CN106446383A - Method for solving uncertain unit commitment problem with security constraint based on improved constraint ordinal optimization - Google Patents
Method for solving uncertain unit commitment problem with security constraint based on improved constraint ordinal optimization Download PDFInfo
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Abstract
The invention discloses a method for solving an uncertain unit commitment problem with a security constraint based on improved constraint ordinal optimization. The method comprises the steps that a discrete variable recognition strategy is blended into a rough model at first, and an ordinal optimization rough module based on a constraint condition is established; and then, a non-valid security constraint reduction strategy is brought into a precise model, and an ordinal optimization precise model aiming at a continuous variable is established. In comparison with a traditional constraint ordinal optimization method aiming at an SCUC model, the improvement strategy disclosed by the invention effectively enhances compactness of an ordinal optimization algorithm, reduces computing redundancy and thus has higher solution efficiency.
Description
Technical field
The invention belongs to power system and automation research field, especially relate to a kind of based on improving what constraint sequence optimized
Uncertain Optimization of Unit Commitment By Improved method for solving with security constraint.
Background technology
Access on a large scale under background in wind-powered electricity generation, the unit group of meter and wind power output probabilistic consideration Network Security Constraints
Closing (Security Constraints Unit Commitment, SCUC) is formulate power system generation schedule a few days ago main
Foundation.SCUC is mathematically a belt restraining, nonlinear extensive mixed integer programming problem, is an allusion quotation on solving
NP (Non-Deterministic Polynomial, NP) the hardly possible problem of type.Continuous expansion with electrical network scale and interval
The extensive access of the regenerative resource of property so that the solution difficulty of SCUC problem increasingly increases, therefore, how fast and effectively
Solve the focus considering that wind power output probabilistic SCUC problem is increasingly becoming people's research.
For the solution of uncertain SCUC model, current main stream approach is based on Benders decomposition, that is,:
First with Benders decomposition method, SCUC model decoupling be Unit Combination and Network Security Constraints check two subproblems, so
Recycle Lagrangian Relaxation, dynamic programming, branch and bound method and various intelligent optimization algorithm that each subproblem is entered afterwards
Row solves.However, because the main advantage of Benders decomposition method is to solve the definitiveness optimization problem with Complex Constraints,
And in terms of corresponding uncertainty optimization problem solving advantage inconspicuous.In recent years, as solution complicated optimum problem
One of effective ways, ordinal optimization theory increasingly causes the concern of people.Study and uncertain for sequence optimization introducing SCUC has been asked
Topic solution field, from engineering reality, abandons asking its optimal solution, then seeks the good enough solution of SCUC problem, successfully will ask
Solution efficiency improves nearly 30 times on the basis of traditional Benders decomposition method, thus demonstrating ordinal optimization theory uncertain
Property SCUC solve field significant advantage.From existing research from the point of view of although sequence optimization be proved to be one kind can with rapid solving not
The effective ways of definitiveness SCUC problem, but because traditional ordinal optimization theory is only started with from solution space, by building rough model
Reduce model feasible zone scale, and ignore the rejecting for model redundancy itself and examination, therefore, in solution efficiency side
Face, sequence optimized algorithm still has larger improvement and room for promotion, therefore needs a kind of band safety improving constraint sequence optimization of research badly
The uncertain Optimization of Unit Commitment By Improved method for solving of constraint.
Content of the invention
For fast and effectively solve containing wind-powered electricity generation SCUC problem, the present invention propose a kind of based on improve constraint sequence optimize
Uncertain Optimization of Unit Commitment By Improved method for solving with security constraint.Discrete variable identification plan is incorporated first in rough model
Omit, and the sequence constructing based on constraints optimizes rough model;Then introduce non-effective security constraint in accurate model to cut down
Strategy, and the sequence constructing for continuous variable optimizes accurate model.Compared to the constraint sequence optimization side to SCUC model for the conventional needle
Method, improvement strategy proposed by the present invention effectively improves the compactedness of sequence optimized algorithm, reduces computing redundancy degree, thus has
Higher solution efficiency.
The technical solution adopted in the present invention is:
A kind of uncertain Optimization of Unit Commitment By Improved method for solving with security constraint based on improvement constraint sequence optimization, construction
The double optimization model of one normally opened normal shutdown group of identification, the unit in this model hypothesis system is all turned on, and then considers
The major constraints relevant with generator output, with the minimum optimization aim of operating cost, its mathematical model is:
According to the result of model solution, for all t=1,2,3 ..., T, if PGitAll meet PGit>PGimin, then i-th
Number unit is normally opened unit;If PGitAll meet PGit<δPGimin, then No. i-th unit is normal shutdown group, and wherein δ is identification ginseng
Number, here takes 0.05;
The chance of all unit starts given at the beginning by this model, is then optimized calculating with operating cost for target,
If generating set is exerted oneself within whole dispatching cycle all in the extremely low level of ratio, show unit under current loads level,
Generating share cannot be obtained by competition, thus may be considered normal shutdown group.On the contrary, if within whole dispatching cycle, machine
It is higher than all that its minimum technology is exerted oneself that group is exerted oneself, then it is considered that in competition this unit can obtain larger Generation Right all the time, because
And it is regarded as normally opened unit.
A kind of uncertain Optimization of Unit Commitment By Improved method for solving with security constraint based on improvement constraint sequence optimization, including
Following steps:
Step 1:Non-effective security constraint is defined as:If after certain constraint is removed, feasible zone in this model with remove
Front is identical, then this is constrained to non-effective constraint.According to definition, it is further proposed that fully must of the identification of non-effective security constraint
The condition is wanted to be:There is not common factor in non-effective constraint and feasible zone or common factor is only a summit of simple body.According to above-mentioned
Necessary and sufficient condition, construction rejects security constraints A{j}(PG1t,PG2t,…PGMt)T≤Bt {j}Feasible zone Optimized model afterwards is:
In formula:ajiThe element of the jth row i row in representing matrix A;A-{j}、Bt -{j}Representing matrix A, B remove jth row respectively
Matrix after element.
Step 2:The constraints of formula (2) is relaxed, builds and recognize the fully inessential of non-effective security constraint
Condition:
Because Z1≤Z2, so it is believed that working as Z2≤Bj,tWhen, constrain A{j}(PG1t,PG2t,…PGMt)T≤Bt {j}For non-effective
Constraint.
Step 3:Analyticity solution is carried out to formula (3), thus proposing to avoid solving-optimizing model, directly using
Know the fully inessential condition of the non-effective security constraint of parameter identification, its step is as follows:
(1), assume i1,i2,…,imFor unit order, therefore have:
(2), when linear programming problem has feasible solution, then have:
Therefore there is integer k to meet:
(3), assume
Then the object function of optimization problem is:
In sum, can obtain the final criterion of non-effective security constraint is:
A kind of uncertain Optimization of Unit Commitment By Improved method for solving with security constraint based on improvement constraint sequence optimization, its mesh
Scalar functions are:
In formula:FGtFor the total operating cost of system, the generating set number in system is M, PGitAnd UGitRepresent i-th respectively
Number unit is exerted oneself and start and stop state in the active of t period, UGit=0 expression generating set is in stopped status, UGit=1 expression is sent out
Group of motors is in open state, Yit(PGit) for generating set operating cost, Sit(τi) for electromotor start-up and shut-down costs;
Wherein, the operating cost of generating set, start-up and shut-down costs concrete mathematical expression form as follows:
In formula:αi、βi、γiFor unit operation cost parameter, S0i、S1i、τiFor the downtime of i unit, ωiFor start and stop
Cost parameter;
For ensureing power system security reliability service, in the SCUC model containing wind-powered electricity generation power system, decision variable also needs
Meet following conventional constraint condition:
1) system power Constraints of Equilibrium
In formula:PDtFor system the t period burden with power;PLtFor system the t period transmission of electricity active power loss;PWtFor wind
Group of motors is in the output of t period;
2) generating set exert oneself bound constraint
PGimin≤PGit≤PGimax(5)
In formula:PGiminAnd PGimaxIt is respectively active lower limit and the upper limit of exerting oneself of generating set;
3) minimum start-stop time constraint
In formula:niFor unit within dispatching cycle maximum allowable start-stop time;
4) unit ramp loss
In formula:WithIt is respectively the maximum landslide ability of the interior per hour active output of unit and maximum climbing energy
Power;
5) Network Security Constraints
A·Pt≤Bt(8)
Wherein:
In formula:T is transfer factor matrix;KP、KDIt is respectively node-electromotor matrix and node-matrix of loadings;PtDuring for t
The node power matrix carved;DtNode load matrix for t;PLmaxFor transmission capacity on transmission line of electricity L;
The wind power output being described using chance constraint method in Optimization of Unit Commitment By Improved is uncertain, and constructing system is positive and negative respectively
Spinning reserve risk indicator;
Qd≤λ (11)
Qu≤λ (12)
In formula:Qd、QuIt is respectively positive and negative spinning reserve risk index;λ is spinning reserve risk threshold value, system call department
Available annual total cost minimum method converts after obtaining reliability standard and obtains, and generally takes between 0~10%.
A kind of uncertain Optimization of Unit Commitment By Improved method for solving with security constraint based on improvement constraint sequence optimization, step
As follows:
Step 1:Construct the double optimization model of a normally opened normal shutdown group of identification, the unit in this model hypothesis system
It is all turned on, then consider the major constraints relevant with generator output, with the minimum optimization aim of operating cost, its mathematical modulo
Type is:
According to the result of model solution, for all t=1,2,3 ..., T, if PGitAll meet PGit>PGimin, then i-th
Number unit is normally opened unit;If PGitAll meet PGit<δPGimin, then No. i-th unit is normal shutdown group, and wherein δ is identification ginseng
Number, here takes 0.05;
Step 2:Rough model is built according to the constraints related to start and stop state, filters out Unit Commitment solution space.
Main inclusion:Power-balance constraint, unit ramp loss, minimum start-stop time constraint, its concrete mathematical description is as follows,
Step 3:Introduce invalid security constraint identification theory, build non-effective security constraint identification model, it specifically includes
Following steps:
Step 3.1:Non-effective security constraint is defined as:If after certain constraint is removed, feasible zone in this model with go
Identical before falling, then this is constrained to non-effective constraint.According to definition, it is further proposed that the identification of non-effective security constraint is abundant
Essential condition is:There is not common factor in non-effective constraint and feasible zone or common factor is only a summit of simple body.According to upper
State necessary and sufficient condition, construction rejects security constraints A{j}(PG1t,PG2t,…PGMt)T≤Bt {j}Feasible zone Optimized model afterwards
For:
In formula:ajiThe element of the jth row i row in representing matrix A;A-{j}、Bt -{j}Representing matrix A, B remove jth row respectively
Matrix after element;
Step 3.2:The constraints of formula (15) is relaxed, building identification the fully non-of non-effective security constraint must
Want condition:
Because Z1≤Z2, so it is believed that working as Z2≤Bj,tWhen, constrain A{j}(PG1t,PG2t,…PGMt)T≤Bt {j}For non-effective
Constraint;
Step 3.3:Analyticity solution is carried out to formula (16), thus proposing to avoid solving-optimizing model, directly profit
Recognize the fully inessential condition of non-effective security constraint with known parameters, its step is as follows:
(1), assume i1,i2,…,imFor unit order, therefore have:
(2), when linear programming problem has feasible solution, then have:
Therefore there is integer k to meet:
(3), assume
Then the object function of optimization problem is:
In sum, can obtain the final criterion of non-effective security constraint is:
On the basis of invalid security constraint is recognized and is cut down, the present invention with SCUC model objective function and with even
Continuous variable PGitBased on related constraints, construction sequence optimizes accurate model, and its mathematical description is as follows:
Compared with the conventional method, a kind of uncertain unit with security constraint based on improvement constraint sequence optimization of the present invention
Combinatorial problem method for solving, has advantages below and beneficial effect:
(1):Although the solution of discrete variable identification model needs the regular hour, optimize slightly because it can reduce sequence
The dimension of rough model solution space, so, as a complete unit, introduce discrete variable Identification Strategy and can lift sequence optimization rough model
Computational efficiency.
(2):Non-effective security constraint is cut down strategy and can be recognized the non-effective safety more than 90% in the short period of time
Constraint, is introduced into sequence and optimizes accurate model, can effectively reduce the computing redundancy degree of accurate model, put forward computational efficiency.
(3):Because improvement strategy improves the compactedness of sequence optimized algorithm, thus improvement random constraints proposed by the present invention
Sequence optimized algorithm has larger lifting compared to traditional sequence optimized algorithm in terms of solution efficiency, and compared to other algorithms, then
Either computational accuracy and efficiency all have a clear superiority.
Brief description
Fig. 1 is inventive algorithm general thought block diagram.
Fig. 2 is that rough model of the present invention builds flow chart.
Fig. 3 is the output of wind electric field curve chart in the embodiment of the present invention.
Fig. 4 is that the security constraint in the embodiment of the present invention cuts down result figure.
Specific embodiment
A kind of uncertain Optimization of Unit Commitment By Improved method for solving with security constraint based on improvement constraint sequence optimization, in profit
During with the uncertain Optimization of Unit Commitment By Improved with security constraint for the sequence Optimization Solution, rough model builds discrete variable identification mould
Type, is identified to normally opened, normal shutdown group, and effective lifting sequence is optimized the solution efficiency of rough model by this.
Construct the double optimization model of a normally opened normal shutdown group of identification, the unit in this model hypothesis system is all opened
Open, then consider the major constraints relevant with generator output, with the minimum optimization aim of operating cost, its mathematical model is:
According to the result of model solution, for all t=1,2,3 ..., T, if PGitAll meet PGit>PGimin, then i-th
Number unit is normally opened unit;If PGitAll meet PGit<δPGimin, then No. i-th unit is normal shutdown group, and wherein δ is identification ginseng
Number, here takes 0.05;
The design of this model is in fact to have incorporated electricity market for Generation Right, has equal opportunities, the thought of free competition,
Give the chance of all unit starts at the beginning, then calculating is optimized for target with operating cost, if generating set goes out
Power within whole dispatching cycle all in the extremely low level of ratio, show unit under current loads level it is impossible to be obtained by competition
Must be generated electricity share, thus may be considered normal shutdown group.On the contrary, if within whole dispatching cycle, unit output is higher than all it
Minimum technology is exerted oneself, then it is considered that in competition this unit can obtain larger Generation Right all the time, thus be regarded as normally opened
Unit.
Although this identification model belongs to belt restraining quadratic programming model, solve more complicated, it only needs to solve once,
The dimension of solution space just can be effectively reduced, thus as a whole, optimize in rough model in sequence and add this model permissible
Lift its overall calculation efficiency.
A kind of uncertain Optimization of Unit Commitment By Improved method for solving with security constraint based on improvement constraint sequence optimization, in sequence
Optimize in accurate model, introduce invalid security constraint identification theory, effectively reduced the redundancy of accurate model, lifting further
Its computational efficiency, comprises the following steps:
Step 1:Non-effective security constraint is defined as:If after certain constraint is removed, feasible zone in this model with remove
Front is identical, then this is constrained to non-effective constraint.According to definition, it is further proposed that fully must of the identification of non-effective security constraint
The condition is wanted to be:There is not common factor in non-effective constraint and feasible zone or common factor is only a summit of simple body.According to above-mentioned
Necessary and sufficient condition, construction rejects security constraints A{j}(PG1t,PG2t,…PGMt)T≤Bt {j}Feasible zone Optimized model afterwards is:
In formula:ajiThe element of the jth row i row in representing matrix A;A-{j}、Bt -{j}Representing matrix A, B remove jth row respectively
Matrix after element.
Step 2:The constraints of formula (2) is relaxed, builds and recognize the fully inessential of non-effective security constraint
Condition:
Because Z1≤Z2, so it is believed that working as Z2≤Bj,tWhen, constrain A{j}(PG1t,PG2t,…PGMt)T≤Bt {j}For non-effective
Constraint.
Step 3:Analyticity solution is carried out to formula (3), thus proposing to avoid solving-optimizing model, directly using
Know the fully inessential condition of the non-effective security constraint of parameter identification, its step is as follows:
(1), assume i1,i2,…,imFor unit order, therefore have:
(2), when linear programming problem has feasible solution, then have:
Therefore there is integer k to meet:
(3), assume
Then the object function of optimization problem is:
In sum, can obtain the final criterion of non-effective security constraint is:
A kind of uncertain Optimization of Unit Commitment By Improved method for solving with security constraint based on improvement constraint sequence optimization, its mesh
Scalar functions are:
In formula:FGtFor the total operating cost of system, the generating set number in system is M, PGitAnd UGitRepresent i-th respectively
Number unit is exerted oneself and start and stop state in the active of t period, UGit=0 expression generating set is in stopped status, UGit=1 expression is sent out
Group of motors is in open state, Yit(PGit) for generating set operating cost, Sit(τi) for electromotor start-up and shut-down costs;
Wherein, the operating cost of generating set, start-up and shut-down costs concrete mathematical expression form as follows:
In formula:αi、βi、γiFor unit operation cost parameter, S0i、S1i、τiFor the downtime of i unit, ωiFor start and stop
Cost parameter;
For ensureing power system security reliability service, in the SCUC model containing wind-powered electricity generation power system, decision variable also needs
Meet following conventional constraint condition:
1) system power Constraints of Equilibrium
In formula:PDtFor system the t period burden with power;PLtFor system the t period transmission of electricity active power loss;PWtFor wind
Group of motors is in the output of t period;
2) generating set exert oneself bound constraint
PGimin≤PGit≤PGimax(5)
In formula:PGiminAnd PGimaxIt is respectively active lower limit and the upper limit of exerting oneself of generating set;
3) minimum start-stop time constraint
In formula:niFor unit within dispatching cycle maximum allowable start-stop time;
4) unit ramp loss
In formula:WithIt is respectively the maximum landslide ability of the interior per hour active output of unit and maximum climbing energy
Power;
5) Network Security Constraints
A·Pt≤Bt(8)
Wherein:
In formula:T is transfer factor matrix;KP、KDIt is respectively node-electromotor matrix and node-matrix of loadings;PtDuring for t
The node power matrix carved;DtNode load matrix for t;PLmaxFor transmission capacity on transmission line of electricity L;
The wind power output being described using chance constraint method in Optimization of Unit Commitment By Improved is uncertain, and constructing system is positive and negative respectively
Spinning reserve risk indicator;
Qd≤λ (11)
Qu≤λ (12)
In formula:Qd、QuIt is respectively positive and negative spinning reserve risk index;λ is spinning reserve risk threshold value, system call department
Available annual total cost minimum method converts after obtaining reliability standard and obtains, and generally takes between 0~10%.
A kind of uncertain Optimization of Unit Commitment By Improved method for solving with security constraint based on improvement constraint sequence optimization, step
As follows:
Step 1:Construct the double optimization model of a normally opened normal shutdown group of identification, the unit in this model hypothesis system
It is all turned on, then consider the major constraints relevant with generator output, with the minimum optimization aim of operating cost, its mathematical modulo
Type is:
According to the result of model solution, for all t=1,2,3 ..., T, if PGitAll meet PGit>PGimin, then i-th
Number unit is normally opened unit;If PGitAll meet PGit<δPGimin, then No. i-th unit is normal shutdown group, and wherein δ is identification ginseng
Number, here takes 0.05;
Step 2:Rough model is built according to the constraints related to start and stop state, filters out Unit Commitment solution space.
Main inclusion:Power-balance constraint, unit ramp loss, minimum start-stop time constraint, its concrete mathematical description is as follows, concrete stream
Journey is as shown in Figure 2.
Step 3:Introduce invalid security constraint identification theory, build non-effective security constraint identification model, it specifically includes
Following steps:
Step 3.1:Non-effective security constraint is defined as:If after certain constraint is removed, feasible zone in this model with go
Identical before falling, then this is constrained to non-effective constraint.According to definition, it is further proposed that the identification of non-effective security constraint is abundant
Essential condition is:There is not common factor in non-effective constraint and feasible zone or common factor is only a summit of simple body.According to upper
State necessary and sufficient condition, construction rejects security constraints A{j}(PG1t,PG2t,…PGMt)T≤Bt {j}Feasible zone Optimized model afterwards
For:
In formula:ajiThe element of the jth row i row in representing matrix A;A-{j}、Bt -{j}Representing matrix A, B remove jth row respectively
Matrix after element;
Step 3.2:The constraints of formula (15) is relaxed, building identification the fully non-of non-effective security constraint must
Want condition:
Because Z1≤Z2, so it is believed that working as Z2≤Bj,tWhen, constrain A{j}(PG1t,PG2t,…PGMt)T≤Bt {j}For non-effective
Constraint;
Step 3.3:Analyticity solution is carried out to formula (16), thus proposing to avoid solving-optimizing model, directly profit
Recognize the fully inessential condition of non-effective security constraint with known parameters, its step is as follows:
(1), assume i1,i2,…,imFor unit order, therefore have:
(2), when linear programming problem has feasible solution, then have:
Therefore there is integer k to meet:
(3), assume
Then the object function of optimization problem is:
In sum, can obtain the final criterion of non-effective security constraint is:
On the basis of invalid security constraint is recognized and is cut down, the present invention with SCUC model objective function and with even
Continuous variable PGitBased on related constraints, construction sequence optimizes accurate model, and its mathematical description is as follows:
Embodiment:
Taking the IEEE-118 node power system changed as a example, this system comprises 54 fired power generating unit, 3 wind-force to the present invention
Generating field, 91 load point, wherein wind energy turbine set are located at node 14 respectively, on 54,95, its rated power respectively 100MW,
200MW, 250MW, active exert oneself as shown in Figure 3.In system, the stand-by requirement of conventional power unit positive rotation is system peak load
8%, negative rotation turns 2% that stand-by requirement is system minimum load, and spinning reserve risk indicator is 0.01.Correlation computations are all in Ying Te
You are Duo i3-3240 processor 3.40GHz, 4G memory computer completes, using Matlab 8.0 and Cplex 12.5 to calculation
Example is programmed solving.
1), model solution:
Spinning reserve needed for system that constrained procedure of improving the occasion is asked for and each wind energy turbine set is as shown in table 1.
The spinning reserve (MW) of each wind energy turbine set of table 1
For verifying the correctness of discrete variable identification model, using this model, the start and stop state of generating set is distinguished
Know, and its result is contrasted based on the final Unit Commitment result that Benders decomposition method is tried to achieve with tradition, its result such as table
Shown in 2.
Table 2 discrete variable identification result contrasts
From comparing result, in 20 normally opened units, the discrete variable identification model of the present invention have identified 3
Individual, discrimination is 15%, and in 31 normal shutdown groups, Model Identification of the present invention has gone out 20, and discrimination is 64.5%, entirely
The situation identifying mistake does not occur in identification process.
From the above results contrast, discrete variable identification model proposed by the present invention for normal shutdown group discrimination relatively
Height, also has higher accuracy of identification simultaneously, is brought in sequence optimization rough model and can effectively reduce rough model
Calculating dimension, lift its solution efficiency.
In order to ensure accuracy of identification, the discrete variable identification model of the present invention identifies condition setting for normally opened unit
More harsh, so that the present invention is kept low for the discrimination of normally opened unit.And in follow-up calculating process,
Sequence optimizes accurate model and also further can be optimized calculating to normally opened unit, thus, for normally opened in early stage identification model
The relatively low solving precision also not interfering with whole algorithm of discrimination of unit.
Table 3 rough model performance table
As shown in Table 3, after sequence optimizes and adds discrete variable recognition strategy in rough model, the solution time of rough model
Although improving nearly 40s it is seen then that solving discrete variable identification model to need time-consuming 2.89s, due to which reducing rough model
Overall dimension, so, as a complete unit, the computational efficiency that sequence after improvement optimizes rough model is improved.
Carried non-effective security constraint by the checking present invention and cut down strategy validity, invalid security constraint is cut
Subtract, after the reduction of each period, remaining security constraint result is as shown in Figure 4.
From fig. 4, it can be seen that in IEEE-118 system per period have 372 security constraints, 24 periods have 8928 safety
Constraints, cuts down model by non-effective security constraint, and 24 periods cut down 8090 invalid security constraints altogether, cut down ratio
Reach more than 90%.The above results show, there is larger redundancy in the security constraint of existing SCUC model, and the present invention
Invalid security constraint cut down strategy can effectively reject above-mentioned redundancy.
From the point of view of each period, the number highest of remaining security constraints 38, minimum 15, and its variation tendency with
Load variations present certain dependency.Its reason is that load is heavier, and the general safety nargin of system can decline therewith, from
And need to check more circuits, that is, have more effective and safe constraints;Whereas if load is lighter, then effective and safe is about
Bundle also can reduce therewith.
Introduce invalid security constraint reduction strategy validity in accurate model to verify to optimize in sequence, be utilized respectively and draw
Enter invalid security constraint and cut down the sequence of strategy to optimize accurate model (after improvement) and traditional sequence optimization accurate model (before improvement) is right
Select each of set S start and stop scheme to be solved, its run time is as shown in table 4 it should be pointed out that this emulation is
Carry out on the basis of improvement sequence proposed by the present invention optimizes rough model.
Table 4 accurate model performance table
As shown in Table 4, the non-effective security constraint of the present invention is cut down strategy and can quickly be identified non-effective security constraint bar
Part, whole calculating process only takes 0.09s, and introduces the solution effect that the sequence after non-effective security constraint is cut down optimizes accurate model
Rate is improved significantly, and the calculating time reduces nearly 42.43s.It follows that adding non-effective in sequence optimization accurate model
Security constraint cuts down strategy, can effectively lift the computational efficiency of accurate model.
By verifying correctness and the effectiveness of the carried method for solving of the present invention, excellent using improvement constraint sequence proposed by the present invention
Change the SCUC model of the Algorithm for Solving present invention, the expense of optimal solution and its conventional power unit start and stop state are as shown in table 5.
Table 5 start and stop scheme
For contrasting effectiveness and the correctness of method for solving proposed by the present invention, the present invention also adopts following two sides simultaneously
Method solves to SCUC problem.
Method one:Traditional sequence optimized algorithm.
Method two:The mixed integer programming decomposed based on Benders.
The result of calculation of three kinds of methods and calculating time are as shown in table 6.
The each algorithm performance table of table 6
As shown in Table 6, sequence optimization method, either in terms of computational efficiency or solving precision, divides compared to benders
Solution method, all has obvious advantage.And proposed by the present invention improvement constrains sequence optimized algorithm, compared to traditional sequence optimization
Method, the total cost cost that it solves slightly reduces about 0.45%, but in terms of computational efficiency, it improves closely
18.85%.
Claims (4)
1. a kind of uncertain Optimization of Unit Commitment By Improved method for solving with security constraint based on improvement constraint sequence optimization, its feature
It is:Construct the double optimization model of a normally opened normal shutdown group of identification, the unit in this model hypothesis system is all turned on,
Then the major constraints relevant with generator output are considered, with the minimum optimization aim of operating cost, its mathematical model is:
According to the result of model solution, for all t=1,2,3 ..., T, if PGitAll meet PGit>PGimin, then No. i-th machine
Organize as normally opened unit;If PGitAll meet PGit<δPGimin, then No. i-th unit is normal shutdown group, and wherein δ is identification parameter,
This takes 0.05;
The chance of all unit starts given at the beginning by this model, is then optimized calculating with operating cost for target, if
Generating set is exerted oneself within whole dispatching cycle all in the extremely low level of ratio, show unit under current loads level it is impossible to
Generating share is obtained by competition, thus may be considered normal shutdown group, on the contrary, if within whole dispatching cycle, unit goes out
Power is higher than all that its minimum technology is exerted oneself, then it is considered that in competition this unit can obtain larger Generation Right all the time, thus can
It is considered normally opened unit.
2. a kind of uncertain Optimization of Unit Commitment By Improved method for solving with security constraint based on improvement constraint sequence optimization, its feature
It is:Comprise the following steps:
Step 1:Non-effective security constraint is defined as:If after certain constraint is removed, feasible zone in this model with remove before
Identical, then this is constrained to non-effective constraint, according to definition, it is further proposed that the fully necessary bar of the identification of non-effective security constraint
Part is:There is not common factor in non-effective constraint and feasible zone or common factor is only a summit of simple body, will according to above-mentioned filling
Condition, construction rejects security constraints A{j}(PG1t,PG2t,…PGMt)T≤Bt {j}Feasible zone Optimized model afterwards is:
In formula:ajiThe element of the jth row i row in representing matrix A;A-{j}、Bt -{j}Representing matrix A, B remove jth row element respectively
Matrix afterwards;
Step 2:The constraints of formula (2) is relaxed, builds the fully inessential condition recognizing non-effective security constraint:
Because Z1≤Z2, so it is believed that working as Z2≤Bj,tWhen, constrain A{j}(PG1t,PG2t,…PGMt)T≤Bt {j}For non-effective constraint;
Step 3:Analyticity solution being carried out to formula (3), thus proposing to avoid solving-optimizing model, directly utilizing known ginseng
Number recognizes the fully inessential condition of non-effective security constraint, and its step is as follows:
(1), assume i1,i2,…,imFor unit order, therefore have:
(2), when linear programming problem has feasible solution, then have:
Therefore there is integer k to meet:
(3), assume
Then the object function of optimization problem is:
In sum, can obtain the final criterion of non-effective security constraint is:
.
3. a kind of uncertain Optimization of Unit Commitment By Improved method for solving with security constraint based on improvement constraint sequence optimization, its feature
It is:Its object function is:
In formula:FGtFor the total operating cost of system, the generating set number in system is M, PGitAnd UGitRepresent No. i-th machine respectively
Group is exerted oneself and start and stop state in the active of t period, UGit=0 expression generating set is in stopped status, UGit=1 expression electromotor
Group is in open state, Yit(PGit) for generating set operating cost, Sit(τi) for electromotor start-up and shut-down costs;
Wherein, the operating cost of generating set, start-up and shut-down costs concrete mathematical expression form as follows:
In formula:αi、βi、γiFor unit operation cost parameter, S0i、S1i、τiFor the downtime of i unit, ωiFor start-up and shut-down costs
Parameter;
For ensureing power system security reliability service, in the SCUC model containing wind-powered electricity generation power system, decision variable also needs to meet
Following conventional constraint condition:
1) system power Constraints of Equilibrium
In formula:PDtFor system the t period burden with power;PLtFor system the t period transmission of electricity active power loss;PWtFor wind turbine
Group is in the output of t period;
2) generating set exert oneself bound constraint
PGimin≤PGit≤PGimax(5)
In formula:PGiminAnd PGimaxIt is respectively active lower limit and the upper limit of exerting oneself of generating set;
3) minimum start-stop time constraint
In formula:niFor unit within dispatching cycle maximum allowable start-stop time;
4) unit ramp loss
In formula:WithIt is respectively maximum landslide ability and the maximum gradeability of the interior per hour active output of unit;
5) Network Security Constraints
A·Pt≤Bt(8)
Wherein:
In formula:T is transfer factor matrix;KP、KDIt is respectively node-electromotor matrix and node-matrix of loadings;PtFor t
Node power matrix;DtNode load matrix for t;PLmaxFor transmission capacity on transmission line of electricity L;
The wind power output being described using chance constraint method in Optimization of Unit Commitment By Improved is uncertain, the positive and negative rotation of constructing system respectively
Standby risk indicator;
Qd≤λ (11)
Qu≤λ (12)
In formula:Qd、QuIt is respectively positive and negative spinning reserve risk index;λ is spinning reserve risk threshold value, and system call department can profit
Obtain conversion after reliability standard with annual total cost minimum method and obtain, generally take between 0~10%.
4. a kind of uncertain Optimization of Unit Commitment By Improved method for solving with security constraint based on improvement constraint sequence optimization, its feature
It is:Step is as follows:
Step 1:Construct the double optimization model of a normally opened normal shutdown group of identification, the unit in this model hypothesis system is whole
Open, then consider the major constraints relevant with generator output, with the minimum optimization aim of operating cost, its mathematical model
For:
According to the result of model solution, for all t=1,2,3 ..., T, if PGitAll meet PGit>PGimin, then No. i-th machine
Organize as normally opened unit;If PGitAll meet PGit<δPGimin, then No. i-th unit is normal shutdown group, and wherein δ is identification parameter,
This takes 0.05;
Step 2:Rough model is built according to the constraints related to start and stop state, filters out Unit Commitment solution space, mainly
Including:Power-balance constraint, unit ramp loss, minimum start-stop time constraint, its concrete mathematical description is as follows,
Step 3:Introduce invalid security constraint identification theory, build non-effective security constraint identification model, it specifically includes following
Step:
Step 3.1:Non-effective security constraint is defined as:If after certain constraint is removed, feasible zone in this model with remove before
Identical, then this is constrained to non-effective constraint;According to definition, it is further proposed that abundant necessity of the identification of non-effective security constraint
Condition is:There is not common factor in non-effective constraint and feasible zone or common factor is only a summit of simple body, is filled according to above-mentioned
Want condition, construction rejects security constraints A{j}(PG1t,PG2t,…PGMt)T≤Bt {j}Feasible zone Optimized model afterwards is:
In formula:ajiThe element of the jth row i row in representing matrix A;A-{j}、Bt -{j}Representing matrix A, B remove jth row element respectively
Matrix afterwards;
Step 3.2:The constraints of formula (15) is relaxed, builds the fully inessential bar recognizing non-effective security constraint
Part:
Because Z1≤Z2, so it is believed that working as Z2≤Bj,tWhen, constrain A{j}(PG1t,PG2t,…PGMt)T≤Bt {j}For non-effective constraint;
Step 3.3:Analyticity solution is carried out to formula (16), thus proposing to avoid solving-optimizing model, directly using
Know the fully inessential condition of the non-effective security constraint of parameter identification, its step is as follows:
(1), assume i1,i2,…,imFor unit order, therefore have:
(2), when linear programming problem has feasible solution, then have:
Therefore there is integer k to meet:
(3), assume
Then the object function of optimization problem is:
In sum, can obtain the final criterion of non-effective security constraint is:
To invalid security constraint recognized and cut down on the basis of, with SCUC model objective function and with continuous variable PGit
Based on related constraints, construction sequence optimizes accurate model, and its mathematical description is as follows:
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Application publication date: 20170222 Assignee: Hubei Yunzhihang Drone Technology Co.,Ltd. Assignor: CHINA THREE GORGES University Contract record no.: X2023980044730 Denomination of invention: A Solution Method for Uncertain Unit Commitment Problem Based on Improved Constraint Order Optimization Granted publication date: 20190924 License type: Common License Record date: 20231027 |