CN111416395B - A joint scheduling method for multi-level power grid nested decomposition coordination active and reactive power - Google Patents

A joint scheduling method for multi-level power grid nested decomposition coordination active and reactive power 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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Hangzhou Qingyan Electric Power Technology Co ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
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Abstract

本发明涉及一种多级电网嵌套分解协调有功无功联合调度方法，属于电力系统运行控制技术领域。首先建立多级电网协同的有功无功联合调度模型，在各级电网之间采用嵌套分解协调的方式求解各级电网协同的有功无功联合调度模型，并基于最优解，对全部层级全部区域电网进行有功无功联合调度。其关键步骤是：分解协调计算某级中某区域电网与其下属电网的有功无功联合调度最优解、计算某级中某区域电网的最优割平面与近似投影函数，这两个步骤之间互相递归调用，实现各级电网协同的有功无功联合调度模型的分解协调计算。本方法收敛速度快，能够保证各级电网运行的安全，避免局部过载、电压越限等运行风险。The invention relates to a multi-level power grid nesting decomposition coordination active and reactive power joint scheduling method, which belongs to the technical field of power system operation control. Firstly, a joint active and reactive power dispatch model of multi-level power grid coordination is established, and the coordinated active and reactive power joint dispatch model of all levels of power grids is solved by nesting decomposition and coordination between power grids at all levels. The regional power grid conducts joint active and reactive power dispatching. The key steps are: decomposing and coordinating the calculation of the optimal solution of the active and reactive power joint scheduling of a regional power grid in a certain level and its subordinate power grids, and calculating the optimal cutting plane and approximate projection function of a regional power grid in a certain level. Call each other recursively to realize the decomposition and coordination calculation of the active and reactive joint dispatching model of the coordination of all levels of power grids. The method has a fast convergence speed, can ensure the safe operation of power grids at all levels, and avoid operation risks such as partial overload and voltage overrun.

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)

1.一种多级电网嵌套分解协调有功无功联合调度方法，其特征在于该方法包括以下步骤：1. a multi-level power grid nested decomposition coordination active and reactive joint scheduling method, is characterized in that the method comprises the following steps: (1)建立一个多级电网协同的有功无功联合调度优化模型：(1) Establish a multi-level grid coordinated active and reactive joint dispatch optimization model: (1.1)设定一个多级电网中共有M个层级电网，层级电网m中共有N(m)个区域电网，建立多级电网协同的有功无功联合调度优化模型的优化目标函数，该优化目标函数为各层级各区域电网的发电成本的总和的最小化，对于层级m中编号n的区域电网，发电成本的表达式为：(1.1) Set a multi-level power grid with M levels of power grids, and there are N(m) regional power grids in the hierarchical power grid m, and establish the optimization objective function of the multi-level power grid coordinated active and reactive power joint dispatch optimization model. The optimization objective The function is the minimization of the sum of the power generation costs of the regional power grids at each level. For the regional power grid numbered n in the level m, the expression of the power generation cost is:
Figure FDA0003019886690000011
Figure FDA0003019886690000011
 上式中，G为电网中发电机组的编号集合，Pi G为发电机组i的发电有功功率，Ci(Pi G)为发电机组i的发电成本函数，将该发电成本函数表示成如下的二次函数：In the above formula, G is the numbered set of generator sets in the power grid, P i G is the active power generated by the generator set i, and C i (P i G ) is the power generation cost function of the generator set i. The power generation cost function is expressed as follows: The quadratic function of : Ci(Pi G)＝a0,i+a1,iPi G+a2,i(Pi G)2 C i (P i G )=a 0,i +a 1,i P i G +a 2,i (P i G ) 2 上式中，a0,i、a1,i、a2,i分别为发电机组i的发电成本常数项、一次项和二次项系数，从电网调度中心获取；In the above formula, a 0,i , a 1,i , a 2,i are the constant term, primary term and quadratic term coefficients of power generation cost of generator set i respectively, which are obtained from the grid dispatch center; (1.2)建立多级电网协同的有功无功联合调度优化模型的约束条件如下：对于层级m中编号n的区域电网，区分以下两种情况：(1.2) The constraints for establishing a multi-level power grid coordinated active and reactive joint dispatch optimization model are as follows: For the regional power grid numbered n in level m, the following two situations are distinguished: (1.2.1)若层级m中编号n的区域电网是环状电网，则约束条件包括：(1.2.1) If the regional power grid numbered n in level m is a ring power grid, the constraints include: (1.2.1.1)支路潮流方程约束：(1.2.1.1) Constraints of branch power flow equation:
Figure FDA0003019886690000012
Figure FDA0003019886690000012
Figure FDA0003019886690000013
Figure FDA0003019886690000013
Figure FDA0003019886690000014
Figure FDA0003019886690000014
Figure FDA0003019886690000015
Figure FDA0003019886690000015
 上式中，Pij与Qij分别为电网中节点i流向节点j的有功功率潮流与无功功率潮流，为待求变量，Pji与Qji分别为节点j流向节点i的有功功率潮流与无功功率潮流，为待求变量，τij为节点i与节点j之间的支路ij的变压器变比，由变压器出厂铭牌获取，
Figure FDA0003019886690000021
与
Figure FDA0003019886690000022
分别为支路ij的电导与电纳，从电网调度中心获取，
Figure FDA0003019886690000023
为支路ij的充电电纳，从电网调度中心获取，Vi与Vj分别为节点i与节点j的电压幅值，为待求变量，θi与θj分别为节点i与节点j的电压相角，为待求变量，φij为支路ij的变压器移相相角，由变压器出厂铭牌获取，L为电网中支路的编号集合；In the above formula, P ij and Q ij are the active power flow and reactive power flow from node i to node j in the power grid, respectively, and are the variables to be determined. P ji and Q ji are the active power flow from node j to node i, respectively, and Reactive power flow, is the variable to be determined, τ ij is the transformer transformation ratio of the branch ij between node i and node j, obtained from the factory nameplate of the transformer,
Figure FDA0003019886690000021
and
Figure FDA0003019886690000022
are the conductance and susceptance of branch ij, respectively, obtained from the power grid dispatch center,
Figure FDA0003019886690000023
is the charging susceptance of branch ij, obtained from the power grid dispatch center, V i and V j are the voltage amplitudes of node i and node j, respectively, and are the variables to be determined, θ i and θ j are the voltage values of node i and node j, respectively. The voltage phase angle is the variable to be determined, φ ij is the phase-shift phase angle of the transformer of the branch ij, which is obtained from the nameplate of the transformer, and L is the set of numbers of the branches in the power grid; (1.2.1.2)节点注入平衡约束：(1.2.1.2) Node injection balance constraints:
Figure FDA0003019886690000024
Figure FDA0003019886690000024
Figure FDA0003019886690000025
Figure FDA0003019886690000025
 上式中，Gi与Di分别为与节点i连接的发电机组与负荷的编号集合，
Figure FDA0003019886690000026
与
Figure FDA0003019886690000027
分别为发电机组y的发电有功功率与无功功率，为待求变量，
Figure FDA00030198866900000217
与
Figure FDA0003019886690000028
分别为负荷z的有功功率需求与无功功率需求，从电网调度中心获取，
Figure FDA0003019886690000029
与
Figure FDA00030198866900000210
分别为节点i的并联电导与并联电纳，从电网调度中心获取，B为系统中节点的编号集合；In the above formula, G i and D i are the numbered sets of generator sets and loads connected to node i, respectively,
Figure FDA0003019886690000026
and
Figure FDA0003019886690000027
are the active power and reactive power of the generator set y, respectively, are the variables to be determined,
Figure FDA00030198866900000217
and
Figure FDA0003019886690000028
are the active power demand and reactive power demand of the load z, respectively, obtained from the grid dispatch center,
Figure FDA0003019886690000029
and
Figure FDA00030198866900000210
are the parallel conductance and parallel susceptance of node i, respectively, obtained from the grid dispatch center, and B is the numbered set of nodes in the system; (1.2.1.3)电压安全约束：(1.2.1.3) Voltage safety constraints:
Figure FDA00030198866900000211
Figure FDA00030198866900000211
 上式中，
Figure FDA00030198866900000212
与Vi 分别为节点i的电压安全幅值上限与电压安全幅值下限，从电网调度中心获取；In the above formula,
Figure FDA00030198866900000212
and V i are the upper limit of the voltage safety amplitude and the lower limit of the voltage safety amplitude of the node i, respectively, obtained from the power grid dispatch center; (1.2.1.4)机组出力约束：(1.2.1.4) Unit output constraints:
Figure FDA00030198866900000213
Figure FDA00030198866900000213
 上式中，
Figure FDA00030198866900000214
与Pi G 分别为发电机组i的发电有功功率上限与发电有功功率下限，从电网调度中心获取，
Figure FDA00030198866900000215
与Qi G 分别为发电机组i的发电无功功率上限与发电无功功率下限，从电网调度中心获取；In the above formula,
Figure FDA00030198866900000214
and P i G are the upper limit and lower limit of active power generation of generator set i respectively, which are obtained from the grid dispatch center,
Figure FDA00030198866900000215
and Q i G are the upper limit and lower limit of generating reactive power of generator set i, respectively, obtained from the grid dispatch center; (1.2.1.5)线路容量约束：(1.2.1.5) Line capacity constraints:
Figure FDA00030198866900000216
Figure FDA00030198866900000216
 上式中，
Figure FDA0003019886690000031
为支路ij的视在功率容量，从电网调度中心获取；In the above formula,
Figure FDA0003019886690000031
is the apparent power capacity of branch ij, obtained from the grid dispatch center; (1.2.2)若层级m中编号n的区域电网是辐射状电网，则约束条件包括：(1.2.2) If the regional power grid numbered n in level m is a radial power grid, the constraints include: (1.2.2.1)松弛的支路潮流方程约束：(1.2.2.1) Relaxed branch power flow equation constraints:
Figure FDA0003019886690000032
Figure FDA0003019886690000032
 上式中，Pij与Qij分别为节点i流向节点j的有功功率潮流与无功功率潮流，为待求变量，vi为节点i的电压幅值的平方，为待求变量，lij为支路ij的电流幅值的平方，为待求变量，L为系统中支路的编号集合；In the above formula, P ij and Q ij are the active power flow and reactive power flow from node i to node j, respectively, are the variables to be determined, vi is the square of the voltage amplitude of node i , and are the variables to be determined, l ij is the square of the current amplitude of the branch ij, is the variable to be determined, and L is the numbered set of the branches in the system; (1.2.2.2)节点注入平衡约束：(1.2.2.2) Node injection balance constraints:
Figure FDA0003019886690000033
Figure FDA0003019886690000033
Figure FDA0003019886690000034
Figure FDA0003019886690000034
 上式中，Gi与Di分别为与节点i连接的发电机组与负荷的编号集合，
Figure FDA0003019886690000035
与
Figure FDA0003019886690000036
分别为发电机组y的发电有功功率与无功功率，为待求变量，Pji与Qji分别为节点j流向节点i的有功功率潮流与无功功率潮流，为待求变量，lji为支路ji的电流幅值的平方，为待求变量，
Figure FDA00030198866900000313
与
Figure FDA00030198866900000312
分别为负荷z的有功功率与无功功率需求，从电网调度中心获取，
Figure FDA0003019886690000037
与
Figure FDA0003019886690000038
分别为节点i的并联电导与并联电纳，从电网调度中心获取，rji与xji分别为支路ji的电阻与电抗，从电网调度中心获取，B为系统中节点的编号集合；In the above formula, G i and D i are the numbered sets of generator sets and loads connected to node i, respectively,
Figure FDA0003019886690000035
and
Figure FDA0003019886690000036
are the generated active power and reactive power of generator set y, respectively, are the variables to be determined, P ji and Q ji are the active power flow and reactive power flow from node j to node i, respectively, are the variables to be determined, l ji is the branch The square of the current amplitude of the path ji is the variable to be determined,
Figure FDA00030198866900000313
and
Figure FDA00030198866900000312
are the active power and reactive power demands of the load z, respectively, obtained from the grid dispatch center,
Figure FDA0003019886690000037
and
Figure FDA0003019886690000038
are the parallel conductance and parallel susceptance of node i, respectively, obtained from the grid dispatch center, r ji and x ji are the resistance and reactance of branch ji, respectively, obtained from the grid dispatch center, and B is the numbered set of nodes in the system; (1.2.2.3)支路电压降落约束：(1.2.2.3) Branch voltage drop constraints:
Figure FDA0003019886690000039
Figure FDA0003019886690000039
 上式中，vj为节点j的电压幅值的平方，为待求变量，rij与xij分别为支路ij的电阻与电抗，从电网调度中心获取；In the above formula, v j is the square of the voltage amplitude of node j, which is the variable to be determined, and r ij and x ij are the resistance and reactance of the branch ij, respectively, obtained from the power grid dispatch center; (1.2.2.4)电压安全约束：(1.2.2.4) Voltage safety constraints:
Figure FDA00030198866900000310
Figure FDA00030198866900000310
 上式中，
Figure FDA00030198866900000311
与vi 分别为节点i的电压安全幅值的平方的上限与下限，从电网调度中心获取；In the above formula,
Figure FDA00030198866900000311
and v i are the upper limit and lower limit of the square of the voltage safety amplitude of node i, respectively, obtained from the power grid dispatch center; (1.2.2.5)机组出力约束：(1.2.2.5) Unit output constraints:
Figure FDA0003019886690000041
Figure FDA0003019886690000041
 上式中，
Figure FDA0003019886690000042
与Pi G 分别为发电机组i的发电有功功率上限与发电有功功率下限，从电网调度中心获取，
Figure FDA0003019886690000043
与
Figure FDA0003019886690000044
分别为发电机组i的发电无功功率上限与发电无功功率下限，从电网调度中心获取；In the above formula,
Figure FDA0003019886690000042
and P i G are the upper limit and lower limit of active power generation of generator set i respectively, which are obtained from the grid dispatch center,
Figure FDA0003019886690000043
and
Figure FDA0003019886690000044
are the upper limit of generating reactive power and the lower limit of generating reactive power of generator set i respectively, which are obtained from the grid dispatch center; (1.2.2.6)线路容量约束：(1.2.2.6) Line capacity constraints:
Figure FDA0003019886690000045
Figure FDA0003019886690000045
 上式中，
Figure FDA0003019886690000046
为支路ij的电流幅值的平方的上限，从电网调度中心获取；In the above formula,
Figure FDA0003019886690000046
is the upper limit of the square of the current amplitude of the branch ij, obtained from the power grid dispatch center; (1.3)将步骤(1.1)的优化目标函数和步骤(1.2)的约束条件组成一个多级电网协同的有功无功联合调度优化模型，表达如下：(1.3) The optimization objective function of step (1.1) and the constraints of step (1.2) are composed of a multi-level grid coordinated active and reactive joint dispatch optimization model, which is expressed as follows:
Figure FDA0003019886690000047
Figure FDA0003019886690000047
 满足：
Figure FDA0003019886690000048
Satisfy:
Figure FDA0003019886690000048
Figure FDA0003019886690000049
Figure FDA0003019886690000049
 上式中，m为多级电网中的层级编号，n为同一层级中的区域电网的编号，xm,n为层级m中编号n的区域电网的内部优化变量，若该区域电网是环状电网，则xm,n包括Pij、Qij、Pji、Qji、Vi、Vj、θi、θj、Pi G和Qi G，如果该区域电网是辐射状电网，则xm,n包括Pij、Qij、vi、lij、Pi G和Qi G；um,n为层级m中编号n的区域电网与上级电网耦合的优化变量，如果该区域电网是环状电网，则um，n包括Vi 2、Pi G和Qi G，如果该区域电网是辐射状电网，则um,n包括vi、Pi G和Qi G；lm,n为层级m中编号n的区域电网与下级电网耦合的优化变量，如果该区域电网是环状电网，则lm,n包括Vi 2、-Pi G和-Qi G，如果该区域电网是辐射状电网，则lm,n包括vi、-Pi G和
Figure FDA00030198866900000410
fm,n(xm,n)为层级m中区域电网n的有功无功联合调度优化目标，与步骤(1.1)中的
Figure FDA00030198866900000411
相对应，Gm,n(xm,n,um,n,lm,n)≤0为层级m中区域电网n的有功无功联合调度的约束条件，若层级m中区域电网n为环状电网，则Gm,n(xm,n,um,n,lm,n)≤0为步骤(1.2.1.1)-步骤(1.2.1.5)的约束条件，若层级m中区域电网n为辐射状电网，则Gm,n(xm,n,um,n,lm,n)≤0为步骤(1.2.2.1)-步骤(1.2.2.6)的约束条件，M为多级电网的总级数，N(m)为层级m中的电网区域总数，U(m,n)为与层级m中区域电网n相连接的上一级区域电网所在的层级m-1中的编号，约束um,n＝Im, nlm-1,U(m,n)表示相连接的上层级电网和下层级电网的边界耦合约束，Im,n为层级m中区域电网n与上级电网的边界耦合约束的映射矩阵，映射矩阵Im,n的各行中，向量um,n中的每个元素在lm-1,U(m,n)中对应的行在Im,n中为单位矩阵，在Im,n中没有对应的其他行为0；In the above formula, m is the level number in the multi-level power grid, n is the number of the regional power grid in the same level, x m,n is the internal optimization variable of the regional power grid number n in the level m, if the regional power grid is ring-shaped. If the power grid in this area is a radial power grid , then x m,n includes P ij , Qi ij , vi , l ij , P i G and Q i G ; um,n is the optimization variable for coupling between the regional power grid numbered n in level m and the upper power grid, if the regional power grid is a ring power grid, then um,n includes V i 2 , P i G and Qi G , if the regional power grid is a radial power grid, then um,n includes V i , P i G and Qi G ; l m,n is the optimization variable of the coupling between the regional power grid numbered n in level m and the subordinate power grid. If the regional power grid is a ring power grid, then lm ,n includes V i 2 , -P i G and -Q i G , if The regional power grid is a radial power grid, then l m,n includes v i , -P i G and
Figure FDA00030198866900000410
f m,n (x m,n ) is the joint active and reactive power scheduling optimization objective of the regional power grid n in the level m, which is the same as that in step (1.1).
Figure FDA00030198866900000411
Correspondingly, G m,n (x m,n , um,n ,l m,n )≤0 is the constraint condition of the joint active and reactive power dispatching of the regional power grid n in the level m, if the regional power grid n in the level m is Ring power grid, then G m,n (x m,n , um,n ,l m,n )≤0 is the constraint condition of step (1.2.1.1)-step (1.2.1.5), if the area in level m The grid n is a radial grid, then G m,n (x m,n , um,n ,l m,n )≤0 is the constraint condition of step (1.2.2.1)-step (1.2.2.6), M is The total number of stages of the multi-level power grid, N(m) is the total number of grid areas in level m, U(m,n) is the level m-1 where the regional power grid of the previous level connected to the regional power grid n in level m is located The number of u m,n =I m, n l m-1,U(m,n) represents the boundary coupling constraint of the connected upper-level power grid and the lower-level power grid, Im,n is the regional power grid in level m The mapping matrix of n and the boundary coupling constraint of the upper power grid, in each row of the mapping matrix I m,n , each element in the vector um,n is in lm -1, and the corresponding row in U(m,n) is in I m,n is the identity matrix, and there is no other corresponding row 0 in I m,n ; (2)各级电网之间采用嵌套分解协调的方法，求解步骤(1)的多级电网协同的有功无功联合调度优化模型，得到多级电网嵌套分解协调有功无功联合调度的调度方法，包括以下步骤：(2) The method of nested decomposition and coordination is adopted between the power grids at all levels to solve the multi-level power grid coordinated active and reactive joint scheduling optimization model in step (1), and the scheduling of the multi-level power grid nested decomposition and coordinated active and reactive power joint scheduling is obtained. method, including the following steps: (2.1)取电网中层级编号m＝1，区域电网编号n＝1；(2.1) Take the level number m=1 in the power grid, and the regional power grid number n=1; (2.2)采用分解协调方法，计算层级m中编号为n的区域电网与该区域电网下属的各区域电网协同的有功无功联合调度最优解，过程如下：(2.2) Using the decomposition coordination method, calculate the optimal solution of the joint active and reactive power dispatching coordinated by the regional power grid numbered n in the level m and the regional power grids subordinate to the regional power grid. The process is as follows: 初始化层级m中编号为n的区域电网与相邻下级区域电网的迭代次数km,n＝1，层级m中编号为n的区域电网求解内部有功无功联合调度模型，对m进行判断：Initialize the number of iterations between the regional power grid numbered n in level m and the adjacent subordinate regional power grid k m,n = 1, the regional power grid numbered n in level m solves the internal active and reactive power joint scheduling model, and judges m: (2.2.1)如果m＝1，则内部有功无功联合调度模型为：(2.2.1) If m=1, the internal active and reactive joint scheduling model is:
Figure FDA0003019886690000051
Figure FDA0003019886690000051
 s.t.Gm,n(xm,n,um,n,lm,n)≤0stG m,n (x m,n , um,n ,l m,n )≤0 求解该模型，得到最优解，将最优解记作
Figure FDA0003019886690000052
和
Figure FDA0003019886690000053
并将最优解处约束Gm,n(xm,n,um,n,lm,n)≤0的对偶乘子记作
Figure FDA0003019886690000054
Solve the model to get the optimal solution, and denote the optimal solution as
Figure FDA0003019886690000052
and
Figure FDA0003019886690000053
and denote the dual multiplier of constraint G m,n (x m,n , um,n ,l m,n )≤0 at the optimal solution as
Figure FDA0003019886690000054
 (2.2.2)如果m≠1，则内部有功无功联合调度模型为：(2.2.2) If m≠1, the internal active and reactive joint scheduling model is:
Figure FDA0003019886690000055
Figure FDA0003019886690000055
 s.t.Gm,n(xm,n,um,n,lm,n)≤0stG m,n (x m,n , um,n ,l m,n )≤0
Figure FDA0003019886690000056
Figure FDA0003019886690000056
 求解该模型，得到最优解，将该最优解记作
Figure FDA0003019886690000057
和
Figure FDA0003019886690000058
并将最优解处约束Gm,n(xm,n,um,n,lm,n)≤0的对偶乘子记作
Figure FDA0003019886690000059
Solve the model to get the optimal solution, and denote the optimal solution as
Figure FDA0003019886690000057
and
Figure FDA0003019886690000058
and denote the dual multiplier of constraint G m,n (x m,n , um,n ,l m,n )≤0 at the optimal solution as
Figure FDA0003019886690000059
 (2.3)对m进行判断：如果m≠M，取n为L(m,n)中的第一项，其中L(m,n)为层级m中编号为n的区域电网在层级电网m+1中所连接的区域电网的编号集合，取m等于m+1，返回到步骤(2.2)；如果m＝M，进行步骤(2.4)；(2.3) Judging m: if m≠M, take n as the first item in L(m,n), where L(m,n) is the regional power grid numbered n in level m in level power grid m+ The numbered set of the regional power grids connected in 1, take m equal to m+1, and return to step (2.2); if m=M, go to step (2.4); (2.4)计算层级m中编号为n的区域电网的最优割平面和近似投影函数，包括以下步骤：(2.4) Calculate the optimal cut plane and approximate projection function of the regional power grid numbered n in level m, including the following steps: (2.4.1)对m进行判断：(2.4.1) Judge m: 如果m＝M，则定义
Figure FDA0003019886690000061
为xm,n，定义
Figure FDA0003019886690000062
为fm,n(xm,n)，定义
Figure FDA0003019886690000063
为Gm,n(xm,n,um,n,lm,n)，定义
Figure FDA0003019886690000064
为
Figure FDA0003019886690000065
If m=M, then define
Figure FDA0003019886690000061
is x m,n , define
Figure FDA0003019886690000062
For f m,n (x m,n ), define
Figure FDA0003019886690000063
For G m,n (x m,n , um,n ,l m,n ), define
Figure FDA0003019886690000064
for
Figure FDA0003019886690000065
 如果m≠M，则定义
Figure FDA0003019886690000066
为
Figure FDA0003019886690000067
定义
Figure FDA0003019886690000068
为
Figure FDA0003019886690000069
定义
Figure FDA00030198866900000610
为
Figure FDA00030198866900000611
定义
Figure FDA00030198866900000612
为
Figure FDA00030198866900000613
If m≠M, then define
Figure FDA0003019886690000066
for
Figure FDA0003019886690000067
definition
Figure FDA0003019886690000068
for
Figure FDA0003019886690000069
definition
Figure FDA00030198866900000610
for
Figure FDA00030198866900000611
definition
Figure FDA00030198866900000612
for
Figure FDA00030198866900000613
 (2.4.2)根据步骤(2.4.1)，得到层级m中编号为n的区域电网的最优割平面
Figure FDA00030198866900000614
为：(2.4.2) According to step (2.4.1), obtain the optimal cut plane of the regional power grid numbered n in level m
Figure FDA00030198866900000614
for:
Figure FDA00030198866900000615
Figure FDA00030198866900000615
 近似投影函数
Figure FDA00030198866900000616
为：Approximate projection function
Figure FDA00030198866900000616
for:
Figure FDA00030198866900000617
Figure FDA00030198866900000617
 上式中，项
Figure FDA0003019886690000071
可通过下式计算：In the above formula, the term
Figure FDA0003019886690000071
It can be calculated by the following formula:
Figure FDA0003019886690000072
Figure FDA0003019886690000072
 上式中，diag()为对角矩阵构造函数；In the above formula, diag() is the diagonal matrix constructor; (2.5)对n进行判断：如果n不是L(m-1,U(m,n))中的最后一项，则取n为L(m-1,U(m,n))中n的下一项，返回步骤(2.2)；如果n是L(m-1,U(m,n))中的最后一项，取n为U(m,n)，m为m-1，进行步骤(2.6)；(2.5) Judge n: If n is not the last item in L(m-1, U(m, n)), then take n as the n in L(m-1, U(m, n)) Next item, go back to step (2.2); if n is the last item in L(m-1, U(m, n)), take n as U(m, n), m as m-1, go to step (2.6); (2.6)求解层级m中编号为n的区域电网内部考虑下级投影函数的有功无功联合调度模型，包括以下步骤：(2.6) Solving the joint active and reactive power scheduling model considering the lower-level projection function in the regional power grid numbered n in level m, including the following steps: 对m进行判断：To judge m: (2.6.1)如果m＝1，内部考虑下级投影函数的有功无功联合调度模型为：(2.6.1) If m=1, the active and reactive joint scheduling model considering the lower-level projection function internally is:
Figure FDA0003019886690000073
Figure FDA0003019886690000073
 s.t.Gm,n(xm,n,um,n,lm,n)≤0stG m,n (x m,n , um,n ,l m,n )≤0
Figure FDA0003019886690000074
Figure FDA0003019886690000074
Figure FDA0003019886690000075
Figure FDA0003019886690000075
 上式中，
Figure FDA0003019886690000076
为辅助变量，物理含义为层级m+1中编号为n*的区域电网的目标，将层级m中编号为n的电网的迭代次数km，n增加1，上式计算出的最优解记作
Figure FDA0003019886690000077
Figure FDA0003019886690000078
最优解处约束Gm,n(xm,n,um,n,lm,n)≤0的对偶乘子记作
Figure FDA0003019886690000079
约束
Figure FDA00030198866900000710
的对偶乘子记作
Figure FDA00030198866900000711
约束
Figure FDA00030198866900000712
的对偶乘子记作
Figure FDA00030198866900000713
In the above formula,
Figure FDA0003019886690000076
is an auxiliary variable, the physical meaning is the target of the regional power grid numbered n * in the level m+1, the iteration times k m of the power grid numbered n in the level m, n is increased by 1, and the optimal solution calculated by the above formula is recorded. do
Figure FDA0003019886690000077
Figure FDA0003019886690000078
The dual multiplier of constraint G m,n (x m,n , um,n ,l m,n )≤0 at the optimal solution is written as
Figure FDA0003019886690000079
constraint
Figure FDA00030198866900000710
The dual multiplier of
Figure FDA00030198866900000711
constraint
Figure FDA00030198866900000712
The dual multiplier of
Figure FDA00030198866900000713
 (2.6.2)如果m≠1，内部考虑下级投影函数的有功无功联合调度模型为：(2.6.2) If m≠1, the active and reactive joint scheduling model considering the lower projection function internally is:
Figure FDA0003019886690000081
Figure FDA0003019886690000081
 s.t.Gm,n(xm,n,um,n,lm,n)≤0stG m,n (x m,n , um,n ,l m,n )≤0
Figure FDA0003019886690000082
Figure FDA0003019886690000082
Figure FDA0003019886690000083
Figure FDA0003019886690000083
Figure FDA0003019886690000084
Figure FDA0003019886690000084
 上式中，
Figure FDA0003019886690000085
为辅助变量，物理含义为层级m+1中编号为n*的区域电网的目标，将层级m中编号为n的电网的迭代次数km,n增加1，上式计算出的最优解记作
Figure FDA0003019886690000086
Figure FDA0003019886690000087
与最优解处约束Gm,n(xm,n,um,n,lm,n)≤0的对偶乘子记作
Figure FDA0003019886690000088
约束
Figure FDA0003019886690000089
的对偶乘子记作
Figure FDA00030198866900000810
约束
Figure FDA00030198866900000811
的对偶乘子记作
Figure FDA00030198866900000812
In the above formula,
Figure FDA0003019886690000085
is an auxiliary variable, the physical meaning is the target of the regional power grid numbered n * in the level m+1, and the number of iterations k m, n of the power grid numbered n in the level m is increased by 1, and the optimal solution calculated by the above formula is recorded. do
Figure FDA0003019886690000086
Figure FDA0003019886690000087
The dual multiplier with the constraint G m,n (x m,n , um,n ,l m,n )≤0 at the optimal solution is written as
Figure FDA0003019886690000088
constraint
Figure FDA0003019886690000089
The dual multiplier of
Figure FDA00030198866900000810
constraint
Figure FDA00030198866900000811
The dual multiplier of
Figure FDA00030198866900000812
 (2.7)对层级m中编号为n的区域电网的计算进行收敛判断，设定收敛条件为
Figure FDA00030198866900000813
如果不满足收敛条件，则返回到步骤(2.3)；如果满足收敛条件，且m≠1，则返回步骤(2.4)；如果满足收敛条件，且m＝1，则进行步骤(3)；(2.7) Convergence judgment is made for the calculation of the regional power grid numbered n in level m, and the convergence condition is set as
Figure FDA00030198866900000813
If the convergence condition is not met, go back to step (2.3); if the convergence condition is met, and m≠1, then go back to step (2.4); if the convergence condition is met, and m=1, go to step (3); (3)根据步骤(2.2.2)、(2.6.1)和(2.6.2)中计算得到的最优解
Figure FDA00030198866900000814
中所包含的每台发电机的有功功率Pi G与无功功率Qi G，对多级电网进行调度，实现多级电网嵌套分解协调有功无功联合调度。(3) According to the optimal solution calculated in steps (2.2.2), (2.6.1) and (2.6.2)
Figure FDA00030198866900000814
The active power P i G and reactive power Q i G of each generator contained in the multi-level power grid are dispatched, and the multi-level power grid is nested, decomposed, coordinated, and dispatched together.
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