CN113742917B - Comprehensive energy system toughness improvement method considering multi-stage recovery process - Google Patents

Comprehensive energy system toughness improvement method considering multi-stage recovery process Download PDF

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CN113742917B
CN113742917B CN202111037647.8A CN202111037647A CN113742917B CN 113742917 B CN113742917 B CN 113742917B CN 202111037647 A CN202111037647 A CN 202111037647A CN 113742917 B CN113742917 B CN 113742917B
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孙琦润
吴志
顾伟
陆于平
周苏洋
刘鹏翔
何品泉
熊钰
罗李子
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Abstract

The invention discloses a comprehensive energy system toughness improvement method considering a multi-stage recovery process, which comprises the following specific steps: firstly, constructing a pre-disaster preparation stage model; secondly, constructing a disaster attack stage model, and identifying fault and non-fault areas in the comprehensive energy system after the disaster happens; then, constructing a fault isolation stage model and reducing the area of a fault region; then, constructing an energy supply recovery stage model based on rapid reconstruction of the net rack, and realizing energy supply recovery of users in a non-fault area; and finally, decomposing the original model into a series of fault scene sub-models capable of being solved in parallel by adopting a step-by-step hedging algorithm, and realizing efficient and rapid solving of the model. The invention provides a comprehensive energy system toughness improvement method considering a multi-stage recovery process and multi-energy flow coordination from the viewpoints of pre-disaster active defense, rapid post-disaster fault isolation and energy supply recovery, and provides a theoretical basis for extreme disaster response capability construction of a toughness comprehensive energy system.

Description

Comprehensive energy system toughness improvement method considering multi-stage recovery process
Technical Field
The invention relates to a comprehensive energy system toughness improvement method considering a multi-stage recovery process, and belongs to the technical field of comprehensive energy system optimization.
Background
With the increasingly prominent global energy and environmental problems, the construction of a cleaner and more efficient comprehensive energy system becomes an important development direction for the energy structure optimization in China. The multi-energy interconnected comprehensive energy system realizes mutual coupling, substitution and supplement of multi-energy forms and promotes the diversified utilization of energy. In recent years, various extreme weather events occur, and the energy supply safety of the comprehensive energy system is seriously threatened. The operation optimization of the current comprehensive energy system does not sufficiently consider the extreme climate risk, on one hand, the influence of extreme weather on the comprehensive energy system can be divided into a plurality of stages, certain coupling relation exists among different stages, and the whole energy supply recovery process needs to be comprehensively considered; on the other hand, protection against its risks cannot rely on only a single energy system. Therefore, it is important to propose a strategy for toughness restoration that takes into account a multi-stage restoration process to construct an integrated energy system with climate toughness.
Disclosure of Invention
In order to solve the technical problems in the background art, the invention provides a comprehensive energy system toughness improvement method considering a multi-stage recovery process, and aims at the toughness improvement problem of the comprehensive energy system under the impact of extreme disasters, the comprehensive energy system toughness improvement method comprehensively considering multi-stage recovery processes of pre-disaster active defense, post-disaster fault rapid isolation, energy supply recovery based on rapid net rack reconstruction and the like and coordination of multi-energy flow systems such as a power distribution network, an air distribution network, an energy concentrator and the like is established, and a theoretical basis is provided for the construction of the extreme disaster response capability of the tough comprehensive energy system.
The invention adopts the following technical scheme for solving the technical problems:
a comprehensive energy system toughness improvement method considering a multi-stage recovery process comprises the following steps:
step 1, constructing a pre-disaster preparation stage model with the purposes of reducing the damage degree of a disaster to a system and improving the post-disaster energy supply recovery speed of the system;
step 2, constructing a disaster attack stage model, identifying fault and non-fault areas in the system after the disaster occurs, and providing a basis for a fault isolation stage;
step 3, constructing a fault isolation stage model, reducing the area of a fault area, and preparing for realizing system energy supply recovery based on rapid network frame reconstruction;
step 4, constructing an energy supply recovery stage model based on rapid net rack reconstruction, and realizing energy supply recovery of a non-fault area;
and 5, converting the model into a series of fault scene sub-models capable of being solved in parallel by adopting a step-by-step hedging algorithm, and realizing rapid solving.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
1. most of the existing researches on the comprehensive energy system toughness recovery strategy consider a single recovery process, and the coordination capacity among different energy subsystems is not considered enough. Considering that a certain coupling relation exists among different stages such as a preparation stage before a disaster, a disaster attack stage, a fault isolation stage and an energy supply recovery stage, meanwhile, energy supply recovery processes can be assisted through multi-energy complementation among different energy subsystems, and comprehensively considering the multi-stage recovery process is very important for enhancing the resistance capability of the comprehensive energy system to extreme weather events. The method considers the multi-stage recovery process and takes the coupling relation among different stages into account, so that the toughness of the comprehensive energy system is effectively improved.
2. The established model is a stochastic programming problem under the condition of considering multiple uncertain scenes, and when the number of scenes is large and the system scale is large, the model has long calculation time and low solving efficiency. The method adopts a step-by-step hedging algorithm to decompose the model into a series of disaster scene subproblems which can be solved in parallel to carry out iterative solution, thereby greatly improving the solution speed of the problems.
Drawings
FIG. 1 is a flow chart of an integrated energy system toughness boosting method of the present invention that contemplates a multi-stage recovery process.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
As shown in fig. 1, a flowchart of the method for improving toughness of an integrated energy system considering a multi-stage recovery process according to the present invention includes the following steps:
step 1, aiming at reducing the damage degree of the system caused by the disaster and improving the energy supply recovery speed of the system after the disaster, constructing a pre-disaster preparation stage model
Step 101, the deployment quantity of the remote switches and the remote valves is restricted as follows:
Figure GDA0003299827250000031
Figure GDA0003299827250000032
in the formula (II)
Figure GDA0003299827250000033
Respectively representing a line set in a power distribution network and a pipeline set in a gas distribution network; ij. mn respectively represents the serial numbers of the lines and the pipelines; z is a radical ofij、zmnRespectively indicating whether the lines ij and mn are provided with 0-1 variables of a remote control switch and a remote control valve, wherein 1 represents installation, and 0 represents non-installation; n is a radical of hydrogenRCS、NRCVRespectively represents the maximum configuration quantity of remote control switches in the power distribution network and remote control valves in the gas distribution network.
Step 102, the net rack topology is constrained as follows:
Figure GDA0003299827250000034
Figure GDA0003299827250000035
Figure GDA0003299827250000036
Figure GDA0003299827250000037
Figure GDA0003299827250000038
Figure GDA0003299827250000039
Figure GDA00032998272500000310
in the formula (II)
Figure GDA00032998272500000311
Respectively representing a transformer substation node set and a distribution network gate station node set; collection
Figure GDA00032998272500000312
Figure GDA0003299827250000041
Respectively representing a power distribution network node set and a gas distribution network node set; ε represents a set of energy hub nodes; pi (i) and delta (i) respectively represent a line head section node set taking a node i as a tail end node and a line tail end node set taking the node i as a head end node in the power distribution network; pi (m) and delta (m) respectively represent a pipeline first section node set taking the node m as a tail end node and a pipeline tail end node set taking the node m as a head end node in the gas distribution network; the superscript Pre represents the Pre-disaster preparation stage;
Figure GDA0003299827250000042
virtual variables respectively representing whether the distribution line ij is put into operation in the forward direction and the reverse direction, wherein 1 represents putting into operation, and 0 represents not putting into operation;
Figure GDA0003299827250000043
a virtual variable representing the connection state of the distribution line ij, wherein 1 represents connection and 0 represents disconnection;
Figure GDA0003299827250000044
the method comprises the following steps of respectively representing commissioning state variables of a distribution line ij and a distribution pipeline mn, wherein 1 represents connection, and 0 represents disconnection;
Figure GDA0003299827250000045
respectively representing virtual power flow variables of the distribution lines ki and ij;
Figure GDA0003299827250000046
respectively representing the virtual airflow variables of km and mn of the gas distribution pipeline; di、DmRespectively representing the virtual load quantities of a power distribution network node i and a gas distribution network node m, wherein 1 represents that the electric load and the gas load are not 0, and 0 represents that the electric load and the gas load are 0; m represents a larger positive integer.
Step 103, power flow constraint of the power distribution network is as follows:
Figure GDA0003299827250000047
Figure GDA0003299827250000048
Figure GDA0003299827250000049
Figure GDA00032998272500000410
Figure GDA00032998272500000411
Figure GDA00032998272500000412
Figure GDA00032998272500000413
Figure GDA00032998272500000414
in the formula (II)
Figure GDA00032998272500000415
Representing a set of gas turbine nodes in a power distribution grid;
Figure GDA00032998272500000416
respectively showing the active power and the reactive power flowing through the distribution line ij,
Figure GDA0003299827250000051
respectively representing active power and reactive power flowing through the distribution line ki;
Figure GDA0003299827250000052
respectively representing active power and reactive power of the gas turbine at the node i;
Figure GDA0003299827250000053
respectively representing active power and reactive power of a node i transformer substation;
Figure GDA0003299827250000054
respectively representing active power and reactive power of the node i flowing to the power distribution network from the energy concentrator;
Figure GDA0003299827250000055
respectively representing the voltage square values of the nodes i and j; pD,i、QD,iRespectively representing the power values of active and reactive loads of the node i; rij、XijAre respectively provided withRepresents the resistance and reactance values of the line ij;
Figure GDA0003299827250000056
respectively representing the minimum value and the maximum value of the voltage of the node i;
Figure GDA0003299827250000057
represents the power capacity of line ij;
Figure GDA0003299827250000058
respectively representing the power factors of the gas turbine and the substation.
Step 104, the power flow constraint of the distribution network is as follows:
Figure GDA0003299827250000059
Figure GDA00032998272500000510
Figure GDA00032998272500000511
Figure GDA00032998272500000512
Figure GDA00032998272500000513
Figure GDA00032998272500000514
Figure GDA00032998272500000515
Figure GDA00032998272500000516
Figure GDA00032998272500000517
in the formula (II)
Figure GDA00032998272500000518
Representing a set of gas turbine nodes in a gas distribution network;
Figure GDA00032998272500000519
respectively representing the gas mass flow of the head end node and the tail end node of the pipeline mn;
Figure GDA00032998272500000520
the gas density of the node m and the node n is represented;
Figure GDA00032998272500000521
respectively representing the gas pressure of the nodes m and n;
Figure GDA00032998272500000522
representing the mass flow of the air stream at the gate station node m;
Figure GDA00032998272500000523
representing the gas consumption of the gas turbine at the node m;
Figure GDA00032998272500000524
representing the gas mass flow of the node m from the energy concentrator to the gas distribution network; Δ tPreRepresenting the duration of a preparation stage before a disaster; l ismn、Amn、dmn、
Figure GDA00032998272500000620
ψmnRespectively representing the length, cross-sectional area, diameter, friction coefficient and average gas flow rate of the pipe mn; c represents the speed of sound;
Figure GDA0003299827250000061
respectively representing the initial values of the gas mass flow of the first end node and the tail end node of the pipeline mn;
Figure GDA0003299827250000062
respectively representing the initial values of the gas density of the nodes m and n;
Figure GDA0003299827250000063
respectively representing the initial values of the gas pressure of the nodes m and n;
Figure GDA0003299827250000064
respectively represents the minimum and maximum gas mass flow of the head end node of the mn pipeline,
Figure GDA0003299827250000065
respectively representing the minimum and maximum gas mass flow of the mn tail end node of the pipeline;
Figure GDA0003299827250000066
representing the maximum gas mass flow at the gate station;
Figure GDA0003299827250000067
representing the maximum gas consumption of the gas turbine.
Step 105, the energy hub power flow constraint is as follows:
Figure GDA0003299827250000068
Figure GDA0003299827250000069
Figure GDA00032998272500000610
Figure GDA00032998272500000611
Figure GDA00032998272500000612
Figure GDA00032998272500000613
Figure GDA00032998272500000614
Figure GDA00032998272500000615
Figure GDA00032998272500000616
Figure GDA00032998272500000617
Figure GDA00032998272500000618
wherein set ε represents the set of energy hub nodes;
Figure GDA00032998272500000619
respectively representing the active power of photovoltaic, energy storage charging, energy storage discharging, electric gas conversion equipment, a gas turbine and a heat pump in the energy concentrator e;
Figure GDA0003299827250000071
respectively representing the gas mass flow of the electric gas conversion equipment, the gas turbine and the gas boiler;
Figure GDA0003299827250000072
respectively representing the thermal power of a gas turbine, a heat pump and a gas boiler;
Figure GDA00032998272500000718
the method comprises the steps of representing the active power of equipment chi, wherein the equipment chi comprises electric gas conversion equipment, a gas turbine and an electric heat pump;
Figure GDA0003299827250000073
respectively representing the active power transmitted to the power distribution network by the energy concentrator e and the gas mass flow transmitted to the gas distribution network;
Figure GDA0003299827250000074
representing the energy storage charging and discharging state, wherein the charging is 1, and the discharging is 0;
Figure GDA0003299827250000075
representing the state of charge of the energy storage battery; pD,e、HD,eRespectively representing the power of an active load and the power of a heat load in the energy concentrator e;
Figure GDA0003299827250000076
respectively representing the maximum values of the stored energy charging power and the discharge power; etaES+、ηES-representing the charging and discharging efficiency of the stored energy, respectively;
Figure GDA0003299827250000077
representing an initial value of the state of charge of the battery;
Figure GDA0003299827250000078
respectively representing the minimum value and the maximum value of the charge state of the energy storage battery;
Figure GDA0003299827250000079
respectively representing the maximum active power values of the electric gas conversion equipment, the gas turbine and the heat pump;
Figure GDA00032998272500000710
respectively representing electric switchesMaximum gas mass flow of gas equipment, gas turbines and gas boilers;
Figure GDA00032998272500000711
respectively representing the maximum thermal power values of the gas boiler and the electric heat pump;
Figure GDA00032998272500000712
representing the initial value of the active power of equipment chi; RDχ、RUχRespectively representing the maximum power values of downward and upward climbing of equipment chi, wherein the equipment chi comprises electric gas conversion equipment, a gas turbine and an electric heat pump; etaPtG、ηGT、ηGBRespectively showing the conversion efficiency of the electric gas conversion equipment, the gas boiler and the electric heat pump; etaGT,gp、ηGT,ghRespectively representing the gas-to-electricity and gas-to-heat efficiency of the gas turbine;
Figure GDA00032998272500000713
respectively representing the upper limit of active power transmitted from the energy concentrator to the distribution grid and the upper limit of gas mass flow transmitted to the distribution grid.
In step 106, the coupling constraints between systems are as follows:
Figure GDA00032998272500000714
Figure GDA00032998272500000715
in the formula (I), the compound is shown in the specification,
Figure GDA00032998272500000716
showing a gas source node set of a gas turbine in a gas distribution network at a node i of a power distribution network,
Figure GDA00032998272500000717
and respectively representing a connection node set of the energy concentrator node e and the power distribution network and a connection node set of the energy concentrator node e and the power distribution network.
Step 2, constructing a disaster attack stage model, identifying fault and non-fault areas in the system after the disaster happens, and providing basis for a fault isolation stage
Step 201, the net rack topology is constrained as follows:
Figure GDA0003299827250000081
Figure GDA0003299827250000082
in the formula, subscript s represents a disaster scene;
Figure GDA0003299827250000083
respectively representing state variables of nodes at two ends of a line or a pipeline ij after being attacked in a disaster scene s, wherein the fault state is 1, and the fault state is 0;
Figure GDA00032998272500000816
and (3) indicating whether the line or the pipeline ij is damaged or not under the disaster scene s, wherein the damage is 1 and the undamaged damage is 0.
Step 202, power flow constraint of the power distribution network is as follows:
Figure GDA0003299827250000084
Figure GDA0003299827250000085
Figure GDA0003299827250000086
Figure GDA0003299827250000087
Figure GDA0003299827250000088
Figure GDA0003299827250000089
Figure GDA00032998272500000810
Figure GDA00032998272500000811
Figure GDA00032998272500000812
Figure GDA00032998272500000813
in the formula (I), the compound is shown in the specification,
Figure GDA00032998272500000817
representing a set of disaster scenarios; the superscript Dis represents the disaster attack stage;
Figure GDA00032998272500000814
representing a commissioning state variable of a distribution line ij under a disaster scene s;
Figure GDA00032998272500000815
respectively representing active power and reactive power flowing through the distribution line ki under a disaster scene s,
Figure GDA0003299827250000091
respectively representing active power and reactive power flowing through a distribution line ij under a disaster scene s;
Figure GDA0003299827250000092
are respectively provided withThe active power and the reactive power of a gas turbine of a node i under a disaster scene s are represented;
Figure GDA0003299827250000093
respectively representing active power and reactive power of a node i transformer substation in a disaster scene s;
Figure GDA0003299827250000094
Figure GDA0003299827250000095
respectively representing active power and reactive power of a node i in a disaster scene s, which flow from an energy concentrator to a power distribution network;
Figure GDA0003299827250000096
respectively representing the active load shedding power and the reactive load shedding power of a node i under a disaster scene s;
Figure GDA0003299827250000097
respectively representing the voltage square values of the nodes i and j under the disaster scene s.
Step 203, the power flow constraint of the distribution network is as follows:
Figure GDA0003299827250000098
Figure GDA0003299827250000099
Figure GDA00032998272500000910
Figure GDA00032998272500000911
Figure GDA00032998272500000912
Figure GDA00032998272500000913
Figure GDA00032998272500000914
Figure GDA00032998272500000915
Figure GDA00032998272500000916
Figure GDA00032998272500000917
in the formula (I), the compound is shown in the specification,
Figure GDA00032998272500000918
representing the commissioning state variable of the gas distribution pipeline mn in a disaster scene s, wherein 1 represents connection and 0 represents disconnection;
Figure GDA00032998272500000919
respectively representing the gas mass flow of the head end node and the tail end node of the pipeline mn in a disaster scene s;
Figure GDA00032998272500000920
respectively representing the gas density of nodes m and n under a disaster scene s;
Figure GDA00032998272500000921
respectively representing the gas pressure of the nodes m and n under the disaster scene s;
Figure GDA00032998272500000922
representing the airflow mass flow of a node m of a lower gate station under a disaster scene s;
Figure GDA0003299827250000101
representing the gas consumption of a gas turbine at a node m under a disaster scene s;
Figure GDA0003299827250000102
representing the gas mass flow of the node m flowing to the gas distribution network from the energy concentrator under the disaster scene s;
Figure GDA0003299827250000103
representing the gas cutting load of a node m under a disaster scene s; Δ tDisRepresenting the duration of the pre-disaster attack phase.
In step 204, the power hub flow constraints are as follows:
Figure GDA0003299827250000104
Figure GDA0003299827250000105
Figure GDA0003299827250000106
Figure GDA0003299827250000107
Figure GDA0003299827250000108
Figure GDA0003299827250000109
Figure GDA00032998272500001010
Figure GDA00032998272500001011
Figure GDA00032998272500001012
Figure GDA00032998272500001013
in the formula (I), the compound is shown in the specification,
Figure GDA00032998272500001014
respectively representing active power of photovoltaic, energy storage charging, energy storage discharging, electric gas conversion equipment, a gas turbine and a heat pump in an energy concentrator e under a disaster scene s;
Figure GDA00032998272500001015
respectively representing the gas mass flow of the electric gas conversion equipment, the gas turbine and the gas boiler under the disaster scene s;
Figure GDA00032998272500001016
respectively representing the thermal power of a gas turbine, a heat pump and a gas boiler under a disaster scene s;
Figure GDA00032998272500001017
showing the magnitude of the active load power and the heat load power in the energy concentrator e;
Figure GDA00032998272500001018
the method comprises the steps of representing the active power of equipment chi under a disaster scene s, wherein the equipment chi comprises electric gas conversion equipment, a gas turbine and an electric heat pump;
Figure GDA0003299827250000111
respectively representing active power transmitted to a power distribution network by an energy concentrator e under a disaster scene s and gas mass flow transmitted to a gas distribution network;
Figure GDA0003299827250000112
representing the charging and discharging state of energy storage under a disaster scene s, wherein the charging is 1, and the discharging is 0;
Figure GDA0003299827250000113
and representing the charge state of the energy storage battery in a disaster scene s.
In step 205, the coupling constraints between systems are as follows:
Figure GDA0003299827250000114
Figure GDA0003299827250000115
Figure GDA0003299827250000116
Figure GDA0003299827250000117
the variables in the formulae are as described above.
Step 3, constructing a fault isolation stage model, reducing the area of a fault area, and preparing for system energy supply recovery based on rapid grid reconstruction
Step 301, the rack topology constraint is as follows:
Figure GDA0003299827250000118
Figure GDA0003299827250000119
Figure GDA00032998272500001110
in the formula, the upper mark Iso represents a fault isolation stage;
Figure GDA00032998272500001111
representing the running state variable of the line or pipeline ij under the fault scene s, wherein 1 represents that the pipeline is in a running state, and otherwise, the running state variable is 0;
Figure GDA00032998272500001112
and respectively representing state variables of nodes at two ends of the line or pipeline ij after being attacked in a disaster scene s, wherein the fault state is 1, and otherwise, the fault state is 0.
Step 302, power flow constraints and intersystem coupling constraints of the power distribution network, the gas distribution network and the energy concentrator are as follows:
the fault isolation phase related constraints are the same as the disaster attack phase.
Step 4, constructing an energy supply recovery stage model based on rapid net rack reconstruction, and realizing energy supply recovery of a non-fault area
Step 401, the net rack topology constraint in the energy supply recovery stage is the same as the net rack topology constraint in the preparation stage before the disaster.
And step 402, related constraints such as a power distribution network, a gas distribution network, an energy concentrator current constraint and an intersystem coupling constraint in the energy supply recovery stage are the same as those in the disaster attack stage.
Step 5, converting the model into a series of fault scene sub-models capable of being solved in parallel by adopting a step-by-step hedging algorithm to realize rapid solving
Step 501, considering the objective functions of the multi-energy flow coordination energy supply recovery model of the preparation stage before disaster, the disaster attack stage, the fault isolation stage and the energy supply recovery stage as follows:
Figure GDA0003299827250000121
in the formula, PrsRepresenting the probability of occurrence, ω, of a disaster scene si、ωm、ωeωiRespectively represent the node i electricity of the power distribution networkThe weight coefficients of the load, the air load of the node m of the air distribution network, the electric load and the heat load of the energy concentrator e,
Figure GDA0003299827250000129
representing the conversion factor of gas mass flow to electrical power.
Step 502, expressing the appellation model in a matrix form as follows:
Figure GDA0003299827250000122
wherein x represents a decision variable in a pre-disaster preparation stage, ysRepresenting decision variables of a disaster attack stage, a fault isolation stage and an energy supply recovery stage under a disaster scene s,
Figure GDA0003299827250000123
a transposed matrix representing the coefficients of the variables under the disaster scenario s,
Figure GDA0003299827250000124
representing a set of constraints under a disaster scenario s.
Step 503, converting the model into a fault scene sub-model capable of being solved in parallel by adopting a step-by-step hedging algorithm, and performing iterative solution specifically comprises the following steps:
(1) setting initial values of a penalty factor upsilon and a convergence coefficient epsilon, setting the iteration times k to be 0, and setting the initial fixed variable quantity sigmak0, initial value of Lagrange multiplier matrix
Figure GDA0003299827250000125
(2) For any fault scene
Figure GDA00032998272500001210
Solving sub-problems
Figure GDA0003299827250000126
(3) Averaging
Figure GDA0003299827250000127
(4) For any fault scene
Figure GDA00032998272500001211
Computing
Figure GDA0003299827250000128
(5) For any fault scene
Figure GDA00032998272500001311
Solving sub-problems
Figure GDA0003299827250000131
(6) Averaging
Figure GDA0003299827250000132
(7) For any fault scene
Figure GDA00032998272500001312
Computing
Figure GDA0003299827250000133
(8) If it satisfies
Figure GDA0003299827250000134
The iteration is terminated; otherwise, entering the step (9);
(9) if K is less than or equal to K3Or σk+1-σkEntering the step (10) when the value is more than or equal to 1; otherwise, entering the step (15);
(10) if K is more than or equal to K1Entering step (11); otherwise, entering a step (12);
(11) if it satisfies
Figure GDA0003299827250000135
Then is fixed
Figure GDA0003299827250000136
Take sigmak+1＝σk+1；
(12) If K is more than or equal to K2Entering step (13); otherwise, entering a step (14);
(13) if it satisfies
Figure GDA0003299827250000137
Then is fixed
Figure GDA0003299827250000138
Take sigmak+1＝σk+1；
(14) Taking k as k +1, and returning to the step (5);
(15) solving model
Figure GDA0003299827250000139
And (6) ending.
Taking a testing system as an example, the established method for improving the toughness of the comprehensive energy system considering the multi-stage recovery process is verified. Five comparative cases were set, which were:
1) case 1: consider a multi-stage recovery process;
2) case 2: considering multi-energy flow coordination, only considering a preparation stage before disaster;
3) case 3: considering multi-energy flow coordination and not considering a preparation stage before disaster;
4) case 4: considering a multi-stage recovery process, independently optimizing a power distribution network, a gas distribution network and an energy concentrator;
5) case 5: the multi-energy flow recovery process is considered, without considering the energy hub.
The percentage of energy recovery during the multi-stage recovery in cases 1-5 is shown in table 1.
TABLE 1 percentage energy recovery in cases 1-5 of the Multi-stage recovery Process
Figure GDA00032998272500001310
Figure GDA0003299827250000141
The result shows that the toughness of the comprehensive energy system in consideration of the multi-stage recovery process is effectively improved by the method for improving the toughness of the comprehensive energy system in response to the uncertain extreme disaster scene.
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the protection scope of the present invention.

Claims (1)

1. A comprehensive energy system toughness improvement method considering a multi-stage recovery process is characterized by comprising the following steps:
step 1, aiming at reducing the damage degree of a disaster to a system and improving the energy supply recovery speed of the system after the disaster, constructing a pre-disaster preparation stage model:
step 1.1, the deployment quantity of the remote control switches and the remote control valves is restricted as follows:
Figure DEST_PATH_FDA0003554445130000011
Figure DEST_PATH_FDA0003554445130000012
in the formula: collection
Figure DEST_PATH_FDA0003554445130000013
Respectively representing a line set in a power distribution network and a pipeline set in a gas distribution network;ij、mnrespectively representing the serial numbers of the lines and the pipelines; z is a radical ofij、zmnRespectively representing linesij、mnWhether a remote control switch and a 0-1 variable of a remote control valve are configured or not, wherein 1 represents installation, and 0 represents non-installation; n is a radical of hydrogenRCS、NRCVRespectively representing the maximum configuration quantity of remote control switches in the power distribution network and remote control valves in the gas distribution network;
step 1.2, the net rack topology constraint is as follows:
Figure DEST_PATH_FDA0003554445130000014
Figure DEST_PATH_FDA0003554445130000015
Figure DEST_PATH_FDA0003554445130000016
Figure DEST_PATH_FDA0003554445130000017
Figure DEST_PATH_FDA0003554445130000018
Figure DEST_PATH_FDA0003554445130000019
Figure DEST_PATH_FDA00035544451300000110
in the formula: collection
Figure DEST_PATH_FDA00035544451300000111
Respectively representing a transformer substation node set and a distribution network gate station node set; collection of
Figure DEST_PATH_FDA00035544451300000112
Figure DEST_PATH_FDA00035544451300000113
Respectively representing a distribution network node set and a distribution network node set; ε represents a set of energy hub nodes; pi (i) and delta (i) respectively represent nodes in the power distribution networkiLine head section node set as tail end node and nodeiA set of line end nodes being head end nodes; pi (m) and delta (m) respectively represent nodes in the gas distribution networkmPipeline first section node set serving as tail end node and nodemA set of pipeline end nodes which are head end nodes; the superscript Pre represents the Pre-disaster preparation stage;
Figure DEST_PATH_FDA0003554445130000021
respectively representing distribution linesijWhether forward or reverse run virtual variables,
Figure DEST_PATH_FDA0003554445130000022
indicating distribution lineskiVirtual variables of whether to put into operation in the forward direction and the reverse direction, wherein 1 represents putting into operation, and 0 represents not putting into operation;
Figure DEST_PATH_FDA0003554445130000023
indicating distribution linesijVirtual variables of the connected state, 1 represents connected, 0 represents not connected;
Figure DEST_PATH_FDA0003554445130000024
respectively representing distribution linesijGas distribution pipelinemn1 represents connected, 0 represents not connected;
Figure DEST_PATH_FDA0003554445130000025
respectively representing distribution lineski、ijA virtual power flow variable of (a);
Figure DEST_PATH_FDA0003554445130000026
respectively representing gas distribution ductskm、mnThe virtual airflow variable of (2); di、DmRespectively representing nodes of a distribution networkiGas distribution network nodem1 represents that the electrical load and the gas load are not 0, and 0 represents that the electrical load and the gas load are 0;Mrepresents a larger positive integer;
step 1.3, power flow constraint of the power distribution network is as follows:
Figure DEST_PATH_FDA0003554445130000027
Figure DEST_PATH_FDA0003554445130000028
Figure DEST_PATH_FDA0003554445130000029
Figure DEST_PATH_FDA00035544451300000210
Figure DEST_PATH_FDA00035544451300000211
Figure DEST_PATH_FDA00035544451300000212
Figure DEST_PATH_FDA00035544451300000213
Figure DEST_PATH_FDA00035544451300000214
in the formula: collection
Figure DEST_PATH_FDA00035544451300000215
Representing a set of gas turbine nodes in a power distribution grid;
Figure DEST_PATH_FDA00035544451300000216
respectively representing distribution linesijThe active power and the reactive power which flow through,
Figure DEST_PATH_FDA00035544451300000217
respectively representing distribution lineskiActive and reactive power flowing through;
Figure DEST_PATH_FDA0003554445130000031
respectively representing nodesiActive and reactive power of the gas turbine;
Figure DEST_PATH_FDA0003554445130000032
respectively representing nodesiActive and reactive power of the transformer substation;
Figure DEST_PATH_FDA0003554445130000033
respectively represent nodesiActive and reactive power flowing from the energy concentrator to the power distribution network;
Figure DEST_PATH_FDA0003554445130000034
respectively representing nodesiNode, nodejThe voltage square value of (a); pD,i、QD,iRespectively representing nodesiThe power values of active and reactive loads;
Figure DEST_PATH_FDA0003554445130000035
respectively representing nodesiMaximum active power of gas turbine and transformer substation; rij、XijAre respectively provided withIndicating lineijResistance, reactance value of (d);
Figure DEST_PATH_FDA0003554445130000036
Figure DEST_PATH_FDA0003554445130000037
respectively representing nodesiMinimum and maximum voltage values;
Figure DEST_PATH_FDA0003554445130000038
indicating lineijThe power capacity of (d);
Figure DEST_PATH_FDA0003554445130000039
Figure DEST_PATH_FDA00035544451300000310
respectively representing power factors of a gas turbine and a transformer substation;
step 1.4, the power flow constraint of the gas distribution network is as follows:
Figure DEST_PATH_FDA00035544451300000311
Figure DEST_PATH_FDA00035544451300000312
Figure DEST_PATH_FDA00035544451300000313
Figure DEST_PATH_FDA00035544451300000314
Figure DEST_PATH_FDA00035544451300000315
Figure DEST_PATH_FDA00035544451300000316
Figure DEST_PATH_FDA00035544451300000317
Figure DEST_PATH_FDA00035544451300000318
Figure DEST_PATH_FDA00035544451300000319
in the formula: collection of
Figure DEST_PATH_FDA00035544451300000320
Representing a set of gas turbine nodes in a gas distribution network;
Figure DEST_PATH_FDA00035544451300000321
respectively representing ductsmnThe gas mass flow of the head end and tail end nodes,
Figure DEST_PATH_FDA00035544451300000322
indicating a pipelmGas mass flow at end node, GD,mRepresenting nodesmGas mass flow of the gas load;
Figure DEST_PATH_FDA00035544451300000323
representing nodesm、nThe gas density of (a);
Figure DEST_PATH_FDA00035544451300000324
respectively representing nodesm、nThe gas pressure of (a);
Figure DEST_PATH_FDA00035544451300000325
representing a gate station nodemMass flow of the gas stream;
Figure DEST_PATH_FDA0003554445130000041
representing nodesmGas consumption of the gas turbine;
Figure DEST_PATH_FDA0003554445130000042
representing nodesmMass flow of gas from the energy concentrator to the gas distribution network; Δ tPreRepresenting the duration of a preparation stage before a disaster; l ismn、Amn、dmn、
Figure DEST_PATH_FDA0003554445130000043
ψmnRespectively representing ductsmnLength, cross-sectional area, diameter, coefficient of friction, and average gas flow rate;crepresents the speed of sound;
Figure 275204DEST_PATH_IMAGE002
、
Figure 647804DEST_PATH_IMAGE004
respectively representing ductsmnInitial values of gas mass flow of the head end node and the tail end node;
Figure DEST_PATH_FDA0003554445130000045
respectively represent nodesmThe minimum and maximum values of the gas pressure,
Figure DEST_PATH_FDA0003554445130000046
respectively representing nodesm、nThe initial value of gas density of (a);
Figure DEST_PATH_FDA0003554445130000047
respectively representing nodesm、nThe initial value of the gas pressure;
Figure DEST_PATH_FDA0003554445130000048
Figure DEST_PATH_FDA0003554445130000049
respectively representing conduitsmnThe minimum and maximum gas mass flow at the head end node,
Figure DEST_PATH_FDA00035544451300000410
respectively representing ductsmnThe minimum and maximum gas mass flow of the end node;
Figure DEST_PATH_FDA00035544451300000411
representing the maximum gas mass flow at the gate station;
Figure DEST_PATH_FDA00035544451300000412
representing a maximum gas consumption of the gas turbine;
step 1.5, the power flow constraint of the energy concentrator is as follows:
Figure DEST_PATH_FDA00035544451300000413
Figure DEST_PATH_FDA00035544451300000414
Figure DEST_PATH_FDA00035544451300000415
Figure DEST_PATH_FDA00035544451300000416
Figure DEST_PATH_FDA00035544451300000417
Figure DEST_PATH_FDA00035544451300000418
Figure DEST_PATH_FDA00035544451300000419
Figure DEST_PATH_FDA00035544451300000420
Figure DEST_PATH_FDA00035544451300000421
Figure DEST_PATH_FDA0003554445130000051
Figure DEST_PATH_FDA0003554445130000052
in the formula: set ε represents the set of energy hub nodes;
Figure DEST_PATH_FDA0003554445130000053
separately representing energy concentratorseActive power of medium photovoltaic, energy storage charging, energy storage discharging, electric gas conversion equipment, a gas turbine and a heat pump;
Figure DEST_PATH_FDA0003554445130000054
respectively representing the gas mass flow of the electric gas conversion equipment, the gas turbine and the gas boiler;
Figure DEST_PATH_FDA0003554445130000055
respectively showing the thermal power of a gas turbine, a heat pump and a gas boiler;
Figure DEST_PATH_FDA0003554445130000056
the method comprises the steps of representing the active power of equipment chi, wherein the equipment chi comprises electric gas conversion equipment, a gas turbine and an electric heat pump;
Figure DEST_PATH_FDA0003554445130000057
separately representing energy concentratorseThe active power transmitted to the power distribution network and the gas mass flow transmitted to the gas distribution network;
Figure DEST_PATH_FDA0003554445130000058
representing the energy storage charging and discharging state, wherein the charging is 1, and the discharging is 0;
Figure DEST_PATH_FDA0003554445130000059
representing the state of charge of the energy storage battery; pD,e、HD,eSeparately representing energy concentratorsePower of medium active load, thermal load;
Figure DEST_PATH_FDA00035544451300000510
respectively representing the maximum values of the stored energy charging power and the discharge power; etaES+、ηES-Respectively representing the charging efficiency and the discharging efficiency of the stored energy;
Figure DEST_PATH_FDA00035544451300000511
representing an initial value of the state of charge of the energy storage battery;
Figure DEST_PATH_FDA00035544451300000512
respectively representing minimum state of charge of energy storage batteryValue, maximum value;
Figure DEST_PATH_FDA00035544451300000513
respectively representing the maximum active power values of the electric gas conversion equipment, the gas turbine and the heat pump;
Figure DEST_PATH_FDA00035544451300000514
respectively representing the maximum values of the gas mass flow of the electric gas conversion equipment, the gas turbine and the gas boiler;
Figure DEST_PATH_FDA00035544451300000515
respectively representing the maximum thermal power values of the gas boiler and the electric heat pump;
Figure 739126DEST_PATH_IMAGE006
representing the initial value of the active power of equipment chi; RDχ、RUχRespectively representing the maximum power values of downward and upward climbing of equipment chi, wherein the equipment chi comprises electric gas conversion equipment, a gas turbine and an electric heat pump; Δ tPreIndicating the duration of the pre-disaster preparation phase, ηPtG、ηGB、ηHPRespectively showing the conversion efficiency of the electric gas conversion equipment, the gas boiler and the electric heat pump; etaGT,gp、ηGT,ghRespectively representing the gas-to-electricity and gas-to-heat efficiency of the gas turbine;
Figure DEST_PATH_FDA00035544451300000517
respectively representing the upper limit of active power transmitted from the energy concentrator to a power distribution network and the upper limit of gas mass flow transmitted to the gas distribution network;
step 1.6, the coupling constraint between systems is as follows:
Figure DEST_PATH_FDA00035544451300000518
Figure DEST_PATH_FDA00035544451300000519
in the formula:
Figure DEST_PATH_FDA0003554445130000061
representing nodes of a power distribution networkiA gas source node set of the gas turbine in the gas distribution network;
Figure DEST_PATH_FDA0003554445130000062
representing energy concentrator nodes separatelyeThe connection node set is connected with the power distribution network and the connection node set is connected with the gas distribution network;
step 2, constructing a disaster attack stage model, identifying fault and non-fault areas in the system after the disaster occurs, and providing a basis for a fault isolation stage:
step 2.1, the net rack topology constraint is as follows:
Figure DEST_PATH_FDA0003554445130000063
Figure DEST_PATH_FDA0003554445130000064
in the formula: subscriptsRepresenting a disaster scenario;
Figure DEST_PATH_FDA0003554445130000065
respectively representing lines or pipesijDisaster scene with nodes at two endssThe state variable after the next attack, the fault state is 1, and the fault is 0; lij,sRepresenting a disaster scenariosLower line or pipeijWhether the damage is caused is 1, and the damage is not caused is 0;
step 2.2, the power flow constraint of the power distribution network is as follows:
Figure DEST_PATH_FDA0003554445130000066
Figure DEST_PATH_FDA0003554445130000067
Figure DEST_PATH_FDA0003554445130000068
Figure DEST_PATH_FDA0003554445130000069
Figure DEST_PATH_FDA00035544451300000610
Figure DEST_PATH_FDA00035544451300000611
Figure DEST_PATH_FDA00035544451300000612
Figure DEST_PATH_FDA0003554445130000071
Figure DEST_PATH_FDA0003554445130000072
Figure DEST_PATH_FDA0003554445130000073
in the formula: s represents a disaster scene set; on the upper partThe logo Dis represents a disaster attack stage;
Figure DEST_PATH_FDA0003554445130000074
representing a disaster scenariosLower distribution lineijThe commissioning state variable of (a);
Figure DEST_PATH_FDA0003554445130000075
respectively representing disaster scenessLower distribution linekiThe active power and the reactive power which flow through,
Figure DEST_PATH_FDA0003554445130000076
respectively representing disaster scenessLower distribution lineijActive and reactive power flowing through;
Figure DEST_PATH_FDA0003554445130000077
respectively representing disaster scenessLower nodeiActive and reactive power of the gas turbine;
Figure DEST_PATH_FDA0003554445130000078
respectively representing disaster scenessLower nodeiActive and reactive power of the transformer substation;
Figure DEST_PATH_FDA0003554445130000079
Figure DEST_PATH_FDA00035544451300000710
respectively representing disaster scenessLower nodeiActive and reactive power flowing from the energy concentrator to the power distribution network;
Figure DEST_PATH_FDA00035544451300000711
respectively representing disaster scenessLower nodeiThe active load shedding power and the reactive load shedding power;
Figure DEST_PATH_FDA00035544451300000712
respectively representing disaster scenessLower nodei、Node pointjThe voltage square value of (a);
step 2.3, the power flow constraint of the gas distribution network is as follows:
Figure DEST_PATH_FDA00035544451300000713
Figure DEST_PATH_FDA00035544451300000714
Figure DEST_PATH_FDA00035544451300000715
Figure DEST_PATH_FDA00035544451300000716
Figure DEST_PATH_FDA00035544451300000717
Figure DEST_PATH_FDA00035544451300000718
Figure DEST_PATH_FDA00035544451300000719
Figure DEST_PATH_FDA00035544451300000720
Figure DEST_PATH_FDA0003554445130000081
Figure DEST_PATH_FDA0003554445130000082
in the formula:
Figure DEST_PATH_FDA0003554445130000083
representing a disaster scenariosLower gas distribution pipelinemn1 represents connected and 0 represents disconnected;
Figure DEST_PATH_FDA0003554445130000084
respectively representing disaster scenessLower pipelinemnThe gas mass flow of the head end and tail end nodes,
Figure DEST_PATH_FDA0003554445130000085
representing a disaster scenariosLower pipelinelmGas mass flow at the end node;
Figure DEST_PATH_FDA0003554445130000086
respectively representing disaster scenessLower nodem、nThe gas density of (a);
Figure DEST_PATH_FDA0003554445130000087
respectively representing disaster scenessLower nodem、nThe gas pressure of (a);
Figure DEST_PATH_FDA0003554445130000088
representing a disaster scenariosLower door station nodemMass flow of the gas stream;
Figure DEST_PATH_FDA0003554445130000089
representing a disaster scenariosLower nodemGas consumption of the gas turbine;
Figure DEST_PATH_FDA00035544451300000810
representing a disaster scenariosLower nodemMass flow of gas from the energy concentrator to the gas distribution network;
Figure DEST_PATH_FDA00035544451300000811
representing a disaster scenariosLower nodemThe gas cutting load of (1);
Figure DEST_PATH_FDA00035544451300000812
indicating gas distribution pipelinemnInmNode-in-disaster scenesThe state variable after the next attack, the fault state is 1, and the fault is 0; Δ tDisRepresenting the duration of the attack stage before the disaster;
step 2.4, the power flow constraint of the energy concentrator is as follows:
Figure DEST_PATH_FDA00035544451300000813
Figure DEST_PATH_FDA00035544451300000814
Figure DEST_PATH_FDA00035544451300000815
Figure DEST_PATH_FDA00035544451300000816
Figure DEST_PATH_FDA00035544451300000817
Figure DEST_PATH_FDA00035544451300000818
Figure DEST_PATH_FDA00035544451300000819
Figure DEST_PATH_FDA00035544451300000820
Figure DEST_PATH_FDA0003554445130000091
Figure DEST_PATH_FDA0003554445130000092
in the formula:
Figure DEST_PATH_FDA0003554445130000093
respectively representing active power of photovoltaic, energy storage charging, energy storage discharging, electric gas conversion equipment, a gas turbine and a heat pump in an energy concentrator e under a disaster scene s;
Figure DEST_PATH_FDA0003554445130000094
respectively representing the gas mass flow of the electric gas conversion equipment, the gas turbine and the gas boiler under the disaster scene s;
Figure DEST_PATH_FDA0003554445130000095
respectively representing the thermal power of a gas turbine, a heat pump and a gas boiler under a disaster scene s;
Figure DEST_PATH_FDA0003554445130000096
representing the magnitude of the tangential active load power and the tangential thermal load power in the energy concentrator e;
Figure DEST_PATH_FDA0003554445130000097
the method comprises the steps of representing the active power of equipment chi under a disaster scene s, wherein the equipment chi comprises electric gas conversion equipment, a gas turbine and an electric heat pump;
Figure DEST_PATH_FDA0003554445130000098
respectively representing active power transmitted to a power distribution network by an energy concentrator e under a disaster scene s and gas mass flow transmitted to a gas distribution network;
Figure DEST_PATH_FDA0003554445130000099
representing the energy storage charging and discharging state under the disaster scene s, wherein the charging is 1, and the discharging is 0;
Figure DEST_PATH_FDA00035544451300000910
representing the charge state of the energy storage battery under a disaster scene s;
Figure DEST_PATH_FDA00035544451300000911
respectively representing the maximum values of the stored energy charging power and the discharging power in the energy concentrator e under the disaster scene s;
step 2.5, the coupling constraint between systems is as follows:
Figure DEST_PATH_FDA00035544451300000912
Figure DEST_PATH_FDA00035544451300000913
Figure DEST_PATH_FDA00035544451300000914
Figure DEST_PATH_FDA00035544451300000915
variables in the formulae are described above;
step 3, constructing a fault isolation stage model, reducing the area of a fault area, and preparing for realizing system energy supply recovery based on rapid network frame reconstruction:
step 3.1, the net rack topology constraint is as follows:
Figure DEST_PATH_FDA0003554445130000101
Figure DEST_PATH_FDA0003554445130000102
Figure DEST_PATH_FDA0003554445130000103
in the formula: the superscript Iso represents the fault isolation phase;
Figure DEST_PATH_FDA0003554445130000104
representing fault scenariossLower line or pipeij1 represents in the running state, otherwise 0;
Figure DEST_PATH_FDA0003554445130000105
respectively representing lines or pipesijDisaster scene with nodes at two endssThe fault state of the state variable after the next attack is 1, otherwise, the state variable is 0;
step 3.2, the power distribution network, the gas distribution network, the energy concentrator flow constraint and the inter-system coupling constraint are the same as the disaster attack stage;
step 4, constructing an energy supply recovery stage model based on rapid net rack reconstruction, and realizing energy supply recovery of a non-fault area:
step 4.1, the net rack topology constraint in the energy supply recovery stage is the same as that in the preparation stage before the disaster;
step 4.2, the power distribution network, the gas distribution network, the energy concentrator flow constraint and the inter-system coupling constraint are the same as the disaster attack stage;
and 5, converting the model into a series of fault scene sub-models capable of being solved in parallel by adopting a step-by-step hedging algorithm to realize quick solving:
step 5.1, considering the objective functions of the multi-energy flow coordination energy supply recovery model in the preparation stage before disaster, the disaster attack stage, the fault isolation stage and the energy supply recovery stage as follows:
Figure DEST_PATH_FDA0003554445130000106
in the formula: pr (Pr) ofsRepresenting the occurrence probability of a disaster scenario s; omegai、ωm、ωeRespectively representing the weight coefficients of an electrical load of a node i of the power distribution network, an electrical load of a node m of the gas distribution network, an electrical load of an energy concentrator e and a thermal load;
Figure DEST_PATH_FDA0003554445130000107
representing a set of a disaster attack stage, a fault isolation stage and an energy supply recovery stage, wherein tau corresponds to each stage;
Figure DEST_PATH_FDA0003554445130000108
representing the tangential active electrical load of the power distribution network node i in the time period tau under the disaster scene s,
Figure DEST_PATH_FDA0003554445130000109
representing the air-cutting load of the distribution network node m in the time period tau under the disaster scene s,
Figure DEST_PATH_FDA00035544451300001010
respectively representing the cut active electric load quantity and the cut heat quantity of the energy concentrator e in the time period tau under the disaster scene sThe load capacity;
Figure DEST_PATH_FDA0003554445130000111
a conversion coefficient representing a gas mass flow rate and an electric power;
step 5.2, representing the model in a matrix form as follows:
Figure DEST_PATH_FDA0003554445130000112
in the formula: x represents a decision variable in a preparation stage before a disaster; y issThe decision variables represent a disaster attack stage, a fault isolation stage and an energy supply recovery stage under a disaster scene s;
Figure DEST_PATH_FDA0003554445130000113
a transposed matrix representing a variable coefficient in a disaster scene s;
Figure DEST_PATH_FDA0003554445130000114
representing a set of constraints under a disaster scenario s;
step 5.3, converting the model into a fault scene sub-model capable of being solved in parallel by adopting a step-by-step hedging algorithm, and carrying out iterative solution specifically comprises the following steps:
(1) setting initial values of a penalty factor upsilon and a convergence coefficient epsilon, setting the iteration times k to be 0, and setting the initial fixed variable quantity sigmak0, initial value of Lagrange multiplier matrix
Figure DEST_PATH_FDA0003554445130000115
(2) For any fault scene
Figure DEST_PATH_FDA0003554445130000116
Solving sub-problems
Figure DEST_PATH_FDA0003554445130000117
(3) Averaging
Figure DEST_PATH_FDA0003554445130000118
(4) For any fault scene
Figure DEST_PATH_FDA0003554445130000119
Computing
Figure DEST_PATH_FDA00035544451300001110
(5) For any fault scene
Figure DEST_PATH_FDA00035544451300001111
Solving sub-problems
Figure DEST_PATH_FDA00035544451300001112
(6) Averaging
Figure DEST_PATH_FDA00035544451300001113
(7) For any fault scene
Figure DEST_PATH_FDA00035544451300001114
Computing
Figure DEST_PATH_FDA00035544451300001115
(8) If it satisfies
Figure DEST_PATH_FDA00035544451300001116
The iteration is terminated; otherwise, entering the step (9);
(9) if K is less than or equal to K1Or σk+1-σkEntering the step (10) when the value is more than or equal to 1; otherwise, entering the step (15);
(10) if it satisfiesk≥K 2The process proceeds to step (11) (ii) a Otherwise, entering a step (12);
(11) if it satisfies
Figure DEST_PATH_FDA0003554445130000121
Then is fixed
Figure DEST_PATH_FDA0003554445130000122
Take sigmak+1＝σk+1
(12) If it satisfiesk≥K 3Entering step (13); otherwise, entering a step (14);
(13) if it satisfies
Figure DEST_PATH_FDA0003554445130000124
Is then fixed
Figure DEST_PATH_FDA0003554445130000125
Take sigmak+1＝σk+1；
(14) Getk=k+1, return to step (5);
(15) solving model
Figure DEST_PATH_FDA0003554445130000127
And then, the process is ended.
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