CN111416395B - Multi-stage power grid nested decomposition coordination active and reactive power joint scheduling method - Google Patents

Multi-stage power grid nested decomposition coordination active and reactive power joint scheduling method Download PDF

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CN111416395B
CN111416395B CN202010236368.3A CN202010236368A CN111416395B CN 111416395 B CN111416395 B CN 111416395B CN 202010236368 A CN202010236368 A CN 202010236368A CN 111416395 B CN111416395 B CN 111416395B
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吴文传
孙宏斌
蔺晨晖
王彬
郭庆来
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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Abstract

The invention relates to a multi-stage power grid nested decomposition coordination active and reactive power joint scheduling method, and belongs to the technical field of power system operation control. Firstly, an active and reactive power combined dispatching model of multi-level power grid cooperation is established, the active and reactive power combined dispatching model of each level power grid cooperation is solved in a nested decomposition coordination mode among all levels of power grids, and active and reactive power combined dispatching is carried out on all regional power grids of all levels based on an optimal solution. The key steps are as follows: the method comprises the steps of decomposing, coordinating and calculating an optimal solution of active and reactive power joint dispatching of a regional power grid and a subordinate power grid in a certain level, and calculating an optimal secant plane and an approximate projection function of the regional power grid in the certain level, wherein the two steps are called recursively, so that the decomposition, coordination and calculation of the cooperative active and reactive power joint dispatching model of the power grids at all levels are realized. The method has high convergence speed, can ensure the operation safety of each level of power grid, and avoids the operation risks of local overload, voltage out-of-limit and the like.

Description

Multi-stage power grid nested decomposition coordination active and reactive power joint scheduling method
Technical Field
The invention relates to a multi-stage power grid nested decomposition coordination active and reactive power joint scheduling method, and belongs to the technical field of operation control of power systems.
Background
Due to the fact that the distributed renewable energy sources are connected into the power grids of all levels in a large quantity, the power grids of different levels and different areas are tightly coupled. The traditional method for operating and scheduling the power grids at all levels without coordination cannot adapt to the power grids at multiple levels under tight coupling, and serious power system safety accidents such as local overload, voltage out-of-limit and the like are easily caused. Therefore, there is a need for joint operation scheduling in coordination with multiple power grids.
Considering that the power grids in different levels and different areas are respectively scheduled by respective control centers, the centralized coordination of the multi-level power grids is difficult to realize in practice.
Disclosure of Invention
The invention aims to provide a multi-stage power grid nested decomposition coordination active and reactive power joint scheduling method, which is used for performing active and reactive power joint scheduling on a multi-stage power grid, wherein the power grid in each stage of each region only needs to calculate the internal active and reactive power joint scheduling problem and exchange boundary information with the adjacent power grid, so that an active and reactive power joint scheduling strategy for ensuring the safety of the overall power grid can be obtained.
The invention provides a multi-stage power grid nesting decomposition coordination active and reactive power combined dispatching method which comprises the following steps:
(1) establishing an active and reactive power combined dispatching optimization model with multi-stage power grid cooperation:
(1.1) setting M levels of power grids in a multi-level power grid, N (M) regional power grids in the level power grid M, and establishing an optimization objective function of an active and reactive power combined dispatching optimization model for cooperation of the multi-level power grids, wherein the optimization objective function is the minimum of the sum of the power generation cost of each regional power grid in each level, and for the regional power grids numbered n in the level M, the expression of the power generation cost is as follows:
Figure GDA0003019886700000011
in the above formula, G is the number set of the generator set in the power grid, Pi GFor generating active power of generator set i, Ci(Pi G) For the power generation cost function of the generator set i, the power generation cost function is expressed as a quadratic function as follows:
Ci(Pi G)＝a0,i+a1,iPi G+a2,i(Pi G)2
in the above formula, a0,i、a1,i、a2,iRespectively obtaining the power generation cost constant term, the primary term and the secondary term coefficient of the generator set i from a power grid dispatching center;
(1.2) establishing the constraint conditions of the active and reactive power combined dispatching optimization model of the multi-stage power grid cooperation as follows: for the regional power grid numbered n in level m, the following two cases are distinguished:
(1.2.1) if the regional power grid numbered n in the hierarchy m is a ring power grid, the constraint condition includes:
(1.2.1.1) branch flow equation constraint:
Figure GDA0003019886700000021
Figure GDA0003019886700000022
Figure GDA0003019886700000023
Figure GDA0003019886700000024
in the above formula, PijAnd QijRespectively the active power flow and the reactive power flow of a node i to a node j in the power grid, which are variables to be solved, PjiAnd QjiRespectively an active power flow and a reactive power flow flowing to a node i from a node j, wherein the active power flow and the reactive power flow are variables to be solved, namely tauijThe transformer transformation ratio of the branch ij between the node i and the node j is obtained by a transformer factory nameplate,
Figure GDA0003019886700000025
and
Figure GDA0003019886700000026
respectively the conductance and susceptance of the branch ij, obtained from a power grid dispatching center,
Figure GDA0003019886700000027
for charging susceptance of branch ij, obtained from the grid dispatching centre, ViAnd VjThe voltage amplitudes of the node i and the node j are respectively used as variables to be solved, thetaiAnd thetajThe voltage phase angles of the node i and the node j are respectively the variables to be solved, phiijThe phase-shifting phase angle of the transformer as branch ij is obtained by the delivery nameplate of the transformerL is a number set of branches in the power grid;
(1.2.1.2) node injection balance constraints:
Figure GDA0003019886700000028
Figure GDA0003019886700000029
in the above formula, GiAnd DiRespectively, the serial numbers of the generator set and the load connected with the node i,
Figure GDA0003019886700000031
and
Figure GDA0003019886700000032
the active power and the reactive power of the generator set y are respectively used as variables to be solved,
Figure GDA0003019886700000033
and
Figure GDA0003019886700000034
respectively the active power demand and the reactive power demand of the load z, are obtained from a power grid dispatching center,
Figure GDA0003019886700000035
and
Figure GDA0003019886700000036
respectively obtaining the parallel conductance and the parallel susceptance of the node i from a power grid dispatching center, wherein B is a serial number set of the nodes in the system;
(1.2.1.3) Voltage safety constraints:
Figure GDA0003019886700000037
in the above formula, the first and second carbon atoms are,
Figure GDA0003019886700000038
and iVrespectively obtaining the upper limit and the lower limit of the voltage safety amplitude of the node i from a power grid dispatching center;
(1.2.1.4) unit output constraint:
Figure GDA0003019886700000039
in the above formula, the first and second carbon atoms are,
Figure GDA00030198867000000310
and i GPrespectively obtaining the upper limit of the generating active power and the lower limit of the generating active power of the generator set i from a power grid dispatching center,
Figure GDA00030198867000000311
and
Figure GDA00030198867000000312
respectively acquiring the upper limit of the generating reactive power and the lower limit of the generating reactive power of the generator set i from a power grid dispatching center;
(1.2.1.5) line capacity constraint:
Figure GDA00030198867000000313
in the above formula, the first and second carbon atoms are,
Figure GDA00030198867000000314
obtaining the apparent power capacity of the branch circuit ij from a power grid dispatching center;
(1.2.2) if the regional power grid numbered n in the hierarchy m is a radial power grid, the constraint conditions include:
(1.2.2.1) relaxed branch flow equation constraints:
Figure GDA00030198867000000315
in the above formula, PijAnd QijRespectively the active power flow and the reactive power flow of the node i flowing to the node j, as variables to be solved, viIs the square of the voltage amplitude of node i, which is the variable to be solved, lijThe square of the current amplitude of the branch ij is used as a variable to be solved, and L is a serial number set of the branch in the system;
(1.2.2.2) node injection balance constraints:
Figure GDA00030198867000000316
Figure GDA0003019886700000041
in the above formula, GiAnd DiRespectively, the serial numbers of the generator set and the load connected with the node i,
Figure GDA0003019886700000042
and
Figure GDA0003019886700000043
the active power and the reactive power of the generator set y are respectively the variables to be solved, PjiAnd QjiRespectively the active power flow and the reactive power flow of the node j flowing to the node i, and is a variable to be solved, ijiThe square of the current amplitude of branch ji, the variable to be solved,
Figure GDA0003019886700000044
and
Figure GDA0003019886700000045
respectively the active power and reactive power requirements of the load z, are obtained from a power grid dispatching center,
Figure GDA0003019886700000046
and
Figure GDA0003019886700000047
the parallel conductance and the parallel susceptance of the node i are respectively obtained from a power grid dispatching center rjiAnd xjiRespectively obtaining the resistance and reactance of the branch ji from a power grid dispatching center, wherein B is a numbering set of nodes in the system;
(1.2.2.3) branch voltage drop constraint:
Figure GDA0003019886700000048
in the above formula, vjIs the square of the voltage amplitude of node j, is the variable to be solved, rijAnd xijRespectively obtaining the resistance and reactance of the branch ij from a power grid dispatching center;
(1.2.2.4) Voltage safety constraints:
Figure GDA0003019886700000049
in the above formula, the first and second carbon atoms are,
Figure GDA00030198867000000410
and ivrespectively obtaining the upper limit and the lower limit of the square of the voltage safety amplitude of the node i from a power grid dispatching center;
(1.2.2.5) unit output constraint:
Figure GDA00030198867000000411
in the above formula, the first and second carbon atoms are,
Figure GDA00030198867000000412
and i GPrespectively obtaining the upper limit of the generating active power and the lower limit of the generating active power of the generator set i from a power grid dispatching center,
Figure GDA00030198867000000413
and
Figure GDA00030198867000000414
respectively acquiring the upper limit of the generating reactive power and the lower limit of the generating reactive power of the generator set i from a power grid dispatching center;
(1.2.2.6) line capacity constraint:
Figure GDA00030198867000000415
in the above formula, the first and second carbon atoms are,
Figure GDA00030198867000000416
obtaining the upper limit of the square of the current amplitude of the branch ij from a power grid dispatching center;
(1.3) forming an active and reactive power combined dispatching optimization model with cooperation of the multilevel power grid by the optimization objective function in the step (1.1) and the constraint condition in the step (1.2), and expressing the following steps:
Figure GDA0003019886700000051
satisfies the following conditions:
Figure GDA0003019886700000052
Figure GDA0003019886700000053
in the above formula, m is the number of the hierarchy in the multi-level power grid, n is the number of the regional power grid in the same hierarchy, and xm,nFor the internal optimization variable of the regional power grid numbered n in the hierarchy m, if the regional power grid is a ring power grid, xm,nIncluding Pij、Qij、Pji、Qji、Vi、Vj、θi、θj、
Figure GDA0003019886700000054
And
Figure GDA0003019886700000055
if the regional grid is a radial grid, xm,nIncluding Pij、Qij、vi、lij、
Figure GDA0003019886700000056
And
Figure GDA0003019886700000057
um,nfor the optimization variable of the coupling of the regional power grid numbered n in the hierarchy m and the superior power grid, if the regional power grid is a ring power grid, um,nIncluded
Figure GDA0003019886700000058
And
Figure GDA0003019886700000059
if the regional grid is a radial grid, um,nIncluding vi、
Figure GDA00030198867000000510
And
Figure GDA00030198867000000511
lm,nfor the optimization variable of the coupling of the regional power grid numbered n in the hierarchy m and the lower-level power grid, if the regional power grid is a ring-shaped power grid, lm,nIncluded
Figure GDA00030198867000000512
And
Figure GDA00030198867000000513
if the regional grid is a radial grid, then lm,nIncluding vi、
Figure GDA00030198867000000514
And
Figure GDA00030198867000000515
fm,n(xm,n) Optimizing the active and reactive power joint dispatching objective of the regional power grid n in the hierarchy m, and the step (1.1)
Figure GDA00030198867000000516
Corresponding to, Gm,n(xm,n,um,n,lm,n) The constraint condition of active and reactive power combined dispatching of the regional power grid n in the hierarchy m is less than or equal to 0, and if the regional power grid n in the hierarchy m is an annular power grid, Gm,n(xm,n,um,n,lm,n) The constraint condition from step (1.2.1.1) to step (1.2.1.5) is not more than 0, and if the regional power grid n in the hierarchy m is a radial power grid, G ism,n(xm,n,um,n,lm,n) The constraint conditions from the step (1.2.2.1) to the step (1.2.2.6) are less than or equal to 0, M is the total level of the multilevel power grid, N (M) is the total number of the power grid areas in the level M, U (M, n) is the number in the level M-1 of the upper level regional power grid connected with the regional power grid n in the level M, and the constraint Um,n＝Im, nlm-1,U(m,n)Representing boundary coupling constraints of connected upper and lower level grids, Im,nA mapping matrix for boundary coupling constraint of regional power grid n and upper power grid in hierarchy m, a mapping matrix Im,nIn each row of (2), vector um,nEach element in lm-1,U(m,n)In the corresponding row of Im,nIs an identity matrix in Im,nNo corresponding other behavior 0;
(2) a nested decomposition coordination method is adopted among all levels of power grids, an active and reactive power combined dispatching optimization model of the multi-level power grid cooperation in the step (1) is solved, and a dispatching method of the nested decomposition coordination active and reactive power combined dispatching of the multi-level power grids is obtained, and the method comprises the following steps:
(2.1) obtaining a power grid, wherein the number m of a middle hierarchy is 1, and the number n of a regional power grid is 1;
(2.2) calculating an optimal solution of the cooperative active and reactive power joint dispatching of the regional power grid numbered n in the hierarchy m and each regional power grid subordinate to the regional power grid by adopting a decomposition coordination method, wherein the process is as follows:
initializing regional grids and phases numbered n in hierarchy mIteration number k of adjacent lower regional power gridm,n1, solving an internal active and reactive power combined scheduling model by using a regional power grid numbered n in the hierarchy m, and judging m:
(2.2.1) if m is 1, the internal active and reactive power joint scheduling model is as follows:
Figure GDA0003019886700000061
s.t.Gm,n(xm,n,um,n,lm,n)≤0
solving the model to obtain an optimal solution, and recording the optimal solution as
Figure GDA0003019886700000062
And
Figure GDA0003019886700000063
and constraining the optimal solution to Gm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure GDA0003019886700000064
(2.2.2) if m is not equal to 1, the internal active and reactive power joint scheduling model is as follows:
Figure GDA0003019886700000065
s.t.Gm,n(xm,n,um,n,lm,n)≤0
Figure GDA0003019886700000066
solving the model to obtain an optimal solution, and recording the optimal solution as
Figure GDA0003019886700000067
And
Figure GDA0003019886700000068
and constraining the optimal solution to Gm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure GDA0003019886700000069
(2.3) judging m: if M ≠ M, taking n as the first entry in L (M, n), where L (M, n) is the number set of regional grids connected in the hierarchical grid M +1 by the regional grid numbered n in the hierarchical M, taking M equal to M +1, returning to step (2.2); if M ═ M, performing step (2.4);
(2.4) calculating an optimal cutting plane and an approximate projection function of the regional power grid numbered n in the hierarchy m, and comprising the following steps:
(2.4.1) judging m:
if M ═ M, then define
Figure GDA00030198867000000610
Is xm,nDefinition of
Figure GDA00030198867000000611
Is fm,n(xm,n) Definition of
Figure GDA00030198867000000612
Is Gm,n(xm,n,um,n,lm,n) Definition of
Figure GDA00030198867000000613
Is composed of
Figure GDA00030198867000000614
If M ≠ M, then define
Figure GDA00030198867000000615
Is [ x ]m,n lm,n objm+1,n*]TDefinition of
Figure GDA00030198867000000616
Is composed of
Figure GDA0003019886700000071
Definition of
Figure GDA0003019886700000072
Is composed of
Figure GDA0003019886700000073
Definition of
Figure GDA0003019886700000074
Is composed of
Figure GDA0003019886700000075
(2.4.2) obtaining the optimal cutting plane of the regional power grid with the number n in the hierarchy m according to the step (2.4.1)
Figure GDA0003019886700000076
Comprises the following steps:
Figure GDA0003019886700000077
approximating a projection function
Figure GDA0003019886700000078
Comprises the following steps:
Figure GDA0003019886700000079
in the above formula, item
Figure GDA00030198867000000710
Can be calculated by the following formula:
Figure GDA00030198867000000711
in the above equation, diag () is a diagonal matrix constructor.
(2.5) judging n: if n is not the last item in L (m-1, U (m, n)), taking n as the next item in L (m-1, U (m, n)), and returning to the step (2.2); if n is the last of L (m-1, U (m, n)), taking n as U (m, n) and m as m-1, carrying out step (2.6);
(2.6) solving an active and reactive power combined dispatching model considering a lower projection function in the regional power grid with the number of n in the hierarchy m, wherein the active and reactive power combined dispatching model comprises the following steps:
and (5) judging m:
(2.6.1) if m is 1, the active and reactive joint scheduling model internally considering the lower projection function is as follows:
Figure GDA0003019886700000081
s.t.Gm,n(xm,n,um,n,lm,n)≤0
Figure GDA0003019886700000082
Figure GDA0003019886700000083
in the above formula, objm+1,n*As an auxiliary variable, the physical meaning is numbered n in the hierarchy m +1*The number of iterations k of the grid numbered n in the hierarchy mm,nIncrement by 1, the optimal solution calculated by the above equation is recorded
Figure GDA0003019886700000084
Figure GDA0003019886700000085
Constraint G at optimal solutionm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure GDA0003019886700000086
Constraining
Figure GDA0003019886700000087
Is recorded as a dual multiplier
Figure GDA0003019886700000088
Constraining
Figure GDA0003019886700000089
Is recorded as a dual multiplier
Figure GDA00030198867000000810
(2.6.2) if m is not equal to 1, an active and reactive power joint scheduling model internally considering the lower projection function is as follows:
Figure GDA00030198867000000811
s.t.Gm,n(xm,n,um,n,lm,n)≤0
Figure GDA00030198867000000812
Figure GDA00030198867000000813
Figure GDA00030198867000000814
in the above formula, objm+1,n*As an auxiliary variable, the physical meaning is numbered n in the hierarchy m +1*The number of iterations k of the grid numbered n in the hierarchy mm,nIncrement by 1, the optimal solution calculated by the above equation is recorded
Figure GDA00030198867000000815
Figure GDA00030198867000000816
Constraint G with optimal solutionm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure GDA00030198867000000817
Constraining
Figure GDA0003019886700000091
Is recorded as a dual multiplier
Figure GDA0003019886700000092
Constraining
Figure GDA0003019886700000093
Is recorded as a dual multiplier
Figure GDA0003019886700000094
(2.7) carrying out convergence judgment on the calculation of the regional power grid with the number of n in the hierarchy m, and setting the convergence condition as
Figure GDA0003019886700000095
If the convergence condition is not met, returning to the step (2.3); if the convergence condition is met and m is not equal to 1, returning to the step (2.4); if the convergence condition is met and m is 1, performing step (3);
(3) according to the optimal solution obtained by calculation in the steps (2.2.2), (2.6.1) and (2.6.2)
Figure GDA0003019886700000096
Active power of each generator included in (1)
Figure GDA0003019886700000097
And reactive power
Figure GDA0003019886700000098
And dispatching the multi-stage power grid to realize the nested decomposition and coordination active and reactive power combined dispatching of the multi-stage power grid.
The invention provides a multi-stage power grid nesting decomposition coordination active and reactive power combined dispatching method which has the characteristics and advantages that:
the invention discloses a multilevel power grid nested decomposition coordination active and reactive power joint scheduling method. Secondly, an active and reactive power joint scheduling model of all levels of power grid cooperation is solved in a nested decomposition coordination mode among all levels of power grids, and active and reactive power joint scheduling is carried out on all regional power grids of all levels based on an optimal solution. The process of solving the cooperative active and reactive power joint dispatching model of each level of power grid in a nested decomposition and coordination mode comprises two key steps: the method comprises the steps of respectively calculating the optimal solution of the active and reactive power combined dispatching of a certain regional power grid and a subordinate power grid in a certain level in a decomposition coordination manner, and calculating the optimal secant plane and the approximate projection function of the certain regional power grid in the certain level, wherein the two steps are called recursively, so that the decomposition coordination calculation of the active and reactive power combined dispatching model of the cooperation of the power grids in all levels is realized. The method establishes an active and reactive power combined dispatching model of multi-level power grid cooperation, solves the active and reactive power combined dispatching model of each level power grid cooperation in a nested decomposition coordination mode among all levels of power grids, and performs active and reactive power combined dispatching on all regional power grids of all levels based on an optimal solution. The method has high convergence speed, can ensure the operation safety of each level of power grid, and avoids the operation risks of local overload, voltage out-of-limit and the like.
Detailed Description
The invention provides a multi-stage power grid nesting decomposition coordination active and reactive power combined dispatching method which comprises the following steps:
(1) establishing an active and reactive power combined dispatching optimization model with multi-stage power grid cooperation:
(1.1) setting M levels of power grids in a multi-level power grid, N (M) regional power grids in the level power grid M, and establishing an optimization objective function of an active and reactive power combined dispatching optimization model for cooperation of the multi-level power grids, wherein the optimization objective function is the minimum of the sum of the power generation cost of each regional power grid in each level, and for the regional power grids numbered n in the level M, the expression of the power generation cost is as follows:
Figure GDA0003019886700000101
in the above formula, G is the number set of the generator set in the power grid,
Figure GDA0003019886700000102
for generating active power of generator set i, Ci(Pi G) For the power generation cost function of the generator set i, the power generation cost function is expressed as a quadratic function as follows:
Ci(Pi G)＝a0,i+a1,iPi G+a2,i(Pi G)2
in the above formula, a0,i、a1,i、a2,iRespectively obtaining the power generation cost constant term, the primary term and the secondary term coefficient of the generator set i from a power grid dispatching center;
(1.2) establishing the constraint conditions of the active and reactive power combined dispatching optimization model of the multi-stage power grid cooperation as follows: for the regional power grid numbered n in level m, the following two cases are distinguished:
(1.2.1) if the regional power grid numbered n in the hierarchy m is a ring power grid, the constraint condition includes:
(1.2.1.1) branch flow equation constraint:
Figure GDA0003019886700000103
Figure GDA0003019886700000104
Figure GDA0003019886700000105
Figure GDA0003019886700000106
in the above formula, PijAnd QijRespectively the active power flow and the reactive power flow of a node i to a node j in the power grid, which are variables to be solved, PjiAnd QjiRespectively an active power flow and a reactive power flow flowing to a node i from a node j, wherein the active power flow and the reactive power flow are variables to be solved, namely tauijThe transformer transformation ratio of the branch ij between the node i and the node j is obtained by a transformer factory nameplate,
Figure GDA0003019886700000107
and
Figure GDA0003019886700000108
respectively the conductance and susceptance of the branch ij, obtained from a power grid dispatching center,
Figure GDA0003019886700000109
for charging susceptance of branch ij, obtained from the grid dispatching centre, ViAnd VjThe voltage amplitudes of the node i and the node j are respectively used as variables to be solved, thetaiAnd thetajThe voltage phase angles of the node i and the node j are respectively the variables to be solved, phiijThe phase-shifting phase angle of the transformer which is the branch ij is obtained by a transformer delivery nameplate, and L is a serial number set of the branch in the power grid;
(1.2.1.2) node injection balance constraints:
Figure GDA0003019886700000111
Figure GDA0003019886700000112
in the above formula, GiAnd DiRespectively, the serial numbers of the generator set and the load connected with the node i,
Figure GDA0003019886700000113
and
Figure GDA0003019886700000114
the active power and the reactive power of the generator set y are respectively used as variables to be solved,
Figure GDA0003019886700000115
and
Figure GDA0003019886700000116
respectively the active power demand and the reactive power demand of the load z, are obtained from a power grid dispatching center,
Figure GDA0003019886700000117
and
Figure GDA0003019886700000118
respectively obtaining the parallel conductance and the parallel susceptance of the node i from a power grid dispatching center, wherein B is a serial number set of the nodes in the system;
(1.2.1.3) Voltage safety constraints:
Figure GDA0003019886700000119
in the above formula, the first and second carbon atoms are,
Figure GDA00030198867000001110
and iVrespectively obtaining the upper limit and the lower limit of the voltage safety amplitude of the node i from a power grid dispatching center;
(1.2.1.4) unit output constraint:
Figure GDA00030198867000001111
in the above formula, the first and second carbon atoms are,
Figure GDA00030198867000001112
and i GPrespectively obtaining the upper limit of the generating active power and the lower limit of the generating active power of the generator set i from a power grid dispatching center,
Figure GDA00030198867000001113
and
Figure GDA00030198867000001114
respectively acquiring the upper limit of the generating reactive power and the lower limit of the generating reactive power of the generator set i from a power grid dispatching center;
(1.2.1.5) line capacity constraint:
Figure GDA00030198867000001115
in the above formula, the first and second carbon atoms are,
Figure GDA00030198867000001116
obtaining the apparent power capacity of the branch circuit ij from a power grid dispatching center;
(1.2.2) if the regional power grid numbered n in the hierarchy m is a radial power grid, the constraint conditions include:
(1.2.2.1) relaxed branch flow equation constraints:
Figure GDA00030198867000001117
in the above formula, PijAnd QijRespectively the active power flow and the reactive power flow of the node i flowing to the node j, as variables to be solved, viIs the square of the voltage amplitude of node i, which is the variable to be solved, lijThe square of the current amplitude of the branch ij is used as a variable to be solved, and L is a serial number set of the branch in the system;
(1.2.2.2) node injection balance constraints:
Figure GDA0003019886700000121
Figure GDA0003019886700000122
in the above formula, GiAnd DiRespectively, the serial numbers of the generator set and the load connected with the node i,
Figure GDA0003019886700000123
and
Figure GDA0003019886700000124
the active power and the reactive power of the generator set y are respectively the variables to be solved, PjiAnd QjiRespectively the active power flow and the reactive power flow of the node j flowing to the node i, and is a variable to be solved, ijiThe square of the current amplitude of branch ji, the variable to be solved,
Figure GDA0003019886700000125
and
Figure GDA0003019886700000126
respectively the active power and reactive power requirements of the load z, are obtained from a power grid dispatching center,
Figure GDA0003019886700000127
and
Figure GDA0003019886700000128
the parallel conductance and the parallel susceptance of the node i are respectively obtained from a power grid dispatching center rjiAnd xjiRespectively obtaining the resistance and reactance of the branch ji from a power grid dispatching center, wherein B is a numbering set of nodes in the system;
(1.2.2.3) branch voltage drop constraint:
Figure GDA0003019886700000129
in the above formula, vjIs the square of the voltage amplitude of node j, is the variable to be solved, rijAnd xijRespectively obtaining the resistance and reactance of the branch ij from a power grid dispatching center;
(1.2.2.4) Voltage safety constraints:
Figure GDA00030198867000001210
in the above formula, the first and second carbon atoms are,
Figure GDA00030198867000001211
and ivrespectively obtaining the upper limit and the lower limit of the square of the voltage safety amplitude of the node i from a power grid dispatching center;
(1.2.2.5) unit output constraint:
Figure GDA00030198867000001212
in the above formula, the first and second carbon atoms are,
Figure GDA00030198867000001213
and Pi GRespectively obtaining the upper limit of the generating active power and the lower limit of the generating active power of the generator set i from a power grid dispatching center,
Figure GDA00030198867000001214
and
Figure GDA00030198867000001215
respectively acquiring the upper limit of the generating reactive power and the lower limit of the generating reactive power of the generator set i from a power grid dispatching center;
(1.2.2.6) line capacity constraint:
Figure GDA00030198867000001216
in the above formula, the first and second carbon atoms are,
Figure GDA00030198867000001217
obtaining the upper limit of the square of the current amplitude of the branch ij from a power grid dispatching center;
(1.3) forming an active and reactive power combined dispatching optimization model with cooperation of the multilevel power grid by the optimization objective function in the step (1.1) and the constraint condition in the step (1.2), and expressing the following steps:
Figure GDA0003019886700000131
satisfies the following conditions:
Figure GDA0003019886700000132
Figure GDA0003019886700000133
in the above formula, m is the number of the hierarchy in the multi-level power grid, n is the number of the regional power grid in the same hierarchy, and xm,nFor the internal optimization variable of the regional power grid numbered n in the hierarchy m, if the regional power grid is a ring power grid, xm,nIncluding Pij、Qij、Pji、Qji、Vi、Vj、θi、θj、
Figure GDA0003019886700000134
And
Figure GDA0003019886700000135
if the regional grid is a radial grid, xm,nIncluding Pij、Qij、vi、lij、
Figure GDA0003019886700000136
And
Figure GDA0003019886700000137
um,nfor the optimization variable of the coupling of the regional power grid numbered n in the hierarchy m and the superior power grid, if the regional power grid is a ring power grid, um,nIncluded
Figure GDA0003019886700000138
And
Figure GDA0003019886700000139
if the regional grid is a radial grid, um,nIncluding vi、
Figure GDA00030198867000001310
And
Figure GDA00030198867000001311
lm,nfor the optimization variable of the coupling of the regional power grid numbered n in the hierarchy m and the lower-level power grid, if the regional power grid is a ring-shaped power grid, lm,nIncluded
Figure GDA00030198867000001312
And
Figure GDA00030198867000001313
if the regional grid is a radial grid, then lm,nIncluding vi、
Figure GDA00030198867000001314
And
Figure GDA00030198867000001315
fm,n(xm,n) Optimizing the active and reactive power joint dispatching objective of the regional power grid n in the hierarchy m, and the step (1.1)
Figure GDA00030198867000001316
Corresponding to, Gm,n(xm,n,um,n,lm,n) The constraint condition of active and reactive power combined dispatching of the regional power grid n in the hierarchy m is less than or equal to 0, and if the regional power grid n in the hierarchy m is an annular power grid, Gm,n(xm,n,um,n,lm,n) The constraint condition from step (1.2.1.1) to step (1.2.1.5) is not more than 0, and if the regional power grid n in the hierarchy m is a radial power grid, G ism,n(xm,n,um,n,lm,n) The constraint condition from the step (1.2.2.1) to the step (1.2.2.6) is less than or equal to 0, M is the total level of the multilevel power grid, N (M) is the total number of power grid areas in the level M, and U (M, n) is the area power grid in the level Mn number in level m-1 of the upper level regional power grid connected with the upper level regional power grid, and constraint um,n＝Im, nlm-1,U(m,n)Representing boundary coupling constraints of connected upper and lower level grids, Im,nA mapping matrix for boundary coupling constraint of regional power grid n and upper power grid in hierarchy m, a mapping matrix Im,nIn each row of (2), vector um,nEach element in lm-1,U(m,n)In the corresponding row of Im,nIs an identity matrix in Im,nNo corresponding other behavior 0;
(2) a nested decomposition coordination method is adopted among all levels of power grids, an active and reactive power combined dispatching optimization model of the multi-level power grid cooperation in the step (1) is solved, and a dispatching method of the nested decomposition coordination active and reactive power combined dispatching of the multi-level power grids is obtained, and the method comprises the following steps:
(2.1) obtaining a power grid, wherein the number m of a middle hierarchy is 1, and the number n of a regional power grid is 1;
(2.2) calculating an optimal solution of the cooperative active and reactive power joint dispatching of the regional power grid numbered n in the hierarchy m and each regional power grid subordinate to the regional power grid by adopting a decomposition coordination method, wherein the process is as follows:
initializing iteration times k of a regional power grid numbered n in a hierarchy m and an adjacent lower-level regional power gridm,n1, solving an internal active and reactive power combined scheduling model by using a regional power grid numbered n in the hierarchy m, and judging m:
(2.2.1) if m is 1, the internal active and reactive power joint scheduling model is as follows:
Figure GDA0003019886700000141
s.t.Gm,n(xm,n,um,n,lm,n)≤0
solving the model to obtain an optimal solution, and recording the optimal solution as
Figure GDA0003019886700000142
And
Figure GDA0003019886700000143
and constraining the optimal solution to Gm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure GDA0003019886700000144
(2.2.2) if m is not equal to 1, the internal active and reactive power joint scheduling model is as follows:
Figure GDA0003019886700000145
s.t.Gm,n(xm,n,um,n,lm,n)≤0
Figure GDA0003019886700000146
solving the model to obtain an optimal solution, and recording the optimal solution as
Figure GDA0003019886700000147
And
Figure GDA0003019886700000148
and constraining the optimal solution to Gm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure GDA0003019886700000149
(2.3) judging m: if M ≠ M, taking n as the first entry in L (M, n), where L (M, n) is the number set of regional grids connected in the hierarchical grid M +1 by the regional grid numbered n in the hierarchical M, taking M equal to M +1, returning to step (2.2); if M ═ M, performing step (2.4);
(2.4) calculating an optimal cutting plane and an approximate projection function of the regional power grid numbered n in the hierarchy m, and comprising the following steps:
(2.4.1) judging m:
if M is equal to M, then decideYi (Chinese character)
Figure GDA00030198867000001410
Is xm,nDefinition of
Figure GDA00030198867000001411
Is fm,n(xm,n) Definition of
Figure GDA00030198867000001412
Is Gm,n(xm,n,um,n,lm,n) Definition of
Figure GDA00030198867000001413
Is composed of
Figure GDA00030198867000001414
If M ≠ M, then define
Figure GDA0003019886700000151
Is [ x ]m,n lm,n objm+1,n*]TDefinition of
Figure GDA0003019886700000152
Is composed of
Figure GDA0003019886700000153
Definition of
Figure GDA0003019886700000154
Is composed of
Figure GDA0003019886700000155
Definition of
Figure GDA0003019886700000156
Is composed of
Figure GDA0003019886700000157
(2.4.2) obtaining the optimal cutting plane of the regional power grid with the number n in the hierarchy m according to the step (2.4.1)
Figure GDA0003019886700000158
Comprises the following steps:
Figure GDA0003019886700000159
approximating a projection function
Figure GDA00030198867000001510
Comprises the following steps:
Figure GDA00030198867000001511
in the above formula, item
Figure GDA00030198867000001512
Can be calculated by the following formula:
Figure GDA00030198867000001513
in the above equation, diag () is a diagonal matrix constructor.
(2.5) judging n: if n is not the last item in L (m-1, U (m, n)), taking n as the next item in L (m-1, U (m, n)), and returning to the step (2.2); if n is the last of L (m-1, U (m, n)), taking n as U (m, n) and m as m-1, carrying out step (2.6);
(2.6) solving an active and reactive power combined dispatching model considering a lower projection function in the regional power grid with the number of n in the hierarchy m, wherein the active and reactive power combined dispatching model comprises the following steps:
and (5) judging m:
(2.6.1) if m is 1, the active and reactive joint scheduling model internally considering the lower projection function is as follows:
Figure GDA0003019886700000161
s.t.Gm,n(xm,n,um,n,lm,n)≤0
Figure GDA0003019886700000162
Figure GDA0003019886700000163
in the above formula, objm+1,n*As an auxiliary variable, the physical meaning is numbered n in the hierarchy m +1*The number of iterations k of the grid numbered n in the hierarchy mm,nIncrement by 1, the optimal solution calculated by the above equation is recorded
Figure GDA0003019886700000164
Figure GDA0003019886700000165
Constraint G at optimal solutionm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure GDA0003019886700000166
Constraining
Figure GDA0003019886700000167
Is recorded as a dual multiplier
Figure GDA0003019886700000168
Constraining
Figure GDA0003019886700000169
Is recorded as a dual multiplier
Figure GDA00030198867000001610
(2.6.2) if m is not equal to 1, an active and reactive power joint scheduling model internally considering the lower projection function is as follows:
Figure GDA00030198867000001611
s.t.Gm,n(xm,n,um,n,lm,n)≤0
Figure GDA00030198867000001612
Figure GDA00030198867000001613
Figure GDA00030198867000001614
in the above formula, objm+1n*As an auxiliary variable, the physical meaning is numbered n in the hierarchy m +1*The number of iterations k of the grid numbered n in the hierarchy mm,nIncrement by 1, the optimal solution calculated by the above equation is recorded
Figure GDA00030198867000001615
Figure GDA0003019886700000171
Constraint G with optimal solutionm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure GDA0003019886700000172
Constraining
Figure GDA0003019886700000173
Is recorded as a dual multiplier
Figure GDA0003019886700000174
Constraining
Figure GDA0003019886700000175
Is recorded as a dual multiplier
Figure GDA0003019886700000176
(2.7) carrying out convergence judgment on the calculation of the regional power grid with the number of n in the hierarchy m, and setting the convergence condition as
Figure GDA0003019886700000177
If the convergence condition is not met, returning to the step (2.3); if the convergence condition is met and m is not equal to 1, returning to the step (2.4); if the convergence condition is met and m is 1, performing step (3);
(3) according to the optimal solution obtained by calculation in the steps (2.2.2), (2.6.1) and (2.6.2)
Figure GDA0003019886700000178
Active power of each generator included in (1)
Figure GDA0003019886700000179
And reactive power
Figure GDA00030198867000001710
And dispatching the multi-stage power grid to realize the nested decomposition and coordination active and reactive power combined dispatching of the multi-stage power grid.

Claims (1)

1. A multi-stage power grid nesting decomposition coordination active and reactive power joint scheduling method is characterized by comprising the following steps:
(1) establishing an active and reactive power combined dispatching optimization model with multi-stage power grid cooperation:
(1.1) setting M levels of power grids in a multi-level power grid, N (M) regional power grids in the level power grid M, and establishing an optimization objective function of an active and reactive power combined dispatching optimization model for cooperation of the multi-level power grids, wherein the optimization objective function is the minimum of the sum of the power generation cost of each regional power grid in each level, and for the regional power grids numbered n in the level M, the expression of the power generation cost is as follows:
Figure FDA0003019886690000011
in the above formula, G is the number set of the generator set in the power grid, Pi GFor generating active power of generator set i, Ci(Pi G) For the power generation cost function of the generator set i, the power generation cost function is expressed as a quadratic function as follows:
Ci(Pi G)＝a0,i+a1,iPi G+a2,i(Pi G)2
in the above formula, a0,i、a1,i、a2,iRespectively obtaining the power generation cost constant term, the primary term and the secondary term coefficient of the generator set i from a power grid dispatching center;
(1.2) establishing the constraint conditions of the active and reactive power combined dispatching optimization model of the multi-stage power grid cooperation as follows: for the regional power grid numbered n in level m, the following two cases are distinguished:
(1.2.1) if the regional power grid numbered n in the hierarchy m is a ring power grid, the constraint condition includes:
(1.2.1.1) branch flow equation constraint:
Figure FDA0003019886690000012
Figure FDA0003019886690000013
Figure FDA0003019886690000014
Figure FDA0003019886690000015
in the above formula, PijAnd QijRespectively an active power tide and a reactive power tide flowing from a node i to a node j in a power gridFlow, being a variable to be solved, PjiAnd QjiRespectively an active power flow and a reactive power flow flowing to a node i from a node j, wherein the active power flow and the reactive power flow are variables to be solved, namely tauijThe transformer transformation ratio of the branch ij between the node i and the node j is obtained by a transformer factory nameplate,
Figure FDA0003019886690000021
and
Figure FDA0003019886690000022
respectively the conductance and susceptance of the branch ij, obtained from a power grid dispatching center,
Figure FDA0003019886690000023
for charging susceptance of branch ij, obtained from the grid dispatching centre, ViAnd VjThe voltage amplitudes of the node i and the node j are respectively used as variables to be solved, thetaiAnd thetajThe voltage phase angles of the node i and the node j are respectively the variables to be solved, phiijThe phase-shifting phase angle of the transformer which is the branch ij is obtained by a transformer delivery nameplate, and L is a serial number set of the branch in the power grid;
(1.2.1.2) node injection balance constraints:
Figure FDA0003019886690000024
Figure FDA0003019886690000025
in the above formula, GiAnd DiRespectively, the serial numbers of the generator set and the load connected with the node i,
Figure FDA0003019886690000026
and
Figure FDA0003019886690000027
are respectively asThe generating active power and the generating reactive power of the generating set y are variables to be solved,
Figure FDA00030198866900000217
and
Figure FDA0003019886690000028
respectively the active power demand and the reactive power demand of the load z, are obtained from a power grid dispatching center,
Figure FDA0003019886690000029
and
Figure FDA00030198866900000210
respectively obtaining the parallel conductance and the parallel susceptance of the node i from a power grid dispatching center, wherein B is a serial number set of the nodes in the system;
(1.2.1.3) Voltage safety constraints:
Figure FDA00030198866900000211
in the above formula, the first and second carbon atoms are,
Figure FDA00030198866900000212
and iVrespectively obtaining the upper limit and the lower limit of the voltage safety amplitude of the node i from a power grid dispatching center;
(1.2.1.4) unit output constraint:
Figure FDA00030198866900000213
in the above formula, the first and second carbon atoms are,
Figure FDA00030198866900000214
and i GPrespectively obtaining the upper limit of the generating active power and the lower limit of the generating active power of the generator set i from a power grid dispatching centerTaking out the raw materials,
Figure FDA00030198866900000215
and i GQrespectively acquiring the upper limit of the generating reactive power and the lower limit of the generating reactive power of the generator set i from a power grid dispatching center;
(1.2.1.5) line capacity constraint:
Figure FDA00030198866900000216
in the above formula, the first and second carbon atoms are,
Figure FDA0003019886690000031
obtaining the apparent power capacity of the branch circuit ij from a power grid dispatching center;
(1.2.2) if the regional power grid numbered n in the hierarchy m is a radial power grid, the constraint conditions include:
(1.2.2.1) relaxed branch flow equation constraints:
Figure FDA0003019886690000032
in the above formula, PijAnd QijRespectively the active power flow and the reactive power flow of the node i flowing to the node j, as variables to be solved, viIs the square of the voltage amplitude of node i, which is the variable to be solved, lijThe square of the current amplitude of the branch ij is used as a variable to be solved, and L is a serial number set of the branch in the system;
(1.2.2.2) node injection balance constraints:
Figure FDA0003019886690000033
Figure FDA0003019886690000034
in the above formula, GiAnd DiRespectively, the serial numbers of the generator set and the load connected with the node i,
Figure FDA0003019886690000035
and
Figure FDA0003019886690000036
the active power and the reactive power of the generator set y are respectively the variables to be solved, PjiAnd QjiRespectively the active power flow and the reactive power flow of the node j flowing to the node i, and is a variable to be solved, ijiThe square of the current amplitude of branch ji, the variable to be solved,
Figure FDA00030198866900000313
and
Figure FDA00030198866900000312
respectively the active power and reactive power requirements of the load z, are obtained from a power grid dispatching center,
Figure FDA0003019886690000037
and
Figure FDA0003019886690000038
the parallel conductance and the parallel susceptance of the node i are respectively obtained from a power grid dispatching center rjiAnd xjiRespectively obtaining the resistance and reactance of the branch ji from a power grid dispatching center, wherein B is a numbering set of nodes in the system;
(1.2.2.3) branch voltage drop constraint:
Figure FDA0003019886690000039
in the above formula, vjIs the square of the voltage amplitude of node j, is the variable to be solved, rijAnd xijThe resistances of the branches ij andthe reactance is obtained from a power grid dispatching center;
(1.2.2.4) Voltage safety constraints:
Figure FDA00030198866900000310
in the above formula, the first and second carbon atoms are,
Figure FDA00030198866900000311
and ivrespectively obtaining the upper limit and the lower limit of the square of the voltage safety amplitude of the node i from a power grid dispatching center;
(1.2.2.5) unit output constraint:
Figure FDA0003019886690000041
in the above formula, the first and second carbon atoms are,
Figure FDA0003019886690000042
and i GPrespectively obtaining the upper limit of the generating active power and the lower limit of the generating active power of the generator set i from a power grid dispatching center,
Figure FDA0003019886690000043
and
Figure FDA0003019886690000044
respectively acquiring the upper limit of the generating reactive power and the lower limit of the generating reactive power of the generator set i from a power grid dispatching center;
(1.2.2.6) line capacity constraint:
Figure FDA0003019886690000045
in the above formula, the first and second carbon atoms are,
Figure FDA0003019886690000046
obtaining the upper limit of the square of the current amplitude of the branch ij from a power grid dispatching center;
(1.3) forming an active and reactive power combined dispatching optimization model with cooperation of the multilevel power grid by the optimization objective function in the step (1.1) and the constraint condition in the step (1.2), and expressing the following steps:
Figure FDA0003019886690000047
satisfies the following conditions:
Figure FDA0003019886690000048
Figure FDA0003019886690000049
in the above formula, m is the number of the hierarchy in the multi-level power grid, n is the number of the regional power grid in the same hierarchy, and xm,nFor the internal optimization variable of the regional power grid numbered n in the hierarchy m, if the regional power grid is a ring power grid, xm,nIncluding Pij、Qij、Pji、Qji、Vi、Vj、θi、θj、Pi GAnd Qi GIf the regional grid is a radial grid, xm,nIncluding Pij、Qij、vi、lij、Pi GAnd Qi G；um,nFor the optimization variable of the coupling of the regional power grid numbered n in the hierarchy m and the superior power grid, if the regional power grid is a ring power grid, um，nComprising Vi 2、Pi GAnd Qi GIf the regional grid is a radial grid, um,nIncluding vi、Pi GAnd Qi G；lm,nFor optimization variables of coupling of the regional power grid numbered n in the hierarchy m with the subordinate power grid if the regional power grid is a ring power gridThen l ism,nComprising Vi 2、-Pi Gand-Qi GIf the regional grid is a radial grid, then lm,nIncluding vi、-Pi GAnd
Figure FDA00030198866900000410
fm,n(xm,n) Optimizing the active and reactive power joint dispatching objective of the regional power grid n in the hierarchy m, and the step (1.1)
Figure FDA00030198866900000411
Corresponding to, Gm,n(xm,n,um,n,lm,n) The constraint condition of active and reactive power combined dispatching of the regional power grid n in the hierarchy m is less than or equal to 0, and if the regional power grid n in the hierarchy m is an annular power grid, Gm,n(xm,n,um,n,lm,n) The constraint condition from step (1.2.1.1) to step (1.2.1.5) is not more than 0, and if the regional power grid n in the hierarchy m is a radial power grid, G ism,n(xm,n,um,n,lm,n) The constraint conditions from the step (1.2.2.1) to the step (1.2.2.6) are less than or equal to 0, M is the total level of the multilevel power grid, N (M) is the total number of the power grid areas in the level M, U (M, n) is the number in the level M-1 of the upper level regional power grid connected with the regional power grid n in the level M, and the constraint Um,n＝Im, nlm-1,U(m,n)Representing boundary coupling constraints of connected upper and lower level grids, Im,nA mapping matrix for boundary coupling constraint of regional power grid n and upper power grid in hierarchy m, a mapping matrix Im,nIn each row of (2), vector um,nEach element in lm-1,U(m,n)In the corresponding row of Im,nIs an identity matrix in Im,nNo corresponding other behavior 0;
(2) a nested decomposition coordination method is adopted among all levels of power grids, an active and reactive power combined dispatching optimization model of the multi-level power grid cooperation in the step (1) is solved, and a dispatching method of the nested decomposition coordination active and reactive power combined dispatching of the multi-level power grids is obtained, and the method comprises the following steps:
(2.1) obtaining a power grid, wherein the number m of a middle hierarchy is 1, and the number n of a regional power grid is 1;
(2.2) calculating an optimal solution of the cooperative active and reactive power joint dispatching of the regional power grid numbered n in the hierarchy m and each regional power grid subordinate to the regional power grid by adopting a decomposition coordination method, wherein the process is as follows:
initializing iteration times k of a regional power grid numbered n in a hierarchy m and an adjacent lower-level regional power gridm,n1, solving an internal active and reactive power combined scheduling model by using a regional power grid numbered n in the hierarchy m, and judging m:
(2.2.1) if m is 1, the internal active and reactive power joint scheduling model is as follows:
Figure FDA0003019886690000051
s.t.Gm,n(xm,n,um,n,lm,n)≤0
solving the model to obtain an optimal solution, and recording the optimal solution as
Figure FDA0003019886690000052
And
Figure FDA0003019886690000053
and constraining the optimal solution to Gm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure FDA0003019886690000054
(2.2.2) if m is not equal to 1, the internal active and reactive power joint scheduling model is as follows:
Figure FDA0003019886690000055
s.t.Gm,n(xm,n,um,n,lm,n)≤0
Figure FDA0003019886690000056
solving the model to obtain an optimal solution, and recording the optimal solution as
Figure FDA0003019886690000057
And
Figure FDA0003019886690000058
and constraining the optimal solution to Gm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure FDA0003019886690000059
(2.3) judging m: if M ≠ M, taking n as the first entry in L (M, n), where L (M, n) is the number set of regional grids connected in the hierarchical grid M +1 by the regional grid numbered n in the hierarchical M, taking M equal to M +1, returning to step (2.2); if M ═ M, performing step (2.4);
(2.4) calculating an optimal cutting plane and an approximate projection function of the regional power grid numbered n in the hierarchy m, and comprising the following steps:
(2.4.1) judging m:
if M ═ M, then define
Figure FDA0003019886690000061
Is xm,nDefinition of
Figure FDA0003019886690000062
Is fm,n(xm,n) Definition of
Figure FDA0003019886690000063
Is Gm,n(xm,n,um,n,lm,n) Definition of
Figure FDA0003019886690000064
Is composed of
Figure FDA0003019886690000065
If M ≠ M, then define
Figure FDA0003019886690000066
Is composed of
Figure FDA0003019886690000067
Definition of
Figure FDA0003019886690000068
Is composed of
Figure FDA0003019886690000069
Definition of
Figure FDA00030198866900000610
Is composed of
Figure FDA00030198866900000611
Definition of
Figure FDA00030198866900000612
Is composed of
Figure FDA00030198866900000613
(2.4.2) obtaining the optimal cutting plane of the regional power grid with the number n in the hierarchy m according to the step (2.4.1)
Figure FDA00030198866900000614
Comprises the following steps:
Figure FDA00030198866900000615
approximating a projection function
Figure FDA00030198866900000616
Comprises the following steps:
Figure FDA00030198866900000617
in the above formula, item
Figure FDA0003019886690000071
Can be calculated by the following formula:
Figure FDA0003019886690000072
in the above equation, diag () is a diagonal matrix constructor;
(2.5) judging n: if n is not the last item in L (m-1, U (m, n)), taking n as the next item in L (m-1, U (m, n)), and returning to the step (2.2); if n is the last of L (m-1, U (m, n)), taking n as U (m, n) and m as m-1, carrying out step (2.6);
(2.6) solving an active and reactive power combined dispatching model considering a lower projection function in the regional power grid with the number of n in the hierarchy m, wherein the active and reactive power combined dispatching model comprises the following steps:
and (5) judging m:
(2.6.1) if m is 1, the active and reactive joint scheduling model internally considering the lower projection function is as follows:
Figure FDA0003019886690000073
s.t.Gm,n(xm,n,um,n,lm,n)≤0
Figure FDA0003019886690000074
Figure FDA0003019886690000075
in the above formula, the first and second carbon atoms are,
Figure FDA0003019886690000076
as an auxiliary variable, the physical meaning is numbered n in the hierarchy m +1*The number of iterations k of the grid numbered n in the hierarchy mm，nIncrement by 1, the optimal solution calculated by the above equation is recorded
Figure FDA0003019886690000077
Figure FDA0003019886690000078
Constraint G at optimal solutionm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure FDA0003019886690000079
Constraining
Figure FDA00030198866900000710
Is recorded as a dual multiplier
Figure FDA00030198866900000711
Constraining
Figure FDA00030198866900000712
Is recorded as a dual multiplier
Figure FDA00030198866900000713
(2.6.2) if m is not equal to 1, an active and reactive power joint scheduling model internally considering the lower projection function is as follows:
Figure FDA0003019886690000081
s.t.Gm,n(xm,n,um,n,lm,n)≤0
Figure FDA0003019886690000082
Figure FDA0003019886690000083
Figure FDA0003019886690000084
in the above formula, the first and second carbon atoms are,
Figure FDA0003019886690000085
as an auxiliary variable, the physical meaning is numbered n in the hierarchy m +1*The number of iterations k of the grid numbered n in the hierarchy mm,nIncrement by 1, the optimal solution calculated by the above equation is recorded
Figure FDA0003019886690000086
Figure FDA0003019886690000087
Constraint G with optimal solutionm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure FDA0003019886690000088
Constraining
Figure FDA0003019886690000089
Is recorded as a dual multiplier
Figure FDA00030198866900000810
Constraining
Figure FDA00030198866900000811
Is recorded as a dual multiplier
Figure FDA00030198866900000812
(2.7) carrying out convergence judgment on the calculation of the regional power grid with the number of n in the hierarchy m, and setting the convergence condition as
Figure FDA00030198866900000813
If the convergence condition is not met, returning to the step (2.3); if the convergence condition is met and m is not equal to 1, returning to the step (2.4); if the convergence condition is met and m is 1, performing step (3);
(3) according to the optimal solution obtained by calculation in the steps (2.2.2), (2.6.1) and (2.6.2)
Figure FDA00030198866900000814
Active power P of each generator included in (1)i GAnd reactive power Qi GAnd dispatching the multi-stage power grid to realize the nested decomposition and coordination active and reactive power combined dispatching of the multi-stage power grid.
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