CN109842114B - Alternating current-direct current hybrid-based power distribution network and main network exchange power flexibility range solving method - Google Patents

Alternating current-direct current hybrid-based power distribution network and main network exchange power flexibility range solving method Download PDF

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CN109842114B
CN109842114B CN201910047252.2A CN201910047252A CN109842114B CN 109842114 B CN109842114 B CN 109842114B CN 201910047252 A CN201910047252 A CN 201910047252A CN 109842114 B CN109842114 B CN 109842114B
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CN109842114A (en
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程亮
黄河
谢珍建
孙琦润
吴志
顾伟
高松
朱磊
韩俊
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State Grid Corp of China SGCC
Southeast University
State Grid Jiangsu Electric Power Co Ltd
Economic and Technological Research Institute of State Grid Jiangsu Electric Power Co Ltd
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State Grid Corp of China SGCC
Southeast University
State Grid Jiangsu Electric Power Co Ltd
Economic and Technological Research Institute of State Grid Jiangsu Electric Power Co Ltd
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Abstract

The invention discloses a method for solving the flexibility range of power exchange between a power distribution network and a main network based on alternating current and direct current mixing. The method comprises the following steps: establishing an objective function of the exchange power between the AC/DC hybrid power distribution network and the main network; determining constraint conditions of operation of the alternating-current and direct-current hybrid power distribution network, and constructing a power exchange solving model of the alternating-current and direct-current hybrid power distribution network and a main network; introducing an intermediate variable, performing second-order cone relaxation on the alternating current and direct current hybrid power distribution network and main network exchange power solving model, and converting the second-order cone relaxation model into a hybrid integer second-order cone planning model; and obtaining the operation parameters of the power distribution network, solving an objective function, and obtaining the flexibility range of the exchange power between the AC/DC hybrid power distribution network and the main network. The method and the device solve the flexibility range of the exchange power between the power distribution network and the main network in which alternating current and direct current are mixed under different operation states from the aspect of flexibility, and can provide reference for operation scheduling personnel of the main network and the power distribution network.

Description

Alternating current-direct current hybrid-based power distribution network and main network exchange power flexibility range solving method
Technical Field
The invention belongs to the field of power distribution of power systems, and particularly relates to a method for solving the flexibility range of power exchange between a power distribution network and a main network based on alternating current and direct current mixing.
Background
The large-scale access of distributed power supplies in the power distribution network is faced, the intermittent and random characteristics increase the uncertainty of network operation, great influence is generated on the supply and demand balance mechanism of the power distribution network, and sufficient flexibility is the basic requirement for ensuring the safe and reliable operation of the power distribution network. The power distribution network has the functions of receiving power from the main network side and distributing the power to each user through a power distribution facility, and the core of the operation of the power distribution network is the maintenance of the supply and demand balance. In the aspect of research on the exchange power between a power distribution network and a main network, currently, the minimum power supply cost is realized and the reliability of power supply is ensured mainly from the aspects of economy and reliability, but the consideration on flexibility is less, so that the exchange power flexibility range between the power distribution network and the main network needs to be solved, and reference is provided for operation scheduling between the power distribution network and the main network.
The direct-current power distribution network has the advantages of large power supply capacity, strong controllability, high power supply reliability, capability of running in a ring network, more flexible running mode, capability of performing flexible power control, contribution to the access of distributed power supplies, and capability of building an alternating-current and direct-current hybrid power distribution network on the basis of an alternating-current power distribution network, which is the development direction of the future power distribution network. Therefore, compared with the flexibility range of the exchange power among the alternating current and direct current power distribution network, the alternating current power distribution network and the main network, the advantage of the alternating current and direct current hybrid power distribution network in the aspect of operation flexibility compared with the traditional alternating current power distribution network can be proved.
Disclosure of Invention
In order to solve the technical problems in the background art, the invention provides a method for solving the flexibility range of the exchange power between an alternating current and direct current hybrid power distribution network and a main network, and the flexibility evaluation of the alternating current and direct current hybrid power distribution network is realized.
In order to achieve the technical purpose, the technical scheme of the invention is as follows:
the method for solving the flexibility range of the exchange power between the power distribution network and the main network based on the alternating current and direct current mixing comprises the following steps:
(1) establishing an objective function of the exchange power between the AC/DC hybrid power distribution network and the main network;
(2) determining constraint conditions of operation of the alternating-current and direct-current hybrid power distribution network, and constructing a power exchange solving model of the alternating-current and direct-current hybrid power distribution network and a main network;
(3) introducing an intermediate variable, performing second-order cone relaxation on the alternating current and direct current hybrid power distribution network and main network exchange power solving model, and converting the second-order cone relaxation model into a hybrid integer second-order cone planning model;
(4) and obtaining the operation parameters of the power distribution network, solving an objective function, and obtaining the flexibility range of the exchange power between the AC/DC hybrid power distribution network and the main network.
Further, in step (1), the objective function is as follows:
Figure BDA0001949617030000021
Figure BDA0001949617030000022
in the above formula, subscript i represents the ith node, ij represents the line with nodes at two ends i and j, respectively, and ΩSubRepresenting a set of substation nodes, ΩLRepresenting a collection of lines, Psub,iRepresenting the active power of the substation injection node i, rij、IijRespectively representing the resistance and current, phi, of line ij1、φ2Representing the weight coefficients.
Further, in step (2), the constraint condition includes a power flow constraint of the ac distribution network:
Figure BDA0001949617030000023
Figure BDA0001949617030000024
Figure BDA0001949617030000025
Figure BDA0001949617030000026
in the above formula, the first and second carbon atoms are,
Figure BDA0001949617030000027
a set of alternating current nodes is represented,
Figure BDA0001949617030000028
denotes a set of AC lines, f (i) denotes a set of head end nodes of a line ending at a node i, b (i) denotes a set of tail end nodes of a line ending at a node i, Pik、QikRespectively representing the active and reactive powers, P, of the line ik flowing from node i to node k at node iIn,i、QIn,iRespectively representing the injected active and reactive power, P, of node iDG,i、PSub,iRespectively representing active power Q of a distributed power supply and an injection node i of a transformerDG,i、QSub,iRespectively representing reactive power P of distributed power supply and transformer injection node iL,i、QL,iRespectively representing the active and reactive load power, r, of node iijAnd xijRespectively representing the resistance and reactance, V, of the line ijiRepresenting the voltage of node I, IijRepresenting the current, y, of line ijijRepresents the running state of the line ij and is a variable from 0 to 1, and the line runsWhen the line is in a state of 1, when the circuit is disconnected, y is in a state of 0, and M represents a positive number which is not less than 0.5 times the square of the corresponding voltage level of the line.
Further, in step (2), the constraint condition comprises a radial running constraint:
Figure BDA0001949617030000031
Figure BDA0001949617030000032
Figure BDA0001949617030000033
Figure BDA0001949617030000034
Figure BDA0001949617030000035
in the above formula, the first and second carbon atoms are,
Figure BDA0001949617030000036
which indicates the number of ac lines,
Figure BDA00019496170300000314
which represents the number of nodes of the substation,
Figure BDA0001949617030000037
which represents the number of the ac nodes,
Figure BDA0001949617030000038
/ΩSuba collection of ac load nodes is represented,
Figure BDA0001949617030000039
representing virtual work of substation iThe ratio of the total weight of the particles,
Figure BDA00019496170300000310
represents the virtual power of the load node i,
Figure BDA00019496170300000311
representing the virtual power of line ij.
Further, in step (2), the constraint condition includes a distributed power supply constraint:
Figure BDA00019496170300000313
Figure BDA00019496170300000312
in the above formula, omegaDGRepresenting a collection of distributed power nodes, PDG,i、QDG,iRespectively representing the active power and the reactive power of the distributed power supply of the node i,
Figure BDA0001949617030000041
represents the maximum output power of the distributed power supply,
Figure BDA0001949617030000042
represents the minimum power factor, α, of the distributed power supplyiRepresenting the distributed power output level of node i.
Further, in step (2), the constraint condition includes an upper and lower limit constraint:
Figure BDA0001949617030000043
Figure BDA0001949617030000044
in the above formula, omegaN、ΩLRespectively represent a collection of nodes and lines,
Figure BDA0001949617030000045
respectively representing the minimum and maximum values of the voltage at node i,
Figure BDA0001949617030000046
representing the maximum value of current allowed to pass through line ij.
Further, in the step (2), the constraint condition includes a power flow constraint of the dc distribution network:
Figure BDA0001949617030000047
Figure BDA0001949617030000048
Figure BDA0001949617030000049
in the above formula, the first and second carbon atoms are,
Figure BDA00019496170300000410
a set of direct current nodes is represented,
Figure BDA00019496170300000411
representing a collection of dc lines.
Further, in step (2), the constraints include voltage source converter constraints:
Figure BDA00019496170300000412
Figure BDA00019496170300000413
Figure BDA00019496170300000414
Figure BDA00019496170300000415
Figure BDA00019496170300000416
in the above formula, omegaVSCRepresenting a set of voltage source converter nodes,
Figure BDA00019496170300000417
representing a set of lines with a head end being an ac node and a tail end node being a dc node,
Figure BDA00019496170300000418
which represents the alternating voltage at the node i,
Figure BDA00019496170300000419
representing the dc voltage converted by the voltage source converter at node i,
Figure BDA0001949617030000051
representing the active power flowing on the ac side on line ij,
Figure BDA0001949617030000052
the active power of a line ij flowing on a direct current side is represented, lambda represents a voltage modulation coefficient of the voltage source converter, K represents a voltage modulation ratio of the voltage source converter, eta represents the power conversion efficiency of the voltage source converter, and P representsVSC,i、QVSC,i、SVSC,iRespectively representing the active, reactive and apparent power flowing through the voltage source converter at node i,
Figure BDA0001949617030000053
representing the capacity of the voltage source converter,
Figure BDA0001949617030000054
representing the minimum value of the voltage source converter power factor.
Further, the specific process of step (3) is as follows:
(301) new variables are defined:
Figure BDA0001949617030000055
in the above formula, the first and second carbon atoms are,
Figure BDA0001949617030000056
which represents the square of the voltage at node i,
Figure BDA0001949617030000057
represents the square of the line ij current;
substituting the new variable into the constraint condition determined in the step (2);
(302) equations (6), (18) and (21) are relaxed and rewritten into a second-order cone form:
Figure BDA0001949617030000058
Figure BDA0001949617030000059
Figure BDA00019496170300000510
Figure BDA00019496170300000511
Figure BDA00019496170300000512
Figure BDA00019496170300000513
the formula (25), the formula (27) and the formula (29) are relaxation forms of the formula (6), the formula (18) and the formula (21) in sequence, and the formula (26), the formula (28) and the formula (30) are corresponding second order taper forms in sequence;
(303) introduction of intermediate variable ζ+And ζ-：
Figure BDA0001949617030000061
Figure BDA0001949617030000062
Therein, ζ+Representing the sum, ζ, of line current and line head end voltage-Representing the difference between the line current and the line head voltage;
obtaining a voltage and current second-order cone constraint of the line:
Figure BDA0001949617030000063
Figure BDA0001949617030000064
further, in the step (4), programming is performed on the MATLAB platform, and a CPLEX commercial solver is called by using a Yalmip toolkit to respectively solve the maximum value and the minimum value of the exchange power between the AC/DC hybrid power distribution network and the main network, so that the exchange power flexibility range is obtained.
Adopt the beneficial effect that above-mentioned technical scheme brought:
(1) the invention is based on the flexibility, calculates the flexibility range of the exchange power of the alternating current-direct current hybrid power distribution network and the main network in different operation states, and can provide reference for operation scheduling personnel of the main network and the power distribution network.
(2) According to the method, the non-convex non-linear model is converted into the mixed integer second-order cone scale model by adopting second-order cone relaxation, so that the model can be effectively simplified, and efficient and rapid solution is realized.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a schematic diagram of the range of flexibility in exchanging power between a distribution network and a main network provided by the present invention;
fig. 3 is a schematic diagram of an improved 94-node ac/dc distribution network example system for example verification provided by the present invention.
Detailed Description
The technical scheme of the invention is explained in detail in the following with the accompanying drawings.
The method for solving the flexibility range of the power exchanged between the power distribution network and the main network based on the alternating current and direct current mixing comprises the following steps as shown in fig. 1:
step 1, establishing an objective function of power exchange between an alternating current-direct current hybrid power distribution network and a main network;
step 2, determining constraint conditions of the operation of the alternating current-direct current hybrid power distribution network, and constructing a power exchange solving model of the alternating current-direct current hybrid power distribution network and a main network;
step 3, introducing an intermediate variable, performing second-order cone relaxation on the alternating current-direct current hybrid power distribution network and main network exchange power solving model, and converting the second-order cone relaxation model into a hybrid integer second-order cone planning model;
and 4, obtaining the operation parameters of the power distribution network, solving an objective function, and obtaining the flexibility range of the exchange power between the alternating current-direct current hybrid power distribution network and the main network.
In this embodiment, the objective function in step 1 is as follows:
the schematic diagram of power exchange between the power distribution network and the main network is shown in fig. 2, the power distribution network receives electric energy from the main network at the substation side and distributes the electric energy to subordinate users, and due to the flexibility of the operation mode of the power distribution network, the feasible power exchange between different substations and the main network in the power distribution network is within a certain range. In order to calculate the flexible exchange power range between the alternating current and direct current hybrid power distribution network and the main network, the maximum value and the minimum value of the feasible exchange power between the alternating current and direct current hybrid power distribution network and the main network are solved:
Figure BDA0001949617030000071
Figure BDA0001949617030000081
wherein, subscript i represents ith node, ij represents lines with nodes at two ends being i and j respectively, and ΩSubRepresenting a set of substation nodes, ΩLRepresenting a collection of lines, Psub,iRepresenting the active power of the substation injection node i, rij、IijRespectively representing the resistance and current, phi, of line ij1、φ2The weight coefficient is expressed and needs to be reasonably set to ensure the accuracy of the second-order cone relaxation.
In this embodiment, the constraint conditions in step 2 include a power flow constraint (node power balance constraint, line voltage drop constraint, line power constraint) of the ac distribution network:
Figure BDA0001949617030000082
Figure BDA0001949617030000083
Figure BDA0001949617030000084
Figure BDA0001949617030000085
wherein the content of the first and second substances,
Figure BDA0001949617030000086
a set of alternating current nodes is represented,
Figure BDA0001949617030000087
denotes a set of AC lines, f (i) denotes a set of head end nodes of a line ending at a node i, b (i) denotes a set of tail end nodes of a line ending at a node i, Pik、QikRespectively representing the active and reactive powers, P, of the line ik flowing from node i to node k at node iIn,i、QIn,iRespectively representing the injected active and reactive power, P, of node iDG,i、PSub,i(QDG,i、QSub,i) Respectively representing active (reactive) power, P, of a distributed power supply and a transformer injection node iL,i、QL,iRespectively representing the active and reactive load power, r, of node iijAnd xijRespectively representing the resistance and reactance, V, of the line ijiRepresenting the voltage of node I, IijRepresenting the current, y, of line ijijThe operation state of the line ij is represented as a variable 0-1, y is equal to 1 when the line is operated, y is equal to 0 when the circuit is disconnected, and M represents a large positive number which is not less than 0.5 times of the square of the corresponding voltage level of the line.
Radial running constraint:
Figure BDA0001949617030000091
Figure BDA0001949617030000092
Figure BDA0001949617030000093
Figure BDA0001949617030000094
Figure BDA0001949617030000095
wherein the content of the first and second substances,
Figure BDA0001949617030000096
which indicates the number of ac lines,
Figure BDA00019496170300000918
which represents the number of nodes of the substation,
Figure BDA0001949617030000097
which represents the number of the ac nodes,
Figure BDA0001949617030000098
/ΩSubrepresenting a collection of ac load nodes.
Figure BDA0001949617030000099
Representing the virtual power of the substation i,
Figure BDA00019496170300000910
represents the virtual power of the load node i,
Figure BDA00019496170300000911
representing the virtual power of line ij.
Distributed power (DG) constraints:
Figure BDA00019496170300000912
Figure BDA00019496170300000913
wherein omegaDGRepresenting a collection of distributed power nodes, PDG,i、QDG,iRespectively representing the DG active and reactive power of node i,
Figure BDA00019496170300000914
represents the maximum of DGThe output power of the power amplifier is high,
Figure BDA00019496170300000915
representing the minimum power factor, α, of DGiRepresenting the DG output level at node i.
And (4) upper and lower limit constraint:
Figure BDA00019496170300000916
Figure BDA00019496170300000917
wherein omegaN、ΩLRespectively represent a collection of nodes and lines,
Figure BDA00019496170300001019
respectively representing the minimum and maximum values of the voltage at node i,
Figure BDA0001949617030000103
representing the maximum value of current allowed to pass through line ij.
Power flow constraint (node power balance constraint, line voltage drop constraint and line power constraint) of the direct-current power distribution network:
Figure BDA0001949617030000104
Figure BDA0001949617030000105
Figure BDA0001949617030000106
wherein the content of the first and second substances,
Figure BDA0001949617030000107
representing a set of DC nodes，
Figure BDA0001949617030000108
Representing a collection of dc lines.
Voltage Source Converter (VSC) constraints:
Figure BDA0001949617030000109
Figure BDA00019496170300001010
Figure BDA00019496170300001011
Figure BDA00019496170300001012
Figure BDA00019496170300001013
wherein omegaVSCRepresenting a set of voltage source converter nodes,
Figure BDA00019496170300001014
representing a set of lines with a head end being an ac node and a tail end node being a dc node,
Figure BDA00019496170300001015
which represents the alternating voltage at the node i,
Figure BDA00019496170300001016
represents the dc voltage of the node i after VSC conversion,
Figure BDA00019496170300001017
representing the active power flowing on the ac side on line ij,
Figure BDA00019496170300001018
the active power of a line ij flowing on a direct current side is shown, lambda represents a voltage modulation coefficient of the VSC, K represents a voltage modulation ratio of the VSC, eta represents the power conversion efficiency of the VSC, and PVSC,i、QVSC,i、SVSC,iRespectively representing the active, reactive and apparent power flowing through the VSC of node i,
Figure BDA0001949617030000111
which is indicative of the VSC capacity,
Figure BDA0001949617030000112
representing the minimum value of the VSC power factor.
It is emphasized that the objective functions and constraints referred to above are a preferred embodiment of the present invention. In the present invention, the selection of the objective function and the constraint condition is not limited to the above form.
In this embodiment, in step 3, a second-order cone relaxation technique is adopted to relax a non-convex nonlinear constraint condition in a model, and the model is converted into a mixed integer second-order cone programming model, which specifically includes:
step 3.1: the new variables are defined as follows:
Figure BDA0001949617030000113
wherein the content of the first and second substances,
Figure BDA0001949617030000114
which represents the square of the voltage at node i,
Figure BDA0001949617030000115
representing the square of the line ij current.
And modifying the corresponding variable in the original constraint condition into a new variable.
Step 3.2: the equations (6), (18) and (21) are relaxed and rewritten in the form of a second order cone:
Figure BDA0001949617030000116
Figure BDA0001949617030000117
Figure BDA0001949617030000118
Figure BDA0001949617030000119
Figure BDA00019496170300001110
Figure BDA00019496170300001111
step 3.3: introduction of intermediate variable ζ+And ζ-：
Figure BDA0001949617030000121
Figure BDA0001949617030000122
Therein, ζ+Representing the sum, ζ, of line current and line head end voltage-Representing the difference between the line current and the line head end voltage. Obtaining a voltage and current second-order cone constraint of the line:
Figure BDA0001949617030000123
Figure BDA0001949617030000124
in this embodiment, the specific flow of step 4 is as follows: the method comprises the steps of obtaining operating parameters of the alternating current-direct current hybrid power distribution network, programming on an MATLAB platform, calling a CPLEX commercial solver by using a Yalmip toolkit to respectively solve the maximum value and the minimum value of the alternating current-direct current power distribution network and the main network exchange power, and obtaining the exchange power flexibility range.
In this embodiment, a simulation solution is performed on an improved 94-node ac/dc hybrid distribution Network example, and related parameters of the original ac distribution Network example may refer to data disclosed in Network configuration of distribution systems using improved-integrated hybrid differential evaluation documents published in volume 18, pages 1022 to 1027 of 2003 in the journal of IEEE Transactions on Power Delivery, and a part of tie lines is adjusted to dc lines, as shown in fig. 3.
In the embodiment, two substations are included, the substation 1 includes main transformers T1 and T2, the substation 2 includes main transformers T3 and T4, and includes 94 nodes, 83 branches and 11 interconnections (in the ac/dc calculation, 6 interconnections are changed to dc interconnections), and the lines with sectionalizers are "5-6", "11-12", "19-20", "26-27", "33-34", "37-38", "38-39", "51-52", "68-69", "74-75" and "78-79". The alternating voltage class is 11.4kV, the maximum value of the current of the alternating current line is 500A, the direct voltage class is 18.6kV, and the maximum value of the current of the direct current line is 300A.
According to the alternating current-direct current hybrid-based power distribution network and main network exchange power flexibility range solving method provided by the invention, different operation states of the embodiment are considered, and the different operation states are solved. The comparison results of the obtained exchange power flexibility ranges of the substation 1 and the main network in the alternating current and direct current hybrid power distribution network and the alternating current power distribution network are shown in table 1 in consideration of different DG output levels. When the VSC capacities are different, the obtained range of the switching power flexibility between the substation 1 and the main grid in the ac/dc hybrid power distribution network is shown in table 2.
TABLE 1
Figure BDA0001949617030000131
TABLE 2
VSC capacity/kVA Pmin(kW) Pmax(kW)
1000 13591 19728
2000 10706 22940
3000 7936 25297
As can be seen from table 1, the range of the exchange power flexibility between the ac/dc hybrid distribution network and the main network is greater than that of the ac distribution network, and the advantages are more obvious when the DG access capacity is lower. As can be seen from Table 2, as the VSC capacity increases, PminValue decreases, PmaxThe value is increased and the exchange power flexibility range is gradually increased. The result verifies the accuracy and the practicability of the method provided by the invention.
The embodiments are only for illustrating the technical idea of the present invention, and the technical idea of the present invention is not limited thereto, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the scope of the present invention.

Claims (5)

1. The method for solving the flexibility range of the exchange power between the power distribution network and the main network based on the alternating current and direct current mixing is characterized by comprising the following steps of:
(1) establishing an objective function of the exchange power between the AC/DC hybrid power distribution network and the main network;
the objective function is as follows:
Figure FDA0002733047060000011
Figure FDA0002733047060000012
in the above formula, f1And f2For the objective function, the index i represents the ith node, ij represents the line with nodes at two ends i and j, respectively, and ΩSubRepresenting a set of substation nodes, ΩLRepresenting a collection of lines, Psub,iRepresenting the active power of the substation injection node i, rij、IijRespectively representing the resistance and current, phi, of line ij1、φ2Representing a weight coefficient;
(2) determining constraint conditions of operation of the alternating-current and direct-current hybrid power distribution network, and constructing a power exchange solving model of the alternating-current and direct-current hybrid power distribution network and a main network;
the constraint conditions comprise the power flow constraint of the alternating current distribution network:
Figure FDA0002733047060000013
Figure FDA0002733047060000014
Figure FDA0002733047060000015
Figure FDA0002733047060000016
in the above formula, the first and second carbon atoms are,
Figure FDA0002733047060000017
a set of alternating current nodes is represented,
Figure FDA0002733047060000018
denotes a set of AC lines, f (i) denotes a set of head end nodes of a line ending at a node i, b (i) denotes a set of tail end nodes of a line ending at a node i, Pik、QikRespectively representing the active and reactive powers, P, of the line ik flowing from node i to node k at node iIn,i、QIn,iRespectively representing the injected active and reactive power, P, of node iDG,i、PSub,iRespectively representing active power Q of a distributed power supply and an injection node i of a transformerDG,i、QSub,iRespectively representing reactive power P of distributed power supply and transformer injection node iL,i、QL,iRespectively representing the active and reactive load power, r, of node iijAnd xijRespectively representing the resistance and reactance, V, of the line ijiRepresenting the voltage of node I, IijRepresenting the current, y, of line ijijThe operation state of the line ij is represented as a variable 0-1, y is equal to 1 when the line is operated, y is equal to 0 when the circuit is disconnected, and M represents a positive number which is not less than 0.5 times of the square of the corresponding voltage level of the line;
the constraint conditions comprise the power flow constraint of the direct current distribution network:
Figure FDA0002733047060000021
Figure FDA0002733047060000022
Figure FDA0002733047060000023
in the above formula, the first and second carbon atoms are,
Figure FDA0002733047060000024
a set of direct current nodes is represented,
Figure FDA0002733047060000025
represents a set of dc lines;
the constraints include voltage source converter constraints:
Figure FDA0002733047060000026
Figure FDA0002733047060000027
Figure FDA0002733047060000028
Figure FDA0002733047060000029
Figure FDA00027330470600000210
in the above formula, omegaVSCRepresenting a set of voltage source converter nodes,
Figure FDA00027330470600000211
representing a set of lines with a head end being an ac node and a tail end node being a dc node,
Figure FDA0002733047060000031
which represents the alternating voltage at the node i,
Figure FDA0002733047060000032
representing the dc voltage converted by the voltage source converter at node i,
Figure FDA0002733047060000033
representing the active power flowing on the ac side on line ij,
Figure FDA0002733047060000034
the active power of a line ij flowing on a direct current side is represented, lambda represents a voltage modulation coefficient of the voltage source converter, K represents a voltage modulation ratio of the voltage source converter, eta represents the power conversion efficiency of the voltage source converter, and P representsVSC,i、QVSC,i、SVSC,iRespectively representing the active, reactive and apparent power flowing through the voltage source converter at node i,
Figure FDA0002733047060000035
representing the capacity of the voltage source converter,F VSCrepresenting a minimum value of a voltage source converter power factor;
(3) introducing an intermediate variable, performing second-order cone relaxation on the alternating current and direct current hybrid power distribution network and main network exchange power solving model, and converting the second-order cone relaxation model into a hybrid integer second-order cone planning model;
the specific process of the step is as follows:
(301) new variables are defined:
Figure FDA0002733047060000036
in the above formula, the first and second carbon atoms are,
Figure FDA0002733047060000037
which represents the square of the voltage at node i,
Figure FDA0002733047060000038
represents the square of the line ij current;
substituting the new variable into the constraint condition determined in the step (2);
(302) equations (6), (9) and (12) are relaxed and rewritten into a second-order cone form:
Figure FDA0002733047060000039
Figure FDA00027330470600000310
Figure FDA00027330470600000311
Figure FDA00027330470600000312
Figure FDA0002733047060000041
Figure FDA0002733047060000042
the formula (16), the formula (18) and the formula (20) are relaxation forms of the formula (6), the formula (9) and the formula (12) in sequence, and the formula (17), the formula (19) and the formula (21) are corresponding second-order taper forms in sequence;
(303) introduction of intermediate variable ζ+And ζ-：
Figure FDA0002733047060000043
Figure FDA0002733047060000044
Therein, ζ+Representing the sum, ζ, of line current and line head end voltage-Representing the difference between the line current and the line head voltage;
obtaining a voltage and current second-order cone constraint of the line:
Figure FDA0002733047060000045
Figure FDA0002733047060000046
(4) and obtaining the operation parameters of the power distribution network, solving an objective function, and obtaining the flexibility range of the exchange power between the AC/DC hybrid power distribution network and the main network.
2. The method for solving the flexibility range of power exchange between the ac-dc hybrid-based power distribution network and the main network according to claim 1, wherein in the step (2), the constraint condition includes a radial operation constraint:
Figure FDA0002733047060000047
Figure FDA0002733047060000048
Figure FDA0002733047060000049
Figure FDA0002733047060000051
Figure FDA0002733047060000052
in the above formula, the first and second carbon atoms are,
Figure FDA0002733047060000053
which indicates the number of ac lines,
Figure FDA0002733047060000054
which represents the number of nodes of the substation,
Figure FDA0002733047060000055
which represents the number of the ac nodes,
Figure FDA0002733047060000056
a collection of ac load nodes is represented,
Figure FDA0002733047060000057
representing the virtual power of the substation i,
Figure FDA0002733047060000058
represents the virtual power of the load node i,
Figure FDA0002733047060000059
representing the virtual power of line ij.
3. The method for solving the flexibility range of power exchange between the power distribution network and the main network based on the hybrid alternating current and direct current as claimed in claim 1, wherein in the step (2), the constraint condition comprises a distributed power supply constraint:
Figure FDA00027330470600000510
Figure FDA00027330470600000511
in the above formula, omegaDGRepresenting a collection of distributed power nodes, PDG,i、QDG,iRespectively representing the active power and the reactive power of the distributed power supply of the node i,
Figure FDA00027330470600000512
represents the maximum output power of the distributed power supply,F DGrepresents the minimum power factor, α, of the distributed power supplyiRepresenting the distributed power output level of node i.
4. The method for solving the flexibility range of the power exchanged between the power distribution network and the main network based on the alternating current-direct current hybrid as claimed in claim 1, wherein in the step (2), the constraint condition comprises an upper limit constraint and a lower limit constraint:
Figure FDA00027330470600000513
Figure FDA00027330470600000514
in the above formula, omegaN、ΩLRespectively represent a collection of nodes and lines,V i、
Figure FDA00027330470600000515
respectively representing the minimum and maximum values of the voltage at node i,
Figure FDA00027330470600000516
representing the maximum value of current allowed to pass through line ij.
5. The method for solving the flexibility range of the exchange power between the alternating current and direct current hybrid-based power distribution network and the main network according to any one of claims 1 to 4, wherein in the step (4), programming is performed on a MATLAB platform, and a Yalmip toolkit is used for calling a CPLEX commercial solver to respectively solve the maximum value and the minimum value of the exchange power between the alternating current and direct current hybrid-based power distribution network and the main network, so as to obtain the flexibility range of the exchange power.
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