CN112217197B - Optimization method for economic dispatch of double-layer distributed multi-region power distribution network - Google Patents

Optimization method for economic dispatch of double-layer distributed multi-region power distribution network Download PDF

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CN112217197B
CN112217197B CN202010900513.3A CN202010900513A CN112217197B CN 112217197 B CN112217197 B CN 112217197B CN 202010900513 A CN202010900513 A CN 202010900513A CN 112217197 B CN112217197 B CN 112217197B
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殷林飞
孙志响
马晨骁
高放
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Guangxi University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/008—Circuit arrangements for ac mains or ac distribution networks involving trading of energy or energy transmission rights
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
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    • G06F17/15—Correlation function computation including computation of convolution operations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/067—Enterprise or organisation modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
    • G06Q50/06—Electricity, gas or water supply
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/003—Load forecast, e.g. methods or systems for forecasting future load demand
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/381—Dispersed generators
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/48—Controlling the sharing of the in-phase component
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/22—The renewable source being solar energy
    • H02J2300/24—The renewable source being solar energy of photovoltaic origin
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/28—The renewable source being wind energy
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/50—Photovoltaic [PV] energy
    • Y02E10/56—Power conversion systems, e.g. maximum power point trackers
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/70—Wind energy
    • Y02E10/76—Power conversion electric or electronic aspects
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/70—Smart grids as climate change mitigation technology in the energy generation sector
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications

Abstract

The invention provides an optimization method for economic dispatch of a double-layer distributed multi-region power distribution network, which comprises a bus tearing method for regional decomposition and a distributed consistency method for sub-region optimization, and also provides an optimization framework for economic dispatch of the double-layer distributed multi-region power distribution network considering new energy sources such as wind power, photovoltaic and the like. Firstly, the bus tearing method can divide a large-scale power system into a plurality of sub-area systems on one hand, so that the problems of high complexity and slow calculation of the large system are solved; on the other hand, distributed optimization among the areas can be realized by sharing partial information of the boundary virtual nodes among the areas, and the information safety among the areas can be well protected. Secondly, the distributed consistency method can effectively solve the problem of information privacy inside each sub-area power distribution network. Finally, in a large-scale interconnected power system, the double-layer distributed optimization method can quickly, safely and effectively obtain economic dispatching instructions of a multi-region power distribution network.

Description

Optimization method for economic dispatch of double-layer distributed multi-region power distribution network
Technical Field
The invention belongs to the field of multi-region economic dispatching in an electric power system, and relates to a double-layer distributed optimization method which is suitable for multi-region distribution network economic dispatching optimization of a large-scale interconnected electric power system.
Background
In recent years, traditional fossil energy is gradually exhausted, and greenhouse effect is also intensified due to large carbon emission. Therefore, the power generation of new energy sources such as wind power and photovoltaic with the characteristics of no pollution, low cost and the like has become necessary research. In addition, with the reasons of unbalanced regional development, uneven energy distribution, wide use of high-voltage transmission lines in modern strong smart power grids and the like, a large-scale multi-region interconnected power system has become a necessary pattern.
The opening of the power market makes the equipment and unit information in multi-region economic dispatch more and more important. The traditional multi-region economic dispatching problem of the power system is solved by a centralized optimization mode, namely, after mastering the load of the whole network and the information of the units, a dispatching center calculates according to a certain optimization method and sends dispatching instructions to the units. However, the optimization method is difficult to meet the communication and calculation requirements of a large-scale power system, and also faces the challenge that the problems of reliability, robustness, information privacy and the like are difficult to guarantee. The double-layer distributed multi-region optimization mode focuses on the individual independence and intelligence of each region participating in scheduling, and the calculation speed can be effectively increased by independently optimizing the subproblems in each region. Only exchanging partial information of the virtual nodes between the areas can effectively protect the operation reliability and the information privacy of each area; only the cost increase rate is exchanged among all the intelligent agents in each area, and the information of all the intelligent agents can be effectively protected. Therefore, the double-layer distributed optimization mode is more suitable for being applied to economic dispatching of a multi-area power distribution network with the modern information privacy problem being more and more concerned.
Disclosure of Invention
The invention provides an optimization method for economic dispatching of a double-layer distributed multi-area power distribution network. Firstly, dividing a large-scale power system into a plurality of smaller sub-area power systems, independently optimizing a sub-problem in each area, and realizing overall coordination optimization by sharing partial information of boundary virtual nodes, namely realizing first-layer distributed optimization; and then, optimizing each sub-region by adopting a distributed consistency method, wherein in the optimization process, the cost increase rate is exchanged among all agents of the sub-region to realize the solution of the sub-region, namely, the second-layer distributed optimization is realized. Therefore, on the premise of ensuring the safety and reliability of the system, the invention not only can accelerate the calculation speed, but also can well ensure the information privacy among and in each area.
After constructing an economic dispatch model with wind and photovoltaic energy, the objective function of the present invention can be described as:
Figure BDA0002659667630000021
wherein the content of the first and second substances,
Figure BDA0002659667630000022
wherein w is a weight coefficient; fGi,t、FWj,tAnd FPz,tThe cost of the ith conventional unit, the jth wind turbine unit and the zth photovoltaic unit at the moment t is respectively shown; n is a radical ofG、NWAnd NPThe number of the conventional units, the wind turbine generator units and the photovoltaic units are respectively; f. ofGi,tThe carbon emission of the ith conventional unit at the moment t; pGi,t、PWj,tAnd PPz,tThe power generation amounts of the ith conventional unit, the jth wind power generation unit and the zth photovoltaic unit are respectively set at the moment t; a isi、biAnd ciRespectively the cost coefficients of a quadratic term, a primary term and a constant term of the ith conventional unit; djAnd ezThe unit power generation economic cost of the jth wind turbine generator set and the zth photovoltaic generator set respectively; alpha is alphai、βiAnd gammaiThe carbon emission coefficients of a quadratic term, a primary term and a constant term of the ith conventional unit are respectively.
In addition, the present invention also satisfies the following equality and inequality constraints:
Figure BDA0002659667630000023
in the formula, PD,tLoad prediction value at time t; the superscripts max and min are the upper and lower limits of the variable; r isdiAnd ruiThe values of the downward slope and the upward slope of the conventional unit are respectively; sWu,t、SWd,tAnd SPu,t、SPd,tRespectively positive and negative rotation standby values of the wind turbine generator and the photovoltaic generator at the moment t; l isW+％、LW-% and LP+％、LP-% is the load positive and negative rotation standby demand coefficient in the wind turbine generator and the photovoltaic generator respectively; wu％、Wd% and Pu％、Pd% positive and negative rotation standby demand coefficients of the wind turbine generator and the photovoltaic generator respectively; t is60And T1060 minutes and 10 minutes, respectively.
The complete system is divided into a plurality of smaller sub-areas by a bus tearing method, and the sub-problem is independently optimized and solved in each sub-area, so that the operation speed can be effectively improved. The economic dispatch model of the multi-zone distribution network at this time can be described as:
Figure BDA0002659667630000031
Figure BDA0002659667630000032
in the formula, y is the number of the subregions; fyAn objective function for the y region; h isy(x) And gy(x) Respectively, equality and inequality constraints in the y-th region.
The invention is described by taking three areas as an example, so the coupling relationship of the boundary virtual nodes can be expressed as follows:
Figure BDA0002659667630000033
in the formula, xA1And xA2Virtual boundary variables for partition a and partition B, C; xiABThe electrical direction correction coefficient is the virtual boundary node between the areas A and B, and the main purpose of the electrical direction correction coefficient is to ensure the consistency of power flow. x is the number ofB1、xB2、xC1、xC2And xiBA、ξBC、ξCB、ξAC、ξCAThe description is the same as above.
For each sub-region, the invention proceeds using a distributed consistency approachLine optimization solution, firstly, determining an adjacency matrix A ═ a according to the network topology structure of the agentmn]And laplace matrix L ═ Lmn]Wherein the relationship between the two can be expressed as:
Figure BDA0002659667630000034
in the formula, amnAnd lmnRespectively adjacency matrix and laplace matrix elements.
Solving the line random matrix d of the agentmnAnd performing consistent cost incremental rate calculations for the follower and leader of the agent, i.e.
Figure BDA0002659667630000041
Figure BDA0002659667630000042
Figure BDA0002659667630000043
Equation (9) is the follower consistency variable calculation; formula (10) is the leader consistency variable calculation; wherein xm(k) And xm(k +1) are consistency variables of the mth intelligent machine set at the kth time and the kth +1 time respectively; epsilon is a power balance factor of the distributed consistency method; Δ P is the power offset.
And (3) calculating the cost micro-increment rate according to the formula (11), and judging whether the output of the unit and the cost micro-increment rate exceed the limit or not according to the formula (12) and the formula (13).
xm＝2PGm[wam+(1-w)αm]+[wbm+(1-w)βm] (11)
Figure BDA0002659667630000044
Figure BDA0002659667630000045
In the formula, m is the mth unit.
Figure BDA0002659667630000046
Calculating the power deviation value delta P by the formula (14), and judging that the absolute value of delta P is less than or equal to delta PmaxAnd if so, convergence of region calculation is carried out, boundary information begins to be exchanged among the regions, and when the active power difference of virtual boundary nodes among the regions is smaller than the set precision, the solution is considered to be finished.
Compared with the prior art, the invention has the following advantages and effects:
(1) the method combines the characteristic of inevitable pattern of large-scale regional interconnected power systems, also considers renewable energy sources such as wind power, photovoltaic energy and the like, and is very suitable for development and application of modern strong intelligent power grids.
(2) The double-layer distributed multi-region power distribution network economic dispatching method provided by the invention can divide the region into a plurality of sub-regions, improves the reliability and the operation speed of the system, and can ensure the safety of information between the regions and the internal devices by utilizing the double-layer distributed optimization characteristic.
Drawings
FIG. 1 is a schematic view of multi-zone bus bar tear for the method of the present invention.
FIG. 2 is a flow chart of a distributed consistency method for sub-regions of the method of the present invention.
FIG. 3 is an overall flow chart of the method of the present invention.
Detailed Description
The invention provides an optimization method for economic dispatch of a double-layer distributed multi-region power distribution network, which is described in detail in the following steps in combination with the attached drawings:
FIG. 1 is a schematic view of multi-zone bus bar tear for the method of the present invention. The middle of the A, B, C three-region tie line is broken to serve as a virtual boundary node of the region, and three complete regions can be obtained. The problem is solved by independent optimization among the regions, and the information of the virtual boundary nodes is exchanged, so that the overall coordination optimization among the regions is realized.
FIG. 2 is a flow chart of a distributed consistency method for sub-regions of the method of the present invention. The distributed consistency method can complete the solution of each sub-area only by exchanging consistency variables among the agents, and can effectively protect the information of each agent. The method comprises the following specific steps:
step 1: inputting a predicted load value, and setting the initial iteration step number k of each sub-region to be 0;
step 2: according to a formula (8) -10, the consistency variable of each agent serving as a follower and a leader is obtained, and the cost micro-increment rates of adjacent agents are exchanged;
and step 3: working out active power output according to a formula (12);
and 4, step 4: solving a consistency variable according to a formula (13);
and 5: solving a power deviation value according to a formula (14);
step 6: judging whether the power deviation value is smaller than the set maximum power deviation value or not, and if so, ending iteration; if not, making the iteration step number k equal to k +1, and then proceeding to step 2.
FIG. 3 is an overall flow chart of the method of the present invention. The method comprises the following specific steps:
step 1: carrying out regional decomposition by using a bus tearing method, and establishing a multi-region power distribution network economic dispatching model considering new energy sources such as wind power, photovoltaic and the like;
step 2: the method is used for single-time-interval optimization, so that an initial time interval t is set to be 1;
and step 3: setting the optimization times v between the regions to be 1;
and 4, step 4: inputting a predicted load value, and setting the initial iteration step number k of each sub-region to be 0;
and 5: according to a formula (8) -10, the consistency variable of each agent serving as a follower and a leader is obtained, and the cost micro-increment rates of adjacent agents are exchanged;
step 6: working out active power output according to a formula (12);
and 7: solving a consistency variable according to a formula (13);
and 8: solving a power deviation value according to a formula (14);
and step 9: judging whether the power deviation value is smaller than the set maximum power deviation value or not, if not, enabling the iteration step number k to be k +1, and then switching to the step 5; and if the active output information is smaller than the preset value, exchanging the active output information of the virtual nodes among the regions.
Step 10: judging whether the active errors of the boundary virtual nodes between the regions are smaller than the set precision, and if not, turning to the step 4; if yes, turning to step 11;
step 11: judging whether the current scheduling time interval reaches the total time interval of a single scheduling cycle, and if not, turning to the step 3; and if so, finishing the optimization solution.

Claims (1)

1. The optimization method for economic dispatch of the double-layer distributed multi-area power distribution network is characterized by comprising the following steps in the using process:
(1) building economic dispatching model with wind power and photovoltaic energy
An objective function:
Figure FDA0003523351060000011
wherein the content of the first and second substances,
Figure FDA0003523351060000012
wherein w is a weight coefficient; fGi,t、FWj,tAnd FPz,tThe cost of the ith conventional unit, the jth wind turbine unit and the zth photovoltaic unit at the moment t is respectively shown; n is a radical ofG、NWAnd NPThe number of the conventional units, the wind turbine generator units and the photovoltaic units are respectively; f. ofGi,tFor the ith station at the time of tCarbon emission of the conventional unit; pGi,t、PWj,tAnd PPz,tThe power generation amounts of the ith conventional unit, the jth wind power generation unit and the zth photovoltaic unit are respectively set at the moment t; a isi、biAnd ciRespectively the cost coefficients of a quadratic term, a primary term and a constant term of the ith conventional unit; djAnd ezThe unit power generation economic cost of the jth wind turbine generator set and the zth photovoltaic generator set respectively; alpha is alphai、βiAnd gammaiThe carbon emission coefficients of a quadratic term, a primary term and a constant term of the ith conventional unit are respectively;
equality constraints and inequality constraints:
Figure FDA0003523351060000013
in the formula, PD,tLoad prediction value at time t; the superscripts max and min are the upper and lower limits of the variable; r isdiAnd ruiThe values of the downward slope and the upward slope of the conventional unit are respectively; sWu,t、SWd,tAnd SPu,t、SPd,tRespectively positive and negative rotation standby values of the wind turbine generator and the photovoltaic generator at the moment t; l isW+％、LW-% and LP+％、LP-% is the load positive and negative rotation standby demand coefficient in the wind turbine generator and the photovoltaic generator respectively; wu％、Wd% and Pu％、Pd% positive and negative rotation standby demand coefficients of the wind turbine generator and the photovoltaic generator respectively; t is60And T1060 minutes and 10 minutes, respectively;
(2) dividing a large-scale power system into a plurality of smaller sub-area systems by adopting a bus tearing method, reconstructing an economic dispatching model of a multi-area power distribution network, exchanging partial information of boundary virtual nodes between areas, and forming first-layer distributed multi-area optimization in double-layer distributed optimization; after the area is decomposed, the mathematical model of the multi-area economic dispatch at the moment is as follows:
Figure 815727DEST_PATH_IMAGE002
Figure FDA0003523351060000022
in the formula, y is the number of the subregions; fyAn objective function for the y region; h isy(x) And gy(x) Respectively, equality and inequality constraints in the y region;
when active information of virtual boundary nodes is exchanged among the sub-regions, the virtual boundary nodes have a coupling relation, and are described as follows:
Figure FDA0003523351060000023
in the formula (I), the compound is shown in the specification,
Figure FDA0003523351060000024
and
Figure FDA0003523351060000025
are respectively the y1An area and the y2Electrical direction coefficients of boundary virtual nodes of the respective regions;
Figure FDA0003523351060000026
and
Figure FDA0003523351060000027
are respectively the y1An area and the y2The active power of each region;
(3) according to the model in the step (2), optimizing and solving the problem of each sub-region by adopting a distributed consistency method to form second-layer sub-region optimization in double-layer distribution; each unit in each sub-area mutually exchanges cost micro-increment rate information to complete distributed optimization of each sub-area; firstly, each sub-region needs to determine an adjacency matrix A ═ a according to respective network topologymn]Laplace matrix L ═ Lmn]And a row random matrix dmnThe concrete formula is as follows:
Figure FDA0003523351060000031
in the formula, k is the kth iteration;
after the predicted load value is input, the consistency variable of each sub-area is updated by calculating the power deviation at the moment, so that the power deviation delta P formula, the follower update formula and the leader update formula are expressed as follows:
Figure FDA0003523351060000032
Figure FDA0003523351060000033
Figure FDA0003523351060000034
wherein xm(k) And xm(k +1) are consistency variables of the mth intelligent machine set at the kth time and the kth +1 time respectively; epsilon is a power balance factor of the distributed consistency method;
then calculating the output P of each sub-areaGmAnd a cost incremental xmThe specific formula is expressed as follows:
Figure FDA0003523351060000035
in the formula, m is the upper standard of the mth unit; max and min are the upper and lower limits of the variable;
finally, judging whether the absolute value of delta P is less than or equal to delta PmaxAnd whether the optimization solution of each sub-area is completed is determined.
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