Dynamic economic dispatch optimization method based on dynamic subspace search

Abstract

The invention discloses a dynamic economic dispatch optimization method based on dynamic subspace search, which comprises the following steps: S1, establishing a model, and establishing an optimization target and constraint conditions based on physical characteristics and power demands of a generator set; s11, taking the minimum fuel consumption and the minimum pollution emission as optimization targets of the model; s12, according to the physical characteristics of the generator set, the electric balance constraint, the power output limitation constraint and the generator climbing constraint serve as constraint conditions needing to be met; and S2, performing operation on the optimization target and the constraint condition by using an optimization method based on dynamic subspace search. The decision variable dimension is reduced by setting the decision variable optimization probability; the convergence speed of the algorithm is improved by preferentially searching a search subspace formed by decision variables with high contribution degrees; the method is high in robustness and can be suitable for power dispatching in different scenes.

Description

Technical Field

[0001] The present invention belongs to the technical field of economic dispatch optimization, and in particular relates to a dynamic economic dispatch optimization method based on dynamic subspace search. Background Art

[0002] Electricity plays an indispensable role in our daily life. In the composition of my country's electricity supply, thermal power generation has always accounted for the highest proportion, which shows the importance of coal resources. At the same time, in the process of generating electricity, a large amount of pollution emissions are inevitably generated, such as CO2, SO2 and NO X However, with the development of economy and the increase of population, the demand for electricity continues to grow, carbon emissions are also gradually increasing, and environmental pollution and greenhouse effect are becoming more and more serious. In order to minimize the impact of environmental pollution on people's lives. Based on this, researchers have gradually paid attention to the problem of dynamic environmental economic dispatch optimization (DEED) of power systems, and try to minimize the emission of pollutants while considering the cost of power generation. Since the demand for electricity is different at different times of the day, this requires the power system to effectively and flexibly manage and dispatch power generation resources to meet the changing load demand.

[0003] In DEED, the power output of each generator set is reasonably dispatched according to the power demand at each moment, while satisfying various constraints such as supply and demand balance and generator ramp constraints. Since the generator set needs to meet the supply and demand balance and contains various output restrictions, it has complex constraints; and due to the operating characteristics of the generator set and the existence of valve point effects, its target has nonlinear characteristics; in addition, since it contains multiple generator sets and needs to dispatch each generator at every moment, the variables have large-scale characteristics. These difficulties make it difficult for existing methods to provide more effective solutions. Summary of the invention

[0004] The purpose of this invention is to provide a dynamic economic dispatch optimization method based on dynamic subspace search to provide a better solution for DEED

[0005] The technical solution adopted by the present invention is: a dynamic economic dispatch optimization method based on dynamic subspace search, comprising the following steps:

[0006] S1, establish the model, establish the optimization objectives and constraints based on the physical characteristics of the generator set and the power demand;

[0007] S11, minimizing fuel consumption and minimizing pollution emissions are taken as the optimization objectives of the model;

[0008] S12, according to the physical characteristics of the generator set, the electric balance constraint, the power output limit constraint and the generator ramp constraint are taken as the constraints that need to be met;

[0009] S2, uses the optimization method based on dynamic subspace search to perform operations on the optimization objectives and constraints.

[0010] Furthermore, the minimization of fuel consumption:

[0011]

[0012] Where: T represents the dispatch period, N is the number of generators, P i,t is the output power of the ith generator at time t, P i,min represents the minimum output power of the ith generator, a i 、b i 、c i ,d i and e i is the cost coefficient of the ith generator;

[0013] The minimization of pollution emissions:

[0014]

[0015] In the formula, α i , η i , γ i , i and is the emission cost coefficient of the ith generator.

[0016] Further, the constraints include electric balance constraints, power output limit constraints and generator ramp constraints;

[0017] The electrical balance constraint

[0018]

[0019] Where: P D,t represents the total power load required at time t, P L,t is the power transmission loss at time t, and its specific calculation formula is as follows:

[0020]

[0021] Where: B i,j , B i,0 and B 0,0 is the transmission loss coefficient of the power system;

[0022] The power output limit constraint

[0023] Pi,min ≤P i,t ≤P i,max (5)

[0024] Where: P i,min and P i,max are the minimum and maximum output powers of the ith generator respectively;

[0025] The generator climbing constraint

[0026] P i,t -P i,t-1 ≤U R,i

[0027] P i,t-1 -P i,t ≤L R,i (6)

[0028] Where: U R,i and L R,i are the ramp-up and ramp-down rate limits for the ith generator.

[0029] Further, step S2 includes the following steps:

[0030] S21, initialize the population P of size NP;

[0031] S22, record the used computing resources Fe=NP;

[0032] S23, executing a decision variable analysis method considering angle and length information, the computing resources used are NS*D*NDV;

[0033] S24, set the maximum computing resource maxFe=maxFe-NS*D*NDV;

[0034] Where NS represents the number of solutions used for decision variable analysis, D is the number of decision variables in the problem, and NDV is the number of times each decision variable is perturbed;

[0035] S25, executing a probability-based offspring generation strategy to generate an offspring population O;

[0036] S26, set P = P∪O;

[0037] S27, execute the improved epsilon environment selection method to select NP individuals to form a new population P;

[0038] S28, set Fe=Fe+NP;

[0039] S29, determine whether the maximum computing resources have been reached, if so, output the population P, otherwise, jump to S25.

[0040] Furthermore, the specific steps of S23 include:

[0041] S231, for each decision variable d, randomly select NS individuals from the population P for decision variable analysis;

[0042] S232, for each selected individual k, randomly perturb its d-th decision variable NDV times, and store the newly generated individuals into the temporary population temP;

[0043] S233, calculate the target values ​​of all individuals in each temP, fit them into a line segment, and calculate its length L d,k ;

[0044] S234, calculate the fitted line segment and f1+…+f M = 1, the angle between the normals d,k ;

[0045] S235, judging whether each selected individual is disturbed, if so, jumping to S236; otherwise, jumping to S232;

[0046] S236, calculate the angle matrix ɑ d,k The average value of d , and the length matrix L d,k The average value L d ;

[0047] S237, judging whether each decision variable has been disturbed, if so, adjusting to S238; otherwise, jumping to S231;

[0048] S238, normalized matrix ɑ d and L d ;

[0049] S239, calculating the index R=ɑ-L combining the angle and length information;

[0050] S2310, sorting the decision variables based on the index R to obtain a sorting vector R_DV.

[0051] Furthermore, the specific steps of S25 include:

[0052] S251, set the initial optimization probability IP of each decision variable based on the sorting vector R_DV d , the minimum is 0 and the maximum is 1;

[0053] S252, perform mutation operation on each decision variable, where the probability of mutation of each decision variable is IP d ;

[0054] S253, update the optimization probability OP of the decision variable d=(1-IP d )*tanh(g*Fe / maxFe)+IP d ;

[0055] S254, output the mutated decision variable as offspring O.

[0056] The beneficial effects of the present invention are:

[0057] (1) The present invention reduces the dimension of decision variables by setting the probability of decision variable optimization;

[0058] (2) The present invention improves the convergence speed of the algorithm by preferentially searching the search subspace composed of decision variables with high contribution;

[0059] (3) The present invention is highly robust and can be applied to power dispatching in different scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is the basic framework diagram of the present invention. DETAILED DESCRIPTION

[0061] The present invention will be further described below in conjunction with the accompanying drawings.

[0062] like Figure 1 As shown, the present invention is a dynamic economic dispatch optimization method based on dynamic subspace search, comprising the following steps:

[0063] S1, establish the model, establish the objective and constraint functions based on the physical characteristics of the generator set and the power demand;

[0064] S12, minimizing fuel consumption and minimizing pollution emissions are taken as the optimization objectives of the model;

[0065] Minimize fuel consumption:

[0066]

[0067] Where: T represents the dispatch period, N is the number of generators, P i,t is the output power of the ith generator at time t, P i,min represents the minimum output power of the ith generator, a i 、b i 、c i ,d i and e i is the cost coefficient of the ith generator;

[0068] Minimize pollution emissions:

[0069]

[0070] In the formula, α i , η i , γ i , i and is the emission cost coefficient of the ith generator.

[0071] S13, according to the physical characteristics of the generator set, the electric balance constraint, the power output limit constraint and the generator ramp constraint are taken as the constraints that need to be met;

[0072] The constraints include power balance constraints, power output limit constraints, and generator ramp constraints;

[0073] Electrical balance constraints

[0074]

[0075] Where: P D,t represents the total power load required at time t, P L,t is the power transmission loss at time t, and its specific calculation formula is as follows:

[0076]

[0077] Where: B i,j , B i,0 and B 0,0 is the transmission loss coefficient of the power system;

[0078] Power output limit constraints

[0079] P i,min ≤P i,t ≤P i,max (5)

[0080] Where: P i,min and P n,max are the minimum and maximum output powers of the ith generator respectively;

[0081] Generator ramp constraint

[0082] P i,t -P i,t-1 ≤U R,i

[0083] P i,t-1 -P i,t ≤L R,i (6)

[0084] Where: U R,i and L R,n are the ramp-up and ramp-down rate limits for the ith generator.

[0085] S2, using the optimization method based on dynamic subspace search to perform operations on the optimization objectives and constraints, including the following steps:

[0086] S21, initialize the population P of size NP;

[0087] S22, record the used computing resources Fe=NP;

[0088] S23, executing a decision variable analysis method considering angle and length information, using a computing resource of NS*D*NDV; comprising the following steps:

[0089] S231, for each decision variable d, randomly select NS individuals from the population P for decision variable analysis;

[0090] S232, for each selected individual k, randomly perturb its d-th decision variable NDV times, and store the newly generated individuals into the temporary population temP;

[0091] S233, calculate the target values ​​of all individuals in each temP, fit them into a line segment, and calculate its length L d,k ;

[0092] S234, calculate the fitted line segment and f1+…+f M = 1, the angle between the normals d,k ;

[0093] S235, judging whether each selected individual is disturbed, if so, jumping to S236; otherwise, jumping to S232;

[0094] S236, calculate the angle matrix α d,k The average value of α d , and the length matrix K d,k The average value K d ;

[0095] S237, judging whether each decision variable has been disturbed, if so, adjusting to S238; otherwise, jumping to S231;

[0096] S238, normalized matrix α d and L d ;

[0097] S239, calculating an index R=α-L combining angle and length information;

[0098] S2310, sorting the decision variables based on the index R to obtain a sorting vector R_DV;

[0099] S24, set the maximum computing resource maxFe=maxFe-NS*D*NDV;

[0100] Where NS represents the number of solutions used for decision variable analysis, D is the number of decision variables in the problem, and NDV is the number of times each decision variable is perturbed;

[0101] S25, executing a probability-based offspring generation strategy to generate an offspring population O; comprising the following steps:

[0102] S251, set the initial optimization probability IP of each decision variable based on the sorting vector R_DV d , the minimum is 0 and the maximum is 1;

[0103] S252, perform mutation operation on each decision variable, where the probability of mutation of each decision variable is IP d ;

[0104] S253, update the optimization probability OP of the decision variable d =(1-IP d )*tanh(g*Fe / maxFe)+IP d ;

[0105] S254, outputting the mutated decision variable as offspring O;

[0106] S26, set P = P∪O;

[0107] S27, execute the improved epsilon environment selection method to select NP individuals to form a new population P;

[0108] S28, set Fe=Fe+NP;

[0109] S29, determine whether the maximum computing resources have been reached, if so, output the population P; otherwise, jump to S25.

[0110] In order to verify the effectiveness of the present invention, the present invention is used to optimize power dispatching in three different scenarios. The parameters of the present invention are: the population size NP is set to 300, and the maximum number of evaluations is 6000*D.

[0111] The optimization method of the present invention is compared with the existing centralized methods, namely ShiP, C3M, BiCo, ATCMEA, LCMOEA, and POCEA. All algorithms are run 30 times to obtain statistical results.

[0112] The inverse generation distance (IGD) values ​​and feasibility rate (FR) obtained by the algorithm are shown in Table 1.

[0113] Table 1 Comparison results of the IGD index of the present invention and other six advanced evolutionary algorithms for the optimization problem of dynamic environmental economic dispatch of power system

[0114]

[0115] Among them, the smaller the IGD value, the better the algorithm effect. When the algorithm cannot find a feasible solution for 25 runs on a problem, the result is expressed as NaN (FR). The larger the FR, the better the algorithm effect. Analysis of the data in Table 1 shows that the method of the present invention has achieved better results than the six comparison methods in terms of the two indicators of IGD and FR in the three scenarios. This is attributed to the proposed decision variable analysis method and probability-based offspring generation strategy. These strategies help the population to search preferentially in the subspace to increase its convergence, and then the subspace gradually expands, and the population gradually searches the entire area to increase its diversity, so that the algorithm obtains better results within limited computing resources. In actual production operations, users can fully combine these solutions according to their own conditions to plan a satisfactory energy scheduling and allocation plan.

Claims

1. A dynamic economic dispatch optimization method based on dynamic subspace search, characterized in that: The following steps are involved: S1, establish the model, establish the optimization objectives and constraints based on the physical characteristics of the generator set and the power demand; S11, minimizing fuel consumption and minimizing pollution emissions are taken as the optimization objectives of the model; S12, according to the physical characteristics of the generator set, the electric balance constraint, the power output limit constraint and the generator ramp constraint are taken as the constraints that need to be met; S2, uses the optimization method based on dynamic subspace search to perform operations on the optimization objectives and constraints.

2. The dynamic economic dispatch optimization method based on dynamic subspace search according to claim 1 is characterized in that: The minimized fuel consumption: Where: T represents the dispatch period, N is the number of generators, P i,t is the output power of the ith generator at time t, P i,min represents the minimum output power of the ith generator, a i , b i 、c i ,d i and e i is the cost coefficient of the ith generator; The minimization of pollution emissions: In the formula, α i , η i , γ i , i and is the emission cost coefficient of the ith generator.

3. The dynamic economic dispatch optimization method based on dynamic subspace search according to claim 1 is characterized in that: The constraints include electric balance constraints, power output limit constraints and generator climbing constraints; the electric balance constraints Where: P D,t represents the total power load required at time t, P L,t is the power transmission loss at time t, and its specific calculation formula is as follows: Where: B i,j , B i,0 and B 0,0 is the transmission loss coefficient of the power system; The power output limit constraint P i,min ≤P i,t ≤P i,max (5) Where: P i,min and P i,max are the minimum and maximum output powers of the ith generator respectively; The generator climbing constraint P i,t -P i,t-1 ≤U R,i P i,t-1 -P i,t ≤L R,i (6) Where: U R,i and L R,i are the ramp-up and ramp-down rate limits for the ith generator.

4. The dynamic economic dispatch optimization method based on dynamic subspace search according to claim 1 is characterized in that: Step S2 includes the following steps: S21, initialize the population P of size NP; S22, record the used computing resources Fe=NP; S23, executing a decision variable analysis method considering angle and length information, the computing resources used are NS*D*NDV; S24, set the maximum computing resource maxFe=maxFe-NS*D*NDV; Where NS represents the number of solutions used for decision variable analysis, D is the number of decision variables in the problem, and NDV is the number of times each decision variable is perturbed; S25, executing a probability-based offspring generation strategy to generate an offspring population O; S26, set P = P∪O; S27, execute the improved epsilon environment selection method to select NP individuals to form a new population P; S28, set Fe=Fe+NP; S29, determine whether the maximum computing resources have been reached, if so, output the population P, otherwise, jump to S25.

5. The dynamic economic dispatch optimization method based on dynamic subspace search according to claim 4 is characterized in that: The specific steps of S23 include: S231, for each decision variable d, randomly select NS individuals from the population P for decision variable analysis; S232, for each selected individual k, randomly perturb its d-th decision variable NDV times, and store the newly generated individuals into the temporary population temP; S233, calculate the target values ​​of all individuals in each temP, fit them into a line segment, and calculate its length L d,k ; S234, calculate the fitted line segment and f1+…+f M = 1, the angle between the normals d,k ; S235, judging whether each selected individual is disturbed, if so, jumping to S236; otherwise, jumping to S232; S236, calculate the angle matrix α d,k The average value of α d , and the length matrix L d,k The average value L d ; S237, judging whether each decision variable has been disturbed, if so, adjusting to S238; otherwise, jumping to S231; S238, normalized matrix ɑ d and L d ; S239, calculating an index R=α-L combining angle and length information; S2310, sorting the decision variables based on the index R to obtain a sorting vector R_DV.

6. The dynamic economic dispatch optimization method based on dynamic subspace search according to claim 4 is characterized in that: The specific steps of S25 include: S251, set the initial optimization probability IP of each decision variable based on the sorting vector R_DV d , the minimum is 0 and the maximum is 1; S252, perform mutation operation on each decision variable, where the probability of mutation of each decision variable is IP d ; S253, update the optimization probability OP of the decision variable d =(1-IP d )*tanh(g*Fe / maxFe)+IP d ; S254, output the mutated decision variable as offspring O.

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