CN110880758B - Decomposition coordination optimal power flow control method for power transmission network and power distribution network in electric power system - Google Patents

Decomposition coordination optimal power flow control method for power transmission network and power distribution network in electric power system Download PDF

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CN110880758B
CN110880758B CN201911152448.4A CN201911152448A CN110880758B CN 110880758 B CN110880758 B CN 110880758B CN 201911152448 A CN201911152448 A CN 201911152448A CN 110880758 B CN110880758 B CN 110880758B
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吴文传
蔺晨晖
孙宏斌
郭庆来
王彬
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Tsinghua University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/008—Circuit arrangements for ac mains or ac distribution networks involving trading of energy or energy transmission rights

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Abstract

The invention relates to a decomposition coordination optimal power flow control method for a transmission network and a power distribution network in an electric power system, and belongs to the technical field of operation control of the electric power system. The method comprehensively considers the polar coordinate optimal power flow control model of the power transmission network and the branch optimal power flow control model of the power distribution network, and establishes the optimal power flow control model of the power transmission and distribution coordination by combining the boundary coupling relation between the power transmission network and the power distribution network. Aiming at the proposed optimal power flow control model which is embossed by adopting a convex relaxation technology, the invention provides an iterative solution algorithm between a power transmission network and a power distribution network in an electric power system, and realizes the decomposition coordination calculation of the optimal power flow control model with power transmission and distribution coordination. The algorithm involved in the method has good convergence rate, can reduce the overall total power generation cost of the power transmission network and the power distribution network, and eliminates the safety problems of power mismatch, voltage out-of-limit and the like of the transmission and distribution boundary.

Description

Decomposition coordination optimal power flow control method for power transmission network and power distribution network in electric power system
Technical Field
The invention relates to a decomposition coordination optimal power flow control method for a power transmission network and a power distribution network in an electric power system, and belongs to the technical field of operation control of the electric power system.
Background
With the access of a large amount of renewable energy sources to the power grid, the development trend of the power system is that the power transmission network is tightly coupled with the power distribution network. The traditional optimal power flow control of the transmission network and the distribution network is independently developed, and the defects of unnecessary power generation cost loss and safety problems of power mismatch, voltage out-of-limit and the like of a transmission and distribution boundary can be caused. Therefore, there is a need to coordinate transmission and distribution networks for joint optimal power flow control.
However, since the transmission network and the distribution network are independently controlled by different control centers, the problem of information privacy exists between the different control centers, which makes it difficult to optimize and control the transmission network and the distribution network in a centralized manner. Therefore, the transmission network and the distribution network are required to decompose the optimal power flow control and coordinate boundary information, and a technology capable of efficiently coordinating according to the mode is not available at present.
Disclosure of Invention
The invention aims to provide a decomposition coordination optimal power flow control method for a power transmission network and a power distribution network in an electric power system, which decomposes optimal power flow control of the power transmission network and optimal power flow control of the power distribution network into each power network for independent solution, and obtains a control method equivalent to a centralized optimal power flow through exchange iteration of boundary information between different power networks.
The invention provides a decomposition coordination optimal power flow control method of a power transmission network and a power distribution network in an electric power system, which comprises the following steps:
(1) setting that an electric power system comprises a power transmission network and a plurality of power distribution networks, and establishing an optimal power flow control model for cooperative control of the power transmission network and the power distribution networks, wherein the target function of the optimal power flow control model is that the total power generation cost of the power transmission network and the power distribution networks is minimum:
Figure BDA0002283913240000011
in the above formula, IGTFor the set of generator sets in the grid, the subscript T denotes the grid, aTi、bTi、cTiRespectively the generating cost quadratic term coefficient, the primary term coefficient and the constant term coefficient of the generating set i in the power transmission network, which are obtained by corresponding generating set specifications,
Figure BDA0002283913240000021
the active power generated by a generator set i in the power transmission network, the variable to be solved, ID of a power distribution network set,
Figure BDA0002283913240000022
for the set of generator sets in the distribution grid k, the subscript D indicates the distribution grid,
Figure BDA0002283913240000023
the secondary coefficient, the primary coefficient and the constant coefficient of the power generation cost of the generator set i in the power distribution network k are respectively obtained by corresponding generator set specifications,
Figure BDA0002283913240000024
the active power generated by a generator set i in a power distribution network k is a variable to be solved;
the constraint conditions of the optimal power flow control of the synergy of the transmission network and the distribution network comprise:
(1-1) optimal power flow control constraint conditions of the power transmission network, comprising:
(1-1-1) branch power flow constraint in the power transmission network:
Figure BDA0002283913240000025
Figure BDA0002283913240000026
Figure BDA0002283913240000027
Figure BDA0002283913240000028
wherein, PTijThe active power flowing from the node i to the node j in the power transmission network, and the variable to be solved, tauTijThe transformer transformation ratio of the branch ij in the power transmission network is obtained by a transformer specification,
Figure BDA0002283913240000029
the conductance of branch ij in the transmission network is obtained by a transmission network line parameter manual VTiIs the voltage amplitude of node i in the transmission network, is the variable to be solved, VTjIs the voltage amplitude of node j in the transmission network, is the variable to be solved, thetaTiIs the voltage phase angle of node i in the transmission network, is the variable to be solved, thetaTjIs the voltage phase angle of node j in the transmission network, is the variable to be solved, phiTijThe phase-shifting phase angle of the transformer of the branch ij in the power transmission network is obtained by the corresponding transformer specification,
Figure BDA00022839132400000210
the susceptance of a branch ij in the power transmission network is obtained by a line parameter manual, the ij is a branch number from a node i to a node j, and IL isTFor a set of branches of a transmission network, PTjiFor the active power of node j flowing to node i in the transmission network, for the variable to be solved, QTijThe reactive power flowing from node i to node j in the transmission network, as the variable to be solved,
Figure BDA0002283913240000031
the susceptance for charging branch ij in the transmission network is obtained by a transmission network line parameter manual, QTjiThe reactive power of a node j flowing to a node i in the power transmission network is a variable to be solved;
(1-1-2) node injection constraint in the power transmission network:
Figure BDA0002283913240000032
Figure BDA0002283913240000033
wherein, IGTiIs the set of generator sets connected to node i in the transmission network,
Figure BDA0002283913240000034
the active power generated by the generator set j in the power transmission network, the variable to be solved,
Figure BDA0002283913240000035
the active load of the node i in the power transmission network is obtained by a load prediction system in the power system,
Figure BDA0002283913240000036
for the parallel conductance of node i in the grid, obtained from the grid line parameter manual, IBTIs a set of nodes of the power transmission network,
Figure BDA0002283913240000037
the generated reactive power of the generator set j in the power transmission network, the variable to be solved,
Figure BDA0002283913240000038
the reactive load of the node i in the power transmission network is obtained by a load prediction system in the power system,
Figure BDA0002283913240000039
the parallel susceptance of the node i in the power transmission network is obtained by a power transmission network line parameter manual;
(1-1-3) voltage safety constraints in power transmission networks:
Figure BDA00022839132400000310
in the above formula, the first and second carbon atoms are, TiVthe lower bound of the voltage amplitude of the node i in the power transmission network is obtained by a power transmission network line parameter manual,
Figure BDA00022839132400000311
obtaining the upper bound of the voltage amplitude of a node i in the power transmission network by a power transmission network line parameter manual;
(1-1-4) generator generated power constraint in the power transmission network:
Figure BDA00022839132400000312
in the above formula, the first and second carbon atoms are,
Figure BDA00022839132400000313
the lower limit of the active power generated by the generator set i in the power transmission network is obtained by the specification of the corresponding generator set,
Figure BDA00022839132400000314
the upper limit of the generating active power of the generator set i in the power transmission network is obtained by the specification of the generator set,
Figure BDA00022839132400000315
the lower limit of the generated reactive power of the generator set i in the power transmission network is obtained by the specification of the corresponding generator set,
Figure BDA00022839132400000316
the generated reactive power of a generator set i in the power transmission network, the variable to be solved,
Figure BDA00022839132400000317
obtaining the upper limit of the generated reactive power of a generator set i in the power transmission network by a corresponding generator set specification;
(1-1-5) line capacity constraints in power transmission networks:
Figure BDA00022839132400000318
in the above formula, the first and second carbon atoms are,
Figure BDA0002283913240000041
obtaining the apparent power capacity of a branch circuit ij in the power transmission network by a circuit parameter manual;
(1-2) optimal power flow control constraint conditions of the power distribution network comprise:
(1-2-1) power distribution network branch flow restriction:
Figure BDA0002283913240000042
in the above formula, the first and second carbon atoms are,
Figure BDA0002283913240000043
the active power of the node i in the distribution network k flowing to the node j, the variable to be solved,
Figure BDA0002283913240000044
the reactive power of the node i in the distribution network k flowing to the node j is the variable to be solved,
Figure BDA0002283913240000045
the square of the voltage amplitude of the node i in the distribution network k, which is a variable to be solved,
Figure BDA0002283913240000046
the square of the current amplitude of the branch ij in the distribution network k is taken as a variable to be solved,
Figure BDA0002283913240000047
a k branch set of the power distribution network is formed;
(1-2-2) power distribution network node injection constraint:
Figure BDA0002283913240000048
Figure BDA0002283913240000049
in the above formula, the first and second carbon atoms are,
Figure BDA00022839132400000410
a set of generator sets connected for node i in distribution network k,
Figure BDA00022839132400000411
the active power generated by the generator set j in the power distribution network k is used as a variable to be solved,
Figure BDA00022839132400000412
the active power flowing from the node j to the node i in the distribution network k, the variable to be solved,
Figure BDA00022839132400000413
the square of the current amplitude of the branch ji in the distribution network k, which is a variable to be solved,
Figure BDA00022839132400000414
the resistance of the branch ji in the distribution network k is obtained by a distribution network line parameter manual,
Figure BDA00022839132400000415
the active load of the node i in the power distribution network k is obtained by a load forecasting system of the power system,
Figure BDA00022839132400000416
is a set of k nodes of the power distribution network,
Figure BDA00022839132400000417
the generated reactive power of the generator set j in the power distribution network k is the variable to be solved,
Figure BDA00022839132400000418
the reactive power of the node j in the distribution network k flowing to the node i is the variable to be solved,
Figure BDA00022839132400000419
the reactance of the branch ji in the distribution network k is obtained by a distribution network line parameter manual,
Figure BDA00022839132400000420
obtaining the reactive load of a node i in a power distribution network k by a load prediction system of a power system;
(1-2-3) power distribution network branch voltage drop constraint:
Figure BDA00022839132400000421
in the above formula, the first and second carbon atoms are,
Figure BDA00022839132400000422
the square of the voltage amplitude of the node j in the distribution network k is taken as a variable to be solved,
Figure BDA00022839132400000423
the resistance of the branch circuit ij in the distribution network k is obtained by a line parameter manual,
Figure BDA00022839132400000424
and obtaining the reactance of the branch ij in the power distribution network k by a line parameter manual.
(1-2-4) voltage safety constraint of a power distribution network:
Figure BDA0002283913240000051
in the above formula, the first and second carbon atoms are,
Figure BDA0002283913240000052
obtaining the lower bound of the voltage amplitude square of the node i in the power distribution network k by a power distribution network line parameter manual，
Figure BDA0002283913240000053
Obtaining the upper limit of the square of the voltage amplitude of a node i in a power distribution network k by a power distribution network line parameter manual;
(1-2-5) power generation power constraint of a power distribution network generator:
Figure BDA0002283913240000054
in the above formula, the first and second carbon atoms are,
Figure BDA0002283913240000055
the lower limit of the generating active power of the generator set i in the power distribution network k is obtained by the specification of the generator set,
Figure BDA0002283913240000056
the upper limit of the active power generated by the generator set i in the power distribution network k is obtained by the specification of the generator set,the lower limit of the generated reactive power of the generator set i in the power distribution network k is obtained by the specification of the generator set,
Figure BDA0002283913240000058
obtaining the generated reactive power upper bound of a generator set i in the power distribution network k by a generator set specification;
(1-2-6) power distribution network line capacity constraint:
Figure BDA0002283913240000059
in the above formula, the first and second carbon atoms are,
Figure BDA00022839132400000510
obtaining the current amplitude square upper limit of a branch ij in a power distribution network k by a power distribution network line parameter manual;
(1-3) constraint conditions for coupling transmission network and distribution network boundaries, including:
(1-3-1) boundary active power matching constraint of the transmission network and the distribution network:
Figure BDA00022839132400000511
in the above formula, the first and second carbon atoms are,
Figure BDA00022839132400000512
for the active power transmitted by the distribution network k to the transmission network, for the variables to be solved,
Figure BDA00022839132400000513
the active power transmitted to a power distribution network k by the power transmission network is a variable to be solved;
(1-3-2) boundary reactive power matching constraint of the transmission network and the distribution network:
Figure BDA00022839132400000514
in the above formula, the first and second carbon atoms are,
Figure BDA00022839132400000515
the reactive power transmitted from the distribution network k to the transmission network is the variable to be solved,
Figure BDA00022839132400000516
the reactive power transmitted to a power distribution network k by the power transmission network is a variable to be solved;
(1-3-3) limiting the boundary voltage amplitude matching of the transmission network and the distribution network:
Figure BDA00022839132400000517
in the above formula, the first and second carbon atoms are,
Figure BDA0002283913240000061
the voltage amplitude of the node in the transmission network, which is connected to the distribution network k, is the variable to be solved,
Figure BDA0002283913240000062
the square of the voltage amplitude of a node connected with the transmission network in the power distribution network k is used as a variable to be solved;
(2) performing convex relaxation treatment on the branch power flow constraint in the power distribution network in the step (1-2-1), and obtaining an expression of the branch power flow constraint in the power distribution network, wherein the expression is as follows:
Figure BDA0002283913240000063
(3) expressing the optimal power flow control model obtained in the step (1) and the step (2) after convex relaxation and used for cooperation of the power transmission network and the power distribution network in a standard abstract form, and obtaining the optimal power flow control model used for cooperation of the power transmission network and the power distribution network as follows:
Figure BDA0002283913240000064
in the above formula, xTColumn vectors consisting of variables for all grids, including PTij、QTij、
Figure BDA0002283913240000065
VTiAnd thetaTi，
Figure BDA0002283913240000066
A column vector consisting of variables for all distribution networks k, including
Figure BDA0002283913240000067
And
Figure BDA0002283913240000068
CT(xT) As a function of the total cost of power generation of the grid, i.e. the term in formula (1) in step (1)
Figure BDA0002283913240000069
Figure BDA00022839132400000610
As a function of the total cost of power generation of the distribution grid k, i.e. the term in equation (1) in step (1)
Figure BDA00022839132400000611
FT(xT) The constraint condition of the power transmission network is less than or equal to 0, and comprises the following steps (2) - (10) in the step (1-2),
Figure BDA00022839132400000612
is a constraint condition of the distribution network k, comprises the formulas (12) to (17) in the step (1-2),
Figure BDA00022839132400000613
boundary coupling constraint conditions of the power transmission network and the power distribution network k comprise the formulas (18) to (20) in the step (1-3);
(4) and (4) solving the optimal power flow control model established in the step (3) and in the abstract form and with convex relaxation, wherein the optimal power flow control model is in cooperation with the power transmission network and the power distribution network, and the concrete process is as follows:
(4-1) setting the initialization iteration number m of the power transmission network to be 1, and calculating the following optimal power flow control problem by the power transmission network:
Figure BDA00022839132400000614
calculating to obtain the optimal solution of (23), and processing the variable x at the optimal solutionTThe value of (A) is denoted as xT (m)Calculate Gk(xT (m)) And the result is recorded as gk (m)G is mixingk (m)To distribution network k, gk (m)The meaning of (a) is a parameter transmitted by the transmission network to the distribution network k when the iteration number m is reached;
(4-2) calculating the g obtained according to the step (4-1)k (m)The power distribution network k calculates the following optimal power flow control problem, and the specific steps are as follows:
(4-2-1) calculating an optimal power flow control problem for a given boundary of the power distribution network using the following equation:
Figure BDA0002283913240000071
in the above formula, betak、γkAs boundary relaxation auxiliary variable of distribution network k, as variable to be solved, kPENAs boundary relaxation penalty term, kPENIs 100, superscript T represents the transpose of the vector;
solving the above formula to obtain the optimal power flow control optimal solution of the power distribution network, and recording the optimal power flow control optimal solution as
Figure BDA0002283913240000072
βk (m)And gammak (m)Constraint at optimal solution
Figure BDA0002283913240000073
Has a Lagrange multiplier of λk (m)；
(4-2-2) calculating an optimal cost lower bound function of the distribution network k by using the following formula
Figure BDA0002283913240000074
Figure BDA0002283913240000075
Wherein, superscript T represents the transpose of the vector;
(4-2-3) calculating an approximate cost function of the distribution network k
Figure BDA0002283913240000076
The specific calculation steps are as follows:
expressing the optimal power flow control problem of the power distribution network in the step (1-2) in a standard quadratic programming mode:
Figure BDA0002283913240000077
in the above formula, the first and second carbon atoms are,
Figure BDA0002283913240000078
is formed by
Figure BDA0002283913240000079
βk、γkThe column vector of the component is composed of,
Figure BDA00022839132400000710
is a matrix of quadratic terms of the objective function in equation (24),
Figure BDA0002283913240000081
is the coefficient of the first order term of the objective function in equation (24),
Figure BDA0002283913240000082
for all linear equation constraints, including (12) - (14), (18) - (20),
Figure BDA0002283913240000083
including equations (15) - (17) for all linear inequality constraints,
Figure BDA0002283913240000084
is the overall second order cone constraint, equation (21);
the optimal solution of equation (26) is expressed as
Figure BDA0002283913240000085
Constraint on optimal solution
Figure BDA0002283913240000086
Is recorded as a lagrange multiplier
Figure BDA0002283913240000087
Constraining
Figure BDA0002283913240000088
Is recorded as a lagrange multiplier
Figure BDA0002283913240000089
Constraining
Figure BDA00022839132400000810
Is recorded as a lagrange multiplier
Figure BDA00022839132400000811
The parameter which is transmitted to a power distribution network k by the transmission network when the iteration number m is changed from gk (m)Becomes gk (m)+dgkThe corresponding optimal solution is multiplied by the Lagrange multiplier
Figure BDA00022839132400000812
Become into
Figure BDA00022839132400000813
Figure BDA00022839132400000814
Wherein dgk、
Figure BDA00022839132400000815
Is an assumed unknown variable in the following equation, written as follows:
Figure BDA00022839132400000816
Figure BDA00022839132400000817
Figure BDA00022839132400000818
Figure BDA00022839132400000819
solving the equation sets (27) - (30) by matrix division to obtain the final product
Figure BDA00022839132400000820
Satisfies the following conditions:
Figure BDA00022839132400000821
then the approximate cost function of the distribution network k
Figure BDA00022839132400000822
Comprises the following steps:
Figure BDA00022839132400000823
(4-2-4) lower bound function of optimal cost of step (4-2-2)
Figure BDA00022839132400000824
And the approximate cost function of step (4-2-3)
Figure BDA00022839132400000825
Transmitting to a power transmission network;
(4-3) traversing all power distribution networks in the power system, repeating the step (4-2), and obtaining the optimal cost lower bound function of all the power distribution networks by the power transmission network
Figure BDA00022839132400000826
And approximate cost function
Figure BDA00022839132400000827
(4-4) calculating the optimal power flow control problem considering the cost of each power distribution network by the power transmission network:
Figure BDA0002283913240000091
in the above formula, αkSolving the above formula for the optimal power generation cost of the power distribution network k to obtain the optimal power flow control optimal solution considering the cost of each power distribution network, and recording the optimal power flow control optimal solution as xT (m+1)；
Calculating the number of iterations byCost lower bound LB for global optimal power flow control of transmission network and multiple distribution networks in power system with time of several meters(m)：
Figure BDA0002283913240000092
Calculating the upper cost bound UB of the global optimal power flow control of the transmission network and the plurality of distribution networks in the power system when the iteration number m is calculated according to the following formula(m)：
Figure BDA0002283913240000093
For upper bound of cost UB(m)Make a judgment if UB(m)-LB(m)＜1×10-4Then x isT (m)And
Figure BDA0002283913240000094
as an optimal control strategy, corresponding to the control quantity of the transmission network and the distribution network k, if UB(m)-LB(m)≥1×10-4Then the number of iterations m is increased by 1 and G is addedk(xT (m)) Is recorded as gk (m)And transmitting gk (m) to the distribution network k, and returning to the step (4-2).
The optimal power flow control method for the decomposition and coordination of the power transmission network and the power distribution network in the power system has the advantages that:
the method comprehensively considers the polar coordinate optimal power flow control model of the power transmission network and the branch optimal power flow control model of the power distribution network, and establishes the optimal power flow control model of the power transmission and distribution coordination by combining the boundary coupling relation between the power transmission network and the power distribution network. Aiming at the proposed optimal power flow control model which is embossed by adopting a convex relaxation technology, the method provides an iterative solution algorithm between a power transmission network and a power distribution network in the power system, and realizes the decomposition coordination calculation of the optimal power flow control model with power transmission and distribution coordination. The invention relates to a decomposition and coordination control method of an optimal power flow control model. The method has good convergence rate, can reduce the overall total power generation cost of the transmission network and the distribution network, and eliminates the safety problems of power mismatch, voltage out-of-limit and the like of the transmission and distribution boundary. Therefore, the method can perform coordinated optimal power flow control on the transmission network and the distribution network, reduce the total power generation cost of the whole network, avoid the control safety risk, and meanwhile, the method has high coordination efficiency on the power system and is beneficial to practical application.
Detailed Description
The invention provides a decomposition coordination optimal power flow control method of a power transmission network and a power distribution network in an electric power system, which comprises the following steps:
(1) setting that an electric power system comprises a power transmission network and a plurality of power distribution networks, and establishing an optimal power flow control model for cooperative control of the power transmission network and the power distribution networks, wherein the target function of the optimal power flow control model is that the total power generation cost of the power transmission network and the power distribution networks is minimum:
Figure BDA0002283913240000101
in the above formula, IGTFor the set of generator sets in the grid, the subscript T denotes the grid, aTi、bTi、cTiRespectively the generating cost quadratic term coefficient, the primary term coefficient and the constant term coefficient of the generating set i in the power transmission network, which are obtained by corresponding generating set specifications,
Figure BDA0002283913240000102
the active power generated by a generator set i in the power transmission network, the variable to be solved, ID of a power distribution network set,
Figure BDA0002283913240000103
for the set of generator sets in the distribution grid k, the subscript D indicates the distribution grid,
Figure BDA0002283913240000104
the secondary coefficient, the primary coefficient and the constant coefficient of the power generation cost of the generator set i in the power distribution network k are respectively obtained by corresponding generator set specifications,
Figure BDA0002283913240000105
the active power generated by a generator set i in a power distribution network k is a variable to be solved;
the constraint conditions of the optimal power flow control of the synergy of the transmission network and the distribution network comprise: the method comprises the following steps of (1) carrying out optimal power flow control constraint conditions on a power transmission network, optimal power flow control constraint conditions on a power distribution network and boundary coupling constraint conditions of the power transmission network and the power distribution network;
(1-1) optimal power flow control constraint conditions of the power transmission network, comprising: the optimal power flow control constraint conditions of the power transmission network comprise branch power flow constraint, node injection constraint, voltage safety constraint, generator power generation constraint and line capacity constraint:
(1-1-1) branch power flow constraint in the power transmission network:
Figure BDA0002283913240000106
Figure BDA0002283913240000107
Figure BDA0002283913240000111
Figure BDA0002283913240000112
wherein, PTijThe active power flowing from the node i to the node j in the power transmission network, and the variable to be solved, tauTijThe transformer transformation ratio of the branch ij in the power transmission network is obtained by a transformer specification,
Figure BDA0002283913240000113
the conductance of branch ij in the transmission network is obtained by a transmission network line parameter manual VTiIs the voltage amplitude of node i in the transmission network, is the variable to be solved, VTjFor voltage amplitude at node j in the transmission networkValue, being a variable to be solved, thetaTiIs the voltage phase angle of node i in the transmission network, is the variable to be solved, thetaTjIs the voltage phase angle of node j in the transmission network, is the variable to be solved, phiTijThe phase-shifting phase angle of the transformer of the branch ij in the power transmission network is obtained by the corresponding transformer specification,
Figure BDA0002283913240000114
the susceptance of a branch ij in the power transmission network is obtained by a line parameter manual, the ij is a branch number from a node i to a node j, and IL isTFor a set of branches of a transmission network, PTjiFor the active power of node j flowing to node i in the transmission network, for the variable to be solved, QTijThe reactive power flowing from node i to node j in the transmission network, as the variable to be solved,
Figure BDA0002283913240000115
the susceptance for charging branch ij in the transmission network is obtained by a transmission network line parameter manual, QTjiThe reactive power of a node j flowing to a node i in the power transmission network is a variable to be solved;
(1-1-2) node injection constraint in the power transmission network:
Figure BDA0002283913240000116
Figure BDA0002283913240000117
wherein, IGTiIs the set of generator sets connected to node i in the transmission network,
Figure BDA0002283913240000118
the active power generated by the generator set j in the power transmission network, the variable to be solved,
Figure BDA0002283913240000119
the active load of the node i in the power transmission network is obtained by a load prediction system in the power system,
Figure BDA00022839132400001110
for the parallel conductance of node i in the grid, obtained from the grid line parameter manual, IBTIs a set of nodes of the power transmission network,
Figure BDA00022839132400001111
the generated reactive power of the generator set j in the power transmission network, the variable to be solved,
Figure BDA00022839132400001112
the reactive load of the node i in the power transmission network is obtained by a load prediction system in the power system,
Figure BDA00022839132400001113
the parallel susceptance of the node i in the power transmission network is obtained by a power transmission network line parameter manual;
(1-1-3) voltage safety constraints in power transmission networks:
Figure BDA0002283913240000121
in the above formula, the first and second carbon atoms are, TiVthe lower bound of the voltage amplitude of the node i in the power transmission network is obtained by a power transmission network line parameter manual,
Figure BDA0002283913240000122
obtaining the upper bound of the voltage amplitude of a node i in the power transmission network by a power transmission network line parameter manual;
(1-1-4) generator generated power constraint in the power transmission network:
Figure BDA0002283913240000123
in the above formula, the first and second carbon atoms are,
Figure BDA0002283913240000124
the lower limit of the active power generated by the generator set i in the power transmission network is obtained by the specification of the corresponding generator set,
Figure BDA0002283913240000125
the upper limit of the generating active power of the generator set i in the power transmission network is obtained by the specification of the generator set,
Figure BDA0002283913240000126
the lower limit of the generated reactive power of the generator set i in the power transmission network is obtained by the specification of the corresponding generator set,
Figure BDA0002283913240000127
the generated reactive power of a generator set i in the power transmission network, the variable to be solved,
Figure BDA0002283913240000128
obtaining the upper limit of the generated reactive power of a generator set i in the power transmission network by a corresponding generator set specification;
(1-1-5) line capacity constraints in power transmission networks:
Figure BDA0002283913240000129
in the above formula, the first and second carbon atoms are,
Figure BDA00022839132400001210
obtaining the apparent power capacity of a branch circuit ij in the power transmission network by a circuit parameter manual;
(1-2) optimal power flow control constraint conditions of the power distribution network: the optimal power flow control constraint conditions of the power distribution network comprise branch power flow constraint, node injection constraint, branch voltage drop constraint, voltage safety constraint, generator power generation constraint and line capacity constraint:
(1-2-1) power distribution network branch flow restriction:
Figure BDA00022839132400001211
in the above formula, the first and second carbon atoms are,
Figure BDA00022839132400001212
the active power of the node i in the distribution network k flowing to the node j, the variable to be solved,
Figure BDA00022839132400001213
the reactive power of the node i in the distribution network k flowing to the node j is the variable to be solved,
Figure BDA00022839132400001214
the square of the voltage amplitude of the node i in the distribution network k, which is a variable to be solved,
Figure BDA00022839132400001215
the square of the current amplitude of the branch ij in the distribution network k is taken as a variable to be solved,
Figure BDA00022839132400001216
a k branch set of the power distribution network is formed;
(1-2-2) power distribution network node injection constraint:
Figure BDA0002283913240000131
Figure BDA0002283913240000132
in the above formula, the first and second carbon atoms are,
Figure BDA0002283913240000133
a set of generator sets connected for node i in distribution network k,
Figure BDA0002283913240000134
the active power generated by the generator set j in the power distribution network k is used as a variable to be solved,
Figure BDA0002283913240000135
the active power flowing from the node j to the node i in the distribution network k, the variable to be solved,
Figure BDA0002283913240000136
the square of the current amplitude of the branch ji in the distribution network k, which is a variable to be solved,
Figure BDA0002283913240000137
the resistance of the branch ji in the distribution network k is obtained by a distribution network line parameter manual,
Figure BDA0002283913240000138
the active load of the node i in the power distribution network k is obtained by a load forecasting system of the power system,
Figure BDA0002283913240000139
is a set of k nodes of the power distribution network,
Figure BDA00022839132400001310
the generated reactive power of the generator set j in the power distribution network k is the variable to be solved,
Figure BDA00022839132400001311
the reactive power of the node j in the distribution network k flowing to the node i is the variable to be solved,
Figure BDA00022839132400001312
the reactance of the branch ji in the distribution network k is obtained by a distribution network line parameter manual,
Figure BDA00022839132400001313
obtaining the reactive load of a node i in a power distribution network k by a load prediction system of a power system;
(1-2-3) power distribution network branch voltage drop constraint:
Figure BDA00022839132400001314
in the above formula, the first and second carbon atoms are,
Figure BDA00022839132400001315
is the square of the voltage amplitude of node j in distribution network k, isThe variables to be solved are then calculated,
Figure BDA00022839132400001316
the resistance of the branch circuit ij in the distribution network k is obtained by a line parameter manual,
Figure BDA00022839132400001317
and obtaining the reactance of the branch ij in the power distribution network k by a line parameter manual.
(1-2-4) voltage safety constraint of a power distribution network:
Figure BDA00022839132400001318
in the above formula, the first and second carbon atoms are,
Figure BDA00022839132400001319
the lower limit of the voltage amplitude square of the node i in the power distribution network k is obtained by a power distribution network line parameter manual,
Figure BDA00022839132400001320
obtaining the upper limit of the square of the voltage amplitude of a node i in a power distribution network k by a power distribution network line parameter manual;
(1-2-5) power generation power constraint of a power distribution network generator:
Figure BDA00022839132400001321
in the above formula, the first and second carbon atoms are,
Figure BDA00022839132400001322
the lower limit of the generating active power of the generator set i in the power distribution network k is obtained by the specification of the generator set,
Figure BDA00022839132400001323
the upper limit of the active power generated by the generator set i in the power distribution network k is obtained by the specification of the generator set,
Figure BDA00022839132400001324
the lower limit of the generated reactive power of the generator set i in the power distribution network k is obtained by the specification of the generator set,
Figure BDA0002283913240000141
obtaining the generated reactive power upper bound of a generator set i in the power distribution network k by a generator set specification;
(1-2-6) power distribution network line capacity constraint:
Figure BDA0002283913240000142
in the above formula, the first and second carbon atoms are,
Figure BDA0002283913240000143
obtaining the current amplitude square upper limit of a branch ij in a power distribution network k by a power distribution network line parameter manual;
(1-3) constraint conditions of boundary coupling of the transmission network and the distribution network:
the voltage amplitude and power needs to match each other at the boundary between the transmission network, where the distribution network is equivalent to a negative generator, and the distribution network, where the transmission network is equivalent to a positive generator. The boundary constraint conditions comprise active power matching, reactive power matching and voltage amplitude matching.
(1-3-1) boundary active power matching constraint of the transmission network and the distribution network:
Figure BDA0002283913240000144
in the above formula, the first and second carbon atoms are,
Figure BDA0002283913240000145
for the active power transmitted by the distribution network k to the transmission network, for the variables to be solved,
Figure BDA0002283913240000146
the active power transmitted to a power distribution network k by the power transmission network is a variable to be solved;
(1-3-2) boundary reactive power matching constraint of the transmission network and the distribution network:
Figure BDA0002283913240000147
in the above formula, the first and second carbon atoms are,
Figure BDA0002283913240000148
the reactive power transmitted from the distribution network k to the transmission network is the variable to be solved,
Figure BDA0002283913240000149
the reactive power transmitted to a power distribution network k by the power transmission network is a variable to be solved;
(1-3-3) limiting the boundary voltage amplitude matching of the transmission network and the distribution network:
Figure BDA00022839132400001410
in the above formula, the first and second carbon atoms are,
Figure BDA00022839132400001411
the voltage amplitude of the node in the transmission network, which is connected to the distribution network k, is the variable to be solved,
Figure BDA00022839132400001412
the square of the voltage amplitude of a node connected with the transmission network in the power distribution network k is used as a variable to be solved;
(2) performing convex relaxation treatment on the branch power flow constraint in the power distribution network in the step (1-2-1), and obtaining an expression of the branch power flow constraint in the power distribution network, wherein the expression is as follows:
Figure BDA00022839132400001413
(3) expressing the optimal power flow control model obtained in the step (1) and the step (2) after convex relaxation and used for cooperation of the power transmission network and the power distribution network in a standard abstract form, and obtaining the optimal power flow control model used for cooperation of the power transmission network and the power distribution network as follows:
Figure BDA0002283913240000151
in the above formula, xTColumn vectors consisting of variables for all grids, including PTij、QTij、
Figure BDA0002283913240000152
VTiAnd thetaTi，
Figure BDA0002283913240000153
A column vector consisting of variables for all distribution networks k, including
Figure BDA0002283913240000154
And
Figure BDA0002283913240000155
CT(xT) As a function of the total cost of power generation of the grid, i.e. the term in formula (1) in step (1)
Figure BDA0002283913240000156
Figure BDA0002283913240000157
As a function of the total cost of power generation of the distribution grid k, i.e. the term in equation (1) in step (1)
Figure BDA0002283913240000158
FT(xT) The constraint condition of the power transmission network is less than or equal to 0, and comprises the following steps (2) - (10) in the step (1-2),
Figure BDA0002283913240000159
is a constraint condition of the distribution network k, comprises the formulas (12) to (17) in the step (1-2),
Figure BDA00022839132400001510
the boundary coupling constraint condition of the transmission network and the distribution network k comprises the formulas (18) - (2) in the step (1-3)0)；
(4) And (4) solving the optimal power flow control model established in the step (3) and in the abstract form and with convex relaxation, wherein the optimal power flow control model is in cooperation with the power transmission network and the power distribution network, and the concrete process is as follows:
(4-1) setting the initialization iteration number m of the power transmission network to be 1, and calculating the following optimal power flow control problem by the power transmission network:
Figure BDA00022839132400001511
calculating to obtain the optimal solution of (23), and processing the variable x at the optimal solutionTThe value of (A) is denoted as xT (m)Calculate Gk(xT (m)) And the result is recorded as gk (m)G is mixingk (m)To distribution network k, gk (m)The meaning of (a) is a parameter transmitted by the transmission network to the distribution network k when the iteration number m is reached;
(4-2) calculating the g obtained according to the step (4-1)k (m)The power distribution network k calculates the following optimal power flow control problem, and the specific steps are as follows:
(4-2-1) calculating an optimal power flow control problem for a given boundary of the power distribution network using the following equation:
Figure BDA0002283913240000161
in the above formula, betak、γkAs boundary relaxation auxiliary variable of distribution network k, as variable to be solved, kPENAs boundary relaxation penalty term, kPENIs 100, superscript T represents the transpose of the vector;
solving the above formula to obtain the optimal power flow control optimal solution of the power distribution network, and recording the optimal power flow control optimal solution as
Figure BDA0002283913240000162
βk (m)And gammak (m)Constraint at optimal solution
Figure BDA0002283913240000163
Has a Lagrange multiplier of λk (m)；
(4-2-2) calculating an optimal cost lower bound function of the distribution network k by using the following formula
Figure BDA0002283913240000164
Figure BDA0002283913240000165
Wherein, superscript T represents the transpose of the vector;
(4-2-3) calculating an approximate cost function of the distribution network k
Figure BDA0002283913240000166
The specific calculation steps are as follows:
expressing the optimal power flow control problem of the power distribution network in the step (1-2) in a standard quadratic programming mode:
Figure BDA0002283913240000167
in the above formula, the first and second carbon atoms are,
Figure BDA0002283913240000168
is formed by
Figure BDA0002283913240000169
βk、γkThe column vector of the component is composed of,
Figure BDA00022839132400001610
is a matrix of quadratic terms of the objective function in equation (24),
Figure BDA00022839132400001611
is the coefficient of the first order term of the objective function in equation (24),
Figure BDA00022839132400001612
for the purpose of the constraint of the overall linear equation,including (12) - (14), (18) - (20),
Figure BDA00022839132400001613
including equations (15) - (17) for all linear inequality constraints,
Figure BDA00022839132400001614
is the overall second order cone constraint, equation (21);
the optimal solution of equation (26) is expressed as
Figure BDA00022839132400001615
Constraint on optimal solution
Figure BDA00022839132400001616
Is recorded as a lagrange multiplier
Figure BDA00022839132400001617
Constraining
Figure BDA00022839132400001618
Is recorded as a lagrange multiplier
Figure BDA00022839132400001619
Constraining
Figure BDA00022839132400001620
Is recorded as a lagrange multiplier
Figure BDA0002283913240000171
The parameter which is transmitted to a power distribution network k by the transmission network when the iteration number m is changed from gk (m)Becomes gk (m)+dgkThe corresponding optimal solution is multiplied by the Lagrange multiplier
Figure BDA0002283913240000172
Become into
Figure BDA0002283913240000173
Figure BDA0002283913240000174
Wherein dgk、
Figure BDA0002283913240000175
Is an assumed unknown variable in the following equation, written as follows:
Figure BDA0002283913240000176
Figure BDA0002283913240000177
Figure BDA0002283913240000178
Figure BDA0002283913240000179
solving the equation sets (27) - (30) by matrix division to obtain the final product
Figure BDA00022839132400001710
Satisfies the following conditions:
Figure BDA00022839132400001711
then the approximate cost function of the distribution network k
Figure BDA00022839132400001712
Comprises the following steps:
Figure BDA00022839132400001713
(4-2-4) lower bound function of optimal cost of step (4-2-2)
Figure BDA00022839132400001714
And the approximate cost function of step (4-2-3)
Figure BDA00022839132400001715
Transmitting to a power transmission network;
(4-3) traversing all power distribution networks in the power system, repeating the step (4-2), and obtaining the optimal cost lower bound function of all the power distribution networks by the power transmission network
Figure BDA00022839132400001716
And approximate cost function
Figure BDA00022839132400001717
(4-4) calculating the optimal power flow control problem considering the cost of each power distribution network by the power transmission network:
Figure BDA00022839132400001718
in the above formula, αkSolving the above formula for the optimal power generation cost of the power distribution network k to obtain the optimal power flow control optimal solution considering the cost of each power distribution network, and recording the optimal power flow control optimal solution as xT (m+1)；
Calculating a lower cost bound LB of global optimal power flow control of a transmission network and a plurality of distribution networks in the power system when the iteration number m is calculated according to the following formula(m)：
Figure BDA0002283913240000181
Calculating the upper cost bound UB of the global optimal power flow control of the transmission network and the plurality of distribution networks in the power system when the iteration number m is calculated according to the following formula(m)：
Figure BDA0002283913240000182
For upper bound of cost UB(m)Make a judgment if UB(m)-LB(m)＜1×10-4Then x isT (m)And
Figure BDA0002283913240000183
as an optimal control strategy, corresponding to the control quantity of the transmission network and the distribution network k, if UB(m)-LB(m)≥1×10-4Then the number of iterations m is increased by 1 and G is addedk(xT (m)) Is recorded as gk (m)G is mixingk (m)And (5) transmitting to the distribution network k, and returning to the step (4-2).

Claims (1)

1. A decomposition coordination optimal power flow control method for a transmission network and a distribution network in an electric power system is characterized by comprising the following steps:
(1) setting that an electric power system comprises a power transmission network and a plurality of power distribution networks, and establishing an optimal power flow control model for cooperative control of the power transmission network and the power distribution networks, wherein the target function of the optimal power flow control model is that the total power generation cost of the power transmission network and the power distribution networks is minimum:
Figure FDA0002781726630000011
in the above formula, IGTFor the set of generator sets in the grid, the subscript T denotes the grid, aTi、bTi、cTiRespectively the generating cost quadratic term coefficient, the primary term coefficient and the constant term coefficient of the generating set i in the power transmission network, which are obtained by corresponding generating set specifications,
Figure FDA0002781726630000012
the active power generated by a generator set i in the power transmission network, the variable to be solved, ID of a power distribution network set,
Figure FDA0002781726630000013
for the set of generator sets in the distribution grid k, the subscript D indicates the distribution grid,
Figure FDA0002781726630000014
the secondary coefficient, the primary coefficient and the constant coefficient of the power generation cost of the generator set i in the power distribution network k are respectively obtained by corresponding generator set specifications,
Figure FDA0002781726630000015
the generated active power of a generator set i in the power distribution network k is a variable to be solved;
the constraint conditions of the optimal power flow control of the synergy of the transmission network and the distribution network comprise:
(1-1) optimal power flow control constraint conditions of the power transmission network, comprising:
(1-1-1) branch power flow constraint in the power transmission network:
Figure FDA0002781726630000016
Figure FDA0002781726630000017
Figure FDA0002781726630000018
Figure FDA0002781726630000021
wherein, PTijThe active power flowing from the node i to the node j in the power transmission network, and the variable to be solved, tauTijThe transformer transformation ratio of the branch ij in the power transmission network is obtained by a transformer specification,
Figure FDA0002781726630000022
the conductance of branch ij in the transmission network is obtained by a transmission network line parameter manual VTiIs the voltage amplitude of node i in the transmission network, is the variable to be solved, VTjIs the voltage amplitude of node j in the transmission network, is the variable to be solved, thetaTiIs the voltage phase angle of node i in the transmission network, is the variable to be solved, thetaTjIs the voltage phase angle of node j in the transmission network, is the variable to be solved, phiTijThe phase-shifting phase angle of the transformer of the branch ij in the power transmission network is obtained by the corresponding transformer specification,
Figure FDA0002781726630000023
the susceptance of a branch ij in the power transmission network is obtained by a line parameter manual, the ij is a branch number from a node i to a node j, and IL isTFor a set of branches of a transmission network, PTjiFor the active power of node j flowing to node i in the transmission network, for the variable to be solved, QTijThe reactive power flowing from node i to node j in the transmission network, as the variable to be solved,
Figure FDA0002781726630000024
the susceptance for charging branch ij in the transmission network is obtained by a transmission network line parameter manual, QTjiThe reactive power of a node j flowing to a node i in the power transmission network is a variable to be solved;
(1-1-2) node injection constraint in the power transmission network:
Figure FDA0002781726630000025
Figure FDA0002781726630000026
wherein, IGTiIs the set of generator sets connected to node i in the transmission network,
Figure FDA0002781726630000027
the active power generated by the generator set j in the power transmission network, the variable to be solved,the active load of the node i in the power transmission network is obtained by a load prediction system in the power system,
Figure FDA0002781726630000029
for the parallel conductance of node i in the grid, obtained from the grid line parameter manual, IBTIs a set of nodes of the power transmission network,
Figure FDA00027817266300000210
the generated reactive power of the generator set j in the power transmission network, the variable to be solved,
Figure FDA00027817266300000211
the reactive load of the node i in the power transmission network is obtained by a load prediction system in the power system,
Figure FDA00027817266300000212
the parallel susceptance of the node i in the power transmission network is obtained by a power transmission network line parameter manual;
(1-1-3) voltage safety constraints in power transmission networks:
Figure FDA00027817266300000213
in the above formula, the first and second carbon atoms are, TiVthe lower bound of the voltage amplitude of the node i in the power transmission network is obtained by a power transmission network line parameter manual,
Figure FDA0002781726630000031
obtaining the upper bound of the voltage amplitude of a node i in the power transmission network by a power transmission network line parameter manual;
(1-1-4) generator generated power constraint in the power transmission network:
Figure FDA0002781726630000032
in the above formula, the first and second carbon atoms are,
Figure FDA0002781726630000033
the lower limit of the active power generated by the generator set i in the power transmission network is obtained by the specification of the corresponding generator set,
Figure FDA0002781726630000034
the upper limit of the generating active power of the generator set i in the power transmission network is obtained by the specification of the generator set,
Figure FDA0002781726630000035
the lower limit of the generated reactive power of the generator set i in the power transmission network is obtained by the specification of the corresponding generator set,
Figure FDA0002781726630000036
the generated reactive power of a generator set i in the power transmission network, the variable to be solved,
Figure FDA0002781726630000037
obtaining the upper limit of the generated reactive power of a generator set i in the power transmission network by a corresponding generator set specification;
(1-1-5) line capacity constraints in power transmission networks:
Figure FDA0002781726630000038
in the above formula, the first and second carbon atoms are,
Figure FDA0002781726630000039
obtaining the apparent power capacity of a branch circuit ij in the power transmission network by a circuit parameter manual;
(1-2) optimal power flow control constraint conditions of the power distribution network comprise:
(1-2-1) power distribution network branch flow restriction:
Figure FDA00027817266300000310
in the above formula, the first and second carbon atoms are,
Figure FDA00027817266300000311
the active power of the node i in the distribution network k flowing to the node j, the variable to be solved,
Figure FDA00027817266300000312
the reactive power of the node i in the distribution network k flowing to the node j is the variable to be solved,
Figure FDA00027817266300000313
the square of the voltage amplitude of the node i in the distribution network k, which is a variable to be solved,
Figure FDA00027817266300000314
the square of the current amplitude of the branch ij in the distribution network k is taken as a variable to be solved,
Figure FDA00027817266300000315
a k branch set of the power distribution network is formed;
(1-2-2) power distribution network node injection constraint:
Figure FDA00027817266300000316
Figure FDA00027817266300000317
in the above formula, the first and second carbon atoms are,
Figure FDA00027817266300000318
a set of generator sets connected for node i in distribution network k,
Figure FDA00027817266300000319
the active power generated by the generator set j in the power distribution network k is used as a variable to be solved,
Figure FDA00027817266300000320
the active power flowing from the node j to the node i in the distribution network k, the variable to be solved,
Figure FDA0002781726630000041
the square of the current amplitude of the branch ji in the distribution network k, which is a variable to be solved,
Figure FDA0002781726630000042
the resistance of the branch ji in the distribution network k is obtained by a distribution network line parameter manual,
Figure FDA0002781726630000043
the active load of the node i in the power distribution network k is obtained by a load forecasting system of the power system,
Figure FDA0002781726630000044
is a set of k nodes of the power distribution network,
Figure FDA0002781726630000045
the generated reactive power of the generator set j in the power distribution network k is the variable to be solved,
Figure FDA0002781726630000046
the reactive power of the node j in the distribution network k flowing to the node i is the variable to be solved,
Figure FDA0002781726630000047
the reactance of the branch ji in the distribution network k is obtained by a distribution network line parameter manual,
Figure FDA0002781726630000048
obtaining the reactive load of a node i in a power distribution network k by a load prediction system of a power system;
(1-2-3) power distribution network branch voltage drop constraint:
Figure FDA0002781726630000049
in the above formula, the first and second carbon atoms are,
Figure FDA00027817266300000410
the square of the voltage amplitude of the node j in the distribution network k is taken as a variable to be solved,
Figure FDA00027817266300000411
the resistance of the branch circuit ij in the distribution network k is obtained by a line parameter manual,
Figure FDA00027817266300000412
obtaining the reactance of a branch ij in a power distribution network k by a line parameter manual;
(1-2-4) voltage safety constraint of a power distribution network:
Figure FDA00027817266300000413
in the above formula, the first and second carbon atoms are,
Figure FDA00027817266300000414
the lower limit of the voltage amplitude square of the node i in the power distribution network k is obtained by a power distribution network line parameter manual,
Figure FDA00027817266300000415
obtaining the upper limit of the square of the voltage amplitude of a node i in a power distribution network k by a power distribution network line parameter manual;
(1-2-5) power generation power constraint of a power distribution network generator:
Figure FDA00027817266300000416
in the above formula, the first and second carbon atoms are,
Figure FDA00027817266300000417
the lower limit of the generating active power of the generator set i in the power distribution network k is obtained by the specification of the generator set,
Figure FDA00027817266300000418
the upper limit of the active power generated by the generator set i in the power distribution network k is obtained by the specification of the generator set,
Figure FDA00027817266300000419
the lower limit of the generated reactive power of the generator set i in the power distribution network k is obtained by the specification of the generator set,
Figure FDA00027817266300000420
obtaining the generated reactive power upper bound of a generator set i in the power distribution network k by a generator set specification;
(1-2-6) power distribution network line capacity constraint:
Figure FDA00027817266300000421
in the above formula, the first and second carbon atoms are,
Figure FDA00027817266300000422
obtaining the current amplitude square upper limit of a branch ij in a power distribution network k by a power distribution network line parameter manual;
(1-3) constraint conditions for coupling transmission network and distribution network boundaries, including:
(1-3-1) boundary active power matching constraint of the transmission network and the distribution network:
Figure FDA0002781726630000051
in the above formula, the first and second carbon atoms are,
Figure FDA0002781726630000052
for k-direction transmission to transmission network of distribution networkThe output active power is a variable to be solved,
Figure FDA0002781726630000053
the active power transmitted to a power distribution network k by the power transmission network is a variable to be solved;
(1-3-2) boundary reactive power matching constraint of the transmission network and the distribution network:
Figure FDA0002781726630000054
in the above formula, the first and second carbon atoms are,
Figure FDA0002781726630000055
the reactive power transmitted from the distribution network k to the transmission network is the variable to be solved,
Figure FDA0002781726630000056
the reactive power transmitted to a power distribution network k by the power transmission network is a variable to be solved;
(1-3-3) limiting the boundary voltage amplitude matching of the transmission network and the distribution network:
Figure FDA0002781726630000057
in the above formula, the first and second carbon atoms are,
Figure FDA0002781726630000058
the voltage amplitude of the node in the transmission network, which is connected to the distribution network k, is the variable to be solved,
Figure FDA0002781726630000059
the square of the voltage amplitude of a node connected with the transmission network in the power distribution network k is used as a variable to be solved;
(2) performing convex relaxation treatment on the branch power flow constraint in the power distribution network in the step (1-2-1), and obtaining an expression of the branch power flow constraint in the power distribution network, wherein the expression is as follows:
Figure FDA00027817266300000510
(3) expressing the optimal power flow control model obtained in the step (1) and the step (2) after convex relaxation and used for cooperation of the power transmission network and the power distribution network in a standard abstract form, and obtaining the optimal power flow control model used for cooperation of the power transmission network and the power distribution network as follows:
Figure FDA00027817266300000511
in the above formula, xTColumn vectors consisting of variables for all grids, including PTij、QTij、
Figure FDA00027817266300000512
VTiAnd thetaTi，
Figure FDA00027817266300000513
A column vector consisting of variables for all distribution networks k, including
Figure FDA00027817266300000514
And
Figure FDA00027817266300000515
CT(xT) As a function of the total cost of power generation of the grid, i.e. the term in formula (1) in step (1)
Figure FDA00027817266300000516
As a function of the total cost of power generation of the distribution grid k, i.e. the term in equation (1) in step (1)
Figure FDA00027817266300000517
FT(xT) The constraint condition of the power transmission network is less than or equal to 0, and comprises the following steps (2) - (10) in the step (1-1),
Figure FDA0002781726630000061
is a constraint condition of the distribution network k, comprises the formulas (11) to (17) in the step (1-2),
Figure FDA0002781726630000062
boundary coupling constraint conditions of the power transmission network and the power distribution network k comprise the formulas (18) to (20) in the step (1-3);
(4) and (4) solving the optimal power flow control model established in the step (3) and in the abstract form and with convex relaxation, wherein the optimal power flow control model is in cooperation with the power transmission network and the power distribution network, and the concrete process is as follows:
(4-1) setting the initialization iteration number m of the power transmission network to be 1, and calculating the following optimal power flow control problem by the power transmission network:
Figure FDA0002781726630000063
calculating to obtain the optimal solution of (23), and processing the variable x at the optimal solutionTThe value of (A) is denoted as xT (m)Calculate Gk(xT (m)) And the result is recorded as gk (m)G is mixingk (m)To distribution network k, gk (m)The meaning of (a) is a parameter transmitted by the transmission network to the distribution network k when the iteration number m is reached;
(4-2) calculating the g obtained according to the step (4-1)k (m)The power distribution network k calculates the following optimal power flow control problem, and the specific steps are as follows:
(4-2-1) calculating an optimal power flow control problem for a given boundary of the power distribution network using the following equation:
Figure FDA0002781726630000064
in the above formula, betak、γkAs boundary relaxation auxiliary variable of distribution network k, as variable to be solved, kPENAs boundary relaxation penalty term, kPENIs 100, superscript T represents the transpose of the vector;
solving the above formula to obtain the optimal power flow control optimal solution of the power distribution network, and recording the optimal power flow control optimal solution as
Figure FDA0002781726630000065
βk (m)And gammak (m)Constraint at optimal solution
Figure FDA0002781726630000066
Has a Lagrange multiplier of λk (m)；
(4-2-2) calculating an optimal cost lower bound function of the distribution network k by using the following formula
Figure FDA0002781726630000067
Figure FDA0002781726630000071
Wherein, superscript T represents the transpose of the vector;
(4-2-3) calculating an approximate cost function of the distribution network k
Figure FDA0002781726630000072
The specific calculation steps are as follows:
expressing the optimal power flow control problem of the power distribution network in the step (1-2) in a standard quadratic programming mode:
Figure FDA0002781726630000073
in the above formula, the first and second carbon atoms are,
Figure FDA0002781726630000074
is formed by
Figure FDA0002781726630000075
βk、γkThe column vector of the component is composed of,
Figure FDA0002781726630000076
is a matrix of quadratic terms of the objective function in equation (24),
Figure FDA0002781726630000077
is the coefficient of the first order term of the objective function in equation (24),
Figure FDA0002781726630000078
for all linear equation constraints, including (12) - (14), (18) - (20),
Figure FDA0002781726630000079
including equations (15) - (17) for all linear inequality constraints,
Figure FDA00027817266300000710
is the overall second order cone constraint, equation (21);
the optimal solution of equation (26) is expressed as
Figure FDA00027817266300000711
Constraint on optimal solution
Figure FDA00027817266300000712
Is recorded as a lagrange multiplier
Figure FDA00027817266300000713
Constraining
Figure FDA00027817266300000714
Is recorded as a lagrange multiplier
Figure FDA00027817266300000715
Constraining
Figure FDA00027817266300000716
Is recorded as a lagrange multiplier
Figure FDA00027817266300000717
The parameter which is transmitted to a power distribution network k by the transmission network when the iteration number m is changed from gk (m)Becomes gk (m)+dgkThe corresponding optimal solution is multiplied by the Lagrange multiplier
Figure FDA00027817266300000718
Become into
Figure FDA00027817266300000719
Figure FDA00027817266300000720
Wherein dgk、
Figure FDA00027817266300000721
Is an assumed unknown variable in the following equation, written as follows:
Figure FDA00027817266300000722
Figure FDA00027817266300000723
Figure FDA00027817266300000724
Figure FDA0002781726630000081
solving the equation sets (27) - (30) by matrix division to obtain the final product
Figure FDA0002781726630000082
Satisfy the requirement of：
Figure FDA0002781726630000083
Then the approximate cost function of the distribution network k
Figure FDA0002781726630000084
Comprises the following steps:
Figure FDA0002781726630000085
(4-2-4) lower bound function of optimal cost of step (4-2-2)
Figure FDA0002781726630000086
And the approximate cost function of step (4-2-3)
Figure FDA0002781726630000087
Transmitting to a power transmission network;
(4-3) traversing all power distribution networks in the power system, repeating the step (4-2), and obtaining the optimal cost lower bound function of all the power distribution networks by the power transmission network
Figure FDA0002781726630000088
And approximate cost function
Figure FDA0002781726630000089
(4-4) calculating the optimal power flow control problem considering the cost of each power distribution network by the power transmission network:
Figure FDA00027817266300000810
in the above formula, αkSolving the above formula for the optimal power generation cost of the power distribution network k to obtain the optimal power flow control optimal solution considering the cost of each power distribution network, and recording the optimal power flow control optimal solution as xT (m+1)；
Calculating a lower cost bound LB of global optimal power flow control of a transmission network and a plurality of distribution networks in the power system when the iteration number m is calculated according to the following formula(m)：
Figure FDA00027817266300000811
Calculating the upper cost bound UB of the global optimal power flow control of the transmission network and the plurality of distribution networks in the power system when the iteration number m is calculated according to the following formula(m)：
Figure FDA0002781726630000091
For upper bound of cost UB(m)Make a judgment if UB(m)-LB(m)＜1×10-4Then x isT (m)And
Figure FDA0002781726630000092
as an optimal control strategy, corresponding to the control quantity of the transmission network and the distribution network k, if UB(m)-LB(m)≥1×10-4Then the number of iterations m is increased by 1 and G is addedk(xT (m)) Is recorded as gk (m)G is mixingk (m)And (5) transmitting to the distribution network k, and returning to the step (4-2).
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