CN108921725A - A kind of Complicated Distribution Network reliability index fast resolving calculation method - Google Patents
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Abstract
A kind of Complicated Distribution Network reliability index fast resolving calculation method.It includes forming M segmentation N using block switch as boundary abbreviation Complicated Distribution Network and getting in touch with reliability calculation unit, calculating forms all branches and equivalent node fault parameter vector in M segmentation N contact reliability calculation unit;The node branch incidence matrix for constructing each M segmentation N contact reliability calculation unit, inverts to node branch incidence matrix, obtains each power supply to the supply path matrix of all equivalent nodes;It determines that three kinds of failures influence type, is based on supply path matrix, constructs three fault estimators of fault element;Three classes fault estimator and fault parameter vector be subjected to matrix algebra operation, obtains the reliability index of power distribution network and equivalent node.The invention can avoid the Fault enumerations and fault coverage search work of the repeatability in Calculation of Reliability, can save and calculate the time, improve computational efficiency.
Description
Technical field
The invention belongs to power distribution technical fields, more particularly to a kind of Complicated Distribution Network reliability index fast resolving
Calculation method.
Background technique
Power distribution network significantly affects the reliability level of power consumer, according to statistics 80% or more user's power outage
From the dependent failure of power distribution network.With opening gradually for social development and electricity market, power consumer wants reliability
Ask continuous improvement, the power supply reliability as one of electricity commodity characteristic also will become user select supplier important references because
Element.In recent years, the access of distributed generation resource, various power electronics equipment, novel load etc., keeps the structure of power distribution network more multiple
Miscellaneous, the raising of the technical levels such as power distribution automation keeps the method for operation of power distribution network more flexible, and research is suitable for structure is complicated, fortune
The flexible distribution network reliability fast evaluation method of line mode is significant.
Currently, the method for distribution network reliability is assessed mainly based on the network model of power distribution network, i.e. failure effect mould
Formula analytic approach analyzes influence of each event of failure to load point, forms the system failure by enumerating all component failure events
Set of modes finally obtains load point and Reliability Index.This analytic process is relatively time consuming, because analyzing each event
When the coverage of barrier event, require to carry out fault coverage search along the branch of power distribution network, with the expansion of network size
With increasing for event of failure, the workload of search can exponentially trend growth, to seriously affect the efficiency of fail-safe analysis,
Therefore, there is an urgent need to find a kind of high efficient and reliable calculation method for large-scale complex distribution network.
Summary of the invention
To solve the above-mentioned problems, the purpose of the present invention is to provide a kind of Complicated Distribution Network reliability index fast resolvings
Calculation method.
In order to achieve the above object, Complicated Distribution Network reliability index fast resolving calculation method provided by the invention includes
The following steps carried out in order:
Step 1) carrys out abbreviation Complicated Distribution Network by boundary of block switch, forms M segmentation N and gets in touch with reliability calculation unit,
And then calculate the fault parameter vector for forming all branches and equivalent node in M segmentation N contact reliability calculation unit;
Step 2) constructs the node branch incidence matrix of each M segmentation N contact reliability calculation unit, and to node branch
Incidence matrix is inverted, and obtains each power supply to the supply path matrix of all equivalent nodes;
Step 3) determines that three kinds of failures influence type, is based on above-mentioned supply path matrix, constructs three events of fault element
Hinder incidence matrix, three fault estimators, which respectively correspond above-mentioned three kinds of failures, influences type;
The fault parameter vector that the three classes fault estimator and step 1) that step 4) obtains step 3) obtain carries out square
Algebra of matrices operation obtains the reliability index of power distribution network and equivalent node.
It is described to carry out abbreviation Complicated Distribution Network by boundary of block switch in step 1), it is reliable to form M segmentation N contact
Property computing unit, and then calculate formed the M segmentation N contact reliability calculation unit in the failure of all branches and equivalent node ginseng
Specific step is as follows for number vector:
Step 1.1) abbreviation Complicated Distribution Network finds the branch that block switch is installed in Complicated Distribution Network first;
Step 1.2) then carries out the equivalent fusion of element using these branches as boundary, and it is reliable that M segmentation N contact is consequently formed
Property computing unit;
Step 1.3) applies depth-priority-searching method, and M segmentation N is searched for since power supply and gets in touch with reliability calculation unit, search
While re-start the number of equivalent node or load bus and branch;
After step 1.4) forms M segmentation N contact reliability calculation unit, need to calculate M segmentation N contact Calculation of Reliability
The fault parameter vector of all branches and equivalent node in unit, fault parameter vector include failure rate and fault correction time two
A fault parameter vector;It is initially formed the failure rate vector sum fault correction time vector of all branches, it can by M segmentation N contact
Ascending sequence is arranged the failure rate and fault correction time of all branches by number respectively in property computing unit,
Form failure rate vector λ=[λ of branch1,λ2,λ3,…,λNl] and fault correction time vector μ=[μ1,μ2,μ3,…,μNl],
Wherein λiIndicate the failure rate of No. i-th branch, μiIndicate the fault correction time of No. i-th branch, NlFor the total quantity of branch;
Step 1.5) calculates the failure rate of each equivalent node, shown in calculation formula such as formula (1):
λ in formula (1)eqFor the failure rate of the equivalent node, λX,iFor i-th of fault element included in the equivalent node
Failure rate, the fault element quantity that X is included for the equivalent node;
Step 1.6) calculates the fault correction time of each equivalent node, using the calculating of series connection element fault repair time
The fault correction time of each equivalent node is calculated in method, as shown in formula (2):
μ in formula (2)eqFor the failure rate of the equivalent node, μX,iFor i-th of fault element included in the equivalent node
Fault correction time, the fault element quantity that X is included for the equivalent node;
Step 1.7) is ascending suitable according to numbering respectively by the failure rate of all equivalent nodes and fault correction time
Sequence is arranged, and the failure rate vector λ of equivalent node can be obtainedeq=[λeq1,λeq2,λeq3,…,λeqNb] and when fault restoration
Between vector μeq=[μeq1,μeq2,μeq3,…,μeqNb], wherein λeqiAnd μeqiRespectively indicate the failure rate and event of No. i-th equivalent node
Hinder repair time, NbFor the total quantity of equivalent node.
In step 2), the node branch incidence matrix of each M segmentation N contact reliability calculation unit of the construction,
And invert to node branch incidence matrix, obtain each power supply to the specific steps of the supply path matrix of all equivalent nodes such as
Under:
Step 2.1) constructs the node branch incidence matrix E of M segmentation N contact reliability calculation unit:eijIt is in matrix E
I row jth column element value;It only include three kinds of elements in node branch incidence matrix E, when equivalent node i and jth branch are not attached to
When, eij=0, when equivalent node i is the starting point of jth branch, eij=1, when equivalent node i is the terminal of jth branch
When, eij=-1;
Step 2.2) deletes the first row in above-mentioned node branch incidence matrix, the i.e. corresponding row of power supply, forms square matrix, so
It inverts afterwards to this square matrix, to obtain supply path matrix.
In step 3), described three kinds of failures of determination influence type, are based on above-mentioned supply path matrix, building failure member
Three fault estimators of part, three fault estimators, which respectively correspond above-mentioned three kinds of failures, influences the specific steps of type such as
Under:
Step 3.1) determines that three kinds of failures influence type:Failure influences type a:Element fault causes load all for circuit
Diameter disconnects, and can just restore electricity after only waiting until fault restoration;Failure influences type b:Element fault leads to all power supplies of load
Path disconnects, and after Fault Isolation, load can restore to be powered by main power source;Failure influences type c:Element fault leads to load
All supply paths disconnect, and after Fault Isolation, load, which can turn to be supplied to backup power source, to restore electricity;
Three fault estimators of step 3.2) building fault element:The influence information that fault element has a power failure to load
It concludes into three fault estimators, the row number of three fault estimators corresponds to the number of fault element, column number pair
Answer the number of equivalent node;Element in fault estimator is that " 1 " indicates that the element fault of corresponding row number will lead to correspondence
The equivalent node of column number has a power failure, conversely, a certain element is the element fault that " 0 " indicates corresponding row number in fault estimator
On equivalent node without influence;
Fault element includes branch trouble and equivalent node failure;
The method of building branch trouble incidence matrix A, B, C include the following steps:
3.2.1 branch trouble incidence matrix A) is constructed
Main power source is obtained to the supply path matrix R of all equivalent nodes first, in accordance with the method for step 2)1;Then according to
The method of step 2) obtains backup power source K to the stand-by power supply path matrix R of all equivalent nodesk;Finally sought according to formula (3)
The intersection matrix of above-mentioned two supply path matrix, obtained intersection matrix are exactly branch trouble incidence matrix A:
A=R1∩Rk (3)
The step-by-step AND operation of operator " ∩ " representing matrix element in formula (3), i.e. two supply path matrixes are corresponding
The value of element is simultaneously 1, then otherwise it is 0 that the element value of intersection matrix corresponding position, which is 1,;
3.1.2 branch trouble incidence matrix B) is constructed
Reliability calculation unit progress subregion is got in touch with firstly the need of N is segmented to M as boundary using the switch of snap action;If M
It is segmented in N contact reliability calculation unit and shares NSThe switch of a snap action, using it as boundary, the M can be segmented to N contact can
N is divided by property computing unitSA subregion;If the set of fingers in each subregion is ΩS;
Then supply path matrix R is corrected according to above-mentioned partitioning scenario1In element, supply path matrix R1In it is each
Row vector liIt is modified all in accordance with formula (4):
L in formula (4)i corFor revised each row vector, the element of all row vectors is after amendment after composition amendment
Supply path matrix R1 cor;Boolean operator " ∪ " in formula (4) is defined as set of fingers ΩSThe step-by-step of middle institute's directed quantity
Inclusive-OR operation, i.e. row vector l1 corIn a certain element value be 0 or 1, it pass through set of fingers ΩSIn all row vector liIt is corresponding
Position element value carries out inclusive-OR operation and obtains;
Finally it is based on revised supply path matrix R1 corBranch trouble incidence matrix B is calculated, is shown below:
3.1.3 branch trouble incidence matrix C) is constructed
Branch trouble incidence matrix C is calculated as follows:
C=R1-A (6)
Construct equivalent node fault estimator Aeq、Beq、CeqMethod include the following steps:
3.2.4 equivalent node fault estimator A) is constructedeq
For equivalent node fault estimator Aeq, the element on diagonal line is " 1 ", indicates equivalent node faults itself
The load that will lead to itself has a power failure;In addition to the element on diagonal line, equivalent node fault estimator AeqThe element of other positions
It is calculated by formula (7):
aeqi,j=ai,j(i≠j) (7)
A in formula (7)eqi,jIndicate equivalent node fault estimator AeqIn the i-th row jth column element, ai,jIt indicates in step
Rapid 3.1.1) in obtain branch trouble incidence matrix A in the i-th row jth column element, formula (7) indicate equivalent node fault correlation
Matrix AeqThe element of off-diagonal is identical as the branch trouble incidence matrix element A obtained in step 3.1.1);
3.2.5 equivalent node fault estimator B) is constructedeq
Equivalent node fault estimator BeqIn element according to branch trouble incidence matrix B in step 3.1.2) method
It obtains;
3.2.6 equivalent node fault estimator C) is constructedeq
Equivalent node fault estimator CeqIt is calculated by formula (8):
Ceq=R1-Aeq (8)。
In step 4), the fault parameter of the three classes fault estimator that step 3) is obtained and step 1) acquisition
Vector carries out matrix algebra operation, and obtaining the reliability index of power distribution network and equivalent node, specific step is as follows:
Using four indices as reliability index, with annual frequency of power cut, i.e. SAIFI and annual power off time,
That is reliability index calculating method of the SAIDI as power distribution network, shown in calculation formula such as formula (9), (10):
Oeprator " ο " in formula (10) indicates Hadamard product, and operation rule is matrix or vector corresponding position element
It is multiplied;tswRepresent the operating time of the block switch isolated fault of branch;topRepresent the interconnection switch operating time;λ, μ are branch
Failure rate vector sum fault correction time vector;λeq、μeqFor equivalent node failure rate vector sum fault correction time vector;A,
B, it is branch trouble incidence matrix that C, which is respectively three,;Aeq、Beq、CeqRespectively three equivalent node fault estimators;N is indicated
The number of users of each load bus arranges the user's number vector to be formed according to ascending sequence is numbered, and N indicates load bus
All numbers of users;
Using the frequency of power cut of each equivalent node and power off time as the reliability index of load bus, calculation method is such as
Shown in formula (11), (12):
R=λ × (A+B+C)+λeq×(Aeq+Beq+Ceq) (11)
R in formula (11) indicates the frequency of power cut of all load bus according to the vector for numbering ascending arrangement, formula
(12) d in indicates the power off time of all load bus according to the vector for numbering ascending arrangement.
The beneficial effect of Complicated Distribution Network reliability index fast resolving calculation method provided by the invention:It is avoided that can
The Fault enumeration and fault coverage search work of repeatability in property calculating, can save and calculate the time, improve computational efficiency.Together
When, by the observation to fault estimator, the weak link for influencing distribution network reliability can be rapidly found out, to be power distribution network
Reliability promoted work provide significantly more efficient analysis means.
Detailed description of the invention
Fig. 1 is Complicated Distribution Network reliability index fast resolving calculation method flow chart provided by the invention.
Fig. 2 is that M is segmented N contact reliability calculation unit abbreviation and number process schematic.
Fig. 3 is supply path matrix forming process schematic diagram.
Fig. 4 is fault estimator A forming process.
Fig. 5 is that M is segmented N contact subregion schematic diagram.
Fig. 6 is supply path matrix R1 makeover process schematic diagram.
Fig. 7 is power distribution network IEEE RBTS Bus6 schematic diagram.
The networked examination M that Fig. 8 is feeder line F4 is segmented N and gets in touch with reliability calculation unit structural schematic diagram.
Specific embodiment
In the following with reference to the drawings and specific embodiments to Complicated Distribution Network reliability index fast resolving meter provided by the invention
Calculation method is described in detail.
As shown in Figure 1, Complicated Distribution Network reliability index fast resolving calculation method provided by the invention includes in order
The following steps of progress:
Step 1) carrys out abbreviation Complicated Distribution Network by boundary of block switch, forms M segmentation N and gets in touch with reliability calculation unit,
And then calculate the fault parameter vector for forming all branches and equivalent node in M segmentation N contact reliability calculation unit;
Specific step is as follows:
Step 1.1) abbreviation Complicated Distribution Network finds the branch that block switch is installed in Complicated Distribution Network, the present invention first
By taking the Complicated Distribution Network that Fig. 2 (a) is shown as an example, i.e., 1,5,9,11,13,15, No. 18 branch;
Step 1.2) then carries out the equivalent fusion of element using these branches as boundary, and it is reliable that M segmentation N contact is consequently formed
Property computing unit;Such as the element in Fig. 2 (a) in dotted line frame includes LP2, LP3 load bus and 2,3, No. 4 branches, this
A little elements are located between 1, No. 5 branch, therefore, are fused into an equivalent node, i.e. No. 1 equivalent node in Fig. 2 (b);
Step 1.3) applies depth-priority-searching method, and M segmentation N is searched for since power supply and gets in touch with reliability calculation unit, search
While re-start the number of equivalent node or load bus and branch.If all elements in Fig. 2 (b) are renumberd,
Shown in number result such as Fig. 2 (c).
After step 1.4) forms M segmentation N contact reliability calculation unit, need to calculate M segmentation N contact Calculation of Reliability
The fault parameter vector of all branches and equivalent node in unit, fault parameter vector include failure rate and fault correction time two
A fault parameter vector, so as to the input parameter calculated as distribution network reliability;Be initially formed the failure rates of all branches to
Amount and fault correction time vector, when M segmentation N is got in touch with the failure rate and fault restoration of all branches in reliability calculation unit
Between ascending sequence is arranged by number respectively, form failure rate vector λ=[λ of branch1,λ2,λ3,…,λNl] and therefore
Hinder repair time vector μ=[μ1,μ2,μ3,…,μNl], wherein λiIndicate the failure rate of No. i-th branch, μiIndicate No. i-th branch
Fault correction time, NlFor the total quantity of branch;
Step 1.5) calculates the failure rate of each equivalent node, due to including multiple fault elements in equivalent node,
Need to calculate the failure rate of all fault elements, so that the failure rate of equivalent node is obtained, shown in calculation formula such as formula (1):
λ in formula (1)eqFor the failure rate of the equivalent node, λX,iFor i-th of fault element included in the equivalent node
Failure rate, the fault element quantity that X is included for the equivalent node.Formula (1) indicates that the failure rate of equivalent node is equal to this etc.
The sum of the failure rate for all fault elements that effect node includes.
Step 1.6) calculates the fault correction time of each equivalent node, using the calculating of series connection element fault repair time
The fault correction time of each equivalent node is calculated in method, as shown in formula (2):
μ in formula (2)eqFor the failure rate of the equivalent node, μX,iFor i-th of fault element included in the equivalent node
Fault correction time, the fault element quantity that X is included for the equivalent node.
Step 1.7) is ascending suitable according to numbering respectively by the failure rate of all equivalent nodes and fault correction time
Sequence is arranged, and the failure rate vector λ of equivalent node can be obtainedeq=[λeq1,λeq2,λeq3,…,λeqNb] and when fault restoration
Between vector μeq=[μeq1,μeq2,μeq3,…,μeqNb], wherein λeqiAnd μeqiRespectively indicate the failure rate and event of No. i-th equivalent node
Hinder repair time, NbFor the total quantity of equivalent node.
Step 2) constructs the node branch incidence matrix of each M segmentation N contact reliability calculation unit, and to node branch
Incidence matrix is inverted, and obtains each power supply to the supply path matrix of all equivalent nodes;
Specific step is as follows:
Since the basic reason that element fault causes load to power off is that the failure of the element causes power supply to the load
The interruption of the supply path of node.The present invention indicates the supply path information of each power supply to all equivalent nodes with matrix, and
It is defined as supply path matrix, to facilitate the matrix of subsequent reliability index to calculate.
Step 2.1) constructs the node branch incidence matrix E of M segmentation N contact reliability calculation unit.eijIt is in matrix E
I row jth column element value;It only include three kinds of elements in node branch incidence matrix E, when equivalent node i and jth branch are not attached to
When, eij=0, when equivalent node i is the starting point of jth branch, eij=1, when equivalent node i is the terminal of jth branch
When, eij=-1.
Step 2.2) deletes the first row in above-mentioned node branch incidence matrix, the i.e. corresponding row of power supply, forms square matrix, so
It inverts afterwards to this square matrix, to obtain supply path matrix.
By taking the M segmentation N contact reliability calculation unit in Fig. 2 as an example, illustrate the process for seeking supply path matrix.It is based on
Above-mentioned node branch incidence matrix E deletes row, i.e. the 1st row corresponding to power supply, obtains square matrix E1, then to square matrix E1It inverts,
Power supply can be obtained in the power distribution network to the supply path matrix R of each equivalent node1, as shown in Figure 3.Supply path matrix R1
Line number and branch number correspond, supply path matrix R1Each column be reference numeral equivalent node for circuit
Diameter.For example, to supply path matrix R1It is observed by column, then 6. arranges b where dotted arrow in Fig. 36, as equivalent section
The supply path of point 6..1,2,3,6 row of behavior where the non-zero element 6. arranged, be also just in Fig. 2 equivalent node 6. arrive power supply
The branch number being required through.Supply path matrix R1In -1 represent supply path direction, 1 generation identical as Branch Power Flow direction
Table supply path direction is contrary with Branch Power Flow.
Step 3) determines that three kinds of failures influence type, is based on above-mentioned supply path matrix, constructs three events of fault element
Hinder incidence matrix, three fault estimators, which respectively correspond above-mentioned three kinds of failures, influences type;
Specific step is as follows:
Step 3.1) determines that three kinds of failures influence type:Failure influences type a:Element fault causes load all for circuit
Diameter disconnects, and can just restore electricity after only waiting until fault restoration;Failure influences type b:Element fault leads to all power supplies of load
Path disconnects, and after Fault Isolation, load can restore to be powered by main power source;Failure influences type c:Element fault leads to load
All supply paths disconnect, and after Fault Isolation, load, which can turn to be supplied to backup power source, to restore electricity;
Three fault estimators of step 3.2) building fault element:The influence information that fault element has a power failure to load
It concludes into three fault estimators, the row number of three fault estimators corresponds to the number of fault element, column number pair
Answer the number of equivalent node;Element in fault estimator is that " 1 " indicates that the element fault of corresponding row number will lead to correspondence
The equivalent node of column number has a power failure, conversely, a certain element is the element fault that " 0 " indicates corresponding row number in fault estimator
On equivalent node without influence;
Fault element in the present invention includes branch trouble and equivalent node failure.Three branches of building are described separately as below
Fault estimator A, B, C and three equivalent node fault estimator Aeq、Beq、CeqProcess.
The method of described building branch trouble incidence matrix A, B, C include the following steps:
3.2.1 branch trouble incidence matrix A) is constructed
Main power source is obtained to the supply path matrix R of all equivalent nodes first, in accordance with the method for step 2)1;Then according to
The method of step 2) obtains backup power source K to the stand-by power supply path matrix R of all equivalent nodesk;Finally sought according to formula (3)
The intersection matrix of above-mentioned two supply path matrix, obtained intersection matrix are exactly branch trouble incidence matrix A.
A=R1∩Rk (3)
The step-by-step AND operation of operator " ∩ " representing matrix element in formula (3), i.e. two supply path matrixes are corresponding
The value of element is simultaneously 1, then otherwise it is 0 that the element value of intersection matrix corresponding position, which is 1,.Two supply path matrixes of formula (3)
The practical significance of AND operation be:When two supply paths of a certain equivalent node have overlapping, the branch road of lap
It breaks down, all supply paths of the equivalent node disconnect, therefore load has a power failure, and can not turn to supply, and can only wait until failure
It can just restore electricity after the completion of repairing.
By Fig. 2 shows power distribution network for, the supply path matrix of backup power source K is as shown in figure 4, main power source and standby electricity
The supply path matrix element of source K obtains branch trouble incidence matrix A, the only member in solid box after carrying out step-by-step AND operation
Element is 1.Such as when No. 6 branch trouble, the supply path of equivalent node 6., 7. is disconnected, and can not turn to supply.Therefore, in Fig. 4
Branch trouble incidence matrix A the 6th row in the element 6., 7. arranged be 1.
3.1.2 branch trouble incidence matrix B) is constructed
Reliability calculation unit progress subregion is got in touch with firstly the need of N is segmented to M as boundary using the switch of snap action.Instantaneously
Step switch be defined as can insantaneous break fault current switchgear, such as breaker, fuse etc..If M is segmented N, contact can
N is shared in property computing unitSThe M can be segmented N and get in touch with Calculation of Reliability list by the switch of a snap action using it as boundary
Member is divided into NSA subregion.If the set of fingers in each subregion is ΩS。
By Fig. 2 shows M segmentation N contact reliability calculation unit for illustrate above-mentioned partition method:Due to No. 1 branch
The switch that can instantaneously cut-off failure is respectively arranged with the head end of No. 6 branch, therefore, using No. 1 branch and No. 6 branch as side
The branch of M segmentation N contact reliability calculation unit is divided into two set, is represented by Ω by boundary1={ 1,2,3,4,5 }, Ω2
={ 6,7 }, subregion schematic diagram are as shown in Figure 5.
Then supply path matrix R is corrected according to above-mentioned partitioning scenario1In element, supply path matrix R1In it is each
Row vector liIt is modified all in accordance with formula (4):
L in formula (4)i corFor revised each row vector, the element of all row vectors is after amendment after composition amendment
Supply path matrix R1 cor.Boolean operator " ∪ " in formula (4) is defined as set of fingers ΩSThe step-by-step of middle institute's directed quantity
Inclusive-OR operation, i.e. row vector l1 corIn a certain element value be 0 or 1, it pass through set of fingers ΩSIn all row vector liIt is corresponding
Position element value carries out inclusive-OR operation and obtains.
By taking the M segmentation N contact reliability calculation unit in Fig. 2 as an example, revised supply path can be obtained with formula (4)
Matrix R1 corAs shown in fig. 6, for set of fingers Ω1, five branches of 1-5 are shared, then in revised supply path matrix R1 cor
In, step-by-step inclusive-OR operation is carried out to the row vector corresponding position element of 1-5 row, to obtain vector [1 11111 1].Together
Reason, for set of fingers Ω2, in revised supply path matrix R1 corIn, the row vector of 6,7 rows is modified to [0 0000
1 1]。
Finally it is based on revised supply path matrix R1 corBranch trouble incidence matrix B is calculated, is shown below:
3.1.3 branch trouble incidence matrix C) is constructed
Branch trouble incidence matrix C is calculated as follows:
C=R1-A (6)。
The building equivalent node fault estimator Aeq、Beq、CeqMethod include the following steps:
3.2.4 equivalent node fault estimator A) is constructedeq
For equivalent node fault estimator Aeq, the element on diagonal line is " 1 ", indicates equivalent node faults itself
The load that will lead to itself has a power failure.In addition to the element on diagonal line, equivalent node fault estimator AeqThe element of other positions
It is calculated by formula (7):
aeqi,j=ai,j(i≠j) (7)
A in formula (7)eqi,jIndicate equivalent node fault estimator AeqIn the i-th row jth column element, ai,jIt indicates in step
Rapid 3.1.1) in obtain branch trouble incidence matrix A in the i-th row jth column element, formula (7) indicate equivalent node fault correlation
Matrix AeqThe element of off-diagonal is identical as the branch trouble incidence matrix element A obtained in step 3.1.1).
3.2.5 equivalent node fault estimator B) is constructedeq
Equivalent node fault estimator BeqIn element according to branch trouble incidence matrix B in step 3.1.2) method
It obtains.
3.2.6 equivalent node fault estimator C) is constructedeq
Equivalent node fault estimator CeqIt is calculated by formula (8):
Ceq=R1-Aeq (8)
The fault parameter vector that the three classes fault estimator and step 1) that step 4) obtains step 3) obtain carries out square
Algebra of matrices operation obtains the reliability index of power distribution network and equivalent node.
Specific step is as follows:
The present invention, as reliability index, is had a power failure using four indices with annual frequency of power cut (SAIFI) and annual
Reliability index calculating method of the time (SAIDI) as power distribution network, shown in calculation formula such as formula (9), (10):
Oeprator " ο " in formula (10) indicates Hadamard product, and operation rule is matrix or vector corresponding position element
It is multiplied;tswRepresent the operating time of the block switch isolated fault of branch;topRepresent the interconnection switch operating time.λ, μ are branch
Failure rate vector sum fault correction time vector.λeq、μeqFor equivalent node failure rate vector sum fault correction time vector.A,
B, it is branch trouble incidence matrix that C, which is respectively three,.Aeq、Beq、CeqRespectively three equivalent node fault estimators.N is indicated
The number of users of each load bus arranges the user's number vector to be formed according to ascending sequence is numbered, and N indicates load bus
All numbers of users.
The present invention is calculated using the frequency of power cut of each equivalent node and power off time as the reliability index of load bus
Shown in method such as formula (11), (12):
R=λ × (A+B+C)+λeq×(Aeq+Beq+Ceq) (11)
R in formula (11) indicates the frequency of power cut of all load bus according to the vector for numbering ascending arrangement, formula
(12) d in indicates the power off time of all load bus according to the vector for numbering ascending arrangement.
The present invention is described further by taking the power distribution network IEEE RBTS Bus6 shown in Fig. 7 as an example below:The power distribution network
Shared load bus 40, fuse 40, distribution transformer 38, breaker 9.Disconnecting switch actuation time is 1 hour,
Interconnection switch actuation time is set as 2 hours.Branch trouble repair time is 5 hours.Branch trouble rate parameter is referring to table 1, failure
Rate unit is times/year.
1 branch trouble rate parameter of table
Step 1) forms M segmentation N and gets in touch with reliability calculation unit
According to the method for step 1.1), the power distribution network of Fig. 7 is subjected to abbreviation, M segmentation N is formed and gets in touch with Calculation of Reliability list
Member.Wherein the branch road of feeder line F1, F2 and F3 is mounted on switch, is not necessarily to abbreviation.The abbreviation process of feeder line F4 is as shown in Figure 8.
After forming M segmentation N contact reliability calculation unit, according to step 1.4) -1.7) method formed branch and equivalent node therefore
Hinder parameter vector, the specific value of fault parameter is referring to table 2.
2 branch of table and equivalent node fault parameter table
Fault element number | Failure rate (times/year) | Fault correction time (hour) |
Equivalent node 2: | 0.754 | 5 |
Equivalent node 3: | 0.6565 | 5 |
Equivalent node 4: | 0.5135 | 5 |
Equivalent node 5: | 0.3705 | 5 |
Equivalent node 6: | 0.6565 | 5 |
Equivalent node 2: | 0.754 | 5 |
Branch 35 | 0.182 | 5 |
Branch 41 | 0.039 | 5 |
Branch 43 | 0.04875 | 5 |
Branch 45 | 0.208 | 5 |
Branch 47 | 0.039 | 5 |
Branch 50 | 0.182 | 5 |
Branch 53 | 0.208 | 5 |
Branch 55 | 0.052 | 5 |
Branch 59 | 0.182 | 5 |
Step 2) constructs the supply path matrix of M segmentation N contact reliability calculation unit.It is formed according to the method for step 2)
The supply path matrix of the M segmentation N contact reliability calculation unit of feeder line F1, F2, F3 and F4.
Step 3) constructs three fault estimators.According to step 3.1) -3.3) method building feeder line F1, F2, F3 and
Branch trouble incidence matrix A, B, C of F4, then according to step 3.4) -3.3) method building feeder line F1, F2, F3 and F4
Equivalent node fault estimator Aeq、Beq、Ceq。
The reliability index of step 4) calculating power distribution network and load bus
The SAIFI that power distribution network is calculated according to the formula (9) in step 4) is 1.0067 times/family year, according in step 4)
The SAIDI that formula (10) calculates power distribution network is 6.669 hours/family year, calculates 40 load bus according to formula (11), (12)
Frequency of power cut (secondary/family year) and power off time (hour/family year) referring to table 3.
3 40 load bus reliability index calculated results of table
Claims (5)
1. a kind of Complicated Distribution Network reliability index fast resolving calculation method, it is characterised in that:The Complicated Distribution Network can
It include the following steps carried out in order by property index fast resolving calculation method:
Step 1) carrys out abbreviation Complicated Distribution Network by boundary of block switch, forms M segmentation N and gets in touch with reliability calculation unit, in turn
Calculate the fault parameter vector for forming all branches and equivalent node in M segmentation N contact reliability calculation unit;
Step 2) constructs the node branch incidence matrix of each M segmentation N contact reliability calculation unit, and is associated with to node branch
Matrix inversion obtains each power supply to the supply path matrix of all equivalent nodes;
Step 3) determines that three kinds of failures influence type, is based on above-mentioned supply path matrix, constructs three fail closes of fault element
Join matrix, three fault estimators, which respectively correspond above-mentioned three kinds of failures, influences type;
The fault parameter vector that the three classes fault estimator and step 1) that step 4) obtains step 3) obtain carries out matrix generation
Number operation, obtains the reliability index of power distribution network and equivalent node.
2. Complicated Distribution Network reliability index fast resolving calculation method according to claim 1, it is characterised in that:In step
It is rapid 1) in, it is described to carry out abbreviation Complicated Distribution Network using block switch as boundary, form M segmentation N and get in touch with reliability calculation unit, into
And calculate formed the M segmentation N contact reliability calculation unit in the fault parameter vector of all branches and equivalent node it is specific
Steps are as follows:
Step 1.1) abbreviation Complicated Distribution Network finds the branch that block switch is installed in Complicated Distribution Network first;
Step 1.2) then carries out the equivalent fusion of element using these branches as boundary, and M segmentation N contact reliability meter is consequently formed
Calculate unit;
Step 1.3) apply depth-priority-searching method, since power supply search for M segmentation N get in touch with reliability calculation unit, search it is same
When re-start the number of equivalent node or load bus and branch;
After step 1.4) forms M segmentation N contact reliability calculation unit, need to calculate M segmentation N contact reliability calculation unit
In all branches and equivalent node fault parameter vector, fault parameter vector include failure rate and fault correction time two therefore
Hinder parameter vector;It is initially formed the failure rate vector sum fault correction time vector of all branches, M segmentation N is got in touch with into reliability
Ascending sequence is arranged the failure rate and fault correction time of all branches by number respectively in computing unit, is formed
Failure rate vector λ=[λ of branch1,λ2,λ3,…,λNl] and fault correction time vector μ=[μ1,μ2,μ3,…,μNl], wherein λi
Indicate the failure rate of No. i-th branch, μiIndicate the fault correction time of No. i-th branch, NlFor the total quantity of branch;
Step 1.5) calculates the failure rate of each equivalent node, shown in calculation formula such as formula (1):
λ in formula (1)eqFor the failure rate of the equivalent node, λX,iFor the event of i-th of fault element included in the equivalent node
Barrier rate, the fault element quantity that X is included for the equivalent node;
Step 1.6) calculates the fault correction time of each equivalent node, using the calculation method of series connection element fault repair time
The fault correction time of each equivalent node is calculated, as shown in formula (2):
μ in formula (2)eqFor the failure rate of the equivalent node, μX,iFor the event of i-th of fault element included in the equivalent node
Hinder repair time, the fault element quantity that X is included for the equivalent node;
Step 1.7) by the failure rate of all equivalent nodes and fault correction time respectively according to number ascending sequence into
Row arrangement, can be obtained the failure rate vector λ of equivalent nodeeq=[λeq1,λeq2,λeq3,…,λeqNb] and fault correction time to
Measure μeq=[μeq1,μeq2,μeq3,…,μeqNb], wherein λeqiAnd μeqiThe failure rate and failure for respectively indicating No. i-th equivalent node are repaired
Multiple time, NbFor the total quantity of equivalent node.
3. Complicated Distribution Network reliability index fast resolving calculation method according to claim 1, it is characterised in that:In step
It is rapid 2) in, the node branch incidence matrix of the described each M segmentation N contact reliability calculation unit of construction, and to node branch
Incidence matrix is inverted, and obtaining supply path matrix of each power supply to all equivalent nodes, specific step is as follows:
Step 2.1) constructs the node branch incidence matrix E of M segmentation N contact reliability calculation unit:eijFor the i-th row in matrix E
Jth column element value;It only include three kinds of elements in node branch incidence matrix E, when equivalent node i is not attached to jth branch,
eij=0, when equivalent node i is the starting point of jth branch, eij=1, when equivalent node i is the terminal of jth branch, eij
=-1;
Step 2.2) deletes the first row in above-mentioned node branch incidence matrix, the i.e. corresponding row of power supply, forms square matrix, then right
This square matrix is inverted, to obtain supply path matrix.
4. Complicated Distribution Network reliability index fast resolving calculation method according to claim 1, it is characterised in that:In step
It is rapid 3) in, three kinds of failures of the determination influence types, are based on above-mentioned supply path matrix, construct three failures of fault element
Incidence matrix, three fault estimators respectively correspond above-mentioned three kinds of failures influence type, and specific step is as follows:
Step 3.1) determines that three kinds of failures influence type:Failure influences type a:Element fault causes all supply paths of load disconnected
It opens, can just restore electricity after only waiting until fault restoration;Failure influences type b:Element fault leads to all supply paths of load
It disconnects, after Fault Isolation, load can restore to be powered by main power source;Failure influences type c:Element fault causes load all
Supply path disconnects, and after Fault Isolation, load, which can turn to be supplied to backup power source, to restore electricity;
Three fault estimators of step 3.2) building fault element:Fault element concludes the influence information that load has a power failure
Into three fault estimators, the row number of three fault estimators corresponds to the number of fault element, column number correspondence etc.
Imitate the number of node;Element in fault estimator is that " 1 " indicates that the element fault of corresponding row number will lead to respective column volume
Number equivalent node have a power failure, conversely, a certain element is the element fault equity that " 0 " indicates corresponding row number in fault estimator
Node is imitated without influence;
Fault element includes branch trouble and equivalent node failure;
The method of building branch trouble incidence matrix A, B, C include the following steps:
3.2.1 branch trouble incidence matrix A) is constructed
Main power source is obtained to the supply path matrix R of all equivalent nodes first, in accordance with the method for step 2)1;Then according to step
2) method obtains backup power source K to the stand-by power supply path matrix R of all equivalent nodesk;It is finally sought according to formula (3) above-mentioned
The intersection matrix of two supply path matrixes, obtained intersection matrix are exactly branch trouble incidence matrix A:
A=R1∩Rk (3)
The step-by-step AND operation of operator " ∩ " representing matrix element in formula (3), i.e. two supply path matrix corresponding elements
Value simultaneously be 1, then the element value of intersection matrix corresponding position be 1, be otherwise 0;
3.1.2 branch trouble incidence matrix B) is constructed
Reliability calculation unit progress subregion is got in touch with firstly the need of N is segmented to M as boundary using the switch of snap action;If M is segmented N
It gets in touch with and shares N in reliability calculation unitSThe M can be segmented N and get in touch with reliability by the switch of a snap action using it as boundary
Computing unit is divided into NSA subregion;If the set of fingers in each subregion is ΩS;
Then supply path matrix R is corrected according to above-mentioned partitioning scenario1In element, supply path matrix R1In every a line to
Measure liIt is modified all in accordance with formula (4):
L in formula (4)i corElement for revised each row vector, all row vectors forms revised power supply after amendment
Path matrix R1 cor;Boolean operator " ∪ " in formula (4) is defined as set of fingers ΩSThe step-by-step inclusive-OR operation of middle institute's directed quantity,
That is row vector l1 corIn a certain element value be 0 or 1, it pass through set of fingers ΩSIn all row vector liCorresponding position element value
Inclusive-OR operation is carried out to obtain;
Finally it is based on revised supply path matrix R1 corBranch trouble incidence matrix B is calculated, is shown below:
3.1.3 branch trouble incidence matrix C) is constructed
Branch trouble incidence matrix C is calculated as follows:
C=R1-A (6)
Construct equivalent node fault estimator Aeq、Beq、CeqMethod include the following steps:
3.2.4 equivalent node fault estimator A) is constructedeq
For equivalent node fault estimator Aeq, the element on diagonal line is " 1 ", indicates that equivalent node faults itself will be led
The load of itself is caused to have a power failure;In addition to the element on diagonal line, equivalent node fault estimator AeqThe element of other positions presses formula
(7) it calculates:
aeqi,j=ai,j(i≠j) (7)
A in formula (7)eqi,jIndicate equivalent node fault estimator AeqIn the i-th row jth column element, ai,jIt indicates in step
3.1.1 the element of the i-th row jth column, formula (7) indicate equivalent node fault correlation square in the branch trouble incidence matrix A obtained in)
Battle array AeqThe element of off-diagonal is identical as the branch trouble incidence matrix element A obtained in step 3.1.1);
3.2.5 equivalent node fault estimator B) is constructedeq
Equivalent node fault estimator BeqIn element obtained according to the method for branch trouble incidence matrix B in step 3.1.2)
?;
3.2.6 equivalent node fault estimator C) is constructedeq
Equivalent node fault estimator CeqIt is calculated by formula (8):
Ceq=R1-Aeq (8)。
5. Complicated Distribution Network reliability index fast resolving calculation method according to claim 1, it is characterised in that:In step
It is rapid 4) in, it is described by step 3) obtain three classes fault estimator and step 1) obtain fault parameter vector carry out matrix
Algebraic operation, obtaining the reliability index of power distribution network and equivalent node, specific step is as follows:
Using four indices as reliability index, with annual frequency of power cut, i.e. SAIFI and annual power off time, i.e.,
Reliability index calculating method of the SAIDI as power distribution network, shown in calculation formula such as formula (9), (10):
Oeprator " ο " in formula (10) indicates Hadamard product, and operation rule is matrix or vector corresponding position element multiplication;
tswRepresent the operating time of the block switch isolated fault of branch;topRepresent the interconnection switch operating time;λ, μ are branch trouble
Rate vector sum fault correction time vector;λeq、μeqFor equivalent node failure rate vector sum fault correction time vector;A, B, C points
Not Wei three be branch trouble incidence matrix;Aeq、Beq、CeqRespectively three equivalent node fault estimators;N indicates each
The number of users of load bus arranges the user's number vector to be formed according to ascending sequence is numbered, and N indicates the institute of load bus
There is number of users;
Using the frequency of power cut of each equivalent node and power off time as the reliability index of load bus, calculation method such as formula
(11), shown in (12):
R=λ × (A+B+C)+λeq×(Aeq+Beq+Ceq) (11)
R in formula (11) indicates the frequencies of power cut of all load bus according to the vector for numbering ascending arrangement, in formula (12)
D indicate the power off times of all load bus according to the vector for numbering ascending arrangement.
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