CN112052543B - Bottom-preserving net rack search modeling method based on mixed integer second-order cone programming - Google Patents

Bottom-preserving net rack search modeling method based on mixed integer second-order cone programming Download PDF

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CN112052543B
CN112052543B CN202010804006.XA CN202010804006A CN112052543B CN 112052543 B CN112052543 B CN 112052543B CN 202010804006 A CN202010804006 A CN 202010804006A CN 112052543 B CN112052543 B CN 112052543B
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CN112052543A (en
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李佩杰
郝志方
何远健
徐莉菲
李滨
韦化
陈碧云
祝云
白晓清
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Guangxi University
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Abstract

The invention discloses a method for searching and modeling a bottom-preserving net rack based on mixed integer second-order cone programming. The method aims to solve the problems of low calculation speed, uncertain result and limitation of the algorithm adopted in the prior art; the invention comprises the following steps: s1: collecting information of a power transmission network to be planned, forming an initial power network topological graph, and establishing a multi-objective optimization function; s2: establishing node active power and reactive power balance constraints based on a power flow equation of a power system; s3: establishing model inequality constraints including line voltage constraints, system power flow constraints, connectivity constraints, unit output constraints and line power constraints; s4, performing second-order cone optimization relaxation on the model, and converting the mixed integer nonlinear programming model into a mixed integer second-order cone model; s5: and solving the model to obtain a planning scheme. The mixed integer second-order cone programming is high in solving efficiency, good in robustness and determined in result. The speed and the accuracy of searching the bottom-protecting net rack are improved.

Description

Mixed integer second order cone programming-based bottom-preserving grid searching and modeling method
Technical Field
The invention relates to the field of guaranteed-net rack planning, in particular to a guaranteed-net rack search modeling method based on mixed integer second-order cone planning.
Background
At the present stage, china is focusing on changing an economic growth mode, optimizing an economic structure, promoting high-quality development of economy, insisting on a green low-carbon development road, and accelerating ecological civilized construction and energy revolution. Reliable power supply has become the most important material basis for ensuring the continuous development of economic society, and the importance of power safety is increasingly highlighted. In recent years, the frequency and degree of natural disasters caused by climate change caused by global warming tend to increase, a series of disastrous heavy power failure accidents are caused to domestic and foreign electric power systems, and how to ensure the safety of a power grid in extreme weather is more and more concerned by electric power system employees.
In general, a large-scale power failure accident is caused by a fault caused by internal or external factors, so that some fragile lines or important nodes in a power grid are quitted from running, large-scale power flow transfer is caused, linkage faults are further caused, and the large-scale power failure accident is finally caused. It is the most direct and effective method for disaster prevention to improve the design standard from the perspective of a primary system to avoid faults, but it is neither economical nor necessary to improve the design and construction standards of the power grid comprehensively. Therefore, many scholars propose to carry out differentiated power grid planning, aim at strengthening power grid construction, and use the power grid construction as a basis for allocating partial transformer substations, lines and power supplies which are mainly protected by manpower and material resources when the extreme natural disasters are faced, namely, a scheme of constructing a bottom-protecting net rack is used for improving the temporary reliability of the power grid when the disasters come. The method has important significance for enhancing the operation stability of the power system, reducing the secondary investment of rush repair and reconstruction of the power grid due to natural disasters and ensuring the safe and reliable operation of the power grid under serious natural disasters.
The method for searching the bottom-protecting net rack relates to a complex network theory and large-scale power system dynamic research. In the existing method for searching and modeling the bottom-preserving net rack, a mixed integer nonlinear programming model is established based on traditional power flow constraints. Because no mature solver can solve the mixed integer nonlinear programming problem at present, researchers mostly use an artificial intelligence algorithm to solve the problem in research. The artificial intelligence method is limited by itself, needs to search for many times, is uncertain in result, and cannot meet the requirement of high-speed accurate solving of a modern power system. Therefore, the effective and quick method for searching the bottom-protecting net rack is of great significance to stable operation and post-disaster reconstruction of the power system.
The construction of the bottom-preserving net rack is a multivariable, nonlinear and multi-constraint combined optimization problem, and most of the solutions to the problems in recent years adopt artificial intelligence algorithms. The method comprises the steps of establishing a core backbone network frame based on an improved BBO optimization algorithm and the survivability of a power grid [ J ]. Chinese Motor engineering journal 2014,34 (16): 2659-2667 ], researching a core backbone network frame searching method based on a biogeography optimization algorithm [ J ]. Shaanxi electric power 2014,42 (08): 1-5 ], and searching the backbone network frame by adopting the improved biogeography optimization algorithm with strong searching capacity. ' core backbone net rack search based on improved binary quantum particle swarm algorithm [ J ]. Chinese Motor engineering Proc, 2014,34 (34): 6127-6133. The backbone net rack searching method is used for searching the backbone net rack by adopting a guided firework algorithm in the study of [ D ]. Nanchang university, 2018 ]. "network reconstruction with comprehensive consideration of node importance and line betweenness [ J ] Power System Automation 2010,34 (12): 29-33." search backbone net rack using Discrete Particle Swarm Optimization (DPSO) in the text. A power grid differentiation core backbone network frame construction and evaluation method researches a backbone network frame by adopting an improved quantum particle swarm algorithm in the sentence of 'Wuhan university, 2017'.
The methods adopt artificial intelligent algorithm to solve, and the problems of low calculation speed, uncertain result, easy falling into local optimum and the like generally exist. The method has great limitation in solving the searching problem of the bottom-preserving net rack and needs to be improved.
Disclosure of Invention
The invention mainly solves the problems that the prior art adopts an artificial intelligence algorithm to solve, has low calculation speed, uncertain result and easy falling into local optimum, and has great limitation in solving the problem of searching the bottom-preserving net rack; the method for searching and modeling the guaranteed-net rack based on the mixed integer second-order cone programming is provided, the problem of searching the guaranteed-net rack under different requirements is solved, the calculation speed is high, the robustness is good, the flexibility is high, the expansibility is strong, and the efficiency of searching the guaranteed-net rack is effectively improved.
The technical problem of the invention is mainly solved by the following technical scheme:
the invention comprises the following steps:
s1: collecting information of a power transmission network to be planned, forming an initial power network topological graph, and establishing a multi-objective optimization function considering minimum number of bottom-protected network frame lines and highest line importance degree;
s2: determining a guaranteed power supply, an important load node and an important site, and establishing node active power and reactive power balance constraint based on a power flow equation of a power system;
s3: establishing model inequality constraints including line voltage constraints, system power flow constraints, connectivity constraints, unit output constraints and line power constraints;
s4, performing second-order cone optimization (SOCP) relaxation on the model, and converting the mixed integer nonlinear programming model into a mixed integer second-order cone model;
s5: and solving the model to obtain a planning scheme.
The method and the device have the advantages that the mixed second-order cone programming model established by the scheme is utilized to search the bottom-preserving net rack, so that the problems of low efficiency and high uncertainty in solving nonlinear problems caused by the traditional algorithm are effectively avoided, and meanwhile, the solved result is more in line with the actual operation condition. The mixed integer second-order cone programming model can be effectively solved by utilizing the existing mature algorithm, the calculation speed is high, the robustness is good, the flexibility is high, the expansibility is strong, and the searching efficiency of the bottom-preserving net rack is effectively improved.
Preferably, the multi-objective optimization function is
Figure 103390DEST_PATH_IMAGE001
Wherein the content of the first and second substances,
Figure 489372DEST_PATH_IMAGE002
is a line set in the system;
Figure 689016DEST_PATH_IMAGE003
as lines i-jIn the operating state of (a) the operating state of (b),
Figure 553066DEST_PATH_IMAGE004
0 is quit and 1 is put into operation;
Figure 836280DEST_PATH_IMAGE005
the weight value of the important degree of the line in the multi-objective optimization function is calculated;
Figure 393164DEST_PATH_IMAGE006
and the power flow betweenness is obtained after line normalization.
The larger the tidal current betweenness is, the higher the importance degree of the line is, and a multi-objective optimization function which considers the minimum number of lines of the bottom-protecting net frame and the highest importance degree of the line is established.
Preferably, the line voltage constraints include a voltage offset constraint and a voltage phase angle constraint, and the voltage offset is less than or equal to +/-10% for a certain node; for a certain section of line, the difference value of the voltage phase angles of the nodes at the first end and the last end is less than or equal to 10 degrees;
the voltage offset constraint is:
Figure DEST_PATH_IMAGE007
wherein the content of the first and second substances,
Figure 847148DEST_PATH_IMAGE008
is the product of two voltage values, i.e.
Figure 718152DEST_PATH_IMAGE009
，
Figure 606604DEST_PATH_IMAGE010
And
Figure 68810DEST_PATH_IMAGE011
respectively is the lower limit and the upper limit of the voltage value of the node i, and N is the set of all nodes in the net rack;
the voltage phase angle constraint is:
Figure DEST_PATH_IMAGE013
Figure DEST_PATH_IMAGE015
in the formula (I), the compound is shown in the specification,
Figure 947773DEST_PATH_IMAGE016
,
Figure 419205DEST_PATH_IMAGE017
;
wherein the content of the first and second substances,
Figure 411432DEST_PATH_IMAGE018
and
Figure 261183DEST_PATH_IMAGE019
respectively the resistance and reactance values of the routes i-j,
Figure 237229DEST_PATH_IMAGE020
，
Figure 433724DEST_PATH_IMAGE021
is the upper limit value of the phase angle difference value of the voltage at the head and tail end points of the circuit, M is a constant,
Figure 546037DEST_PATH_IMAGE022
respectively representing the values of the active and reactive power of the lines i-j flowing from node i to node j,
Figure 350045DEST_PATH_IMAGE023
and
Figure 547808DEST_PATH_IMAGE024
respectively the susceptance value and the conductance value of the charging capacitors in the lines i-j,
Figure 111776DEST_PATH_IMAGE025
to take into account the characteristics of the transformers I-j of the phase shifter, R, I are used to identify the real number of the complex numberA partial part and an imaginary part.
In order to guarantee the requirement of each node in the bottom-preserving net rack on normal working voltage, it should be guaranteed that voltage deviation should not be larger than +/-10% for a certain node, and voltage phase angle difference values of the nodes at the first end and the last end of a section of line should not be larger than 10 degrees generally. The constraint ensures that the difference value of the phase angles of the voltages at the head end and the tail end of the line is in a fixed range, and meets the operation requirement of a power grid under a specific condition.
Preferably, the system power flow constraints include line power loss constraints and line voltage drop constraints;
according to the trend formula
Figure 78595DEST_PATH_IMAGE026
It can be seen that the power loss on line i-j is
Figure 319083DEST_PATH_IMAGE027
；
In the formula (I), the compound is shown in the specification,
Figure 738563DEST_PATH_IMAGE028
for the apparent power of lines i-j flowing from node i to node j,
Figure 339178DEST_PATH_IMAGE029
the apparent power flowing from node j to node i for line j-i,
Figure 363765DEST_PATH_IMAGE030
for the admittance values of the lines i-j,
Figure 40734DEST_PATH_IMAGE031
and
Figure 898576DEST_PATH_IMAGE032
the voltage values of node i and node j respectively,
Figure 53613DEST_PATH_IMAGE033
a conjugate value representing a numerical value;
and further deducing, respectively establishing second-order cone constraints of active power and reactive power of the line i-j:
Figure 995025DEST_PATH_IMAGE035
Figure 826583DEST_PATH_IMAGE037
Figure 423918DEST_PATH_IMAGE039
Figure 913805DEST_PATH_IMAGE041
according to the trend formula
Figure 398138DEST_PATH_IMAGE026
It can be seen that the power loss on lines i-j is
Figure 151331DEST_PATH_IMAGE042
And further deducing to establish a second-order cone constraint of the voltage drop of the line i-j:
Figure 32699DEST_PATH_IMAGE044
Figure 529539DEST_PATH_IMAGE046
wherein, the first and the second end of the pipe are connected with each other,
Figure DEST_PATH_IMAGE047
e is the set of all lines in the system;
Figure 898073DEST_PATH_IMAGE048
is the square of the value of the current on lines i-j.
The method has the advantages that active power, reactive power and other factors are considered comprehensively, and the defects that when a mathematical programming method is used for searching the bottom-preserving net rack, the solving difficulty is high, only the active power can be considered, reactive power check needs to be carried out and the like are effectively improved.
Preferably, the connectivity constraint is:
Figure DEST_PATH_IMAGE049
Figure 25429DEST_PATH_IMAGE050
Figure 407475DEST_PATH_IMAGE051
Figure 442427DEST_PATH_IMAGE052
Figure 416199DEST_PATH_IMAGE054
Figure 494883DEST_PATH_IMAGE055
wherein J is a set of load nodes in the power system, I is a set of nodes left in the power system except the load nodes, S is a set of all nodes in the power system,
Figure 350843DEST_PATH_IMAGE056
indicating whether the line connected to node j remains in the net-bottom rack,
Figure 455065DEST_PATH_IMAGE057
indicating whether node i remains in the net bottom rack,
Figure 814503DEST_PATH_IMAGE058
indicating whether node i is required to remain in the net-bottom,
Figure 831131DEST_PATH_IMAGE059
whether the line e is reserved in the bottom-retaining net rack or not is shown, x, y, z and a are all variables of 0 or 1, 0 is taken to indicate that the line is not reserved, and 1 is taken to indicate that the line is reserved; e (S) is the set of bidirectional lines in the virtual network, and H is the set of node S and nodes adjacent to node S.
The first constraint ensures that there must be at least one line connected to the load node. The second constraint ensures that a line i-j can only be selected if node i is retained in the shelf. The third constraint ensures that node i is not selected to be the surviving frame if node i is required to be discarded before computation. The fourth constraint and the fifth constraint ensure that the formed topology map of the bottom-protecting net rack is a tree, thereby avoiding the occurrence of looped network and ensuring the connectivity of the bottom-protecting net rack.
Preferably, the unit output constraint is as follows:
Figure 908809DEST_PATH_IMAGE060
Figure 754405DEST_PATH_IMAGE061
wherein the content of the first and second substances,
Figure 483195DEST_PATH_IMAGE062
the starting and stopping conditions of the unit are represented, 0 represents that the unit is stopped, and 1 represents that the unit is started;
Figure 919993DEST_PATH_IMAGE063
in order to have an active power output,
Figure 484967DEST_PATH_IMAGE064
respectively representing the lower limit and the upper limit of the active power output of the generator;
Figure 930991DEST_PATH_IMAGE065
in order to have no reactive power output,
Figure 12824DEST_PATH_IMAGE066
respectively representing the lower limit and the upper limit of the active output of the generator.
The processing constraints of the motor set comprise active power output and reactive power output, the calculation is more comprehensive, and the defects that when a mathematical programming method is used for searching the bottom-protecting net rack, the solving difficulty is high, only the active power can be considered, the reactive power check needs to be carried out and the like are effectively improved.
Preferably, the line power constraint is:
Figure 823785DEST_PATH_IMAGE067
Figure 876054DEST_PATH_IMAGE068
Figure DEST_PATH_IMAGE069
when the line i-j is not selected,
Figure 312721DEST_PATH_IMAGE070
、
Figure DEST_PATH_IMAGE071
and
Figure 235677DEST_PATH_IMAGE072
are all 0.
The considerations are more comprehensive.
Preferably, the second-order cone optimized relaxation is as follows:
Figure DEST_PATH_IMAGE073
wherein the content of the first and second substances,
Figure 233852DEST_PATH_IMAGE074
for lines i-jThe square of the value of the flow is,
Figure 773417DEST_PATH_IMAGE075
is the product of the voltage values at node i.
And converting the mixed integer nonlinear programming model into a mixed integer second-order cone model through second-order cone optimization (SOCP) relaxation.
Preferably, the step S5 includes solving the mixed integer second order cone planning bottom-preserving net rack search model established in the present invention by using a CPLEX solver, and analyzing the search result. The method for solving the mixed integer second-order cone programming problem by using the CPLEX algorithm is mature in technology, and is used for processing the problem of searching the bottom-preserving net rack under different requirements based on the model provided by the invention, so that the method is high in calculation speed, good in robustness, high in flexibility and strong in expansibility, and the efficiency of searching the bottom-preserving net rack is effectively improved.
The beneficial effects of the invention are:
1. the method has comprehensive consideration factors, and effectively overcomes the defects that when a mathematical programming method is used for searching the bottom-protecting net rack, the solving difficulty is high, only active power can be considered, reactive power check needs to be carried out, and the like.
2. Through mixed integer second order cone planning, compare in artificial intelligence algorithm, this scheme solves efficient, the robustness is good and the result is confirmed.
3. The mixed integer second-order cone programming model can be effectively solved by utilizing the existing mature algorithm, and the speed and the accuracy of searching the bottom-preserving net rack are improved.
Drawings
FIG. 1 is a flow chart of a protected net rack search modeling of the present invention.
FIG. 2 is a system connectivity topology diagram of IEEE14 nodes in an embodiment of the present invention;
Detailed Description
The technical scheme of the invention is further specifically described by the following embodiments and the accompanying drawings.
The embodiment is as follows:
in this embodiment, as shown in fig. 1, a method for searching and modeling a bottom-preserving net rack based on mixed integer second-order cone programming includes the following steps:
s1: collecting information of a power transmission network to be planned, forming an initial power grid topological graph, and establishing a multi-objective optimization function considering minimum number of bottom-protected network frame lines and highest line importance degree.
Collecting information about the planned grid includes determining load nodes, load capacity, power nodes, power output limits, line capacity, and network node topology connections in the network. And forming an initial power grid topological graph. In the present embodiment, the IEEE14 node system shown in fig. 2 is taken as an example.
And determining a guaranteed power supply, important load nodes and important sites, and determining the capacity of the important load needing to be guaranteed. And judging the importance degree of each node and each line according to the normal operation condition, and determining the construction cost of each node and each line.
Establishing a multi-objective optimization function considering the minimum number of the bottom-protected network frame lines and the highest line importance degree:
Figure 295666DEST_PATH_IMAGE076
wherein, the first and the second end of the pipe are connected with each other,
Figure 853555DEST_PATH_IMAGE077
is a line set in the system;
Figure 803056DEST_PATH_IMAGE078
in order to be the operational state of the lines i-j,
Figure 564339DEST_PATH_IMAGE079
0 is quit and 1 is put into operation;
Figure 890278DEST_PATH_IMAGE080
the weight of the importance degree of the line in the multi-objective optimization function is 0.3 in the embodiment;
Figure 801209DEST_PATH_IMAGE081
and the power flow betweenness is obtained after line normalization.
The importance degree of the line takes the line flow betweenness as a reference factor. The flow betweenness of the IEEE14 nodes can be calculated as follows:
line number Tidal current betweenness Line number Median tidal current
1-2 1 9-10 0.2871
1-5 0.5802 9-14 0.2435
5-6 0.5549 6-13 0.2363
2-4 0.5454 6-11 0.2322
4-5 0.4829 10-11 0.2259
2-3 0.4782 4-9 0.2178
2-5 0.473 13-14 0.2057
3-4 0.4383 6-12 0.1400
7-9 0.3784 12-13 0.1047
4-7 0.3702 　
S2: and determining a guaranteed power supply, important load nodes and important sites, and establishing node active power and reactive power balance constraints on the basis of a power flow equation of the power system.
And a part of important power supply nodes and load nodes must be reserved in the selected bottom-protecting net rack, the power supply to the important loads is ensured, and the power exchange capacity between the important power supply nodes and the important loads is ensured.
In the IEEE14 node system in this embodiment, there are 3 power source nodes and 11 load nodes, and it is assumed that the backbone network holds all the load nodes and holds power that is normally 30% loaded. And (4) establishing equality constraint, and establishing node active power and reactive power balance constraint based on kirchhoff current law.
The following equality constraints are established according to kirchhoff's current law:
Figure 921611DEST_PATH_IMAGE082
Figure 435769DEST_PATH_IMAGE083
Figure 299820DEST_PATH_IMAGE084
；
wherein the content of the first and second substances,
Figure 566722DEST_PATH_IMAGE063
and
Figure 123606DEST_PATH_IMAGE065
respectively sending out active power and reactive power for the node i;
Figure 859480DEST_PATH_IMAGE085
and
Figure 527222DEST_PATH_IMAGE086
respectively the active power and reactive power requirements of the rigid load of the node i;
Figure 150096DEST_PATH_IMAGE087
and
Figure 877880DEST_PATH_IMAGE088
respectively representing the active power and reactive power values of the lines i-j flowing from the node i to the node j;
Figure 101051DEST_PATH_IMAGE089
and
Figure 572484DEST_PATH_IMAGE090
the conductance values and the susceptance values of the capacitor and the reactor which are nodes i respectively;
Figure 813978DEST_PATH_IMAGE075
is the product of two voltage values at node i, i.e.
Figure 712664DEST_PATH_IMAGE091
(ii) a And N is the set of all nodes in the net rack.
S3: and establishing model inequality constraints including line voltage constraints, system power flow constraints, connectivity constraints, unit output constraints and line power constraints.
S31: a line voltage constraint is established.
The line voltage constraints include a voltage offset constraint and a voltage phase angle constraint.
In order to ensure the requirement of each node in the bottom-protecting net rack on normal working voltage, the voltage deviation of a certain node is ensured to be not more than +/-10%, and the voltage phase angle difference value of the nodes at the first end and the last end of a certain section of line is generally not more than 10 degrees.
The voltage offset constraints are:
Figure 891973DEST_PATH_IMAGE007
wherein, the first and the second end of the pipe are connected with each other,
Figure 901517DEST_PATH_IMAGE092
and
Figure 761632DEST_PATH_IMAGE093
respectively, a lower voltage value limit and an upper voltage value limit of the node i.
Because the bottom-protecting net frame is operated under the extreme condition of the power grid, the node voltage constraint can be properly relaxed and taken
Figure 565640DEST_PATH_IMAGE094
。
Figure 763403DEST_PATH_IMAGE095
The lower limit of the voltage value in the normal case,
Figure 311059DEST_PATH_IMAGE096
is the upper limit of the voltage value under the normal condition.
The voltage phase angle constraint is:
Figure 527146DEST_PATH_IMAGE097
Figure 502055DEST_PATH_IMAGE098
in the formula (I), the compound is shown in the specification,
Figure 187114DEST_PATH_IMAGE099
,
Figure 538461DEST_PATH_IMAGE100
;
wherein the content of the first and second substances,
Figure 110519DEST_PATH_IMAGE101
and
Figure 990750DEST_PATH_IMAGE102
respectively the resistance and reactance values of the routes i-j,
Figure 897527DEST_PATH_IMAGE103
；
Figure 36253DEST_PATH_IMAGE104
the upper limit value of the voltage phase angle difference value of the head end point and the tail end point of the line is obtained;
m is a very large constant, in this example taken to be 10000;
Figure 977664DEST_PATH_IMAGE105
and
Figure 294376DEST_PATH_IMAGE106
respectively the susceptance value and the conductance value of the charging capacitors in the lines i-j;
Figure 688448DEST_PATH_IMAGE107
to take into account the characteristics of the transformers I-j of the phase shifter, R, I are used to identify the real and imaginary parts of the complex number.
Figure 152838DEST_PATH_IMAGE108
To account for the transformer characteristics of the phase shifter, the IEEE14 node system transformer has no phase shifting characteristics and therefore only the transformation ratio is considered. The common line is t =1, and the transformer line data is as follows:
node i Node j Transformation ratio
4 7 0.978
4 9 0.969
5 6 0.932
Figure 948755DEST_PATH_IMAGE109
As is the impedance of the line(s),
Figure 701948DEST_PATH_IMAGE110
for the line to ground charging the capacitive reactance, the data is as follows:
node i Node j r x
Figure DEST_PATH_IMAGE111
Figure 301425DEST_PATH_IMAGE112
1 2 0.01938 0.05917 0 0.0264
1 5 0.05403 0.22304 0 0.0246
2 3 0.04699 0.19797 0 0.0219
2 4 0.05811 0.17632 0 0.0187
2 5 0.05695 0.17388 0 0.017
3 4 0.06701 0.17103 0 0.0173
4 5 0.01335 0.04211 0 0.0064
6 11 0.09498 0.19890 0 0
6 12 0.12291 0.15581 0 0
6 13 0.06615 0.13027 0 0
7 8 0.0 0.17615 0 0
7 9 0.0 0.11001 0 0
9 10 0.03181 0.08450 0 0
12 13 0.22092 0.19988 0 0
13 14 0.17038 0.34802 0 0
14 9 0.12711 0.27038 0 0
10 11 0.08205 0.19207 0 0
4 7 0.0 0.20912 0 0
4 9 0.0 0.55618 0 0
5 6 0.0 0.25202 0 0
S32: and establishing system power flow constraint.
The system power flow constraints include line power loss constraints and line voltage drop constraints.
According to the trend formula
Figure DEST_PATH_IMAGE113
It can be seen that the power loss on line i-j is
Figure 1528DEST_PATH_IMAGE114
；
In the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE115
for apparent power flowing from node i to node j for lines i-j,
Figure 871526DEST_PATH_IMAGE116
the apparent power flowing from node j to node i for line j-i,
Figure DEST_PATH_IMAGE117
is the admittance value of the line i-j,
Figure 61199DEST_PATH_IMAGE031
and
Figure 633126DEST_PATH_IMAGE032
the voltage values of node i and node j respectively,
Figure 464816DEST_PATH_IMAGE118
representing the conjugate of the value.
And further deducing, and respectively establishing second-order cone constraints of active power and reactive power loss of the lines i-j:
Figure DEST_PATH_IMAGE119
Figure 687855DEST_PATH_IMAGE120
Figure 986113DEST_PATH_IMAGE121
Figure 589876DEST_PATH_IMAGE122
according to the formula of trend
Figure 162940DEST_PATH_IMAGE113
It can be seen that the power loss on lines i-j is
Figure 787956DEST_PATH_IMAGE123
And further deducing to establish a second-order cone constraint of the voltage drop of the line i-j:
Figure 53852DEST_PATH_IMAGE124
Figure 380797DEST_PATH_IMAGE125
wherein, the first and the second end of the pipe are connected with each other,
Figure 23131DEST_PATH_IMAGE126
(ii) a E is the set of all lines in the system;
Figure 502654DEST_PATH_IMAGE074
is the square of the value of the current on lines i-j.
S33: connectivity constraints are established.
Besides satisfying constraints such as power constraint, voltage constraint, and line capacity constraint, the bottom-preserving network frame must also satisfy topology connectivity constraint, that is, it must be ensured that the searched sub-graph of the bottom-preserving network frame is a connected graph. This greatly enhances the reliability of the bottoming net frame under extreme conditions.
The connectivity constraints are:
Figure 939452DEST_PATH_IMAGE049
Figure 255158DEST_PATH_IMAGE127
Figure 170024DEST_PATH_IMAGE051
Figure 769633DEST_PATH_IMAGE052
Figure 377332DEST_PATH_IMAGE053
Figure 678869DEST_PATH_IMAGE055
the method comprises the following steps that J is a load node set in the power system, I is a set of nodes left by removing load nodes in the power system, and S is a set of all nodes of the power system;
Figure 397426DEST_PATH_IMAGE056
indicating whether the line connected to node j remains in the net-bottom rack,
Figure 851541DEST_PATH_IMAGE057
indicating whether node i remains in the net bottom rack,
Figure 630141DEST_PATH_IMAGE058
indicating whether node i is required to remain in the net bottom rack,
Figure 917510DEST_PATH_IMAGE059
whether the line e is reserved in the bottom-retaining net rack or not is shown, x, y, z and a are all variables of 0 or 1, 0 is taken to indicate that the line is not reserved, and 1 is taken to indicate that the line is reserved; e (S) is the set of bidirectional lines in the virtual network, and H is the set of node S and nodes adjacent to node S.
The first constraint ensures that there must be at least one line connected to the load node. The second constraint ensures that a line i-j can only be selected if node i is retained in the shelf. The third constraint ensures that node i is not selected to be the surviving net rack if node i is required to be discarded before computation. The fourth constraint and the fifth constraint ensure that the formed topology map of the bottom-preserving net rack is a tree, thereby avoiding the occurrence of looped network and ensuring the connectivity of the bottom-preserving net rack.
S34: and establishing unit output constraint.
Figure 439758DEST_PATH_IMAGE128
Figure 748380DEST_PATH_IMAGE129
Wherein the content of the first and second substances,
Figure 697881DEST_PATH_IMAGE062
the starting and stopping conditions of the unit are represented, 0 represents that the unit is stopped, and 1 represents that the unit is started;
Figure 708431DEST_PATH_IMAGE063
in order to have an active power output,
Figure 34370DEST_PATH_IMAGE064
respectively representing the lower limit and the upper limit of the active output of the generator;
Figure 197499DEST_PATH_IMAGE065
in order to have no power output,
Figure 317901DEST_PATH_IMAGE066
respectively representing the lower limit and the upper limit of the active output of the generator.
Assuming no loss of power supply nodes, the power generation nodes are integrated into
Figure 582792DEST_PATH_IMAGE130
The active power output and reactive power output upper and lower limit data are as follows:
Figure 446842DEST_PATH_IMAGE131
s35: a line power constraint is established.
Figure 464477DEST_PATH_IMAGE132
Figure 21360DEST_PATH_IMAGE068
Figure 6503DEST_PATH_IMAGE069
When the line i-j is not selected,
Figure 408665DEST_PATH_IMAGE070
、
Figure 546385DEST_PATH_IMAGE071
and
Figure 274170DEST_PATH_IMAGE072
are all 0.
And S4, performing second-order cone optimization (SOCP) relaxation on the model, and converting the mixed integer nonlinear programming model into a mixed integer second-order cone model.
The second order cone optimized relaxation is:
Figure 979564DEST_PATH_IMAGE073
Figure 450997DEST_PATH_IMAGE126
；
wherein the content of the first and second substances,
Figure 443224DEST_PATH_IMAGE074
is the square of the current value of line i-j,
Figure 76331DEST_PATH_IMAGE075
is the product of the voltage values at node i.
According to the tidal current equation
Figure 36065DEST_PATH_IMAGE133
Considering the power flow of the line i-j after the transformer
Figure 311189DEST_PATH_IMAGE134
Is expressed as
Figure 157922DEST_PATH_IMAGE135
Obtained by
Figure 227509DEST_PATH_IMAGE136
. Is provided with
Figure 910425DEST_PATH_IMAGE137
Is the square of the current value of line i-j,
Figure 723661DEST_PATH_IMAGE075
the product of the voltage values of the node i is obtained by a second order cone programming relaxation
Figure 690480DEST_PATH_IMAGE138
。
S5: and solving the model to obtain a planning scheme.
And solving the mixed integer second order cone planning bottom-preserving net rack searching model established by the invention by using a CPLEX solver, and analyzing a searching result.
The method for searching the bottom-preserving net rack by using the hybrid second-order cone programming model established by the invention can effectively avoid the problems of low efficiency and large uncertainty in solving the nonlinear problem caused by the traditional algorithm, and simultaneously, the solved result is more in line with the actual operation condition.
The method for solving the mixed integer second-order cone programming problem by using the CPLEX algorithm is mature in technology, and is used for processing the problem of searching the bottom-preserving net rack under different requirements based on the model provided by the invention, so that the method is high in calculation speed, good in robustness, high in flexibility and strong in expansibility, and the efficiency of searching the bottom-preserving net rack is effectively improved.
The above disclosure is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of changes or modifications within the technical scope of the present invention, and shall be covered by the scope of the present invention.

Claims (2)

1. A method for searching and modeling a bottom-preserving network frame based on mixed integer second-order cone programming is characterized by comprising the following steps:
s1: collecting information of a power transmission network to be planned, forming an initial power network topological graph, and establishing a multi-objective optimization function considering minimum number of bottom-protected network frame lines and highest line importance degree;
s2: determining a guaranteed power supply, an important load node and an important site, and establishing node active power and reactive power balance constraint based on a power flow equation of a power system;
s3: establishing model inequality constraints including line voltage constraints, system power flow constraints, connectivity constraints, unit output constraints and line power constraints;
s4: performing second-order cone optimization (SOCP) relaxation on the model, and converting the mixed integer nonlinear programming model into a mixed integer second-order cone model;
s5: solving the model to obtain a planning scheme;
the multi-objective optimization function is
Figure FDA0003908568650000011
Wherein omega i Is a line set in the system; y is ij For the operational state of the lines i-j,
Figure FDA0003908568650000012
0 is quit and 1 is put into operation; omega is the weight of the important degree of the line in the multi-objective optimization function; f ij The power flow betweenness after line normalization is obtained;
the line voltage constraint comprises a voltage deviation constraint and a voltage phase angle constraint, and for a certain node, the voltage deviation is less than or equal to +/-10%; for a certain section of line, the difference value of the voltage phase angles of the nodes at the first end and the last end is less than or equal to 10 degrees;
the voltage offset constraint is:
Figure FDA0003908568650000013
wherein w i Is the product of two voltage values, i.e. w i ＝|v i | 2 ，
Figure FDA0003908568650000014
And
Figure FDA0003908568650000015
respectively is the lower limit and the upper limit of the voltage value of the node i, and N is the set of all nodes in the net rack;
the voltage phase angle constraint is:
Figure FDA0003908568650000021
Figure FDA0003908568650000022
in the formula (I), the compound is shown in the specification,
Figure FDA0003908568650000023
wherein r is ij And x ij The resistance and reactance values of the paths i-j, i, j ∈ Ω i ，e Δ Is the upper limit value of the phase angle difference value of the voltage at the head and tail end points of the line, M is a constant, p ij ，q ij Respectively representing the values of the active and reactive power of the lines i-j flowing from node i to node j,
Figure FDA0003908568650000024
and
Figure FDA0003908568650000025
respectively susceptance and conductance, t, of the charging capacitors in the lines i-j ij To take into account the characteristics of the transformers I-j of the phase shifter, R, I are used to identify the real and imaginary parts of the complex number;
the system power flow constraint comprises a line power loss constraint and a line voltage drop constraint;
according to the formula of trend
Figure FDA0003908568650000026
It can be seen that the power loss on lines i-j is
Figure FDA0003908568650000027
In the formula, S ij Apparent power, S, flowing from node i to node j for lines i-j ji Apparent power, Y, flowing from node j to node i for line j-i ij Is the admittance value, V, of the line i-j i And V j Voltage values of node i and node j, respectively, (.) * A conjugate value representing a numerical value; and further deducing, respectively establishing second-order cone constraints of active power and reactive power of the line i-j:
Figure FDA0003908568650000031
Figure FDA0003908568650000032
Figure FDA0003908568650000033
Figure FDA0003908568650000034
according to the formula of trend
Figure FDA0003908568650000035
It can be seen that the power loss on line i-j is
Figure FDA0003908568650000036
Further derivation, establishing a second order cone constraint of the voltage drop of the line i-j:
Figure FDA0003908568650000037
Figure FDA0003908568650000038
wherein i, j belongs to E, and E is a set of all lines in the system; l ij Is the square of the current value on lines i-j;
the connectivity constraint is as follows:
Figure FDA0003908568650000039
Figure FDA00039085686500000310
Figure FDA0003908568650000041
x(E(S))＝y(S)-1
Figure FDA0003908568650000042
(x，y，z，a)∈{0，1}
wherein J is the set of load nodes in the power system, I is the set of nodes left by removing the load nodes in the power system, S is the set of all nodes in the power system, a ij Indicating whether the line connected to node j remains in the net frame, z i Indicating whether node i remains in the net rack, y i Indicating whether node i is required to remain in the net rack, x e Whether the line e is reserved in the bottom-retaining net rack or not is shown, x, y, z and a are all variables of 0 or 1, 0 is taken to indicate that the line is not reserved, and 1 is taken to indicate that the line is reserved; e (S) isA set of bidirectional lines in a virtual network, H being a set of a node S and a node adjacent to the node S;
the unit output constraint is as follows:
Figure FDA0003908568650000043
Figure FDA0003908568650000044
wherein u is i E {0,1} represents the starting and stopping conditions of the unit, 0 represents the shutdown of the unit, and 1 represents the start of the unit;
Figure FDA0003908568650000045
in order to have an active power output,
Figure FDA0003908568650000046
respectively representing the lower limit and the upper limit of the active power output of the generator;
Figure FDA0003908568650000047
in order to have no power output,
Figure FDA0003908568650000048
respectively representing the lower limit and the upper limit of the active power output of the generator;
the line power constraint is as follows:
-y ij M≤p ij ≤y ij M
-y ij M≤q ij ≤y ij M
-y ij M≤l ij ≤y ij M
when no line i-j is selected, p ij 、q ij And l ij Are all 0.
2. The method for searching and modeling of the bottom-preserving net rack based on the mixed integer second-order cone programming according to claim 1, wherein the second-order cone optimization relaxation is as follows:
Figure FDA0003908568650000051
wherein l ij Is the square of the i-j current value of the line, w i Is the product of the voltage values at node i.
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