CN110350508B - Method for constructing unified fault recovery model of active power distribution network - Google Patents

Method for constructing unified fault recovery model of active power distribution network Download PDF

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CN110350508B
CN110350508B CN201910406777.0A CN201910406777A CN110350508B CN 110350508 B CN110350508 B CN 110350508B CN 201910406777 A CN201910406777 A CN 201910406777A CN 110350508 B CN110350508 B CN 110350508B
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load
representing
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CN110350508A (en
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汤一达
顾伟
盛万兴
吴志
宋晓辉
高菲
赵毅
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Southeast University
China Electric Power Research Institute Co Ltd CEPRI
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China Electric Power Research Institute Co Ltd CEPRI
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/12—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load
    • H02J3/14—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load by switching loads on to, or off from, network, e.g. progressively balanced loading
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • 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]
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/388—Islanding, i.e. disconnection of local power supply from the network
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A30/00—Adapting or protecting infrastructure or their operation
    • Y02A30/60—Planning or developing urban green infrastructure
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
    • Y02B70/00—Technologies for an efficient end-user side electric power management and consumption
    • Y02B70/30—Systems integrating technologies related to power network operation and communication or information technologies for improving the carbon footprint of the management of residential or tertiary loads, i.e. smart grids as climate change mitigation technology in the buildings sector, including also the last stages of power distribution and the control, monitoring or operating management systems at local level
    • Y02B70/3225—Demand response systems, e.g. load shedding, peak shaving
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S20/00—Management or operation of end-user stationary applications or the last stages of power distribution; Controlling, monitoring or operating thereof
    • Y04S20/20—End-user application control systems
    • Y04S20/222—Demand response systems, e.g. load shedding, peak shaving

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Abstract

The invention discloses a method for recovering a unified model of a fault of an active power distribution network by simultaneously considering reconstruction and islanding, which comprises the following steps: 1) acquiring power grid fault information and power distribution network information, and summarizing data required by model building; 2) determining an objective function of a fault recovery operation strategy; 3) constructing a unified mathematical model which comprises DistFlow power flow constraint and connectivity constraint using virtual power flow and comprises reconstruction and island division; 4) and solving the established unified mathematical model containing reconstruction and island division to obtain a final active power distribution network fault recovery operation strategy. The power distribution network fault recovery operation strategy simultaneously considers two strategies of network fault reconstruction and island division, considers controllability of load and distributed power supply output, and compared with the traditional power distribution network fault recovery, the fault recovery strategy is enabled to cover more possibilities in an optimized mode, the problem is converted into mixed integer linear programming, strategy generation time is saved, and the optimal solution can be obtained more accurately.

Description

Method for constructing unified fault recovery model of active power distribution network
Technical Field
The invention relates to a method for constructing a unified fault recovery model of an active power distribution network, and belongs to the field of operation and planning of the power distribution network.
Background
Nowadays, due to the access of distributed power sources and the popularization of flexible loads, a power distribution network is developed to a more controllable, more variable and more complex network, and students are also prompted to improve the fault recovery operation strategy of the traditional power distribution network. Meanwhile, after a subsequent line is automatically split when a network fault occurs, the peripheral load is driven by using the black start function of the distributed power supply, so that partial load is restored to power supply, namely, island division optimization. In the aspect of a model, active power distribution network fault reconstruction and island division are brought into a unified mathematical model for solving, and compared with the existing research, the integrated model is divided into two layers of operation, so that the optimal solution is easier to obtain.
In terms of the algorithm, for island division, a learner uses a knapsack Tree (TKP) tree algorithm and adds island fusion judgment after calculation is finished, island fusion is carried out after optimization by the method, the optimization result is modified, and the optimization result is determined to be influenced. However, the scholars use the mixed integer second-order cone programming, but set the island number as the number of the distributed power supplies, namely island fusion is not considered, and further optimization of the strategy is also limited. The invention solves the problem by adopting the radial constraint and the connectivity constraint suitable for the island division, establishes a unified model solution by using mixed integer second-order cone programming, is easier to obtain an optimal solution, and can save a power distribution network fault recovery operation strategy.
Disclosure of Invention
The invention aims to solve the problems and provides a method for constructing a fault recovery unified model of an active power distribution network.
In order to achieve the purpose, the method adopted by the invention is as follows: a method for constructing a unified fault recovery model of an active power distribution network comprises the following steps:
step 1) acquiring power grid fault information, a network topology structure, distribution network branches, a distributed power supply and switch state information, predicting load and fault time required by a fault period, and summarizing data required by model building;
step 2) determining a target function of a fault recovery operation strategy, considering the economy of a power grid, considering multi-period load shedding cost, considering the switch operation cost, and considering the load shedding cost and the weight grade of the load;
step 3) constructing a unified mathematical model containing reconstruction and island division, wherein the unified mathematical model contains DistFlow power flow constraint and connectivity constraint using virtual power flow;
and 4) solving the established unified mathematical model containing reconstruction and island division, and obtaining a final active power distribution network fault recovery operation strategy.
Preferably, in step 1), the input fault time period fault information is discretized, the fault time period is divided into n time intervals, and the corresponding predicted load is discretized in the same time scale, so as to prepare for establishing a multi-time-period dynamic unified mathematical model including reconstruction and island division.
Preferably, in step 2), the objective function of the fail-back operation strategy is determined by considering the load shedding cost and the weight level of the load while considering the load shedding cost, with the main objective of minimizing the load shedding amount and considering the switch operation cost. To ensure that the node load shedding amount is minimum, namely the recovery load amount is maximum, the predicted load is set as a constant, the load shedding amount of each node is set as an optimized variable, and meanwhile, the on-off state of a switch is set as a variable from 0 to 1, wherein 0 represents that the switch is off, and 1 represents that the switch is on. The target function considers the whole fault time interval, and the target function expression of the fault recovery operation strategy is as follows:
Figure GDA0002758793340000021
wherein, CopeRepresents the total cost, cloadRepresenting the load shedding cost factor, NTRepresenting the total number of time intervals of the fault period, NbusRepresenting the total number of nodes in the network, at representing the length of each time interval of the fault period,
Figure GDA0002758793340000022
represents t time period, i node load shedding amount, lambdaiThe load weight of the ith node is obtained; c. CswitchRepresents a switch operation cost coefficient, and is an optimized variable of 0-1, alphapRepresenting the fault recovery of the No. p branchThe switch state of the complex time interval is 0-1 constant,
Figure GDA0002758793340000023
representing the switching state before fault in branch No. p, NlineRepresenting the total number of branches in the network.
Preferably, in step 3), the constraint condition of the established unified mathematical model including reconstruction and islanding is as follows:
the method comprises the following steps of firstly, DistFlow power flow constraint, writing out a state equation of a system by taking active power, reactive power and a node voltage square as state variables of the system, and expressing the state equation as a constraint condition form. Considering the change of the patent in the aspect of network topology structure change during reconstruction and island division, a large M method is used for correction to obtain a corresponding node active power balance equation and a node reactive power balance equation:
Figure GDA0002758793340000024
Figure GDA0002758793340000025
wherein, the flow of the initial node to the final node in the branch information is specified to be a positive direction,
Figure GDA0002758793340000026
represents the sum of the active power injected by the j node in the t period,
Figure GDA0002758793340000027
representing the sum of the outgoing active power,
Figure GDA0002758793340000028
representing the sum of the active line losses injected into the j node line at time t,
Figure GDA0002758793340000029
representing lines with i node as the starting node and j node as the end node during t periodThe square term of the line current is,
Figure GDA00027587933400000210
the j node predicts the active load representing the t period,
Figure GDA00027587933400000211
represents the sum of all DG active power output of j nodes in the period t,
Figure GDA00027587933400000212
representing the j node active load shedding amount in the t period,
Figure GDA00027587933400000213
representing the sum of the reactive power injected at node j during time t,
Figure GDA00027587933400000214
representing the sum of the reactive power flowing out,
Figure GDA00027587933400000215
representing the sum of the reactive line losses injected into the j node line at time t,
Figure GDA00027587933400000216
the reactive load is predicted at node j on behalf of time t,
Figure GDA0002758793340000031
represents the sum of all DG reactive power outputs of j nodes in the t period,
Figure GDA0002758793340000032
representing the reactive load throwing amount of the j node in the t period;
and a line pressure drop equilibrium equation, the following equation constraints and model conversion processing being applicable to any time period t, for each branch of each time period:
Figure GDA0002758793340000033
wherein M represents a value of largeThe constant number is a constant number,
Figure GDA0002758793340000034
represents the square term of the voltage of the node i in the time period t (to eliminate the square term and achieve the linearization effect),
Figure GDA0002758793340000035
representing the opening and closing condition of a branch circuit with an i node as a starting node and a j node as a tail node in a period t, wherein 0 or 1 represents that the circuit is opened, and 1 represents that the circuit is closed;
and secondly, limiting the branch power, wherein the rated capacity of the line transmission power needs to be considered in the topology changing process because the line transmission power of the actual power distribution network is limited. Secondly, the branch circuit state of opening and shutting decides whether line power can circulate, and when the branch circuit disconnection, branch circuit transmission power should be clamped as zero:
Figure GDA0002758793340000036
Figure GDA0002758793340000037
wherein,
Figure GDA0002758793340000038
the active power and the reactive power circulating on the circuit in the time period t of the branch with i as the starting node and j as the last node are respectively represented, and the equation (6) restricts the circulating condition of the circuit by using a large M method, wherein M is a large number.
Node voltage quota restraint, need guarantee that electric wire netting node voltage is within the safety interval in the active power distribution network fault recovery period, voltage deviation does not exceed k% promptly, and general k gets 5 ~ 10:
Figure GDA0002758793340000039
wherein,
Figure GDA00027587933400000310
a square term representing a rated voltage of the load node;
and fourthly, DG capacity constraint, wherein the output of the distributed power supply connected into the power distribution network needs to be within a rated interval:
Figure GDA00027587933400000311
wherein,
Figure GDA00027587933400000312
respectively representing the square terms of the active power and the reactive power output of the W-number distributed power supply in the t time period, S2 max DGSquare term representing rated capacity of load node, NDGRepresenting the total number of distributed power supplies;
current amplitude constraint, wherein the current of the line in each time period in the fault is required to be within a rated range, so that the current amplitude constraint is newly increased:
Figure GDA0002758793340000041
wherein,
Figure GDA0002758793340000042
in the time period t, the square term of the current flowing through the line with i as a starting node and j as a final node is given;
sixthly, relaxing the secondary constraint into conical constraint:
Figure GDA0002758793340000043
radial and connectivity constraints are generated, in the process of dynamic reconfiguration and island division of a distribution network, a network structure needs to be kept radial, a virtual power flow model is built herein to standardize active power distribution network fault reconfiguration, the island division exists in an active power distribution network fault recovery optimization model, so that the distribution network is possibly divided into a plurality of areas, the number of root nodes is uncertain, the root nodes can be a transformer substation or a distributed power supply, the number of islands is also a part of optimization, the traditional radial and connectivity constraints cannot well adapt to the model built herein, and therefore the radiating and connectivity constraints of the island division suitable for the mixed integer second-order cone model are innovatively set herein:
Figure GDA0002758793340000044
Figure GDA0002758793340000045
Figure GDA0002758793340000046
wherein N isDGIs the total DG number, NsubIs the total number of substations, CqSelecting a variable for the root node, wherein the root node can be a DG (distributed generation) or a transformer substation for the 0-1 variable, and when the value of the variable C corresponding to the DG or the transformer substation is 1, the DG or the transformer substation is shown as the root node of one partition area, then
Figure GDA0002758793340000047
The number of main nets additionally arranged outside the island is the number of the divided areas; a is one NlineLine, NDG+NsubThe 0-1 of the column optimizes the variable matrix.
Let NDG+Nsub＝NrootThen in the active power distribution network fault recovery strategy, at most N occursrootA divided area including divided islands and main area left after division, Apq1 denotes a node for which the p-th node is selected as the q-th partition (q-th column), and if the distributed power supply is not selected as the root node of the partition, the corresponding C variable is set to zeroG corresponds to a node within the partition, i.e. a DG that is not selected does not partition out the partition. The expression (13) indicates that each node of the grid participating in the islanding optimization belongs to one and only one partition area. Equation (14) ensures that the root node corresponding to each partition is selected.
Therefore, in order to ensure radial constraint, namely, in the island division of the power grid, the number of the nodes of the power distribution network minus the number of the divided areas minus the number of the isolated nodes needs to be equal to the number of the running branches:
Figure GDA0002758793340000051
wherein,
Figure GDA0002758793340000052
the number of main nets added outside the island; in the step a, columns with all zeros are removed, each column represents a partition area, so that connectivity in the area needs to be ensured during optimization, nodes in each partition area need to be connected with each other after the topology structure is changed, at this time, a model of "virtual power flow" is used to determine connectivity in an island, the load of a selected node in each partition area is set to be 1, power is injected from a root node, and if the connectivity in the partition area can be proved (a virtual power balance equation is satisfied):
Figure GDA0002758793340000053
wherein,
Figure GDA0002758793340000054
for the virtual contribution of the root node (distributed power source),
Figure GDA0002758793340000055
the line virtual power of i as the starting node and j as the end node,
Figure GDA0002758793340000056
being k nodesAnd (4) virtual load. Compared with the common power flow, the virtual power flow greatly reduces the calculation amount and is more efficient.
The load shedding constraint is characterized in that loads in the active power distribution network can be divided into uncontrollable loads and controllable loads (flexible loads), the load shedding amount of the controllable loads is controllable, the uncontrollable loads have only two conditions, one is to shed all loads of the node, the other is not to execute the load shedding operation, and the load shedding amount has the following constraint requirements:
Figure GDA0002758793340000057
Figure GDA0002758793340000058
wherein, the subscript c represents the controllable load, the formula (16) is the load shedding constraint of the controllable load, the subscript uc represents the uncontrollable load, the formula (17) represents the load shedding constraint of the uncontrollable load, and z is a variable of 0-1.
As the optimization of the invention, the Mixed Integer Second Order Cone Problem (MISOCP) is solved, and an optimization result is obtained, so as to obtain a strategy for recovering unified operation according to dynamic information, network topology operation, DG output and load shedding in a fault time period, namely a fault recovery unified operation strategy of the active power distribution network.
Has the advantages that:
the method simultaneously considers two strategies of network fault reconstruction and island division, considers the controllability of load and distributed power supply output, enables the fault recovery strategy to be optimized and cover more possibilities compared with the traditional power distribution network fault recovery, converts the problem into mixed integer linear programming, saves the strategy generation time, and can more accurately obtain the optimal solution.
Detailed Description
The technical solution of the present invention is further described in detail with reference to the following specific embodiments.
The invention discloses a method for constructing a fault recovery unified model of an active power distribution network, which comprises the following steps of: the method comprises the following steps:
step 1) acquiring power grid fault information, a network topology structure, distribution network branches, a distributed power supply and switch state information, predicting load and fault time required in a fault period, and summarizing data required by model building. Discretizing the input fault information in the fault time interval, dividing the fault time interval into n time intervals, discretizing the corresponding predicted load in the same time scale and preparing for establishing a multi-time-interval dynamic reconstruction and island division model.
And 2) determining a target function of a fault recovery operation strategy, considering the economy of a power grid, considering multi-period load shedding cost, considering the switch operation cost, and considering the load shedding cost and the weight grade of the load.
And determining an objective function of the fault recovery operation strategy by taking the minimum load shedding amount as a main target and considering the switch operation cost, and considering the load shedding cost and the weight grade of the load. To ensure that the node load shedding amount is minimum, namely the recovery load amount is maximum, the predicted load is set as a constant, the load shedding amount of each node is set as an optimized variable, and meanwhile, the on-off state of a switch is set as a variable from 0 to 1, wherein 0 represents that the switch is off, and 1 represents that the switch is on. The target function considers the whole fault time interval, and the target function expression of the fault recovery operation strategy is as follows:
Figure GDA0002758793340000061
wherein, CopeRepresents the total cost, cloadRepresenting the load shedding cost factor, NTRepresenting the total number of time intervals of the fault period, NbusRepresenting the total number of nodes in the network, at representing the length of each time interval of the fault period,
Figure GDA0002758793340000062
represents t time period, i node load shedding amount, lambdaiThe load weight of the ith node is obtained; c. CswitchRepresentative switch operating asThe coefficient, an optimization variable, alpha, of 0 to 1uThe switch state representing the fault recovery period of the u-th branch is a constant of 01,
Figure GDA0002758793340000063
representing the switching state before fault in branch u, NlineRepresenting the total number of branches in the network.
Step 3) constructing a unified mathematical model containing reconstruction and island division, wherein the unified mathematical model contains DistFlow power flow constraint and connectivity constraint using virtual power flow; the established constraint conditions of the unified mathematical model containing reconstruction and island division are as follows:
the method comprises the following steps of firstly, DistFlow power flow constraint, writing out a state equation of a system by taking active power, reactive power and a node voltage square as state variables of the system, and expressing the state equation as a constraint condition form. Considering the change of the patent in the aspect of network topology structure change during reconstruction and island division, a large M method is used for correction to obtain a corresponding node active power balance equation and a node reactive power balance equation:
Figure GDA0002758793340000071
Figure GDA0002758793340000072
wherein, the flow of the initial node to the final node in the branch information is specified to be a positive direction,
Figure GDA0002758793340000073
represents the sum of the active power injected by the j node in the t period,
Figure GDA0002758793340000074
represents the sum of the active power flowing out from the j node in the t period,
Figure GDA0002758793340000075
representing the sum of the active line losses injected into the j node line at time t,
Figure GDA0002758793340000076
the square term of the line current of the line with the node i as the starting node and the node j as the end node in the period t is shown,
Figure GDA0002758793340000077
the j node predicts the active load representing the t period,
Figure GDA0002758793340000078
represents the sum of all DG active power output of j nodes in the period t,
Figure GDA0002758793340000079
representing the j node active load shedding amount in the t period,
Figure GDA00027587933400000710
representing the sum of the reactive power injected at node j during time t,
Figure GDA00027587933400000711
representing the sum of the reactive power flowing out of node j during time t,
Figure GDA00027587933400000712
representing the sum of the reactive line losses injected into the j node line at time t,
Figure GDA00027587933400000713
the reactive load is predicted at node j on behalf of time t,
Figure GDA00027587933400000714
represents the sum of all DG reactive power outputs of j nodes in the t period,
Figure GDA00027587933400000715
representing the reactive load throwing amount of the j node in the t period;
and a line pressure drop equilibrium equation, the following equation constraints and model conversion processing being applicable to any time period t, for each branch of each time period:
Figure GDA00027587933400000716
wherein, M represents a constant with a large value,
Figure GDA00027587933400000717
represents the square term of the voltage of the node i in the time period t (to eliminate the square term and achieve the linearization effect),
Figure GDA00027587933400000718
and representing the opening and closing condition of the branch circuit with the node i as a starting node and the node j as a tail node in the period t, wherein 0 or 1, 0 represents that the circuit is opened, and 1 represents that the circuit is closed.
And secondly, limiting the branch power, wherein the rated capacity of the line transmission power needs to be considered in the topology changing process because the line transmission power of the actual power distribution network is limited. Secondly, the branch circuit state of opening and shutting decides whether line power can circulate, and when the branch circuit disconnection, branch circuit transmission power should be clamped as zero:
Figure GDA0002758793340000081
Figure GDA0002758793340000082
wherein,
Figure GDA0002758793340000083
the active power and the reactive power circulating on the circuit in the time period t of the branch with i as the starting node and j as the last node are respectively represented, and the equation (6) restricts the circulating condition of the circuit by using a large M method, wherein M is a large number.
Node voltage quota restraint, need guarantee that electric wire netting node voltage is within the safety interval in the active power distribution network fault recovery period, voltage deviation does not exceed k% promptly, and general k gets 5 ~ 10:
Figure GDA0002758793340000084
wherein,
Figure GDA0002758793340000085
a square term representing a rated voltage of the load node;
and fourthly, DG capacity constraint, wherein the output of the distributed power supply connected into the power distribution network needs to be within a rated interval:
Figure GDA0002758793340000086
wherein,
Figure GDA0002758793340000087
respectively representing the square terms of the active power and the reactive power output of the W-number distributed power supply in the t time period, S2 max DGSquare term representing rated capacity of load node, NDGRepresenting the total number of distributed power supplies;
current amplitude constraint, wherein the current of the line in each time period in the fault is required to be within a rated range, so that the current amplitude constraint is newly increased:
Figure GDA0002758793340000088
wherein,
Figure GDA0002758793340000089
in the time period t, the square term of the current flowing through the line with i as the starting node and j as the end node,
Figure GDA00027587933400000810
representing the branch current rating.
Sixthly, relaxing the secondary constraint into conical constraint:
Figure GDA00027587933400000811
radial and connectivity constraints are generated, in the process of dynamic reconfiguration and island division of a distribution network, a network structure needs to be kept radial, a virtual power flow model is built herein to standardize active power distribution network fault reconfiguration, the island division exists in an active power distribution network fault recovery optimization model, so that the distribution network is possibly divided into a plurality of areas, the number of root nodes is uncertain, the root nodes can be a transformer substation or a distributed power supply, the number of islands is also a part of optimization, the traditional radial and connectivity constraints cannot well adapt to the model built herein, and therefore the radiating and connectivity constraints of the island division suitable for the mixed integer second-order cone model are innovatively set herein:
Figure GDA0002758793340000091
Figure GDA0002758793340000092
Figure GDA0002758793340000093
wherein N isDGIs the total DG number, NsubIs the total number of substations, CqSelecting a variable for the root node, wherein the root node can be a DG (distributed generation) or a transformer substation for the 0-1 variable, and when the value of the variable C corresponding to the DG or the transformer substation is 1, the DG or the transformer substation is shown as the root node of one partition area, then
Figure GDA0002758793340000094
The number of main nets additionally arranged outside the island is the number of the divided areas; a is one NlineLine, NDG+NsubThe 0-1 of the column optimizes the variable matrix.
Let NDG+Nsub＝NrootAnd in the active power distribution network fault recovery strategy, the mostMultiple occurrence of NrootA divided area including divided islands and main area left after division, ApqBy 1, it means that the p-th node is selected as a node of the q-th partition area (q-th column), and if the distributed power supply is not selected as a root node of the partition area, the corresponding C variable is set to zero. The expression (13) indicates that each node of the grid participating in the islanding optimization belongs to one and only one partition area. Equation (14) ensures that the root node corresponding to each partition is selected.
Therefore, in order to ensure radial constraint, namely in the island division of the power grid, the number of the nodes of the power distribution network minus the number of the division areas needs to be equal to the number of the operating branches:
Figure GDA0002758793340000095
wherein,
Figure GDA0002758793340000096
the number of main nets added outside the island; in the step a, columns with all zeros are removed, each column represents a partition area, so that connectivity in the area needs to be ensured during optimization, nodes in each partition area need to be connected with each other after the topology structure is changed, at this time, a model of "virtual power flow" is used to determine connectivity in an island, the load of a selected node in each partition area is set to be 1, power is injected from a root node, and if the connectivity in the partition area can be proved (a virtual power balance equation is satisfied):
Figure GDA0002758793340000101
wherein,
Figure GDA0002758793340000102
as root node (distributed power supply)) The virtual output of (a) is determined,
Figure GDA0002758793340000103
for a period t, i is taken as a starting node, j is taken as a line virtual power of an end node,
Figure GDA0002758793340000104
is the virtual load of the k node. Compared with the common power flow, the virtual power flow greatly reduces the calculation amount and is more efficient.
The load shedding constraint is characterized in that loads in the active power distribution network can be divided into uncontrollable loads and controllable loads (flexible loads), the load shedding amount of the controllable loads is controllable, the uncontrollable loads have only two conditions, one is to shed all loads of the node, the other is not to execute the load shedding operation, and the load shedding amount has the following constraint requirements:
Figure GDA0002758793340000105
Figure GDA0002758793340000106
wherein, the subscript c represents the controllable load, the formula (16) is the load shedding constraint of the controllable load, the subscript uc represents the uncontrollable load, the formula (17) represents the load shedding constraint of the uncontrollable load, and z is a variable of 0-1.
And 4) solving the established unified mathematical model containing reconstruction and island division, and obtaining a final active power distribution network fault recovery operation strategy. And solving the Mixed Integer Second Order Cone Problem (MISOCP), obtaining an optimization result, and obtaining a dynamic information, network topology operation, DG output and load shedding strategy according to the fault time period, namely a fault recovery unified operation strategy of the active power distribution network.
The above description is only a preferred embodiment of the present invention, and the scope of the present invention is not limited to the above embodiment, but equivalent modifications or changes made by those skilled in the art according to the present disclosure should be included in the scope of the present invention as set forth in the appended claims.

Claims (4)

1. A method for constructing a unified model for fault recovery of an active power distribution network simultaneously considers two topological transformation strategies of reconstruction and islanding, and converts a non-convex nonlinear optimization problem into a solvable mixed integer second-order cone problem by setting various constraint conditions, and is characterized in that: the method comprises the following steps:
step 1) acquiring power grid fault information, a network topology structure, distribution network branches, a distributed power supply and switch state information, predicting load and fault time required by a fault period, and summarizing data required by model building;
step 2) determining a target function of the fault recovery operation strategy;
step 3) constructing a unified mathematical model containing reconstruction and island division, wherein the unified mathematical model contains DistFlow power flow constraint and connectivity constraint using virtual power flow; the constraint conditions of the established unified mathematical model containing the reconstruction and the island division are as follows:
firstly, DistFlow power flow constraint, taking active power, reactive power and node voltage square as state variables of a system, writing out a state equation of the system in a column, expressing the state equation as a constraint condition form, and correcting by using a large M method to obtain a corresponding node active power balance equation and a node reactive power balance equation:
Figure FDA0002758793330000011
Figure FDA0002758793330000012
wherein, the flow of the initial node to the final node in the branch information is specified to be a positive direction,
Figure FDA0002758793330000013
representing j nodes in t periodThe sum of the active power is injected,
Figure FDA0002758793330000014
represents the sum of the active power flowing out from the j node in the t period,
Figure FDA0002758793330000015
representing the sum of the active line losses injected into the j node line at time t,
Figure FDA0002758793330000016
the square term of the line current of the line with the node i as the starting node and the node j as the end node in the period t is shown,
Figure FDA0002758793330000017
the j node predicts the active load representing the t period,
Figure FDA0002758793330000018
represents the sum of all DG active power output of j nodes in the period t,
Figure FDA0002758793330000019
representing the j node active load shedding amount in the t period,
Figure FDA00027587933300000110
representing the sum of the reactive power injected at node j during time t,
Figure FDA00027587933300000111
representing the sum of the reactive power flowing out of node j during time t,
Figure FDA00027587933300000112
representing the sum of the reactive line losses injected into the j node line at time t,
Figure FDA00027587933300000113
the reactive load is predicted at node j on behalf of time t,
Figure FDA00027587933300000114
represents the sum of all DG reactive power outputs of j nodes in the t period,
Figure FDA00027587933300000115
represents the reactive load rejection of the j node in the t period, NTRepresenting the total number of time intervals of the fault period;
and a line pressure drop equilibrium equation, the following equation constraints and model conversion processing being applicable to any time period t, for each branch of each time period:
Figure FDA0002758793330000021
wherein M represents a number having a large value,
Figure FDA0002758793330000022
represents the squared term of the voltage at node i during the t period,
Figure FDA0002758793330000023
representing the opening and closing condition of a branch circuit with an i node as a starting node and a j node as a tail node in a t period, wherein 0 or 1 represents that the circuit is opened and 1 represents that the circuit is closed;
secondly, the branch power limitation constraint needs to consider the rated capacity of the transmission power of the line in the topology changing process, and then the branch switching state determines whether the line power can circulate, and when the branch is switched off, the transmission power of the branch is clamped to zero:
Figure FDA0002758793330000024
Figure FDA0002758793330000025
wherein,
Figure FDA0002758793330000026
respectively representing active power and reactive power circulating on a line in a time period t by taking i as a starting node and taking j as a final node, and constraining the circulation condition of the line by using a large M method in the formula (6), wherein M is a large number;
and limiting the node voltage, and ensuring that the node voltage of the power grid is within a safety interval within the fault recovery period of the active power distribution network, namely the voltage deviation is not more than k%, and k is 5-10:
Figure FDA0002758793330000027
wherein,
Figure FDA0002758793330000028
a square term representing a rated voltage of the load node;
and fourthly, DG capacity constraint, wherein the output of the distributed power supply connected into the power distribution network needs to be within a rated interval:
Figure FDA0002758793330000029
wherein,
Figure FDA00027587933300000210
respectively representing the square terms of the active power and the reactive power output of the W-number distributed power supply in the t time period, S2 maxDGSquare term representing rated capacity of load node, NDGRepresenting the total number of distributed power supplies;
current amplitude constraint, wherein the current of the line in each time period in the fault is required to be within a rated range, so that the current amplitude constraint is newly increased:
Figure FDA00027587933300000211
wherein,
Figure FDA00027587933300000212
in the time period t, the square term of the current flowing through the line with i as the starting node and j as the end node,
Figure FDA00027587933300000213
representing the rated current of the branch circuit;
sixthly, relaxing the secondary constraint into conical constraint:
Figure FDA0002758793330000031
and seventhly, radial and connectivity constraint, namely setting island division radial and connectivity constraint applicable to a mixed integer second-order cone model:
Figure FDA0002758793330000032
Figure FDA0002758793330000033
Figure FDA0002758793330000034
wherein N isDGIs the total DG number, NsubIs the total number of substations, CqSelecting a variable for the root node, wherein the variable is a 0-1 variable, the root node can be a DG or a substation, and when the DG or the corresponding variable C of the substationqThe value is 1, and the DG or the transformer substation is a root node of a partition area; a is one NlineLine, NDG+Nsub0-1 optimization variable matrix of columns, NbusRepresenting the total number of nodes in the network;
let NDG+Nsub＝NrootThen in the active power distribution network fault recovery strategy, at most N occursrootA divided area including divided islands and main area left after division, Apq1 indicates that the node p is selected to become a partition area q, if the distributed power supply is not selected to become a root node of the partition area, the corresponding C variable is set to zero, and according to the limitation, no load node is selected to become a node in the partition area corresponding to the unselected DG, that is, the unselected DG does not partition the partition area; the formula (13) represents that each node of the power grid participating in the islanding optimization belongs to one and only one partition area; equation (14) ensures that the root node corresponding to each partition region is selected;
therefore, in order to ensure radial constraint, namely in the island division of the power grid, the number of the nodes of the power distribution network minus the number of the division areas needs to be equal to the number of the operating branches:
Figure FDA0002758793330000035
wherein,
Figure FDA0002758793330000036
the number of main nets added outside the island; in the step A, columns which are all zero are removed, each column represents a partition area, so that the connectivity in the area needs to be ensured during optimization, nodes in each partition area need to be mutually communicated after the topological structure is changed, at the moment, the connectivity in an island is determined by using a virtual power flow model, the load of a selected node in each partition area is set to be 1, power is injected from a root node, and if the power can be circulated and a virtual power balance equation is met, the connectivity in the partition areas can be proved:
Figure FDA0002758793330000041
wherein,
Figure FDA0002758793330000042
is the virtual output of the root node, the distributed power supply,
Figure FDA0002758793330000043
for a period t, i is taken as a starting node, j is taken as a line virtual power of an end node,
Figure FDA0002758793330000044
is the virtual load of the k node;
and eighthly, load shedding constraint, namely the controllable load shedding amount is a controllable amount, and for an uncontrollable load, only two conditions are provided, one is to shed all loads of the node, and the other is not to execute the load shedding operation, so that the following constraint requirements are provided for the load shedding amount:
Figure FDA0002758793330000045
Figure FDA0002758793330000046
wherein, the subscript c represents controllable load, the formula (16) is load shedding constraint of the controllable load, the subscript uc represents uncontrollable load, the formula (17) represents load shedding constraint of the uncontrollable load, and z is a variable of 0-1;
and 4) solving the established unified mathematical model containing reconstruction and island division, and obtaining a final active power distribution network fault recovery operation strategy.
2. The method for constructing the unified model for fault recovery of the active power distribution network according to claim 1, wherein the unified model comprises the following steps: in the step 1), the input fault time interval fault information is discretized, the fault time interval is divided into n time intervals, the corresponding predicted load is discretized in the same time scale, and preparation is made for establishing a multi-time-interval dynamic unified mathematical model containing reconstruction and island division.
3. The method for constructing the unified model for fault recovery of the active power distribution network according to claim 1, wherein the unified model comprises the following steps: in the step 2), the predicted load is set as a constant, the load shedding amount of each node is set as an optimized variable, the on-off state of the switch is set as a variable of 0-1, 0 represents that the switch is off, 1 represents that the switch is on, and the objective function expression is as follows:
Figure FDA0002758793330000047
wherein, CopeRepresents the total cost, cloadRepresenting the load shedding cost factor, NTRepresenting the total number of time intervals of the fault period, NbusRepresenting the total number of nodes in the network, at representing the length of each time interval of the fault period,
Figure FDA0002758793330000051
represents t time period, i node load shedding amount, lambdaiThe load weight of the ith node is obtained; c. CswitchRepresents a switch operation cost coefficient, and is an optimized variable of 0-1, alphauThe switch state representing the fault recovery time period of the u-th branch is a constant value of 0-1,
Figure FDA0002758793330000052
representing the switching state before fault in branch u, NlineRepresenting the total number of branches in the network.
4. The method for constructing the unified model for failure recovery of the active power distribution network according to claim 1, wherein a mixed integer second order cone problem is solved, an optimization result is obtained, and a dynamic information, a network topology operation, a DG output and load shedding strategy according to a failure time period, namely a unified operation strategy for failure recovery of the active power distribution network, is obtained.
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