CN107968439B - Active power distribution network joint optimization algorithm based on mixed integer linear programming - Google Patents

Active power distribution network joint optimization algorithm based on mixed integer linear programming Download PDF

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CN107968439B
CN107968439B CN201711476257.4A CN201711476257A CN107968439B CN 107968439 B CN107968439 B CN 107968439B CN 201711476257 A CN201711476257 A CN 201711476257A CN 107968439 B CN107968439 B CN 107968439B
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distribution network
power distribution
cost
active power
loss
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CN107968439A (en
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吴衍达
陈波涛
李晓
王明强
徐珂
侯广松
王洋
踪凯
邓帅
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Hongfujin Precision Industry Wuhan Co Ltd
State Grid Corp of China SGCC
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State Grid Corp of China SGCC
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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
    • H02J3/38—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
    • H02J3/28—Arrangements for balancing of the load in a network by storage of energy
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/003—Load forecast, e.g. methods or systems for forecasting future load demand

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Abstract

The invention discloses an active power distribution network joint optimization algorithm based on mixed integer linear programming, which comprises the following steps: modeling uncertainty factors in planning of the active power distribution network; inputting basic data in active power distribution network planning; constructing an active power distribution network comprehensive planning model which takes the minimum comprehensive cost as a target function and meets all constraint conditions; and linearizing the nonlinear active power distribution network comprehensive planning model, and solving the model by adopting a mixed integer linear optimization algorithm. The invention converts the complex large-scale mixed integer nonlinear programming problem of active power distribution network programming into a mixed integer linear programming problem through a linearization method, thereby solving the problem by depending on a mature MILP commercial solver, greatly simplifying the solving difficulty of the active power distribution network programming problem and improving the efficiency and reliability of model solving.

Description

Active power distribution network joint optimization algorithm based on mixed integer linear programming
Technical Field
The invention relates to the technical field of power distribution networks of power systems, in particular to a combined optimization algorithm of Distributed Generation (DG) capacity and line selection of an active power distribution network based on mixed integer linear programming.
Background
An active power distribution network is a power distribution system that manages the flow of power through a flexible network topology for active control and management of distributed energy sources. The distributed energy resource management system can increase the system accepting capacity to distributed energy resources, improve the system consumption level to renewable energy resources, improve the asset utilization efficiency of the power distribution system, slow down the upgrading investment of the power distribution system, and improve the power supply quality and the power supply reliability.
The power distribution network planning is to meet the requirements of load growth and power grid development in the future, and determine when, where, what types of lines, substations, distributed energy sources and other equipment are built. The distribution network planning result directly influences the distribution network investment, the income and the safety, the reliability and the stability of system operation.
The optimization variables in the active power distribution network planning are more, the output power of the distributed power supply is influenced by meteorological conditions, larger uncertainty exists, the complexity of the active power distribution network planning is increased, and the method belongs to a large-scale mixed integer nonlinear solving problem.
At present, artificial intelligence algorithms are mostly adopted in the research on active power distribution network planning at home and abroad, a large amount of load flow calculation is required in the optimization process, the calculation amount is greatly increased, the calculation time is long, the global optimal solution is difficult to ensure, and the requirement on active power distribution network planning in actual engineering is difficult to meet.
In summary, an effective solution to the problem of the active power distribution network optimization algorithm in the prior art is still lacking.
Disclosure of Invention
In order to solve the defects of the prior art, the invention aims to provide an active power distribution network joint optimization algorithm based on mixed integer linear programming.
An active power distribution network joint optimization algorithm based on mixed integer linear programming comprises the following steps:
modeling uncertainty factors in planning of the active power distribution network;
inputting basic data in active power distribution network planning;
constructing an active power distribution network comprehensive planning model which takes the minimum comprehensive cost as a target function and meets all constraint conditions;
and linearizing the nonlinear active power distribution network comprehensive planning model, and solving the model by adopting a mixed integer linear optimization algorithm.
Further, modeling is performed on uncertainty factors in planning of the active power distribution network, specifically:
according to load prediction data and regional environmental factor statistical data (wind speed, illumination and the like) in the planning year of the power grid, 4 typical daily scenes representing all seasons of the power distribution network in the year are generated for each year in the planning year. In each typical daily scene, 24 planning periods are divided, each period is one hour, and the load prediction data and environmental parameters such as wind speed and illumination are assumed to be kept unchanged in each period. The load prediction data of each typical day scene is obtained according to a power distribution network load prediction technology, and the environmental parameters such as wind speed and illumination are obtained through regional historical wind speed and illumination data statistics.
Further, an objective function corresponding to the comprehensive cost of the active power distribution network comprehensive planning model is represented as:
minTC＝CDG_inv+CL_inv+Cgrid+CDG_oper+Closs+CLOL
wherein, TC (total cost) is the total cost of the planning cost converted to one year, and the total cost comprises the investment cost C of the distributed power supply DG converted to one yearDG_invInvestment cost of line CL_invOperation cost C of equivalent generator set of superior power gridgridDistributed generation DG operating cost CDG_operLoss on network cost ClossPenalty cost for loss of load CLOLIn the six parts, a superior power grid is equivalent to a generator, the operation variable cost is the electricity price, and the upper limit of output is the upper limit of the capacity of the transformer at the outlet of the transformer substation.
Further, the distributed generation DG in the objective function translates to one yearInvestment cost CDG_invThe calculation formula of (A) is as follows:
Figure BDA0001532891610000021
Figure BDA0001532891610000022
wherein i is an index of the newly-built distributed power supply, and N isDGIn order to increase the number of distributed power sources,
Figure BDA0001532891610000023
the conversion coefficient of the ith distributed power supply investment cost, namely the conversion rate, is used for converting the initial investment cost of the distributed power supply to each year in the service life of the distributed power supply.
Figure BDA0001532891610000024
Is the planned construction capacity of the ith distributed power supply. r is the depreciation rate of the distributed power supply or the investor's internal rate of return, niIs the service life of the ith distributed power source in years.
Further, the investment cost C of the line in the objective functionL_invClosely related to the transmission capacity and length of the line, pair CLThe calculation of (A) is as follows:
Figure BDA0001532891610000025
Figure BDA0001532891610000026
wherein i is the index of the newly created line, Nl is the number of lines,
Figure BDA0001532891610000027
a conversion factor, i.e. a depreciation rate, for the investment cost of the ith line, for converting the initial investment cost of the line to each year, C, within its lifetimeiIs the ith lineRoad unit length (1km) construction cost, LiIs the length of the ith line, r is the depreciation rate of the distributed power supply or the internal rate of return of the investor, nliIs the service life of the ith line, and the unit is year.
Further, overhead lines commonly used in 10kV medium voltage distribution networks are of the types LGJ-120, LGJ-150, LGJ-185, LGJ-240 and the like. In the model, the four models of the to-be-built lines between every two nodes ij in the planned power distribution network are assumed to be available for selection (more types of selection can be available in actual engineering), and the optimal model of each distribution network line is planned. Admittance Y of line ll＝Gl+jBlMaximum allowed power, i.e. line capacity, is ClOrder:
Yl＝Yl1·L·bl1+Yl2·L·bl2+Yl3·L·bl3+Yl4·L·bl4
bl1+bl2+bl3+bl4＝1
bli∈(0,1),i＝1,2,3,4
wherein, Yl1,Yl2,Yl3,Yl4The admittance per kilometer length of the lines of four types LGJ-120, LGJ-150, LGJ-185 and LGJ-240, respectively, bliA variable of 0,1 indicates that for each line, only one of the four line types can be selected. Introduction of 0,1 variable bliLine capacity C of the line llCan be expressed as:
Cl＝Cl1·bl1+Cl2·bl2+Cl3·bl3+Cl4·bl4
wherein, CliThe maximum allowable power of the four types of lines, namely the line capacity, of LGJ-120, LGJ-150, LGJ-185 and LGJ-240 are respectively shown. This expression indicates that for each line, the capacity can be selected and only one of the four line types specified. Capacity C for different types of lineslConstruction cost per unit length CiAnd depreciation rate
Figure BDA0001532891610000031
All being different, 0,1 variable bliWill affect the investment cost C of the lineL_invAnd corresponding constraints such as line capacity and the like, so that the mathematical model is changed into a mixed integer nonlinear programming model.
Further, the operation cost C of the equivalent generator set of the upper-level power grid in the objective functiongridThe calculation formula of (2) is as follows:
Figure BDA0001532891610000032
wherein, pitTo the electricity price, PgridAnd (t) is the power flowing into the feeder line from the power inflow point of the superior power grid (substation) at the time t, and the product 365 represents the conversion from one day to one year.
Further, the running cost C of the distributed generator DG in the objective functionDG_operThe calculation is made by the following formula:
Figure BDA0001532891610000033
in the formula, NDGNumber of newly added distributed power sources, Ci,tVariable cost factor for the operation of the ith distributed power supply, i.e. the cost of generating 1kWh of electricity, PpDGi，tAnd (4) outputting power of the ith distributed power supply at the time t.
Further, the cost C for the network loss in the objective functionlossThe calculation of (c) can be given by:
Figure BDA0001532891610000041
wherein, Ploss(t) is line loss power of distribution network system at t moment, pitIs the electricity price.
Further, the loss of load cost C in the objective functionLOLRepresenting the loss caused by the loss of load in the active power distribution network after the expected accident occurs to the active power distribution network; penalty cost for loss of load CLOLThe calculation formula is as follows:
Figure BDA0001532891610000042
in the formula, VOLLi,tIs the loss load penalty coefficient, LOL, of the ith node at the tth momenti,tThe load loss of the ith node in the t period is referred to. N is a radical ofiIs the total number of nodes in the distribution network.
Further, the constraint conditions of the active power distribution network planning model include: the distributed power supply output limit, the access capacity limit of distributed power supply access point, join in marriage net system total power balanced type, node power balanced type, branch capacity restraint, electric automobile relevant restraint, wherein, electric automobile relevant restraint includes: the energy limiting method comprises the following steps of charge and discharge power constraint of the electric automobile, energy limiting constraint of an energy storage unit and charge and discharge energy constraint of the electric automobile.
Further, the nonlinear comprehensive planning model of the active power distribution network is linearized, a mixed integer linear optimization algorithm is adopted for model solution, nonlinear constraint is converted into linear representation through a linearization method, and therefore the nonlinear planning model of the active power distribution network is converted into the mixed integer linearization model for solution.
The specific linearization solution method is as follows: firstly, carrying out linearization processing on the network loss of a network distribution system, wherein the linearization processing comprises a piecewise linearization technology and an absolute value linearization technology; obtaining a branch power linear expression according to the obtained network loss expression of the linear expression; and finally, carrying out linearization treatment on the nonlinear constraints containing the variables 0 and 1 in the model to finally obtain the mixed integer linear programming model with linear constraints.
The specific solving process is as follows: in an electric power system, the branch ac active power flow is expressed as:
Figure BDA0001532891610000043
Figure BDA0001532891610000044
in the formula, PijFor power flowing from node i to node j, PjiFor power flowing from node j to node i, UiIs the voltage on node i, UjIs the voltage on node j, θijIs the phase angle difference, G, of the node voltages at the two ends of branch ijijAnd BijFor the real and imaginary parts of the node admittance matrix elements, i.e.:
θij＝θi-θj
Figure BDA0001532891610000051
wherein r isijRepresenting the resistance, x, of branch ijijRepresenting the reactance of branch ij.
In the calculation, the effective value of the voltage at each point is considered to be 1, and the phase difference of the voltages at two ends of the element is considered to be not large, so that the voltages are approximately similar to each other
Figure BDA00015328916100000510
Therefore, the branch alternating current active power flow formula is simplified in an adding way to obtain:
Pij+Pji＝2Gij-2Gijcosθij＝2Gij(1-cosθij)
therefore, there are:
Figure BDA0001532891610000052
the above formula explains the line loss PlossCan be simplified into the voltage angular difference theta of two ends of the branchijThe quadratic function is further subjected to piecewise linearization to be converted into linear representation, and the quadratic function is divided into three sections to be subjected to linearization;
since the second quadrant is identical to the first quadrant, only linearization in the first quadrant is considered, for which the following definition is introduced for linearization of absolute values:
θij＝|θi-θj|
Figure BDA0001532891610000053
Figure BDA0001532891610000054
i.e. the total network loss in the distribution network is equal to the slope k of each segmentij(l) Multiplied by the phase angle difference thetaij(l) Multiplied by the line conductance GijAnd summing the network losses of all the lines after the line loss of the single line is obtained. However, since the absolute value is non-linear, the absolute value can be converted into linear to be solved by the following method, and two variables are newly defined here: thetaij +、θij -Order:
Figure BDA0001532891610000055
Figure BDA0001532891610000056
Figure BDA0001532891610000057
with the above linearized expression, the power tidal flow expression on line ij can also be linearized as:
Figure BDA0001532891610000058
Figure BDA0001532891610000059
in addition, the 0,1 variable b in the model due to the line model selectionliThe introduction of (2) can turn the model into a mixed integer programming problem. For the case of 0,1 variable multiplied by 0,1 variable and 0,1 variable multiplied by continuous variable when the model is solved, the linearization process can be performed by the following method:
let b, c be 0,1 variable, x be a continuous variable, and the variable z 1-b c, and the variable z 2-b x.
The method for linearizing z1 ═ b × c, i.e., the 0,1 variable multiplied by the 0,1 variable, is as follows:
z1≥0；
z1≤b；
z1≤c；
z1≥b+c-1；
namely, a non-linear expression of z1 ═ b × c is converted into the four linear expressions.
The method for linearizing the z2 ═ b × x, i.e., 0,1 variable multiplied by the continuous variable, is as follows:
z2≥b*xmin；
z2≤b*xmax；
z2≥x-xmax*(1-b)；
z2≤x-xmin*(1-b)；
in the above formula, xminAnd xmaxRespectively, the minimum value and the maximum value that the continuous variable x can take. The conversion converts the non-linear expression z2 ═ b × x into the four linear expressions described above.
So far, the nonlinear constraints of the whole planning model are all converted into linear constraints, the whole planning model is converted into a mixed integer linear planning model, and then a commercial mixed integer linear planning solver such as a CPLEX can be adopted for solving.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention constructs a combined planning model for planning DGs and lines of the active power distribution network simultaneously, can plan a constant volume scheme of the DGs and a model selection scheme of the lines simultaneously, has more comprehensive and comprehensive planning results, and improves the engineering application value of planning the active power distribution network.
2. The planning model considers the novel loads of the power distribution networks such as the electric automobile and the like, and can effectively adapt to the change of the power distribution network under the new situation at present.
3. The invention converts the complex large-scale mixed integer nonlinear programming problem of active power distribution network programming into a mixed integer linear programming problem through a linearization method, thereby solving the problem by depending on a mature MILP commercial solver, greatly simplifying the solving difficulty of the active power distribution network programming problem and improving the efficiency and reliability of model solving.
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The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and are not intended to limit the application.
FIG. 1 is a flow chart of an active power distribution network joint optimization algorithm based on mixed integer linear programming according to the present invention;
fig. 2 is a piecewise linearization diagram.
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
As introduced by the background art, the prior art has the defect that the optimization algorithm of the active power distribution network is complex, and in order to solve the technical problems, the application provides the active power distribution network joint optimization algorithm based on the mixed integer linear programming.
In an exemplary embodiment of the present application, as shown in fig. 1, an active distribution network joint optimization algorithm based on mixed integer linear programming is provided, where the active distribution network joint optimization algorithm based on mixed integer linear programming includes the following steps:
step (1): and modeling uncertainty in planning, including fluctuation factors such as wind power, photovoltaic, load, electricity price and the like.
Step (2): inputting planning basic data, including planning year, investment data, depreciation rate, branch set to be selected and the like;
and (3): constructing an active power distribution network comprehensive planning model which takes the minimum comprehensive cost as a target function and meets all constraint conditions;
and (4): linearizing the nonlinear programming problem by a linearization method, and solving a model by adopting a mixed integer linear optimization algorithm;
and (5): and outputting a planning scheme, which comprises a capacity fixing scheme of DG and a model selecting scheme of lines. The fixed volume scheme of the DG is a DG capacity value obtained by solving the model, and the model selection scheme of the line is a model of each line corresponding to the capacity of each line obtained by solving the model.
In the step (1), 4 typical daily scenes representing all seasons of the power distribution network in the year are generated for each year in the planning year according to load prediction data in the planning year of the power grid and statistical data (wind speed, illumination and the like) of regional environmental factors. In each typical daily scene, 24 planning periods are divided, each period is one hour, and the load prediction data and environmental parameters such as wind speed and illumination are assumed to be kept unchanged in each period. The load prediction data of each typical day scene is obtained according to a power distribution network load prediction technology, and the environmental parameters such as wind speed and illumination are obtained through regional historical wind speed and illumination data statistics.
In the step (3), the comprehensive cost of the active power distribution network planning model is represented as:
minTC＝CDG_inv+CL_inv+Cgrid+CDG_oper+Closs+CLOL(1)
wherein, TC (total cost) is the total cost of the planning cost converted to one year, and the total cost comprises the investment cost C of the distributed power supply DG converted to one yearDG_invInvestment cost of line CL_invOperation cost C of equivalent generator set of superior power gridgridDistributed generation DG operating cost CDG_operLoss on network cost ClossPenalty cost for loss of load CLOLSix parts. In the application, a superior power grid (transformer substation) is equivalent to a generator, the operation variable cost of the generator is the electricity price, and the upper limit of output is the upper limit of the capacity of an outlet transformer of the transformer substation.
Investment cost C of converting distributed power supply DG into one year in objective functionDG_invThe calculation formula of (A) is as follows:
Figure BDA0001532891610000081
Figure BDA0001532891610000082
wherein i is an index of the newly-built distributed power supply, and N isDGIn order to increase the number of distributed power sources,
Figure BDA0001532891610000083
the conversion coefficient of the ith distributed power supply investment cost, namely the conversion rate, is used for converting the initial investment cost of the distributed power supply to each year in the service life of the distributed power supply.
Figure BDA0001532891610000084
Is the planned construction capacity of the ith distributed power supply. r is the depreciation rate of the distributed power supply or the investor's internal rate of return, niIs the service life of the ith distributed power source in years.
Investment cost C of line in objective functionL_invClosely related to the transmission capacity and length of the line, pair CL_invThe calculation of (A) is as follows:
Figure BDA0001532891610000085
Figure BDA0001532891610000086
wherein i is the index of the newly created line, Nl is the number of lines,
Figure BDA0001532891610000087
a conversion factor, i.e. a depreciation rate, for the investment cost of the ith line, for converting the initial investment cost of the line to each year, C, within its lifetimeiIs the unit length (1km) construction cost, L, of the ith lineiIs the length of the ith line, r is the depreciation rate of the distributed power supply or the internal rate of return of the investor, nliIs the service life of the ith line, and the unit is year.
The goal of the present planning model is to optimize the line best choice and DG capacity. Overhead lines commonly used in 10kV medium voltage distribution networks are of the types LGJ-120, LGJ-150, LGJ-185, LGJ-240 and the like. In the model, the four models of the to-be-built lines between every two nodes ij in the planned power distribution network are assumed to be available for selection (more types of selection can be available in actual engineering), and the optimal model of each distribution network line is planned. Admittance Y of line ll＝Gl+jBlMaximum allowed power, i.e. line capacity, is ClOrder:
Yl＝Yl1·L·bl1+Yl2·L·bl2+Yl3·L·bl3+Yl4·L·bl4
bl1+bl2+bl3+bl4＝1
bli∈(0,1),i＝1,2,3,4 (6)
wherein, Yl1,Yl2,Yl3,Yl4The admittance per kilometer length of the lines of four types LGJ-120, LGJ-150, LGJ-185 and LGJ-240, respectively, bliA variable of 0,1 indicates that for each line, only one of the four line types can be selected. Introduction of 0,1 variable bliLine capacity C of the line llCan be expressed as:
Cl＝Cl1·bl1+Cl2·bl2+Cl3·bl3+Cl4·bl4(7)
wherein the content of the first and second substances,Clirespectively showing the maximum allowable capacity of the four types of lines LGJ-120, LGJ-150, LGJ-185 and LGJ-240. This expression indicates that for each line, the capacity can be selected and only one of the four line types specified. After the planning result determines the line capacity, the line selection is determined.
Operation cost C of equivalent generator set of upper-level power grid in objective functiongridThe calculation formula of (2) is as follows:
Figure BDA0001532891610000091
wherein, pitTo the electricity price, PgridAnd (t) is the power flowing into the feeder line from the power inflow point of the superior power grid (substation) at the time t, and the product 365 represents the conversion from one day to one year.
Distributed Generation (DG) running cost C in objective functionDG_operThe calculation is made by the following formula:
Figure BDA0001532891610000092
in the formula, NDGNumber of newly added distributed power sources, Ci,tVariable cost factor for the operation of the ith distributed power supply, i.e. the cost of generating 1kWh of electricity, PpDGi，tAnd (4) outputting power of the ith distributed power supply at the time t.
Cost C for loss of network in objective functionlossThe calculation of (c) can be given by:
Figure BDA0001532891610000093
wherein, Ploss(t) is line loss power of distribution network system at t moment, pitIs the electricity price.
Loss of load cost C in the objective functionLOLThe loss caused by the loss of the load in the active power distribution network after the expected accident occurs to the active power distribution network is represented. It can be expressed as the product of the value of load loss (VOLL) and the load loss (load of load, LOL). Loss of loadThe loss of load (lol) refers to the difference between the available capacity of the power generation system and the load demand, and when the power generation amount of the power supply in the system cannot meet the load demand of a user, the system cuts off part of the load amount so as to meet the load flow balance. The LOL is therefore closely related to the reliability of the system, and its quantification reflects the reliability of the system. Therefore, the load loss cost is put into the objective function as a penalty term when the system capacity is insufficient under the expected accident, so that the model considers the economy and the reliability of the system at the same time. Penalty cost for loss of load CLOLThe calculation formula is as follows:
Figure BDA0001532891610000101
in the formula, VOLLi,tIs the loss load penalty coefficient, LOL, of the ith node at the tth momenti,tThe load loss of the ith node in the t period is referred to. N is a radical ofiIs the total number of nodes in the distribution network.
In the step (3), the constraint conditions of the active power distribution network planning model include:
distributed power supply output limitation:
Figure BDA0001532891610000102
in the formula, Pi,tFor the output power, P, of the distributed power supply i at time ti DG_minFor the ith distributed power supply minimum output power,
Figure BDA0001532891610000103
is the capacity of the distributed power source.
Access capacity limitation of distributed power access points:
Figure BDA0001532891610000104
in the formula, omegaiTo be the set of all distributed power sources connected on node i,
Figure BDA0001532891610000105
is the maximum capacity of the distributed power supply of node i allowed to access.
For any time t, the system meets the following system total power balance formula:
Figure BDA0001532891610000106
wherein N isGThe total number of the distributed power sources in the active power distribution network. Note that an upper power supply is also included therein. N is a radical ofiIs the total number of nodes in the active distribution network, Di,tFor the predicted value of the load on node i at time t, LOLi,tIs the magnitude of the load loss at the node i at time t.
Furthermore, the system should satisfy the node power balance:
Pi,t-(Di,t-DRMi,t-LOLi,t)＝∑Pl_in-∑Pl_out(16)
wherein, DMRitResponding to the power regulation quantity of the load i at the time t at the demand side, sigma Pl_inSum of incoming power for the branches connected to node il_outThe sum of the outgoing powers for the branches connected to node i.
The calculation formula of the branch power is as follows:
Pij≈-Bij(θi-θj) (17)
wherein, BijThe susceptance value of branch ij, B, is the value of the four different types of lines that can be selectedijInstead of a constant, a variable containing a 0,1 variable can be calculated accordingly from equation (6).
Branch capacity constraint:
Figure BDA0001532891610000111
wherein the content of the first and second substances,
Figure BDA0001532891610000112
is the l-th lineCapacity.
Electric automobile relevant restraint in the distribution network system:
Figure BDA0001532891610000113
Figure BDA0001532891610000114
C(0)＝Cs(21)
Figure BDA0001532891610000115
Figure BDA0001532891610000116
wherein, the formula (19) requires that the charge and discharge power of the electric automobile cannot exceed the upper limit and the lower limit; the formula (20) represents the energy limit constraint of the energy storage unit, and in order to ensure the power output efficiency and the service life of the stored energy, the energy of the energy storage unit must be limited within a certain range to prevent overcharge and overdischarge; c (0) in equation (21) represents the remaining energy of the electric vehicle at the initial time of the entire scheduling cycle, C (t) in equation (22) represents the remaining energy of the electric vehicle at the charging end time, and the charging start time and the charging end time are given in the input data. The formula (23) is the charge and discharge energy constraint of the electric automobile, C (t +1) is the energy of the energy storage unit at the time of t +1, C (t) is the energy of the energy storage unit at the time of t, dTIs the time interval of each of the divided adjacent periods,
Figure BDA0001532891610000117
is the discharge power of the energy storage unit,
Figure BDA0001532891610000118
for charging power, ηEThe discharge efficiency of the electric automobile.
In the step (4), the step of converting the active power distribution network planning nonlinear model into the mixed integer linearized model is as follows: firstly, carrying out linearization processing on the network loss of a network distribution system, wherein the linearization processing comprises a piecewise linearization technology and an absolute value linearization technology; obtaining a branch power linear expression according to the obtained network loss expression of the linear expression; and finally, carrying out linearization treatment on the nonlinear constraints containing the variables 0 and 1 in the model to finally obtain the mixed integer linear programming model with linear constraints. The specific linearized solution method is as follows:
in an electric power system, the branch ac active power flow can be expressed as:
Figure BDA0001532891610000119
Figure BDA00015328916100001110
in the formula, PijFor power flowing from node i to node j, PjiFor power flowing from node j to node i, UiIs the voltage on node i, UjIs the voltage on node j, θijIs the phase angle difference, G, of the node voltages at the two ends of branch ijijAnd BijFor the real and imaginary parts of the node admittance matrix elements, i.e.:
θij＝θi-θj(26)
Figure BDA0001532891610000121
wherein r isijRepresenting the resistance, x, of branch ijijRepresenting the reactance of branch ij.
In the calculation, it is generally considered that the effective value of the voltage at each point is 1, and the phase difference of the voltages at both ends of the element is not large, and the voltages are approximated to be 1
Figure BDA0001532891610000129
Therefore, the addition of equation (24) and equation (25) can be simplified:
Pij+Pji＝2Gij-2Gijcosθij＝2Gij(1-cosθij) (29)
therefore, there are:
Figure BDA0001532891610000122
the above formula explains the line loss PlossCan be simplified into the voltage angular difference theta of two ends of the branchijThe second order function of (2) can be further converted into a linearized representation by dividing each half of the second order function into three segments as shown in fig. 2 below:
since the second quadrant is identical to the first quadrant case, here only linearization within the first quadrant is considered, for which the following definition is introduced for linearization of absolute values:
θij＝|θi-θj| (31)
Figure BDA0001532891610000123
Figure BDA0001532891610000124
wherein L is the total branch number of the distribution network system, GijConductance, k, for branch ijij(l) Indicating the magnitude of the slope of each piecewise line segment in the piecewise linearization. Since the absolute value of equation (31) is non-linear, it still needs to be further linearized. The solution can be performed by converting the absolute value into linearity in the following manner. Here, two variables, theta, are newly definedij +、θij -Order:
Figure BDA0001532891610000125
Figure BDA0001532891610000126
Figure BDA0001532891610000127
with the above linearized expression, the power tidal flow expression on line ij can also be linearized as:
Figure BDA0001532891610000128
Figure BDA0001532891610000131
in addition, the 0,1 variable b in the model due to the line model selectionliThe introduction of (2) can turn the model into a mixed integer programming problem. For the case of 0,1 variable multiplied by 0,1 variable and 0,1 variable multiplied by continuous variable when the model is solved, the linearization process can be performed by the following method:
let b, c be 0,1 variable, x be a continuous variable, and the variable z 1-b c, and the variable z 2-b x.
The method for linearizing z1 ═ b × c, i.e., the 0,1 variable multiplied by the 0,1 variable, is as follows:
Figure BDA0001532891610000132
namely, a non-linear expression of z1 ═ b × c is converted into the four linear expressions.
The method for linearizing the z2 ═ b × x, i.e., 0,1 variable multiplied by the continuous variable, is as follows:
Figure BDA0001532891610000133
in the above formula, xminAnd xmaxRespectively, the minimum value and the maximum value that the continuous variable x can take. The conversion converts the non-linear expression z2 ═ b × x into the four linear expressions described above.
So far, the nonlinear constraint of the whole model is converted into the linear constraint, the whole planning model is converted into the problem of solving the mixed integer linear programming, and then a commercial mixed integer linear programming solver such as CPLEX can be adopted for solving.
The above description is only a preferred embodiment of the present application and is not intended to limit the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims (7)

1. An active power distribution network joint optimization algorithm based on mixed integer linear programming is characterized by comprising the following steps:
modeling uncertainty factors in planning of the active power distribution network;
inputting basic data in active power distribution network planning;
constructing an active power distribution network comprehensive planning model which takes the minimum comprehensive cost as a target function and meets all constraint conditions;
linearizing a nonlinear active power distribution network comprehensive planning model, and solving the model by adopting a mixed integer linear optimization algorithm;
the objective function corresponding to the comprehensive cost of the active power distribution network comprehensive planning model is expressed as follows:
min TC＝CDG_inv+CL_inv+Cgrid+CDG_oper+Closs+CLOL
wherein, TC (total cost) is the total cost of the planning cost converted to one year, and the total cost comprises the investment cost C of the distributed power supply DG converted to one yearDG_invInvestment cost of line CL_invOperation cost C of equivalent generator set of superior power gridgridDistributed generation DG operating cost CDG_operLoss on network cost ClossPenalty cost for loss of load CLOLThe six parts are used for enabling a superior power grid to be equivalent to a generator, the operation variable cost is the electricity price, and the upper limit of output is the upper limit of the capacity of a transformer at the outlet of the transformer substation;
loss of load cost C in the objective functionLOLRepresenting the loss caused by the loss of load in the active power distribution network after the expected accident occurs to the active power distribution network; loss of loadPenalty cost CLOLThe calculation formula is as follows:
Figure FDA0002431133510000011
in the formula, VOLLi，tIs the loss load penalty coefficient, LOL, of the ith node at the tth momenti，tThe magnitude of the load loss of the ith node in the t period, NiThe total number of nodes in the power distribution network;
the constraint conditions of the active power distribution network planning model comprise: the distributed power supply output limit, the access capacity limit of distributed power supply access point, join in marriage net system total power balanced type, node power balanced type, branch capacity restraint, electric automobile relevant restraint, wherein, electric automobile relevant restraint includes: the energy limiting method comprises the following steps of (1) charge and discharge power constraint of the electric automobile, energy limiting constraint of an energy storage unit and charge and discharge energy constraint of the electric automobile;
the nonlinear active power distribution network comprehensive planning model is linearized, a mixed integer linear optimization algorithm is adopted for model solution, nonlinear constraint is converted into linear representation through a linearization method, and therefore the active power distribution network comprehensive planning nonlinear model is converted into a mixed integer linearization model for solution;
the specific linearization solution method is as follows: firstly, carrying out linearization processing on the network loss of a network distribution system, wherein the linearization processing comprises a piecewise linearization technology and an absolute value linearization technology; obtaining a branch power linear expression according to the obtained network loss expression of the linear expression; and finally, carrying out linearization treatment on the nonlinear constraints containing the variables 0 and 1 in the model to finally obtain the mixed integer linear programming model with linear constraints.
2. The joint optimization algorithm for the active distribution network based on the mixed integer linear programming as claimed in claim 1, wherein uncertainty factors in active distribution network programming are modeled, specifically:
according to load prediction data and regional environment factor statistical data in a power grid planning year, 4 typical day scenes representing all seasons of a power distribution network in the year are generated for each year in the planning year, in each typical day scene, 24 planning time periods are divided, each time period interval is one hour, and supposing that the load prediction data and environmental parameters such as wind speed and illumination are kept unchanged in each time period, wherein the load prediction data of each typical day scene is obtained according to a power distribution network load prediction technology, and the environmental parameters are obtained by regional historical wind speed and illumination data statistics.
3. The active power distribution network joint optimization algorithm based on mixed integer linear programming as claimed in claim 1, wherein the distributed power supply DG in the objective function is converted to an investment cost C of one yearDG_invThe calculation formula of (A) is as follows:
Figure FDA0002431133510000021
Figure FDA0002431133510000022
wherein i is an index of the newly-built distributed power supply, and N isDGIn order to increase the number of distributed power sources,
Figure FDA0002431133510000023
a conversion coefficient of the ith distributed power supply investment cost, namely, the depreciation rate, is used for converting the initial investment cost of the distributed power supply to each year in the service life of the distributed power supply,
Figure FDA0002431133510000024
is the planned construction capacity of the ith distributed power supply, r is the depreciation rate of the distributed power supply or the internal return rate of an investor, niIs the service life of the ith distributed power source in years.
4. The joint optimization algorithm for active power distribution network based on mixed integer linear programming as claimed in claim 1, wherein the investment cost of the line in the objective functionCL_invClosely related to the transmission capacity and length of the line, pair CL_invThe calculation of (A) is as follows:
Figure FDA0002431133510000025
Figure FDA0002431133510000026
wherein i is the index of the newly created line, Nl is the number of lines,
Figure FDA0002431133510000027
a conversion factor, i.e. a depreciation rate, for the investment cost of the ith line, for converting the initial investment cost of the line to each year, C, within its lifetimeiIs the planned construction capacity, L, of the ith lineiIs the length of the ith line, r is the depreciation rate of the distributed power supply or the internal rate of return of the investor, nliIs the service life of the ith line, and the unit is year.
5. The joint optimization algorithm for active distribution networks based on mixed integer linear programming according to claim 1,
operation cost C of upper-level power grid equivalent generator set in objective functiongridThe calculation formula of (2) is as follows:
Figure FDA0002431133510000031
wherein, pitTo the electricity price, PgridAnd (t) is the power flowing into the feeder line from the superior power grid, namely the substation power inflow point at the time t, and the product 365 represents the conversion from one day to one year.
6. The joint optimization algorithm for active power distribution networks based on mixed integer linear programming according to claim 1, wherein the operation cost C of distributed generation DG in the objective functionDG_operThe calculation is made by the following formula:
Figure FDA0002431133510000032
in the formula, NDGNumber of newly added distributed power sources, Ci，tVariable cost factor for the operation of the ith distributed power supply, i.e. the cost of generating 1kWh of electricity, PpDGi，tAnd (4) outputting power of the ith distributed power supply at the time t.
7. The joint optimization algorithm for active power distribution networks based on mixed integer linear programming as claimed in claim 1, wherein the cost C for network loss in the objective functionlossThe calculation of (c) can be given by:
Figure FDA0002431133510000033
wherein, Ploss(t) is line loss power of distribution network system at t moment, pitIs the electricity price.
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