CN107038489B - Multi-target unit combination optimization method based on improved NBI method - Google Patents

Multi-target unit combination optimization method based on improved NBI method Download PDF

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CN107038489B
CN107038489B CN201710243273.2A CN201710243273A CN107038489B CN 107038489 B CN107038489 B CN 107038489B CN 201710243273 A CN201710243273 A CN 201710243273A CN 107038489 B CN107038489 B CN 107038489B
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刘新元
黄少伟
郑惠萍
王晗
杨尉薇
陈颖
郝鑫杰
严正
王玮茹
郝捷
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Electric Power Research Institute of State Grid Shanxi Electric Power Co Ltd
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Abstract

A multi-target unit combination optimization method based on an improved NBI method includes the steps of constructing a multi-target unit combination optimization model according to generator unit parameters, converting multi-target problems in the model into m single-target problems based on the improved NBI method, carrying out linearization processing on quadratic inequality constraints in the m single-target problems according to a linearization strategy to obtain m mixed integer linear programming problems, obtaining m uniformly distributed non-inferior solutions on a Pareto frontier, and taking a compromise solution in the m uniformly distributed non-inferior solutions as a multi-target unit combination optimization result. The invention reduces the complexity of the original quadratic constraint solving, greatly reduces the calculation time and improves the overall calculation efficiency.

Description

Multi-target unit combination optimization method based on improved NBI method
Technical Field
The invention relates to a technology in the field of power system control, in particular to a multi-target unit combination optimization method based on an improved NBI method.
Background
With the continuous development of the power industry, the environmental pollution problem is becoming more severe, and it is necessary to control the emission of pollution gas in the power production process. Therefore, the Unit Composition (UC) as an important link for scheduling and operating the power system also faces a new challenge. In the traditional unit combination problem which only aims at the minimum economic cost, the influence of the unit polluted gas emission on the environment is ignored, and the polluted gas emission amount of the single-target optimal solution obtained by the minimum economic cost is possibly large, so that the energy conservation and emission reduction are not facilitated. Therefore, with further research, the multi-target unit combination model with the minimum economic cost and the minimum pollutant gas emission has higher application value, and a plurality of solving methods of the multi-target unit combination model are provided, including a Lagrange relaxation algorithm, an intelligent algorithm combined with a priority method and the like, and finally a series of non-inferior solutions on Pareto frontier can be obtained, and then a compromise solution is selected as a reference setting of the final unit output.
The normal boundary crossing (NBI) method is a quick and effective method for solving a complex multi-target problem. The NBI method converts the multi-objective optimization problem into a series of single-objective optimization problems to be solved, and finally obtains non-inferior solutions which are uniformly distributed on the Pareto front edge. When the NBI method is used for solving, the obtained non-inferior solutions on the Pareto front edge can be uniformly distributed, and the distribution condition of the Pareto front edge is described to the maximum extent. However, in the conventional NBI method, secondary constraint is introduced when a multi-target problem is converted into a single-target problem, so that the solving time is long, and the solving efficiency is reduced.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a multi-target unit combination optimization method based on an improved NBI method, which reduces the complexity of the original quadratic constraint solving, greatly reduces the calculation time and improves the overall calculation efficiency.
The invention is realized by the following technical scheme:
according to the method, a multi-target unit combination optimization model is established according to generator unit parameters, then multi-target problems in the model are converted into m single-target problems based on an improved NBI method, then secondary inequality constraints in the m single-target problems are subjected to linearization treatment according to a linearization strategy, m mixed integer linear programming problems are obtained, m uniformly distributed non-inferior solutions on the Pareto front edge are obtained, and a compromise solution is used as a multi-target unit combination optimization result.
The multi-target unit combination optimization model is constructed by obtaining various constraint parameters of the generator unit, the model takes the minimum economic cost and the minimum pollutant gas emission as targets, the secondary target function in the model is linearized according to a linearization strategy in an improved NBI method, and the minimum value f of the target function under the condition of a single target is respectively solved1minAnd f2minAs the end point of the Pareto front.
min F(x)＝{f1(x),f2(x)}
The multi-target unit combination optimization model is as follows:
Figure GDA0002687355330000021
wherein: the expression of the objective function is:
Figure GDA0002687355330000022
Figure GDA0002687355330000023
f1(x) The primary energy consumption cost of the conventional generator set is reduced; a isi、bi、ciThe cost coefficient of the unit i is obtained; f. of2(x) Carbon dioxide emission of the generator set; x is the number ofi，yi，ziThe carbon dioxide emission coefficient of the unit i is obtained;
Figure GDA0002687355330000024
the active power of the unit i at the moment t is obtained;
Figure GDA0002687355330000025
is a state variable of 0-1 for starting and stopping the unit i at the moment t, and
Figure GDA0002687355330000026
indicating that the unit is in a starting state; siThe starting cost of the unit; t represents the number of time periods; n represents the number of the sets of the machines.
And solving the processed m mixed integer linear programming problems by adopting an optimization tool to obtain the non-inferior solution.
The linearization treatment specifically comprises the following steps:
1) the improved NBI method converts a multi-target problem into m single-target problems, namely:
Figure GDA0002687355330000027
wherein: x is a vector of unknown variables; diAn intercept variable added after conversion to a single target problem; f. of1minAs an objective function f1(x) Minimum value of (d); f. of1maxAs an objective function f1(x) Maximum value of (d); f. of2minAs an objective function f2(x) Minimum value of (d); f. of2maxAs an objective function f2(x) Maximum value of (d); k is the order of the single target problem.
2) And (3) sorting the function part containing the quadratic term to obtain:
Figure GDA0002687355330000028
Figure GDA0002687355330000029
3) according to a linearization strategy in an improved NBI method, carrying out linearization processing on inequality constraints containing quadratic terms to obtain the following linear inequality constraints:
for an objective function f containing a quadratic term1(x) To convert to:
Figure GDA0002687355330000031
wherein: d is the number of linearization stages;
Figure GDA0002687355330000032
and
Figure GDA0002687355330000033
the linearization parameters calculated by interpolation method and the lines of the same unit i at different timeThe parameters after the denaturation were the same.
For an objective function f containing quadratic terms2(x) To convert to:
Figure GDA0002687355330000034
wherein:
Figure GDA0002687355330000035
and
Figure GDA0002687355330000036
and calculating the linearization parameters obtained by the interpolation method, wherein the linearization parameters of the same unit i at different moments are the same.
4) The objective function is integrated with linear constraints (e.g.: upper and lower limit constraints of unit output, minimum start-stop time constraints of the unit, climbing constraints of the unit and the like) to obtain m mixed integer linear programming problems.
The compromise solution is selected by, but not limited to, a top-to-bottom solution distance method (TOPSIS).
The invention relates to a system for realizing the method, which comprises the following steps: data reading module, model building module and operation processing module, wherein: the data reading module reads unit data and outputs the unit data to the model establishing module to establish a multi-target unit combination optimization model; the model establishing module outputs the established multi-target unit combination optimization model to the operation processing module for operation to obtain and output a multi-target unit combination optimization result.
The unit data comprises: the system comprises an upper limit and a lower limit of unit output, minimum start-stop time constraint of the unit, climbing constraint of the unit, the number of linearization sections and coefficients of a target function.
Technical effects
Compared with the prior art, the method has the advantages that the quadratic function and the quadratic objective function in the traditional NBI method are subjected to linearization processing and converted into a mixed integer linear programming problem, so that the calculation precision is guaranteed, the solution time is reduced, the calculation efficiency is greatly improved, and the solution technology has higher practicability.
Drawings
FIG. 1 is a flow chart of a multi-target unit combination optimization method based on an improved NBI method;
FIG. 2 is a graph comparing the modified NBI method linearization 10 section with the Pareto front edge obtained by the traditional NBI method;
FIG. 3 is a compromise solution on the Pareto front found based on the improved NBI method linearization segment 10;
fig. 4 is a graph of the output curve of the corresponding generator set based on the Pareto frontier compromise solution obtained in the section 10 of the improved NBI method linearization.
Detailed Description
As shown in fig. 1, the present embodiment includes the following steps:
step 1: obtaining all constraint parameters of the generator set, and constructing a multi-target unit combination optimization model with the minimum economic cost and the minimum pollutant gas emission as targets, wherein the compact form of the model is as follows:
minF(x)＝{f1(x),f2(x)}
Figure GDA0002687355330000041
objective function f1(x) And f2(x) The expression of (a) is:
Figure GDA0002687355330000042
Figure GDA0002687355330000043
wherein: g (x) is an equality constraint; h (x) is an inequality constraint; a isi，bi，ciThe cost coefficient of the unit i is obtained; siIs a start-up cost factor; x is the number ofi，yi，ziAnd (4) the emission coefficient of the polluted gas of the unit i.
In the model, the specific constraints of the generator set comprise the upper and lower limit constraints of the output of the generator set, the start-stop cost constraint of the generator set, the minimum start-stop time constraint of the generator set, the climbing constraint of the generator set and the rotation reserve capacity constraint of the generator set.
Step 2: according to the linearization strategy in the improved NBI method, carrying out linearization processing on a quadratic objective function in the optimization model to obtain an objective function f2(x) For example, when a single-target minimum is solved after introducing a linearization strategy, the objective function f2(x) The expression can be written as:
Figure GDA0002687355330000044
wherein:
Figure GDA0002687355330000045
corresponding to the pollutant gas discharge amount at the moment t of the ith unit.
The constraint conditions are as follows:
Figure GDA0002687355330000046
taking d sections on the parabola of the quadratic function to carry out linear interpolation, wherein the corresponding constraint conditions after linearization are:
Figure GDA0002687355330000047
wherein: converted j (j ═ 1 … d) th linearly constrained linearization parameter
Figure GDA0002687355330000048
And
Figure GDA0002687355330000049
the parameters are obtained by interpolation calculation, and the linearized parameters of the same unit i at different moments are the same.
Objective function f1(x) The second order economic cost function in (1) can also be subjected to the same linearization treatment.
And step 3: respectively solving the minimum value f of the objective function under the condition of a single target according to the model after the linearization processing in the step 21minAnd f2minAs the end point of Pareto frontier;
and 4, step 4: converting the multi-target problem into m single-target problems based on the improved NBI method, wherein the m single-target problems are as follows:
Figure GDA0002687355330000051
and 5: and 4, sorting the function part containing the quadratic term in the step 4 to obtain the following inequality constraints:
Figure GDA0002687355330000052
Figure GDA0002687355330000053
according to a linearization strategy in an improved NBI method, carrying out linearization processing on inequality constraints containing quadratic terms to obtain the following linear inequality constraints:
for an objective function f containing a quadratic term1(x) To convert to:
Figure GDA0002687355330000054
wherein: d is the number of linearization stages;
Figure GDA0002687355330000055
and
Figure GDA0002687355330000056
and calculating the linearization parameters obtained by the interpolation method, wherein the linearization parameters of the same unit i at different moments are the same.
For an objective function f containing quadratic terms2(x) To convert to:
Figure GDA0002687355330000057
wherein: d is the number of linearization stages;
Figure GDA0002687355330000058
and
Figure GDA0002687355330000059
and calculating the linearization parameters obtained by the interpolation method, wherein the linearization parameters of the same unit i at different moments are the same.
And (4) synthesizing the objective function and other linear constraint conditions to obtain m mixed integer linear programming problems.
Step 6: solving the processed m mixed integer linear programming problems by using Cplex to obtain m uniformly distributed non-inferior solutions on the Pareto front edge;
and 7: and selecting a compromise solution from the obtained Pareto non-inferior solution set.
The present embodiment will be described by taking a 10-machine system as an example. Some parameters of 10 units are shown in table 1.
TABLE 1 part parameters of the plant
Figure GDA00026873553300000510
Figure GDA0002687355330000061
Respectively utilizing a traditional NBI method and an improved NBI method to carry out linearization on 10 sections to solve non-inferior solutions on the Pareto front edge of the multi-objective 10-machine system, wherein the solving result of the minimum value of the single objective is shown in the table 2.
TABLE 2 comparison of Single target results
Figure GDA0002687355330000062
By comparison, the improved NBI method linearizes 10 segments, and has an error with the traditional NBI method, which is caused by linearization, but the error is small and can be ignored in the actual system analysis. And the NBI method is improved in calculation time, so that the calculation time is short, and the method has obvious advantages.
As shown in FIG. 2, which is a graph comparing the improved NBI method linearization 10 section with the Pareto front edge obtained by the traditional NBI method, it can be seen that the Pareto front edge obtained by the improved NBI method is basically the same as the result obtained by the traditional NBI method, and the effectiveness of the method is verified. Meanwhile, as the calculation time is shown in table 3, it can be seen that the solution efficiency of the improved NBI method is greatly improved.
TABLE 3 Multi-objective Pareto frontier computation time comparison
Figure GDA0002687355330000071
As shown in fig. 3, the position of the compromise solution on the Pareto front edge obtained based on the improved NBI method linearization section 10 is selected by using the TOPSIS method as a practical solution provided for the user under multiple objectives. Fig. 4 shows the output curve of the corresponding generator set based on the Pareto frontier compromise solution obtained in the section 10 of the modified NBI method.
The embodiment is only one case of application of the method, and the method can be applied to improve the solving efficiency when the solution of the multi-target unit combination optimization problem is involved under other system conditions.
The foregoing embodiments may be modified in many different ways by those skilled in the art without departing from the spirit and scope of the invention, which is defined by the appended claims and all changes that come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.

Claims (7)

1. A multi-target unit combination optimization method based on an improved NBI method is characterized in that a multi-target unit combination optimization model is established according to generator unit parameters, then multi-target problems in the model are converted into m single-target problems based on the improved NBI method, then quadratic inequality constraints in the m single-target problems are subjected to linearization processing according to a linearization strategy to obtain m mixed integer linear programming problems, m uniformly distributed non-inferior solutions on a Pareto front edge are obtained, and a compromise solution is used as a multi-target unit combination optimization result;
the linearization treatment specifically comprises the following steps:
1) the improved NBI method converts a multi-target problem into m single-target problems, namely:
Figure FDA0002687355320000011
wherein: x is a vector of unknown variables; diAn intercept variable added after conversion to a single target problem; f. of1minAs an objective function f1(x) Minimum value of (d); f. of1maxAs an objective function f1(x) Maximum value of (d); f. of2minAs an objective function f2(x) Minimum value of (d); f. of2maxAs an objective function f2(x) Maximum value of (d); k is the order of the single target problem; g (x) is an equality constraint; h (x) is an inequality constraint;
2) and (3) sorting the function part containing the quadratic term to obtain:
Figure FDA0002687355320000012
3) according to a linearization strategy in an improved NBI method, carrying out linearization processing on inequality constraints containing quadratic terms to obtain the following linear inequality constraints:
for an objective function f containing a quadratic term1(x) To convert to:
Figure FDA0002687355320000013
wherein: d is the number of linearization stages;
Figure FDA0002687355320000014
and
Figure FDA0002687355320000015
calculating a linearization parameter for an interpolation method, wherein the linearization parameters of the same unit i at different moments are the same as the number of linearization sections;
Figure FDA0002687355320000016
and
Figure FDA0002687355320000017
calculating linear parameters obtained by an interpolation method, wherein the linear parameters of the same unit i at different moments are the same;
for an objective function f containing quadratic terms2(x) To convert to:
Figure FDA0002687355320000021
wherein:
Figure FDA0002687355320000022
and
Figure FDA0002687355320000023
calculating linear parameters obtained by an interpolation method, wherein the linear parameters of the same unit i at different moments are the same;
4) and synthesizing the objective function and the linear constraint condition to obtain m mixed integer linear programming problems.
2. The method as claimed in claim 1, wherein the multi-objective unit combination optimization model is constructed by obtaining each constraint parameter of the generator unit, the model takes the minimum economic cost and the minimum pollutant gas emission as the target, and the quadratic objective function in the model is linearized according to the linearization strategy in the improved NBI method, and the minimum value f of the objective function under the condition of single target is solved respectively1minAnd f2minAs the end point of the Pareto front.
3. The method according to claim 1 or 2, wherein the multi-objective unit combination optimization model is as follows:
Figure FDA0002687355320000024
wherein: the expression of the objective function is:
Figure FDA0002687355320000025
Figure FDA0002687355320000026
f1(x) The primary energy consumption cost of the conventional generator set is reduced;ai、bi、cithe cost coefficient of the unit i is obtained; f. of2(x) Carbon dioxide emission of the generator set; x is the number ofi，yi，ziThe carbon dioxide emission coefficient of the unit i is obtained;
Figure FDA0002687355320000027
the active power of the unit i at the moment t is obtained;
Figure FDA0002687355320000028
is a state variable of 0-1 for starting and stopping the unit i at the moment t, and
Figure FDA0002687355320000029
indicating that the unit is in a starting state; siThe starting cost of the unit; t represents the number of time periods; n represents the number of the sets of the machines.
4. The method of claim 1, wherein the non-inferior solution is obtained by solving m mixed integer linear programming problems processed by an optimization tool.
5. The method of claim 1, wherein the linear constraints comprise: the method comprises the following steps of upper and lower limit restraint of unit output, minimum start-stop time restraint of the unit and climbing restraint of the unit.
6. The method of claim 1, wherein the compromise solution is selected by a distance between good and bad solutions.
7. A system for implementing the method of any preceding claim, comprising: data reading module, model building module and operation processing module, wherein: the data reading module reads unit data and outputs the unit data to the model establishing module to establish a multi-target unit combination optimization model; the model establishing module outputs the established multi-target unit combination optimization model to the operation processing module for operation to obtain and output a multi-target unit combination optimization result;
the unit data comprises: the system comprises an upper limit and a lower limit of unit output, minimum start-stop time constraint of the unit, climbing constraint of the unit, the number of linearization sections and coefficients of a target function.
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