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CN106779313A - Multiple target distributed power source addressing constant volume method based on mixed integer programming - Google Patents

Multiple target distributed power source addressing constant volume method based on mixed integer programming Download PDF

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CN106779313A
CN106779313A CN201611053304.XA CN201611053304A CN106779313A CN 106779313 A CN106779313 A CN 106779313A CN 201611053304 A CN201611053304 A CN 201611053304A CN 106779313 A CN106779313 A CN 106779313A
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multiple target
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邢海军
田书欣
范宏
赵晓莉
符杨
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Shanghai University of Electric Power
University of Shanghai for Science and Technology
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Abstract

The present invention relates to a kind of multiple target distributed power source addressing constant volume method based on mixed integer programming, based on DG temporal characteristicses, set up and consider DG investments, operation and maintenance cost, the multiple target DG addressing constant volume models of via net loss expense.For the Pareto front ends solution being evenly distributed, multi-objective problem is processed using orthogonal edges intersection point NBI.DG addressing constant volume plan models are converted into Second-order cone programming model for power flow equation and constraint Relaxation Strategy by being pushed back before use power distribution network, problem is solved using CVX platforms and GUROBI solution musical instruments used in a Buddhist or Taoist mass.SOCP models coupling orthogonal edges intersection point NBI methods solve power distribution network multiple objective programming and are equally applicable to other power distribution network relevant issues, can provide new thinking and can computational methods for distribution network planning, running optimizatin.

Description

Multiple target distributed power source addressing constant volume method based on mixed integer programming
Technical field
The present invention relates to a kind of distributed power supply management technology, more particularly to a kind of multiple target based on mixed integer programming Distributed power source addressing constant volume method.
Background technology
Under the increasingly serious background of global energy crisis and environmental pollution, power supply (Distributed in a distributed manner Generation, DG) it is that the renewable energy power generation of representative is increasingly taken seriously.DG can reduce the transimission power of circuit, Reduce distribution system loss and improve quality of voltage;Improve the reliability of power distribution network.But the access of DG also brings one to power distribution network The problem of series, such as harmonic pollution, the rising of access point voltage, system bidirectional trend, short circuit current are raised, three-phase imbalance, electricity Pressure fluctuation etc., while the presence of these problems can also limit the access of DG.If DG on-positions and capacity can suitably be reduced System network loss, improvement network reliability, quality of voltage;If but DG on-positions or capacity are unreasonable, can not only cause power distribution network to provide Produce and leave unused, and the negative effect of some row can be brought.With the increase of DG permeabilities in power distribution network, DG is grid-connected to alleviating electricity Power demand is nervous, improve energy resource structure etc. serves important function, but simultaneously also to including a series of power trains including planning System optimization problem brings new challenge.Therefore, DG addressing constant volumes are studied using the method for science, to the warp of power distribution network Ji, safe operation are significant.
The content of the invention
The present invention be directed to distributed power source development and with the problem for existing, it is proposed that one kind is based on mixed integer programming Multiple target distributed power source addressing constant volume method, DG addressing constant volume model conversions are into Second-order cone programming model (Second- Order Cone Programming, SOCP) solved, accelerated model solution can be carried out using ripe solution musical instruments used in a Buddhist or Taoist mass, obtain Globally optimal solution.
The technical scheme is that:A kind of multiple target distributed power source addressing constant volume side based on mixed integer programming Multiobjective programming models are converted into exercisable single goal Second-order cone programming model SOCP by method, specifically include following steps:
1) based on DG temporal characteristicses, set up and consider DG investments, operation and maintenance cost, the multiple target DG choosings of via net loss expense Location constant volume model;
2) optimal solution is asked with single target minimum:By DG addressing constant volume model conversions into SOCP models, with reference to solution musical instruments used in a Buddhist or Taoist mass pair Each target carries out accelerated model solution, obtains the optimal solution of each single target;
3) multiple target is processed using orthogonal edges intersection point NBI methods:It is feasible for one in Multiobjective Programming Point x*, when a lifting for target must to sacrifice other targets as cost when, then claim point x*It is a Pareto optimal solution, Mapping matrix Φ is formed by the mode of 1 Pareto optimal solutions correspondence multiple targetb, by mapping φb, each target of setting Weight vectors βkIt is mapped in object space L, obtains Utopia's line, normal vector n on Utopia's linebBefore multiple target Pareto End disaggregation constitutes the intercept D of the point of intersection of Pareto curved surfaceskWhen maximum, the point on corresponding Pareto curved surfaces is multiple target DG choosings Location constant volume optimal solution.
The beneficial effects of the present invention are:Multiple target distributed power source addressing constant volume of the present invention based on mixed integer programming Method, SOCP models coupling orthogonal edges intersection point NBI methods solve power distribution network multiple objective programming and are equally applicable to other power distribution network phases Pass problem, can provide new thinking and can computational methods for distribution network planning, running optimizatin.
Brief description of the drawings
Fig. 1 is that NBI methods of the present invention solve schematic diagram;
Fig. 2 solves flow chart figure for the present invention;
Fig. 3 is the node example initial network figures of IEEE of the present invention 33;
Fig. 4 is WTG of the present invention, PVG, load typical case's day curve map;
Fig. 5 is the Pareto curve maps of present invention investment and via net loss.
Specific embodiment
The present invention is based on DG temporal characteristicses, sets up and considers DG investments, operation and maintenance cost, the multiple target of via net loss expense DG addressing constant volume models.For the Pareto front ends solution being evenly distributed, using orthogonal edges intersection point (Normal Boundary Intersection, NBI) multi-objective problem is processed.Pushed back for power flow equation before by using power distribution network And DG addressing constant volume plan models are converted into Second-order cone programming model by constraint Relaxation Strategy, solved using CVX platforms and GUROBI Musical instruments used in a Buddhist or Taoist mass is solved to problem.
The present invention is realized by following approach:
1) DG addressings constant volume is set up for Multiobjective programming models, and object function includes:Minimize total investment in project period, Operation and maintenance cost and total grid loss in project period is minimized, it is specific as follows:
min f1=Cinv+Co+Cm+Cgrid (1)
min f2=Cploss (2)
DG investment costs
DG operating costs
DG maintenance costs
Power distribution network top-ranking's power supply power purchase expense
Via net loss expense
δy=1/ (1+r)y-1 (8)
Wherein:f1It is the total cost in project period, f2It is the total system via net loss in project period;ΨD, ΨjRespectively treat Build DG set of types, the set of node to be selected of jth class DG;The unit DG quantity installed at k-th node is represented, if 0 represents DG is not installed;It is the unit DG capacity at k-th node;Represent unit capacity jth class DG investment costs;For Operating costs of the unit capacity jth class DG in t;It is the year maintenance cost of unit capacity jth class DG;Y is planning Year, δyIt is the present value factor of y, r is discount rate;For typical day t purchases power from higher level's power network;It is typical case Day t is from higher level's power network purchase electricity price;For typical day t grid is lost.
2) setting up constraints includes DG investment and recoveries and network operation security constraint, specific as follows:
First, DG investment and recoveries
Wherein, (9) are the constraint of node k unit capacity DG installation numbers,It is unit capacity DG at k-th node Maximum allowable installation number;(10) it is the total installed capacity constraints of DG, i.e., DG permeabilities are less than β;ΦjFor jth class DG has installed section Point set;To have installed the rated capacity of DG at g-th node;It is the load power at n-th node.
2nd, network operation security constraint
Wherein, Ψb, ΨnTo represent power distribution network branch road collection and set of node respectively;(11) for node voltage bound is constrained, Vn,It is respectively node voltage, lower voltage limit and the upper limit;(12) for branch current is constrained, Iij,It is respectively Branch road (i, j) electric current and the upper limit.
Formula (13-15) is to push back for power flow equation constraint before power distribution network, carries out solution to be converted to SOCP models and does standard It is standby;It is node j loads active power and reactive power;At respectively node j DG active power outputs with It is idle to exert oneself;For reactive-load compensation capacitor injects idle amount at node j.rij, xijResistance and reactance for branch road (i, j); Pij, QijFor the head end of branch road (i, j) is active and reactive power;Vi, VjIt is node i and j voltage magnitudes;Pjk, QjkFor branch road (j, K) the active and reactive power of head end;Formula (16) is active power loss expression formula;Formula (17) is DG units limits,It is DG active power outputs lower limit and the upper limit at node j.Formula (18) is DG active reactive units limits,It is DG power-factor angles at node j.
3) by model conversion MIXED INTEGER Second-order cone programming model
SOCP problems are a Nonlinear Convex problems, and Feasible Solution Region is SOC, because SOCP problems are that polynomial time can be counted Calculation problem, is applied in substantial amounts of practical problem.The present invention utilizes model conversion MIXED INTEGER Second-order cone programming model CVX modeling tools bag and GUROBI solution musical instruments used in a Buddhist or Taoist mass are solved to model.
Needing can representative function into second order cone by Restriction condition treat.Introduce new variables Then constraint (13-16) can be exchanged into:
Increase new equality constraint simultaneously:
Formula (23) can be converted into following SOC forms by lax:
Wherein | | | |2It is euclideam norm.
Constraint (11-12) can be expressed as form using new variables:
4) Multi-Objective Electric Power Network Planning model is converted into single goal model solution using NBI methods.Pareto curves by Pareto front ends disaggregation is constituted, and Pareto curves are constituted by the Pareto front ends disaggregation of two or more multi-objective problems. It is under some constraintss, while considering the Electric Power Network Planning problem of two and two or more object function.Relative to single goal Planning, multiple objective programming finds the global solution being optimal with season multiple target due to being difficult, and generally requires to object function Processed, be a complex optimization problem.The present invention is used for the Pareto front ends solution being evenly distributed NBI methods are processed multi-objective problem.
For a typical multi-objective optimization question:
Wherein, n is target number to be optimized;X is solution vector;fiX () is i-th object function to be optimized;h(x) Equation and inequality constraints are respectively with g (x).
Generally, formula (27) individually solves x in the absence of one*, make all of object function fi(x*) while minimum.When and Only when in the absence of such point x, for all of i=1 ..., n, there is fi(x)≤fi(x*), and at least one for it is strict not Equation.I.e. when a lifting for target must to sacrifice other targets as cost when, then claim point x*It is that a Pareto is optimal Solution.
For each Pareto optimal solution, a Pareto forward terminal is all correspond in object space.Obviously, It is more uniform that Pareto forward terminals are distributed in object space, and the reference information provided to policymaker is also more comprehensive and accurate, And NBI rules are a kind of better methods that generation is uniformly distributed Pareto front ends disaggregation.NBI methods are given birth to by the method for geometric projection Into Pareto forward terminals, main solution procedure is divided into Coordinate Conversion, normal vector projection and intercept and optimizes three parts.
With two object function f1, f2As a example by, make the mapping matrix beWherein:x1Not examine Consider object function f1, only consider object function f2When optimal solution;x2Not consider object function f2When, only consider object function f1 When optimal solution.
By mapping φb, the weight vectors β that will can be setkIt is mapped in object space L:
L (β)=Φbβk (28)
In formula, weight vectors βkMeetN is the quantity of Utopia's line decile.
It can be seen from definition according to formula (28), L1=[f1(x1),f2(x1)]TAnd L2=[f1(x2),f2(x2)]TBe respectively β= [1,0]TWith β=[0,1]TUnder two points.Obviously, this 2 points is two end points in object space, the company between the two-end-point Line is referred to as Utopia's line.Therefore the effect of Coordinate Conversion is exactly by weight relationship βkIt is mapped to point L (β) on Utopia's line On.
In actual applications, different physical significances and dimension are there may be between different targets.To avoid in model Solution procedure in produce numerical problem, different targets can be normalized.Two end points of Utopia's line after specification L1b, L2bAs shown in formula (29).
The solution schematic diagram of NBI methods is as shown in Figure 1 after specification.According to Pareto optimality conditions, to make object function most It is small, normal vector nbWith the intercept D of the point of intersection of Pareto curved surfaceskIt is inevitable maximum.Therefore the Multiobjective programming models that the present invention sets up turn It is changed to as the intercept between the solution of formula (30) objective programming model, i.e. Utopia's line and Pareto curved surfaces is maximum.
H (x)=0, g (x)≤0
By formula (30), you can obtain given weight relationship βkUnder Pareto optimal solutions.NBI methods can not only be obtained The Pareto front ends solution of even distribution, it is ensured that for multiple target SOCP problems, can be equally continuing with SOCP models carried out Solve, specific solution flow is as shown in Figure 2.
Model and algorithm are verified using example in Fig. 3.DG types include wind-powered electricity generation (Wind Turbine Generator, WTG), photovoltaic (Photovoltaic Generator, PVG) and miniature gas turbine (Micro Turbine Generator, MTG), DG nodes to be installed, investment, operation and maintenance cost are as shown in table 1.DG and load typical case's day curve are as schemed Shown in 4.
Power reference value takes 10MVA, and voltage reference value takes 12.66kV.Node voltage constraint perunit value be 0.95~ 1.05p.u., branch power is constrained to 5MVA.DG permeabilities are constrained to 35%.Electricity price is for 0.06 ten thousand yuan/MWh discount rates 10%, planning is limited to 5 years in year.
Table 1
Such as table 1DG mount messages, to invest operating cost minimum (f1) it is the f of single goal1(x1) it is 6921.2 ten thousand yuan, together When via net loss f2(x1) it is 145.4 ten thousand yuan;With via net loss expense minimum (f2) it is the f of single goal2(x2) it is 132.4 ten thousand yuan, Operating cost f is invested simultaneously2(x1) it is 7831.8 ten thousand yuan.Corresponding decision variable x1And x2DG installation results as shown in table 2.
It is identical dimension because the multi-objective problem object function is all expense, is not normalized herein.Wu Tuo Two end points of nation's line are (6921.2,145.4), (7831.8,132.4), its normal vector nbIt is (- 0.9714, -0.2376). Utopia's line is carried out into 10 deciles, k-th Along ent is βk=[1-k/10, k/10]T.Being changed by object function to obtain Following new object function:
H (x)=0, g (x)≤0
K takes 1 to 9, and solution formula is carried out to model using CVX, obtains the Pareto front ends disaggregation after specification as shown in table 3 Pareto front ends solve.
Table 2
Table 3
Table 3 gives totally 10 Pareto Along ents corresponding target function value.As seen from table, in the first half of table, The increase of DG costs of investment can bring the reduction of via net loss;In the latter half of table, DG costs of investment are to reducing grid The influence of loss diminishes, and this is, because the DG capacity of some node installations is more than load, to cause reversal tidal current.In DG investments Above the economy of economy and system operation, the front end solution that table 3 is given can to planning personnel according to region actual conditions and Expense preference of interest selects optimal DG capital projects.
In the Pareto front ends disaggregation point such as Fig. 5 that are obtained using NBI methods shown in " o ".As a comparison, many using NSGA-II Target algorithm is solved to example, and algorithm population scale 20, maximum iteration is 200.In acquired results such as Fig. 5 Shown in " * " point.As seen from the figure, NBI methods can generate more equally distributed Pareto front ends solution, be obtained more than NSGA-II Uniformly.
The present invention proposes power distribution network multiple target DG addressing constant volume plan models, and using being pushed back for trend side before power distribution network Journey and constraint relaxing techniques have obtained the computable SOCP models of DG addressing constant volumes, and multi-objective problem is solved using NBI methods.Pass through Example Verification is just like drawing a conclusion:DG addressing constant volume model conversions are solved into SOCP models, can be entered using ripe solution musical instruments used in a Buddhist or Taoist mass Row accelerated model is solved, and obtains globally optimal solution.
With NSGA-II methods contrast the Pareto front ends solution for showing that NBI methods can be evenly distributed.SOCP models Power distribution network multiple objective programming is solved with reference to NBI methods and be equally applicable to other power distribution network relevant issues, can be distribution network planning, fortune Row optimization provides new thinking and can computational methods.

Claims (1)

1. a kind of multiple target distributed power source addressing constant volume method based on mixed integer programming, it is characterised in that by multiple target Plan model is converted into exercisable single goal Second-order cone programming model SOCP, specifically includes following steps:
1)Based on DG temporal characteristicses, set up and consider DG investments, operation and maintenance cost, the multiple target DG addressings of via net loss expense are determined Molar type;
2)Optimal solution is asked with single target minimum:By DG addressing constant volume model conversions into SOCP models, with reference to solution musical instruments used in a Buddhist or Taoist mass to each Target carries out accelerated model solution, obtains the optimal solution of each single target;
3)Multiple target is processed using orthogonal edges intersection point NBI methods:For a feasible point in Multiobjective Programming, When a lifting for target must to sacrifice other targets as cost when, then claim the pointIt is a Pareto optimal solution, by 1 The mode of individual Pareto optimal solutions correspondence multiple target forms mapping matrix Φ b , by mapping φ b , the power of each target of setting Weight vectorβ k It is mapped to object spaceLIn, obtain Utopia's line, normal vector on Utopia's linen b Solved with multiple target Pareto front ends Collection constitutes the intercept of the point of intersection of Pareto curved surfacesWhen maximum, the point on corresponding Pareto curved surfaces is multiple target DG addressings Constant volume optimal solution.
CN201611053304.XA 2016-11-25 2016-11-25 Multiple target distributed power source addressing constant volume method based on mixed integer programming Pending CN106779313A (en)

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CN108258724A (en) * 2018-01-22 2018-07-06 佛山科学技术学院 A kind of wind power plant unit is laid out Multipurpose Optimal Method
CN108599235A (en) * 2018-04-20 2018-09-28 国网湖北省电力有限公司宜昌供电公司 A kind of constant volume method that distributed photovoltaic networks
CN108629499A (en) * 2018-04-25 2018-10-09 国家电网公司 A kind of power distribution network photovoltaic plant addressing constant volume method based on second order cone theazy
CN109255558A (en) * 2018-10-31 2019-01-22 国家电网有限公司 Site selection method and system for connecting heat accumulating type electric boiler to power distribution network
CN111598718A (en) * 2020-04-03 2020-08-28 广东电网有限责任公司电力调度控制中心 STATCOM configuration planning method, device and equipment
CN113762622A (en) * 2021-09-09 2021-12-07 国网上海市电力公司 Virtual power plant access point and capacity optimization planning method

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CN108258724A (en) * 2018-01-22 2018-07-06 佛山科学技术学院 A kind of wind power plant unit is laid out Multipurpose Optimal Method
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CN108629499A (en) * 2018-04-25 2018-10-09 国家电网公司 A kind of power distribution network photovoltaic plant addressing constant volume method based on second order cone theazy
CN109255558A (en) * 2018-10-31 2019-01-22 国家电网有限公司 Site selection method and system for connecting heat accumulating type electric boiler to power distribution network
CN109255558B (en) * 2018-10-31 2021-08-17 国家电网有限公司 Site selection method and system for connecting heat accumulating type electric boiler to power distribution network
CN111598718A (en) * 2020-04-03 2020-08-28 广东电网有限责任公司电力调度控制中心 STATCOM configuration planning method, device and equipment
CN111598718B (en) * 2020-04-03 2021-11-30 广东电网有限责任公司电力调度控制中心 STATCOM configuration planning method, device and equipment
CN113762622A (en) * 2021-09-09 2021-12-07 国网上海市电力公司 Virtual power plant access point and capacity optimization planning method
CN113762622B (en) * 2021-09-09 2023-09-19 国网上海市电力公司 Virtual power plant access point and capacity optimization planning method

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Application publication date: 20170531