CN105741193A - Multi-target distribution network reconstruction method considering distributed generation and load uncertainty - Google Patents

Abstract

The invention discloses a multi-target distribution network reconstruction method considering distributed generation and load uncertainty. Wind power output force, photovoltaic power generation and load uncertainty are taken into consideration in the method. The three most important evaluation indexes, of optimized operation of a distribution network, including active loss, minimal voltage value of nodes and load balancing degree, namely three optimizing reconstruction targets, are given. Wind power output force, photovoltaic power output force and load uncertainty factors are processed through a scene analytical method. The final reconstruction scheme is obtained through multi-target disturbance biogeographic algorithm and fuzzy set theory. A multi-target reconstruction decision solution can be rapidly found, and high searching efficiency is ensured. Under an absorbing distributed power supply condition, various indexes of a network can be improved substantially through network reconstruction, so that the reconstruction is more adaptable to a real decision-making process.

Description

Take into account the multiple target Distribution system method of distributed power source and negative rules

Technical field

The invention belongs to Operation of Electric Systems analysis and control technical field, particularly to a kind of multiple target Distribution system method taking into account distributed power source and negative rules.

Technical background

In recent years, wind-powered electricity generation, photovoltaic are increasingly widely applied in worldwide as green energy resource pollution-free, reproducible, and the proportion being incorporated to constantly increases.Inherently there is many uncertain factors such as load fluctuation in practical power systems, and wind-powered electricity generation, photovoltaic grid-connected has been further exacerbated by that it is uncertain, and traditional Distribution system technology is proposed new challenge.

Distribution system technology as the basis implementing intelligent grid future, is one of the key technology of power distribution automation, its ensureing the quality of power supply, reduce important role in via net loss etc..In the starting stage of research Distribution system, mainly using a certain item evaluation index of distribution as optimization aim, along with research deepens continuously, the research for single goal reconstruct tends to perfect.But, Distribution system is actually a complicated Nonlinear Multiobjective combinatorial optimization problem, this is had some to study by recent Chinese scholars, but on multiobject choosing, conventional research considers not comprehensive, additionally, the process of uncertain factor is also complex in distribution, thus the invention discloses a kind of new multiple target Distribution system method taking into account distributed power source and negative rules.

Summary of the invention

Goal of the invention: present invention aims to the deficiencies in the prior art, propose a kind of multiple target Distribution system method taking into account distributed power source and negative rules, adopt scene analysis method to process wind power output, photovoltaic to exert oneself and uncertain factor in load, utilize multiple target disturbance biogeography algorithm to obtain final reconfiguration scheme with fuzzy set theory, provide decision scheme for operations staff.

Technical scheme: the present invention provides a kind of multiple target Distribution system method taking into account distributed power source and negative rules, comprises the following steps:

Step 1: set up three object functions of reconstruction and optimization, it may be assumed that active loss, node minimum amount of voltage that, load balancing degree；

Step 2: adopt scene analysis method to process wind power output, photovoltaic and exert oneself and uncertain factor in load；

Step 3: utilize multiple target disturbance biogeography algorithm to obtain final reconfiguration scheme with fuzzy set theory.

Further, described step 1 comprises the following steps:

Step 101: set up the first aim of reconstruction and optimization: distribution network systems active loss, is:

$min\underset{k=1}{\overset{N_b}{\Σ}}{R}_k\frac{{P_k}^2+{Q_k}^2}{{V_k}^2}$

In formula, N_bRepresent circuitry number；R_kRepresent the resistance of branch road k；P_kRepresent the active power of branch road k；Q_kRepresent the reactive power of branch road k；V_kRepresent the terminal voltage of branch road k；

Step 102: set up the second target of reconstruction and optimization: maximize voltage lowest section point voltage, be:

$\begin{array}{cc}-min\left\{V_j\right\}& \∀j\∈N\end{array}$

In formula, V_jRepresenting the voltage perunit value of node j, N represents nodes；

Step 103: set up the 3rd target of reconstruction and optimization: load balancing.Loaded portion on heavier for load circuit is transferred on the circuit that load is lighter by network reconfiguration by it, weighs with system loading evenness index (systemloadbalancingindex, SLBI), and its value is the smaller the better, is:

$\min SLBI=min\left(\frac{1}{N_b}\underset{j=1}{\overset{N_b}{\Σ}}\frac{S_j}{{S_j}^{\max }}\right)$

In formula, S_jRepresent the actual current size flowing through branch road j；Represent and allow to flow through the maximum current of branch road j；

Additionally, in Load flow calculation, in addition it is also necessary to consider following constraints:

$\begin{array}{cc}{V}^{min}\≤V_j\≤V^{max}& \∀j\∈N\end{array}$

$\begin{array}{cc}\left|S_k\right|\≤S_k^{\max }& \∀k\∈N_b\end{array}$

In formula: V^min, V^maxRepresent the bound of node voltage when distribution is properly functioning respectively；S_kRepresent the current-carrying capacity of branch road k, S^maxRepresent the maximum carrying capacity of circuit k.

Further, described step 2 comprises the following steps:

Step 201: blower fan is exerted oneself, photovoltaic is exerted oneself and load carries out scene partitioning:

It is generally acknowledged wind speed Follow Weibull Distribution at present, probability density function is following formula such as:

$f_v\left(v\right)=\frac{d}{c}{\left(\frac{v}{c}\right)}^{d-1}\exp \[-{\left(\frac{v}{c}\right)}^d\]$

In formula, f_vFor the probability density function of wind speed, c and d is scale parameter and form parameter respectively, it is possible to the historical data identification according to field measurement wind speed, and v represents wind speed m/s.When known wind speed random distribution parameter, it is possible to obtaining the probability of any wind speed interval, computing formula is as follows:

$P\left\{{\mathrm{case}}_i\right\}=P\{v_m<v\&le;v_n\}={\&Integral;}_{v_m}^{v_n}{f}_v\left(v\right)dv$

Case in above formula_iRepresent i-th scene, v_nAnd v_mRepresent the up-and-down boundary of wind speed scene interval.

Intensity of the sunlight can be similar to regards Beta distribution as:

$f\left(s\right)=\frac{\mathrm{\&Gamma;}(\mathrm{\&alpha;}+\mathrm{\&beta;})}{\mathrm{\&Gamma;}\left(\mathrm{\&alpha;}\right)\mathrm{\&Gamma;}\left(\mathrm{\&beta;}\right)}{\left(\frac{s}{s_{\max }}\right)}^{\mathrm{\&alpha;}-1}{(1-\frac{s}{s_{\max }})}^{\mathrm{\&beta;}-1}$

In formula, s and s_max(W/m²) the respectively actual light intensity in a time period and largest light intensity, α and β is the form parameter of Beta distribution in a period of time.

Solar cell array output is:

P_sun=sA η

Wherein, P_sunFor battery array output (kW), A is the solar cell array gross area (m²), η is electricity conversion.

Adopt the scene partitioning method exerting oneself same with Wind turbines, divide light intensity interval, calculate the probability of different interval (scene) according to Intensity Probability Density function.

In distribution network, daily load curve, monthly load curve and yearly load curve have bigger fluctuation, and along with distributed power source is grid-connected, load prediction is more difficult, hence in so that the uncertainty in Distribution system is higher.Load is divided into three typical scenes by the present invention: normality load scenarios, underload scene and high load scenarios.

Step 202: scene number determines strategy and the evaluation of schemes synthesis optimality:

Uncertain factor is transformed into definitiveness scene by scene analysis method, wind-powered electricity generation, grid-connected after, in Distribution system, uncertain factor is essentially from three aspects: Wind turbines output, solar panel output, load, thus the scene selected in reconstruction model is the combination of scene contained by above three.The present invention adopts synchronization back substitution "flop-out" method that large-scale scene is cut down, for the combination property of scheme: compare the object function expected value size based on scene probability of happening, such as following formula:

In formula: n_sFor the scene number after cutting down；PB_kFor the scene k probability occurred；F_ikFor the comprehensive evaluation value of i-th prioritization scheme under kth scene；D_iFor i-th prioritization scheme.E[F(D_i)] for the object function expected value of i-th prioritization scheme.

Further, described step 3 comprises the following steps:

Step 301: the present invention adopts disturbance biogeography algorithm to obtain multiple target reconfiguration scheme.This algorithm adopts disturbance transfer operator and cosine migration models, designs habitat suitability evaluation index to guide Evolution of Population according to the principle minimizing each sub-goal, preserves the non-domination solution in evolutionary process with filing population.Wherein, disturbance transfer operator is pressed following formula and is obtained:

q_i,j=p_k,j+ceil(ξ(p_k1,j-p_k2,j))

In formula, ξ is the random number of 0-1；Jth variable (the p of kth habitat is determined by roulette_k,j) move to the jth variable (q of i-th habitat_i,j) position, stochastic generation k1, k2 ∈ 1,2 ..., N}/{ i}.

Cosine migration models is as follows:

${\mathrm{\&lambda;}}_k=\frac{I}{2}\&lsqb;cos\left(\frac{k\mathrm{\&pi;}}{n}\right)+1\&rsqb;$

${\mathrm{\&mu;}}_k=\frac{E}{2}\&lsqb;-cos\left(\frac{k\mathrm{\&pi;}}{n}\right)+1\&rsqb;$

In formula, λ_kFor moving into probability, μ_kFor removal probability, I is maximum immigration probability, and E is maximum removal probability.

It is defined as comprehensive evaluation index, is used for guiding Evolution of Population:

$F=\underset{i=1}{\overset{3}{\&Sigma;}}\frac{w_i(f_i-f_{o,min})}{(f_{i,\max }-f_{i,min})}+rank\&CenterDot;(1-ratio)$

In formula, F represents habitat suitability vector, f_iRepresent habitat the i-th target function value vector, f_i,max, f_i,minRepresent the maximin of all habitat i-th targets respectively, rank represents habitat non-dominant ranking vector, ratio represents that in population, non-dominant grade is 1 individual shared ratio, iteration early stage, dominance hierarchy be 1 individuality less, dominance hierarchy proportion in aggregative indicator is relatively big, along with population iterative evolution, non-dominant grade be 1 individuality get more and more, dominance hierarchy effect in comprehensive evaluation index reduces.w₁, w₂, w₃Initial value is disposed as 1, according to the attention degree to each target, it is possible to arrange weight flexibly, three's and be 1.

Step 302: in actual distribution runs, policymaker needs to determine a best reconstructed operation scheme from candidate solution, and the present invention adopts fuzzy set theory to determine that best compromise solution is by each sub-goal Fuzzy processing, defines as follows:

$h_i=\left\{\begin{array}{cc}1,& f_i\&le;f_i^{min}\\ \frac{f_i^{max}-f_i}{f_i^{max}-f_i^{\min }},& f_i^{\min }<f_i<f_i^{\max }\\ 0,& f_i\&GreaterEqual;f_i^{\max }\end{array}\right.$

In formula: i ∈ 1,2 ..., N_obj}；f_iFor object function；N_objFor object function number；The respectively maximum of the i-th object function, minima；h_iTake 0 and 1 represent completely dissatisfied respectively and be entirely satisfactory.Non-domination solution concentrates the satisfaction of each solution can use following formula scalarization:

$h=\frac{1}{N_{obj}}\underset{i=1}{\overset{N_{obj}}{\&Sigma;}}{h}_i$

The maximum solution of h value is decided to be best compromise solution.

Operation principle: first the present invention provides three important evaluation indexes that distribution optimization runs: active loss, node minimum amount of voltage that, load balancing degree, i.e. 3 targets of reconstruction and optimization.Then, adopt scene analysis method to process wind power output, photovoltaic to exert oneself and uncertain factor in load.Finally, multiple target disturbance biogeography algorithm is utilized to obtain final reconfiguration scheme with fuzzy set theory.The present invention can be quickly found out the decision-making solution of multiple target Distribution system, has higher search efficiency, when dissolving distributed power source, can be obviously improved the indices of network by network reconfiguration so that reconstruct more conforms to practice decision process.

Beneficial effect: compared with existing reconfiguration technique, the invention have the advantages that and technique effect:

(1) multiple target reconstruct can consider via net loss, network voltage quality, load balancing degree so that reconstructs more application of load practical situations；

(2) reconstruction strategy of wind-powered electricity generation, photovoltaic and negative rules is considered, it is possible to when dissolving distributed power source, the indices of network can be obviously improved by network reconfiguration；

(3) the multiple target disturbance biogeography algorithm that the present invention adopts can be quickly found out the decision-making solution of multiple target Distribution system, it is ensured that the formation efficiency of strategy.

Accompanying drawing explanation

Fig. 1 is the present invention 69 node distribution topological diagram；

Fig. 2 is Wind turbines power characteristic of the present invention；

Fig. 3 is cosine migration models figure of the present invention；

Fig. 4 is multiple target disturbance biogeography algorithm flow chart of the present invention；

Fig. 5 is network loss convergence curve of the present invention；

Fig. 6 is voltage distribution graph of the present invention.

Detailed description of the invention:

Below in conjunction with the drawings and specific embodiments, it is further elucidated with the present invention, it should be understood that these embodiments are merely to illustrate the present invention rather than restriction the scope of the present invention, after having read the present invention, the amendment of the various equivalent form of values of the present invention is all fallen within the application claims limited range by those skilled in the art.

The present invention uses 69 node distribution network systems as shown in Figure 1, and this distribution network systems contains 73 branch roads, 5 basic rings, reference power 10kVA, reference voltage 12.66kV, system-wide load 3.90MW and 2.70Mvar.The current-carrying capacity of every branch road is respectively as follows: No. 1-9 for 400A, and No. 46-49 and No. 52-64 is 300A, other circuit 200A.Under initial condition, branch road 69,70,71,72,73 disconnects, and network loss is 224.93kW.Using MATLABR2013a coding, computing environment is: Intel (R) Core (TM) i3-2120CPU3.30GH, 4GBRAM.

Multiple target disturbance biogeography algorithm parameter is provided that population scale N_p=70, maximum iteration time K_max=50, maximum sudden change rate m_max=0.05, maximum entry/leave rate all takes E=I=1 (cosine migration models is shown in Fig. 3).Blower fan and distribution of solar energy parameter k=1.99, c=9.94, α=0.28, β=2.05.The incision of blower fan, specified, cut-out wind speed respectively 3m/s, 14m/s, 25m/s (Wind turbines power characteristic such as Fig. 2), rated power 400kW；Photovoltaic battery matrix single component area 2.16m², photoelectric transformation efficiency 13.44%, 400 assembly one photovoltaic battery matrixes of composition, maximum intensity of sunshine 0.5w/m².Access 3 typhoon power generators at node 8,13,18 place respectively, be respectively connected to 50 photovoltaic battery matrixes at node 20,26,29.1.1 times of high underload respectively conventional load, 0.9 times, height Load Probability all takes 0.2, and conventional load probability takes 0.6.In table 1, table 2 table, desired value is expected value, and scheme is the final decision scheme (multiple target disturbance biogeography Algorithm for Solving flow process such as Fig. 4) after obfuscation.

Fig. 5 provides the convergence curve of network loss target desired value, and algorithm enters convergence state after iteration 11 times, has good convergence.

Table 1 reconfiguration scheme contrast table

As shown in Table 1, each index that the multiple target reconstruction result without DG is compared under primitive network has bigger lifting: active loss reduces by 52.97%, and minimum voltage promotes 4.3%, and load balancing degree reduces by 19.47%, and reconstruction and optimization result is more apparent.Take into account the multiple target reconstruct of DG, network loss and load balancing degree are reduced further, compare the reconstruct taking no account of DG, these two indexs reduce 14.45% and 7.14% respectively, in Fig. 6, disregard the network node voltage of the reconstruct of DG to compare primitive network and have a distinct increment, after taking into account DG, the voltage of part of nodes compares the optimum results taking no account of DG further lifting, thus showing, suitable DG is grid-connected and optimal reconfiguration, regenerative resource of not only having dissolved, and can be obviously improved the indices of system.

In the process cutting down scene, it is thus necessary to determine that final scene number, table 2 gives the reconstruction and optimization result under three scene numbers.

Optimum results table under the different scene number of table 2

As seen from table, when scene number is less, active loss is more, and load balancing degree is relatively low, calculates the time shorter；When scene number is bigger, active loss is relatively low, and load balancing degree is higher, but the time of calculating is longer；Minimum voltage is not affected by different scene numbers.

To sum up, example describes correctness and the practicality of the present invention.

Claims (4)

1. the multiple target Distribution system method taking into account distributed power source and negative rules, it is characterised in that: comprise the following steps:

Step 1: set up three object functions of reconstruction and optimization, it may be assumed that active loss, node minimum amount of voltage that, load balancing degree；

Step 2: adopt scene analysis method to process wind power output, photovoltaic and exert oneself and uncertain factor in load；

Step 3: utilize multiple target disturbance biogeography algorithm to obtain final reconfiguration scheme with fuzzy set theory.

2. the multiple target Distribution system method taking into account distributed power source and negative rules according to claim 1, it is characterised in that: described step 1 comprises the following steps:

Step 101: set up the first aim of reconstruction and optimization: distribution network systems active loss, is:

$min\underset{k=1}{\overset{N_b}{\mathrm{\&Sigma;}}}{R}_k\frac{{P_k}^2+{Q_k}^2}{{V_k}^2}$

In formula, N_bRepresent circuitry number；R_kRepresent the resistance of branch road k；P_kRepresent the active power of branch road k；Q_kRepresent the reactive power of branch road k；V_kRepresent the terminal voltage of branch road k；

Step 102: set up the second target of reconstruction and optimization: maximize voltage lowest section point voltage, be:

$\begin{array}{cc}-min\left\{V_j\right\}& \&ForAll;j\&Element;N\end{array}$

In formula, V_jRepresenting the voltage perunit value of node j, N represents nodes；

Step 103: setting up the 3rd target of reconstruction and optimization: load balancing, transfer on the circuit that load is lighter by network reconfiguration by the loaded portion on heavier for load circuit, weigh with system loading evenness index, its value is the smaller the better, is:

$\min SLBI=min\left(\frac{1}{N_b}\underset{j=1}{\overset{N_b}{\mathrm{\&Sigma;}}}\frac{S_j}{{S_j}^{\max }}\right)$

In formula, N_bRepresent circuitry number；S_jRepresent the actual current size flowing through branch road j；Represent and allow to flow through the maximum current of branch road j；

Additionally, in Load flow calculation, in addition it is also necessary to consider following constraints:

$\begin{array}{cc}{V}^{min}\&le;V_j\&le;V^{max}& \&ForAll;j\&Element;N\end{array}$

$\begin{array}{cc}\left|S_k\right|\&le;S_k^{\max }& \&ForAll;k\&Element;N_b\end{array}$

In formula: V^min, V^maxRepresent the bound of node voltage when distribution is properly functioning respectively；S_kRepresent the current-carrying capacity of branch road k, S^maxRepresent the maximum carrying capacity of circuit k.

3. the multiple target Distribution system method taking into account distributed power source and negative rules according to claim 1, it is characterised in that: described step 2 comprises the following steps:

Step 201: blower fan is exerted oneself, photovoltaic is exerted oneself and load carries out scene partitioning:

It is generally acknowledged wind speed Follow Weibull Distribution at present, probability density function is following formula such as:

$f_v\left(v\right)=\frac{d}{c}{\left(\frac{v}{c}\right)}^{d-1}\exp \&lsqb;-{\left(\frac{v}{c}\right)}^d\&rsqb;$

In formula, f_vFor the probability density function of wind speed, c and d is scale parameter and form parameter respectively, it is possible to the historical data identification according to field measurement wind speed, v represents wind speed m/s, when known wind speed random distribution parameter, it is possible to obtaining the probability of any wind speed interval, computing formula is as follows:

$P\left\{{\mathrm{case}}_i\right\}=P\{v_m<v\&le;v_n\}={\&Integral;}_{v_m}^{v_n}{f}_v\left(v\right)dv$

Case in above formula_iRepresent i-th scene, v_nAnd v_mRepresent the up-and-down boundary of wind speed scene interval respectively；

Intensity of the sunlight can be similar to regards Beta distribution as:

$f\left(s\right)=\frac{\mathrm{\&Gamma;}(\mathrm{\&alpha;}+\mathrm{\&beta;})}{\mathrm{\&Gamma;}\left(\mathrm{\&alpha;}\right)\mathrm{\&Gamma;}\left(\mathrm{\&beta;}\right)}{\left(\frac{s}{s_{\max }}\right)}^{\mathrm{\&alpha;}-1}{(1-\frac{s}{s_{\max }})}^{\mathrm{\&beta;}-1}$

In formula, s and s_maxThe respectively actual light intensity in the time period and largest light intensity, α and β is the form parameter of Beta distribution in a period of time；

Solar cell array output is:

P_sun=sA η

Wherein, P_sunFor battery array output, A is the solar cell array gross area, and η is electricity conversion；

Adopt the scene partitioning method exerting oneself same with Wind turbines, divide light intensity interval, calculate the probability of different interval i.e. different scenes according to Intensity Probability Density function；

In distribution network, daily load curve, monthly load curve and yearly load curve have bigger fluctuation, along with distributed power source is grid-connected, load prediction is more difficult, hence in so that the uncertainty in Distribution system is higher, load is divided into three typical scenes: normality load scenarios, underload scene and high load scenarios；

Step 202: scene number determines strategy and the evaluation of schemes synthesis optimality:

Uncertain factor is transformed into definitiveness scene by scene analysis method, wind-powered electricity generation, grid-connected after, in Distribution system, uncertain factor is essentially from three aspects: Wind turbines output, solar panel output, load, thus the scene selected in reconstruction model is the combination of scene contained by above three, adopt synchronization back substitution "flop-out" method that large-scale scene is cut down, combination property for scheme: compare the object function expected value size based on scene probability of happening, such as following formula:

$D_{best}\&DoubleLeftRightArrow;\underset{i}{\min }or\underset{i}{\max }\left\{E\&lsqb;F\left(D_i\right)\&rsqb;\right\}\&DoubleLeftRightArrow;\underset{i}{\min }or\underset{i}{\max }\left(\underset{k=1}{\overset{n_s}{\mathrm{\&Sigma;}}}{\mathrm{PB}}_k{F}_{ik}\right)$

In formula: n_sFor the scene number after cutting down；PB_kFor the scene k probability occurred；F_ikFor the comprehensive evaluation value of i-th prioritization scheme under kth scene；D_iFor i-th prioritization scheme.E[F(D_i)] for the object function expected value of i-th prioritization scheme.

4. the multiple target Distribution system method taking into account distributed power source and negative rules according to claim 1, it is characterised in that: described step 3 comprises the following steps:

Step 301: adopt disturbance biogeography algorithm to obtain multiple target reconfiguration scheme；This algorithm adopts disturbance transfer operator and cosine migration models, designs habitat suitability evaluation index to guide Evolution of Population according to the principle minimizing each sub-goal, preserves the non-domination solution in evolutionary process with filing population；Wherein, disturbance transfer operator is pressed following formula and is obtained:

q_i,j=p_k,j+ceil(ξ(p_k1,j-p_k2,j))

In formula, ξ is the random number of 0-1；Jth variable (the p of kth habitat is determined by roulette_k,j) move to the jth variable (q of i-th habitat_i,j) position, stochastic generation k1, k2 ∈ 1,2 ..., N}/{ i}；

Cosine migration models is as follows:

${\mathrm{\&lambda;}}_k=\frac{I}{2}\&lsqb;cos\left(\frac{k\mathrm{\&pi;}}{n}\right)+1\&rsqb;$

${\mathrm{\&mu;}}_k=\frac{E}{2}\&lsqb;-cos\left(\frac{k\mathrm{\&pi;}}{n}\right)+1\&rsqb;$

In formula, λ_kFor moving into probability, μ_kFor removal probability, I is maximum immigration probability, and E is maximum removal probability；

It is defined as comprehensive evaluation index, is used for guiding Evolution of Population:

$F=\underset{i=1}{\overset{3}{\&Sigma;}}\frac{w_i(f_i-f_{i,min})}{(f_{i,\max }-f_{i,min})}+rank\&CenterDot;(1-ratio)$

In formula, F represents habitat suitability vector, f_iRepresent habitat the i-th target function value vector, f_i,max, f_i,minRepresent the maximin of all habitat i-th targets respectively, rank represents habitat non-dominant ranking vector, ratio represents that in population, non-dominant grade is 1 individual shared ratio, iteration early stage, dominance hierarchy be 1 individuality less, dominance hierarchy proportion in aggregative indicator is relatively big, along with population iterative evolution, non-dominant grade be 1 individuality get more and more, dominance hierarchy effect in comprehensive evaluation index reduces；w₁, w₂, w₃Initial value is disposed as 1, according to the attention degree to each target, it is possible to arrange weight flexibly, three's and be 1；

Step 302: in actual distribution runs, policymaker needs to determine a best reconstructed operation scheme from candidate solution, adopts fuzzy set theory to determine that best compromise solution is by each sub-goal Fuzzy processing, defines as follows:

$h_i=\left\{\begin{array}{cc}1,& f_i\&le;f_i^{\min }\\ \frac{f_i^{\max }-f_i}{f_i^{\max }-f_i^{\min }},& f_i^{\min }<f_i<f_i^{\max }\\ 0,& f_i\&GreaterEqual;f_i^{\max }\end{array}\right.$

In formula: i ∈ 1,2 ..., N_obj}；f_iFor object function；N_objFor object function number；f_i ^max,f_i ^minThe respectively maximum of the i-th object function, minima；h_iTake 0 and 1 represent completely dissatisfied respectively and be entirely satisfactory；Non-domination solution concentrates the satisfaction of each solution can use following formula scalarization:

$h=\frac{1}{N_{obj}}\underset{i=1}{\overset{N_{obj}}{\&Sigma;}}{h}_i$

The maximum solution of h value is decided to be best compromise solution.