CN108549985A - A kind of improvement monte carlo method of solution interval DC flow model - Google Patents

A kind of improvement monte carlo method of solution interval DC flow model Download PDF

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CN108549985A
CN108549985A CN201810332052.7A CN201810332052A CN108549985A CN 108549985 A CN108549985 A CN 108549985A CN 201810332052 A CN201810332052 A CN 201810332052A CN 108549985 A CN108549985 A CN 108549985A
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power
flow model
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CN108549985B (en
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史军
徐旭辉
林子钊
程韧俐
张宇童
郑涵
何晓峰
华栋
张聪
孙高星
祝宇翔
车诒颖
张炀
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Shenzhen Power Supply Bureau Co Ltd
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Abstract

The present invention discloses a kind of improvement monte carlo method of solution interval DC flow model, includes the following steps:1)Establish section DC flow model;2)Stochastic variable is generated in the section of corresponding load, generated power output and transmission line parameter using stochastic simulation technology, which is known as scene;3)In step 2)Increase extreme scenes on the basis of the scene of generation, which refers to the up-and-down boundary in parameter section;4)Count the maximum value and minimum value of the trend variable under all scenes;5)Output is as a result, result includes the interval computation result of phase angle and transimission power.The improvement monte carlo method of solution interval DC flow model of the present invention generates a series of scenes using stochastic simulation technology in the section of input data, generates the maximum and minimum value of DC power flow variable under scene by statistics to obtain the section of trend.And the extreme scenes by considering input data, further improve the precision of section DC flow model solution.

Description

A kind of improvement monte carlo method of solution interval DC flow model
Technical field
The present invention relates to technical field of power systems, and in particular to a kind of improvement illiteracy of solution interval DC flow model is special Carlow method.
Background technology
DC flow model is the inearized model of AC Ioad flow model, has mainly made following four on AC Ioad flow model The simplification of aspect:1) all node voltage amplitudes of system are 1p.u. (perunit value);2) ignore the resistance and over the ground simultaneously of all circuits Join reactance;3) ignore all reactive balance equations;4) the non-standard no-load voltage ratio of all transformers is not considered.DC power flow is a kind of quick Obtain power grid node voltage phase angle and each line transmission power rough result method, be mainly used for power transmission line operational management, In the Practical Projects such as the Expansion Planning of transmission line of electricity, the Unit Combination model for considering safety.However, it is contemplated that in actual electric network The factors such as various inside and outside uncertain factors, such as the uncertainty of new energy unit output and load, direct current Power input data and network parameter in tide model are uncertain.Therefore, DC flow model is actually one containing not The computational problem of certainty factor.Existing method is based primarily upon Krawczyk algorithms and section Hull algorithms.
Krawczyk algorithms utilize the theory of intervl mathematics, establish the iterative solution model of an Interval linear equation. Section Gaussian reduction solution interval DC flow model is first used, obtained flow solution section is as the first of Krawczyk iteration Initial value.Then, continuous loop iteration, final convergence can obtain an interval vector for including disaggregation shell.In algorithm iteration In the process, it is iterated calculating using the inverse matrix of section admittance matrix intermediate value, to reduce conservative.Finally, with interval solutions to The reduction amplitude of the Infinite Norm of amount is as iteration termination condition.The method can obtain more closer than section Gaussian reduction The solution of equation assembly housing.But the effect is unsatisfactory for the convergence of this algorithm, and the interval computation result in iterative process is susceptible to quick-fried , finally there is the case where not restraining in the growth of fried formula, and is not used to real system calculating.
Section Hull algorithms mainly by pretreatment, form the Interval matrix that a leading diagonal is dominant, then Coefficient H- matrixes are obtained using section Hull algorithms.In calculating process, it is utilized respectively at approximate and downward approximation method upwards The comparator matrix of H- matrixes is managed, further uses alternative manner to acquire the bound of section DC power flow distribution, further increases The precision of Interval Power Flow result.But obtained result is still overly conservative, and the convergence problem of iterative algorithm does not obtain To being fully solved, the efficiency of algorithm can not be fundamentally improved.
Invention content
The present invention is directed to solve technical problem present in traditional algorithm to a certain extent, a kind of solution interval direct current is proposed The improvement monte carlo method of tide model uses extreme scenes while using Monte Carlo method solution interval tide model The sampling efficiency of Monte Carlo method is further increased, to improving the precision and section direct current of existing section DC power flow result The efficiency of power flow algorithm.
In order to realize that the object of the invention, embodiment of the present invention specifically adopt the following technical scheme that;
A kind of improvement monte carlo method of solution interval DC flow model, this method comprises the following steps:
1) section DC flow model is established;
After load, generated power output and transmission line parameter are expressed as the form in section, it is updated to really Qualitative DC power flow equation obtains section DC flow model instead of corresponding parameter in equation;
2) stochastic simulation technology is used to be generated in the section of corresponding load, generated power output and transmission line parameter Stochastic variable, the stochastic variable are known as scene;
3) increase extreme scenes on the basis of the scene that step 2) generates, which refers to the upper following of parameter section Boundary;
4) maximum value and minimum value of the trend variable under all scenes are counted;
5) output is as a result, the result includes the interval computation result of phase angle and transimission power.
Further, the step 2) comprises provide that all stochastic variables in load, generated power output and power transmission line It is to obey to be uniformly distributed in the section of road parameter, then uniformly distributed function (unifrnd functions) is used to generate stochastic variable.
Further, the step 4), which is included under all scenes, solves DC flow model, obtain corresponding phase angle and Transimission power is calculated the maximum value and minimum value of phase angle and transimission power by statistics, obtains the section of phase angle and transimission power.
Further, the step 1) is established section DC flow model and is specifically included:
1.1) generated power output is expressed as sectionWithIts Middle SGAnd SLRespectively represent not include balancing machine all generating sets at set and all loads composition set,For hair The lower limit of motor active power output waving interval,For the upper limit of generated power output waving interval,For burden with power wave The lower limit in dynamic section,For the upper limit of burden with power waving interval;
In formula, n is system node sum, θjFor the phase angle of j-th of node,It is node admittance square Battle array imaginary part the i-th row jth column element BijSection;
Self-admittance elementIt needs to be calculated with following formula:
For the active power interval of injection of each node,P i sFor section lower bound,For the section upper bound, may be used Following formula obtains:
1.2) formula (4) is updated in formula (1), obtains section DC flow model:
In formula, θiAnd θjThe phase angle of respectively i-th and j-th node,It is that the i-th row of node admittance matrix imaginary part the 1st arranges Element Bi1Section,It is node admittance matrix imaginary part the i-th row jth column element BijSection, For the active power interval of injection of each node,P i sFor section lower bound,For the section upper bound.
Further, the step 2) specifically includes:Using uniformly distributed function (unifrnd functions) in section WithGenerate N number of stochastic variableWithThe wherein equally distributed density function expression in any one section [a, b] Formula is
Wherein, a and b respectively represents injecting power sectionCoboundary and lower boundary or node admittance matrix member Plain sectionCoboundary and lower boundary.
Further, in the step 3), the extreme scenes specifically include:
First kind extreme scenes,
Second class extreme scenes,
Third class extreme scenes,
4th class extreme scenes,
Further, the step 4) specifically includes:
4.1) according to the N+4 scene generated in step 2) and step 3)WithIt is straight to establish section shown in formula (5) Flow the corresponding certainty DC flow model of tide model:
In formula, θiAnd θjThe phase angle of respectively i-th and j-th node,It is the i-th row of node admittance matrix imaginary part the 1st The section of column elementInterior scene,It is the section of node admittance matrix imaginary part the i-th row jth column elementInterior scene,For the active power interval of injection of each nodeInterior scene;
4.2) Gaussian reduction is used to solve system of linear equations in formula (7);
Corresponding system of linear equations under N+4 scene is solved, and counts corresponding phase angle and line transmission under N+4 scene Power, line transmission power need to calculate by following formula:
In formula, n is system node sum, PijBe from node i to the transimission power node j,It is node admittance square The section of battle array imaginary part the i-th row jth column elementInterior scene, θiAnd θjRespectively i-th and j-th section The phase angle of point;
4.3) maximum value and minimum value of corresponding phase angle and line transmission power under all N+4 scenes are counted.
Compared with prior art, implement the above embodiment of the present invention to has the following advantages:
(1) this method can be used for solving the direct current tide for considering uncertain new energy unit output, load and line parameter circuit value Flow problem, result can be used for differentiating whether Line Flow is out-of-limit;
(2) this method need not carry out any type of using stochastic simulation technology come solution interval DC flow model Interval computation and algorithm iteration calculate, and convergence problem is not present;
(3) this method using section, to unascertained information, (such as contribute, burden with power and circuit are joined by generated power Number) it is modeled, these interval border information are in practical engineering application than other unascertained informations (such as probability density letter The membership function of number and fuzzy set) it is easier to obtain, realize the potentiality bigger of engineer application.
Description of the drawings
It, below will be to embodiment in order to illustrate more clearly of embodiment of the present invention or technical solution in the prior art Or attached drawing needed to be used in the description of the prior art is briefly described, it should be apparent that, the accompanying drawings in the following description is only It is some embodiments of the present invention, for those of ordinary skill in the art, without creative efforts, Other drawings may also be obtained based on these drawings.
Fig. 1 is the algorithm steps that monte carlo method solution interval DC flow model is improved in embodiment of the present invention;
Fig. 2 is the phase angle range for the IEEE118 node systems that two class monte carlo methods obtain in embodiment of the present invention Schematic diagram;
Fig. 3 is the line transmission for the IEEE118 node systems that two class monte carlo methods obtain in embodiment of the present invention Power interval schematic diagram.
Specific implementation mode
In being described below, for illustration and not for limitation, it is proposed that such as tool of particular system structure, technology etc Body details understands embodiment of the present invention to cut thoroughly.However, it will be clear to one skilled in the art that in these no tools The present invention can also be realized in the other embodiment of body details.In other situations, it omits to well-known system, dress It sets, the detailed description of circuit and method, in case unnecessary details interferes description of the invention.
In order to illustrate technical solutions according to the invention, illustrated below by specific implementation mode combination attached drawing.
Embodiment of the present invention proposes a kind of improvement monte carlo method of solution interval DC flow model, this method stream Journey figure is as shown in Figure 1, specifically, this method comprises the following steps:
1) section DC flow model is established, including load, generated power output and transmission line parameter are indicated After the form in section, it is updated to certainty DC power flow equation, instead of corresponding parameter in equation, to obtain section DC flow model;
2) stochastic simulation technology is used to be generated in the section of corresponding load, generated power output and transmission line parameter Stochastic variable, the stochastic variable are known as scene;
3) increase extreme scenes on the basis of the scene that step 2) generates, which refers to the upper following of parameter section Boundary;
4) maximum value and minimum value of the trend variable under all scenes are counted;
5) output is as a result, the result includes the interval computation result of phase angle and transimission power.
The improvement monte carlo method of embodiment of the present invention is produced using stochastic simulation technology in the section of input data A series of raw scenes generate the maximum and minimum value of DC power flow variable under scene to obtain the section of trend by statistics.Together When, by considering the extreme scenes of input data, further improve the precision of section DC flow model solution.
Further, the step 2) comprises provide that all stochastic variables in load, generated power output and power transmission line It is to obey to be uniformly distributed in the section of road parameter, then uses the uniformly distributed function (unifrnd functions) in MATLAB softwares Generate stochastic variable.
Further, the step 4), which is included under all scenes, solves DC flow model, obtain corresponding phase angle and Transimission power is calculated the maximum value and minimum value of phase angle and transimission power by statistics, obtains the section of phase angle and transimission power.
Further, the step 1) is established section DC flow model and is specifically included:
1.1) generated power output is expressed as sectionWithIts Middle SGAnd SLRespectively represent not include balancing machine all generating sets at set and all loads composition set,For hair The lower limit of motor active power output waving interval,For the upper limit of generated power output waving interval,For burden with power wave The lower limit in dynamic section,For the upper limit of burden with power waving interval;
In formula, n is system node sum, θjFor the phase angle of j-th of node,It is node admittance square Battle array imaginary part the i-th row jth column element BijSection;
Self-admittance elementIt needs to be calculated with following formula:
For the active power interval of injection of each node,P i sFor section lower bound,For the section upper bound, may be used Following formula obtains:
1.2) formula (4) is updated in formula (1), obtains section DC flow model:
In formula, θiAnd θjThe phase angle of respectively i-th and j-th node,It is that the i-th row of node admittance matrix imaginary part the 1st arranges Element Bi1Section,It is node admittance matrix imaginary part the i-th row jth column element BijSection, For the active power interval of injection of each node,P i sFor section lower bound,For the section upper bound.
Further, the step 2) specifically includes:Using uniformly distributed function (unifrnd functions) in section WithGenerate N number of stochastic variableWithThe wherein equally distributed density function expression in any one section [a, b] Formula is
Wherein, a and b respectively represents injecting power sectionCoboundary and lower boundary or node admittance matrix member Plain sectionCoboundary and lower boundary, that is to say, that there are two types of value modes by a and b.
Further, following a few class extreme scenes are considered in the step 3):
First kind extreme scenes,
Second class extreme scenes,
Third class extreme scenes,
4th class extreme scenes,
Further, the step 4) specifically includes:
4.1) according to the N+4 scene generated in step 2) and step 3)WithIt is straight to establish section shown in formula (5) Flow the corresponding certainty DC flow model of tide model:
Wherein, N is the number that step 2 generates scene, θiAnd θjThe phase angle of respectively i-th and j-th node,It is section The section of the 1st column element of the i-th row of point admittance matrix imaginary partInterior scene,It is node admittance matrix imaginary part the i-th row jth row The section of elementInterior scene,For the active power interval of injection of each nodeInterior field Scape;
4.2) Gaussian reduction is used to solve system of linear equations in formula (7);
Corresponding system of linear equations under N+4 scene is solved, and counts corresponding phase angle and line transmission under N+4 scene Power, line transmission power need to calculate by following formula:
In formula, n is system node sum, PijBe from node i to the transimission power node j,It is node admittance square The section of battle array imaginary part the i-th row jth column elementInterior scene, θiAnd θjRespectively i-th and j-th section The phase angle of point;
4.3) maximum value and minimum value of corresponding phase angle and line transmission power under all N+4 scenes are counted.
As can be seen from the above description, embodiment of the present invention proposes a kind of improvement illiteracy of solution interval DC power flow problem Special Carlow method, section DC flow model regard the injecting power of each node and line parameter circuit value (node admittance matrix) as area Between, therefore, obtained DC flow model variable (phase angle and line transmission power) is also interval variable.The improvement Meng Teka Lip river method generates a series of scenes using stochastic simulation technology in the section of injecting power and line parameter circuit value, then solves each DC flow model under scene records phase angle and line transmission power results under each scene.Scene is generated by statistics Under each DC power flow variable (phase angle and line transmission power) maximum value and minimum value obtain section DC power flow variable Section.Meanwhile in order to further improve the precision of section DC flow model solution, embodiment of the present invention method is random The extreme scenes of injecting power and line parameter circuit value, the i.e. interval border of injecting power and line parameter circuit value are added in simulation process Value.The addition of these extreme scenes improves the precision of section DC power flow greatly, while also improving the efficiency of sampling.Pole is added Monte carlo method after the scene of end is the improvement monte carlo method in embodiment of the present invention.
IEEE118 node systems are used to be covered with the improvement of present invention be described in more detail embodiment as example below Special Carlow method.
The system includes 54 generating sets (including 1 balance unit), 169 transmission lines branches, 9 transformer branch Road, 9 reactive compensation points, 64 load bus.The reference power of system takes 100MVA, the calculating of all parameters all to use perunit Value.For convenience, we are ranked up all nodes and circuit, and No. 1 node is balance nodes, No. 2 to No. 54 nodes For generator node, No. 55 to No. 118 nodes are load bus.Line branches and transformer branch are using the smaller section of number Period numbers big node number rear preceding.When sequence, all branches are all arranged by the node number before branch from small to large, If front nodal number is identical, node serial number small branch in back comes front.Simultaneously, it is assumed that all generated powers go out Power, burden with power and line parameter circuit value (node admittance matrix) are in one ± 20% waving interval.It improves in Monte Carlo Times N=5000 of stochastic simulation.
The algorithm steps of rectangular co-ordinate Interval Power Flow calculating are specifically described below:
S101, input system data include all generator parameters, burden with power, line parameter circuit value, transformer branch ginseng Number and uncertain parameter section (i.e. ± 20% waving interval).It should be noted that this stage also needs to chase after using branch Addition forms the imaginary part of node admittance matrix.Node admittance matrix is being formed, the resistance for ignoring circuit, the electricity over the ground of circuit are needed It receives, the compensation of capacitance and the non-standard no-load voltage ratio of transformer.
S102 is contributed using stochastic simulation technology in generated power, and burden with power and line parameter circuit value section generate accordingly Scene.Assuming that all stochastic variables are to obey uniformly in the section of load, generated power output and transmission line parameter Then distribution uses the uniformly distributed function (unifrnd functions) in MATLAB softwares to generate stochastic variable.
S103 increases by 4 extreme scenes on the basis of the scene that second step generates, i.e. line parameter circuit value takes minimum boundary, Injecting power takes minimum boundary;Line parameter circuit value takes minimum boundary, injecting power to take maximum boundary;Line parameter circuit value takes maximum boundary, Injecting power takes minimum boundary;Line parameter circuit value takes maximum boundary, injecting power to take maximum boundary.
The maximum value and minimum of DC power flow variable under the scene that S104, statistics and calculating second step and third step generate Value.
The DC flow model that formula (7) is solved using Gaussian reduction needs to solve corresponding line under N+4 scene altogether Property equation group, further count N+4 scene under corresponding phase angle and line transmission power, count right under all N+4 scenes The maximum value and minimum value of the phase angle and line transmission power answered.
S105, output is as a result, export the interval computation result of phase angle and transimission power.
In order to further verify improve monte carlo method validity and superiority, by method proposed by the present invention with do not have There is improvement monte carlo method (not plus extreme scenes) to be compared.
Interval Power Flow model is solved using MATLAB programmings, obtains the phase angle range of IEEE118 node systems such as Shown in Fig. 2, the line transmission power interval of IEEE118 node systems is as shown in Figure 3.
Monte carlo method is improved as can be seen from Figure 2 obtains the section of phase angle than the monte carlo method before improvement Greatly, Monte carlo algorithm is improved as can be seen from Figure 3 obtains the section of line transmission power than the Monte Carlo calculation before improvement Method is big, illustrates the validity for improving monte carlo method.This is mainly due to the monte carlo methods before improvement in random mould In quasi- sampling process, extreme scenes can not be drawn into, and these extreme scenes are typically all to determine the pass of trend range of variables Key scene.
Further, from figure 3, it can be seen that transmission work(with generator phase connecting lines (No. 14 and No. 16 outlet in figure) The fluctuation of rate is larger.This is because the fluctuation of generator power can influence the transmission of surrounding line power.Above-mentioned improvement Meng Teka The in a hurry of Lip river method solution interval DC power flow is about 0.8 second, it is shown that it is used for the potentiality of practical implementation.More than Analytic explanation improvement monte carlo method can efficiently solution interval DC flow model, while it obtains DC power flow solution Interval precision it is higher than original monte carlo method.
Part not deployed in method in embodiment of the present invention, can refer to the corresponding part of embodiment of above method, It is no longer developed in details herein.
In the description of this specification, reference term " embodiment ", " some embodiments ", " schematically implementation The description of mode ", " example ", " specific example " or " some examples " etc. means the tool described in conjunction with the embodiment or example Body characteristics, structure, material or feature are contained at least one embodiment or example of the present invention.In the present specification, Schematic expression of the above terms are not necessarily referring to identical embodiment or example.Moreover, the specific features of description, knot Structure, material or feature can be combined in any suitable manner in any one or more embodiments or example.
Any process described otherwise above or method description are construed as in flow chart or herein, and expression includes It is one or more for realizing specific logical function or process the step of executable instruction code module, segment or portion Point, and the range of the preferred embodiment of the present invention includes other realization, wherein can not press shown or discuss suitable Sequence, include according to involved function by it is basic simultaneously in the way of or in the opposite order, to execute function, this should be of the invention Embodiment person of ordinary skill in the field understood.
Although embodiments of the present invention have been shown and described above, it is to be understood that the above embodiment is Illustratively, it is not considered as limiting the invention, those skilled in the art within the scope of the invention can be right The above embodiment is changed, changes, replacing and modification.

Claims (7)

1. a kind of improvement monte carlo method of solution interval DC flow model, which is characterized in that this method includes following step Suddenly:
1) section DC flow model is established;
After load, generated power output and transmission line parameter are expressed as the form in section, it is updated to certainty DC power flow equation obtains section DC flow model instead of corresponding parameter in equation;
2) stochastic simulation technology is used to be generated in the section of corresponding load, generated power output and transmission line parameter random Variable, the stochastic variable are known as scene;
3) increase extreme scenes on the basis of the scene that step 2) generates, which refers to the up-and-down boundary in parameter section;
4) maximum value and minimum value of the trend variable under all scenes are counted;
5) output is as a result, the result includes the interval computation result of phase angle and transimission power.
2. a kind of improvement monte carlo method of solution interval DC flow model according to claim 1, feature exist In the step 2) comprises provide that all stochastic variables in the section of load, generated power output and transmission line parameter It is to obey to be uniformly distributed, then uniformly distributed function (unifrnd functions) is used to generate stochastic variable.
3. a kind of improvement monte carlo method of solution interval DC flow model according to claim 2, feature exist In the step 4), which is included under all scenes, solves DC flow model, obtains corresponding phase angle and transimission power, passes through system Meter calculates the maximum value and minimum value of phase angle and transimission power, obtains the section of phase angle and transimission power.
4. a kind of improvement monte carlo method of solution interval DC flow model according to claim 1, feature exist In the step 1) is established section DC flow model and specifically included:
1.1) generated power output is expressed as sectionWithWherein SGWith SLRespectively represent not include balancing machine all generating sets at set and all loads composition set,For generator The lower limit of active power output waving interval,For the upper limit of generated power output waving interval,For burden with power wave zone Between lower limit,For the upper limit of burden with power waving interval;
In formula, n is system node sum, θjFor the phase angle of j-th of node,It is node admittance matrix void Portion the i-th row jth column element BijSection;
Self-admittance elementIt needs to be calculated with following formula:
For the active power interval of injection of each node,P i sFor section lower bound,For the section upper bound, following public affairs may be used Formula obtains:
1.2) formula (4) is updated in formula (1), obtains section DC flow model:
In formula, θiAnd θjThe phase angle of respectively i-th and j-th node,It is the 1st column element of the i-th row of node admittance matrix imaginary part Bi1Section,It is node admittance matrix imaginary part the i-th row jth column element BijSection,It is each The active power interval of injection of node,P i sFor section lower bound,For the section upper bound.
5. a kind of improvement monte carlo method of solution interval DC flow model according to claim 2, feature exist In the step 2) specifically includes:Using uniformly distributed function (unifrnd functions) in sectionWithGenerate N A stochastic variableWithThe equally distributed density function expression formula in wherein any one section [a, b] is
Wherein, a and b respectively represents injecting power sectionCoboundary and lower boundary or node admittance matrix element area Between) coboundary and lower boundary.
6. a kind of improvement monte carlo method of solution interval DC flow model according to claim 3, feature exist In in the step 3), the extreme scenes specifically include:
First kind extreme scenes,
Second class extreme scenes,
Third class extreme scenes,
4th class extreme scenes,
7. a kind of improvement monte carlo method of solution interval DC flow model according to claim 4, feature exist In the step 4) specifically includes:
4.1) according to the N+4 scene generated in step 2) and step 3)WithEstablish section DC power flow shown in formula (5) The corresponding certainty DC flow model of model:
In formula, θiAnd θjThe phase angle of respectively i-th and j-th node,It is the 1st column element of the i-th row of node admittance matrix imaginary part SectionInterior scene,It is the section of node admittance matrix imaginary part the i-th row jth column elementInterior Scene,For the active power interval of injection of each nodeInterior scene;
4.2) Gaussian reduction is used to solve system of linear equations in formula (7);
Corresponding system of linear equations under N+4 scene is solved, and counts corresponding phase angle and line transmission work(under N+4 scene Rate, line transmission power need to calculate by following formula:
In formula, n is system node sum, PijBe from node i to the transimission power node j,It is node admittance matrix void The section of portion's the i-th row jth column elementInterior scene, θiAnd θjRespectively i-th and j-th node Phase angle;
4.3) maximum value and minimum value of corresponding phase angle and line transmission power under all N+4 scenes are counted.
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