CN111969609B - Second-order cone optimal power flow model construction method and device for alternating current-direct current power transmission network - Google Patents

Second-order cone optimal power flow model construction method and device for alternating current-direct current power transmission network Download PDF

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CN111969609B
CN111969609B CN202010638395.3A CN202010638395A CN111969609B CN 111969609 B CN111969609 B CN 111969609B CN 202010638395 A CN202010638395 A CN 202010638395A CN 111969609 B CN111969609 B CN 111969609B
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power flow
node
constraint
line
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CN111969609A (en
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翟鹤峰
赵利刚
王长香
周挺辉
甄鸿越
黄冠标
吴小珊
徐原
戴仲覆
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CSG Electric Power Research Institute
China Southern Power Grid Co Ltd
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China Southern Power Grid Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/12—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load
    • H02J3/16—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load by adjustment of reactive power
    • 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
    • H02J3/36—Arrangements for transfer of electric power between ac networks via a high-tension dc link
    • 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
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/30—Reactive power compensation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/60—Arrangements for transfer of electric power between AC networks or generators via a high voltage DC link [HVCD]

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Abstract

The invention discloses a second-order cone optimal power flow model construction method of an alternating current-direct current power transmission network, which comprises the following steps: constructing an optimal power flow model of the alternating current-direct current transmission network considering reactive voltage according to an equivalent model of a voltage source converter-containing type high-voltage direct current transmission system; simplifying a power flow equation of line transmission capacity constraint and power balance constraint in the optimal power flow model by adopting a first-order Taylor series expansion under a flat start method; and (3) performing relaxation treatment on the simplified power flow equation of the line transmission capacity constraint and the power balance constraint by adopting a second-order cone relaxation method, setting the negative line conductance in the AC/DC power transmission network to be zero, and improving the voltage amplitude of the node of the generator to obtain a final second-order cone optimal power flow model. The embodiment of the invention can effectively take the reactive voltage constraint of the power transmission network into account, has higher model solving efficiency and calculating precision, is suitable for solving a large-scale power grid, and has better robustness.

Description

Second-order cone optimal power flow model construction method and device for alternating current-direct current power transmission network
Technical Field
The invention relates to the technical field of power systems, in particular to a method for constructing a second-order cone optimal power flow model of an alternating current-direct current power transmission network of a high-voltage direct current power transmission system with a voltage source converter.
Background
The Optimal Power Flow (OPF) problem is an optimization process for adjusting various controllable devices in a system from the perspective of Power system optimization and minimizing an objective function under the conditions of satisfying normal Power balance of nodes and various safety constraints. The traditional optimal power flow problem is a nonlinear problem, which is usually solved by a nonlinear optimization method, such as the newton method, the interior point method, and the like. In addition, many experts and scholars propose to use genetic algorithm, particle swarm algorithm and the like for solving the nonlinear optimal power flow problem. In recent years, with continuous research of a linear power flow equation method, a plurality of experts provide an optimal power flow model based on a quadratic programming and linear programming method.
However, in the process of implementing the invention, the inventor finds that the prior art has at least the following problems: when the active power optimization is carried out on the optimal power flow problem by adopting a linear programming method, a direct current power flow equation is mostly adopted, a secondary function of the power generation cost needs to be linearized, the reactive voltage problem of system operation cannot be effectively accounted, the obtained result cannot meet the requirement of the system operation on the voltage level, and the optimization result can not be applied to the practical system to guide the system operation; and the linearized cost has a certain calculation error, and the actual cost of the system operation cannot be truly reflected. Although the optimal power flow calculation method based on the nonlinear programming can take the reactive voltage constraint of the power transmission network into account, the calculation difficulty is often high, the calculation time is long, the calculation difficulty is high for the actual large-scale power grid application, and the optimality of model solution cannot be guaranteed.
Disclosure of Invention
The embodiment of the invention aims to provide a second-order cone optimal power flow model construction method and device for an alternating current-direct current power transmission network, which can effectively take the reactive voltage constraint of the power transmission network into account, have higher model solving efficiency and calculation precision, are suitable for solving a large-scale power grid and have better robustness.
In order to achieve the above object, an embodiment of the present invention provides a method for constructing a second-order cone optimal power flow model of an ac/dc power transmission network, which is suitable for an ac/dc power transmission network of a voltage source converter-containing type high-voltage dc power transmission system, and includes:
constructing an optimal power flow model of the alternating current-direct current transmission network considering reactive voltage according to the equivalent model of the voltage source converter-containing type high-voltage direct current transmission system; the objective function of the optimal power flow model is that the power generation cost of the alternating current-direct current power transmission network is the lowest; the constraint conditions comprise output upper limit and output lower limit constraints of the generator set, line transmission capacity constraints, node phase angle constraints, power balance constraints and node voltage amplitude constraints;
simplifying a power flow equation of line transmission capacity constraint and power balance constraint in the optimal power flow model by adopting a first-order Taylor series expansion under a flat start method;
performing relaxation processing on the simplified power flow equation of the line transmission capacity constraint and the power balance constraint by adopting a second-order cone relaxation method;
after relaxation processing is carried out on the simplified power flow equation of the line transmission capacity constraint and the power balance constraint, the positive and negative values of the line conductance in the alternating current-direct current power transmission network are judged, and the negative value of the line conductance is set to be zero;
according to a preset adjustment step length, improving the upper and lower limits of the voltage amplitude of a node where a generator is located in the alternating current-direct current power transmission network to obtain a final second-order cone optimal power flow model;
and solving the final second-order cone optimal power flow model by adopting a preset solver.
As an improvement of the above scheme, the objective function of the optimal power flow model specifically includes:
Figure GDA0003301268460000021
g is a generator set in the alternating current-direct current transmission network; a isg、bg、cgRespectively are a secondary term, a primary term and a constant term of a power generation cost function of the generator set g; pgIs the active output power of the generator set g.
As an improvement of the above scheme, a power flow equation of a line transmission capacity constraint and a power balance constraint in the optimal power flow model is simplified by using a first-order taylor series expansion under a flat start method, specifically:
aiming at the power flow equation of the line transmission capacity constraint and the power balance constraint, a first-order Taylor series expansion is adopted for approximation under a flat starting method to obtain an approximation condition:
vivj≈1+(vi-1)+(vj-1)＝vi+vj-1；
sinθij≈θij,cosθij≈1；
vivjθij≈θij；
and substituting the approximate conditions into the power flow equation of the line transmission capacity constraint and the power balance constraint to obtain a simplified power flow equation of the line transmission capacity constraint:
Figure GDA0003301268460000031
Figure GDA0003301268460000032
Figure GDA0003301268460000033
wherein, PijAnd QijRespectively, the active power and the reactive power of the line (i, j); v. ofiAnd vjVoltage amplitudes of the node i and the node j are respectively; gijAnd bijRespectively the conductance and susceptance of the transmission line ij; thetaijIs the phase angle difference between node i and node j;
Figure GDA0003301268460000034
and
Figure GDA0003301268460000035
upper and lower limits of the active transmission power of the line (i, j), respectively; l represents a set of all lines;
and, a simplified power flow equation for the power balance constraint:
Figure GDA0003301268460000036
Figure GDA0003301268460000037
wherein, PgAnd QgRespectively the active output power and the reactive output power of the generator set g; pi d、
Figure GDA0003301268460000038
Respectively the active load and the reactive load of the node i;
Figure GDA0003301268460000039
reactive compensation capacity for parallel connection of nodes; gijAnd BijAre respectively asConductance and susceptance between i and j in the node admittance array; u shapejIs the voltage amplitude of node j; b isi′jForming an electric nano array formed by neglecting parallel electric nano in an electric nano array in a node electric nano array; i is a node set; thetajThe voltage phase angle at node j.
As an improvement of the above scheme, the relaxation processing is performed on the simplified power flow equation of the line transmission capacity constraint and the power balance constraint by using a second-order cone relaxation method, specifically:
and relaxing the simplified power flow equation constrained by the transmission capacity of the line to obtain a relaxed power flow equation constrained by the transmission capacity of the line:
Pij＝gij(vi-vj)-bijθij；
Qij＝-bij(vi-vj)-gijθij；
Figure GDA0003301268460000041
and relaxing the simplified power flow equation of the power balance constraint to obtain a relaxed power flow equation of the power balance constraint:
Figure GDA0003301268460000042
Figure GDA0003301268460000043
as an improvement of the above scheme, the upper and lower limit constraints of the output of the generator set specifically include:
Figure GDA0003301268460000044
wherein the content of the first and second substances,
Figure GDA0003301268460000045
respectively the maximum value and the minimum value of the g output of the generator set;
the node phase angle constraint specifically includes:
Figure GDA0003301268460000046
Figure GDA0003301268460000047
wherein, thetai minAnd thetai maxRespectively an upper limit value and a lower limit value of a phase angle of a node i; thetaij minAnd thetaij maxRespectively an upper limit value and a lower limit value of the phase angle difference between the node i and the node j;
the node voltage amplitude constraint specifically comprises:
Figure GDA0003301268460000048
wherein the content of the first and second substances,
Figure GDA0003301268460000049
the upper limit and the lower limit of the voltage amplitude of the node i are respectively.
The embodiment of the invention also provides a second-order cone optimal power flow model construction device of the alternating current and direct current power transmission network, which is suitable for the alternating current and direct current power transmission network of the high-voltage direct current power transmission system with the voltage source converter, and comprises the following steps:
the optimal power flow model building module is used for building an optimal power flow model of the alternating current-direct current transmission network considering reactive voltage according to the equivalent model of the voltage source converter-containing type high-voltage direct current transmission system; the objective function of the optimal power flow model is that the power generation cost of the alternating current-direct current power transmission network is the lowest; the constraint conditions comprise output upper limit and output lower limit constraints of the generator set, line transmission capacity constraints, node phase angle constraints, power balance constraints and node voltage amplitude constraints;
the constraint condition simplification module is used for simplifying a power flow equation of line transmission capacity constraint and power balance constraint in the optimal power flow model by adopting a first-order Taylor series expansion under a flat start method;
the constraint condition relaxation module is used for performing relaxation processing on the simplified power flow equation of the line transmission capacity constraint and the power balance constraint by adopting a second-order cone relaxation method;
the line conductance parameter setting module is used for loosening the simplified power flow equation of the line transmission capacity constraint and the power balance constraint, judging the positive and negative values of the line conductance in the alternating current-direct current power transmission network, and setting the negative value of the line conductance to be zero;
the generator node voltage adjusting module is used for increasing the upper limit and the lower limit of the voltage amplitude of a node where a generator is located in the alternating current-direct current power transmission network according to a preset adjusting step length to obtain a final second-order cone optimal power flow model;
and the optimal power flow model solving module is used for solving the final second-order cone optimal power flow model by adopting a preset solver.
As an improvement of the above scheme, the objective function of the optimal power flow model specifically includes:
Figure GDA0003301268460000051
g is a generator set in the alternating current-direct current transmission network; a isg、bg、cgRespectively are a secondary term, a primary term and a constant term of a power generation cost function of the generator set g; pgIs the active output power of the generator set g.
As an improvement of the above scheme, the constraint condition simplification module is specifically configured to:
aiming at the power flow equation of the line transmission capacity constraint and the power balance constraint, a first-order Taylor series expansion is adopted for approximation under a flat starting method to obtain an approximation condition:
vivj≈1+(vi-1)+(vj-1)＝vi+vj-1；
sinθij≈θij,cosθij≈1；
vivjθij≈θij；
and substituting the approximate conditions into the power flow equation of the line transmission capacity constraint and the power balance constraint to obtain a simplified power flow equation of the line transmission capacity constraint:
Figure GDA0003301268460000061
Figure GDA0003301268460000062
Figure GDA0003301268460000063
wherein, PijAnd QijRespectively, the active power and the reactive power of the line (i, j); v. ofiAnd vjVoltage amplitudes of the node i and the node j are respectively; gijAnd bijRespectively the conductance and susceptance of the transmission line ij; thetaijIs the phase angle difference between node i and node j;
Figure GDA0003301268460000064
and
Figure GDA0003301268460000065
upper and lower limits of the active transmission power of the line (i, j), respectively; l represents a set of all lines;
and, a simplified power flow equation for the power balance constraint:
Figure GDA0003301268460000066
Figure GDA0003301268460000067
wherein, PgAnd QgRespectively the active output power and the reactive output power of the generator set g; pi d、
Figure GDA0003301268460000068
Respectively the active load and the reactive load of the node i;
Figure GDA0003301268460000069
reactive compensation capacity for parallel connection of nodes; gijAnd BijRespectively the conductance and susceptance between i and j in the node admittance array; u shapejIs the voltage amplitude of node j; b isi′jForming an electric nano array formed by neglecting parallel electric nano in an electric nano array in a node electric nano array; i is a node set; thetajThe voltage phase angle at node j.
As an improvement of the above scheme, the constraint condition relaxation module is specifically configured to:
and relaxing the simplified power flow equation constrained by the transmission capacity of the line to obtain a relaxed power flow equation constrained by the transmission capacity of the line:
Pij＝gij(vi-vj)-bijθij；
Qij＝-bij(vi-vj)-gijθij；
Figure GDA00033012684600000610
and relaxing the simplified power flow equation of the power balance constraint to obtain a relaxed power flow equation of the power balance constraint:
Figure GDA0003301268460000071
Figure GDA0003301268460000072
as an improvement of the above scheme, the upper and lower limit constraints of the output of the generator set specifically include:
Figure GDA0003301268460000073
wherein the content of the first and second substances,
Figure GDA0003301268460000074
respectively the maximum value and the minimum value of the g output of the generator set;
the node phase angle constraint specifically includes:
Figure GDA0003301268460000075
Figure GDA0003301268460000076
wherein, thetai minAnd thetai maxRespectively an upper limit value and a lower limit value of a phase angle of a node i; thetaij minAnd thetaij maxRespectively an upper limit value and a lower limit value of the phase angle difference between the node i and the node j;
the node voltage amplitude constraint specifically comprises:
Figure GDA0003301268460000077
wherein the content of the first and second substances,
Figure GDA0003301268460000078
the upper limit and the lower limit of the voltage amplitude of the node i are respectively.
Compared with the prior art, the second-order cone optimal power flow model construction method and device for the alternating current-direct current power transmission network are suitable for the alternating current-direct current power transmission network of the voltage-containing source converter type high-voltage direct current power transmission system, and the optimal power flow model of the alternating current-direct current power transmission network considering reactive voltage is constructed according to the equivalent model of the voltage-containing source converter type high-voltage direct current power transmission system; simplifying a power flow equation of line transmission capacity constraint and power balance constraint in the optimal power flow model by adopting a first-order Taylor series expansion under a flat start method; performing relaxation processing on the simplified power flow equation of the line transmission capacity constraint and the power balance constraint by adopting a second-order cone relaxation method; and judging the positive and negative value conditions of the line conductance in the AC/DC power transmission network, setting the negative value line conductance to be zero, and then increasing the upper and lower limits of the voltage amplitude of the node where the generator is located in the AC/DC power transmission network according to a preset adjustment step length to obtain a final second-order cone optimal power flow model. The invention provides a new second-order cone relaxation power flow equation constraint, aiming at the optimal power flow problem of a power transmission network, the approximately simplified power flow equation can be adopted to effectively calculate reactive voltage in the active power optimization problem of the power transmission network, a second-order cone optimal power flow model for calculating the reactive voltage is constructed, and the possibility is provided for the application to the operation of an actual power system. The second-order cone optimal power flow model optimizes the operation mode of the power system by taking the minimum power generation cost as an objective function, so that the operation economy of the system can be improved. And the optimal power flow model is subjected to relaxation treatment by combining with an actual solving problem, so that the convenience of model solving is obviously improved. Meanwhile, compared with the traditional nonlinear alternating current optimal power flow model, the second-order cone optimal power flow model has remarkable calculation advantages, is high in calculation precision, does not depend on algorithm parameter setting, can ensure the uniqueness of a solution, and is good in robustness.
Drawings
Fig. 1 is a schematic flowchart illustrating steps of a second-order cone optimal power flow model building method for an ac/dc power transmission network according to an embodiment of the present invention;
fig. 2 is a schematic diagram of an equivalent model of the hvdc transmission system according to the first embodiment of the present invention;
FIG. 3 is a diagram illustrating the results of a system calculation using a modified IEEE 30 node according to one embodiment of the present invention;
FIG. 4 is a diagram illustrating results calculated by a modified IEEE 118 node system in accordance with one embodiment of the present invention;
FIG. 5 is a diagram illustrating the results of a system calculation using a modified IEEE 300 node according to one embodiment of the present invention;
FIG. 6 is a diagram illustrating the results of a system calculation using a modified IEEE 3375 node according to one embodiment of the present invention;
fig. 7 is a schematic structural diagram of a second-order cone optimal power flow model building device for an ac/dc power transmission network according to a second embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Fig. 1 is a schematic flow chart illustrating steps of a method for constructing a second-order cone optimal power flow model of an ac/dc power transmission network according to an embodiment of the present invention. The second-order cone optimal power flow model construction method for the alternating current-direct current power transmission network, provided by the embodiment of the invention, is suitable for the alternating current-direct current power transmission network of the high-voltage direct current power transmission system with the voltage source converter, and is specifically executed through steps S1 to S6:
s1, constructing an optimal power flow model of the alternating current-direct current transmission network considering reactive voltage according to the equivalent model of the voltage source converter-containing type high-voltage direct current transmission system; the objective function of the optimal power flow model is that the power generation cost of the alternating current-direct current transmission network is the lowest; the constraint conditions comprise output upper limit and output lower limit constraints of the generator set, line transmission capacity constraints, node phase angle constraints, power balance constraints and node voltage amplitude constraints.
S2, simplifying a power flow equation of line transmission capacity constraint and power balance constraint in the optimal power flow model by adopting a first-order Taylor series expansion under a flat start method.
And S3, adopting a second-order cone relaxation method to relax the simplified power flow equation of the line transmission capacity constraint and the power balance constraint.
S4, after relaxation processing is carried out on the simplified power flow equation of the line transmission capacity constraint and the power balance constraint, the positive and negative values of the line conductance in the alternating current-direct current power transmission network are judged, and the negative value of the line conductance is set to be zero;
and S5, according to the preset adjustment step length, increasing the upper and lower limits of the voltage amplitude of the node where the generator is located in the alternating current-direct current power transmission network to obtain a final second-order cone optimal power flow model.
And S6, solving the final second-order cone optimal power flow model by adopting a preset solver.
Specifically, referring to fig. 2, an equivalent model schematic diagram of a high-voltage direct-current transmission system including a voltage source converter according to a first embodiment of the present invention is shown. The equivalent model of the high-voltage direct-current transmission system comprises an alternating-current side, equivalent impedance of a converter transformer, an ideal voltage source type converter and a direct-current filter. The alternating current side is connected with the equivalent impedance of the converter transformer through a node S, the equivalent impedance of the converter transformer is connected with the ideal voltage source type converter through a node C, and the ideal voltage source type converter is connected with the direct current filter through a node D.
Aiming at the alternating current side of the equivalent model, an alternating current power flow equation based on a polar coordinate form and line transmission power are constructed as follows:
Figure GDA0003301268460000101
Figure GDA0003301268460000102
Figure GDA0003301268460000103
Figure GDA0003301268460000104
wherein, PiAnd QiRespectively the active power and the reactive power of the node i; pijAnd QijRespectively, the active power and the reactive power of the line (i, j); v. ofiAnd vjVoltage amplitudes of the node i and the node j are respectively; gijAnd BijRespectively the conductance and susceptance between i and j in the node admittance array; gijAnd bijRespectively the conductance and susceptance of the transmission line ij; thetaijIs the phase angle difference between node i and node j.
And (3) approximating the power flow equation by adopting a first-order Taylor series expansion under a flat starting method. The flat start method comprises the following steps: setting the initial value of the voltage amplitude to be 1 and the initial value of the phase angle to be 0, that is, v is 1 and θ is 0, the approximate conditions can be obtained as follows:
vivj≈1+(vi-1)+(vj-1)＝vi+vj-1；
sinθij≈θij,cosθij≈1；
vivjθij≈θij；
substituting the approximate conditions into the power flow equation at the alternating current side to obtain a simplified alternating current power flow equation and the transmission power of the line, wherein the simplified alternating current power flow equation and the transmission power of the line are as follows:
Figure GDA0003301268460000105
Figure GDA0003301268460000106
Figure GDA0003301268460000107
Figure GDA0003301268460000108
wherein, UjIs the voltage amplitude of node j; thetajIs the voltage phase angle of node j; b isi′jThe electric nano array formed by neglecting parallel electric nano in the electric nano array in the node electric nano array.
Further, a power flow equation of the injected power at the equivalent model node S bus is:
Figure GDA0003301268460000111
the power flow equation of the injected power at the node C bus is as follows:
Figure GDA0003301268460000112
wherein G istThe corresponding conductance of the converter transformer; b istThe power susceptance is corresponding to the converter transformer; thetas and thetac are voltage phase angles at a node S and a node C in the equivalent model of the high-voltage direct-current power transmission system respectively; delta thetasc＝θs-θc。
Considering the injection power of the direct-current node of the alternating-current and direct-current system of the voltage source converter as follows: pd＝Pdg-Pdl+Pc；
Wherein, Pdg、PdlRespectively representing the power generation active power injection power of a node D in the equivalent model of the high-voltage direct-current power transmission system and the active power consumed by the load; pcThe power delivered for the dc line.
Similarly, the same approximation method as that of the alternating current system is adopted, and the approximation condition is substituted into the injection power flow equation to obtain:
Figure GDA0003301268460000113
Figure GDA0003301268460000114
and:
Pc＝Gt(Us-Uc)-Bt(θs-θc)
＝GtUs-Btθs-GtUc+Btθc；
Qc＝Bt(Uc+Us)+Gt(θs-θc)
＝BtUs+Gtθs+BtUc-Gtθc.
each VSC contains Us，θs，Uc，θcFour state variables, where Us，θsCan be solved by the AC system equation, therefore, two constraint equations need to be added to realize the state variable Uc，θcObtaining the target value. Corresponding constraint equations are given according to different control modes generally adopted by the direct current system. And obtaining a secondarily formed power flow equation of the alternating current and direct current transmission network of the voltage-containing source converter type high-voltage direct current transmission system, and using the secondarily formed power flow equation to construct an optimal power flow model of the alternating current and direct current transmission network of the voltage-containing source converter type high-voltage direct current transmission system.
Specifically, the optimal power flow model takes the lowest power generation cost of the alternating current/direct current transmission network of the voltage-source-contained converter type high-voltage direct current transmission system as an objective function. The objective function of the optimal power flow model is specifically as follows:
Figure GDA0003301268460000121
wherein G isAn alternating current-direct current transmission network generator set; a isg、bg、cgRespectively are a secondary term, a primary term and a constant term of a power generation cost function of the generator set g; pgIs the active output power of the generator set g.
The constraint conditions of the optimal power flow model specifically include: the method comprises the following steps of output upper and lower limit constraints of a generator set, line transmission capacity constraints, node phase angle constraints, power balance constraints and node voltage amplitude constraints.
The upper and lower limit constraints of the output of the generator set are specifically as follows:
Figure GDA0003301268460000122
wherein the content of the first and second substances,
Figure GDA0003301268460000123
respectively the maximum value and the minimum value of the g output of the generator set;
and (3) adopting a first-order Taylor series expansion formula to carry out simplified power flow equation of line transmission capacity constraint under a flat start method:
Figure GDA0003301268460000124
Figure GDA0003301268460000125
Figure GDA0003301268460000126
wherein, PijAnd QijRespectively, the active power and the reactive power of the line (i, j); v. ofiAnd vjVoltage amplitudes of the node i and the node j are respectively; gijAnd bijRespectively the conductance and susceptance of the transmission line ij; thetaijIs the phase angle difference between node i and node j;
Figure GDA0003301268460000127
and
Figure GDA0003301268460000128
upper and lower limits of the active transmission power of the line (i, j), respectively; l represents a set of all lines;
the node phase angle constraint specifically includes:
Figure GDA0003301268460000131
Figure GDA0003301268460000132
wherein, thetai minAnd thetai maxRespectively an upper limit value and a lower limit value of a phase angle of a node i; thetaij minAnd thetaij maxRespectively an upper limit value and a lower limit value of the phase angle difference between the node i and the node j;
and (3) carrying out simplified power balance constraint power flow equation by adopting a first-order Taylor series expansion under a flat start method:
Figure GDA0003301268460000133
Figure GDA0003301268460000134
wherein, PgAnd QgRespectively the active output power and the reactive output power of the generator set g; pi d、
Figure GDA0003301268460000135
Respectively the active load and the reactive load of the node i;
Figure GDA0003301268460000136
is a nodeReactive compensation capacity in parallel; gijAnd BijRespectively the conductance and susceptance between i and j in the node admittance array; u shapejIs the voltage amplitude of node j; b isi′jForming an electric nano array formed by neglecting parallel electric nano in an electric nano array in a node electric nano array; i is a node set; thetajThe voltage phase angle at node j.
The node voltage amplitude constraint specifically comprises:
Figure GDA0003301268460000137
wherein the content of the first and second substances,
Figure GDA0003301268460000138
the upper limit and the lower limit of the voltage amplitude of the node i are respectively.
Further, the constructed optimal power flow model is a quadratic constraint quadratic programming problem, and when a commercial solver CPLEX is used for solving, a large-scale system may have a non-positive condition, so that the model cannot be solved.
Specifically, the relaxation processing is performed on the simplified power flow equation of the line transmission capacity constraint and the power balance constraint by using a second-order cone relaxation method, and specifically includes:
and relaxing the simplified power flow equation constrained by the transmission capacity of the line to obtain a relaxed power flow equation constrained by the transmission capacity of the line:
Pij＝gij(vi-vj)-bijθij；
Qij＝-bij(vi-vj)-gijθij；
Figure GDA0003301268460000141
and relaxing the simplified power flow equation of the power balance constraint to obtain a relaxed power flow equation of the power balance constraint:
Figure GDA0003301268460000142
Figure GDA0003301268460000143
preferably, after the corresponding constraint conditions of the optimal power flow model are relaxed, the optimal power flow model needs to be positively determined before the solver can complete the solution. To avoid the line conductance g occurring in large-scale systemsijIn the embodiment of the present invention, it is further necessary to further determine the positive and negative values of the line conductance in the hvdc transmission system, and to apply the negative line conductance g to the case where the secondary constraint of the optimal power flow model is not positive, which is caused by a negative valueijAnd setting the value to be 0, and changing the value into a positive array so as to obtain a final second-order cone optimal power flow model.
Because the arrangement only affects the line power network loss, and the number of the lines in the system is very small, such as only one line in an IEEE 300 node system, and the negative value of the line conductance gijIs smaller, so that a negative line conductance g is obtainedijAfter the value is set to 0, the influence on the active calculation precision is extremely small and can be completely ignored.
Preferably, considering that a node where a generator is located in an actual power grid is often a node supporting the voltage level of a system, and therefore the voltage level of such a node is often higher, in the embodiment of the present invention, the upper and lower voltage amplitude limits of the node where the generator is located are further increased according to a preset adjustment step length, so as to ensure the voltage level of the whole system operation. For example, the per unit values of the upper and lower voltage amplitude limits of the common load node are set to 0.95 to 1.05, the adjustment step length of the upper voltage amplitude limit is set to 0.03 in advance, and the adjustment step length of the lower voltage amplitude limit is set to 0.01, so that the per unit values of the upper and lower voltage amplitude limits of the generator node in the ac/dc power transmission network can be set to 0.98 to 1.06.
It can be understood that the values of the upper and lower limit adjustment steps related to the above scenario are only examples, and in practical applications, an appropriate adjustment step may be set according to practical situations, and is not specifically limited herein.
By adopting the technical means of the embodiment of the invention, the final second-order cone optimal power flow model of the alternating current-direct current power transmission network of the voltage source converter type high-voltage direct current power transmission system taking the reactive voltage into account is constructed. And solving the final second-order cone optimal power flow model by adopting a preset solver to obtain an optimal solution of the second-order cone optimal power flow model.
Preferably, the preset solver is a CPLEX solver.
In an implementation manner, for the second-order cone optimal power flow model construction method of the ac/dc power transmission network provided in the embodiment of the present invention, test calculations are respectively performed on modified IEEE 30, 118, 300, and 3375 node systems. And meanwhile, the method is compared with an optimal power flow model adopting a traditional alternating current power flow equation. The programming is based on GAMS (general algebra modeling system) Studio 27.3 software, a CPLEX solver is called to solve the QCP problem, and a test computer is configured to be an Intel (R) core (TM) i5-6300U series CPU, a main frequency of 2.4GHz and an internal memory of 8G.
Referring to fig. 3 to 6, fig. 3 is a schematic diagram illustrating a result calculated by a modified IEEE 30 node system according to an embodiment of the present invention; FIG. 4 is a diagram illustrating results calculated by a modified IEEE 118 node system in accordance with one embodiment of the present invention; FIG. 5 is a diagram illustrating results calculated by a modified IEEE 300 node system in accordance with one embodiment of the present invention; fig. 6 is a diagram illustrating the results of a system calculation using a modified IEEE 3375 node according to an embodiment of the present invention. The optimal power flow model using the conventional alternating current power flow equation and the optimal power flow model constructed by the method provided by the first embodiment of the present invention are shown in table 1 for time pair ratios calculated for different modified IEEE systems.
TABLE 1 comparison of computation time and computation accuracy
Figure GDA0003301268460000151
As can be seen from the cost errors and the calculation time results of fig. 3 to 6 and table 1, the optimal power flow model construction method provided by the embodiment of the invention has high model calculation efficiency and calculation accuracy, the cost error of the objective function is not more than 2%, the maximum error of the node voltage amplitude is not more than 10%, and the error requirement in the actual system operation can be met, so that reference and guidance are provided for the actual system operation.
The embodiment of the invention provides a second-order cone optimal power flow model construction method for an alternating current-direct current power transmission network, which is suitable for the alternating current-direct current power transmission network of a voltage source converter-containing type high-voltage direct current power transmission system, and the optimal power flow model of the alternating current-direct current power transmission network considering reactive voltage is constructed according to an equivalent model of the voltage source converter-containing type high-voltage direct current power transmission system; simplifying a power flow equation of line transmission capacity constraint and power balance constraint in the optimal power flow model by adopting a first-order Taylor series expansion under a flat start method; performing relaxation processing on the simplified power flow equation of the line transmission capacity constraint and the power balance constraint by adopting a second-order cone relaxation method; and judging the positive and negative value conditions of the line conductance in the AC/DC power transmission network, setting the negative value line conductance to be zero, and then increasing the upper and lower limits of the voltage amplitude of the node where the generator is located in the AC/DC power transmission network according to a preset adjustment step length to obtain a final second-order cone optimal power flow model.
The embodiment of the invention provides a new second-order cone relaxation power flow equation constraint, aiming at the optimal power flow problem of a power transmission network, the approximately simplified power flow equation can be adopted to effectively calculate reactive voltage in the active power optimization problem of the power transmission network, and a second-order cone optimal power flow model for calculating the reactive voltage is constructed, so that the possibility is provided for the application to the operation of an actual power system. The second-order cone optimal power flow model optimizes the operation mode of the power system by taking the minimum power generation cost as an objective function, so that the operation economy of the system can be improved. And the optimal power flow model is subjected to relaxation treatment by combining with an actual solving problem, so that the convenience of model solving is obviously improved. Meanwhile, compared with the traditional nonlinear alternating current optimal power flow model, the second-order cone optimal power flow model has remarkable calculation advantages, is high in calculation precision, does not depend on algorithm parameter setting, can ensure the uniqueness of a solution, and is good in robustness.
Fig. 7 is a schematic structural diagram of a second-order cone optimal power flow model building device for an ac/dc power transmission network according to the second embodiment of the present invention. The second embodiment of the present invention provides a second-order cone optimal power flow model building apparatus 20 for an ac/dc power transmission network, which is suitable for an ac/dc power transmission network including a voltage source converter type high-voltage dc transmission system, and includes: the optimal power flow model construction module 21, the constraint condition simplification module 22, the constraint condition relaxation module 23, the line conductance parameter setting module 24, the generator node voltage adjustment module 25 and the optimal power flow model solving module 26; wherein the content of the first and second substances,
the optimal power flow model building module 21 is configured to build an optimal power flow model of the ac/dc power transmission network considering reactive voltage according to an equivalent model of the voltage source converter-containing type high-voltage dc power transmission system; the objective function of the optimal power flow model is that the power generation cost of the alternating current-direct current power transmission network is the lowest; the constraint conditions comprise output upper limit and output lower limit constraints of the generator set, line transmission capacity constraints, node phase angle constraints, power balance constraints and node voltage amplitude constraints;
the constraint condition simplifying module 22 is used for simplifying a power flow equation of line transmission capacity constraint and power balance constraint in the optimal power flow model by adopting a first-order Taylor series expansion under a flat start method;
the constraint condition relaxation module 23 is configured to relax the simplified power flow equation of the line transmission capacity constraint and the power balance constraint by using a second-order cone relaxation method;
the line conductance parameter setting module 24 is configured to, after relaxation processing is performed on the simplified power flow equation of the line transmission capacity constraint and the power balance constraint, determine the positive and negative values of the line conductance in the ac/dc power transmission network, and set the negative value of the line conductance to zero;
the generator node voltage adjusting module 25 is configured to increase upper and lower limits of a voltage amplitude of a node where a generator is located in the alternating current/direct current power transmission network according to a preset adjustment step length to obtain a final second-order cone optimal power flow model;
and the optimal power flow model solving module 26 is configured to solve the final second-order cone optimal power flow model by using a preset solver.
Specifically, the objective function of the optimal power flow model is specifically:
Figure GDA0003301268460000171
wherein G is a generator set of the high-voltage direct-current transmission system; a isg、bg、cgRespectively are a secondary term, a primary term and a constant term of a power generation cost function of the generator set g; pgIs the active output power of the generator set g.
As a preferred embodiment, the constraint condition simplification module 22 is specifically configured to:
aiming at the power flow equation of the line transmission capacity constraint and the power balance constraint, a first-order Taylor series expansion is adopted for approximation under a flat starting method to obtain an approximation condition:
vivj≈1+(vi-1)+(vj-1)＝vi+vj-1；
sinθij≈θij,cosθij≈1；
vivjθij≈θij；
and substituting the approximate conditions into the power flow equation of the line transmission capacity constraint and the power balance constraint to obtain a simplified power flow equation of the line transmission capacity constraint:
Figure GDA0003301268460000181
Figure GDA0003301268460000182
Figure GDA0003301268460000183
wherein, PijAnd QijRespectively, the active power and the reactive power of the line (i, j); v. ofiAnd vjVoltage amplitudes of the node i and the node j are respectively; gijAnd bijRespectively the conductance and susceptance of the transmission line ij; thetaijIs the phase angle difference between node i and node j;
Figure GDA0003301268460000184
and
Figure GDA0003301268460000185
upper and lower limits of the active transmission power of the line (i, j), respectively; l represents a set of all lines;
and, a simplified power flow equation for the power balance constraint:
Figure GDA0003301268460000186
Figure GDA0003301268460000187
wherein, PgAnd QgRespectively the active output power and the reactive output power of the generator set g; pi d、
Figure GDA0003301268460000188
Respectively the active load and the reactive load of the node i;
Figure GDA0003301268460000189
reactive compensation capacity for parallel connection of nodes; gijAnd BijRespectively the conductance and susceptance between i and j in the node admittance array; u shapejIs the voltage amplitude of node j; b isi′jForming an electric nano array formed by neglecting parallel electric nano in an electric nano array in a node electric nano array; i is a node set; thetajThe voltage phase angle at node j.
As a preferred embodiment, the constraint relaxation module 23 is specifically configured to:
and relaxing the simplified power flow equation constrained by the transmission capacity of the line to obtain a relaxed power flow equation constrained by the transmission capacity of the line:
Pij＝gij(vi-vj)-bijθij；
Qij＝-bij(vi-vj)-gijθij；
Figure GDA0003301268460000191
and relaxing the simplified power flow equation of the power balance constraint to obtain a relaxed power flow equation of the power balance constraint:
Figure GDA0003301268460000192
Figure GDA0003301268460000193
further, the upper and lower limit constraints of the output of the generator set are specifically:
Figure GDA0003301268460000194
wherein the content of the first and second substances,
Figure GDA0003301268460000195
respectively the maximum value and the minimum value of the g output of the generator set;
the node phase angle constraint specifically includes:
Figure GDA0003301268460000196
Figure GDA0003301268460000197
wherein, thetai minAnd thetai maxRespectively an upper limit value and a lower limit value of a phase angle of a node i; thetaij minAnd thetaij maxRespectively an upper limit value and a lower limit value of the phase angle difference between the node i and the node j;
the node voltage amplitude constraint specifically comprises:
Figure GDA0003301268460000198
wherein the content of the first and second substances,
Figure GDA0003301268460000199
the upper limit and the lower limit of the voltage amplitude of the node i are respectively.
It should be noted that the second-order cone optimal power flow model building apparatus for the ac/dc power transmission network according to the second embodiment of the present invention is configured to execute all the process steps of the first-order cone optimal power flow model building method for the ac/dc power transmission network according to the first embodiment, and working principles and beneficial effects of the two are in one-to-one correspondence, so that details are not repeated.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by a computer program, which can be stored in a computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a Read-only memory (ROM), a Random Access Memory (RAM), or the like.
The embodiment II of the invention provides a second-order cone optimal power flow model construction device of an alternating current-direct current transmission network, which is suitable for the alternating current-direct current transmission network of a voltage source converter-containing high-voltage direct current transmission system, and an optimal power flow model of the alternating current-direct current transmission network considering reactive voltage is constructed according to an equivalent model of the voltage source converter-containing high-voltage direct current transmission system; simplifying a power flow equation of line transmission capacity constraint and power balance constraint in the optimal power flow model by adopting a first-order Taylor series expansion under a flat start method; performing relaxation processing on the simplified power flow equation of the line transmission capacity constraint and the power balance constraint by adopting a second-order cone relaxation method; and judging the positive and negative value conditions of the line conductance in the AC/DC power transmission network, setting the negative value line conductance to be zero, and then increasing the upper and lower limits of the voltage amplitude of the node where the generator is located in the AC/DC power transmission network according to a preset adjustment step length to obtain a final second-order cone optimal power flow model.
The embodiment of the invention provides a new second-order cone relaxation power flow equation constraint, aiming at the optimal power flow problem of a power transmission network, the approximately simplified power flow equation can be adopted to effectively calculate reactive voltage in the active power optimization problem of the power transmission network, and a second-order cone optimal power flow model for calculating the reactive voltage is constructed, so that the possibility is provided for the application to the operation of an actual power system. The second-order cone optimal power flow model optimizes the operation mode of the power system by taking the minimum power generation cost as an objective function, so that the operation economy of the system can be improved. And the optimal power flow model is subjected to relaxation treatment by combining with an actual solving problem, so that the convenience of model solving is obviously improved. Meanwhile, compared with the traditional nonlinear alternating current optimal power flow model, the second-order cone optimal power flow model has remarkable calculation advantages, is high in calculation precision, does not depend on algorithm parameter setting, can ensure the uniqueness of a solution, and is good in robustness.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention.

Claims (6)

1. A method for constructing a second-order cone optimal power flow model of an alternating current-direct current power transmission network is suitable for the alternating current-direct current power transmission network of a high-voltage direct current power transmission system with a voltage source converter, and is characterized by comprising the following steps of:
constructing an optimal power flow model of the alternating current-direct current transmission network considering reactive voltage according to the equivalent model of the voltage source converter-containing type high-voltage direct current transmission system; the objective function of the optimal power flow model is that the power generation cost of the alternating current-direct current power transmission network is the lowest; the constraint conditions comprise output upper limit and output lower limit constraints of the generator set, line transmission capacity constraints, node phase angle constraints, power balance constraints and node voltage amplitude constraints;
simplifying a power flow equation of line transmission capacity constraint and power balance constraint in the optimal power flow model by adopting a first-order Taylor series expansion under a flat start method;
performing relaxation processing on the simplified power flow equation of the line transmission capacity constraint and the power balance constraint by adopting a second-order cone relaxation method;
after relaxation processing is carried out on the simplified power flow equation of the line transmission capacity constraint and the power balance constraint, the positive and negative values of the line conductance in the alternating current-direct current power transmission network are judged, and the negative value of the line conductance is set to be zero;
according to a preset adjustment step length, improving the upper and lower limits of the voltage amplitude of a node where a generator is located in the alternating current-direct current power transmission network to obtain a final second-order cone optimal power flow model;
solving the final second-order cone optimal power flow model by adopting a preset solver;
the objective function of the optimal power flow model is specifically as follows:
Figure FDA0003301268450000011
g is a generator set in the alternating current-direct current transmission network; a isg、bg、cgRespectively are a secondary term, a primary term and a constant term of a power generation cost function of the generator set g; pgThe active output power of the generator set g is obtained;
the power flow equation of the line transmission capacity constraint and the power balance constraint in the optimal power flow model is simplified by adopting a first-order Taylor series expansion under a flat start method, and the method specifically comprises the following steps:
aiming at the power flow equation of the line transmission capacity constraint and the power balance constraint, a first-order Taylor series expansion is adopted for approximation under a flat starting method to obtain an approximation condition:
vivj≈1+(vi-1)+(vj-1)＝vi+vj-1；
sinθij≈θij,cosθij≈1；
vivjθij≈θij；
and substituting the approximate conditions into the power flow equation of the line transmission capacity constraint and the power balance constraint to obtain a simplified power flow equation of the line transmission capacity constraint:
Figure FDA0003301268450000021
Figure FDA0003301268450000022
Figure FDA0003301268450000023
wherein, PijAnd QijRespectively, the active power and the reactive power of the line (i, j); v. ofiAnd vjVoltage amplitudes of the node i and the node j are respectively; gijAnd bijRespectively the conductance and susceptance of the transmission line ij; thetaijIs the phase angle difference between node i and node j;
Figure FDA0003301268450000024
and
Figure FDA0003301268450000025
upper and lower limits of the active transmission power of the line (i, j), respectively; l represents a set of all lines;
and, a simplified power flow equation for the power balance constraint:
Figure FDA0003301268450000026
Figure FDA0003301268450000027
wherein, PgAnd QgRespectively the active output power and the reactive output power of the generator set g; pi d、
Figure FDA0003301268450000028
Respectively the active load and the reactive load of the node i;
Figure FDA0003301268450000029
reactive compensation capacity for parallel connection of nodes; gijAnd BijRespectively the conductance and susceptance between i and j in the node admittance array; u shapejIs the voltage amplitude of node j; b'ijForming an electric nano array formed by neglecting parallel electric nano in an electric nano array in a node electric nano array; i is a node set; thetajThe voltage phase angle at node j.
2. The method for constructing the second-order cone optimal power flow model of the alternating current-direct current power transmission network according to claim 1, wherein the method for relaxing the second-order cone is adopted to relax the simplified power flow equation of the line transmission capacity constraint and the power balance constraint, and specifically comprises the following steps:
and relaxing the simplified power flow equation constrained by the transmission capacity of the line to obtain a relaxed power flow equation constrained by the transmission capacity of the line:
Pij＝gij(vi-vj)-bijθij；
Qij＝-bij(vi-vj)-gijθij；
Figure FDA0003301268450000031
and relaxing the simplified power flow equation of the power balance constraint to obtain a relaxed power flow equation of the power balance constraint:
Figure FDA0003301268450000032
Figure FDA0003301268450000033
3. the method for constructing the second-order cone optimal power flow model of the alternating current-direct current power transmission network according to claim 2, wherein the constraints on the upper limit and the lower limit of the output of the generator set are specifically as follows:
Figure FDA0003301268450000034
wherein the content of the first and second substances,
Figure FDA0003301268450000035
respectively the maximum value and the minimum value of the g output of the generator set;
the node phase angle constraint specifically includes:
Figure FDA0003301268450000036
Figure FDA0003301268450000037
wherein, thetai minAnd thetai maxRespectively an upper limit value and a lower limit value of a phase angle of a node i; thetaij minAnd thetaij maxRespectively an upper limit value and a lower limit value of the phase angle difference between the node i and the node j;
the node voltage amplitude constraint specifically comprises:
Figure FDA0003301268450000038
wherein the content of the first and second substances,
Figure FDA0003301268450000039
the upper limit and the lower limit of the voltage amplitude of the node i are respectively.
4. The utility model provides a second order awl optimal power flow model construction equipment of alternating current-direct current transmission network, is applicable to the alternating current-direct current transmission network who contains voltage source converter type HVDC system, its characterized in that includes:
the optimal power flow model building module is used for building an optimal power flow model of the alternating current-direct current transmission network considering reactive voltage according to the equivalent model of the voltage source converter-containing type high-voltage direct current transmission system; the objective function of the optimal power flow model is that the power generation cost of the alternating current-direct current power transmission network is the lowest; the constraint conditions comprise output upper limit and output lower limit constraints of the generator set, line transmission capacity constraints, node phase angle constraints, power balance constraints and node voltage amplitude constraints;
the constraint condition simplification module is used for simplifying a power flow equation of line transmission capacity constraint and power balance constraint in the optimal power flow model by adopting a first-order Taylor series expansion under a flat start method;
the constraint condition relaxation module is used for performing relaxation processing on the simplified power flow equation of the line transmission capacity constraint and the power balance constraint by adopting a second-order cone relaxation method;
the line conductance parameter setting module is used for loosening the simplified power flow equation of the line transmission capacity constraint and the power balance constraint, judging the positive and negative values of the line conductance in the alternating current-direct current power transmission network, and setting the negative value of the line conductance to be zero;
the generator node voltage adjusting module is used for increasing the upper limit and the lower limit of the voltage amplitude of a node where a generator is located in the alternating current-direct current power transmission network according to a preset adjusting step length to obtain a final second-order cone optimal power flow model;
the optimal power flow model solving module is used for solving the final second-order cone optimal power flow model by adopting a preset solver;
the objective function of the optimal power flow model is specifically as follows:
Figure FDA0003301268450000041
g is a generator set in the alternating current-direct current transmission network; a isg、bg、cgRespectively are a secondary term, a primary term and a constant term of a power generation cost function of the generator set g; pgThe active output power of the generator set g is obtained;
the constraint condition simplification module is specifically configured to:
aiming at the power flow equation of the line transmission capacity constraint and the power balance constraint, a first-order Taylor series expansion is adopted for approximation under a flat starting method to obtain an approximation condition:
vivj≈1+(vi-1)+(vj-1)＝vi+vj-1；
sinθij≈θij,cosθij≈1；
vivjθij≈θij；
and substituting the approximate conditions into the power flow equation of the line transmission capacity constraint and the power balance constraint to obtain a simplified power flow equation of the line transmission capacity constraint:
Figure FDA0003301268450000051
Figure FDA0003301268450000052
Figure FDA0003301268450000053
wherein, PijAnd QijRespectively, the active power and the reactive power of the line (i, j); v. ofiAnd vjVoltage amplitudes of the node i and the node j are respectively; gijAnd bijRespectively the conductance and susceptance of the transmission line ij; thetaijIs the phase angle difference between node i and node j;
Figure FDA0003301268450000054
and
Figure FDA0003301268450000055
upper and lower limits of the active transmission power of the line (i, j), respectively; l represents a set of all lines;
and, a simplified power flow equation for the power balance constraint:
Figure FDA0003301268450000056
Figure FDA0003301268450000057
wherein, PgAnd QgRespectively the active output power and the reactive output power of the generator set g; pi d、
Figure FDA0003301268450000058
Respectively the active load and the reactive load of the node i;
Figure FDA0003301268450000059
reactive compensation capacity for parallel connection of nodes; gijAnd BijRespectively the conductance and susceptance between i and j in the node admittance array; u shapejIs the voltage amplitude of node j; b'ijForming an electric nano array formed by neglecting parallel electric nano in an electric nano array in a node electric nano array; i is a node set; thetajThe voltage phase angle at node j.
5. The apparatus for constructing a second-order cone optimal power flow model for an ac/dc power transmission network according to claim 4, wherein the constraint condition relaxation module is specifically configured to:
and relaxing the simplified power flow equation constrained by the transmission capacity of the line to obtain a relaxed power flow equation constrained by the transmission capacity of the line:
Pij＝gij(vi-vj)-bijθij；
Qij＝-bij(vi-vj)-gijθij；
Figure FDA0003301268450000061
and relaxing the simplified power flow equation of the power balance constraint to obtain a relaxed power flow equation of the power balance constraint:
Figure FDA0003301268450000062
Figure FDA0003301268450000063
6. the second-order cone optimal power flow model construction device of the alternating current-direct current power transmission network according to claim 5, wherein the constraints on the upper limit and the lower limit of the output of the generator set are specifically as follows:
Figure FDA0003301268450000064
wherein the content of the first and second substances,
Figure FDA0003301268450000065
respectively the maximum value and the minimum value of the g output of the generator set;
the node phase angle constraint specifically includes:
Figure FDA0003301268450000066
Figure FDA0003301268450000067
wherein, thetai minAnd thetai maxRespectively an upper limit value and a lower limit value of a phase angle of a node i; thetaij minAnd thetaij maxRespectively an upper limit value and a lower limit value of the phase angle difference between the node i and the node j;
the node voltage amplitude constraint specifically comprises:
Figure FDA0003301268450000068
wherein the content of the first and second substances,
Figure FDA0003301268450000069
the upper limit and the lower limit of the voltage amplitude of the node i are respectively.
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