CN110533263A - A kind of hot integrated system Multipurpose Optimal Method of electric-gas-based on improvement NSGA-II algorithm - Google Patents
A kind of hot integrated system Multipurpose Optimal Method of electric-gas-based on improvement NSGA-II algorithm Download PDFInfo
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Abstract
The present invention discloses a kind of based on the hot integrated system Multipurpose Optimal Method of electric-gas-for improving NSGA-II algorithm, this method are as follows: (1) using energy system constraint, natural gas system constraint and therrmodynamic system constraint as constraint condition, using cost is minimum and carbon emission is at least as two objective functions, electric-thermal-gas integrated energy system Multiobjective Optimal Operation model is established；(2) NSGA-II algorithm is improved using global Pareto set maintaining method, the Multiobjective Optimal Operation model that improved NSGA-II algorithm obtains step (1) solves.The present invention is reduced using dimension and the method for dynamic adjustment improves the probability that feasible solution is found under higher-dimension equality constraint.The economic load dispatching of integrated system hot for electric-gas-and environmental protection are all of great significance.
Description
Technical field
Present document relates to Optimized Operation field more particularly to a kind of comprehensive systems of the electric-gas based on improvement NSGA-II algorithm-heat
System Multipurpose Optimal Method.
Technical background
The fast development of social economy brings the serious energy and environmental crisis, seriously threatens the existence of the mankind.For solution
Certainly this problem, scholar propose the concept of energy internet.In energy internet, electric power, natural gas, heating power and transport system
System is highly coupled, and is deeply nearly interacted.
Energy internet is the effective use for solving the problems, such as renewable energy, provides feasible technical solution.Therefore it grinds
Study carefully the feature and intension of energy internet, inquire into the various key technologies for realizing energy internet, for pushing energy internet
Development, and gradually make traditional power grid to energy internet develop, have most important theories meaning and practical value.
Summary of the invention
The purpose of the present invention is minimum for electric-thermal-gas integrated energy system operating cost, and reduce to the maximum extent dirty
Discharge amount is contaminated, is proposed a kind of based on the hot integrated system Multipurpose Optimal Method of electric-gas-for improving NSGA-II algorithm.
The purpose of the present invention is what is be achieved through the following technical solutions: a kind of based on the electric-gas-for improving NSGA-II algorithm
Hot integrated system Multipurpose Optimal Method, this method are as follows:
(1) minimum with cost using energy system constraint, natural gas system constraint and therrmodynamic system constraint as constraint condition
It is at least used as two objective functions with carbon emission, establishes electric-thermal-gas integrated energy system Multiobjective Optimal Operation model；
(2) NSGA-II algorithm is improved using global Pareto set maintaining method, improved NSGA-II is calculated
The Multiobjective Optimal Operation model that method obtains step (1) solves.
Further, the energy system constraint condition includes: unit output constraint, power-balance constraint, transimission power
Constraint.The natural gas system constraint condition include: Combustion gas balance constraint, the constraint of natural gas line flow, gas pressure about
Beam.The therrmodynamic system constraint condition include: electric, the hot relation constraint of CHP unit, heat yields constraint, equalized temperature about
Beam.
Further, keep system cost minimum as objective function (1) so that cost is minimum, including the operation of non-Gas Generator Set
Expense and system fuel gas supply cost；Using carbon emission at least as objective function (2), keep system carbon emission amount minimum, such two
A objective function；Wherein
(1) minimization of cost is as objective function:
Wherein, C indicates objective function, PiIt is the power output of unit i, Fi cIt is the operating cost of unit i, ρGASIt is gas price,
vwIt is the gas production rate of gas well v；
Wherein a1,i,a2,i,a3,iFor multinomial coefficient, NGUFor Gas Generator Set set；
(2) carbon emission, which minimizes, is used as objective function:
U in above formulacoalAnd ugasFor the carbon emission coefficient of coal and combustion gas, Fi RIt is the consumption of coal function of non-Gas Generator Set i；
Wherein b1,i,b2,i,b3,iFor multinomial coefficient, obtained by the experiment of unit carbon emission.
Further, in order to increase the quantity of Pareto optimal solution, make Pareto font distribution more it is big more evenly, it is right
NSGA-II algorithm is improved, and aiming at the problem that traditional genetic algorithm is difficult to handle higher-dimension equality constraint, proposes dimensionality reduction,
Dynamic adjusts and increases the method for penalty, improves the probability for finding feasible solution.
Due to being had difficulties in IES optimization problem using NSGA-II.Firstly, since there is no be distributed in different generations
The maintenance of global Pareto font, therefore the quantity of Pareto optimal solution is relatively fewer.Secondly as existing in model a large amount of
Equality constraint, solution space greatly reduced, and the selection of optimized variable is extremely important for the search of solution.On solving
Problem is stated, this paper presents a kind of improved NSGA-II algorithms.
The maintenance of one, overall situation Pareto optimality collection
The Pareto optimal solution of traditional NSGA-II algorithm is only derived from the present age, it is difficult to more Pareto optimal solutions are obtained, and
And it is difficult to control Population Size in suitable range.
Improved NSGA-II algorithm maintains global Pareto optimality set, is calculating every generation Pareto non-domination solution
Afterwards, following operation is executed:
(1) these non-domination solutions are compared with global Pareto optimality collection.
(2) global Pareto optimality collection is updated.That will not be dominated by global Pareto optimality set in non-dominant individual
Body is added in global Pareto optimality set.
(3) non-domination solution dominated by global Pareto optimality set is punished by reducing adaptability.
Two, constrain processing method
(1) Nonlinear Equality Constrained
In the hot integrated system Optimal Scheduling of electric-gas-, only one Nonlinear Equality Constrained.Therefore, first by institute
Some air pressure π1, π2..., πNgasIt is set as optimized variable, all natural gas trend gmnIt can be determined by nonlinear equation.
Then remaining linear restriction is gradually solved by dimensionality reduction and dynamic adjustment.
(2) dimensionality reduction
Assuming that the total number of variable in all equality constraints is n, the number of equality constraint is m, m≤n, then equality constraint can table
It is shown as:
Theoretically, it at most can choose n-m variable as optimized variable.Its dependent variable can be former by equation solution
Beginning problem can be fully converted to the problem of only including inequality constraints.However, in actual operation, if arbitrarily selecting n-m
A variable carrys out reduced equation as optimized variable, remaining equation is likely to morbid state, that is to say, that its dependent variable can not be asked
Solution.Therefore, when selecting optimized variable, it is necessary to which being avoided as much as some optimized variable can combine from based on fixed linear
Other optimized variables in obtain.
(3) dynamic adjusts
Even if having selected one group of good optimized variable, in this case it is still possible to be unsatisfactory for certain equality constraints.Dynamic adjustment can be with
Correct one group of variable for being unsatisfactory for equality constraint but only a small amount of violation.
Assuming that there is a linear equality constraints fec(x1,x2,...,xk,...,xn)=0, wherein x1To xk+1It is that optimization becomes
Amount.
xk+1To xnIt is supplementary variable, it can calculated by optimized variable and other equality constraints.For simplicity, f is rememberedec
(x1,x2,...,xk,...,xn)=0 is fec(x)=0.
If dynamic adjustment threshold value is TminAnd Tmax(Tmin<Tmax, TminShould be a lesser value), maximum dynamic adjusts secondary
Number Nmax。
Variable x0 is organized to Mr. Yu, remembers fec(x0)=Δ y.If | Δ y | < T2, then it is assumed that meet approximate.Otherwise, if T2≤
|Δy|<T1, then start dynamic and adjust, original state may be expressed as:
It is adjusted assuming that t dynamic has been carried out, when carrying out the t+1 times dynamic adjustment, optimized variable is according to Δ yt=
fec(xt) be updated.
As shown in above formula, calculate firstThen according to Δ yt+1=f (xt+1) can calculate t+1 times
It measures in violation of rules and regulations.If Δ yt+1< T2 then meets loose equality constraint, exits dynamic and adjusts and take xt+1 as optimized variable value.Such as
Fruit still without the optimized variable for meeting relaxation equality constraint, then stops dynamic and adjusts and will remember constraint not as t=Nmax-1
Meet.
(4) penalty
It, can be in objective function f in order to ensure optimized variable meets constraint conditioniOn the basis of add penalty term, to kind
Group's number is punished.Define inequality constraints penalty factoric, the equality constraint penalty factor of two ranksec1, Cec2
(Cec1<Cec2).If dynamic variables collection adjusted is xd, the collection of all equality constraints is combined into Fec, all inequality constraints
Collection is combined into Fic.
For inequality constraints fic(x)∈[ymin,ymax].If fic(xd)=y, corresponding punishment is:
For equality constraint fec(x)=0, if | fec(xd) |=y, corresponding punishment is:
Total punishment xd are as follows:
Fpi is defined to calculate variable x after consideration objective function and constraint conditiondComprehensive fitness degree.
(5) model solution step
Step 1: initialization
Step 1.1 simplifies equality constraint using dimensionality reduction, selects optimized variable, the boundary of variable is arranged.
Step 1.2 creates a random father group P0.Define global Pareto optimality disaggregation Sg.Set population maximum algebra gmax
(gmax>=1) current algebra g=1, is set.
Step 2: iteration updates
Step 2.1 dynamically adjusts Pt to Pt', calculates comprehensive fitness degree fpi (Pt').
The quick non-dominated ranking fpi (Pt') of step 2.2.Update Sg.
Step 2.3 sets g=g+1, if g > gmax, step 3 is gone to, otherwise, goes to step 2.4.
Step 2.4 creates R of new generation by selection, multiple point crossover, variationt.Dynamic adjusts, and calculates comprehensive fitness degree fpi
(Rt)。
Step 2.5 combines father group Pt-1And RtAs Pt
Step 3: output Sg.
(6) Pareto set search process
The Pareto set of NSGA-II is generated by the individual of Current generation, is properly termed as local Pareto set.Set forth herein
Improved NSGA-II algorithm maintain a global Pareto set, to obtain more Pareto optimal solutions.It should be pointed out that
The distribution solved in order to prevent is excessively concentrated, and before updating local Pareto set or global Pareto set every time, should be used and is based on
The filtering of crowding distance.
Local Pareto set and the 20th generation, the global Pareto set in the 50th generation and the 100th generation.
(7) trend of Pareto optimal solution
With the increase of generation, the average value and minimum value of the local Pareto solution of two objective functions are shown than the overall situation
The stronger fluctuation of Pareto optimality collection.The global minimum of totle drilling cost reaches stable after 3rd generation, global carbon row after the 43rd generation
Total amount is put to settle out.
(8) solution efficiency
With the increase of generation, the quantity of locally optimal solution keeps stablizing, and the quantity of globally optimal solution linearly increases
Gesture.In the 100th generation, the quantity of global Pareto optimal solution is 14.18 times of local Pareto optimal solution.
Herein in the platform with Intel (R) Core (TM) i7-5500U CPU@2.40GHz 2.39GHz and 4GB RAM
It is calculated on formula computer.
(9) state recognition of system
Since the distribution of Pareto set global in solution space is relatively uniform, it is easily found and meets specified conditions
Solution.
For example, if system carbon emission be limited in 67t hereinafter, if can be focused to find out cost in the Pareto in the 100th generation
Minimum Pareto solution (totle drilling cost: 3737.467 $, carbon emission: 66.999t).
Above-mentioned model is solved in python3 using improved NSGA-II algorithm.
Beneficial effects of the present invention: by based on improve NSGA-II algorithm the hot integrated system multiple-objection optimization of electric-gas-,
Reduce economic operation cost, and reduces discharge amount of pollution to greatest extent on this basis, system comprehensive for electric-gas-heat
The economic load dispatching of system and environmental protection are all of great significance.
Detailed description of the invention
The following drawings are only intended to schematically illustrate and explain the present invention, not delimit the scope of the invention.Wherein,
Fig. 1 is electric-thermal of the invention-gas integrated system constraint condition schematic diagram；
Fig. 2 is model emergency step of the invention；
Fig. 3 is electric-thermal of the invention-gas integrated system topological structure.
Specific embodiment
To make the object, technical solutions and advantages of the present invention clearer, embodiment of the present invention is made below further
Ground detailed description.
The purpose of the present invention is minimum for electric-thermal-gas integrated energy system operating cost, and reduce to the maximum extent dirty
Contaminate discharge amount.It proposes a kind of based on the hot integrated system Multipurpose Optimal Method of electric-gas-for improving NSGA-II algorithm.
The purpose of the present invention is what is be achieved through the following technical solutions: a kind of based on the electric-gas-for improving NSGA-II algorithm
Hot integrated system Multipurpose Optimal Method, it is based on physical characteristic, establishes the multiple-objection optimization of electric-thermal-gas integrated energy system
Scheduling model.The model is minimum by cost and carbon emission is at least used as two objective functions, enables policymaker's balanced economy
And environmental protection problem；In order to increase the quantity of Pareto optimal solution, mention Pareto font distribution more greatly more evenly,
A kind of Pareto set maintaining method of overall situation is gone out；Aiming at the problem that traditional genetic algorithm is difficult to handle higher-dimension equality constraint, mention
Dimensionality reduction is gone out, dynamic adjusts and increases the method for penalty, improves the probability for finding feasible solution.
The present invention is based on the hot integrated system multiple-objection optimization of electric-gas-for improving NSGA-II algorithm, the Optimized Operation moulds
The target of type is to minimize system cost, and reduce discharge amount of pollution to the maximum extent under IES constraint condition.The energy
System constraints include: unit output constraint, power-balance constraint, transimission power constraint.The natural gas system constrains item
Part includes: Combustion gas balance constraint, the constraint of natural gas line flow, gas pressure constraint.The therrmodynamic system constraint condition packet
It includes: electric, the hot relation constraint of CHP unit, heat yields constraint, equalized temperature constraint.As shown in Figure 1
It is had difficulties in IES optimization problem using NSGA-II.Firstly, since there is no the overall situations for being distributed in different generations
The maintenance of Pareto font, therefore the quantity of Pareto optimal solution is relatively fewer.Secondly as existing in model a large amount of etc.
Formula constraint, solution space are greatly reduced, and the selection of optimized variable is extremely important for the search of solution.To solve above-mentioned ask
Topic, this paper presents a kind of improved NSGA-II algorithms.
The maintenance of one, overall situation Pareto optimality collection
The Pareto optimal solution of traditional NSGA-II algorithm is only derived from the present age, it is difficult to more Pareto optimal solutions are obtained, and
And it is difficult to control Population Size in suitable range.
The improvement NSGA-II algorithm proposed maintains global Pareto optimality set, and calculating, every generation Pareto is non-
After dominating solution, following operation is executed:
(1) these non-domination solutions are compared with global Pareto optimality collection.
(2) global Pareto optimality collection is updated.That will not be dominated by global Pareto optimality set in non-dominant individual
Body is added in global Pareto optimality set.
(3) non-domination solution dominated by global Pareto optimality set is punished by reducing adaptability.
(4) count these related non-dominants it is individual in how many be global Pareto optimality concentration existing solution.If weight
Again there are many number, then consider to enhance population diversity using Gauss mutation.
Two, constrain processing method
(1) Nonlinear Equality Constrained
In the hot integrated system Optimal Scheduling of electric-gas-, only one Nonlinear Equality Constrained (13).Therefore, first
By all π1, π2..., πNgasIt is set as optimized variable, all gmnIt can be determined by nonlinear equation.Then pass through drop
Peacekeeping dynamic adjustment gradually solves remaining linear restriction.
(2) assume that the total number of variable in all equality constraints is n, the number of equality constraint is m, m≤n, then equality constraint
It may be expressed as:
Theoretically, it at most can choose n-m variable as optimized variable.Its dependent variable can be former by equation solution
Beginning problem can be fully converted to the problem of only including inequality constraints.However, in actual operation, if arbitrarily selecting n-m
A variable carrys out reduced equation as optimized variable, remaining equation is likely to morbid state, that is to say, that its dependent variable can not be asked
Solution.
Therefore, when selecting optimized variable, it is necessary to which being avoided as much as some optimized variable can be from based on fixed linear
It is obtained in other optimized variables of combination.
It is as shown in Figure 2 that optimized variable finds process
(3) dynamic adjusts
Even if having selected one group of good optimized variable, in this case it is still possible to be unsatisfactory for certain equality constraints.Dynamic adjustment can be with
Correct one group of variable for being unsatisfactory for equality constraint but only a small amount of violation.
Assuming that there is a linear equality constraints fec(x1,x2,...,xk,...,xn)=0, wherein x1To xk+1It is that optimization becomes
Amount.xk+1To xnIt is supplementary variable, it can calculated by optimized variable and other equality constraints.For simplicity, f is rememberedec(x1,
x2,...,xk,...,xn)=0 is fec(x)=0.
If dynamic adjustment threshold value is TminAnd Tmax(Tmin<Tmax, TminShould be a lesser value), maximum dynamic adjusts secondary
Number Nmax。
Variable x is organized to Mr. Yu0, remember fec(x0)=Δ y.If | Δ y | < T2, then it is assumed that meet approximate.Otherwise, if Tmin
≤|Δy|≤Tmax, then start dynamic and adjust.Original state may be expressed as:
It is adjusted assuming that t dynamic has been carried out, when carrying out the t+1 times dynamic adjustment, optimized variable is according to Δ yt=
fec(xt) be updated.
As shown in above formula, calculate firstThen according to Δ yt+1=f (xt+1) can calculate t+1 times
It measures in violation of rules and regulations.If Δ yt+1<Tmin , then meet loose equality constraint, exit dynamic and adjust and take xt+1 as optimized variable value.
If working as t=Nmax-1When still without meet relaxation equality constraint optimized variable, then stop dynamic adjust and by note constraint not
Meet.
(4) penalty
In order to ensure optimized variable meets constraint condition, penalty term can be added on the basis of objective function fi, to kind
Group's number is punished.Define inequality constraints penalty factoric, the equality constraint penalty factor of two ranksec1, Cec2
(Cec1<Cec2).If dynamic variables collection adjusted is xd, the collection of all equality constraints is combined into Fec, all inequality constraints
Collection is combined into Fic.
For inequality constraints fic(x)∈[ymin,ymax].If fic(xd)=y, corresponding punishment is:
For equality constraint fec(x)=0, if | fec(xd) |=y, corresponding punishment is:
Total punishment xd are as follows:
Define fpiTo calculate variable x after consideration objective function and constraint conditiondComprehensive fitness degree.
Model solution step is as shown in Figure 3:
Example 1
On the basis of 6 electrical -6 combustion gas node system, the heating power network comprising four heat exchangers, shape are increased
At electricity-heat-gas integrated system.
(1) Pareto set search process
The Pareto set of NSGA-II is generated by the individual of Current generation, is properly termed as local Pareto set.Set forth herein
Improved NSGA-II algorithm maintain a global Pareto set, to obtain more Pareto optimal solutions.It should be pointed out that
The distribution solved in order to prevent is excessively concentrated, and before updating local Pareto set or global Pareto set every time, should be used and is based on
The filtering of crowding distance.
Local Pareto set and the 20th generation, the global Pareto set in the 50th generation and the 100th generation.
(2) trend of Pareto optimal solution
With the increase of generation, the average value and minimum value of the local Pareto solution of two objective functions are shown than the overall situation
The stronger fluctuation of Pareto optimality collection.The global minimum of totle drilling cost reaches stable after 3rd generation, global carbon row after the 43rd generation
Total amount is put to settle out.
(3) solution efficiency
With the increase of generation, the quantity of locally optimal solution keeps stablizing, and the quantity of globally optimal solution linearly increases
Gesture.
In the 100th generation, the quantity of global Pareto optimal solution is 14.18 times of local Pareto optimal solution.
Herein in the platform with Intel (R) Core (TM) i7-5500U CPU@2.40GHz 2.39GHz and 4GB RAM
It is calculated on formula computer.
(4) state recognition of system
Since the distribution of Pareto set global in solution space is relatively uniform, it is easily found and meets specified conditions
Solution, rather than analyze corresponding integrated energy system state.
For example, if system carbon emission be limited in 67t hereinafter, if can be focused to find out cost in the Pareto in the 100th generation
Minimum Pareto solution (totle drilling cost: 3737.467 $, carbon emission: 66.999t).
This paper presents a kind of methods of the hot integrated energy system Multiobjective Optimal Operation of electric-gas-, can be used for solving non-convex
Restricted model.By dimensionality reduction, the method for dynamic adjustment and penalty, the model solution solved under a large amount of equality constraints is difficult
Topic.By being arranged and safeguarding global Pareto set, the significant increase of the quantity for the Pareto optimal solution searched for per unit time, and
And the distribution and uniformity of solution are improved.Pass through the validity of the proposed method of case verification.
Model proposed in this paper does not account for the dynamic characteristic of natural gas and heating power network, this optimization to multiple periods
Precision has a certain impact.Relevant issues will discuss in later research.
Claims (7)
1. a kind of based on the hot integrated system Multipurpose Optimal Method of electric-gas-for improving NSGA-II algorithm, which is characterized in that the party
Method are as follows:
(1) using energy system constraint, natural gas system constraint and therrmodynamic system constraint as constraint condition, with cost is minimum and carbon
Minimum emissions establish electric-thermal-gas integrated energy system Multiobjective Optimal Operation model as two objective functions；
(2) NSGA-II algorithm is improved using global Pareto set maintaining method, improved NSGA-II algorithm pair
The Multiobjective Optimal Operation model that step (1) obtains is solved.
2. according to claim 1 a kind of based on the hot integrated system multiple-objection optimization of electric-gas-for improving NSGA-II algorithm
Method, which is characterized in that
The energy system constraint includes: unit output constraint, power-balance constraint, transimission power constraint；
The natural gas system constraint includes: Combustion gas balance constraint, the constraint of natural gas line flow, gas pressure constraint；
The therrmodynamic system constraint includes: electric, the hot relation constraint of CHP unit, heat yields constraint, equalized temperature constraint.
3. according to claim 2 a kind of based on the hot integrated system multiple-objection optimization of electric-gas-for improving NSGA-II algorithm
Method, which is characterized in that keep system cost minimum as objective function (1) so that cost is minimum, including non-Gas Generator Set running cost
With with system fuel gas supply cost；Using carbon emission at least as objective function (2), keep system carbon emission amount minimum, two such
Objective function；Wherein
(1) minimization of cost is as objective function:
Wherein, C indicates objective function, PiIt is the power output of unit i, Fi cIt is the operating cost of unit i, ρGASIt is gas price, vwIt is
The gas production rate of gas well v；
Wherein a1,i,a2,i,a3,iFor multinomial coefficient, NGUFor Gas Generator Set set；
(2) carbon emission, which minimizes, is used as objective function:
U in above formulacoalAnd ugasFor the carbon emission coefficient of coal and combustion gas, Fi RIt is the consumption of coal function of non-Gas Generator Set i；
Wherein b1,i,b2,i,b3,iFor multinomial coefficient, obtained by the experiment of unit carbon emission.
4. the Pareto set maintaining method according to claim 3 using the overall situation is to NSGA-II algorithm, which is characterized in that
There is non-convex constraint in multiple-objection optimization, therefore cannot directly be calculated using CPLEX or Gurobi, using improved NSGA-II
Algorithm, by maintenance one global Pareto optimality disaggregation, to obtain more Pareto optimal solutions.
5. according to the Pareto set maintaining method described in claim 1 using the overall situation to NSGA-II algorithm, which is characterized in that institute
Improved NSGA-II algorithm is stated, the means such as penalty are adjusted and be arranged using dimensionality reduction, dynamic, reduce Optimized model equation
The restriction to feasible solution search efficiency is constrained, the acquisition efficiency of Pareto optimal solution is improved.
6. according to the Pareto set maintaining method as claimed in claim 3 using the overall situation to NSGA-II algorithm, which is characterized in that institute
It states improved NSGA-II algorithm and realizes that steps are as follows:
Step 1: initialization
Step 1.1 simplifies equality constraint using dimensionality reduction, selects optimized variable, the boundary of variable is arranged；
Step 1.2 creates a random father group P0, define global Pareto set Sg, population maximum is set for gmax(gmax>=1), if
Settled former generation g=1；
Step 2: updating
Step 2.1 dynamically adjusts Pt to Pt', calculates comprehensive fitness degree fpi(Pt')；
The quick non-dominated ranking fpi (Pt') of step 2.2 updates Sg；
Step 2.3 sets g=g+1, if g > gmax, step 3 is gone to, otherwise, goes to step 2.4；
Step 2.4 creates Rt of new generation by selection, multiple point crossover, variation, and dynamic adjusts, and calculates comprehensive fitness degree fpi
(Rt)；
Step 2.5 combines father group Pt-1And RtAs Pt；
Step 3: output Sg.
7. according to claim 1 a kind of based on the hot integrated system multiple-objection optimization of electric-gas-for improving NSGA-II algorithm
Method, which is characterized in that above-mentioned model is solved in python3 using improved NSGA-II algorithm.
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