-line, tail node-line association matrix,/>For node-energy production facility association matrix,/>The node-energy conversion equipment incidence matrix;
Obtaining an energy supply path leading to a cell S based on the solving of the energy supply path model, and obtaining all the needed energy supply paths by continuously carrying out loop iteration solving on each constraint expression model;
Step three: analyzing fault probability events from two aspects of load outage time in an accident and load outage time after the accident, and establishing a probability event model:
Step 3.1: for probabilistic events related to phase outage time in an accident:
In the accident middle stage of the multi-element power distribution network, positioning, isolating and repairing are carried out aiming at the equipment with faults or damages so as to recover the normal operation of the multi-element power distribution network, thereby defining that when the fault event meets the following event conditions, the load in the corresponding node dependent cell is stopped to supply to the disaster end:
Event 1: extreme faults occur inside the node dependent cells;
event 2: extreme faults occur in all possible energy supply paths of the node dependent cells;
expected value for loss based on probability of occurrence of event 1 and event 2 E The probability P d i,τd in the expression is expressed as:
；
Wherein, cell (i) is the index of the internal equipment of cell i; path (i, m i) provides a path index for cell i, where m i is the number of path entries for cell i; then A set of fault events representing a fault state within cell i at time t d -1,/>A set of fault events representing that the mth i energy supply paths of the cell i are in a fault state at time t d -1;
step 3.2: for probability events related to post-accident phase power failure time:
The system needs to be repaired and reconfigured after a fault event to ensure the reliability and stability of the power supply, thereby defining that the corresponding cells resume normal energy supply when the service measures meet the following event conditions:
event 3: repairing a fault element in the node dependency cell by using the overhaul resource;
Event 4: repairing one feasible energy supply path of the node dependent cell by using the overhaul resource;
Expected value for loss based on probability of occurrence of event 3 and event 4 E The probability P e i,τe in the expression is expressed as:
；
In the method, in the process of the invention, Indicates that the energy supply path of the cell is in a fault state at the time T d+τe +1, and the energy supply path of the cell is in a fault state at the time TThe node cell is in a fault state at the moment T d+τe, and B [ cell (i), tau e ] and B [ path (i, m i),τe ] respectively represent the time period/>A set of devices in the cell interior, energy supply path, greater than τ e, namely:
And
；
Step four: analyzing and expressing each elastic index, and specifically, analyzing and expressing event probability as a function of line fault probability based on a method of conditional probability, full probability and topology simplification:
step 4.1: establishing a power distribution network fault probability model:
based on normal distribution characteristics of tensile bending strength of the multi-element power distribution network frame, a mathematical model of the failure rate of the multi-element power distribution network under disasters is established, and the expression is as follows:
；
Wherein: σ l PDS is the failure rate of the first power line in the power distribution network, and x g is the stress which can be borne by the section of the first power line; x l is the tensile and bending strength of the first power line, and mu l and delta l are the tensile and bending strength mean value and standard deviation of the power line respectively;
Step 4.2: analyzing and expressing the power failure time in the accident stage:
When the corresponding device is in a non-fault state at time t d, then it must be in a non-fault state at time t d -1, i.e. conform to Therefore, satisfy/>；
When the corresponding device is in a fault state at the time t d -1, the corresponding device is in a fault state at the time t d, namely, the corresponding device accords withTherefore, it meets
；
Thereby converting the formula according to the full probabilityThe expression of probability P d i,τd based on the probability of occurrence of event 1 and event 2 is translated into:
；
The energy supply path based on the same monoblock has repeated cellular channels, so the transformed upper part still comprises the non-independent outage event intersection probability, namely There is also a need for a method based on the full probability transformation formula and the conditional probability transformation formula/>The following transformations were carried out:
；
In the method, in the process of the invention, Representing the probability that for the node dependent cell i, the first energy supply channel is not in a fault state at the time t d, and all other energy supply channels are in the fault state;
Defining an index Then the following is satisfied:
；
for convenience of description, further description will be made The second energy supply channel is decoupled from other energy supply channels in the conversion formula of (a), and an equivalent expression comprising three parts can be obtained:
the first part is related to the uncoupling path, and has the following expressions An item;
The second part is singly related to each energy supply path of decoupling, and has the following expression An item;
the third part is related to all decoupled energy supply paths, and is expressed by An item;
The expression is:
；
For the continuous application of the energy supply path simplification method based on the conditional probability, the complex non-independent fault event related to the energy supply path is decoupled, and the aim is achieved Equivalent formulas after v-th decoupling of conversion formulas of (a) are sharedThe term, expression is:
；
The first category corresponds to energy supply path fault event probabilities for unassociated line removal (ω=0);
the second class corresponds to the energy supply path fault event probability of removing one associated line (ω=1);
the third class corresponds to the energy supply path failure event probability of removing two associated lines (ω=2);
And so on, for the node dependency cell i, after m i -1 decoupling, completely removing the complex non-independent fault event in the probability expression, and obtaining the non-simulation expression of the load outage event for representing the toughness in the energy system accident based on the general form, wherein the expression is as follows:
；
；
step 4.3: analyzing and expressing the power failure time at the post-accident stage:
when the corresponding equipment is overhauled at the moment T d+τe, the corresponding equipment is in a non-fault state at the moment T d+τe +1, namely, accords with Therefore, it meets
；
When the corresponding device is in a fault state at the moment T d+τe +1, the corresponding device is in a fault state at the moment T d+τe, namely the corresponding device accords withTherefore, it meets
；
Combining a full probability conversion formula, converting an expression of the probability P e i,τe based on the occurrence probability of the event 3 and the event 4 into:
；
continuously applying an energy supply path simplification method based on conditional probability to obtain a non-simulation expression of a load outage event for representing the toughness of an energy system after an accident, wherein the expression is as follows:
；
。
2. The power distribution network system restoring force evaluation method based on construction of multiple evaluation indexes according to claim 1, wherein the method comprises the following steps of: the specific method for recovering the normal operation of the multi-element power distribution network in the accident stage in the step 3.1 comprises the following steps:
fault detection and localization: the power distribution network operators receive fault alarms and then determine the position of the fault through fault detection and positioning technologies;
isolation and fault removal: after the fault position is determined, operators take necessary measures to isolate the fault equipment, so as to prevent the fault from continuing to spread or affecting other equipment;
Repair and replacement equipment: after isolating the fault, operators repair or replace the fault equipment, wherein the repair may comprise replacement of the fault element, repair of damaged cables or equipment, and replacement of new equipment is required if the equipment cannot be repaired;
Functional recovery and testing: after the repair or replacement of the fault equipment is finished, system testing and function recovery are carried out by power distribution network operators, so that the equipment can be ensured to normally operate;
And (5) power supply recovery: and after the fault equipment in the power distribution network is repaired and passes the test, the operators gradually recover the power supply, the affected node cells are reconnected to the power grid, and the power supply of the users is recovered.
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