CN109390946B - Optimal probability load flow rapid calculation method based on multi-parameter planning theory - Google Patents

Optimal probability load flow rapid calculation method based on multi-parameter planning theory Download PDF

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CN109390946B
CN109390946B CN201811165701.5A CN201811165701A CN109390946B CN 109390946 B CN109390946 B CN 109390946B CN 201811165701 A CN201811165701 A CN 201811165701A CN 109390946 B CN109390946 B CN 109390946B
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output power
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余娟
杨知方
林伟
张梦晗
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Chongqing University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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Abstract

The invention discloses a method for quickly calculating optimal probability load flow based on a multi-parameter planning theory, which mainly comprises the following steps: 1) sampling the power network to extract samplesAnd (4) data. 2) And establishing a direct current optimization model according to the operation cost and the constraint of the traditional generator set. 3) Based on a multi-parameter planning theory, calculating to obtain an analytic relation between an optimal power flow result and the output power of the renewable energy source unit 4) extracting the output power sample of the kth renewable energy source generator according to the probability characteristic of the renewable energy source
Figure DDA0001821017320000011
Determining renewable energy generator output power
Figure DDA0001821017320000012
Belonging critical domain, and calculating the optimal output power of the conventional generator set
Figure DDA0001821017320000013
Ith critical region CRiMedium optimal objective function
Figure DDA0001821017320000014
Sum branch power flow
Figure DDA0001821017320000015
5) And (5) convergence judgment, and counting and outputting an optimal power flow result. The invention has flexible expandability, and the improved fast calculation method can be embedded in any improved sampling algorithm, thereby further accelerating the convergence speed.

Description

Optimal probability load flow rapid calculation method based on multi-parameter planning theory
Technical Field
The invention relates to the field of economic dispatching of power systems, in particular to a method for quickly calculating optimal probability load flow based on a multi-parameter planning theory.
Background
The increasing large scale of renewable energy power generation leads to the explosive increase of uncertainty factors of power systems. The optimal probability trend can effectively consider the uncertainty influence of renewable energy sources, so that the method is widely applied to the operation optimization of the power system. Existing optimal probability power flow methods can be divided into simulation methods and analytic methods. The traditional Monte Carlo method is taken as a typical representative of a simulation method, and an optimal probability power flow result is obtained through a statistical mode after an optimal power flow result of each sample is solved. However, in order to ensure the calculation accuracy, the simulation method needs to perform repeated optimization calculation on a large number of samples. In order to overcome the defect of time consumption of calculation of a simulation method, the prior scholars also provide analytical methods such as a point estimation method, a traceless transformation method and the like. The point estimation method and the unscented transformation method only need to solve individual typical samples, and then each order of statistical moment describing the probability characteristics of the optimal power flow result can be obtained. However, the point estimation method is difficult to obtain accurate high-order moment, and the unscented variation method cannot even obtain information of third order and higher order moment. Therefore, the existing optimal probability power flow method is difficult to simultaneously consider both the calculation precision and the calculation time.
Disclosure of Invention
The present invention is directed to solving the problems of the prior art.
The technical scheme adopted for achieving the purpose of the invention is that the optimal probability power flow rapid calculation method based on the multi-parameter planning theory mainly comprises the following steps:
1) and setting a sampling frequency threshold value, and sampling the power network so as to extract sample data. The sample data mainly comprises the output power P of the renewable energy source unitRAnd the power consumer load PD。
2) And establishing a direct current optimization model according to the operation cost and the constraint of the traditional generator set.
The direct current optimization model objective function is as follows:
Figure GDA0002434662200000011
in the formula, PGThe power is output by the traditional generator set. h (×) is a conventional generator set operating cost function.
Figure GDA0002434662200000012
The minimum running cost of the traditional generator set is achieved.
The direct current optimization model constraint conditions are respectively shown in formula (2) to formula (5), namely:
eGPG+eRPR＝eDPD。 (2)
in the formula, PRAnd outputting power for the renewable energy source unit. PDIs the load of the power consumer. e.g. of the typeG、eRAnd eDIs a unit vector.
Figure GDA0002434662200000021
In the formula (I), the compound is shown in the specification,(*)and
Figure GDA0002434662200000022
respectively, represent a lower limit and an upper limit.
Figure GDA0002434662200000023
In the formula, PLineIs the branch tidal power.
PLine＝PTDF×(MGPG+MRPR-MDPD)。 (5)
In the formula, PTDF is a power transmission distribution matrix. MG、MRAnd MDAre respectively and PG、PRAnd PDThe relevant node-branch incidence matrix.
3) And calculating to obtain an analytic relation between the optimal power flow result and the output power of the renewable energy source unit based on a multi-parameter planning theory.
The method for obtaining the analytic relation between the optimal power flow result and the output power of the renewable energy source unit through calculation mainly comprises the following steps:
3.1) setting a decision variable x as the output power P of the traditional generator setGAnd the planning parameter w is the output power P of the renewable energy source unitR。
Figure GDA0002434662200000024
3.2) optimization objectives are as follows:
Figure GDA0002434662200000025
in the formula (I), the compound is shown in the specification,
Figure GDA0002434662200000026
the minimum operating cost of the optimized generator set is achieved. The matrix A, the matrix C and the matrix D are deterministic matrices used for establishing generator set power flow balance constraints, generator capacity constraints and line transmission limit constraints.
3.3) calculating an optimal segmentation equation of the planning parameter w.
Let K be the subscript of the constraint of equation (6). Recording arbitrary constraint set
Figure GDA0002434662200000027
Is AJ、CJAnd DJA corresponding sub-matrix, which is the constraint corresponding to the lower index J of all the constraints.
For a given multidimensional space
Figure GDA0002434662200000028
If it is
Figure GDA0002434662200000029
Its optimal segmentation definition is (gamma (w), gammac(w)), namely:
Figure GDA00024346622000000210
in the formula, w is a planning parameter. x is a decision variable. x is the number of*(w) is the optimal solution over the critical domain i.
3.4) calculating the critical domain of the planning parameter w.
For given planning parameters
Figure GDA0002434662200000031
Definition (γ)0,γ0 c) Is (gamma (w)0),γc(w0) Then corresponds to γ)0The critical domains of (a) are as follows:
Figure GDA0002434662200000032
wherein the ith critical region CRiThe Countak conditions are as follows:
Figure GDA0002434662200000033
in the formula, JiIs at CRiThe effective constraint set in (1).
Figure GDA0002434662200000034
Is CRi▽ corresponding to the effective constraintxIs the gradient operator for the decision variable x.
3.5) obtaining a critical domain CR according to the critical domain of the planning parameter w and the optimal segmentation equationiOutput power of medium-optimal traditional generator set
Figure GDA0002434662200000035
And the output power P of the renewable energy source unitRThe relationship in (1), namely:
Figure GDA0002434662200000036
in the formula, FxiAnd GxiIs in a critical region CRiThe coefficient matrix obtained by equation (9) above.
3.6) substituting equation (10) into the objective function z ═ h (P)G) In order to obtain a critical region CRiMedium optimal objective function
Figure GDA0002434662200000037
Namely:
Figure GDA0002434662200000038
substituting equation (10) into the branch power flow
Figure GDA0002434662200000039
In order to obtain branch power flow
Figure GDA00024346622000000310
And the output power P of the renewable energy source unitRThe relationship of (1), namely:
Figure GDA00024346622000000311
substituting equation (10) into the invalid constraint set γ of equation (7)c(w) obtaining a critical region CRiThe expression of (c), namely:
Figure GDA00024346622000000312
in the formula, GiAnd HiFor the purpose of determining the critical region CRiA coefficient matrix of the range.
Wherein the coefficient matrix GiSum coefficient matrix HiRespectively as follows:
Figure GDA00024346622000000313
in the formula (I), the compound is shown in the specification,
Figure GDA00024346622000000314
and
Figure GDA00024346622000000315
the row submatrices in matrix a and matrix G, respectively, corresponding to the invalid constraint set.
Figure GDA00024346622000000316
In the formula (I), the compound is shown in the specification,
Figure GDA0002434662200000041
is the row submatrix in matrix D corresponding to the invalid constraint set.
4) According to the probability characteristic of the renewable energy sources, extracting the output power sample of the kth renewable energy source generator
Figure GDA0002434662200000042
Determining renewable energy generator output power
Figure GDA0002434662200000043
Belonging critical domain, and calculating the optimal output power of the conventional generator set
Figure GDA0002434662200000044
Ith critical region CRiMedium optimal objective function
Figure GDA0002434662200000045
Sum branch power flow
Figure GDA0002434662200000046
5) And (6) convergence judgment.
And if the number k of the samples is more than or equal to the number k of the samples, stopping sampling calculation, and counting the optimal load flow result. The optimal power flow result mainly comprises the output power P of the traditional generator setGRunning cost
Figure GDA0002434662200000047
Branch flow
Figure GDA0002434662200000048
Mean and standard deviation of. Number of samples k<Then k is made k +1 and the procedure returns to step 3.
The technical effect of the present invention is undoubted. The invention provides a method for rapidly calculating a probability optimal power flow. And further combining a Monte Carlo simulation method, and directly obtaining the result of the optimal probability load flow, thereby avoiding a large amount of repeated optimization calculation. In addition, the invention has flexible expandability: 1) any improved sampling algorithm can be embedded into the provided fast calculation method, so that the convergence speed is further accelerated; 2) renewable energy dependencies and other important uncertainty characteristics may also be taken into account by some conventional processing in the sampling.
Drawings
FIG. 1 is a process flow diagram.
Detailed Description
The present invention is further illustrated by the following examples, but it should not be construed that the scope of the above-described subject matter is limited to the following examples. Various substitutions and alterations can be made without departing from the technical idea of the invention and the scope of the invention is covered by the present invention according to the common technical knowledge and the conventional means in the field.
Example 1:
referring to fig. 1, a method for rapidly calculating an optimal probabilistic power flow based on a multi-parameter planning theory mainly includes the following steps:
1) and setting a sampling frequency threshold value, and sampling the power network so as to extract sample data. The sample data mainly comprises the output power P of the renewable energy source unitRAnd the power consumer load PD。
2) And establishing a direct current optimization model according to the operation cost and the constraint of the traditional generator set. The traditional generator set mainly refers to a traditional thermal power generation generator set.
The direct current optimization model objective function is as follows:
Figure GDA0002434662200000051
in the formula, PGThe power is output by the traditional generator set. h (P)G) As a function of the cost of operation of the conventional generator set.
Figure GDA0002434662200000052
The minimum running cost of the traditional generator set is achieved.
The direct current optimization model constraint conditions are respectively shown in formula (2) to formula (5), namely:
eGPG+eRPR＝eDPD。 (2)
in the formula, PRAnd outputting power for the renewable energy source unit. PDIs the load of the power consumer. e.g. of the typeG、eRAnd eDIs a unit vector.
Figure GDA0002434662200000053
In the formula (I), the compound is shown in the specification,(*)and
Figure GDA0002434662200000054
respectively, represent a lower limit and an upper limit.P GThe lower limit of the output power of the traditional generator set is provided.
Figure GDA0002434662200000055
The output power of the traditional generator set is limited.
Figure GDA0002434662200000056
In the formula, PLineIs the branch tidal power.P LineThe lower limit of branch tidal current power is shown.
Figure GDA0002434662200000057
Is the branch tidal current power upper limit.
PLine＝PTDF×(MGPG+MRPR-MDPD)。 (5)
In the formula, PTDF is a power transmission distribution matrix. MG、MRAnd MDAre respectively equal to PG、PRAnd PDThe relevant node-branch incidence matrix.
3) Based on a multi-parameter planning theory, calculating to obtain an analytic relation between an optimal power flow result and the output power of a renewable energy source unit, and mainly comprising the following steps of:
3.1) setting a decision variable x as the output power P of the traditional generator setGAnd the planning parameter w is the output power P of the renewable energy source unitR。
Figure GDA0002434662200000058
Figure GDA0002434662200000059
And the output power of the renewable energy source unit is the upper limit.
3.2) optimization objectives are as follows:
Figure GDA00024346622000000510
in the formula (I), the compound is shown in the specification,
Figure GDA00024346622000000511
the minimum operating cost of the optimized generator set is achieved. The matrix A, the matrix C and the matrix D are deterministic matrices used for establishing generator set power flow balance constraints, generator capacity constraints and line transmission limit constraints.
3.3) calculating an optimal segmentation equation of the planning parameter w. Let K be the subscript of the constraint of equation (6). Recording arbitrary constraint set
Figure GDA0002434662200000061
Is AJ、CJAnd DJA corresponding sub-matrix, which is the constraint corresponding to the lower index J of all the constraints.
For a given multidimensional space
Figure GDA0002434662200000062
If it is
Figure GDA0002434662200000063
Its optimal segmentation definition is (gamma (w), gammac(w)), namely:
Figure GDA0002434662200000064
in the formula, w is a planning parameter. x is a decision variable. x is the number of*(w) is the optimal solution over the critical domain i. Matrix AJIs a sub-matrix of matrix a, is a constraint represented by constraint set J. Matrix CJIs a sub-matrix of matrix C and is a constraint represented by constraint set J. Matrix DJIs a sub-matrix of DThe matrix is a constraint represented by a constraint set J.
3.4) calculating the critical domain of the planning parameter w.
For given planning parameters
Figure GDA0002434662200000065
Definition of
Figure GDA0002434662200000066
Is composed of
Figure GDA0002434662200000067
Then corresponds to gamma0The critical domains of (a) are as follows:
Figure GDA0002434662200000068
γ0for the planning parameter w0Optimal segmentation of (1).
Wherein the ith critical region CRiThe Countak conditions are as follows:
Figure GDA0002434662200000069
in the formula, JiIs at CRiThe effective constraint set in (1).
Figure GDA00024346622000000610
Is CRi▽ corresponding to the effective constraintxIs the gradient operator for the decision variable x.
Figure GDA00024346622000000611
Is a sub-matrix of matrix A, is composed of effective constraint set JiThe represented constraints.
Figure GDA00024346622000000612
Is a sub-matrix of matrix D, is formed by an effective constraint set JiThe represented constraints.
Figure GDA00024346622000000613
Is a sub-matrix of matrix C, is formed by an effective constraint set JiThe represented constraints.
3.5) obtaining a critical domain CR according to the critical domain of the planning parameter w and the optimal segmentation equationiOutput power of medium-optimal traditional generator set
Figure GDA00024346622000000614
And the output power P of the renewable energy source unitRThe relationship in (1), namely:
Figure GDA00024346622000000615
in the formula, FxiAnd GxiIs in a critical region CRiThe coefficient matrix obtained by equation (9) above.
3.6) substituting equation (10) into the objective function z ═ h (P)G) In order to obtain a critical region CRiMedium optimal objective function
Figure GDA0002434662200000071
Namely:
Figure GDA0002434662200000072
h(GxiPR+Fxi) To be Gxi、PRAnd/or FxiIs a function of the traditional generator set operating cost of the variables.
Substituting equation (10) into the branch power flow
Figure GDA0002434662200000073
In order to obtain branch power flow
Figure GDA0002434662200000074
And the output power P of the renewable energy source unitRThe relationship of (1), namely:
Figure GDA0002434662200000075
substituting equation (10) into the invalid constraint set γ of equation (7)c(w) obtaining a critical region CRiThe expression of (c), namely:
Figure GDA0002434662200000076
in the formula, GiAnd HiFor the determined critical region CRiA coefficient matrix of the range.
Wherein the coefficient matrix GiSum coefficient matrix HiRespectively as follows:
Figure GDA0002434662200000077
in the formula (I), the compound is shown in the specification,
Figure GDA0002434662200000078
and
Figure GDA0002434662200000079
the row submatrices in matrix a and matrix G, respectively, corresponding to the invalid constraint set.
Figure GDA00024346622000000710
And
Figure GDA00024346622000000711
see equation (7), respectively, with the second equation of equation (7) denoted on c, the second equation of equation (7) only works on part of the decision variable x.
Figure GDA00024346622000000712
In the formula (I), the compound is shown in the specification,
Figure GDA00024346622000000713
is the row submatrix in matrix D corresponding to the invalid constraint set. The formula (14) and the formula (15) are obtained by substituting the formula (10) into the formula (7).
4) According to the probabilistic characteristics of renewable energy sourcesSampling the output power of the kth renewable energy generator
Figure GDA00024346622000000714
Determining renewable energy generator output power
Figure GDA00024346622000000715
Belonging critical domain, and calculating the optimal output power of the conventional generator set
Figure GDA00024346622000000716
Ith critical region CRiMedium optimal objective function
Figure GDA00024346622000000717
Sum branch power flow
Figure GDA00024346622000000718
5) And (6) convergence judgment. If the number k of samples is not less than or equal to the number k of samples, stopping sampling calculation, and counting an optimal power flow result, wherein the optimal power flow result mainly comprises the output power P of the traditional generator setGRunning cost
Figure GDA00024346622000000719
Branch flow
Figure GDA00024346622000000720
Mean and standard deviation of. Number of samples k<Then k is made k +1 and the procedure returns to step 3.
The method is based on a direct current optimization model, and the operation cost and the state variable in the optimization model are expressed as a function expression of the output power of the renewable energy generator set through multi-parameter planning; and further combining a Monte Carlo simulation method, and analyzing and solving the single optimal power flow calculation result. When the output power of the renewable energy power generator set is changed, the accurate optimal probability tide result can be obtained by simple matrix operation according to the analytic relation. The whole process only needs to solve the matrix problem once, and huge calculation amount caused by repeated optimization calculation is avoided.
Example 2:
the experiment for verifying the optimal probability load flow rapid calculation method based on the multi-parameter planning theory mainly comprises the following steps:
1) 8 wind power plants are respectively connected into an IEEE 118 node system, an IEEE300 node system and a Poland 2383 node system, and 1600MW installed capacity is calculated.
2) The optimal probability load flow rapid calculation method based on the multi-parameter planning theory is compared with the traditional Monte Carlo method (accurate solution) and the point estimation method in the aspects of calculation precision and calculation time. The number of sample samplings is 50000. The IEEE 118 node system information is shown in tables 1 to 3. The IEEE300 node system information is shown in table 4 and table 5. The system information of the Poland 2383 nodes is shown in Table 6.
TABLE 1 IEEE 118 node System information I
Figure GDA0002434662200000081
TABLE 2 IEEE 118 node System information II
Figure GDA0002434662200000091
TABLE 3 IEEE 118 node System information III
Figure GDA0002434662200000092
TABLE 4 IEEE300 node System information I
Figure GDA0002434662200000101
TABLE 5 IEEE300 node System information II
Figure GDA0002434662200000102
TABLE 6 Poland 2383 node System information
Figure GDA0002434662200000111
In the columns of Bus Type in IEEE 118 node system information tables 1 to 3, 1 denotes a PQ node, 2 denotes a PV node, and 3 denotes a balance node. In the Poland 2383 node system, all wind speeds follow a two-parameter Weibull distribution. The specific comparison is as follows:
2.1) calculation accuracy. The mean and standard deviation of the operating cost results are shown in table 7:
TABLE 7 comparison of operating cost results and error analysis thereof
Figure GDA0002434662200000112
Note "-" indicates that the result was not obtained.
The optimal probability load flow rapid calculation method based on the multi-parameter planning theory can obtain accurate operation cost result mean value and standard deviation. But there is significant relative error in obtaining the mean value based on the point estimation method, and the maximum relative error can reach 53.38%. In the Poland 2383 node test system, the standard deviation of the operating cost is obtained by the point estimation method, because the variance calculated by the point estimation method is a negative value.
In addition, the mean value of the point estimation method also has significant relative error, the maximum absolute error can reach 496MW and 606 NW. respectively, and the mean value and standard deviation of PG and P L ine obtained by the optimal probability power flow fast calculation method based on the multi-parameter planning theory are completely consistent with the accurate solution.
2.2) calculating time
Table 8 gives the calculated time comparisons for the three methods. Compared with the traditional Monte Carlo method, the optimal probability load flow fast calculation method based on the multi-parameter planning theory has the advantage that the calculation time is greatly reduced. For example, in the Poland 2383 node test system, the conventional Monte Carlo method has a computation time about 34 times that of the proposed method. Although the time tP1 required for the multi-parameter planning analysis is about 24% of the total computation time ttol2, the multi-parameter planning analysis only needs to be performed once in most cases. This is because the multi-parameter planning analysis is only related to wind farm location and installed capacity. Once the wind farm location and installed capacity are determined, they do not change for a long period of time.
TABLE 8 calculated time comparisons
Figure GDA0002434662200000121
Note ttol1Only the time required to solve the sample by the traditional monte carlo method is included. t is tp1The analysis time is planned for multiple parameters. t is tp2Time to solve for the sample for the proposed method. t is ttol2＝tP1+tP2.ttol3Only point estimation methods are involved to calculate the time of a typical sample.

Claims (4)

1. A method for quickly calculating optimal probability load flow based on a multi-parameter planning theory is characterized by mainly comprising the following steps:
1) setting a sampling time threshold, and sampling the power network so as to extract sample data;
2) establishing a direct current optimization model;
3) calculating to obtain an analytic relation between an optimal power flow result and the output power of the renewable energy source unit based on a multi-parameter planning theory;
4) according to the probability characteristic of the renewable energy sources, extracting the output power sample of the kth renewable energy source generator
Figure FDA0002434662190000011
Determining renewable energy generator output power
Figure FDA0002434662190000012
Belonging critical domain, and calculating the optimal output power of the conventional generator set
Figure FDA0002434662190000013
Ith critical region CRiMedium and optimum purposeStandard function
Figure FDA0002434662190000014
Sum branch power flow
Figure FDA0002434662190000015
5) Convergence judgment;
if the number k of the samples is more than or equal to the number k of the samples, stopping sampling calculation, and counting and outputting an optimal load flow result; the optimal power flow result mainly comprises the output power P of the traditional generator setGRunning cost
Figure FDA0002434662190000016
Branch flow
Figure FDA0002434662190000017
Mean and standard deviation of;
and if the number of samples k <, making k equal to k +1, and returning to the step 3.
2. The method for rapidly calculating the optimal probabilistic power flow based on the multi-parameter planning theory as claimed in claim 1, wherein: the sample data mainly comprises the output power P of the renewable energy source unitRAnd the power consumer load PD。
3. The method for rapidly calculating the optimal probabilistic power flow based on the multi-parameter planning theory as claimed in claim 1, wherein: the direct current optimization model objective function is as follows:
Figure FDA0002434662190000018
in the formula, PGOutputting power for the traditional generator set; h (#) is a traditional generating set operation cost function;
Figure FDA0002434662190000019
is the smallest of the traditional generator setThe running cost;
the direct current optimization model constraint conditions are respectively shown in formula (2) to formula (5), namely:
eGPG+eRPR＝eDPD； (2)
in the formula, PROutputting power for the renewable energy source unit; pDIs a power consumer load; e.g. of the typeG、eRAnd eDIs a unit vector;
Figure FDA00024346621900000110
in the formula (I), the compound is shown in the specification,(*)and
Figure FDA0002434662190000021
represents a lower limit and an upper limit, respectively;
Figure FDA0002434662190000022
in the formula, PLineIs branch tidal current power;
PLine＝PTDF×(MGPG+MRPR-MDPD)； (5)
in the formula, PTDF is a power transmission distribution matrix; mG、MRAnd MDAre respectively and PG、PRAnd PDThe relevant node-branch incidence matrix.
4. The method for rapidly calculating the optimal probabilistic power flow based on the multi-parameter planning theory as claimed in claim 1, wherein: the method for obtaining the analytic relation between the optimal power flow result and the output power of the renewable energy source unit through calculation mainly comprises the following steps:
1) setting decision variable x as output power P of traditional generator setGAnd the planning parameter w is the output power P of the renewable energy source unitR；
Figure FDA0002434662190000023
2) The optimization objectives are as follows:
Figure FDA0002434662190000024
in the formula (I), the compound is shown in the specification,
Figure FDA0002434662190000025
the minimum operating cost of the generator set is optimized; the matrix A, the matrix C and the matrix D are deterministic matrices used for establishing generator set power flow balance constraint, generator capacity constraint and line transmission limit constraint;
3) calculating an optimal segmentation equation of a planning parameter w;
let K be the subscript of the constraint of equation (6); recording arbitrary constraint set
Figure FDA0002434662190000026
Is AJ、CJAnd DJA corresponding sub-matrix, which is a constraint corresponding to a lower index J among all the constraints;
for a given multidimensional space
Figure FDA0002434662190000027
If it is
Figure FDA0002434662190000028
Its optimal segmentation definition is (gamma (w), gammac(w)), namely:
Figure FDA0002434662190000029
in the formula, w is a planning parameter; x is a decision variable; x is the number of*(w) is the optimal solution over the critical domain i;
4) calculating a critical domain of a planning parameter w;
for given planning parameters
Figure FDA00024346621900000210
Definition of
Figure FDA00024346621900000211
Is (gamma (w)0),γc(w0) Then corresponds to γ)0The critical domains of (a) are as follows:
Figure FDA00024346621900000212
wherein the ith critical region CRiThe Countak conditions are as follows:
Figure FDA0002434662190000031
in the formula, JiIs at CRiThe effective constraint set in (1);
Figure FDA0002434662190000032
is CRiCorresponding to the effective constraint of ▽xA gradient operator for the decision variable x;
5) obtaining a critical domain CR according to the critical domain of the planning parameter w and the optimal segmentation equationiOutput power of medium-optimal traditional generator set
Figure FDA0002434662190000033
And the output power P of the renewable energy source unitRThe relationship in (1), namely:
Figure FDA0002434662190000034
in the formula, FxiAnd GxiIs in a critical region CRiThe coefficient matrix obtained by the equation (9);
6) substituting equation (10) into the objective function z ═ h (P)G) In order to obtain a critical region CRiMedium optimal objective function
Figure FDA0002434662190000035
Namely:
Figure FDA0002434662190000036
substituting equation (10) into the branch power flow
Figure FDA0002434662190000037
In order to obtain branch power flow
Figure FDA0002434662190000038
And the output power P of the renewable energy source unitRThe relationship of (1), namely:
Figure FDA0002434662190000039
substituting equation (10) into the invalid constraint set γ of equation (7)c(w) obtaining a critical region CRiThe expression of (c), namely:
Figure FDA00024346621900000310
in the formula, GiAnd HiFor the purpose of determining the critical region CRiA coefficient matrix of ranges;
wherein the coefficient matrix GiSum coefficient matrix HiRespectively as follows:
Figure FDA00024346621900000311
in the formula (I), the compound is shown in the specification,
Figure FDA00024346621900000312
and
Figure FDA00024346621900000313
in matrix A and matrix G, respectively, corresponding toA row submatrix of the invalid constraint set;
Figure FDA00024346621900000314
in the formula (I), the compound is shown in the specification,
Figure FDA00024346621900000315
is the row submatrix in matrix D corresponding to the invalid constraint set.
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