CN108549985B - Improved Monte Carlo method for solving interval direct current power flow model - Google Patents

Improved Monte Carlo method for solving interval direct current power flow model Download PDF

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CN108549985B
CN108549985B CN201810332052.7A CN201810332052A CN108549985B CN 108549985 B CN108549985 B CN 108549985B CN 201810332052 A CN201810332052 A CN 201810332052A CN 108549985 B CN108549985 B CN 108549985B
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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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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

Improved Monte Carlo method for solving interval direct current power flow model
Technical Field
The invention relates to the technical field of power systems, in particular to an improved Monte Carlo method for solving an interval direct current power flow model.
Background
The direct current power flow model is a linear model of the alternating current power flow model, and is mainly simplified on the alternating current power flow model by 1) the voltage amplitude of all nodes of the system is 1p.u. (per unit value); 2) neglecting the resistance and the parallel reactance to ground of all lines; 3) ignoring all reactive balance equations; 4) all transformer nonstandard transformation ratios are not considered. The direct current power flow is a method for rapidly obtaining node voltage phase angles of a power grid and rough results of transmission power of each line, and is mainly used in practical projects such as power transmission line operation management, power transmission line extension planning, unit combination models considering safety and the like. However, the power input data and network parameters in the dc power flow model are uncertain considering various internal and external uncertainty factors in the actual grid, such as uncertainty of new energy cluster output and load. Therefore, the dc power flow model is actually a calculation problem with uncertainty factors. The existing method is mainly based on Krawczyk algorithm and interval Hull algorithm.
The Krawczyk algorithm establishes an iterative solution model of an interval linear equation by using the interval mathematical theory. Firstly, an interval direct current power flow model is solved by adopting an interval Gaussian elimination method, and an obtained power flow solution interval is used as an initial value of Krawczyk iteration. And then, continuously looping and iterating, and finally converging to obtain an interval vector containing a solution set shell. In the iterative process of the algorithm, iterative computation is carried out by using an inverse matrix of the median of the interval admittance matrix so as to reduce conservatism. And finally, taking the reduced amplitude of the infinite norm of the interval solution vector as an iteration end condition. The method can yield a solution that is closer to the envelope of the equation set than an interval gaussian elimination method. However, the convergence effect of the algorithm is not ideal, the interval calculation result in the iterative process is easy to increase explosively, and finally, the situation of non-convergence occurs, so that the algorithm cannot be used for calculation of an actual system.
The interval Hull algorithm is mainly characterized in that an interval coefficient matrix with dominant diagonal lines is formed through preprocessing, and then a coefficient H-matrix is obtained through the interval Hull algorithm. In the calculation process, the comparison matrix of the H-matrix is processed by utilizing an upward approximation method and a downward approximation method respectively, and the upper and lower boundaries of the interval direct current power flow distribution are further obtained by adopting an iteration method, so that the accuracy of the interval power flow result is further improved. However, the obtained result is still too conservative, and the convergence problem of the iterative algorithm is not completely solved, so that the efficiency of the algorithm cannot be fundamentally improved.
Disclosure of Invention
The invention aims to solve the technical problems in the traditional algorithm to a certain extent, and provides an improved Monte Carlo method for solving an interval direct current power flow model.
In order to achieve the purpose of the invention, the following technical scheme is specifically adopted in the embodiment of the invention;
an improved Monte Carlo method for solving an interval direct current power flow model comprises the following steps:
1) establishing an interval direct current power flow model;
after representing the load, the active power output of the generator and the parameters of the power transmission line into an interval form, substituting the interval form into a deterministic direct current power flow equation to replace the corresponding parameters in the equation to obtain 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 the interval calculation result of the phase angle and the transmission power.
Further, the step 2) includes assuming that all random variables are subject to uniform distribution in the intervals of the load, the generator active output and the transmission line parameters, and then generating the random variables by using a uniform distribution function (uniform distribution function).
Further, the step 4) includes solving the direct current power flow model in all the scenes to obtain a corresponding phase angle and transmission power, and obtaining an interval of the phase angle and the transmission power by statistically calculating a maximum value and a minimum value of the phase angle and the transmission power.
Further, the step 1) of establishing the interval direct current power flow model specifically includes:
1.1) the active output of the generator is expressed as intervals
Figure BDA0001628227560000031
And
Figure BDA0001628227560000032
wherein SGAnd SLRespectively representing the set of all generators and the set of all loads not comprising the balancing machine,
Figure BDA0001628227560000033
the lower limit of the active power output fluctuation interval of the generator,
Figure BDA0001628227560000034
is the upper limit of the active output fluctuation interval of the generator,
Figure BDA0001628227560000035
the lower limit of the active load fluctuation interval is,
Figure BDA0001628227560000036
the upper limit of the active load fluctuation interval is;
Figure BDA0001628227560000037
wherein n is the total number of system nodes, thetajIs the phase angle of the jth node,
Figure BDA0001628227560000038
is the ith row and jth column element B of the imaginary part of the node admittance matrixijThe interval of (1);
self admittance element
Figure BDA0001628227560000039
It needs to be calculated with the following formula:
Figure BDA00016282275600000310
Figure BDA00016282275600000311
for the active power injection interval of each node,P i sin order to be the lower bound of the interval,
Figure BDA00016282275600000312
for the upper bound of the interval, the following formula can be used:
Figure BDA00016282275600000313
Figure BDA00016282275600000314
1.2) substituting the formula (4) into the formula (1) to obtain an interval direct current power flow model:
Figure BDA00016282275600000315
in the formula, thetaiAnd thetajThe phase angles of the ith and jth nodes respectively,
Figure BDA00016282275600000316
is the element B of the ith row and the 1 st column of the imaginary part of the node admittance matrixi1The interval of (a) to (b),
Figure BDA00016282275600000317
is the ith row and jth column element B of the imaginary part of the node admittance matrixijThe interval of (a) to (b),
Figure BDA0001628227560000041
for the active power injection interval of each node,P i sin order to be the lower bound of the interval,
Figure BDA0001628227560000042
is the upper bound of the interval.
Further, the step 2) specifically includes: using uniformly distributed functions (unifrnd functions) in intervals
Figure BDA0001628227560000043
And
Figure BDA0001628227560000044
generating N random variables
Figure BDA0001628227560000045
And
Figure BDA0001628227560000046
in which any interval [ a, b ]]Is expressed as a uniformly distributed density function of
Figure BDA0001628227560000047
Wherein a and b represent injection power intervals, respectively
Figure BDA0001628227560000048
Upper and lower boundaries, or node admittance matrix element intervals
Figure BDA0001628227560000049
An upper boundary and a lower boundary.
Further, in step 3), the extreme scenario specifically includes:
in the first category of extreme scenarios, the first,
Figure BDA00016282275600000410
in the second category of extreme scenarios, the extreme,
Figure BDA00016282275600000411
in the third category of extreme scenarios, the extreme scenarios,
Figure BDA00016282275600000412
in the fourth category of extreme scenes,
Figure BDA00016282275600000413
further, the step 4) specifically includes:
4.1) based on the N +4 scenes generated in step 2) and step 3)
Figure BDA00016282275600000414
And
Figure BDA00016282275600000415
establishing a deterministic direct current power flow model corresponding to the interval direct current power flow model shown in the vertical type (5):
Figure BDA00016282275600000416
in the formula, thetaiAnd thetajThe phase angles of the ith and jth nodes respectively,
Figure BDA00016282275600000417
is the interval of the element of the ith row and the 1 st column of the imaginary part of the node admittance matrix
Figure BDA00016282275600000418
The scene(s) within (c) is (are) in,
Figure BDA00016282275600000419
is the interval of the ith row and jth column element of the imaginary part of the node admittance matrix
Figure BDA00016282275600000420
The scene(s) within (c) is (are) in,
Figure BDA00016282275600000421
active power injection interval for each node
Figure BDA00016282275600000422
A scene within;
4.2) solving a linear equation set in the formula (7) by adopting a Gaussian elimination method;
solving a linear equation set corresponding to N +4 scenes, and counting phase angles and line transmission power corresponding to the N +4 scenes, wherein the line transmission power needs to be calculated through the following formula:
Figure BDA0001628227560000051
wherein n is the total number of system nodes, PijIs the transmission power from node i to node j,
Figure BDA0001628227560000052
is the interval of the ith row and jth column element of the imaginary part of the node admittance matrix
Figure BDA0001628227560000053
Inner scene, θiAnd thetajPhase angles of the ith and jth nodes respectively;
4.3) counting the maximum value and the minimum value of the corresponding phase angle and the transmission power of the line under all the N +4 scenes.
Compared with the prior art, the implementation of the above embodiment of the invention has the following advantages:
(1) the method can be used for solving the direct current power flow problem of the new energy source unit considering uncertainty in output, load and line parameters, and the result can be used for judging whether the line power flow is out of limit or not;
(2) the method adopts a random simulation technology to solve the interval direct current power flow model, does not need interval calculation and algorithm iterative calculation in any form, and does not have the problem of convergence;
(3) the method adopts intervals to model uncertainty information (such as active output, active load and line parameters of the generator), and boundary information of the intervals is easier to obtain in actual engineering application than other uncertainty information (such as a probability density function and a membership function of a fuzzy set), so that the potential for realizing engineering application is greater.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a block diagram of the steps of an algorithm for solving an interval direct current power flow model by an improved Monte Carlo method according to an embodiment of the present invention;
FIG. 2 is a schematic phase angle interval diagram of an IEEE118 node system obtained by two types of Monte Carlo methods according to an embodiment of the present invention;
fig. 3 is a schematic diagram of line transmission power intervals of an IEEE118 node system obtained by two types of monte carlo methods according to an embodiment of the present invention.
Detailed Description
In the following description, for purposes of explanation and not limitation, specific details are set forth, such as particular system structures, techniques, etc. in order to provide a thorough understanding of the embodiments of the invention. It will be apparent, however, to one skilled in the art that the present invention may be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present invention with unnecessary detail.
In order to explain the technical solution of the present invention, the following description is made with reference to the accompanying drawings by way of specific embodiments.
The embodiment of the invention provides an improved Monte Carlo method for solving an interval direct current power flow model, a flow chart of the method is shown in figure 1, and specifically the method comprises the following steps:
1) establishing an interval direct current power flow model, wherein after the load, the active power output of a generator and the parameters of a power transmission line are all expressed into an interval form, the interval direct current power flow model is substituted into a deterministic direct current power flow equation to replace the corresponding parameters in the equation, so that the interval direct current power flow model is obtained;
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 the interval calculation result of the phase angle and the transmission power.
The improved Monte Carlo method provided by the embodiment of the invention utilizes a random simulation technology to generate a series of scenes in an interval of input data, and obtains the interval of the power flow by counting the maximum value and the minimum value of a direct current power flow variable under the generated scenes. Meanwhile, the accuracy of the interval direct current power flow model solution is further improved by considering the extreme scene of the input data.
Further, the step 2) includes assuming that all random variables are subject to uniform distribution in the intervals of the load, the generator active output and the transmission line parameters, and then generating the random variables by using a uniform distribution function (uniform function) in MATLAB software.
Further, the step 4) includes solving the direct current power flow model in all the scenes to obtain a corresponding phase angle and transmission power, and obtaining an interval of the phase angle and the transmission power by statistically calculating a maximum value and a minimum value of the phase angle and the transmission power.
Further, the step 1) of establishing the interval direct current power flow model specifically includes:
1.1) the active output of the generator is expressed as intervals
Figure BDA0001628227560000071
And
Figure BDA0001628227560000072
wherein SGAnd SLRespectively representing the set of all generators and the set of all loads not comprising the balancing machine,
Figure BDA0001628227560000073
the lower limit of the active power output fluctuation interval of the generator,
Figure BDA0001628227560000074
is the upper limit of the active output fluctuation interval of the generator,
Figure BDA0001628227560000075
the lower limit of the active load fluctuation interval is,
Figure BDA0001628227560000076
the upper limit of the active load fluctuation interval is;
Figure BDA0001628227560000077
wherein n is the total number of system nodes, thetajIs the phase angle of the jth node,
Figure BDA0001628227560000078
is the ith row and jth column element B of the imaginary part of the node admittance matrixijThe interval of (1);
self admittance element
Figure BDA0001628227560000079
It needs to be calculated with the following formula:
Figure BDA00016282275600000710
Figure BDA00016282275600000711
for the active power injection interval of each node,P i sin order to be the lower bound of the interval,
Figure BDA00016282275600000712
for the upper bound of the interval, the following formula can be used:
Figure BDA00016282275600000713
Figure BDA00016282275600000714
1.2) substituting the formula (4) into the formula (1) to obtain an interval direct current power flow model:
Figure BDA0001628227560000081
in the formula, thetaiAnd thetajThe phase angles of the ith and jth nodes respectively,
Figure BDA0001628227560000082
is the element B of the ith row and the 1 st column of the imaginary part of the node admittance matrixi1The interval of (a) to (b),
Figure BDA0001628227560000083
is the ith row and jth column element B of the imaginary part of the node admittance matrixijThe interval of (a) to (b),
Figure BDA00016282275600000818
for the active power injection interval of each node,P i sin order to be the lower bound of the interval,
Figure BDA0001628227560000084
is the upper bound of the interval.
Further, the step 2) specifically includes: using uniformly distributed functions (unifrnd functions) in intervals
Figure BDA0001628227560000085
And
Figure BDA0001628227560000086
generating N random variables
Figure BDA0001628227560000087
And
Figure BDA0001628227560000088
in which any interval [ a, b ]]Is expressed as a uniformly distributed density function of
Figure BDA0001628227560000089
Wherein a and b represent injection power intervals, respectively
Figure BDA00016282275600000810
Upper and lower boundaries, or node admittance matrix element intervals
Figure BDA00016282275600000811
There are two ways of taking the values of the upper and lower bounds, i.e., a and b.
Further, the following extreme scenes are considered in the step 3):
in the first category of extreme scenarios, the first,
Figure BDA00016282275600000812
in the second category of extreme scenarios, the extreme,
Figure BDA00016282275600000813
in the third category of extreme scenarios, the extreme scenarios,
Figure BDA00016282275600000814
in the fourth category of extreme scenes,
Figure BDA00016282275600000815
further, the step 4) specifically includes:
4.1) based on the N +4 scenes generated in step 2) and step 3)
Figure BDA00016282275600000816
And
Figure BDA00016282275600000817
establishing a deterministic direct current power flow model corresponding to the interval direct current power flow model shown in the vertical type (5):
Figure BDA0001628227560000091
wherein N is the number of scenes generated in step 2, and thetaiAnd thetajThe phase angles of the ith and jth nodes respectively,
Figure BDA0001628227560000092
is the interval of the element of the ith row and the 1 st column of the imaginary part of the node admittance matrix
Figure BDA0001628227560000093
The scene(s) within (c) is (are) in,
Figure BDA0001628227560000094
is the interval of the ith row and jth column element of the imaginary part of the node admittance matrix
Figure BDA0001628227560000095
The scene(s) within (c) is (are) in,
Figure BDA0001628227560000096
active power injection interval for each node
Figure BDA0001628227560000097
A scene within;
4.2) solving a linear equation set in the formula (7) by adopting a Gaussian elimination method;
solving a linear equation set corresponding to N +4 scenes, and counting phase angles and line transmission power corresponding to the N +4 scenes, wherein the line transmission power needs to be calculated through the following formula:
Figure BDA0001628227560000098
wherein n is the total number of system nodes, PijIs the transmission power from node i to node j,
Figure BDA0001628227560000099
is the interval of the ith row and jth column element of the imaginary part of the node admittance matrix
Figure BDA00016282275600000910
Inside ofScene, thetaiAnd thetajPhase angles of the ith and jth nodes respectively;
4.3) counting the maximum value and the minimum value of the corresponding phase angle and the transmission power of the line under all the N +4 scenes.
As can be seen from the above description, the embodiment of the present invention provides an improved monte carlo method for solving an interval direct current power flow problem, where an interval direct current power flow model regards the injection power and the line parameters (node admittance matrix) of each node as an interval, and therefore, the obtained direct current power flow model variables (phase angle and line transmission power) are also interval variables. The improved Monte Carlo method utilizes a random simulation technology to generate a series of scenes in the interval of the injection power and the line parameters, then solves a direct current power flow model under each scene, and records the phase angle and the line transmission power result under each scene. The interval of the interval direct current power flow variables is obtained by counting the maximum value and the minimum value of each direct current power flow variable (phase angle and line transmission power) under the generation scene. Meanwhile, in order to further improve the precision of the interval direct current power flow model solution, the method provided by the embodiment of the invention adds an extreme scene of the injection power and the line parameters, namely the interval boundary value of the injection power and the line parameters, in the random simulation process. The addition of the extreme scenes greatly improves the precision of the interval direct current power flow and improves the sampling efficiency. The monte carlo method after the extreme scene is added is the improved monte carlo method in the embodiment of the invention.
The improved monte carlo method of the embodiments of the present invention will be described in further detail below using the IEEE118 node system as an example.
The system comprises 54 generator sets (including 1 balancing unit), 169 transmission line branches, 9 transformer branches, 9 reactive compensation points and 64 load nodes. The reference power of the system is 100MVA, and the per unit value is adopted for calculating all parameters. For convenience of description, all nodes and lines are ordered, wherein the node 1 is a balance node, the nodes 2 to 54 are generator nodes, and the nodes 55 to 118 are load nodes. The transmission line branch and the transformer branch adopt node numbers with smaller numbers at the front and node numbers with larger numbers at the back. And during sorting, all branches are arranged from small to large according to the node numbers in front of the branches, and if the node numbers in front are the same, the branch with the small node number in the back is arranged in front. Meanwhile, assuming that all the generators have active power output, the active load and the line parameters (node admittance matrix) are in a fluctuation range of +/-20%. The number of random simulations in modified monte carlo N is 5000.
The following specifically describes the algorithm steps of the rectangular coordinate interval load flow calculation:
and S101, inputting system data, including all generator parameters, active loads, line parameters, transformer branch parameters and uncertain parameter intervals (namely +/-20% fluctuation intervals). It should be noted that this stage also requires the formation of the imaginary part of the node admittance matrix using branch addition. In forming the node admittance matrix, the resistance of the line, the susceptance to ground of the line, the compensation of the capacitance, and the nonstandard transformation ratio of the transformer need to be ignored.
And S102, generating corresponding scenes in the intervals of the active power output, the active load and the line parameters of the generator by adopting a random simulation technology. Assuming that all random variables are subject to uniform distribution in the intervals of load, generator active power output and transmission line parameters, then a uniform distribution function (uniform function) in MATLAB software is adopted to generate the random variables.
S103, adding 4 extreme scenes on the basis of the scenes generated in the second step, namely, taking the minimum boundary of the line parameters and taking the minimum boundary of the injected power; the minimum boundary is taken as the line parameter, and the maximum boundary is taken as the injected power; the maximum boundary is taken as the line parameter, and the minimum boundary is taken as the injected power; the line parameters take the maximum boundary and the injected power takes the maximum boundary.
And S104, counting and calculating the maximum value and the minimum value of the direct current flow variable under the scene generated in the second step and the third step.
Solving the direct current power flow model of the formula (7) by adopting a Gaussian elimination method, wherein a linear equation set corresponding to N +4 scenes needs to be solved, further counting the corresponding phase angles and line transmission power under the N +4 scenes, and counting the maximum values and the minimum values of the corresponding phase angles and line transmission power under all the N +4 scenes.
And S105, outputting the result, and outputting the interval calculation result of the phase angle and the transmission power.
To further verify the effectiveness and superiority of the improved monte carlo method, the method proposed by the present invention was compared with the non-improved monte carlo method (no extreme scenario).
The MATLAB programming is adopted to solve the interval power flow model, the phase angle interval of the IEEE118 node system is shown in figure 2, and the line transmission power interval of the IEEE118 node system is shown in figure 3.
It can be seen from fig. 2 that the improved monte carlo method has a larger phase angle interval than the monte carlo method before the improvement, and it can be seen from fig. 3 that the improved monte carlo algorithm has a larger line transmission power interval than the monte carlo algorithm before the improvement, which illustrates the effectiveness of the improved monte carlo method. The main reason is that extreme scenes cannot be extracted in the sampling process of random simulation by the improved monte carlo method, and the extreme scenes are generally key scenes for determining the flow variable interval.
Further, as can be seen from fig. 3, the fluctuation of the transmission power of the lines (No. 14 and No. 16 outgoing lines in the drawing) connected to the generator is large. This is because fluctuations in generator power can affect the transmission of ambient line power. The driving time of the improved Monte Carlo method for solving the inter-interval direct current power flow is about 0.8 second, and the potential of the improved Monte Carlo method for engineering practical application is shown. The analysis shows that the improved Monte Carlo method can efficiently solve the interval direct current power flow model, and the interval precision of the direct current power flow solution obtained by the improved Monte Carlo method is higher than that of the original Monte Carlo method.
The parts of the method in the embodiments of the present invention that are not developed can be referred to the corresponding parts of the method in the above embodiments, and are not developed in detail here.
In the description herein, references to the description of the terms "one embodiment," "some embodiments," "an illustrative embodiment," "an example," "a specific example" or "some examples" or the like mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps of the process, and alternate implementations are included within the scope of the preferred embodiment of the present invention in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of implementing the present invention.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and not to be construed as limiting the present invention, and those skilled in the art can make changes, modifications, substitutions and alterations to the above embodiments within the scope of the present invention.

Claims (6)

1. A method for solving an interval direct current power flow model based on an improved Monte Carlo is characterized by comprising the following steps:
1) establishing an interval direct current power flow model;
after representing the load, the active power output of the generator and the parameters of the power transmission line into an interval form, substituting the interval form into a deterministic direct current power flow equation to replace the corresponding parameters in the equation to obtain 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) outputting a result, wherein the result comprises an interval calculation result of the phase angle and the transmission power;
the step 4) specifically comprises the following steps:
4.1) based on the N +4 scenes generated in step 2) and step 3)
Figure FDA0003454071820000011
And
Figure FDA0003454071820000012
establishing a deterministic direct current power flow model corresponding to the interval direct current power flow model shown in the vertical type (7):
Figure FDA0003454071820000013
in the formula, thetaiAnd thetajThe phase angles of the ith and jth nodes respectively,
Figure FDA0003454071820000014
is the interval of the element of the ith row and the 1 st column of the imaginary part of the node admittance matrix
Figure FDA0003454071820000015
The scene(s) within (c) is (are) in,
Figure FDA0003454071820000016
is the interval of the ith row and jth column element of the imaginary part of the node admittance matrix
Figure FDA0003454071820000017
The scene(s) within (c) is (are) in,
Figure FDA0003454071820000018
active power injection interval for each node
Figure FDA0003454071820000019
The scene(s) within (c) is (are) in,P i sin order to be the lower bound of the interval,
Figure FDA00034540718200000110
is the upper bound of the interval;
4.2) solving a linear equation set in the formula (7) by adopting a Gaussian elimination method;
solving a linear equation set corresponding to N +4 scenes, and counting phase angles and line transmission power corresponding to the N +4 scenes, wherein the line transmission power needs to be calculated through the following formula:
Figure FDA0003454071820000021
wherein n is the total number of system nodes, PijIs the transmission power from node i to node j,
Figure FDA0003454071820000022
is the interval of the ith row and jth column element of the imaginary part of the node admittance matrix
Figure FDA0003454071820000023
Inner scene, θiAnd thetajPhase angles of the ith and jth nodes respectively;
4.3) counting the maximum value and the minimum value of the corresponding phase angle and the transmission power of the line under all the N +4 scenes.
2. The improved Monte Carlo-based method for solving the interval direct current power flow model is characterized in that the step 2) comprises assuming that all random variables are subjected to uniform distribution in the intervals of the load, the generator active output and the transmission line parameters, and then generating the random variables by adopting a uniform distribution function.
3. The method for solving the interval direct current power flow model based on the improved monte carlo as claimed in claim 2, wherein said step 4) comprises solving the direct current power flow model under all the scenes to obtain the corresponding phase angle and transmission power, and obtaining the interval of the phase angle and the transmission power by statistically calculating the maximum value and the minimum value of the phase angle and the transmission power.
4. The method for solving the inter-region direct current power flow model based on the improved monte carlo as claimed in claim 1, wherein the step 1) of establishing the inter-region direct current power flow model specifically comprises:
1.1) the active output of the generator is expressed as intervals
Figure FDA0003454071820000024
And
Figure FDA0003454071820000025
wherein SGAnd SLRespectively representing the set of all generators and the set of all loads not comprising the balancing machine,
Figure FDA0003454071820000026
the lower limit of the active power output fluctuation interval of the generator,
Figure FDA0003454071820000027
is the upper limit of the active output fluctuation interval of the generator,
Figure FDA0003454071820000028
the lower limit of the active load fluctuation interval is,
Figure FDA0003454071820000029
the upper limit of the active load fluctuation interval is;
Figure FDA00034540718200000210
wherein n is the total number of system nodes, thetajIs as followsThe phase angles of the j nodes are,
Figure FDA00034540718200000211
is the ith row and jth column element B of the imaginary part of the node admittance matrixijThe interval of (1);
self admittance element
Figure FDA0003454071820000031
It needs to be calculated with the following formula:
Figure FDA0003454071820000032
Figure FDA0003454071820000033
for the active power injection interval of each node,P i sin order to be the lower bound of the interval,
Figure FDA0003454071820000034
for the upper bound of the interval, the following formula is adopted to obtain:
Figure FDA0003454071820000035
Figure FDA0003454071820000036
1.2) substituting the formula (4) into the formula (1) to obtain an interval direct current power flow model:
Figure FDA0003454071820000037
in the formula, thetaiAnd thetajThe phase angles of the ith and jth nodes respectively,
Figure FDA0003454071820000038
is the element B of the ith row and the 1 st column of the imaginary part of the node admittance matrixi1The interval of (a) to (b),
Figure FDA0003454071820000039
is the ith row and jth column element B of the imaginary part of the node admittance matrixijThe interval of (a) to (b),
Figure FDA00034540718200000310
for the active power injection interval of each node,P i sin order to be the lower bound of the interval,
Figure FDA00034540718200000311
is the upper bound of the interval.
5. The method for solving the interval direct current power flow model based on the improved monte carlo as claimed in claim 2, wherein the step 2) specifically comprises: using uniformly distributed functions in intervals
Figure FDA00034540718200000312
And
Figure FDA00034540718200000313
generating N random variables
Figure FDA00034540718200000314
And
Figure FDA00034540718200000315
in which any interval [ a, b ]]Is expressed as a uniformly distributed density function of
Figure FDA00034540718200000316
Wherein a and b represent injection power intervals, respectively
Figure FDA00034540718200000317
Upper and lower boundaries, or node admittance matrix element intervals
Figure FDA00034540718200000318
An upper boundary and a lower boundary.
6. The method for solving the inter-region direct current power flow model based on the improved monte carlo as claimed in claim 3, wherein in the step 3), the extreme scenario specifically includes:
in the first category of extreme scenarios, the first,
Figure FDA0003454071820000041
in the second category of extreme scenarios, the extreme,
Figure FDA0003454071820000042
in the third category of extreme scenarios, the extreme scenarios,
Figure FDA0003454071820000043
in the fourth category of extreme scenes,
Figure FDA0003454071820000044
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