CN105470986A - Power system partitioning method - Google Patents

Abstract

The invention provides a power system partitioning method in a system recovery process. In order to increase the system recovery speed, the invention provides a partitioning method which considers various constraints such as a capacity constraint of a black start power supply, power balance of an island, and island observability based on distribution of PMU in a power grid in a partitioning process. According to the method, applying a wide area measurement system (WARMS) enables the island formed in the system recovery process satisfy the observability requirement. According to the method, after the network is preliminarily partitioned, buses which do not satisfy the observability requirement are processed according to a rule, thereby finally obtaining a power system partitioning scheme which satisfies the constraints. The invention provides the power network partitioning method which uses the optimum PMU distribution in the power network, thereby accelerating system recovery in a black start process. The method ensures the observability of the formed island and satisfies various operating constraints comprising a classical load constraint and an observability constraint in WARMS.

Description

A kind of electric power system partition method

Technical field

The present invention relates to a kind of electric power system partition method, especially relate to a kind of black starting-up partition method of base PMU best distribution.

Background technology

Power system blackstart refers to that whole network system is because of after fault stoppage in transit, by there is self-startup ability also referred to as the startup with black start-up ability unit in system, drive the unit of non self starting, and expand system power supply scope gradually, finally realize the recovery of whole system.

When black starting-up power supply point has been determined and system has multiple black starting-up power supply point, in order to improve the resume speed of electrical network, should according to the design feature of electrical network, large scale electric network is divided into two or more subsystem to recover independently, grid-connected after each subsystem stable operation a period of time, and then recover whole system.Take parallel recovery plan, greatly can shorten the recovery time of electrical network, if any one subsystem causes recovering unsuccessfully because of some unpredictable factor, also do not affect the recovering process of other subsystem, this provides for improved the speed of System recover.Therefore, Study system have a power failure on a large scale after recovery process in how subregion is carried out to whole network, namely how whole Iarge-scale system is divided into several subsystems, implement parallel recovery, have important meaning to the fast quick-recovery realizing whole electric power system.

In the middle of the research carried out at present, relate to the little of black starting-up partitioning problem.The general artificial appointment partitioned mode adopted by rule of thumb, lacked the foundation of science in the past.Conventional method has application ordered binary decision diagram to carry out model solution, the method carries out reasonable off-the-line according to established constraint on the basis of the unit and important load that set needs startup, determines that in backbone network, the connected state of circuit realizes subregion.Also have and use black starting-up power supplys all in dummy node equivalent system, call after traditional Bellman-ford algorithm and Prim algorithm construct and recover rack, then dummy node is reduced with the object reaching subregion.But the constraints that these researchs are considered is little, do not consider whether subnet meets the problem running constraint yet.Visible, the research in system subdivision is in the starting stage of a development, and a lot of detailed problem also needs deeply and carefully to inquire into.

Summary of the invention

Object of the present invention is exactly a kind of method in order to obtain electric power system subregion, ensures subregion observability, and meets institute's Constrained.

Object of the present invention can be achieved through the following technical solutions:

1 .the invention provides a kind of method of electric power system subregion, step is as follows:

1) first this method determines the optimum PMU distribution ensureing electric power networks observability;

2) the preliminary partition method of electric power networks is carried out;

3) partition scheme is modified be met constrained partition scheme.

2. step 1) described in problem for solving minimum PMU distribution problem:

If f is a 0-1 variable, be used for the distribution situation of PMU in expression system, i-th element definition of f is:

Optimum PMU distribution problem can represent with following mathematic(al) representation:

N represents n-th bus, A=[a _ij] represent network adjacent matrix, be defined as follows:

3. after trying to achieve PMU best distribution, ask for the preliminary partition scheme of electric power system:

Do not contact each other to allow between all isolated islands, each transformer and coupled bus should be placed in same isolated island.Therefore transformer and the bus at its two ends, the generator be connected with these buses and load are all equivalent to the bus of a band equivalent generator be attached thereto and equivalent load.For New England 39 bus-bar system in accompanying drawing 1, bus 19,20,33,34 is by bus 17 equivalence in accompanying drawing 2, and bus 17 is used for replacing generator G4 and G5 in accompanying drawing 1 and the load on bus 20 with an equivalent generator and an equivalent load.When hereafter carrying out mission observability detection, the generator of equivalence, load and bus are reduced.Accompanying drawing 1 is carried out simplification and obtains accompanying drawing 2.

In order to carry out the System recover in black starting-up process, at least should comprise a black starting-up power supply in each isolated island, one is used for the load that recovers and ensure the PMU of mission observability.Determine possible maximum isolated island number m:

B _iand l _ibe defined as follows:

First two concepts are put forward:

Center bus: center bus is the center of each isolated island in this algorithm, it must have the combination of generator or PMU or load or three to hang on this bus.

Boundary line: the connecting line between isolated island, will open in the process of carrying out subregion.

To accompanying drawing 2 application of formula (5), assuming that black starting-up power supply is positioned at bus 2,17,20,22.Center bus number equals isolated island number.Due to so m=4.

The first step recursive matrix I of isolated island ¹defining like that according to formula (8), is a upper triangular matrix.

If the i-th j in matrix element representation bus j belongs to isolated island i, be set to 1, otherwise be 0.I can be found out ¹each provisional capital have a non-zero entry usually to represent the center bus of this isolated island, like this center bus is bus 2,17,20 and 22.

By I ¹modify to carry out recursion next time, amendment specification is as follows:

I′ ^(k+1)＝I ^k×A(9)

To I ' ^(k+1)apply following rule and obtain I ^(k+1):

Center bus rule: because each isolated island needs a center bus, then this bus position element zero setting in other isolated islands.

Historical rule: then next step can not be placed on other isolated islands if certain bus is placed in certain isolated island by back.So, show multiple 1 if a certain, except back being element zero setting except 1.

The minimum rule of bus: if certain bus is placed in how each isolated island and is first time appear in these isolated islands in a certain step, then bus will be placed in the isolated island of bus negligible amounts to accelerate resume speed.Idea bus quantity here refers to the bus quantity containing transformer bus in accompanying drawing 1.

Connect closely rule: if two isolated islands have identical bus number in previous rule, then this bus should be placed in the larger isolated island of the value of this bus position.Because representative has more bus to be connected with this bus by boundary line in this isolated island like this.

The shorter rule in boundary line: if in previous rule in all isolated islands this bus to be sitting in the value of position identical, then this bus should be placed in the shorter isolated island in the boundary line that is connected with this bus.

After above step terminates, the element being greater than 1 in matrix is put 1, so obtain next step matrix.Carry out this process always and know that all buses all belong to a not isolated island.

Accompanying drawing 3 represents the result of the preliminary subregion of 39 bus-bar system.

4. by step 3) try to achieve network primary partition after check the load constraint of isolated island:

After network is divided into different isolated island, each isolated island should meet and comprises WARMS and constrain in interior constraints, ensures completing smoothly of System recover.Constraint set is as follows:

1) load meets the minimum energy output of isolated island.

This constraint should represent by mathematical formulae as follows:

Wherein, J _iisolated island i bus number, the minimum load of generator j, P _liit is the workload demand of bus j.

If certain isolated island does not meet constraint (10), the boundary line of this this isolated island of inspection.If the non-central bus that adjacent isolated island exists the suitable load of band makes to meet constraint (10), and the adjacent isolated island removing this bus also meets constraint (10), then this bus moves on to the isolated island not meeting constraint.

To 39 node systems, suppose that the minimum load of every platform generator is 10% of its rated capacity, for the partition scheme of accompanying drawing 3, each isolated island meets constraint (10).

2) observability constraint.

In order to check the observability of isolated island, the element zero setting that the boundary line in formula (4) goes out is obtained matrix A _i.The following observability representing isolated island median generatrix with variable ο:

ο＝A _I×f(11)

The bus that 0 element representation in ο is unobservable.If there is unobservable bus, by following formula definition matrix U:

U＝A _u×PIM(12)

Wherein, A _ube the network connection matrix obtained by formula (4), u is bus number unobservable in all isolated islands, equals the quantity of all 0 elements in ο.

It is as follows that definition PMU installs matrix PIM:

Each line display unobservable bus in U, and have individual nonzero element to represent PMU is installed makes it possible to be that unobservable bus becomes Observable.

For making unobservable bus become observable, first define the observability degree of isolated island:

Wherein, ο _ja jth element of ο, w _jbe the observability degree of bus j, be defined as follows:

Wop _ivalue higher showing has more bus to be observation in isolated island i.

Unobservable bus is become observable by following three rules of application:

1) unobservable bus Bu Shi center bus

Unobservable bus should be transferred to the bus that comprises and installed PMU and is connected with this bus by boundary line.If (10) do not meet after transfer, then calculate the wop of the unobservable bus of this isolated island _ivalue.If be greater than 0.9, unobservable bus is retracted original isolated island, because observability degree accelerates resume speed enough greatly.If be less than or equal to 0.9, two isolated islands are merged.

2) unobservable bus is center bus but does not install PMU

The bus having installed PMU should be transferred in the isolated island comprising this unobservable bus.If (10) are broken after transfer, calculate the wop of unobservable bus place isolated island _ivalue.If be greater than 0.9 the bus installing PMU is retracted original isolated island, if be less than or equal to, two isolated islands are merged.

3) unobservable bus and the bus Dou Shi center bus having installed PMU

If wop _ibe less than or equal to 0.9 two isolated islands are merged.

Form the flow chart of complete partition scheme as shown in Figure 5.

Use formula (11) can show that bus 4,18,27 is unobservable to 39 node buses of accompanying drawing 3.Bus 4 Bu Shi center bus, the Observable that it can be become by the bus 14 having installed PMU.So bus 4 is moved on to the isolated island comprising bus 14.Bus 18 neither center bus, and bus 17 can make its Observable, so bus 18 should move on to bus 17 place isolated island.Bus 27 Bu Shi center bus also should move on to bus 17 place isolated island.The partition scheme of accompanying drawing 4 can be obtained through these adjustment.

Compared with prior art, the present invention has the following advantages:

The present invention proposes a kind of by utilizing the electric power networking partition method of optimum PMU distribution in electric power networks, accelerating the System recover in black starting-up process with this.This method ensure that the observability of formed isolated island, and meet the multiple observability constraint run in the load constraint and WARMS retraining and comprise classics.

Accompanying drawing explanation

Fig. 1 is New England 39 bus-bar system figure;

Fig. 2 is the simplified system diagram after New England 39 bus-bar system equivalent process transformer and load;

Fig. 3 is preliminary division result;

Fig. 4 is final division result;

Fig. 5 is subregion process flow diagram.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.The present embodiment is implemented premised on technical solution of the present invention, give detailed execution mode and concrete operating process, but protection scope of the present invention is not limited to following embodiment.

As shown in Figure 5, the present embodiment provides a kind of electric power system partition method, comprises step:

S1, solve minimum PMU distribution problem:

If f is a 0-1 variable, be used for the distribution situation of PMU in expression system, i-th element definition of f is:

Optimum PMU distribution problem can represent with following mathematic(al) representation:

N represents n-th bus, A=[a _ij] represent network adjacent matrix, be defined as follows:

S2, try to achieve PMU best distribution after ask for the preliminary partition scheme of electric power system:

Do not contact each other to allow between all isolated islands, each transformer and coupled bus should be placed in same isolated island.Therefore transformer and the bus at its two ends, the generator be connected with these buses and load are all equivalent to the bus of a band equivalent generator be attached thereto and equivalent load.For New England 39 bus-bar system in accompanying drawing 1, bus 19,20,33,34 is by bus 17 equivalence in accompanying drawing 2, and bus 17 is used for replacing generator G4 and G5 in accompanying drawing 1 and the load on bus 20 with an equivalent generator and an equivalent load.When hereafter carrying out mission observability detection, the generator of equivalence, load and bus are reduced.Accompanying drawing 1 is carried out simplification and obtains accompanying drawing 2.

In order to carry out the System recover in black starting-up process, at least should comprise a black starting-up power supply in each isolated island, one is used for the load that recovers and ensure the PMU of mission observability.Determine possible maximum isolated island number m:

B _iand l _ibe defined as follows:

First two concepts are put forward:

Center bus: center bus is the center of each isolated island in this algorithm, it must have the combination of generator or PMU or load or three to hang on this bus.

Boundary line: the connecting line between isolated island, will open in the process of carrying out subregion.

To accompanying drawing 2 application of formula (5), assuming that black starting-up power supply is positioned at bus 2,17,20,22.Center bus number equals isolated island number.Due to so m=4.

The first step recursive matrix I of isolated island ¹defining like that according to formula (8), is a upper triangular matrix.

If the i-th j in matrix element representation bus j belongs to isolated island i, be set to 1, otherwise be 0.I can be found out ¹each provisional capital have a non-zero entry usually to represent the center bus of this isolated island, like this center bus is bus 2,17,20 and 22.

By I ¹modify to carry out recursion next time, amendment specification is as follows:

I′ ^(k+1)＝I ^k×A(9)

To I ' ^(k+1)apply following rule and obtain I ^(k+1):

Center bus rule: because each isolated island needs a center bus, then this bus position element zero setting in other isolated islands.

Historical rule: then next step can not be placed on other isolated islands if certain bus is placed in certain isolated island by back.So, show multiple 1 if a certain, except back being element zero setting except 1.

The minimum rule of bus: if certain bus is placed in how each isolated island and is first time appear in these isolated islands in a certain step, then bus will be placed in the isolated island of bus negligible amounts to accelerate resume speed.Idea bus quantity here refers to the bus quantity containing transformer bus in accompanying drawing 1.

Connect closely rule: if two isolated islands have identical bus number in previous rule, then this bus should be placed in the larger isolated island of the value of this bus position.Because representative has more bus to be connected with this bus by boundary line in this isolated island like this.

The shorter rule in boundary line: if in previous rule in all isolated islands this bus to be sitting in the value of position identical, then this bus should be placed in the shorter isolated island in the boundary line that is connected with this bus.

After above step terminates, the element being greater than 1 in matrix is put 1, so obtain next step matrix.Carry out this process always and know that all buses all belong to a not isolated island.

Accompanying drawing 3 represents the result of the preliminary subregion of 39 bus-bar system.

S3, try to achieve network primary partition after check isolated island load constraint:

After network is divided into different isolated island, each isolated island should meet and comprises WARMS and constrain in interior constraints, ensures completing smoothly of System recover.Constraint set is as follows:

1) load meets the minimum energy output of isolated island.

This constraint should represent by mathematical formulae as follows:

Wherein, J _iisolated island i bus number, the minimum load of generator j, P _liit is the workload demand of bus j.

If certain isolated island does not meet constraint (10), the boundary line of this this isolated island of inspection.If the non-central bus that adjacent isolated island exists the suitable load of band makes to meet constraint (10), and the adjacent isolated island removing this bus also meets constraint (10), then this bus moves on to the isolated island not meeting constraint.

To 39 node systems, suppose that the minimum load of every platform generator is 10% of its rated capacity, for the partition scheme of accompanying drawing 3, each isolated island meets constraint (10).

2) observability constraint.

In order to check the observability of isolated island, the element zero setting that the boundary line in formula (4) goes out is obtained matrix A _i.The following observability representing isolated island median generatrix with variable ο:

ο＝A _I×f(11)

The bus that 0 element representation in ο is unobservable.If there is unobservable bus, by following formula definition matrix U:

U＝A _u×PIM(12)

Wherein, A _ube the network connection matrix obtained by formula (4), u is bus number unobservable in all isolated islands, equals the quantity of all 0 elements in ο.

It is as follows that definition PMU installs matrix PIM:

Each line display unobservable bus in U, and have individual nonzero element to represent PMU is installed makes it possible to be that unobservable bus becomes Observable.

For making unobservable bus become observable, first define the observability degree of isolated island:

Wherein, ο _ja jth element of ο, w _jbe the observability degree of bus j, be defined as follows:

Wop _ivalue higher showing has more bus to be observation in isolated island i.

Unobservable bus is become observable by following three rules of application:

1) unobservable bus Bu Shi center bus

Unobservable bus should be transferred to the bus that comprises and installed PMU and is connected with this bus by boundary line.If (10) do not meet after transfer, then calculate the wop of the unobservable bus of this isolated island _ivalue.If be greater than 0.9, unobservable bus is retracted original isolated island, because observability degree accelerates resume speed enough greatly.If be less than or equal to 0.9, two isolated islands are merged.

2) unobservable bus is center bus but does not install PMU

The bus having installed PMU should be transferred in the isolated island comprising this unobservable bus.If (10) are broken after transfer, calculate the wop of unobservable bus place isolated island _ivalue.If be greater than 0.9 the bus installing PMU is retracted original isolated island, if be less than or equal to, two isolated islands are merged.

3) unobservable bus and the bus Dou Shi center bus having installed PMU

If wop _ibe less than or equal to 0.9 two isolated islands are merged.

Form the flow chart of complete partition scheme as shown in Figure 5.

Use formula (11) can show that bus 4,18,27 is unobservable to 39 node buses of accompanying drawing 3.Bus 4 Bu Shi center bus, the Observable that it can be become by the bus 14 having installed PMU.So bus 4 is moved on to the isolated island comprising bus 14.Bus 18 neither center bus, and bus 17 can make its Observable, so bus 18 should move on to bus 17 place isolated island.Bus 27 Bu Shi center bus also should move on to bus 17 place isolated island.The partition scheme of accompanying drawing 4 can be obtained through these adjustment.

Above-described specific embodiment is only and illustrates and of the present inventionly realize effect, not in order to limit the present invention.The amendment of any unsubstantiality done within all basic ideas in method proposed by the invention and framework, conversion and improvement, all should be included within protection scope of the present invention.

Claims (4)

1. a method for electric power system subregion, is characterized in that, comprises the steps:

1) the optimum PMU distribution ensureing electric power networks observability is determined;

2) the preliminary partition method of electric power networks is carried out;

3) partition scheme is modified be met constrained partition scheme.

2. the method for electric power system subregion according to claim 1, is characterized in that, described step 1) in, solve minimum PMU distribution problem:

If f is a 0-1 variable, be used for the distribution situation of PMU in expression system, i-th element definition of f is:

Optimum PMU distribution problem can represent with following mathematic(al) representation:

$min\underset{i=1}{\overset{n}{\Σ}}{f}_i---\left(2\right)$

$\begin{array}{cc}s.t.& A\×f\≥{\left[\begin{array}{cccc}1& 1& ...& 1\end{array}\right]}_{1\×n}^T\end{array}---\left(3\right)$

N represents n-th bus, A=[a _ij] represent network adjacent matrix, be defined as follows:

3. the method for electric power system subregion according to claim 1, is characterized in that, asks for electric power system preliminary partition scheme concrete steps as follows after trying to achieve PMU best distribution:

Do not contact each other to allow between all isolated islands, each transformer and coupled bus should be placed in same isolated island; Therefore transformer and the bus at its two ends, the generator be connected with these buses and load are all equivalent to the bus of a band equivalent generator be attached thereto and equivalent load; In order to carry out the System recover in black starting-up process, at least should comprise a black starting-up power supply in each isolated island, one is used for the load that recovers and ensure the PMU of mission observability; Determine possible maximum isolated island number m:

$m=min\left\{\begin{array}{ccc}\underset{i=1}{\overset{n}{\Σ}}{b}_i,& \underset{i=1}{\overset{n}{\Σ}}{l}_i& \underset{i=1}{\overset{n}{\Σ}}{f}_i\end{array}\right\}---\left(5\right)$

B _iand l _ibe defined as follows:

First two concepts are put forward:

Center bus: center bus is the center of each isolated island in this algorithm, it must have the combination of generator or PMU or load or three to hang on this bus;

Boundary line: the connecting line between isolated island, will open in the process of carrying out subregion;

The first step recursive matrix I of isolated island ¹defining like that according to formula (8), is a upper triangular matrix;

$\begin{array}{c}{I}^1=G=\left[\begin{array}{ccc}{g}_{11}& ...& g_{1n}\\ \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}\\ \\ \end{array}& \begin{array}{c}\\ \\ \end{array}\\ g_{m1}& ...& g_{mn}\end{array}\right]\\ =\left[\begin{array}{cccc}{b}_1& b_2\left(1-g_{11}\right)& ...& b_n(1-g_{11})...(1-g_{1(n-1)})\\ 0& b_2\left(1-g_{12}\right)& & b_n(1-g_{1n})(1-g_{22})...(1-g_{2(n-1)})\\ 0& 0& & b_n(1-g_{1n})(1-g_{2n})(1-g_{33})...(1-g_{3(n-1)})\\ \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}\\ \\ \end{array}& \begin{array}{c}\\ \\ \end{array}& \begin{array}{c}\\ \\ \end{array}\\ 0& 0& & b_n(1-g_{1n})...(1-g_{(n-1)n})\end{array}\right]\end{array}---\left(8\right)$

If the i-th j in matrix element representation bus j belongs to isolated island i, be set to 1, otherwise be 0; I can be found out ¹each provisional capital have a non-zero entry usually to represent the center bus of this isolated island;

By I ¹modify to carry out recursion next time, amendment specification is as follows:

I′ ^(k+1)＝I ^k×A(9)

To I ' ^(k+1)apply following rule and obtain I ^(k+1):

Center bus rule: because each isolated island needs a center bus, then this bus position element zero setting in other isolated islands;

Historical rule: then next step can not be placed on other isolated islands if certain bus is placed in certain isolated island by back; So, show multiple 1 if a certain, except back being element zero setting except 1;

The minimum rule of bus: if certain bus is placed in how each isolated island and is first time appear in these isolated islands in a certain step, then bus will be placed in the isolated island of bus negligible amounts to accelerate resume speed; Idea bus quantity here refers to the bus quantity containing transformer bus in accompanying drawing 1;

Connect closely rule: if two isolated islands have identical bus number in previous rule, then this bus should be placed in the larger isolated island of the value of this bus position; Because representative has more bus to be connected with this bus by boundary line in this isolated island like this;

The shorter rule in boundary line: if in previous rule in all isolated islands this bus to be sitting in the value of position identical, then this bus should be placed in the shorter isolated island in the boundary line that is connected with this bus;

After above step terminates, the element being greater than 1 in matrix is put 1, so obtain next step matrix; Carry out this process until all buses all belong to an isolated island always.

4. the method for electric power system subregion according to claim 1, is characterized in that, described step 3) try to achieve network primary partition after check isolated island load constraint:

After network is divided into different isolated island, each isolated island should meet and comprises WARMS and constrain in interior constraints, ensures completing smoothly of System recover; Constraint set is as follows:

1) load meets the minimum energy output of isolated island;

This constraint should represent by mathematical formulae as follows:

$\underset{j=1}{\overset{J_i}{\Σ}}{P}_{Gj}^{\min }\≤\underset{j=1}{\overset{J_i}{\Σ}}{P}_{Lj},i=1,2...m---\left(10\right)$

Wherein, J _iisolated island i bus number, the minimum load of generator j, P _liit is the workload demand of bus j;

If certain isolated island does not meet constraint (10), the boundary line of this this isolated island of inspection; If the non-central bus that adjacent isolated island exists the suitable load of band makes to meet constraint (10), and the adjacent isolated island removing this bus also meets constraint (10), then this bus moves on to the isolated island not meeting constraint;

To 39 node systems, suppose that the minimum load of every platform generator is 10% of its rated capacity, for the partition scheme of accompanying drawing 3, each isolated island meets constraint (10);

2) observability constraint;

In order to check the observability of isolated island, the element zero setting that the boundary line in formula (4) goes out is obtained matrix A _i; The following observability representing isolated island median generatrix with variable ο:

ο＝A _I×f(11)

The bus that 0 element representation in ο is unobservable; If there is unobservable bus, by following formula definition matrix U:

U＝A _u×PIM(12)

Wherein, A _ube the network connection matrix obtained by formula (4), u is bus number unobservable in all isolated islands, equals the quantity of all 0 elements in ο;

It is as follows that definition PMU installs matrix PIM:

$PIM={\left[\begin{array}{cccc}{f}_1& & & \\ & f_2& & \\ & & ...& \\ & & & f_n\end{array}\right]}_{n\×n}---\left(13\right)$

Each line display unobservable bus in U, and have individual nonzero element to represent PMU is installed makes it possible to be that unobservable bus becomes Observable;

For making unobservable bus become observable, first define the observability degree of isolated island:

${\mathrm{wop}}_i=\underset{j=1}{\overset{J_i}{\Σ}}\frac{w_j\×o_j}{w_j},i=1,...m---\left(14\right)$

Wherein, ο _ja jth element of ο, w _jbe the observability degree of bus j, be defined as follows:

Wop _ivalue higher showing has more bus to be observation in isolated island i;

Unobservable bus is become observable by following three rules of application:

1) unobservable bus Bu Shi center bus

Unobservable bus should be transferred to the bus that comprises and installed PMU and is connected with this bus by boundary line; If (10) do not meet after transfer, then calculate the wop of the unobservable bus of this isolated island _ivalue; If be greater than 0.9, unobservable bus is retracted original isolated island, because observability degree accelerates resume speed enough greatly; If be less than or equal to 0.9, two isolated islands are merged;

2) unobservable bus is center bus but does not install PMU

The bus having installed PMU should be transferred in the isolated island comprising this unobservable bus; If (10) are broken after transfer, calculate the wop of unobservable bus place isolated island _ivalue; If be greater than 0.9 the bus installing PMU is retracted original isolated island, if be less than or equal to, two isolated islands are merged;

3) unobservable bus and the bus Dou Shi center bus having installed PMU

If wop _ibe less than or equal to 0.9 two isolated islands are merged.