CN108549985A - Improved Monte Carlo method for solving interval direct current power flow model - Google Patents
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Abstract
The invention discloses an improved Monte Carlo method for solving an interval direct current power flow model, which comprises the following steps: 1) establishing an interval direct current power flow model; 2) generating random variables in intervals of corresponding loads, active power output of a generator and parameters of a power transmission line by adopting a random simulation technology, wherein the random variables are called as scenes; 3) adding an extreme scene on the basis of the scene generated in the step 2), wherein the extreme scene refers to the upper boundary and the lower boundary of the parameter interval; 4) counting the maximum value and the minimum value of the flow variables in all scenes; 5) and outputting a result, wherein the result comprises an interval calculation result of the phase angle and the transmission power. The improved Monte Carlo method for solving the interval direct current power flow model generates a series of scenes in the interval of input data by using a random simulation technology, and obtains the interval of the power flow by counting the maximum value and the minimum value of the direct current power flow variable under the generated scenes. And the accuracy of the interval direct current power flow model solution is further improved by considering the extreme scene of the input data.
Description
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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