CN104765967B - A kind of multi-objective optimization design of power method of mixing renewable energy system from net - Google Patents

Abstract

The invention discloses a kind of multi-objective optimization design of power method of mixing renewable energy system from net, described method is by considering the meteorological data such as illumination, wind speed, temperature in somewhere, supply damaged rate with the mixing annualized cost of renewable energy system and power and be minimised as target, the two objective optimization models that are applicable to the belt restraining that mixes renewable energy system are built, to obtaining the photovoltaic panel quantity of construction system best configuration and the quantity of mounted angle, wind energy conversion system quantity and setting height(from bottom), energy storage device and diesel-driven generator. Utilize Evolutionary Multiobjective Optimization NSGAII to solve this model, obtained one group of Pareto optimal solution, how finally to have introduced according to policymaker's preference information, determined final embodiment. The present invention adopts Multipurpose Optimal Method to carry out the planning of HRES, more tallies with the actual situation, feasibility is stronger.

Description

A kind of multi-objective optimization design of power method of mixing renewable energy system from net

Technical field

The present invention relates to a kind of planning and designing method that mixes renewable energy system from net, specifically consider in energy resource systemThe configuration of quantity and associated component mounted angle, height etc. of each assembly, each target of optimization system.

Background technology

The energy is the important foundation that the mankind depend on for existence and development. Enter 21 century, the development rapidly of economic society needs the energyAsk continuous increase, fossil energy is if coal, oil etc. are along with quick consumption also constantly reduces, and the making in a large number of these fossil energiesDay by day serious with the problem of environmental pollution causing. Energy problem and environmental pollution become the important of restriction social sustainable development day by dayFactor. Face the dual-pressure that energy problem and environmental problem are brought, greatly develop new forms of energy, strengthen utilizing regenerative resource to becomeFor the one of socio-economic development in the urgent need to.

It is a kind of with suitable mode group mixing renewable energy system (HybridRenewableEnergySystems, HRES)Close the system that uses different types of regenerative resource and fossil energy, can overcome intermittence, the shakiness of single regenerative resourceThe shortcoming such as qualitative. Specifically comprise the energy system of photovoltaic generation, wind-power electricity generation, diesel-driven generator generating and energy storage deviceSystem. Refer to that from net this system does not have connecting system electrical network. From net mix renewable energy system be generally applicable to island, mountain area itThe remote districts of class. Conventionally user is fewer in these areas, and duty factor is lower, and it is more difficult and inadequate that present stage is incorporated to large electrical networkEconomical.

Planning and designing about HRES can be divided into single goal optimization and multi-objective Optimization, and most of research at present is all examinedConsider the optimization of single goal, as the totle drilling cost of minimization system, maximum reliability, minimize greenhouse gas emissions etc. SoAnd from actual angle, a normally multi-objective optimization question of the planning and designing of HRES, multiple targets as cost, canNeed to optimize by property etc. simultaneously, need in addition to consider quantity, photovoltaic panel mounted angle, the blower fan peace of each assembly in hybrid systemDress height etc., therefore the planning and designing of HRES are a multivariable, discrete, nonlinear complicated optimum problem.

Summary of the invention

Due to the complexity of multi-objective optimization question, traditional optimized algorithm can not be separated effectively as linear programming, gradient method etc.Certainly problem, the defect existing for prior art, the object of the invention is to propose a kind of from netting the many of mixing renewable energy systemObjective optimization method for designing.

Technical scheme of the present invention is:

The first step, design mixes optimization aim and the constraint function of renewable energy system, foundation mixing renewable energy systemMulti-objective optimization design of power model;

Supply miss rate as target taking the annualized cost of minimization system and system power, build two objective optimization problems of belt restraining,As follows:

Wherein F_costThe annual cost that expression system is total, comprising: in system in the initial outlay cost of various kinds of equipment, use procedureThe alternative costs of Operation and Maintenance cost and equipment component; F_reliablilityRepresent system power supply miss rate, system can not expireTime shared ratio in simulation time of foot load, is worth less expression system reliability higher; N_pv、N_wg、N_bat、N_dgRepresent to mix respectively the quantity of photovoltaic panel, blower fan, battery pack and diesel-driven generator to be optimized in renewable energy system; H_wgTableShow the setting height(from bottom) of blower fan, H_lowAnd H_highRepresent respectively assembling height H_wgMinimum of a value and the maximum of excursion, βRepresent the mounted angle of solar energy photovoltaic panel;

The model of supposing the each equipment that forms HRES system is known, i.e. the property of photovoltaic panel, blower fan, battery pack and diesel-driven generatorMatter and relevant parameter are determined; Wherein photovoltaic panel parameter comprises open-circuit voltage, short circuit current, maximum working voltage, maximum workDo electric current, nominal operation temperature (NCOT), initial outlay cost, operating maintenance cost and service life, fan parameter bagDraw together rated power, initial outlay cost, operating maintenance cost and service life, it is specified that energy storage device is that battery pack parameter comprisesCapacity, voltage, maximum depth of discharge (DOD), initial outlay cost, operating maintenance cost, alternative costs and use longevityLife, diesel-driven generator parameter comprises rated power, initial outlay cost, operating maintenance cost per hour and service life;

According to above-mentioned known each equipment-related data, set up for off-grid HRES multi-objective optimization design of power model;

HRES planning and designing model relates to the variable of multiple types, comprise photovoltaic panel quantity, blower fan quantity, battery pack quantity,Diesel engine quantity, assembling height and photovoltaic panel mounted angle, encode above-mentioned variable, and coding rule is: if compileCode is shown as (22,8,28,3,23.55,59.76), uses so 22 given photovoltaic panel, 8 wind-driven generators, 28Battery pack, 3 diesel-driven generators, assembling height is 23.55 meters simultaneously, photovoltaic panel mounted angle is 59.76 °;

In conjunction with the life-span of each equipment, taking 25 years as the project cycle, HRES system annual cost object function is:

$\begin{array}{c}ACS=C_{ainv}(PV+WG+Tower+BAT+DG)\\ +C_{aom}(PV+WG+Tower+BAT+DG)\\ +C_{aerp}\left(BAT\right)\end{array}---\left(2\right)$

Wherein ACS represents to mix renewable energy system annual cost, and PV represents photovoltaic panel, and WG represents blower fan, Tower tableShow blower fan tower, BAT represents battery pack, and DG represents diesel-driven generator, C_ainvAnnual initial outlay cost, C_aomIt is yearOperation and maintenance cost, C_arepBe year alternative costs, calculate with following formula respectively:

C_ainv＝ΣC_inv·CRF(i,L_com)(3)

$CRF(i,L_{com})=\frac{i\·{(1+i)}^{L_{com}}}{{(1+i)}^{L_{com}}-1}---\left(4\right)$

$i=\frac{i_{nom}-f}{1+f}---\left(5\right)$

Wherein C_invBe the initial outlay cost of each element, element comprises photovoltaic panel, blower fan, blower fan tower, battery pack and diesel oilGenerator, CRF is the capital recovery factor, L_comBe component life, unit is year; I is a year true rate of interest, i_nomIt is name profitRate, f is a year inflation;

C_arep＝C_rep·SFF(i,L_rep)(6)

$SFF(i,L_{rep})=\frac{i}{{(1+i)}^{L_{rep}}-1}---\left(7\right)$

C_aom(n)＝C_aom(1)·(1+f)ⁿ(8)

Wherein C_repBe the alternative costs of each element, element comprises photovoltaic panel, blower fan, blower fan tower, battery pack and diesel generationMachine, SFF is the reticent fund factor, L_repThe Replacement life-span, C_aom(n) be the Operation and Maintenance cost of n;

Power supply disappearance probability object function in HRES one-year age is:

$LPSP=\frac{{\&Sigma;}_{t=0}^{T}T\left(P_{avail}\right(t)<P_{load}\left(t\right))}{T}---\left(9\right)$

Wherein T is 1 year i.e. 8760, P of total hourage_availAnd P (t)_load(t) be respectively the power that each simulation time step-length can be usedSupply and loading demand; Load is obtained by user side, and power supply comprises supply, the energy storage supply of photovoltaic generation and wind-power electricity generationWith four parts of diesel-driven generator supply; Power supply process is: first by photovoltaic generation and the direct supply load of wind-power electricity generation withSatisfy the demands, in the time that the power of photovoltaic generation and solar electrical energy generation is greater than load, unnecessary electric weight is just given batteries charging; On the contraryIn the time that generated energy can not meet load, first to be discharged by energy storage device, battery pack reaches maximum depth of discharge still can not meet loadTime, diesel-driven generator uses as stand-by power supply, and remaining still unappeasable load meeting is cut off with protection system;

The power of system represents for application following formula:

P_avail(t)＝P_pv(t)+P_wg(t)+P_bat(t)+P_dg(t)(10)

Wherein P_pv(t) represent the power output of photovoltaic panel in time t, P_wg(t) represent the power output of blower fan in time t, P_bat(t)Represent the power output of battery pack in time t, P_dg(t) represent the power output of diesel-driven generator in time t; Photovoltaic generationCalculated by following formula respectively with the power of blower fan generating:

$T_C\left(t\right)=T_A\left(t\right)+\frac{NCOT-20}{800}{S}_p(t,\mathrm{\&beta;})---\left(11\right)$

V_OC(t)＝V_OC,STC-K_V·T_C(t)(13)

$\begin{array}{c}{P}_{pv}(t,\mathrm{\&beta;})=N_S\&CenterDot;N_P\&CenterDot;V_{OC}\left(t\right)\&CenterDot;I_{SC}(t,\mathrm{\&beta;})\&CenterDot;FF\left(t\right)\\ =N_{pv}\&CenterDot;V_{OC}\left(t\right)\&CenterDot;I_{SC}(t,\mathrm{\&beta;})\&CenterDot;FF\left(t\right)\end{array}---\left(14\right)$

Wherein T_C(t) be the photovoltaic battery temperature at time t, T_A(t) environment temperature while being time t, NCOT is that manufacturer is carriedThe specified battery operated temperature of confession, S_p(t, β) is perpendicular to the solar radiation on photovoltaic panel inclined surface, I_SC,STCAnd V_OC,STCIt is mould(temperature 25, the solar radiation 1kW/m of group under standard test condition²) short circuit current and open-circuit voltage, I_SC(t, β) is photovoltaicThe short circuit current of module, V_OC(t) open-circuit voltage of expression photovoltaic module, K_IAnd K_VIt is corresponding temperature coefficient; P_pv(t, β) be byOne comprises N_SIndividual series connection, N_PThe power output of the photovoltaic array of individual module in parallel, N_pvRepresent the total quantity of photovoltaic panel, FF (t)It is fill factor, curve factor;

$P_{wg}\left(t\right)=\left\{\begin{array}{cc}0,& v<V_c\\ \frac{1}{2}{C}_P{\mathrm{\&rho;A}}_{WG}{v}^3,& V_c\&le;v<V_r\\ P_{WGR},& V_r\&le;v<V_f\\ 0,& v\&GreaterEqual;V_f\end{array}\right.---\left(15\right)$

Wherein v is the wind speed in each moment, C_PBe fan performance coefficient, ρ is atmospheric density, A_WGThe inswept area of rotor,P_WGRThe rated power of blower fan; V_cThe cutting speed of blower fan, V_rThe rated wind speed of blower fan, V_fIt is the cut-out wind speed of blower fan;

Solar radiation, wind speed profile and the temperature data in HRES planning, used carry out phase according to the historical data of research areaShould process the average data of obtaining over 10 years, or produce analogue data according to distribution function;

Second step, utilizes NSGAII Algorithm for Solving HRES plan model, and idiographic flow is:

(1) algorithm parameter setting: mainly comprise population scale and end condition, population N is set to 100 here, end conditionAdopt maximum operation algebraically, be set to maxGen=100;

(2) initialize population, generate at random N=100 initial parent population S; Each individual x has 6 codings,x＝(N_pv,N_wg,N_bat,N_dg,H_wg, β), wherein 0≤N_pv≤30，0≤N_wg≤20，0≤N_bat≤30，0≤N_dg≤10，5≤H_wg≤30，0≤β≤90；

(3) if meet end condition, stop calculating, export current non-domination disaggregation; Otherwise, based on current population S,Produce progeny population Sc by Genetic Recombination operator, scale is also N. Concrete operation step:

(a) for the each individual x in current population S_i, in conjunction with random two other individual x selecting_mAnd x_n, through type (17)Produce new individual x_new. WhereinRepresent new k individual variate-value,Represent a temporary variable value,WithRepresent respectively k the variate-value of individual i, individual m and individual n, k=[1 here, 2 ..., 6]; F and CR are respectivelyTwo parameters of this operation, are set to 0.9 and 0.05 here; Rand represents to be positioned at the random number of interval (0,1); k_randRepresent oneIndividual random generation be positioned at interval [1,6] integer; Floor () represents downward bracket function.

$\begin{array}{c}{x}_{temp}^k=\left\{\begin{array}{c}\begin{array}{ccc}{x}_i^k+F\&times;(x_m^k-x_n^k)& if& rand<CRork=k_{rand}\end{array}\\ x_i^k\end{array}\right.\\ x_{new}^k=\left\{\begin{array}{c}\begin{array}{ccc}floor\left(x_{temp}^k\right)& if& k<5\end{array}\\ x_{temp}^k\end{array}\right.\end{array}---\left(16\right)$

(b), if the new individuality producing is infeasible solutions, variate-value has exceeded the bound of definition, takes following measures to be repaiiedIt is being just feasible solution. Wherein ub^kAnd lb^kRepresent respectively the bound of k variable. All x_newForm progeny population Sc.

$x_{new}^k=\frac{({\mathrm{ub}}^k+{\mathrm{lb}}^k)}{2}---\left(17\right)$

(4) parent S and filial generation Sc are merged, what the scale of obtaining was 2N closes population S_all=S ∪ Sc, carries out the individuality in RNon-bad layering, then calculates each individual local congestion distance of non-bad layer, last according to individual residing non-bad layer and crowdedDistance, sorts to all individualities.

Wherein: the non-bad layered approach of described individuality is specially:

(a) by the individual normalization in population: obtain each object function f_mMaximum, max (f_m) and minimum of a value,min(f_m), object function f_mRefer to the F in formula (1)_costWith_{Freliablility}, then according to following formula by each individual goal functional valueBe transformed into interval [0,1].

${\stackrel{\&OverBar;}{f}}_i\left(x\right)=\frac{f_i\left(x\right)-min\left(f_i\right)}{max\left(f_i\right)-\min \left(f_i\right)},i=1,2,...,M---\left(18\right)$

Wherein, f_i(x) the primal objective function value of i the target of individual x in expression evolutionary process,Represent individual x normalizationAfter target function value;

(b) find out synthetic population S_allIn not by the individuality of any individual constraint Pareto domination, and be kept at set A₁In, asThe first non-bad layer; In the time that following one of them condition meets, the individual y:(i of individual x constrain domination) individual x and y all meet approximatelyBundle condition and(ii) individual x meets constraints, and y does not meet constraints; (iii) individual x and y all do not meetConstraints, the degree of individual x violation constraints is less than the degree of individual y violation constraints.Represent that individual x props upJoin individual y, and if only iff_j(x)＜f_j(y), M represents orderScalar functions number; Be that individual x is not worse than individual y on all object functions, and x is at least better than y on an object function.

(c) from S_allIn remove all in set A₁In individuality, the synthetic population of residue is designated as S_all\A₁, repeat (a), find out kindGroup S_all\A₁In not by the individuality of any individual constraint Pareto domination, and be kept at set A₂In, as the second non-bad layer.

(d) the like, until whole population is complete by layering.

Described crowding distance (being designated as dist), can be seen as individual x intuitively_iComprise individual x around_iBut do not comprise other individualitiesMinimum rectangle; Crowding distance is less, illustrates individual denser around. Its circular is as follows:

(a) for each object function f_m, the individuality in population is sorted;

(b) (have minimum f for border individuality_mThe individuality of value), definition crowding distance dist is infinitely great;

(c) flash trimming other individual x out-of-bounds in same non-bad layer_iCrowding distance be

$dist\left(i\right)=\underset{m=1}{\overset{2}{\&Sigma;}}\frac{f_m^{i-1}-f_m^{i+1}}{f_m^{max}-f_m^{\min }}---\left(19\right)$

WhereinWithRepresent respectively object function f in current population_mMaximum and minimum of a value;WithRepresent respectivelyI-1 and i+1 individual target function value.

Described according to the residing non-bad layer of individuality and crowding distance sort method, specifically refer to: (i) individuality in the non-bad layer of i(j > is the individuality of non-bad layer i) to be better than j; (ii) individuality in same non-bad layer, the individuality that crowding distance is large is more excellent.

(5) choose from front to back N individuality as new parent population S according to ranking results.

(6) repeat (3) to (5) step, until meet end condition, reach maximum operation algebraically, export non-in SJoin individual as solved solution;

The 3rd step, in conjunction with policymaker's preference information, from multiple Pareto optimal solutions, selects a last HRES's of conductEmbodiment;

In the time that policymaker payes attention to cost compare,, in the situation that meeting cost restriction, select the highest scheme of reliability,The scheme of power supply miss rate minimum; In the time of the heavier viewing system power supply reliability of policymaker, meeting power supply disappearanceUnder the requirement of rate, the scheme of selective system cost minimization.

In the present invention: mix renewable energy system planning from net and refer to: the photovoltaic panel of how to confirm suitable quantity, blower fan,Diesel-driven generator, energy storage device and mounting means to be to make whole energy resource system As soon as possible Promising Policy area load demand, simultaneouslyEconomic, environmental protection.

Multi-objective optimization question refers to: multiple targets are optimized, owing to normally linking together between each target simultaneouslyAnd condition each other, compete mutually, i.e. the improvement of certain target may cause the degeneration of other targets, be difficult to find a real meaningOptimal solution in justice makes each optimization aim reach optimum simultaneously, therefore the optimal solution of multi-objective optimization question normally one non-The set of inferior solution, i.e. Pareto optimal solution set. The core that solves multi-objective optimization question is to find the uniform Pareto of a component clothOptimal solution.

Evolutionary Multiobjective Optimization is the optimization based on population developing by simulating or disclose some natural phenomena or processAlgorithm, its thought and content relate to mathematics, biology and Computer Subject etc. Such algorithm does not rely on gradient information, onceOperation can be found one group of Pareto optimal solution, has the features such as the overall situation, parallel, efficient, robust and highly versatile. To solveThe effective ways of complex nonlinear multi-objective optimization question. It is different from the method for traditional processing multi-objective optimization question, as addsQuan Fa, leash law, Objective Programming etc., these conventional methods, by building an evaluation function, are converted into multi-objective problemSingle-object problem, then utilizes general method for solving to calculate a solution of problem. NSGAII is that evolution multiple target is excellentChange a classic algorithm in algorithm.

Useful technique effect of the present invention is:

(1) the present invention adopts Multipurpose Optimal Method to carry out the planning of HRES, more tallies with the actual situation, feasibility is stronger.

(2) adopt Evolutionary Multiobjective Optimization when Solve problems of the present invention, can find one group of each advantageous Pareto simultaneouslyOptimal solution,, selects to implement according to different situations for policymaker.

Brief description of the drawings

Fig. 1 typical case mixes renewable energy system schematic diagram from net

Fig. 2 HRES design coding

Fig. 3 Evolutionary Multiobjective Optimization NSGAII solves the flow chart of HRES planning problem

The non-domination disaggregation of Pareto of Fig. 4 HRES planning

Detailed description of the invention

Multi-objective optimization design of power method of mixing renewable energy system from net provided by the invention, concrete steps are as follows:

The first step, optimization aim and the constraint function of design HRES, set up the multi-objective optimization design of power model of HRES.

One typically from net wind-solar-diesel storage energy resource system as shown in Figure 1. For this quasi-representative system, with minimization system yearChanging into this and system power supply miss rate is target, considers the constraints of relevant decision variable, two targets of structure belt restrainingOptimization problem is as follows

Wherein F_costThe annual cost that expression system is total, comprising: in system in the initial outlay cost of various kinds of equipment, use procedureThe alternative costs of Operation and Maintenance cost and equipment component; F_reliablilityRepresent system power supply miss rate, system can not expireTime (taking 1 year as example) shared ratio in simulation time of foot load, is worth less expression system reliability higher. N_pvDengRepresent the quantity of the various kinds of equipment such as photovoltaic in HRES system, i.e. photovoltaic panel to be optimized, blower fan, battery pack and diesel-driven generatorQuantity; H_wgRepresent the setting height(from bottom) of blower fan, H_lowAnd H_highRepresent respectively assembling height H_wgExcursionLittle value and maximum, β represents the mounted angle of solar energy photovoltaic panel.

The model of supposing the each equipment that forms HRES system is known, i.e. the property of photovoltaic panel, blower fan, battery pack and diesel-driven generatorMatter and relevant parameter are determined. The analogue data of these equipment is respectively as shown in table 1-4. Wherein photovoltaic panel parameter comprises open circuitVoltage, short circuit current, maximum working voltage, maximum operating currenbt, nominal operation temperature (NCOT), initial outlay cost withAnd operating maintenance cost etc., fan parameter comprises rated power, initial outlay cost, operating maintenance cost, service life etc.,Energy storage device (battery pack) parameter comprises rated capacity, voltage, maximum depth of discharge (DOD), initial outlay cost, behaviourMake maintenance cost and alternative costs etc., diesel-driven generator relevant parameter comprises rated power, initial outlay cost, behaviour per hourDo maintenance cost and service life etc.

Table 1 photovoltaic panel relevant parameter (supposes that every photovoltaic panel area is 1 meter²)

Table 2 wind energy conversion system relevant parameter

Table 3 energy storage device relevant parameter

Table 4 diesel engine relevant parameter

, set up for off-grid HRES multi-objective optimization design of power model, tool to the equipment-related data providing in 4 according to table 1Body, refers to and finds out the optimum composition method of various kinds of equipment quantity and photovoltaic panel mounted angle, assembling height etc., makesNot only economy but also have higher reliability of HRES.

HRES planning and designing model relates to the variable of multiple types, as: use the quantity (integer variable) of certain type equipment,Photovoltaic panel mounted angle, assembling height (real variable). The coding rule of a concrete embodiment is as Fig. 2.

Scheme coding consideration 6 variablees, comprise photovoltaic panel quantity, blower fan quantity, battery pack quantity, diesel engine quantity, windMachine setting height(from bottom) and photovoltaic panel mounted angle. Following face code is example, if coding is shown as (22,8,28,3,23.55,59.76),Use so 22 given photovoltaic panel, 8 wind-driven generators, 28 battery pack, 3 diesel-driven generators, simultaneously blower fan peaceDress is highly 23.55 meters, and photovoltaic panel mounted angle is 59.76 °.

In conjunction with the life-span of each equipment, taking 25 years as the project cycle, in simulation process, only have thus battery pack need to consider alternative costs,HRES system annual cost object function is:

$\begin{array}{c}ACS=C_{ainv}(PV+WG+Tower+BAT+DG)\\ +C_{aom}(PV+WG+Tower+BAT+DG)\\ +C_{arep}\left(BAT\right)\end{array}---\left(21\right)$

Wherein ACS represents to mix renewable energy system annual cost, and PV represents photovoltaic panel, and WG represents blower fan, Tower tableShow blower fan tower, BAT represents battery pack, and DG represents diesel-driven generator, C_ainvAnnual initial outlay cost, C_aomIt is yearOperation and maintenance cost, C_arepBe year alternative costs, can calculate with following formula respectively:

C_ainv＝ΣC_inv·CRF(i,L_com)(22)

$CRF(i,L_{com})=\frac{i\&CenterDot;{(1+i)}^{L_{com}}}{{(1+i)}^{L_{com}}-1}---\left(23\right)$

$i=\frac{i_{nom}-f}{1+f}---\left(24\right)$

Wherein C_invBe the initial outlay cost of each element, element comprises photovoltaic panel, blower fan, blower fan tower, battery pack and diesel oilGenerator, CRF is the capital recovery factor, L_comBe component life, unit is year; I is a year true rate of interest, i_nomIt is name profitRate, f is a year inflation.

C_arep＝C_rep·SFF(i,L_rep)(25)

$SFF(i,L_{rep})=\frac{i}{{(1+i)}^{L_{rep}}-1}---\left(26\right)$

C_aom(n)＝C_aom(1)·(1+f)ⁿ(27)

Wherein C_repBe the alternative costs of each element, element comprises photovoltaic panel, blower fan, blower fan tower, battery pack and diesel generationMachine, SFF is the reticent fund factor, L_repThe Replacement life-span, C_aom(n) be the Operation and Maintenance cost of n.

Power supply disappearance probability object function in HRES one-year age is:

$LPSP=\frac{{\&Sigma;}_{t=0}^{T}T\left(P_{avail}\right(t)<P_{load}\left(t\right))}{T}---\left(28\right)$

Wherein T is i.e. 8760, the P of 1 year total hourage considering_availAnd P (t)_load(t) be respectively that each simulation time step-length can be usedPower supply and loading demand. Load can be obtained by user side, power supply comprise photovoltaic generation and wind-power electricity generation supply,Four parts such as energy storage supply and diesel-driven generator supply. Power supply process is: first direct by photovoltaic generation and wind-power electricity generationSupply load is to satisfy the demands, and in the time that the power of photovoltaic generation and solar electrical energy generation is greater than load, unnecessary electric weight is just given battery packCharging. In the time that generated energy can not meet load, first discharged by energy storage device on the contrary, battery pack reaches maximum depth of discharge still notCan meet load time, diesel-driven generator uses as stand-by power supply, and remaining still unappeasable load meeting is cut off to protect systemSystem.

The power supply of system can be represented by the formula:

P_avail(t)＝P_pv(t)+P_wg(t)+P_bat(t)+P_dg(t)(29)

Wherein P_pv(t) represent the power output of photovoltaic panel in time t, P_wg(t) represent the power output of blower fan in time t, P_bat(t)Represent the power output of battery pack in time t, P_dg(t) represent the power output of diesel-driven generator in time t;

The power of photovoltaic generation and blower fan generating can be calculated by following formula respectively:

$T_C\left(t\right)=T_A\left(t\right)+\frac{NCOT-20}{800}{S}_p(t,\mathrm{\&beta;})---\left(30\right)$

V_OC(t)＝V_OC,STC-K_V·T_C(t)(32)

$\begin{array}{c}{P}_{pv}(t,\mathrm{\&beta;})=N_S\&CenterDot;N_P\&CenterDot;V_{OC}\left(t\right)\&CenterDot;I_{SC}(t,\mathrm{\&beta;})\&CenterDot;FF\left(t\right)\\ =N_{pv}\&CenterDot;V_{OC}\left(t\right)\&CenterDot;I_{SC}(t,\mathrm{\&beta;})\&CenterDot;FF\left(t\right)\end{array}---\left(33\right)$

Wherein T_C(t) be the photovoltaic battery temperature at time t, T_A(t) environment temperature while being time t, NCOT is that manufacturer is carriedThe specified battery operated temperature of confession, S_p(t, β) is perpendicular to the solar radiation on photovoltaic panel inclined surface, I_SC,STCAnd V_OC,STCIt is mould(temperature 25, the solar radiation 1kW/m of group under standard test condition²) short circuit current and open-circuit voltage, I_SC(t, β) is photovoltaicThe short circuit current of module, V_OC(t) open-circuit voltage of expression photovoltaic module, K_IAnd K_VIt is corresponding temperature coefficient; P_pv(t, β) be byOne comprises N_SIndividual series connection, N_PThe power output of the photovoltaic array of individual module in parallel, N_pvRepresent the total quantity of photovoltaic panel, FF (t)It is fill factor, curve factor.

$P_{wg}\left(t\right)=\left\{\begin{array}{cc}0,& v<V_c\\ \frac{1}{2}{C}_P{\mathrm{\&rho;A}}_{WG}{v}^3,& V_c\&le;v<V_r\\ P_{WGR},& V_r\&le;v<V_f\\ 0,& v\&GreaterEqual;V_f\end{array}\right.---\left(34\right)$

Wherein v is the wind speed in each moment, C_PBe fan performance coefficient, ρ is atmospheric density, A_WGThe inswept area of rotor,P_WGRThe rated power of blower fan. V_cThe cutting speed of blower fan, V_rThe rated wind speed of blower fan, V_fIt is the cut-out wind speed of blower fan.

Solar radiation, wind speed profile and the temperature data in HRES planning, used can enter according to the historical data of research areaRow respective handling obtains, as gets over the average data of 10 years, also can produce analogue data according to distribution function.

Second step, utilizes NSGAII Algorithm for Solving HRES Combinatorial Optimization Model, and as shown in Figure 3, idiographic flow is:

(1) algorithm parameter setting: mainly comprise population scale and end condition, population N is set to 100 here, end conditionAdopt maximum operation algebraically, be set to maxGen=100. Certainly for different problems and problem scale, can select differenceParameter value.

(2) initialize population, generate at random N=100 initial parent population S. Each individual x has 6 codings,x＝(N_pv,N_wg,N_bat,N_dg,H_wg, β), wherein 0≤N_pv≤30，0≤N_wg≤20，0≤N_bat≤30，0≤N_dg≤10，5≤H_wg≤30，0≤β≤90；

(3) if meet end condition, stop calculating, export current non-domination disaggregation; Otherwise, based on current population S,Produce progeny population Sc by Genetic Recombination operator, scale is also N. Concrete operation step:

(a) for the each individual x in current population S_i, in conjunction with random two other individual x selecting_mAnd x_n, pass through following formulaProduce new individual x_new. WhereinRepresent new k individual variate-value,Represent a temporary variable value,WithRepresent respectively k the variate-value of individual i, individual m and individual n, k=[1 here, 2 ..., 6]; F and CR are respectivelyTwo parameters of this operation, are set to 0.9 and 0.05 here; Rand represents to be positioned at the random number of interval (0,1); k_randRepresent oneIndividual random generation be positioned at interval [1,6] integer; Floor () represents downward bracket function.

$\begin{array}{c}{x}_{temp}^k=\left\{\begin{array}{c}\begin{array}{ccc}{x}_i^k+F\&times;(x_m^k-x_n^k)& if& rand<CRork=k_{rand}\end{array}\\ x_i^k\end{array}\right.\\ x_{new}^k=\left\{\begin{array}{c}\begin{array}{ccc}floor\left(x_{temp}^k\right)& if& k<5\end{array}\\ x_{temp}^k\end{array}\right.\end{array}---\left(35\right)$

(b) if the new individual infeasible solutions producing takes following measures to be modified to feasible solution. Wherein ub^kAnd lb^kTable respectivelyShow the bound of k variable. All x_newForm progeny population Sc.

$x_{new}^k=\frac{({\mathrm{ub}}^k+{\mathrm{lb}}^k)}{2}---\left(36\right)$

(4) parent S and filial generation Sc are merged, what the scale of obtaining was 2N closes population S_all=S ∪ Sc, to S_allIn individuality enterThe non-bad layering of row, then calculates individual local congestion distance of each non-bad layer, last according to individual residing non-bad layer and gather aroundSqueeze distance, all individualities are sorted.

The non-bad layered approach of described individuality is specially:

(a) by the individual normalization in population: obtain each object function f_mMaximum, max (f_m) and minimum of a value, min (f_m)，Object function f_mRefer to the F in formula (1)_costAnd F_reliablility, then according to following formula, each individual goal functional value is transformed into interval[0,1]。

${\stackrel{\&OverBar;}{f}}_i\left(x\right)=\frac{f_i\left(x\right)-min\left(f_i\right)}{max\left(f_i\right)-\min \left(f_i\right)},i=1,2,...,M---\left(37\right)$

Wherein, f_i(x) the primal objective function value of i the target of individual x in expression evolutionary process,Represent that individual x returnsTarget function value after one change;

(b) find out synthetic population S_allIn not by the individuality of any individual constraint Pareto domination, and be kept at set A₁In, asThe first non-bad layer; When following one of them condition meets, the individual y:(i of individual x constrain domination) individual x and all satisfied constraints of yCondition and(ii) individual x meets constraints, and y does not meet constraints; (iii) individual x and y all do not meet approximatelyBundle condition, the degree of individual x violation constraints is less than the degree of individual y violation constraints.Represent individual x dominationIndividual y, and if only iff_j(x)＜f_j(y), M represents targetFunction number; Be that individual x is not worse than individual y on all object functions, and x is at least better than y on an object function.

(c) from S_allIn remove all in set A₁In individuality, the synthetic population of residue is designated as S_all\A₁, repeat (a), find out kindGroup S_all\A₁In not by the individuality of any individual constraint Pareto domination, and be kept at set A₂In, as the second non-bad layer.

(d) the like, until whole population is complete by layering.

Described crowding distance (being designated as dist), can be seen as individual x intuitively_iComprise individual x around_iBut do not comprise other individualitiesMinimum rectangle; Crowding distance is less, illustrates individual denser around. Its circular is as follows:

(a) for each object function f_m, the individuality in population is sorted;

(b) (have minimum f for border individuality_mThe individuality of value), definition crowding distance dist is infinitely great;

(c) flash trimming other individual x out-of-bounds in same non-bad layer_iCrowding distance be

$dist\left(i\right)=\underset{m=1}{\overset{2}{\&Sigma;}}\frac{f_m^{i-1}-f_m^{i+1}}{f_m^{max}-f_m^{\min }}---\left(38\right)$

WhereinWithRepresent respectively object function f in current population_mMaximum and minimum of a value;WithRepresent respectivelyI-1 and i+1 individual target function value.

Described according to the residing non-bad layer of individuality and crowding distance sort method, specifically refer to: (i) individuality in the non-bad layer of i(j > is the individuality of non-bad layer i) to be better than j; (ii) individuality in same non-bad layer, the individuality that crowding distance is large is more excellent.

(5) choose from front to back N individuality as new parent population S according to ranking results.

(6) repeat (3) to (5) step, until meet end condition, reach maximum operation algebraically, export non-in SJoin individual as solved solution;

According to table 1, to the data in 4, and other known meteorological data in model is as illumination, wind speed and temperature etc., negativeCarrying data also can be obtained by user side. Taking 1 year as the emulation cycle, within one hour, be simulation step length, finally solve the Pareto obtainingThe most non-dominant set as shown in Figure 4.

The 3rd step, in conjunction with policymaker's preference information, from multiple Pareto optimal solutions, selects a last HRES's of conductEmbodiment. Can consider from two kinds of situations: in the time that policymaker payes attention to cost compare, in the situation that meeting cost restriction,Select the highest scheme of reliability, i.e. the scheme of power supply miss rate minimum; When the heavier viewing system power supply reliability of policymakerTime, meeting under the requirement of power supply miss rate the scheme of selective system cost minimization.

In sum, although the present invention discloses as above with better enforcement, so it is not in order to limit the present invention, any this areaThose of ordinary skill, without departing from the spirit and scope of the present invention, when doing various changes and retouching, therefore guarantor of the present inventionThe scope of protecting is worked as the scope defining depending on claims and is as the criterion.

Claims (4)

1. a multi-objective optimization design of power method of mixing renewable energy system from net, is characterized in that comprising the following steps:

The first step, design mixes optimization aim and the constraint function of renewable energy system, foundation mixing renewable energy systemMulti-objective optimization design of power model;

Supply miss rate as target taking the annualized cost of minimization system and system power, build two objective optimization problems of belt restraining,As follows:

min{F_cost,F_reliablility}

s.t.(N_pv,N_wg,N_bat,N_dg)≥0(1)

H_low≤H_wg≤H_high

0°≤β≤90°

Wherein F_costThe annual cost that expression system is total, comprising: in system in the initial outlay cost of various kinds of equipment, use procedureThe alternative costs of Operation and Maintenance cost and equipment component; F_reliablilityRepresent system power supply miss rate, system can not expireTime shared ratio in simulation time of foot load, is worth less expression system reliability higher; N_pv、N_wg、N_bat、N_dgRepresent to mix respectively the quantity of photovoltaic panel, blower fan, battery pack and diesel-driven generator to be optimized in renewable energy system; H_wgTableShow the setting height(from bottom) of blower fan, H_lowAnd H_highRepresent respectively assembling height H_wgMinimum of a value and the maximum of excursion, βRepresent the mounted angle of solar energy photovoltaic panel;

The model of supposing the each equipment that forms mixing renewable energy system system is known, i.e. photovoltaic panel, blower fan, battery pack and diesel oilCharacter and the relevant parameter of generator are determined; Wherein photovoltaic panel parameter comprise open-circuit voltage, short circuit current, maximum working voltage,Maximum operating currenbt, nominal operation temperature, initial outlay cost, operating maintenance cost and service life, fan parameter comprises volumeDetermine power, initial outlay cost, operating maintenance cost and service life, energy storage device be battery pack parameter comprise rated capacity,Voltage, maximum depth of discharge, initial outlay cost, operating maintenance cost, alternative costs and service life, diesel-driven generator ginsengNumber comprises rated power, initial outlay cost, operating maintenance cost per hour and service life;

According to above-mentioned known each equipment-related data, set up for off-grid mixing renewable energy system multi-objective optimization design of power mouldType;

Mix the variable that renewable energy system planning and designing model relates to multiple types, comprise photovoltaic panel quantity, blower fan quantity,Battery pack quantity, diesel engine quantity, assembling height and photovoltaic panel mounted angle, encode above-mentioned variable, coding rule: if coding is shown as (22,8,28,3,23.55,59.76), use so 22 given photovoltaic panel, 8 wind-power electricity generationsMachine, 28 battery pack, 3 diesel-driven generators, assembling height is 23.55 meters simultaneously, photovoltaic panel mounted angle is 59.76 °;

In conjunction with the life-span of each equipment, taking 25 years as the project cycle, mixing renewable energy system system annual cost object function is:

$\begin{array}{c}ACS=C_{ainv}(PV+WG+Tower+BAT+DG)\\ +C_{aom}\left(PV+WG+Tower+BAT+DG\right)\\ +C_{arep}\left(BAT\right)\end{array}---\left(2\right)$

Wherein ACS represents to mix renewable energy system annual cost, and PV represents photovoltaic panel, and WG represents blower fan, and Tower representsBlower fan tower, BAT represents battery pack, DG represents diesel-driven generator, C_ainvAnnual initial outlay cost, C_aomBe year operation andMaintenance cost, C_arepBe year alternative costs, calculate with following formula respectively:

C_ainv＝∑C_inv·CRF(i,L_com)(3)

$CRF(i,L_{com})=\frac{i\&CenterDot;{(1+i)}^{L_{com}}}{{(1+i)}^{L_{com}}-1}---\left(4\right)$

$i=\frac{i_{nom}-f}{1+f}---\left(5\right)$

Wherein C_invBe the initial outlay cost of each element, element comprises that photovoltaic panel, blower fan, blower fan tower, battery pack and diesel oil sends outMotor, CRF is the capital recovery factor, L_comBe component life, unit is year; I is a year true rate of interest, i_nomNorminal interest rate,F is a year inflation;

C_arep＝C_rep·SFF(i,L_rep)(6)

$SFF(i,L_{rep})=\frac{i}{{(1+i)}^{L_{rep}}-1}---\left(7\right)$

C_aom(n)＝C_aom(1)·(1+f)ⁿ(8)

Wherein C_repBe the alternative costs of each element, element comprises photovoltaic panel, blower fan, blower fan tower, battery pack and diesel-driven generator,SFF is the reticent fund factor, L_repThe Replacement life-span, C_aom(n) be the Operation and Maintenance cost of n;

The power supply disappearance probability object function mixing in renewable energy system one-year age is:

$LPSP=\frac{{\mathrm{\&Sigma;}}_{t=0}^{T}T\left(P_{avail}\right(t)<P_{load}\left(t\right))}{T}---\left(9\right)$

Wherein T is 1 year i.e. 8760, P of total hourage_availAnd P (t)_load(t) be respectively that the power that each simulation time step-length can be used suppliesShould and loading demand; Load is obtained by user side, and power supply comprises supply, energy storage supply and the bavin of photovoltaic generation and wind-power electricity generationFour parts of fry dried food ingredients motor supply; Power supply process is: first by photovoltaic generation and the direct supply load of wind-power electricity generation to meet needAsk, in the time that the power of photovoltaic generation and solar electrical energy generation is greater than load, unnecessary electric weight is just given batteries charging; The contrary generated energy of working asCan not meet load time, first discharged by energy storage device, when battery pack reaches maximum depth of discharge and still can not meet load, diesel oil is sent outMotor uses as stand-by power supply, and remaining still unappeasable load meeting is cut off with protection system;

The power of system represents for application following formula:

P_avail(t)＝P_pv(t)+P_wg(t)+P_bat(t)+P_dg(t)(10)

Wherein P_pv(t) represent the power output of photovoltaic panel in time t, P_wg(t) represent the power output of blower fan in time t, P_bat(t)Represent the power output of battery pack in time t, P_dg(t) represent the power output of diesel-driven generator in time t;

The power of photovoltaic generation and blower fan generating is calculated by following formula respectively:

$T_C\left(t\right)=T_A\left(t\right)+\frac{NCOT-20}{800}{S}_p(t,\mathrm{\&beta;})---\left(11\right)$

V_OC(t)＝V_OC,STC-K_V·T_C(t)(13)

$\begin{array}{c}{P}_{pv}\left(t,\mathrm{\&beta;}\right)=N_S\&CenterDot;N_P{V}_{OC}\left(t\right)\&CenterDot;I_{SC}\left(t,\mathrm{\&beta;}\right)\&CenterDot;FF\left(t\right)\\ =N_{pv}\&CenterDot;V_{OC}\left(t\right)\&CenterDot;I_{SC}\left(t,\mathrm{\&beta;}\right)\&CenterDot;FF\left(t\right)\end{array}---\left(14\right)$

Wherein T_C(t) be the photovoltaic battery temperature at time t, T_A(t) environment temperature while being time t, NCOT is that manufacturer providesSpecified battery operated temperature, S_p(t, β) is perpendicular to the solar radiation on photovoltaic panel inclined surface, I_SC,STCAnd V_OC,STCThat module is at markShort circuit current under accurate test condition and open-circuit voltage, wherein standard test condition refers to that temperature is 25 degree, solar radiation is 1kW/m²；I_SC(t, β) is the short circuit current of photovoltaic module, V_OC(t) open-circuit voltage of expression photovoltaic module, K_IAnd K_VCorrespondingTemperature coefficient; P_pv(t, β) comprises N by one_SIndividual series connection, N_PThe power output of the photovoltaic array of individual module in parallel, N_pvRepresent lightThe total quantity of volt plate, FF (t) is fill factor, curve factor;

$P_{wg}\left(t\right)=\left|\begin{array}{cc}0,& v<V_c\\ \frac{1}{2}{C}_P{\mathrm{\&rho;A}}_{WG}{v}^3,& V_c\&le;v<V_r\\ P_{WGR},& V_r\&le;v<V_f\\ 0,& v\&GreaterEqual;V_f\end{array}\right.---\left(15\right)$

Wherein v is the wind speed in each moment, C_PBe fan performance coefficient, ρ is atmospheric density, A_WGThe inswept area of rotor,P_WGRThe rated power of blower fan; V_cThe cutting speed of blower fan, V_rThe rated wind speed of blower fan, V_fIt is the cut-out wind speed of blower fan;

Mix solar radiation, wind speed profile and temperature data the going through according to research area of using in renewable energy system planningHistory data are carried out the average data that respective handling is obtained over 10 years, or produce analogue data according to distribution function;

Second step, utilizes NSGAII Algorithm for Solving mixing renewable energy system plan model, and idiographic flow is:

(1) algorithm parameter setting: comprise population scale and end condition, population N is set to 100 here, end condition adoptsMaximum operation algebraically, is set to maxGen=100;

(2) initialize population, generate at random N=100 initial parent population S; Each individual x has 6 codings,x＝(N_pv,N_wg,N_bat,N_dg,H_wg, β), wherein 0≤N_pv≤30，0≤N_wg≤20，0≤N_bat≤30，0≤N_dg≤10，5≤H_wg≤30，0≤β≤90；

(3) if meet end condition, stop calculating, export current non-domination disaggregation; Otherwise, based on current population S, logicalCross Genetic Recombination operator and produce progeny population Sc, scale is also N; Concrete operation step:

(a) for the each individual x in current population S_i, in conjunction with random two other individual x selecting_mAnd x_n, through type (17)Produce new individual x_new; WhereinRepresent new k individual variate-value,Represent a temporary variable value,WithRepresent respectively k the variate-value of individual i, individual m and individual n, k=[1 here, 2 ..., 6]; F and CR are respectivelyTwo parameters of this operation, are set to 0.9 and 0.05 here; Rand represents to be positioned at the random number of interval (0,1); k_randRepresent oneRandom produce be positioned at interval [1,6] integer; Floor () represents downward bracket function;

$\begin{array}{c}{x}_{temp}^k=\left\{\begin{array}{c}\begin{array}{ccc}{x}_i^k+F\&times;\left(x_m^k-x_n^k\right)& if& rand<CRork=k_{rand}\end{array}\\ x_i^k\end{array}\right.\\ x_{new}^k=\left\{\begin{array}{c}\begin{array}{ccc}floor\left(x_{temp}^k\right)& if& k<5\end{array}\\ x_{temp}^k\end{array}\right.\end{array}---\left(17\right)$

(b), if the new individuality producing is infeasible solutions, variate-value has exceeded the bound of definition, takes following measures to be repaiiedIt is being just feasible solution; Wherein ub^kAnd lb^kRepresent respectively the bound of k variable; All x_newForm progeny population Sc;

$x_{new}^k=\frac{({\mathrm{ub}}^k+{\mathrm{lb}}^k)}{2}---\left(18\right)$

(4) parent S and filial generation Sc are merged, what the scale of obtaining was 2N closes population S_all=S ∪ Sc, carries out the individuality in RIndividual non-bad layering, R refer to scale be 2N close population S_all, then calculate each individual local congestion distance of non-bad layer,Last according to individual residing non-bad layer and crowding distance, all individualities are sorted;

(5) choose from front to back N individuality as new parent population S according to ranking results;

(6) repeat (3) to (5) step, until meet end condition, reach maximum operation algebraically, export non-in SJoin individual as solved solution;

The 3rd step, in conjunction with policymaker's preference information, from multiple Pareto optimal solutions, selects the last mixing of a conduct renewableThe embodiment of energy resource system;

In the time that policymaker payes attention to cost compare,, in the situation that meeting cost restriction, select the highest scheme of reliability, i.e. meritThe scheme of rate supply miss rate minimum; In the time of the heavier viewing system power supply reliability of policymaker, meeting power supply miss rateUnder requirement, the scheme of selective system cost minimization.

2. multi-objective optimization design of power method of mixing renewable energy system from net according to claim 1, is characterized in thatIn (4) step by step of described second step, individual non-bad layered approach is specially:

(a) by the individual normalization in population: obtain each object function f_mMaximum, max (f_m) and minimum of a value,min(f_m), object function f_mRefer to the F in formula (1)_costAnd F_reliablility, then according to following formula by each individual orderOffer of tender numerical value is transformed into interval [0,1];

${\stackrel{\&OverBar;}{f}}_i\left(x\right)=\frac{f_i\left(x\right)-min\left(f_i\right)}{max\left(f_i\right)-\min \left(f_i\right)},i=1,2,...,M---\left(16\right)$

Wherein, f_i(x) the primal objective function value of i the target of individual x in expression evolutionary process,Represent individual x normalizationAfter target function value;

(b) find out synthetic population S_allIn not by the individuality of any individual constraint Pareto domination, and be kept at set A₁In, asThe first non-bad layer; In the time that following one of them condition meets, the individual y:(i of individual x constrain domination) individual x and all satisfied constraints of yCondition and x < y; (ii) individual x meets constraints, and y does not meet constraints; (iii) individual x and y all do not meet constraintCondition, the degree of individual x violation constraints is less than the degree of individual y violation constraints; X < y represents that individual x domination is individualY, and if only if $\&ForAll;i\&Element;1,2,\mathrm{...},M,f_i\left(x\right)\&le;f_i\left(y\right)\&cap;\&Exists;j\&Element;1,2,...,M,f_j\left(x\right)<f_j\left(y\right),$ M represents object functionNumber; Be that individual x is not worse than individual y on all object functions, and x is at least better than y on an object function;

(c) from S_allIn remove all in set A₁In individuality, the synthetic population of residue is designated as S_all\A₁, repeat (a), find out kindGroup S_all\A₁In not by the individuality of any individual constraint Pareto domination, and be kept at set A₂In, as the second non-bad layer;

(d) the like, until whole population is complete by layering.

3. multi-objective optimization design of power method of mixing renewable energy system from net according to claim 2, is characterized in thatIn (4) step by step of described second step, its circular of described crowding distance is as follows:

(a) for each object function f_m, the individuality in population is sorted;

(b) have minimum f for border individuality_mThe individuality of value, definition crowding distance dist is infinitely great;

(c) flash trimming other individual x out-of-bounds in same non-bad layer_iCrowding distance be

$dist\left(i\right)=\underset{m=1}{\overset{2}{\&Sigma;}}\frac{f_m^{i-1}-f_m^{i+1}}{f_m^{max}-f_m^{\min }}---\left(19\right)$

WhereinWithRepresent respectively object function f in current population_mMaximum and minimum of a value;WithRepresent respectivelyI-1 and i+1 individual target function value.

4. multi-objective optimization design of power method of mixing renewable energy system from net according to claim 3, is characterized in thatIn (4) step by step of described second step, described according to the residing non-bad layer of individuality and crowding distance, all individualities are arrangedOrder, specifically refers to: (i) be better than the individuality of the non-bad layer of j in the individuality of the non-bad layer of i, wherein j > i; (ii) in same non-The individuality of bad layer, the individuality that crowding distance is large is more excellent.