CN106099915B - Additional PMU Optimal Configuration Methods based on topological model and singular value decomposition - Google Patents
Additional PMU Optimal Configuration Methods based on topological model and singular value decomposition Download PDFInfo
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- CN106099915B CN106099915B CN201610498147.7A CN201610498147A CN106099915B CN 106099915 B CN106099915 B CN 106099915B CN 201610498147 A CN201610498147 A CN 201610498147A CN 106099915 B CN106099915 B CN 106099915B
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
- Y02E40/70—Smart grids as climate change mitigation technology in the energy generation sector
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
- Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
- Y04S10/00—Systems supporting electrical power generation, transmission or distribution
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
- Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
- Y04S10/00—Systems supporting electrical power generation, transmission or distribution
- Y04S10/22—Flexible AC transmission systems [FACTS] or power factor or reactive power compensating or correcting units
Abstract
The invention discloses the additional PMU Optimal Configuration Methods based on topological model and singular value decomposition, in the case where zero injection condition missing and system model change, comprise the following steps：Step 1 on the basis of original configuration, establishes the equation between measurement and quantity of state, judgment matrix whether full rank；If not full rank, inconsiderable node is obtained using singular value decomposition for step 2；PMU is respectively configured with the presence or absence of points of common connection according to inconsiderable node in step 3；Step 4 until no inconsiderable node, obtains all additional configurations.Inconsiderable node is obtained using singular value decomposition, avoids complicated topological analysis, while only considers inconsiderable node, has both reduced the quantity of node analysis, while enhances the flexibility of configuration, the redundancy of configuration is improved, accelerates configuration speed.
Description
Technical field
The present invention relates to the additional PMU Optimal Configuration Methods based on topological model and singular value decomposition.
Background technology
Means of the state estimation as modern computer real time data processing are improving data precision, and detection and identification are not
It plays an important role in good data and tie lines identification, guarantee is provided for the safety of electric system and economical operation.But
The implementation of state estimation needs the metric data that whole system can be made completely considerable.Traditional Energy Management System (energy
Management system, EMS) though necessary metric data can be provided for state estimation, it is unable to real-time monitoring system
Dynamic behaviour, and the application of phasor measurement unit (phasor measurement unit, PMU) is the safety fortune of electric system
Row creates advantage.Compared with EMS system, PMU can measure the node voltage phasor at installation node and be attached thereto
All branches electric current phasor, and with higher measurement frequency and precision.If in all node installation PMU, need huge
Big investment.Therefore, it is necessary to a kind of effective PMU collocation methods, can be the configuration minimum number of PMU and make be entirely
It unites considerable.
At present, the collocation method of PMU is segmented into two kinds, and one kind is didactic optimization algorithm, including genetic algorithm, mould
Intend annealing method, TS algorithm etc..But the essence of this optimization algorithm is a kind of thought of iteration, contains substantial amounts of matrix fortune
It calculates, therefore operand is big, operation time is long.Another kind is to obtain the installation site of PMU, such as integer using the topological model of system
Linear programming technique, depth-first search, minimum spanning tree method.
Meanwhile in order to ensure system in the line break and it is single measure loss in the case of, system is still considerable, is configuring
During PMU, the influence of these factors is considered.Document《The non-dominant measured based on synchronous vector searches for genetic algorithm》It has obtained in list
The configuration result of PMU in the case of line interruption.Document《Consider to measure loss and the optimal PMU collocation methods of line interruption》
Both the interruption of single line had been considered, it is contemplated that the influence that the loss of single measurement configures PMU, and utilize didactic excellent
Change algorithm and obtain the configuration result of PMU.But this method is analyzed using the numerical value ornamental of system, has substantial amounts of numerical value
Computing, therefore, operation time are long.But they do not account for zero injection condition missing and the change of system topological model can to system
The influence for the property seen.
In initial configuration PMU, in order to reduce PMU configuration quantity, the influence of zero injection node is often considered.But it is transporting
During row, due to actual needs, some node installations generator or load, and make some nodes due to zero injection condition
It lacks and becomes inconsiderable or topological model change so that some nodes are no longer considerable.In order to ensure system in these situations
Under it is considerable, it is necessary to consider additional PMU configurations.
The content of the invention
The purpose of the present invention is exactly to solve the above-mentioned problems, to provide additional based on topological model and singular value decomposition
PMU Optimal Configuration Methods, in the case where zero injection condition missing and system model change, this method is first with unusual
Value decomposition obtains inconsiderable node, for inconsiderable node, is configured using the topological model of system, considered simultaneously
Not using the influence of zero injection node；Inconsiderable node is obtained using singular value decomposition, avoids complicated topological analysis, together
When only consider inconsiderable node, both reduced the quantity of node analysis, while enhanced the flexibility of configuration, improved configuration
Redundancy, accelerate configuration speed.
To achieve these goals, the present invention adopts the following technical scheme that：
Additional PMU Optimal Configuration Methods based on topological model and singular value decomposition, in the situation of zero injection condition missing
Under, comprise the following steps：
Step 1 on the basis of original configuration, establishes the equation between measurement and quantity of state, and whether judgment matrix is full
Order；
If not full rank, inconsiderable node is obtained using singular value decomposition for step 2；
PMU is respectively configured with the presence or absence of points of common connection according to inconsiderable node in step 3；
Step 4 until no inconsiderable node, obtains all additional configurations.
Additional PMU distributes rationally to reduce the configuration quantity of PMU, and the redundancy for improving configuration is target.
βiAfter representing node i installation PMU, the quantity of increased considerable node seeks the β value of all PMU additionally installed
With, be exactly additional PMU configuration redundancy.
βiMeet constraints：βi≤ηi+ 1, wherein ηiFor the maximum circuitry number of node i connection.
The method of the step 2 is to have A=UWV to arbitrary m × n dimension matrix AsT, wherein, U is the unitary matrice of m × m,
W is the diagonal matrix of m × n, and V is the unitary matrice of n × n；
Assuming that the cornerwise element number of non-zero is r in diagonal matrix W, then after carrying out singular value decomposition, unitary matrice V's
R+1, r+2 ..., n are classified as the basic course laboratory of equation AX=B, and X is the dimensional vector of n × 1, and B is the dimensional vector of m × 1, is denoted as VP；If VP
In the i-th behavior zero, then i-th of node in system is considerable that otherwise, node i is not considerable.
In the step 3, if inconsiderable node, there are points of common connection, consideration points of common connection configures, and according to public affairs
Tie point connects the quantity of inconsiderable node altogether, configures PMU successively, should if the node of points of common connection connection is considerable
Common point is not as the collocation point of PMU.
It is all what is be connected with inconsiderable node if points of common connection is not present in inconsiderable node in the step 3
In node, including inconsiderable node, to connect the most node of branch as PMU collocation points.
Beneficial effects of the present invention：
In the case where zero injection condition missing and system model change, this method is obtained first with singular value decomposition
It to inconsiderable node, for inconsiderable node, is configured using the topological model of system, while considers and do not apply zero
Inject the influence of node.Inconsiderable node is obtained using singular value decomposition, complicated topological analysis is avoided, while only considers
Inconsiderable node, had both reduced the quantity of node analysis, while enhanced the flexibility of configuration, improved the redundancy of configuration
Property, accelerate configuration speed.
Description of the drawings
Fig. 1 is 5 node system figures containing zero injection node；
Fig. 2 is 6 node system figures containing zero injection node；
Fig. 3 is the 7 node single systems for increasing a node on the basis of Fig. 2；
Fig. 4 is 6 node system figures for increasing by a node on the basis of Fig. 1；
Fig. 5 is 7 node single system figures；
Fig. 6 is the flow chart of additional PMU configuration process.
Specific embodiment
The invention will be further described with embodiment below in conjunction with the accompanying drawings.
The Observability Analysis of 1 system
For a system, if the voltage phasor of some node can be by directly measuring or being calculated, claiming should
Node is considerable.At present for the analysis of ornamental, there are mainly two types of methods, and one kind is numerical analysis method, and another kind is to open up
Flutter analytic approach.Numerical analysis method is to judge the ornamental of system by judging the order of Jacobian matrix or gain matrix.Due to
This method operand is big, it will usually using the method for topological analysis.Zero injection node of topological analysis and consideration based on system
Influence, rule as follows can be obtained：
If 1) node installation PMU, node and the coupled all nodes for installing PMU are considerable.
If 2) node is zero injection node, and all nodes being connected with the node are considerable, then can using KCL equations
Know that the node is considerable.
If 3) there is m zero injection node, the node total number with this m zero injection node adjacency is k, then in m+k node
In, have that k node is considerable, then understand that remaining m node is also considerable using KCL equations.
If for containing the system of N number of node, if this N number of node is all considerable, claim whole system considerable, otherwise
Title system is inconsiderable.
2. influence of the zero injection missing to system ornamental
When configuring PMU using the topological model of system, consider zero injection, the configuration of PMU can be reduced to a certain extent
Quantity.When carrying out numerical analysis, if not using zero injection as a part for measurement, the order of system will be unable to determine.Such as Fig. 1
It is a single system figure containing zero injection node, node 2 is zero injection node, in configuration process, considers zero injection pair
The influence of configuration.Make in system 5 nodes considerable and PMU minimum number, installation site of the node 3 as PMU.But
When carrying out numerical analysis, not using zero injection as measurement, at this time by calculating, system is full rank.
Fig. 2 is 6 node system figures containing zero injection node.Node 2 is zero injection node.When configuring PMU, if
Consider the influence of zero injection, it is only necessary to a PMU, at node 3.If without considering the influence of zero injection, 2 are at least needed
A PMU can just make this 6 nodes considerable.When topological analysis considers zero injection and numerical analysis, it is not intended that zero injection
It influences, system is not full rank at this time.
Fig. 1 and Fig. 2 considers zero injection when topology distribution is put, and numerical analysis is without considering zero injection, and full rank situation is but
It is different.By Fig. 1 analyses it is recognized that while considering zero injection node in configuration process, but the ornamental of 5 nodes in system
It is to be obtained by the voltage or current measurement of PMU, and is to inject this by using zero there is no the ornamental of some node
A condition obtains.And in Fig. 2, considerable node 6 is since node 2 is zero injection node.Therefore, system in numerical analysis
It is considerable due to zero injection node with the presence or absence of some nodes in system whether order is influenced to depend on by zero injection node, if depositing
Then the order of system is impacted, if being not present, the order of system is unaffected.
In order to make full use of zero injection, the zero injection node number do not applied and its position at place can pass through
It is true to judge that all zero injections come not as the relation between the rank of matrix of measurement and the node number of zero injection number and system
Determine in system not using the number of zero injection node.Such as in a n node system, the number of zero injection node is k, Suo Youfei
The order of the measurement matrix of zero injection is m, then the zero injection number do not applied is
ZN=k- (n-m) (1)
Zero all injections is added in original measurement, the order of calculating matrix, is then eliminated one by one as measurement
Zero injection of amount judges whether the zero of node injection is employed by calculating the rank of matrix under remaining measure.If matrix
Still full rank, then zero injection of the node are not applied.If affecting rank of matrix, some nodes are there will necessarily be in the system
Because the zero injection node is considerable.
By above analysis, when configuring PMU, consider that zero injection can reduce the configuration of PMU in any case
Quantity.Therefore, when being configured to system, in order to reduce the configuration quantity of PMU, it is necessary to consider the influence of zero injection node.
Meanwhile zero injection is considered in topological analysis, the ornamental of system can be but influenced without considering zero injection in numerical analysis, therefore
When carrying out numerical analysis, it is necessary to using zero injection as measurement.And it by certain numerical computations, can not applied
The number of zero injection node and position.
If among operational process, due to actual needs, it is mounted with generator at some zero injection nodes or carries
New electric load, and some nodes when causing the first wife to put no longer are one zero injection nodes.At this point, system is due to losing zero
This condition is injected, the ornamental of system will be unable to determine.If the missing of some zero injection conditions has no effect on the considerable of system
Property, i.e. system still full rank, then need not be configured.But under normal circumstances, for a larger system, zero note is considered
Ingress will be attempted to reduce the configuration quantity of PMU using zero this condition of injection.And the intricate property of system, it is such as multiple
The situation or some zero injection node condition missing that zero injection node is connected, can cause multiple nodes inconsiderable, be difficult profit at this time
With the node that the model determination system of topology is not considerable, it is therefore desirable to obtain inconsiderable node by the method for numerical value.Together
When, if configuring PMU as research object, and using topological model and matrix element computing using obtained inconsiderable node, subtract
Lack the configuration quantity of PMU and accelerate configuration speed.
The influence considerable to system of 3 junction styles
In actual operation, the difference of junction style can cause different electric network compositions to power grid.And the change of electric network composition
Originally completely considerable system may be caused to become the considerable system in part.Power circuit is such as put into original system, is not being increased
In the case of adding number of nodes, the ornamental of system is constant, i.e., original considerable system is still considerable.But cut off circuit and increasing
Add new node, while increase new branch, the ornamental of system will be affected.
If increase a node 7 on the basis of Fig. 2, and the node is connected with node 6, as shown in Figure 3.If do not increase
The configuration quantity of PMU, increased node 7 is inconsiderable at this time.If increased node 7 is connected directly with node 3, without considering
In the case that PMU measures passage limitation, node 7 is considerable.In addition, if increasing by 6 nodes in Fig. 1, and the section
Point is connected directly with node 2, as shown in Figure 4.Then by analyzing, node 6 is considerable by zero injection node of node 2.
By above analysis, after newly increasing node, what the ornamental that newly increases node represented whole system can
The property seen.Newly increase node ornamental can by the direct measurement of PMU, at this time without considering PMU measurement passage limitation or
Person is considerable using the zero injection node do not applied.Therefore, in the case where increasing new node, in order to reduce the configuration of PMU
Quantity, can be the node newly increased and untapped zero note in the case where each condition meets and is influenced from other factors
Ingress is connected or the limitation without considering PMU measurement passages, increased node and the node of installation PMU is made to be connected, so not
It needs to increase additional PMU.What if the connection of node was to determine, and increased number of nodes is more, connection is opposite
Complexity, increasing the ornamental of node can not be directly obtained by the topological model of system, at this point it is possible to be obtained using the method for numerical value
Inconsiderable node is obtained, and is configured for inconsiderable node.
Some circuits in excision system, the ornamental of system because cut off circuit it is different due to it is different.If the circuit of excision
It is connected with the node for installing PMU or is connected with some zero injection node, analysis is understood on topological model, cuts off circuit, some
Node cannot make its considerable by measuring calculating or zero injection analysis.Numerically, be equivalent to PMU measurement branch current or
Injection Current measures loss, and it is not full rank to cause system.After judging circuit excision, whether the ornamental of node is by shadow
It rings, the ornamental of system can be judged by the order of judgment matrix.If it is few to cut off circuit, and topological model is simpler, can be straight
It connects and obtains inconsiderable node using topological model.But if system model is relative complex, can be obtained not using numerical analysis method
Considerable node.
The position of 4 additional PMU
Using the definition of numerical analysis, and the characteristics of measured according to PMU, the measurement of foundation and the equation of quantity of state are lines
Property, i.e. H is the matrix of m × n.If H-matrix meets
Rank (H)=N (2)
Then system is full rank.
The mathematical model of 4.1 additional PMU configurations
Identical with the target of PMU initial configurations, additional PMU configurations are also required to minimum PMU configuration quantity, improve simultaneously
The redundancy of measurement.Its mathematical model is as follows：
s.t RH=N
Wherein, C0For candidate's installation site of additional PMU,For the quantity of PMU candidate's installation sites, xiRepresent PMU's
Installation site is defined as follows shown：
βiAfter representing node i installation PMU, the quantity of increased considerable node seeks the β value of all PMU additionally installed
With represent the redundancy value of additional PMU configuration, and βiMeet following constraints：
βi≤ηi+1 (5)
Wherein ηiFor the maximum circuitry number of node i connection.
4.2 singular value decomposition
4.2.1 the form of Solution for System of Linear Equations
If a system of linear equations is such as shown in (6).Wherein A ties up matrix for m × n, and X is the dimensional vector of n × 1, B for m × 1 tie up to
Amount.Quantity of state number is usually less than in view of measuring number in real system, i.e. system is that part is considerable, setting m ＜ n.
AX=B (6)
Because m ＜ n, equation group (6) there will necessarily be infinite multiple solutions.If the order of matrix A is r, then solution of equation
It can represent as follows：
Wherein, XPFor the particular solution of equation group, XiBased on solve system, XiNumber is n-r, ciFor coefficient.If Xi(i=1,
2...n-r in) all elements of certain a line all be 0, then, no matter ciIt is taken as how being worth, values of the corresponding X at the row position is equal
Do not change, which is considerable variable.If XiThere are multirow all elements in (i=1,2...n-r) is all zero, that
It there is multiple considerable variables.And if XiAll elements of certain a line are not all 0 in (i=1,2...n-r), then, phase
The variable answered is different and different with coefficient, and variable is not considerable.
4.2.2 application of the singular value decomposition method in significant part judgement
Arbitrary Matrix A all can to carry out singular value decomposition, form is as follows：
A=UWVT (8)
Wherein, U is the unitary matrice of m × m, and W is the diagonal matrix of m × n, and V is the unitary matrice of n × n.
Assuming that the cornerwise element number of non-zero is r in diagonal matrix W, then after carrying out singular value decomposition, unitary matrice V's
R+1, r+2 ..., n row are the basic course laboratory of equation AX=B, are denoted as VP.As can be known from the above analysis, if VPIn the i-th behavior
Zero, then i-th of node in system is considerable that otherwise, node i is not considerable.It accordingly, can be directly according to the order (matrix of matrix A
During A morbid state, according to the number of non-zero diagonal element in matrix W) and singular value decomposition after matrix V, the considerable portion of trip current
Point.
System not full rank, then certainly exist inconsiderable node.Using the method for numerical value, i.e., obtained using singular value decomposition
When additionally being configured using PMU, the object using inconsiderable node as configuration is avoided to institute for inconsiderable node
Some nodes are analyzed, and are accelerated the configuration speed of PMU, while using inconsiderable node as research object, have been established and subtracted
Few PMU configuration quantity and the basis for improving redundancy.
The principle of 4.3 additional PMU configurations
To reduce the configuration quantity of PMU, the redundancy for improving configuration is target for the configuration of additional PMU.
Fig. 5 is a 7 node single system figures.If node 1,4,6 is inconsiderable node.From map analysis, this 3
Inconsiderable node has been all connected on node 2, and node 4 and node 6 have been both connected on node 3, and node 3 is compared with node
2 have more connection branches, and PMU is installed at node 3, has higher redundancy compared with node 2.If in inconsiderable section
PMU at point is installed, then needs 3 PMU；If installing PMU at points of common connection 3,2 PMU are needed, respectively in 2 He of node
At node 3.If installing PMU at points of common connection 2, a PMU is only needed, so that it may so that 3 nodes are considerable, in order to subtract
The configuration quantity of few PMU, using node 2 as the installation site of PMU.It will thus be seen that pacify compared at inconsiderable node
PMU is filled, considers that points of common connection can reduce the configuration quantity of PMU.In addition, it is also contemplated that commonly connected connection it is inconsiderable
The quantity of node can also reduce the configuration quantity of PMU to a certain extent.
If points of common connection is not present in inconsiderable node, at this time to improve the redundancy of configuration as target.In Fig. 5, if
Within the system, only node 4 is inconsiderable node, in order to improve the redundancy of data, in node 3 rather than node 2 or
PMU at node 4 is installed, though such install the configuration quantity that cannot reduce PMU, improves the superfluous of configuration to a certain extent
Remaining.Therefore, on the basis of the configuration of PMU is to ensure minimum PMU configuration quantity, the redundancy of configuration is improved.
Based on above analysis, the method for PMU configurations is as follows：
Rule 1：If inconsiderable node there are points of common connection, considers points of common connection configuration, and according to commonly connected
Point connects the quantity of inconsiderable node, configures PMU successively, if the node of points of common connection connection is considerable, the common point
Not as the collocation point of PMU.
Rule 2：If there is no points of common connection, in all nodes being connected with inconsiderable node, including inconsiderable
Node, to connect the most node of branch as PMU collocation points.
The process of 4.4 additional PMU configurations
This method obtains inconsiderable node by singular value decomposition, by the configuration rule configuration PMU of PMU, and according to
Matrix element with or and realize, accelerate configuration speed.Detailed process is as follows：
1) on the basis of original configuration, establish the equation between measurement and quantity of state, judgment matrix whether full rank.
If 2) not full rank, inconsiderable node is obtained using singular value decomposition, the set P of inconsiderable node is set0And volume
The initial value of the location sets AP of outer PMU；
3) PMU is configured according to rule 1, updates P0Value, judge P0In quantity whether be zero；If zero, then step is gone to
5；
4) if not zero configures PMU by rule 2；
5) terminate configuration, obtain all additional configurations.
The flow chart of detailed process is as shown in Figure 6.
5 sample calculation analysis
In order to verify the correctness of this method and validity, by this method be applied to standard example IEEE14, IEEE30 and
IEEE118 node systems are verified.Table 1 is the metric data based on system topological model, and table 2 is what zero injection condition lacked
In the case of, the installation site of rank of matrix and its PMU.The number that zero injection is not applied in system in order to obtain, calculates all zero
Order and PMU configurations in the case of injection missing.PMU configuring conditions when table 3 changes with table 4 for system topology.
Table 1 is based on the considerable metric data of topology
| System | Measure quantity | Node voltage measures quantity | Branch current measures quantity |
| IEEE14 | 3 | 3 | 12 |
| IEEE30 | 7 | 7 | 24 |
| IEEE118 | 28 | 28 | 110 |
Table 2 zero injects the configuring condition not as measurement
From the data in table 2, IEEE14 node systems, the order of the system of IEEE118 nodes and zero injection number
Difference is zero, is shown in the two systems, and all zero injection is applied, and makes other nodes considerable.IEEE30 nodes system
The difference of the rank of matrix of system and zero injection number is 1, illustrates in zero injection node, is not apply there are one zero injection
, remove zero injection successively, the order of calculating matrix is understood, zero injection of node 22 is not applied.
Table 3 considers the PMU configuration comparing results of common connection node
| System | Consider common connection node | Consider the configuration in inconsiderable node |
| IEEE14 | 4 | 4 |
| IEEE30 | 10 | 12 |
| IEEE118 | 35 | 38 |
Table 3 installs PMU in the points of common connection of inconsiderable node for consideration and considers to install PMU's at inconsiderable node
Configuration result compares, and from the data in table, compared with the PMU configuring conditions considered in inconsiderable node, considers inconsiderable
The points of common connection of node can reduce the configuration quantity of PMU.
Table 4 is counted and the comparing result of the PMU of redundancy configuration quantity and redundancy
Table 4 is when configure PMU, considers the configuration quantity and its redundancy value of the PMU of redundancy, wherein redundancy 1 for
When configuring PMU, redundancy value during without considering redundancy.Redundancy 2 is to consider the redundancy value of redundancy.From the data in table,
In the case where PMU configurations quantity is identical, consider that redundancy can improve the redundancy value of configuration.
The PMU configuration results of circuit excision in 5 topology transformation of table
Table 5 is the PMU configuring conditions in the case of the circuit excision in topology transformation.Wherein, (3,4) represent node 3 and section
The connected branch of point 4 is removed.From the data in table, the quantity of rank of matrix and inconsiderable node is not consistent
, removing a branch may make multiple nodes inconsiderable.
The PMU configuration results of the other nodes of increase in 6 topology transformation of table
| System | Connected node | Order | Inconsiderable node | PMU is configured |
| IEEE14 | 7 | 14 | 15 | 7 |
| IEEE30 | 22 | 31 | 0 | 0 |
| IEEE118 | 40 | 119 | 0 | 0 |
Table 6 is increasing the PMU configuring conditions of other nodes for system.Wherein, the node being connected in table refers to what is newly increased
The node location that node is connected with original system.From the data in table, in IEEE14 nodes, the node being connected with node 7 is
It is inconsiderable.Analysis understands that, although node 7 is zero injection node, this zero injection condition has been applied, therefore even if is injected with zero
Node 7 be connected, the node newly increased is not still considerable.And in IEEE30 node systems, node 22 is one zero injection section
No matter point, and from the data in table 2, zero injection condition of node 22 from theory analysis or are imitated there is no applying
From the point of view of true result, the node newly increased is all considerable.IEEE118 node systems are considerable be since node 40 is mounted with PMU,
In the case of passage limitation is measured, 119 nodes newly increased are considerable.
Above-mentioned, although the foregoing specific embodiments of the present invention is described with reference to the accompanying drawings, not protects model to the present invention
The limitation enclosed, those skilled in the art should understand that, based on the technical solutions of the present invention, those skilled in the art are not
Need to make the creative labor the various modifications or changes that can be made still within protection scope of the present invention.
Claims (7)
1. the additional PMU Optimal Configuration Methods based on topological model and singular value decomposition, it is characterized in that, it is lacked in zero injection condition
In the case of changing with system model, comprise the following steps：
Step 1 on the basis of original configuration, establishes the equation between measurement and quantity of state, judgment matrix whether full rank；
If not full rank, inconsiderable node is obtained using singular value decomposition for step 2；
PMU is respectively configured with the presence or absence of points of common connection according to inconsiderable node in step 3；
Step 4 until no inconsiderable node, obtains all additional configurations.
2. the additional PMU Optimal Configuration Methods based on topological model and singular value decomposition as described in claim 1, it is characterized in that,
Additional PMU distributes rationally to reduce the configuration quantity of PMU, and the redundancy for improving configuration is target.
3. the additional PMU Optimal Configuration Methods based on topological model and singular value decomposition as claimed in claim 2, it is characterized in that, βi
After representing node i installation PMU, the quantity of increased considerable node sums to the β value of all PMU additionally installed, is exactly additionally
The redundancy of PMU configurations.
4. the additional PMU Optimal Configuration Methods based on topological model and singular value decomposition as claimed in claim 3, it is characterized in that, βi
Meet constraints：βi≤ηi+ 1, wherein ηiFor the maximum circuitry number of node i connection.
5. the additional PMU Optimal Configuration Methods based on topological model and singular value decomposition as described in claim 1, it is characterized in that,
The method of the step 2 is to have A=UWV to arbitrary m × n dimension matrix AsT, wherein, U is the unitary matrice of m × m, and W is m × n
Diagonal matrix, V be n × n unitary matrice；
Assuming that the cornerwise element number of non-zero is r in diagonal matrix W, then after carrying out singular value decomposition, the r+ of unitary matrice V
1, r+2 ..., n are classified as the basic course laboratory of equation AX=B, are denoted as VP, X is the dimensional vector of n × 1, and B is the dimensional vector of m × 1；If VP
In the i-th behavior zero, then i-th of node in system is considerable that otherwise, node i is not considerable.
6. the additional PMU Optimal Configuration Methods based on topological model and singular value decomposition as described in claim 1, it is characterized in that,
In the step 3, if inconsiderable node, there are points of common connection, consideration points of common connection configures, and according to points of common connection
The quantity of the inconsiderable node of connection, configures PMU successively, if the node of points of common connection connection is considerable, the common point is not
Collocation point as PMU.
7. the additional PMU Optimal Configuration Methods based on topological model and singular value decomposition as described in claim 1, it is characterized in that,
In the step 3, if points of common connection is not present in inconsiderable node, in all nodes being connected with inconsiderable node, bag
Inconsiderable node is included, to connect the most node of branch as PMU collocation points.
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