CN114784796A - Multi-stage recovery method for flexible interconnected power distribution system based on multi-terminal SOP - Google Patents

Multi-stage recovery method for flexible interconnected power distribution system based on multi-terminal SOP Download PDF

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CN114784796A
CN114784796A CN202210423138.7A CN202210423138A CN114784796A CN 114784796 A CN114784796 A CN 114784796A CN 202210423138 A CN202210423138 A CN 202210423138A CN 114784796 A CN114784796 A CN 114784796A
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power
node
line
sop
time
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卢俊杰
张有兵
冯文波
熊美淞
任冬冬
凌锋
龚瑛
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Zhejiang University of Technology ZJUT
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Zhejiang University of Technology ZJUT
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • 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]

Abstract

A multi-stage recovery method of a flexible interconnection power distribution system based on multi-terminal SOP comprises the following steps: acquiring the position and the number of a fault line and normal line topology information in the interconnected power distribution network; calculating the information of the nodes and lines which lose power supply after fault isolation according to the fault line information, and determining the range of the power loss area; acquiring output data of renewable energy sources such as photovoltaic energy sources of fans in the interconnected power distribution network, corresponding data of loads of all nodes in a required time period, positions of all interconnection switches and breaking switches and impedance of corresponding lines; setting the positions and the capacities of all ports of a Distributed Generation (DG), a capacitor bank and a multi-port soft Switch (SOP), and establishing an equipment model; establishing a multi-stage mixed integer programming model of the multi-terminal SOP-containing flexible interconnected power distribution system; solving a target function of the interconnected power grid recovery process through a solver, formulating a multi-stage recovery strategy of the flexible interconnected power distribution system with the multi-terminal SOP, and determining the action condition of a switch at each stage and the output condition of each device.

Description

Multi-stage recovery method for flexible interconnected power distribution system based on multi-terminal SOP
Technical Field
The invention provides a multi-stage recovery method for an interconnected power distribution system.
Background
With the general access of distributed power sources, energy storage and the like and the large-scale application of technologies such as demand side response and the like, the traditional power distribution network is changed into a novel intelligent power distribution network system. In the new mode, the distribution network actively performs optimization control on Distributed Generators (DGs), energy storage, demand response resources, reactive compensation equipment, line topology and various intelligent equipment to form an operation mode of the active distribution network.
In active power distribution networks, the interconnected grid is a common form. The interconnected power grid is formed by connecting a plurality of independent power networks through connecting lines or other connecting equipment, so that the power supply reliability and the fault recovery capability of each sub-network can be improved, the tide of the power grid can be improved, the voltage and reactive power distribution can be changed, and the electric energy quality of the power grid can be improved. The traditional interconnected power grid is mainly formed by connecting lines or sub-networks into a whole power grid through tie lines and tie switches. The connected power grid has certain self-healing capability after encountering a fault, and the on-off state of each line can be changed through network reconstruction, so that each power grid node which is possibly recovered after the fault gradually recovers the normal operation state.
The intelligent Soft switch (Soft Open Point, SOP) generally refers to a double-end SOP, and can continuously adjust the active power and the reactive power of a power grid, control the power flow of the power grid and reduce the grid loss in the fault recovery of the power distribution network. The SOP can replace tie line and interconnection switch, realizes the flexible interconnection between the distribution net, has not only effectively promoted the effect that resumes, has also avoided the power supply interruption that conventional switch switching operation arouses simultaneously, has closed the ring and has strikeed the scheduling problem.
For a power distribution network with a large scale, if a better recovery effect is to be achieved and the flexible interconnection requirement under a multi-line power supply scene is adapted, a multi-end SOP capable of further realizing flexible interconnection of a plurality of feeder lines on the basis of a conventional double-end soft switch becomes an important development direction. When a fault occurs, the multi-end SOP can effectively prevent the fault current from passing through the feeder line connected with the multi-end SOP because the direct current bus has the function of isolating the fault current; in the power supply recovery process, the multi-terminal SOP can be used as an interconnection switch between subnets and an energy hub, so that mutual energy support of a plurality of subnets is realized, effective voltage support is provided for a fault side, the power supply recovery range is expanded, and the elasticity of a power grid system is enhanced. In addition, compared with a double-end SOP, the multi-end SOP has greater potential in the aspects of improving the quality of electric energy, coping with uncertainty of renewable energy sources, three-phase imbalance and the like. In summary, a multi-terminal SOP needs to be introduced into the flexible interconnected power distribution network, and a more detailed and more effective multi-stage recovery scheme is formulated.
Disclosure of Invention
The present invention is to overcome the above disadvantages of the prior art, and provide a multi-stage recovery method for a flexible interconnection power distribution system based on multi-terminal SOP.
In an active power distribution network environment, a fault recovery process is different from that of a traditional power grid, and not only reconstruction problems and traditional reactive compensation equipment related to a tie switch and a breaking switch need to be considered, but also equipment which can be actively controlled, such as a distributed power supply including renewable energy sources, a novel power electronic device including an SOP (service on programmable) and the like need to be considered. In order to play a role of the devices in recovery after a fault and solve various problems caused by the introduction of the devices, the invention provides a multi-stage recovery method of a flexible interconnected power distribution system based on multi-terminal SOP.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a multi-stage recovery method for a flexible interconnected power distribution system based on multi-terminal SOP is characterized by comprising the following steps:
s1: acquiring the position, the number and other conditions of a fault line in the interconnected power distribution network and the line topology information in a normal operation state, and turning to the step S2;
s2: calculating the information of the nodes and lines which lose power supply after fault isolation according to the fault line information, determining the range of the power-losing area, and turning to the step S3;
s3: acquiring output data of renewable energy sources such as fans, photovoltaics and the like in the interconnected power distribution network, corresponding data of loads of all nodes in a required time period, positions of all interconnection switches and disconnecting switches and impedance of corresponding lines, and turning to step S4;
s4: setting the positions and capacities of ports of a Distributed Generation (DG), a capacitor bank and a multi-terminal soft Switch (SOP), and establishing models of various devices according to the characteristics and parameters of the DG, the capacitor, the multi-terminal SOP and other devices;
s5: based on the equipment model established in the step S4, considering reconstruction and power flow distribution, establishing a line power flow model of the interconnected power grid, and performing second-order cone conversion on the power flow model, thereby establishing a multi-stage mixed integer planning model of the flexible interconnected power distribution system with the multi-end SOP;
s6: according to the step information, an objective function of the interconnected power grid recovery process is solved through a solver, a multi-stage recovery strategy of the flexible interconnected power distribution system with the multi-terminal SOP is formulated, and the action condition of each stage of switch and the output condition of each device are determined.
Further, in step S2, the determining the range of the power loss region includes the following steps:
s2-1: establishing an objective function with a minimum of power-loss nodes
Figure BDA0003607304580000031
In the formula, NIThe number of nodes of the power distribution network; chi-type food processing machineiThe power-on state of the node i in the fault isolation state is 1 when the node i is powered on, and otherwise the node i is 0.
S2-2: solving the objective function according to the radial power flow constraint to calculate all chiijLines ij and χ of 0iAnd the node i is 0, namely the power-off node and line are obtained.
Figure BDA0003607304580000041
Figure BDA0003607304580000042
Figure BDA0003607304580000043
Figure BDA0003607304580000044
Figure BDA0003607304580000045
In the formula, bijIndicating that node i is a parent node of node j; w is the set of all lines; ΨijIs the virtual power flow through line ij; chi shapeijThe power-on state of the line ij in the fault isolation state is 1 when the line ij is powered on, otherwise, the line ij is 0; m is a sufficiently large number.
Further, in the step S4, establishing models of various types of devices includes the following steps:
s4-1: modeling capacitor bank
The first time interval is set before fault isolation is recovered, and the recovery process after the first time interval is short, so that the gear positions of the capacitor bank after the nodes are recovered are kept consistent and are not adjusted along with time change. The constraints of the capacitor bank during recovery are as follows:
Figure BDA0003607304580000046
Figure BDA0003607304580000047
Figure BDA0003607304580000048
Figure BDA0003607304580000049
in the formula (I), the compound is shown in the specification,
Figure BDA00036073045800000410
representing the gear of the capacitor bank connected with the node i at the moment t;
Figure BDA00036073045800000411
representing the reactive power regulating quantity of each gear of the capacitor bank connected with the node i; xt,iThe power supply state of the node i at the time t is shown, wherein 1 represents power supply, and 0 represents no power supply.
S4-2: establishing a Soft Open Points (SOP) model of a multi-terminal
The multi-terminal SOP can accurately control the active power flow and the reactive power flow of a power grid at lower operation cost, realize optimal power distribution among connected ports and avoid risks caused by frequent switching operation. The multi-terminal SOP model takes power loss, capacity constraint and power balance into account, and the constraint conditions of the multi-terminal SOP at the moment t are as follows:
Figure BDA0003607304580000051
Figure BDA0003607304580000052
Figure BDA0003607304580000053
in the formula (I), the compound is shown in the specification,
Figure BDA0003607304580000054
respectively representing the active and reactive power of a port m at the moment t;
Figure BDA0003607304580000055
representing the active power loss of port m at time tConsumption;
Figure BDA0003607304580000056
represents the apparent power limit of port m; a. themRepresents the power loss coefficient of port m; n is a radical ofvscNumber of ports that are SOPs;
s4-3: building Distributed Generator (DG) model
the constraint conditions of the DG model at the time t are as follows:
Figure BDA0003607304580000057
Figure BDA0003607304580000058
Figure BDA0003607304580000059
Figure BDA00036073045800000510
Figure BDA00036073045800000511
in the formula (I), the compound is shown in the specification,
Figure BDA00036073045800000512
respectively representing the active power output and the reactive power output of DG at a node i at the moment t;
Figure BDA0003607304580000061
representing the power-on state of the DG at the node i at the time t, wherein the power-on state is 1, and otherwise, the power-on state is 0;
Figure BDA0003607304580000062
representing the climbing limiting power of the DG at the node i between every two time periods; pi DG,min、Pi DG,max、
Figure BDA0003607304580000063
Respectively the active and reactive upper and lower limits of the DG at the node i.
Linearizing the constraint in equation (18) yields:
Figure BDA0003607304580000064
further, in step S5, the establishing of the multi-stage mixed integer planning model of the flexible interconnected power distribution system includes the following steps:
s5-1: establishing a line reconstruction model
The reconstruction process of the power distribution system containing the multi-terminal SOP needs to meet the requirements of the limitation that the line topology has connectivity, no island exists and the normal operation area is not influenced, and the corresponding line topology is constrained as follows:
Figure BDA0003607304580000065
Figure BDA0003607304580000066
Figure BDA0003607304580000067
Figure BDA0003607304580000068
Figure BDA0003607304580000069
Figure BDA00036073045800000610
in the formula, bij,tRepresenting whether the i node is the father node of the j node at the time t, if so, the i node is 1, otherwise, the i node is 0; xij,tRepresenting the power-on state of the circuit at the moment ij, the power-on is 1, otherwise, the power-on is 0.
Furthermore, to ensure that the system can meet the radiometric constraints without connecting the SOP, and that the line can be powered by the SOP with the SOP connected. The SOP port is set as a power supply capable of providing virtual power flow, and traditional single-mode power flow (SCF) constraints are added, so that improved virtual power flow constraints are formed.
Figure BDA0003607304580000071
Figure BDA0003607304580000072
Figure BDA0003607304580000073
In the formula, Fij,tIs the virtual power flow of line ij at time t;
Figure BDA0003607304580000074
the virtual power flow is sent by a node i with SOP at the moment t;
Figure BDA0003607304580000075
the state is the open state of the SOP port m connected with the node i, the port is opened to 1, otherwise, the port is 0.
S5-2: establishing a multi-stage recovery model
A single node or a plurality of nodes connected by non-switchable lines form a line block, and the original interconnected power grid is simplified into the interconnected power grid formed by all the lines with remote controllable switches and the line block. Because the line can be electrified when power is supplied to one side of the line, the power supply state of the line cannot be switched and the line cannot be connected with the power supply stateAll nodes of the switchable circuit are powered in the same state, and at least one node connected to the switchable circuit is powered in the state before the switchable circuit is able to transmit power. Line energized state Xij,tThe constraints that need to be satisfied are as follows:
Figure BDA0003607304580000076
Figure BDA0003607304580000077
Figure BDA0003607304580000078
in the formula, WSIs a set of disconnectable lines; w is a group ofLOSSIs a collection of lines within a power loss zone determined by fault isolation.
The constraint of equation (29) may introduce an intermediate variable aij,tLinearized to obtain the constraint as follows
aij,t≤Xt-1,i+Xt-1,j (32)
aij,t≥Xt-1,i (33)
aij,t≥Xt-1,j (34)
Xij,t≤aij,t (35)
S5-3: establishing a line flow model
The Distflow power flow model suitable for the radial power distribution system is improved, a load switch for controlling the on-off of the load is added, and the Distflow power flow model suitable for the research is obtained as follows. Introduction of
Figure BDA0003607304580000081
Performing equivalent transformation, and relaxing power, current and voltage constraints to disconnect active power, reactive power and lines of the branchThe current of the circuit is zero, and no constraint is provided for the closed branch.
Figure BDA0003607304580000082
Figure BDA0003607304580000083
Figure BDA0003607304580000084
Figure BDA0003607304580000085
Figure BDA0003607304580000086
Figure BDA0003607304580000087
Figure BDA0003607304580000088
In the formula (I), the compound is shown in the specification,
Figure BDA0003607304580000089
the square of the voltage of the node i at the time t;
Figure BDA00036073045800000810
the square of the line ij current at time t; u shapestdIs the reference voltage of the power grid; i ismaxRepresents the maximum current that the line can pass; pij,tThe active power transmitted for the line ij at time t; qij,tThe reactive power transmitted for line ij at time t.
The translated power flow constraints are as follows:
Figure BDA0003607304580000091
Figure BDA0003607304580000092
Figure BDA0003607304580000093
Figure BDA0003607304580000094
Figure BDA0003607304580000095
Figure BDA0003607304580000096
in the formula, Pt,iIs the active power difference of the node i at time t; qt,iIs the reactive power difference at node i at time t;
Figure BDA0003607304580000097
is the active power generated by the photovoltaic at the node i at time t;
Figure BDA0003607304580000098
is the reactive power generated by the photovoltaic at the node i at the time t;
Figure BDA0003607304580000099
is the active power emitted by the fan at the node i at the time t;
Figure BDA00036073045800000910
is the reactive power generated by the fan at the node i at the moment t;
Figure BDA00036073045800000911
is the active power required by the load at node i at time t;
Figure BDA00036073045800000912
is the reactive power required by the load at node i at time t; l is a radical of an alcoholt,iIf the load switch at the node i at the time t is on or off, the on state is 1, otherwise the on state is 0; r is a radical of hydrogenijRepresents the resistance of line ij; x is the number ofijRepresenting the reactance of line ij.
S5-4: judging SOP port operation mode
In order to ensure that a line which is not connected with an external power grid and is only supported by the voltage provided by the SOP port can have a balance node, the node connected with the SOP port is set as the balance node, the control mode of the corresponding SOP port is V-f control, and the control modes of other SOP ports are P-Q control.
Figure BDA00036073045800000913
Figure BDA0003607304580000101
Figure BDA0003607304580000102
In the formula, fij,tIs another virtual power flow for line ij at time t,
Figure BDA0003607304580000103
and indicating whether the node i with the SOP at the time t is communicated with an external power grid, wherein the communication is 1, and otherwise, the communication is 0.
S5-4: performing second-order cone conversion on the nonlinear part of the power flow model
To ensure that the domain of the variables in the solution process is a convex set, the second order cone relaxation is performed on equation (48) to obtain
Figure BDA0003607304580000104
The original problem can be changed into a mixed integer second-order cone problem by using the formula (52), and a commercial solver can conveniently solve the problem.
Further, the objective function of the interconnected network restoration process of step S6 is as follows:
the objective function contains three parts: and the load unrecovered quantity of the load importance degree, the total action time of the switch in the recovery process, the network loss of the line and the loss of the SOP are taken into consideration.
min:Fobj＝KreFre+KswFsw+KlossFloss (53)
Figure BDA0003607304580000105
Figure BDA0003607304580000106
Figure BDA0003607304580000107
In the formula DiRepresenting the importance of the load of the node i; lambda [ alpha ]ijRepresents the action time of the switch at the line ij; k isre、Ksw、KlossThe weight factors of the load recovery amount, the total switch action time, the line network loss and the SOP loss in the objective function are respectively represented.
The invention comprehensively considers the data information of interconnected power grid structure, line impedance, node load, multi-terminal SOP, DG, fan, photovoltaic and other equipment, constructs a flexible interconnected power grid model with 5-terminal SOP connected with the sub-network, designs new line topology limitation based on the new line tide characteristics of the multi-terminal SOP interconnected power grid, can effectively embody the functions of various equipment in the system in the recovery process, ensures that the power distribution system can have more flexible tide distribution in the recovery process, obtains the optimal recovery strategy, aims to effectively increase the load recovery rate, promotes the high-permeability renewable energy and the distributed power supply of the system to play greater roles in fault recovery, and improves the elasticity and reliability of the system. Under the condition of using the multi-terminal SOP, the calculation complexity is not obviously increased, and higher calculation efficiency is ensured. The beneficial effects of the invention are:
1. the method can fully play the role of various devices such as DG, SOP, capacitor bank and the like in the interconnected power grid and the role of renewable energy in fault recovery.
2. The invention solves the reconstruction problem of the power grid containing the SOP, designs new line topology limitation based on the new line tide characteristic of the multi-terminal SOP interconnected power grid, ensures that a power distribution system can have more flexible tide distribution in the recovery process, and meets the power supply recovery scheme with better effect.
2. The multi-terminal SOP and a new topological mode are introduced, so that the fault recovery speed and the fault recovery capability of the active power distribution network can be improved, the power loss of the power grid is reduced, and the elasticity and the reliability of the system are improved.
Drawings
FIG. 1 is a diagram of a flexible interconnected power distribution system including a multi-terminal SOP of the present invention.
Figure 2 is a power curve over recovery time for a wind turbine and photovoltaic of the present invention.
Fig. 3 is a power curve of the load of the present invention over the recovery time.
Fig. 4 is a schematic diagram of the restoration process of the interconnected network under 6-line fault conditions according to the present invention.
Fig. 5 is a load recovery rate variation curve of the interconnected power grid under the condition of 6 line faults.
Fig. 6 is an active power variation curve of the interconnected grid SOP under a 6-line fault condition according to the present invention.
Fig. 7 is an interconnected network SOP reactive power variation curve under 6 line fault conditions of the present invention.
Fig. 8 is a graph of the variation of the DG output of the interconnected grid in the case of 6 line faults according to the present invention.
Fig. 9 is a schematic diagram of a recovery process of the interconnected power grid under the condition of the equivalent transformer TA fault.
Fig. 10 is a load recovery rate variation curve of the interconnected power grid under the condition of the equivalent transformer TA fault.
Fig. 11 is an SOP active power variation curve of the interconnected network under the equivalent transformer TA fault.
Fig. 12 is an SOP reactive power variation curve of the interconnected network under the equivalent transformer TA fault of the present invention.
Fig. 13 is an active power variation curve of the interconnected grid DG in the case of a fault of the equivalent transformer TA according to the present invention.
Fig. 14 is a schematic diagram of the interconnected grid using tie switches of the present invention.
Fig. 15 is a load recovery rate variation curve during interconnection of the grid under 6 line fault conditions in accordance with the present invention.
Fig. 16 is a load recovery rate variation curve in the process of interconnecting the power grids under the equivalent transformer TA fault.
FIG. 17 is a flow chart of the method of the present invention.
Detailed description of the preferred embodiment
The present invention will be further described with reference to the accompanying drawings.
Referring to fig. 1 to 16, a multi-stage restoration method for a flexible interconnected power distribution system based on multi-terminal SOP establishes a novel topological structure constraint and a multi-stage restoration strategy including a multi-terminal SOP power grid, and the method includes the following steps:
s1: acquiring the position, the number and other conditions of a fault line in the interconnected power distribution network and the line topology information in a normal operation state, and turning to the step S2;
s2: calculating the information of the nodes and lines which lose power supply after fault isolation according to the fault line information, determining the range of the power-losing area, and turning to the step S3;
s3: acquiring output data of renewable energy sources such as fans, photovoltaics and the like in the interconnected power distribution network, corresponding data of loads of all nodes in a required time period, positions of all interconnection switches and disconnecting switches and impedance of corresponding lines, and turning to step S4;
s4: setting the positions and the capacities of all ports of a Distributed Generation (DG), a capacitor bank and a multi-terminal soft Switch (SOP), and establishing models of various devices according to the characteristics and parameters of the DG, the capacitor bank, the multi-terminal SOP and other devices;
s5: based on the equipment model established in the step S4, considering reconstruction and power flow distribution, establishing a line power flow model of the interconnected power grid, and performing second-order cone conversion on the power flow model, thereby establishing a multi-stage mixed integer planning model of the flexible interconnected power distribution system with the multi-terminal SOP;
s6: according to the step information, an objective function of the interconnected power grid recovery process is solved through a solver, a multi-stage recovery strategy of the flexible interconnected power distribution system with the multi-terminal SOP is formulated, and the action condition of each stage of switch and the output condition of each device are determined.
In step S2, determining the range of the power loss region includes the following steps:
s2-1: setting up an objective function with a minimum of power-loss nodes
Figure BDA0003607304580000141
In the formula, NIThe number of nodes of the power distribution network; chi-type food processing machineiThe power-on state of the node i in the fault isolation state is 1 when the node i is powered on, and otherwise the node i is 0.
S2-2: solving the objective function according to the radial power flow constraint to calculate all chiijLines ij and χ of 0iAnd the node i is 0, namely the power-off node and line are obtained.
Figure BDA0003607304580000142
Figure BDA0003607304580000143
Figure BDA0003607304580000144
Figure BDA0003607304580000145
Figure BDA0003607304580000146
In the formula, bijIndicating that node i is a parent node of node j; w is the set of all lines; ΨijIs the virtual power flow through line ij; chi shapeijThe power-on state of the line ij under the fault isolation state is 1 when the line ij is powered on, otherwise, the line ij is 0; m is a sufficiently large number.
In the step S4, establishing models of various devices includes the following steps:
s4-1: modeling capacitor bank
The first time interval is set before fault isolation is recovered, and the recovery process after the first time interval is short, so that the gear positions of the capacitor bank after the nodes are recovered are kept consistent and are not adjusted along with time change. The constraints of the capacitor bank during recovery are as follows:
Figure BDA0003607304580000151
Figure BDA0003607304580000152
Figure BDA0003607304580000153
Figure BDA0003607304580000154
in the formula (I), the compound is shown in the specification,
Figure BDA0003607304580000155
representing the gear of the capacitor bank connected with the node i at the time t;
Figure BDA0003607304580000156
representing the reactive power regulating quantity of each gear of the capacitor bank connected with the node i; xt,iThe power supply state of the node i at the time t is shown, 1 represents power supply, and 0 represents no power supply.
S4-2: establishing a Soft Open Points (SOP) model
The multi-terminal SOP can accurately control the active power flow and the reactive power flow of a power grid at lower operation cost, realize optimal power distribution among connected ports and avoid risks caused by frequent switching operation. The multi-terminal SOP model takes power loss, capacity constraint and power balance into account, and the constraint conditions of the multi-terminal SOP at the moment t are as follows:
Figure BDA0003607304580000157
Figure BDA0003607304580000158
Figure BDA0003607304580000159
in the formula (I), the compound is shown in the specification,
Figure BDA00036073045800001510
respectively representing the active and reactive power of a port m at the moment t;
Figure BDA00036073045800001511
representing the active power loss of the port m at the moment t;
Figure BDA00036073045800001512
represents the apparent power limit of port m; a. themRepresents the power loss coefficient of port m; n is a radical ofvscNumber of ports that is SOP;
s4-3: building a Distributed Generator (DG) model
the constraints of the DG model at the time t are as follows:
Figure BDA0003607304580000161
Figure BDA0003607304580000162
Figure BDA0003607304580000163
Figure BDA0003607304580000164
Figure BDA0003607304580000165
in the formula (I), the compound is shown in the specification,
Figure BDA0003607304580000166
respectively representing the active power output and the reactive power output of DG at a node i at the moment t;
Figure BDA0003607304580000167
representing the energization state of DG at a node i at the time t, wherein the energization state is 1, and otherwise, the energization state is 0;
Figure BDA0003607304580000168
representing the climbing limit power of DG at the node i between every two time periods; p isi DG,min、Pi DG,max、
Figure BDA0003607304580000169
Respectively are the upper limit and the lower limit of DG active power and reactive power at the node i.
Linearizing the constraint in equation (18) yields:
Figure BDA00036073045800001610
in step S5, the establishing of the multi-stage mixed integer programming model of the flexible interconnected power distribution system includes the following steps:
s5-1: establishing a line reconstruction model
The reconstruction process of the power distribution system containing the multi-terminal SOP needs to meet the requirements of the limitation that the line topology has connectivity, no island exists and the normal operation area is not influenced, and the corresponding line topology is constrained as follows:
Figure BDA00036073045800001611
Figure BDA00036073045800001612
Figure BDA00036073045800001613
Figure BDA0003607304580000171
Figure BDA0003607304580000172
Figure BDA0003607304580000173
in the formula, bij,tRepresenting whether the i node is the father node of the j node at the time t, if so, the i node is 1, otherwise, the i node is 0; xij,tRepresenting the power-on state of the circuit at the moment ij, the power-on is 1, otherwise, the power-on is 0.
Furthermore, to ensure that the system can meet the radiometric constraints without connecting the SOP, and that the line can be powered by the SOP with the SOP connected. The SOP port is set as a power supply capable of providing virtual power flow, and traditional single-mode flow (SCF) constraint is added, so that improved virtual power flow constraint is formed.
Figure BDA0003607304580000174
Figure BDA0003607304580000175
Figure BDA0003607304580000176
In the formula, Fij,tIs the virtual power flow of line ij at time t;
Figure BDA0003607304580000177
the virtual power flow is sent by a node i with SOP at the time t;
Figure BDA0003607304580000178
the state is the open state of the SOP port m connected with the node i, the port is opened to 1, otherwise, the port is 0.
S5-2: establishing a multi-stage recovery model
In the research, a single node or a plurality of nodes connected by non-switchable lines form a line block, and the original interconnected power grid is simplified into the interconnected power grid formed by all the lines with remote controllable switches and the line block. Since the line can only be energized when power is supplied to one side of the line, the power supply state of the non-switchable line is the same as the power supply states of all nodes connected thereto, and the switchable line can transmit power requiring at least one node connected thereto to be in a powered state at a previous time. Line energized state Xij,tThe constraints that need to be satisfied are as follows:
Figure BDA0003607304580000181
Figure BDA0003607304580000182
Figure BDA0003607304580000183
in the formula, WSIs a set of disconnectable lines; wLOSSIs a collection of lines within a power loss zone determined by fault isolation.
The constraint of equation (29) may introduce an intermediate variable aij,tLinearized with the constraints as follows
aij,t≤Xt-1,i+Xt-1,j (32)
aij,t≥Xt-1,i (33)
aij,t≥Xt-1,j (34)
Xij,t≤aij,t (35)
S5-3: establishing a line flow model
The Distflow power flow model suitable for the radial power distribution system is improved, a load switch for controlling the on-off of the load is added, and the Distflow power flow model suitable for the research is obtained as follows. Introduction of
Figure BDA0003607304580000184
And performing equivalent transformation, and relaxing power, current and voltage constraints to ensure that the active power, reactive power and line current of the disconnected branch are zero and no constraint is applied to the closed branch.
Figure BDA0003607304580000185
Figure BDA0003607304580000186
Figure BDA0003607304580000187
Figure BDA0003607304580000188
Figure BDA0003607304580000191
Figure BDA0003607304580000192
Figure BDA0003607304580000193
In the formula (I), the compound is shown in the specification,
Figure BDA0003607304580000194
the square of the voltage of the node i at the time t;
Figure BDA0003607304580000195
is the square of the line ij current at time t; u shapestdIs the reference voltage of the power grid; I.C. AmaxRepresents the maximum current that the line can pass; pij,tThe active power transmitted for the line ij at time t; qij,tThe reactive power transmitted for line ij at time t.
The translated power flow constraints are as follows:
Figure BDA0003607304580000196
Figure BDA0003607304580000197
Figure BDA0003607304580000198
Figure BDA0003607304580000199
Figure BDA00036073045800001910
Figure BDA00036073045800001911
in the formula, Pt,iIs the active power difference of the node i at time t; qt,iIs the reactive power difference at node i at time t;
Figure BDA00036073045800001912
is the active power generated by the photovoltaic at the node i at time t;
Figure BDA00036073045800001913
is the reactive power generated by the photovoltaic at the node i at the time t;
Figure BDA00036073045800001914
is the active power generated by the fan at the node i at the moment t;
Figure BDA00036073045800001915
is the reactive power generated by the fan at the node i at the moment t;
Figure BDA00036073045800001916
is the active power required by the load at node i at time t;
Figure BDA00036073045800001917
is the reactive power required by the load at the node i at time t; l ist,iIf the load switch at the node i at the time t is on or off, the on state is 1, otherwise the on state is 0; r is a radical of hydrogenijRepresents the resistance of line ij; x is a radical of a fluorine atomijRepresenting the reactance of line ij.
S5-4: judging SOP port operation mode
In order to ensure that a line which is not connected with an external power grid and is only supported by the voltage provided by the SOP port can have a balanced node, the node connected with the SOP port is set as the balanced node, the control mode of the corresponding SOP port is V-f control, and the control modes of other SOP ports are P-Q control.
Figure BDA0003607304580000201
Figure BDA0003607304580000202
Figure BDA0003607304580000203
In the formula, fij,tIs another virtual power flow for line ij at time t,
Figure BDA0003607304580000204
and indicating whether the node i with the SOP at the time t is communicated with an external power grid, wherein the communication is 1, and otherwise, the communication is 0.
S5-4: performing second-order cone conversion on the nonlinear part of the power flow model
In order to ensure that the definition domain of the variable in the solving process is a convex set, performing second-order cone relaxation on the formula (48) to obtain
Figure BDA0003607304580000205
The original problem can be changed into a mixed integer second order cone problem by using the formula (52), and a commercial solver can be used for solving the problem conveniently.
Further, the objective function of the interconnected grid restoration process of step S6 is as follows:
the objective function contains three parts: and the load unrecovered quantity of the load importance degree, the total action time of the switch in the recovery process, the network loss of the line and the loss of the SOP are taken into consideration.
min:Fobj＝KreFre+KswFsw+KlossFloss (53)
Figure BDA0003607304580000211
Figure BDA0003607304580000212
Figure BDA0003607304580000213
In the formula, DiRepresenting the importance of the load of the node i; lambda [ alpha ]ijRepresents the action time of the switch at the line ij; k isre、Ksw、KlossThe weight factors of the load recovery amount, the total switch action time, the line network loss and the SOP loss in the objective function are respectively represented.
To enable those skilled in the art to better understand the present invention, an exemplary analysis includes the following components:
first, description of examples and analysis of simulation results
The invention takes an interconnected power grid system with 5-end SOPs connected with an IEEE33 node system and an IEEE69 node system as an example, and verifies the effectiveness and the correctness of multi-stage recovery software of a multi-end SOP flexible interconnected power distribution system. The simulation is solved by adopting a tool box YALMIP and a commercial solver GUROBI under the MATLAB environment, and the time for research is from 9: 00 begins, for a total of 7 time periods, with a time interval of 1.2 minutes.
The network topology structure of the power distribution system with the multi-terminal SOP flexible interconnection is shown in figure 1. Typical fan and photovoltaic output power of a flexible interconnected power distribution system in a day is shown in fig. 2, and the active and reactive load conditions are shown in fig. 3. The system comprises a system reference voltage 12.66KV, a reference capacity 1MVA, a voltage safety range 0.95-1.05p.u., a 5-end SOP with a capacity 2MVA at each end, a loss coefficient 0.02, a remote controllable interconnection switch 101 and 108, wherein the remote controllable disconnection switches are respectively arranged on lines of 8, 11, 14, 19, 27, 35, 44, 50, 58, 66, 70, 74, 76, 82, 88, 95 and 98, a total number of 3 distributed power supplies (DG) and a maximum power of 2.8MW, 1 time period is set for supplying proper voltage from a node connected with the DG to the restoration power supply of the distributed power supplies, and the climbing power is limited to 0.5 MW/time period. In addition, the system also has 4 photovoltaic power supplies and 3 wind power supplies, and the specific parameters are shown in table 1.
TABLE 1 distributed power supply, blower, photovoltaic parameter table
Figure BDA0003607304580000221
The validity of the method of the invention is first verified in two typical failure cases.
(1) Line fault 73, 95, 22, 37, 43, 58
The on-off condition of the line controllable switch in the fault recovery process is shown in table 2, the corresponding internet recovery process is shown in fig. 4, the recovery rate change is shown in fig. 5, and the active power, the reactive power and the active output change of the DG of each port of the SOP are shown in fig. 6-8. It can be seen that the entire grid has only 36.78% of the load left after fault isolation, and that 94.88% of the load has been restored over 4 periods, leaving only the load at node 38 unrecovered. After recovery, the SOP port 2 is the main power supply for the power loss zone, and other ports supply power to the SOP zone through SOPs.
On-off condition of the controllable switch of the interconnected network line under the condition of 26 line fault meters
Figure BDA0003607304580000222
(2) Line 1 fault (equivalent transformer TA outlet fault)
The on-off condition of the line controllable switch in the fault recovery process is shown in table 3, the corresponding internet recovery process is shown in fig. 9, the recovery rate change is shown in fig. 10, and the active and reactive power of each port of the SOP and the active output change of the DG are shown in fig. 11-13. It can be seen that 49.42% of the load of the whole power grid after fault isolation recovers 100% of the load after 4 periods, and the power supply is completely recovered. In the recovery process, 3 SOP ports at the 69-node subnet supply power to the power-off area, and 2 ports at the 33-node subnet supply power to the SOP.
TABLE 3 on-off condition of controllable switch of interconnected network line under TA fault of equivalent transformer
Figure BDA0003607304580000231
To verify the effectiveness of the method of the invention, a comparative study was carried out with two other modes:
mode 1: separate IEEE33 node models and IEEE69 node models, i.e., models in which no energy flows between two subnets, are used.
Mode 2: a model of tie switch connection using the IEEE33 node model and the IEEE69 node model is adopted, as shown in fig. 14.
Mode 3: the invention provides a sequence recovery scheduling model of a flexible interconnection power distribution system based on multi-terminal SOP.
Under the 73 rd, 95 th, 22 th, 37 th, 43 th and 58 th line fault conditions, the load recovery rate changes in the fault recovery process of the three model schemes are shown in fig. 15. Under the condition of the 1 st line fault (fault at the outlet of the equivalent transformer TA), the load recovery rate changes in the fault recovery process of the three model schemes are shown in fig. 16.
Under three schemes and two fault conditions, the complexity of a multi-stage recovery model of the flexible interconnected power distribution system based on the multi-terminal SOP and the running time of the flexible interconnected power distribution system on an Intel (R) core (TM) i7-8700@3.2GHz computer are shown in a table 4.
TABLE 4 three schemes, correlation calculation data under two fault conditions
Figure BDA0003607304580000241
In conclusion, the flexible interconnection power distribution system sequence recovery software based on the multi-terminal SOP can effectively embody the functions of various devices in the system in the recovery process, ensure that the power distribution system can have more flexible power flow distribution in the recovery process so as to meet a power supply recovery scheme with better effect, meet the recovery requirement under the condition of complex fault, clearly give detailed recovery steps of multiple stages after the fault, and under the condition of using the multi-terminal SOP, the calculation complexity is not obviously increased, the calculation efficiency is higher, and the prediction time can meet the actual calculation requirement.
In the description of the present specification, the schematic representations of the invention do not necessarily refer to the same embodiment or example, and those skilled in the art may combine and combine different embodiments or examples described in this specification. Furthermore, the implementation of the additional content described in the present description is only a list of implementation forms of the inventive concept, and the scope of protection of the present invention should not be considered as being limited to the specific forms set forth in the implementation examples, but also includes equivalent technical means as can be conceived by one skilled in the art according to the inventive concept.

Claims (5)

1. A multi-stage recovery method of a flexible interconnected power distribution system based on multi-terminal SOP is characterized by comprising the following steps:
s1: acquiring the position, the number and other conditions of a fault line in the interconnected power distribution network and the line topology information in a normal operation state, and turning to the step S2;
s2: calculating the information of the nodes and lines which lose power supply after fault isolation according to the fault line information, determining the range of the power-losing area, and turning to the step S3;
s3: acquiring output data of renewable energy sources such as a fan photovoltaic and the like in the interconnected power distribution network, corresponding data of loads of all nodes in a required time period, positions of all interconnection switches and breaking switches and impedance of corresponding lines, and turning to step S4;
s4: setting the positions and the capacities of all ports of a Distributed Generation (DG), a capacitor bank and a multi-terminal soft Switch (SOP), and establishing models of various devices according to the characteristics and parameters of the DG, the capacitor bank, the multi-terminal SOP and other devices;
s5: based on the equipment model established in the step S4, considering reconstruction and power flow distribution, establishing a line power flow model of the interconnected power grid, and performing second-order cone conversion on the power flow model, thereby establishing a multi-stage mixed integer planning model of the flexible interconnected power distribution system with the multi-terminal SOP;
s6: according to the information of the steps, an objective function of the interconnected power grid recovery process is solved through a solver, a multi-stage recovery strategy of the flexible interconnected power distribution system with the multi-terminal SOP is formulated, and the action condition of a switch at each stage and the output condition of each device are determined.
2. The multi-stage restoration method for the flexible interconnected power distribution system based on multi-terminal SOP of claim 1, wherein the determining the range of the power loss region in step S2 specifically comprises:
s2-1: establishing a target function with the least power-loss nodes;
Figure FDA0003607304570000021
in the formula, NIThe number of nodes of the power distribution network; chi-type food processing machineiThe power-on state of the node i in the fault isolation state is 1 when the node i is powered on, and otherwise the power-on state is 0;
s2-2: solving the objective function according to the radial power flow constraint to calculate all chiijLines ij and χ of 0iThe node i is 0, namely a power-off node and a power-off line are obtained;
Figure FDA0003607304570000022
Figure FDA0003607304570000023
Figure FDA0003607304570000024
Figure FDA0003607304570000025
Figure FDA0003607304570000026
in the formula, bijIndicating that node i is a parent node of node j; w is the set of all wires; ΨijIs the virtual power flow through line ij; chi shapeijThe power-on state of the line ij in the fault isolation state is 1 when the line ij is powered on, otherwise, the line ij is 0; m is a sufficiently large number.
3. The multi-stage recovery method for the multi-terminal SOP flexible interconnected power distribution system according to claim 1 or 2, wherein the step S4 of establishing a model of each type of equipment specifically comprises:
s4-1: establishing a capacitor bank model;
setting a first time interval before recovery after fault isolation, wherein the recovery process after the first time interval is short, and the gears of the capacitor bank after the nodes are recovered are kept consistent and are not adjusted along with time change; the constraints of the capacitor bank during recovery are as follows:
Figure FDA0003607304570000031
Figure FDA0003607304570000032
Figure FDA0003607304570000033
Figure FDA0003607304570000034
in the formula (I), the compound is shown in the specification,
Figure FDA0003607304570000035
representing the gear of the capacitor bank connected with the node i at the moment t;
Figure FDA0003607304570000036
representing the reactive power regulating quantity of each gear of the capacitor bank connected with the node i; xt,iThe power supply state of the node i at the time t is represented, wherein 1 represents power supply, and 0 represents no power supply;
s4-2: establishing a multi-terminal Soft Switch (SOP) model;
the multi-terminal SOP can accurately control the active power flow and the reactive power flow of a power grid at lower operation cost, realize optimal power distribution among connected ports and avoid risks caused by frequent switching operation; the multi-terminal SOP model takes power loss, capacity constraint and power balance into account, and the constraint conditions of the multi-terminal SOP at the moment t are as follows:
Figure FDA0003607304570000037
Figure FDA0003607304570000038
Figure FDA0003607304570000039
in the formula (I), the compound is shown in the specification,
Figure FDA00036073045700000310
respectively representing the active power and the reactive power of a port m at the moment t;
Figure FDA00036073045700000311
representing the active power loss of the port m at the moment t;
Figure FDA00036073045700000312
represents the apparent power limit of port m; a. themRepresents the power loss coefficient of port m; n is a radical ofvscNumber of ports that is SOP;
s4-3: establishing a Distributed Generator (DG) model;
the constraint conditions of the DG model at the time t are as follows:
Figure FDA00036073045700000313
Figure FDA0003607304570000041
Figure FDA0003607304570000042
Figure FDA0003607304570000043
Figure FDA0003607304570000044
in the formula (I), the compound is shown in the specification,
Figure FDA0003607304570000045
respectively represents the active sum of DGs at the node i at the time tOutputting reactive power;
Figure FDA0003607304570000046
representing the power-on state of the DG at the node i at the time t, wherein the power-on state is 1, and otherwise, the power-on state is 0; a. thei DGRepresenting the climbing limit power of DG at the node i between every two time periods; pi DG,min、Pi DG,max、Qi DG,min、Qi DG,maxRespectively representing the upper limit and the lower limit of the DG active power and the reactive power at the node i;
linearizing the constraint in equation (18) yields:
Figure FDA0003607304570000047
4. the multi-stage recovery method for the flexible interconnected power distribution system of the multi-terminal SOP according to claim 1 or 2, wherein the multi-stage mixed integer programming model building of the flexible interconnected power distribution system of the step S5 comprises the following steps:
s5-1: establishing a line reconstruction model;
the reconstruction process of the power distribution system containing the multi-terminal SOP needs to meet the requirements of the limitation that the line topology has connectivity, no island exists and the normal operation area is not influenced, and the corresponding line topology is constrained as follows:
Figure FDA0003607304570000048
Figure FDA0003607304570000049
Figure FDA00036073045700000410
Figure FDA00036073045700000411
Figure FDA0003607304570000051
Figure FDA0003607304570000052
in the formula, bij,tRepresenting whether the i node is the father node of the j node at the time t, if so, the i node is 1, otherwise, the i node is 0; xij,tRepresenting the power-on state of the ij line at the time t, wherein the power-on state is 1, and otherwise, the power-on state is 0;
furthermore, in order to ensure that the system can meet the radiometric constraints without connecting the SOP, and that the line can be powered by the SOP with the SOP connected; the SOP port is set as a power supply capable of providing virtual power flow, and traditional single-mode power flow (SCF) constraint is added to form improved virtual power flow constraint;
Figure FDA0003607304570000053
Figure FDA0003607304570000054
Figure FDA0003607304570000055
in the formula, Fij,tIs the virtual power flow of line ij at time t;
Figure FDA0003607304570000056
the virtual power flow is sent by a node i with SOP at the time t;
Figure FDA0003607304570000057
the state is the opening state of an SOP port m connected with a node i, the opening state of the port is 1, otherwise, the state is 0;
s5-2: establishing a multi-stage recovery model;
a single node or a plurality of nodes connected by non-switchable lines form a line block, and the original interconnected power grid is simplified into the interconnected power grid formed by all the lines with remote controllable switches and the line block; because the line can be electrified when power is supplied to one side of the line, the power supply state of the non-switchable line is the same as the power supply state of all nodes connected with the non-switchable line, and the switchable line can transmit power in a state that at least one node connected with the switchable line is powered at the previous moment; line energized state Xij,tThe constraints that need to be satisfied are as follows:
Figure FDA0003607304570000061
Figure FDA0003607304570000062
Figure FDA0003607304570000063
in the formula, WSIs a set of disconnectable lines; wLOSSIs a set of lines in a power-off area determined by fault isolation;
the constraint of equation (29) may introduce an intermediate variable aij,tLinearized with the constraints as follows
aij,t≤Xt-1,i+Xt-1,j (32)
aij,t≥Xt-1,i (33)
aij,t≥Xt-1,j (34)
Xij,t≤aij,t (35)
S5-3: establishing a line power flow model;
the Distflow power flow model suitable for the radial power distribution system is improved, and a load switch for controlling the on-off of the load is added to obtain the following Distflow power flow model; distflow power flow model introduction
Figure FDA0003607304570000064
Performing equivalent transformation, and relaxing power, current and voltage constraints to ensure that the active power, reactive power and line current of the disconnected branch are zero and no constraint is applied to the closed branch;
Figure FDA0003607304570000065
Figure FDA0003607304570000066
Figure FDA0003607304570000067
Figure FDA0003607304570000068
Figure FDA0003607304570000069
Figure FDA0003607304570000071
Figure FDA0003607304570000072
in the formula (I), the compound is shown in the specification,
Figure FDA0003607304570000073
is the square of the voltage of the node i at the time t;
Figure FDA0003607304570000074
the square of the line ij current at time t; u shapestdIs the reference voltage of the power grid; I.C. AmaxRepresents the maximum current that the line can pass; pij,tThe active power transmitted for line ij at time t; qij,tThe reactive power transmitted for the line ij at the time t;
the translated power flow constraints are as follows:
Figure FDA0003607304570000075
Figure FDA0003607304570000076
Figure FDA0003607304570000077
Figure FDA0003607304570000078
Figure FDA0003607304570000079
Figure FDA00036073045700000710
in the formula, Pt,iIs the active power of node i at time tA difference; qt,iIs the reactive power difference at node i at time t;
Figure FDA00036073045700000711
is the active power generated by the photovoltaic at the node i at time t;
Figure FDA00036073045700000712
is the reactive power generated by the photovoltaic at the node i at time t;
Figure FDA00036073045700000713
is the active power generated by the fan at the node i at the moment t;
Figure FDA00036073045700000714
is the reactive power emitted by the fan at the node i at the time t;
Figure FDA00036073045700000715
is the active power required by the load at node i at time t;
Figure FDA00036073045700000716
is the reactive power required by the load at node i at time t; l ist,iIf the load switch at the node i at the time t is on or off, the on state is 1, otherwise the on state is 0; r isijRepresents the resistance of line ij; x is the number ofijRepresents the reactance of line ij;
s5-4: judging the operation mode of the SOP port;
in order to ensure that a line which is not connected with an external power grid and is only supported by voltage provided by an SOP port can have a balance node, the node connected with the SOP port is set as the balance node, the control mode corresponding to the SOP port is V-f control, and the control modes of other SOP ports are P-Q control;
Figure FDA0003607304570000081
Figure FDA0003607304570000082
Figure FDA0003607304570000083
in the formula (f)ij,tIs another virtual power flow for line ij at time t,
Figure FDA0003607304570000084
indicating whether a node i with SOP at the time t is communicated with an external power grid, wherein the communication is 1, and otherwise, the communication is 0;
s5-4: performing second-order cone conversion on the nonlinear part of the power flow model;
in order to ensure that the definition domain of the variable in the solving process is a convex set, performing second-order cone relaxation on the formula (48) to obtain
Figure FDA0003607304570000085
The original problem can be changed into a mixed integer second-order cone problem by using the formula (52), and a commercial solver can conveniently solve the problem.
5. The multi-stage restoration method for the flexible interconnected power distribution system of multi-terminal SOP according to claim 1 or 2, wherein the objective function of the interconnected network restoration process of the step S6 is as follows:
the model objective function contains three parts: load unrecoverable quantity of the load importance degree, total action time of a switch in the recovery process, network loss of a line and loss of an SOP are calculated;
min:Fobj＝KreFre+KswFsw+KlossFloss (53)
Figure FDA0003607304570000091
Figure FDA0003607304570000092
Figure FDA0003607304570000093
in the formula DiRepresenting the importance of the load of the node i; lambda [ alpha ]ijRepresenting the action time of the switch at the line ij; kre、Ksw、KlossThe load recovery amount, the total switch action time, the line network loss and the SOP loss are respectively represented as weight factors in an objective function.
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