CN111416395A - 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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CN111416395A
CN111416395A CN202010236368.3A CN202010236368A CN111416395A CN 111416395 A CN111416395 A CN 111416395A CN 202010236368 A CN202010236368 A CN 202010236368A CN 111416395 A CN111416395 A CN 111416395A
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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
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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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 RE-GDA0002473902520000011
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 RE-GDA0002473902520000021
Figure RE-GDA0002473902520000022
Figure RE-GDA0002473902520000023
Figure RE-GDA0002473902520000024
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 RE-GDA0002473902520000025
and
Figure RE-GDA0002473902520000026
respectively the conductance and susceptance of the branch ij, obtained from a power grid dispatching center,
Figure RE-GDA0002473902520000027
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 RE-GDA0002473902520000028
Figure RE-GDA0002473902520000029
in the above formula, GiAnd DiRespectively, the serial numbers of the generator set and the load connected with the node i,
Figure RE-GDA00024739025200000210
and
Figure RE-GDA00024739025200000211
the active power and the reactive power of the generator set y are respectively the variables to be solved, Pz DAnd Qz DActive power demand and reactive power, respectively, of load zThe rate demand is obtained from the power grid dispatching center,
Figure RE-GDA0002473902520000031
and
Figure RE-GDA0002473902520000032
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 RE-GDA0002473902520000033
in the above formula, the first and second carbon atoms are,
Figure RE-GDA0002473902520000034
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 RE-GDA0002473902520000035
in the above formula, the first and second carbon atoms are,
Figure RE-GDA0002473902520000036
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 RE-GDA0002473902520000037
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 RE-GDA0002473902520000038
in the above formula, the first and second carbon atoms are,
Figure RE-GDA0002473902520000039
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 RE-GDA00024739025200000314
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 a variable to be solved, and L is a number set of the branches in the system;
(1.2.2.2) node injection balance constraints:
Figure RE-GDA00024739025200000310
Figure RE-GDA00024739025200000311
in the above formula, GiAnd DiRespectively, the serial numbers of the generator set and the load connected with the node i,
Figure RE-GDA00024739025200000312
and
Figure RE-GDA00024739025200000313
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 isTo-be-sought variable, Pz DAnd Qz DRespectively the active power and reactive power requirements of the load z, are obtained from a power grid dispatching center,
Figure RE-GDA0002473902520000041
and
Figure RE-GDA0002473902520000042
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 RE-GDA0002473902520000043
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 RE-GDA0002473902520000044
in the above formula, the first and second carbon atoms are,
Figure RE-GDA0002473902520000045
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 RE-GDA0002473902520000046
in the above formula, the first and second carbon atoms are,
Figure RE-GDA0002473902520000047
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 RE-GDA0002473902520000048
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;
(1.2.2.6) line capacity constraint:
Figure RE-GDA0002473902520000049
in the above formula, the first and second carbon atoms are,
Figure RE-GDA00024739025200000410
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 RE-GDA0002473902520000051
satisfies the following conditions:
Figure RE-GDA0002473902520000052
Figure RE-GDA0002473902520000053
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、θi、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 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,nComprising Vi 2、-Pi Gand-Qi GIf the regional grid is a radial grid, then lm,nIncluding vi、-Pi Gand-Qi G，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 RE-GDA0002473902520000054
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,nFor regional grids n and above in level mMapping matrix of boundary coupling constraints of a hierarchical grid, 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 RE-GDA0002473902520000061
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 RE-GDA0002473902520000062
And
Figure RE-GDA0002473902520000063
and constraining the optimal solution to Gm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure RE-GDA0002473902520000064
(2.2.2) if m is not equal to 1, the internal active and reactive power joint scheduling model is as follows:
Figure RE-GDA0002473902520000065
s.t.Gm,n(xm,n,um,n,lm,n)≤0
Figure RE-GDA0002473902520000066
solving the model to obtain an optimal solution, and recording the optimal solution as
Figure RE-GDA0002473902520000067
And
Figure RE-GDA0002473902520000068
and constraining the optimal solution to Gm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure RE-GDA0002473902520000069
(2.3) judging M, if M ≠ M, taking n as the first item in L (M, n), wherein L (M, n) is the number set of regional power grids connected by the regional power grid numbered n in the hierarchy M +1, taking M equal to M +1, and returning to the step (2.2), if M ≠ M, performing the 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 RE-GDA00024739025200000610
Is xm,nDefinition of
Figure RE-GDA00024739025200000611
Is fm,n(xm,n) Definition of
Figure RE-GDA00024739025200000612
Is Gm,n(xm,n,um,n,lm,n) Definition of
Figure RE-GDA00024739025200000613
Is composed of
Figure RE-GDA00024739025200000614
If M ≠ M, then define
Figure RE-GDA00024739025200000615
Is composed of
Figure RE-GDA00024739025200000619
Definition of
Figure RE-GDA00024739025200000616
Is composed of
Figure RE-GDA00024739025200000617
Definition of
Figure RE-GDA00024739025200000618
Is composed of
Figure RE-GDA0002473902520000071
Definition of
Figure RE-GDA0002473902520000072
Is composed of
Figure RE-GDA0002473902520000073
(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 RE-GDA0002473902520000074
Comprises the following steps:
Figure RE-GDA0002473902520000075
approximating a projection function
Figure RE-GDA0002473902520000076
Comprises the following steps:
Figure RE-GDA0002473902520000077
in the above formula, item
Figure RE-GDA0002473902520000078
Can be calculated by the following formula:
Figure RE-GDA0002473902520000079
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)), returning to the step (2.2), if n is the last item in L (m-1, U (m, n)), taking n as U (m, n), m as m-1, and performing the 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 RE-GDA0002473902520000081
s.t.Gm,n(xm,n,um,n,lm,n)≤0
Figure RE-GDA0002473902520000082
Figure RE-GDA0002473902520000083
in the above formula, the first and second carbon atoms are,
Figure RE-GDA00024739025200000821
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 RE-GDA0002473902520000084
Figure RE-GDA0002473902520000085
Constraint G at optimal solutionm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure RE-GDA0002473902520000086
Constraining
Figure RE-GDA0002473902520000087
Is recorded as a dual multiplier
Figure RE-GDA0002473902520000088
Constraining
Figure RE-GDA0002473902520000089
Is recorded as a dual multiplier
Figure RE-GDA00024739025200000810
(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 RE-GDA00024739025200000811
s.t.Gm,n(xm,n,um,n,lm,n)≤0
Figure RE-GDA00024739025200000812
Figure RE-GDA00024739025200000813
Figure RE-GDA00024739025200000814
in the above formula, the first and second carbon atoms are,
Figure RE-GDA00024739025200000822
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 RE-GDA00024739025200000815
Figure RE-GDA00024739025200000816
Constraint G with optimal solutionm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure RE-GDA00024739025200000817
Constraining
Figure RE-GDA00024739025200000818
Is recorded as a dual multiplier
Figure RE-GDA00024739025200000819
Constraining
Figure RE-GDA00024739025200000820
Is recorded as a dual multiplier
Figure RE-GDA0002473902520000091
(2.7) receiving the calculation of the regional grid numbered n in the hierarchy mConvergence judgment, setting convergence conditions as
Figure RE-GDA0002473902520000092
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 RE-GDA0002473902520000093
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.
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 RE-GDA0002473902520000094
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 RE-GDA0002473902520000101
Figure RE-GDA0002473902520000102
Figure RE-GDA0002473902520000103
Figure RE-GDA0002473902520000104
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 RE-GDA0002473902520000105
and
Figure RE-GDA0002473902520000106
respectively the conductance and susceptance of the branch ij, obtained from a power grid dispatching center,
Figure RE-GDA0002473902520000107
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 RE-GDA0002473902520000108
Figure RE-GDA0002473902520000111
in the above formula, GiAnd DiRespectively, the serial numbers of the generator set and the load connected with the node i,
Figure RE-GDA0002473902520000112
and
Figure RE-GDA0002473902520000113
the active power and the reactive power of the generator set y are respectively the variables to be solved, Pz DAnd Qz DRespectively the active power demand and the reactive power demand of the load z, are obtained from a power grid dispatching center,
Figure RE-GDA0002473902520000114
and
Figure RE-GDA0002473902520000115
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 RE-GDA0002473902520000116
in the above formula, the first and second carbon atoms are,
Figure RE-GDA0002473902520000117
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 RE-GDA0002473902520000118
in the above formula, the first and second carbon atoms are,
Figure RE-GDA0002473902520000119
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 RE-GDA00024739025200001110
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 RE-GDA00024739025200001111
in the above formula, the first and second carbon atoms are,
Figure RE-GDA00024739025200001112
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 RE-GDA00024739025200001113
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 a variable to be solved, and L is a number set of the branches in the system;
(1.2.2.2) node injection balance constraints:
Figure RE-GDA00024739025200001114
Figure RE-GDA0002473902520000121
in the above formula, GiAnd DiNumber sets, P, of generator sets and loads respectively connected to node iy GAnd
Figure RE-GDA0002473902520000122
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, ijiIs the square of the current amplitude of branch ji, is the variable to be solved, Pz DAnd Qz DRespectively the active power and reactive power requirements of the load z, are obtained from a power grid dispatching center,
Figure RE-GDA0002473902520000123
and
Figure RE-GDA0002473902520000124
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 RE-GDA0002473902520000125
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 RE-GDA0002473902520000126
in the above formula, the first and second carbon atoms are,
Figure RE-GDA0002473902520000127
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 RE-GDA0002473902520000128
in the above formula, the first and second carbon atoms are,
Figure RE-GDA0002473902520000129
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 RE-GDA00024739025200001210
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;
(1.2.2.6) line capacity constraint:
Figure RE-GDA00024739025200001211
in the above formula, the first and second carbon atoms are,
Figure RE-GDA00024739025200001212
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 RE-GDA0002473902520000131
satisfies the following conditions:
Figure RE-GDA0002473902520000132
Figure RE-GDA0002473902520000133
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、θi、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 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,nComprising Vi 2、-Pi Gand-Qi GIf the regional grid is a radial grid, then lm,nIncluding vi、-Pi Gand-Qi G，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 RE-GDA0002473902520000134
Corresponding to, Gm,n(xm,n,um,n,lm,n) Not more than 0 in the hierarchy mConstraint conditions of active and reactive power combined dispatching of the regional power grid n, 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 RE-GDA0002473902520000141
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 RE-GDA0002473902520000142
And
Figure RE-GDA0002473902520000143
and constraining the optimal solution to Gm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure RE-GDA0002473902520000144
(2.2.2) if m is not equal to 1, the internal active and reactive power joint scheduling model is as follows:
Figure RE-GDA0002473902520000145
s.t.Gm,n(xm,n,um,n,lm,n)≤0
Figure RE-GDA0002473902520000146
solving the model to obtain an optimal solution, and recording the optimal solution as
Figure RE-GDA0002473902520000147
And
Figure RE-GDA0002473902520000148
and constraining the optimal solution to Gm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure RE-GDA0002473902520000149
(2.3) judging M, if M ≠ M, taking n as the first item in L (M, n), wherein L (M, n) is the number set of regional power grids connected by the regional power grid numbered n in the hierarchy M +1, taking M equal to M +1, and returning to the step (2.2), if M ≠ M, performing the 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 RE-GDA00024739025200001410
Is xm,nDefinition of
Figure RE-GDA00024739025200001411
Is fm,n(xm,n) Definition of
Figure RE-GDA00024739025200001412
Is Gm,n(xm,n,um,n,lm,n) Definition of
Figure RE-GDA00024739025200001413
Is composed of
Figure RE-GDA00024739025200001414
If M ≠ M, then define
Figure RE-GDA00024739025200001415
Is composed of
Figure RE-GDA00024739025200001419
Definition of
Figure RE-GDA00024739025200001416
Is composed of
Figure RE-GDA00024739025200001417
Definition of
Figure RE-GDA00024739025200001418
Is composed of
Figure RE-GDA0002473902520000151
Definition of
Figure RE-GDA0002473902520000152
Is composed of
Figure RE-GDA0002473902520000153
(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 RE-GDA0002473902520000154
Comprises the following steps:
Figure RE-GDA0002473902520000155
approximating a projection function
Figure RE-GDA0002473902520000156
Comprises the following steps:
Figure RE-GDA0002473902520000157
in the above formula, item
Figure RE-GDA0002473902520000158
Can be calculated by the following formula:
Figure RE-GDA0002473902520000159
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)), returning to the step (2.2), if n is the last item in L (m-1, U (m, n)), taking n as U (m, n), m as m-1, and performing the 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 RE-GDA0002473902520000161
s.t.Gm,n(xm,n,um,n,lm,n)≤0
Figure RE-GDA0002473902520000162
Figure RE-GDA0002473902520000163
in the above formula, the first and second carbon atoms are,
Figure RE-GDA00024739025200001621
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 RE-GDA0002473902520000164
Figure RE-GDA0002473902520000165
Constraint G at optimal solutionm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure RE-GDA0002473902520000166
Constraining
Figure RE-GDA0002473902520000167
Is recorded as a dual multiplier
Figure RE-GDA0002473902520000168
Constraining
Figure RE-GDA0002473902520000169
Is recorded as a dual multiplier
Figure RE-GDA00024739025200001610
(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 RE-GDA00024739025200001611
s.t.Gm,n(xm,n,um,n,lm,n)≤0
Figure RE-GDA00024739025200001612
Figure RE-GDA00024739025200001613
Figure RE-GDA00024739025200001614
in the above formula, the first and second carbon atoms are,
Figure RE-GDA00024739025200001622
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 RE-GDA00024739025200001615
Figure RE-GDA00024739025200001616
Constraint G with optimal solutionm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure RE-GDA00024739025200001617
Constraining
Figure RE-GDA00024739025200001618
Is recorded as a dual multiplier
Figure RE-GDA00024739025200001619
Constraining
Figure RE-GDA00024739025200001620
Is recorded as a dual multiplier
Figure RE-GDA0002473902520000171
(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 RE-GDA0002473902520000172
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 RE-GDA0002473902520000173
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.

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 RE-FDA0002473902510000011
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 RE-FDA0002473902510000012
Figure RE-FDA0002473902510000013
Figure RE-FDA0002473902510000014
Figure RE-FDA0002473902510000015
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 RE-FDA0002473902510000021
and
Figure RE-FDA0002473902510000022
respectively the conductance and susceptance of the branch ij, obtained from a power grid dispatching center,
Figure RE-FDA0002473902510000023
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 RE-FDA0002473902510000024
Figure RE-FDA0002473902510000025
in the above formula, GiAnd DiRespectively, the serial numbers of the generator set and the load connected with the node i,
Figure RE-FDA0002473902510000026
and
Figure RE-FDA0002473902510000027
the active power and the reactive power of the generator set y are respectively used as variables to be solved,
Figure RE-FDA0002473902510000028
and
Figure RE-FDA0002473902510000029
respectively the active power demand and the reactive power demand of the load z, are obtained from a power grid dispatching center,
Figure RE-FDA00024739025100000210
and
Figure RE-FDA00024739025100000211
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 RE-FDA00024739025100000212
in the above formula, the first and second carbon atoms are,
Figure RE-FDA00024739025100000213
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 RE-FDA00024739025100000214
in the above formula, the first and second carbon atoms are,
Figure RE-FDA00024739025100000215
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 RE-FDA00024739025100000216
and
Figure RE-FDA00024739025100000217
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 RE-FDA00024739025100000218
in the above formula, the first and second carbon atoms are,
Figure RE-FDA00024739025100000219
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 RE-FDA0002473902510000031
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 a variable to be solved, and L is a number set of the branches in the system;
(1.2.2.2) node injection balance constraints:
Figure RE-FDA0002473902510000032
Figure RE-FDA0002473902510000033
in the above formula, GiAnd DiRespectively, the serial numbers of the generator set and the load connected with the node i,
Figure RE-FDA0002473902510000034
and
Figure RE-FDA0002473902510000035
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 RE-FDA0002473902510000036
and
Figure RE-FDA0002473902510000037
respectively the active power and reactive power requirements of the load z, are obtained from a power grid dispatching center,
Figure RE-FDA0002473902510000038
and
Figure RE-FDA0002473902510000039
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 RE-FDA00024739025100000310
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 RE-FDA00024739025100000311
in the above formula, the first and second carbon atoms are,
Figure RE-FDA00024739025100000312
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 RE-FDA00024739025100000313
in the above formula, the first and second carbon atoms are,
Figure RE-FDA0002473902510000041
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 RE-FDA0002473902510000042
and
Figure RE-FDA0002473902510000043
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 RE-FDA0002473902510000044
in the above formula, the first and second carbon atoms are,
Figure RE-FDA0002473902510000045
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 RE-FDA0002473902510000046
satisfies the following conditions:
Figure RE-FDA0002473902510000047
Figure RE-FDA0002473902510000048
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、θi、Pi GAnd
Figure RE-FDA0002473902510000049
if the regional grid is a radial grid, xm,nIncluding Pij、Qij、vi、lij、Pi GAnd
Figure RE-FDA00024739025100000410
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
Figure RE-FDA00024739025100000411
if the regional grid is a radial grid, um,nIncluding vi、Pi GAnd
Figure RE-FDA00024739025100000412
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,nComprising Vi 2、-Pi GAnd
Figure RE-FDA00024739025100000413
if the regional grid is a radial grid, then lm,nIncluding vi、-Pi GAnd
Figure RE-FDA00024739025100000414
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 RE-FDA00024739025100000415
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)Represents connected toBoundary coupling constraints of the hierarchical 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 RE-FDA0002473902510000051
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 RE-FDA0002473902510000052
And
Figure RE-FDA0002473902510000053
and constraining the optimal solution to Gm,n(xm,n,um,n,lm,n) The dual is less than or equal to 0The multiplier is recorded as
Figure RE-FDA0002473902510000054
(2.2.2) if m is not equal to 1, the internal active and reactive power joint scheduling model is as follows:
Figure RE-FDA0002473902510000055
s.t.Gm,n(xm,n,um,n,lm,n)≤0
Figure RE-FDA0002473902510000056
solving the model to obtain an optimal solution, and recording the optimal solution as
Figure RE-FDA0002473902510000057
And
Figure RE-FDA0002473902510000058
and constraining the optimal solution to Gm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure RE-FDA0002473902510000059
(2.3) judging M, if M ≠ M, taking n as the first item in L (M, n), wherein L (M, n) is the number set of regional power grids connected by the regional power grid numbered n in the hierarchy M +1, taking M equal to M +1, and returning to the step (2.2), if M ≠ M, performing the 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 RE-FDA0002473902510000061
Is xm,nDefinition of
Figure RE-FDA0002473902510000062
Is fm,n(xm,n) Definition ofIs Gm,n(xm,n,um,n,lm,n) Definition of
Figure RE-FDA0002473902510000064
Is composed of
Figure RE-FDA0002473902510000065
If M ≠ M, then define
Figure RE-FDA0002473902510000066
Is composed of
Figure RE-FDA0002473902510000067
Definition of
Figure RE-FDA0002473902510000068
Is composed of
Figure RE-FDA0002473902510000069
Definition of
Figure RE-FDA00024739025100000610
Is composed of
Figure RE-FDA00024739025100000611
Definition of
Figure RE-FDA00024739025100000612
Is composed of
Figure RE-FDA00024739025100000613
(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 RE-FDA00024739025100000614
Comprises the following steps:
Figure RE-FDA00024739025100000615
approximating a projection function
Figure RE-FDA00024739025100000616
Comprises the following steps:
Figure RE-FDA00024739025100000617
in the above formula, item
Figure RE-FDA00024739025100000618
Can be calculated by the following formula:
Figure RE-FDA0002473902510000071
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)), returning to the step (2.2), if n is the last item in L (m-1, U (m, n)), taking n as U (m, n), m as m-1, and performing the 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 RE-FDA0002473902510000072
s.t.Gm,n(xm,n,um,n,lm,n)≤0
Figure RE-FDA0002473902510000073
Figure RE-FDA0002473902510000074
in the above formula, the first and second carbon atoms are,
Figure RE-FDA0002473902510000075
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 RE-FDA0002473902510000076
Figure RE-FDA0002473902510000077
Constraint G at optimal solutionm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure RE-FDA0002473902510000078
Constraining
Figure RE-FDA0002473902510000079
Is recorded as a dual multiplier
Figure RE-FDA00024739025100000710
Constraining
Figure RE-FDA00024739025100000711
Is recorded as a dual multiplier
Figure RE-FDA00024739025100000712
(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 RE-FDA0002473902510000081
s.t.Gm,n(xm,n,um,n,lm,n)≤0
Figure RE-FDA0002473902510000082
Figure RE-FDA0002473902510000083
Figure RE-FDA0002473902510000084
in the above formula, the first and second carbon atoms are,
Figure RE-FDA0002473902510000085
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 RE-FDA0002473902510000086
Figure RE-FDA0002473902510000087
Constraint G with optimal solutionm,n(xm,n,um,n,lm,n) Notation of dual multiplier not greater than 0
Figure RE-FDA0002473902510000088
Constraining
Figure RE-FDA0002473902510000089
Is recorded as a dual multiplier
Figure RE-FDA00024739025100000810
Constraining
Figure RE-FDA00024739025100000811
Is recorded as a dual multiplier
Figure RE-FDA00024739025100000812
(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 RE-FDA00024739025100000813
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 RE-FDA00024739025100000814
Active power P of each generator included in (1)i GAnd reactive power
Figure RE-FDA00024739025100000815
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.
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