CN104217255B - A kind of power system multiple target optimized maintenance method under market environment - Google Patents
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Abstract
The invention discloses a kind of power system multiple target optimized maintenance method under market environment.The present invention includes that step is as follows：Obtain each generating quotient data；Set up power network multiple target optimized maintenance model under market environment；Unit output variable and unit maintenance variable to model carry out real coding, 01 binary codings are carried out to the machine set on line state variable and unit starting state variable in model, and it is transformed into the dependent variable represented by unit output variable and unit maintenance variable from independent variable；Unit output variable and unit maintenance variable are initialized；The initialization of population input of the initialization of variable value that will be obtained as quick non-dominated ranking method is solved, and obtains optimal solution set；Final unit maintenance and scheme of exerting oneself is determined from the optimal solution set for obtaining using Multiobjective Decision Making Method.The present invention performs simple, scalability by force, can be used to solve the multiple target optimized maintenance model of different target function and constraints.
Description
Technical Field
The invention belongs to the technical field of optimization of power systems, and particularly relates to a multi-target maintenance optimization method for a power system.
Background
In the power market environment, the arrangement of the generator set maintenance plan is greatly different from the traditional generator maintenance plan arrangement. In the power market environment, each power generator pursues maximization of own interests, and meanwhile, a system operation mechanism, such as a power dispatching center, needs to ensure safety and reliability of the system. The generator wants to arrange the generator set at a low electricity price time period for overhauling, the system operating mechanism wants to arrange the generator set at a low load time period for overhauling, and because the low electricity price time period is not completely consistent with the low load time period, the generator and the system operating mechanism have a conflict relationship in the aspect of arranging the unit overhauling time period; on the other hand, since the maximum number of service modules that can be scheduled and the service capacity during a low load period are limited, there is a conflicting relationship among the benefits of the individual power generators. The existing maintenance plan adjustment mechanism is generally as follows: each generator submits a maintenance plan scheme to a system operation mechanism, and the system operation mechanism modifies the maintenance plan of the generator through a certain mechanism, such as an incentive/punishment mechanism, a willingness payment mechanism and the like, so as to achieve the compromise between the safety and the reliability of the system and the benefits of the generator. The mechanism can achieve a satisfactory overhaul scheme for all parties, including power generators and system operating mechanisms, but neglects the research on the conflict relationship among the parties and cannot comprehensively understand the relationship among the parties.
Disclosure of Invention
The invention aims to provide a multi-objective maintenance optimization method for an electric power system in a market environment aiming at the defects of the prior art.
The technical scheme adopted by the invention for solving the technical problems is as follows:
step (1) obtaining power generation cost coefficient data C of each power generator0ij,C1ij,C2ijIn $/MW; cost of maintenanceCoefficient dataThe unit is $/MW; unit start-up cost dataThe unit is $; capacity data of unitThe unit is MW; load data PD(t, s) in MW, and market price data λ (t, s) in $/MWh;
step (2) establishing a power grid multi-target maintenance optimization model in a market environment;
step (3) carrying out real number coding on the unit output variable and the unit overhaul variable of the model in the step (2), carrying out 0-1 binary coding on the unit on-line state variable and the unit starting state variable in the model, and then converting the unit on-line state variable and the unit starting state variable from independent variables into dependent variables represented by the unit output variable and the unit overhaul variable;
initializing a unit output variable and a unit overhaul variable in the multi-target overhaul optimization model;
step (5) adopting the variable initialization value obtained in the step (4) as population initialization input of a rapid non-dominated sorting method, and adopting NSGA-II to solve the multi-target maintenance optimization model to obtain an optimal solution set;
and (6) determining a final unit overhaul and output scheme from the obtained optimal solution set by adopting a multi-objective decision method.
The objective function of the optimization model in the step (2) comprises the following 3 types: the method comprises the following steps of (1) maximizing the profit of each power generator, maximizing the reliability of a system and minimizing the total power generation cost of the system;
the constraints of the optimization model include the following 5 classes: the system standby is higher than the minimum standby value required by the system, the total output of the generator set is balanced with the system load, the number of the simultaneously overhauled generator sets is smaller than the upper limit value, the output of the generator set is within the rated output range of the generator set, and the generator set cannot be in an overhauled state and an online state simultaneously;
the income objective function of the ith generator is expressed as pf (i), and the expression of the income objective function is shown as the formula (1):
in the formula (1), GiA set of units representing the ith generator;the active output of a jth unit of an ith generator in a sub-period s of a period t is represented; t (T, s) represents the time length of the sub-period s of the period T, in hours; y isij(t, s) indicates the starting state of the unit if yijWhen (t, s) ═ 1 indicates that the jth power generator unit of the ith power generator is started at the beginning of the sub-period s of the period t, if yijIf (t, s) is 0, no start is performed; x is the number ofijIndicating the overhaul starting week of the jth unit of the ith generator; dijThe continuous overhaul duration of the jth unit of the ith generator is represented, and the unit is a week;representing the maximum capacity of the jth unit of the ith generator; v represents logic or; wherein i and j are natural numbers; m is an integer; t represents the total number of periods; n represents the total number of subintervals;
the reliability index I (t, s) of the sub-period s in the period t is represented by dividing the net reserve by the gross reserve, the gross reserve is obtained by subtracting the system load from the capacity of all the units, the net reserve is obtained by subtracting the capacity of the unit in maintenance from the gross reserve, as shown in the formula (2), and the system reliability objective function is obtained by averaging the reliability index I (t, s) of all the sub-periods as shown in the formula (3);
in the formula (2), PD(t, s) represents the system load for time period t sub-time period s;
the total power generation cost objective function of the system is represented as tc, and the expression is shown as the formula (4):
the system standby constraint is as shown in equation (5):
in the formula (5), Rmin(t, s) represents the minimum backup required by the system for time period t sub-time period s;
the constraint condition of the maximum simultaneous overhaul unit number is shown as the formula (6):
in the formula (6), Ni(t) represents the maximum number of simultaneous overhaul panels allowed by the ith generator during time period t;
the constraint condition of unit output is shown as formula (7):
in the formula (7), the reaction mixture is,represents the lower limit of the output of the unit when on-line, vij(t, s) represents an online state variable, online is 1, and offline is 0;
the online constraint during unit maintenance is as shown in formula (8):
the system power balance constraint is shown as equation (9):
the step (3) specifically comprises the following steps:
3-1. unit output variableReal number coding is adopted;
3-2. unit maintenance variable xijUsing real number encoding, then rounding, xijRepresenting the jth unit maintenance starting week of the ith generator, wherein the maintenance duration is DijRepresents;
3-3. unit on-line state variable vij(t, s) is represented by a unit output variable, and is converted from an independent variable into a dependent variable, as shown in formula (10):
3-4. unit starting state variable yij(t, s) may be represented by an online state variable vij(t, s) is the independent variable converted into the dependent variable, as shown in formula (11):
the initialization scheme of the step (4) is as follows:
4-1. the set overhaul initialization subprogram consists of the following 6 steps:
4-1-1. input data np and gidx, let t be 0 and j be 0; the np is the sum of the number of the units of all the power generators, and the gidx is the number sequence of the units obtained by sequencing the units from large to small according to the maximum capacity value;
4-1-2, if the unit gidx [ j ] is in maintenance, judging whether the standby constraint shown in the formula (5) and the maximum simultaneous maintenance unit number constraint shown in the formula (6) are simultaneously met; if the formula (5) and the formula (6) are both established at the same time, the unit gidx [ j ] is maintained; if at least one of the formulas (5) and (6) is not established, the unit gidx [ j ] is not maintained;
4-1-3. let j ═ j + 1;
4-1-4, judging whether j < np is true, and if not, skipping to execute the step 4-1-6; if the result is positive, making t equal to t + 1;
4-1-5, judging whether T < T is true, and if so, executing a step 4-1-2; if not, executing the step 4-1-6; wherein T is the total number of weeks considered by the maintenance schedule;
4-1-6, returning to the sub-maintenance scheme, and ending the maintenance initial sub-program;
4-2. the unit output initialization subprogram consists of the following 6 steps:
4-2-1, making the output of all units be 0, and making j be 0;
4-2-2. let k be 0;
4-2-3, judging, and if the unit ping [ k ] is in maintenance, executing the step 4-2-4; if the unit ping [ k ] is not in overhaul, executing the step 4-2-5;
4-2-4. let k be k + 1; judging, if k < ng is true, skipping to execute the step 4-2-3, and if k < ng is not true, executing the step 4-2-6;
4-2-5, assuming that the output of the unit ping [ k ] is in the upper limit of the output, judging, if the sum of the outputs of all the units is greater than the load, reducing the unit ping [ k ] to meet the power balance constraint shown in the formula (9), and executing the step 4-2-6; if the sum of the output power of all the units is not greater than the load, enabling the unit ping [ k ] to be at the upper limit of the output power of the unit ping [ k ], and executing the step 4-2-4;
4-2-6.j ═ j + 1; judging, if j < nday is true, skipping to execute the step 4-2-2; if j < nday is not true, returning to the unit output scheme, and ending the unit output initialization subprogram;
where nday is the total number of days considered by the service plan, and has a value of T multiplied by 7; the multiple pinc groups are the number sequence of the units obtained by the units according to the sequence from small to large of the average energy consumption value of the units;
4-3, the obtained unit maintenance initialization scheme and the unit output initialization scheme consist of the following 7 steps:
4-3-1, permutation and combination are carried out on 1 to I, so that the permutation and combination schemes are totalPerforming steps 4-3-2 to 4-3-6 for each permutation and combination scheme;
4-3-2, the permutation and combination scheme is noted as (i)1,i2,…,ik,…,iI)，ikDenotes the ithkA power generator;
4-3-3. let k be 1;
4-3-4, note ithkThe number of the units owned by each power generator is np, the units are sorted from large to small according to the maximum capacity value of the units, and the obtained unit number sequence is placed in the set gidx; calling a unit maintenance initialization subprogram, and recording the obtained unit maintenance initialization scheme;
4-3-5. let k be k + 1; judging, if k is less than or equal to I, skipping to execute the step 4-3-4; if k is larger than I, executing the step 4-3-6;
4-3-6, combining the I unit maintenance initialization schemes obtained in the step 4-3-4 to obtain maintenance initialization schemes of all the units;
and 4-3-7, calling a unit output initialization subprogram to obtain a unit output initialization scheme.
The fast non-dominated sorting method in the step (5) comprises the following 7 steps:
5-1, generating an initialization population, wherein the number of individuals in the population is NpopThe initialization population is composed of two parts, the first part is the one described in step (4)A seed unit maintenance and output initialization scheme; and a second part randomly generates: setting a unit overhaul variable as a randomly generated integer between 1 and T-1, and setting a unit output variable as a randomly generated real number between a unit output lower limit and a unit output upper limit;
5-2, using current population PgGeneration of progeny populations Q by selection, crossover and mutation of these 3 genetic operatorsgMerging the current population PgAnd progeny population QgObtaining a mixed population Rg＝Pg∪Qg；
5-3. to RgA series of pareto fronts are obtained by using the fast non-dominated sorting method shown in Table 1, and are marked as F ═ { F }1,F2,F3,…,Fn}；
5-4 from RgWherein N is selected as followspopIndividual as next generation population Pg+1: if pareto front F1The number of the medium elements is less than NpopThen F is1All elements in (1) are put into Pg+1Performing the following steps; the next pareto front F is then compared2If set Pg+1∪F2The number of elements in (1) is less than NpopThen F is2All elements in (A) are also put into Pg+1(ii) a And so on until a pareto front F appearskWhere k ∈ {1,2,3, …, n }, makes the set Pg+1∪FkThe number of elements in (1) is more than NpopThen, F is calculated as shown in Table 2kThe degree of congestion I of each element is arranged from large to small, and the arrangement result is set to F'kMiddle, take F'kFront N inpop-|Pg+1I elements put into Pg+1In (i) Pg+1＝Pg+1∪F′k[1:(Npop-|Pg+1|)]；
5-5, using next generation population Pg+1Generating next generation offspring population Q by selecting, crossing and mutating the 3 genetic operatorsg+1Merging the next generation population Pg+1And the next generation offspring population Qg+1Obtaining the next generation mixed population Rg+1＝Pg+1∪Qg+1；
5-6, circularly executing the steps 5-3 to 5-5 until the maximum circulation times are reached;
5-7, outputting the population P when the maximum cycle number is outputg+1Namely, the solution is the optimal solution set;
wherein, | PgI represents the set PgNumber of middle elements, Pg+1∪FiRepresents Pg+1And FiA union of (1);
TABLE 1 fast non-dominated sorting method program pseudo-code table
In Table 1, the notation < is given as an example of multi-objective minimization, i.e., the smaller the objective function, the better q < p is satisfied if and only if any of i ∈ {1,2, …, NobjAll are provided withAnd at least one j ∈ {1,2, …, N is presentobjMake
Table 2 program pseudo code table for calculating congestion degree
The multi-target decision method in the step (6) adopts a sequencing method approaching to an ideal value, and is specifically divided into 5 steps:
6-1. first, a per-unit weighted decision matrix v is calculatedij：
vij＝ωi(fi +-fij)/(fi +-fi -),i＝1,2,3,…Nobj,j＝1,2,3,…J (12)
Wherein f isijFor the ith objective function value of the jth solution in the optimal solution set, Nobjthe number of targets in the multi-target optimization, J is the number of solutions in the optimal solution set,
6-2, respectively calculating the optimal pointsAnd the most undesirable pointWherein,
6-3, respectively calculating the distance D from each optimal solution to the optimal point+And a distance D to the least ideal point-：
6-4, calculating the distance ratio of each optimal solution
6-5, mixing RjAnd selecting the maximum optimal solution as a final unit overhaul and output scheme.
The invention has the beneficial effects that:
the invention provides a multi-target maintenance optimization method for an electric power system in a market environment. The maintenance in the power market is a multi-objective optimization problem, if a single-objective optimization algorithm is adopted, the weight of each objective needs to be given according to the experience, then an optimal solution is obtained, the weight of each objective is changed, then another optimal solution is obtained, and a series of Pareto (Pareto) optimal solutions can be obtained by calculating for many times; and the multi-objective optimization method, such as NSGA-II, does not need to give the weighted value of each objective when solving the multi-objective optimization problem, and can obtain all pareto optimal solutions through one-time calculation, thereby being beneficial to researching the relationship between the benefits of each power generator and the system reliability in the power market, and obtaining a maintenance and output scheme which is satisfactory for all parties through final decision. The multi-objective optimization method provided by the invention can well solve the problem of the maintenance plan of the generator set in the power market environment, and has the following advantages: (1) real number coding is carried out on the unit output variable and the unit overhaul variable of the model, the unit on-line state variable and the unit starting state variable are converted from independent variables into dependent variables represented by the unit output variable and the unit overhaul variable, and the coding and conversion processing of the variables can better meet the constraint conditions in the model; (2) population initialization is carried out on NSGA-II, the multi-target maintenance optimization model can be solved more effectively, and a better feasible solution is obtained; (3) all pareto optimal solutions can be obtained through one-time calculation without giving the weight of each target; (4) a maintenance and output scheme satisfying all parties can be obtained through the final decision method; (5) the method is simple to execute, has strong expandability and can be used for solving the multi-objective maintenance optimization model with different objective functions and constraint conditions.
Drawings
Fig. 1 is a flow chart of a unit overhaul and export scheme initialization procedure used in the present invention.
Fig. 2 is a flow chart of a unit overhaul initialization subroutine used in the present invention.
FIG. 3 is a flow chart of a unit capacity initialization subroutine used in the present invention.
FIG. 4 is a flow diagram of the NSGA-II main loop used in the present invention.
Detailed Description
The invention is further illustrated by the following figures and examples.
A multi-objective maintenance optimization method for an electric power system in a market environment specifically comprises the following steps:
step (1) obtaining power generation cost coefficient data C of each power generator0ij,C1ij,C2ijIn $/MW; maintenance cost systemNumerical dataThe unit is $/MW; unit start-up cost dataThe unit is $; capacity data of unitThe unit is MW; load data PD(t, s) in MW, and market price data λ (t, s) in $/MWh.
Step (2) establishing a power grid multi-target maintenance optimization model in a market environment;
the objective function of the optimization model includes the following 3 classes: the method comprises the following steps of (1) maximizing the profit of each power generator, maximizing the reliability of a system and minimizing the total power generation cost of the system;
the constraints of the optimization model include the following 5 classes: the system standby is higher than the minimum standby value required by the system, the total output of the generator set is balanced with the system load, the number of the simultaneously overhauled generator sets is smaller than the upper limit value, the output of the generator set is within the rated output range of the generator set, and the generator set cannot be in an overhauled state and an online state simultaneously;
the income objective function of the ith generator is expressed as pf (i), and the expression of the income objective function is shown as the formula (1):
in the formula (1), GiA set of units representing the ith generator;the active output of a jth unit of an ith generator in a sub-period s of a period t is represented; t (T, s) represents the time length of the sub-period s of the period T, in hours; y isij(t, s) shows the state of the plant at start-upState if yijWhen (t, s) ═ 1 indicates that the jth power generator unit of the ith power generator is started at the beginning of the sub-period s of the period t, if yijIf (t, s) is 0, no start is performed; x is the number ofijIndicating the overhaul starting week of the jth unit of the ith generator; dijThe continuous overhaul duration of the jth unit of the ith generator is represented, and the unit is a week;representing the maximum capacity of the jth unit of the ith generator; v represents logic or; wherein i and j are natural numbers; m is an integer; t represents the total number of periods; n denotes the total number of subintervals.
The reliability index I (t, s) of the sub-period s in the period t is represented by dividing the net reserve by the gross reserve, the gross reserve is obtained by subtracting the system load from the capacity sum of all the units, the net reserve is obtained by subtracting the capacity of the unit in maintenance from the gross reserve, as shown in the formula (2), and the system reliability objective function is obtained by averaging the reliability index I (t, s) of all the sub-periods as shown in the formula (3).
In the formula (2), PD(t, s) represents the system load for time period t sub-time period s.
The total power generation cost objective function of the system is represented as tc, and the expression is shown as the formula (4):
the system standby constraint is as shown in equation (5):
in the formula (5), Rmin(t, s) represents the minimum backup required by the system for time period t sub-period s.
The constraint condition of the maximum simultaneous overhaul unit number is shown as the formula (6):
in the formula (6), Ni(t) represents the maximum number of simultaneous servicing units allowed by the ith generator during time period t.
The constraint condition of unit output is shown as formula (7):
in the formula (7), the reaction mixture is,represents the lower limit of the output of the unit when on-line, vij(t, s) represents an online state variable, online is 1, and offline is 0;
the online constraint during unit maintenance is as shown in formula (8):
the system power balance constraint is shown as equation (9):
step (3) carrying out real number coding on the unit output variable and the unit overhaul variable of the model in the step (2), carrying out 0-1 binary coding on the unit on-line state variable and the unit starting state variable in the model, and then converting the unit on-line state variable and the unit starting state variable from independent variables into dependent variables represented by the unit output variable and the unit overhaul variable; the method comprises the following specific steps:
3-1. unit output variableReal number coding is adopted;
3-2. unit maintenance variable xijUsing real number encoding, then rounding, xijRepresenting the jth unit maintenance starting week of the ith generator, wherein the maintenance duration is DijRepresents;
3-3. unit on-line state variable vij(t, s) is represented by a unit output variable, and is converted from an independent variable into a dependent variable, as shown in formula (10):
3-4. unit starting state variable yij(t, s) may be represented by an online state variable vij(t, s) is the independent variable converted into the dependent variable, as shown in formula (11):
and (4) initializing the unit output variable and the unit overhaul variable in the multi-target overhaul optimization model. The initialization scheme is as follows:
the unit overhaul initialization sub-program is firstly described, then the unit output initialization sub-program is described, and finally the unit overhaul initialization scheme and the unit output initialization scheme obtained by the first two sub-programs are described.
As shown in fig. 1, the set overhaul initialization subroutine consists of the following 6 steps:
4-1-1. input data np and gidx, let t be 0 and j be 0; the np is the sum of the number of the units of all the power generators, and the gidx is the number sequence of the units obtained by sequencing the units from large to small according to the maximum capacity value;
4-1-2, if the unit gidx [ j ] is in maintenance, judging whether the standby constraint shown in the formula (5) and the maximum simultaneous maintenance unit number constraint shown in the formula (6) are simultaneously met; if the formula (5) and the formula (6) are both established at the same time, the unit gidx [ j ] is maintained; if at least one of the formulas (5) and (6) is not established, the unit gidx [ j ] is not maintained;
4-1-3. let j ═ j + 1;
4-1-4, judging whether j < np is true, and if not, skipping to execute the step 4-1-6; if yes, making t equal to t + 1;
4-1-5, judging whether T < T is true, and if so, executing a step 4-1-2; if not, executing the step 4-1-6; wherein T is the total number of weeks considered by the maintenance schedule;
4-1-6, returning to the sub-maintenance scheme, and ending the maintenance initial sub-program;
as shown in fig. 2, the unit output initialization subroutine consists of the following 6 steps:
4-2-1, making the output of all units be 0, and making j be 0;
4-2-2. let k be 0;
4-2-3, judging, and if the unit ping [ k ] is in maintenance, executing the step 4-2-4; if the unit ping [ k ] is not in overhaul, executing the step 4-2-5;
4-2-4. let k be k + 1; judging, if k < ng is true, skipping to execute the step 4-2-3, and if k < ng is not true, executing the step 4-2-6;
4-2-5, assuming that the output of the unit ping [ k ] is in the upper limit of the output, judging, if the sum of the outputs of all the units is greater than the load, reducing the unit ping [ k ] to meet the power balance constraint shown in the formula (9), and executing the step 4-2-6; if the sum of the output power of all the units is not greater than the load, enabling the unit ping [ k ] to be at the upper limit of the output power of the unit ping [ k ], and executing the step 4-2-4;
4-2-6.j ═ j + 1; judging, if j < nday is true, skipping to execute the step 4-2-2; if j < nday is not true, returning to the unit output scheme, and ending the unit output initialization subprogram;
where nday is the total number of days considered by the service plan, and has a value of T multiplied by 7; the multiple pinc groups are the number sequence of the units obtained by the units according to the average energy consumption value of the units from small to large.
As shown in fig. 3, the method for obtaining the unit overhaul initialization scheme and the unit output initialization scheme includes the following 7 steps:
4-3-1, permutation and combination are carried out on 1 to I, so that the permutation and combination schemes are totalPerforming steps 4-3-2 to 4-3-6 for each permutation and combination scheme;
4-3-2, the permutation and combination scheme is noted as (i)1,i2,…,ik,…,iI)，ikDenotes the ithkA power generator;
4-3-3. let k be 1;
4-3-4, note ithkThe number of the units owned by each power generator is np, the units are sorted from large to small according to the maximum capacity value of the units, and the obtained unit number sequence is placed in the set gidx; calling a unit maintenance initialization subprogram, and recording the obtained unit maintenance initialization scheme;
4-3-5. let k be k + 1; judging, if k is less than or equal to I, skipping to execute the step 4-3-4; if k is larger than I, executing the step 4-3-6;
4-3-6, combining the I unit maintenance initialization schemes obtained in the step 4-3-4 to obtain maintenance initialization schemes of all the units;
and 4-3-7, calling a unit output initialization subprogram to obtain a unit output initialization scheme.
The unit overhaul and output scheme initialization routine shown in fig. 3 successively calls the unit overhaul initialization subroutine shown in fig. 1 and the unit output initialization subroutine shown in fig. 2.
And (5) adopting the variable initialization value obtained in the step (4) as population initialization input of a fast non-dominated sorting method (NSGA-II), and adopting the NSGA-II to solve the multi-target maintenance optimization model to obtain an optimal solution set:
as shown in fig. 4, NSGA-II comprises the following 7 steps:
5-1, generating an initialization population, wherein the number of individuals in the population is NpopThe initialization population is composed of two parts, the first part is the one described in step (4)A seed unit maintenance and output initialization scheme; and a second part randomly generates: and setting the unit overhaul variable as a randomly generated integer between 1 and T-1, and setting the unit output variable as a randomly generated real number between the unit output lower limit and the unit output upper limit.
5-2, using current population PgGeneration of progeny populations Q by selection, crossover and mutation of these 3 genetic operatorsgMerging the current population PgAnd progeny population QgObtaining a mixed population Rg＝Pg∪Qg。
5-3. to RgA series of pareto fronts (pareto) were obtained using the fast non-dominated sorting method shown in table 1, and are noted as F ═ F1,F2,F3,…,Fn}。
5-4 from RgWherein N is selected as followspopIndividual as next generation population Pg+1: if pareto front F1The number of the medium elements is less than NpopThen F is1All elements in (1) are put into Pg+1Performing the following steps; the next pareto front F is then compared2If set Pg+1∪F2The number of elements in (1) is less than NpopThen F is2All elements in (A) are also put into Pg+1(ii) a And so on until a pareto front F appearskWhere k ∈ {1,2,3, …, n }, makes the set Pg+1∪FkThe number of elements in (1) is more than NpopThen, F is calculated as shown in Table 2kThe degree of congestion I of each element is arranged from large to small, and the arrangement result is set to F'kMiddle, take F'kFront N inpop-|Pg+1I elements put into Pg+1In (i) Pg+1＝Pg+1∪F′k[1:(Npop-|Pg+1|)]。
5-5, using next generation population Pg+1Generating next generation offspring population Q by selecting, crossing and mutating the 3 genetic operatorsg+1Merging the next generation population Pg+1And the next generation offspring population Qg+1Obtaining the next generation mixed population Rg+1＝Pg+1∪Qg+1。
And 5-6, circularly executing the steps 5-3 to 5-5 until the maximum circulation times are reached.
5-7, outputting the population P when the maximum cycle number is outputg+1I.e. the optimal solution set.
Wherein, | PgI represents the set PgNumber of middle elements, Pg+1∪FiRepresents Pg+1And FiThe union of (a).
TABLE 1 fast non-dominated sorting method program pseudo-code table
In Table 1, the notation < is illustrated with multi-objective minimizationFor example, the condition that q < p holds if and only if the objective function is smaller is that for any one of i ∈ {1,2, …, NobjAll are provided withAnd at least one j ∈ {1,2, …, N is presentobjMake
Table 2 program pseudo code table for calculating congestion degree
And (6) determining a final unit overhaul and output scheme from the obtained optimal solution set by adopting a multi-objective decision method. The multi-target decision method adopts a sorting method (TOPSIS) approaching to an Ideal value. Toposis can be divided into 5 steps:
6-1. first, calculate the weighted decision matrix vi per unitj：
vij＝ωi(fi +-fij)/(fi +-fi -),i＝1,2,3,…Nobj,j＝1,2,3,…J (12)
Wherein f isijFor the ith objective function value of the jth solution in the optimal solution set, Nobjthe number of targets in the multi-target optimization, J is the number of solutions in the optimal solution set,
6-2, respectively calculating the optimal pointsAnd the most undesirable pointWherein,
6-3, respectively calculating the distance D from each optimal solution to the optimal point+And a distance D to the least ideal point-：
6-4, calculating the distance ratio of each optimal solution
6-5, mixing RjAnd selecting the maximum optimal solution as a final unit overhaul and output scheme.
And (7) the power dispatching center transmits the overhaul state and the output value of each unit to the power plant distributed control system through the information processing and communication device according to the final unit overhaul and output scheme in the step (6), so that the running state of the generator set is automatically controlled, and the output of the generator set is adjusted.
Two concepts will be briefly introduced for the convenience of the following description: a power plant decentralized control system and automatic power generation control. A Distributed Control System (DCS) of a power plant is based on a microcomputer, and integrates a computer technology, a Control technology, a communication technology and a graphic display technology according to the concept of System Control, so that centralized management and Distributed Control are realized. The DCS system has become a main device for controlling and monitoring a power plant. Automatic Generation Control (AGC), which is an important component of an energy management system. And sending the command to a relevant power plant or unit according to a control target of the power grid dispatching center, and realizing automatic control of the unit power through an automatic control adjusting device of the power plant or unit.
In a power plant network monitoring system, an information processing and communication device D200 is often employed. To date, more than 200 plants nationwide, including more than 65% of large plants, have implemented D200 for AGC control and telemechanical functions of scheduling power plants. The power plant comprises a plurality of 600MW units, such as Zhejiang Jiaxing power plant, Ninghai power plant, three gorges power plant and the like. The power dispatching center can directly send AGC commands to the DCS through the information processing and communication device D200 so as to realize the output adjustment of the unit.
And (4) the power dispatching center issues the overhaul state and the output value of each unit to a DCS (distributed control system) through the information processing and communication device D200 according to the final unit overhaul and output scheme in the step (6), so that the running state of the generator set is automatically controlled, and the output of the generator set is adjusted. If the unit needs to be overhauled, the power dispatching center issues an automatic stop signal to a computer monitoring system of a power plant through an information processing and communication device D200 in the form of an AGC command, and the computer monitoring system of the power plant sends a stop and overhaul instruction to the unit after receiving the dispatching AGC command. If the units do not need to be overhauled, the power dispatching center can directly send the output value of each unit to a DCS of the generator set in the form of an AGC command through the information processing and communication device D200 so as to realize the automatic control of the output of the generator set. The method comprises the following specific steps: the power dispatching center obtains the output value of each generator set and sends the output value to each power plant through an information processing and communication device D200 by an AGC instruction; the main CPU board of the power plant D200 receives an AGC instruction issued by a dispatching center, and then digitalizes the AGC instruction through protocol information processing and sends the AGC instruction to the CPU board of the D20C combination board; the D20C combination board converts the received digitized AGC command into a code value corresponding to 0-100% of output of the generator set, and outputs 4-20 mA direct current analog quantity to a DCS (distributed control system) of the generator set according to the code value, so that the output of the generator set is adjusted.
Example 1
This patent assumes 3 generators in the electric power market, then according to permutation and combination, according to the precedence order of confirming the generator unit maintenance scheme different, can haveSpecies, i.e., (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2) and (3,2,1) of these 6 species. (1,2,3) shows a flow chart of firstly determining the unit maintenance scheme of the generator 1, then determining the unit maintenance scheme of the generator 2 and finally determining the unit maintenance scheme of the generator 3. The opportunity cost for arranging the unit to overhaul in the low electricity price period is lower, and because the unit capacity and the unit total number overhauled simultaneously in each period are limited, if the unit overhaul scheme of the generator 1 is determined firstly, the income of the generator 1 is higher; whereas if the generator 2 crew overhaul scheme is first determined, the generator 2 revenue will be greater. In the patent, 6 machine set overhauling and output initializing schemes are obtained.
Example 2
Data such as the power generation cost, the overhaul cost, the startup and shutdown cost, the unit capacity, and the future 52 weeks, i.e., T52, of each generator obtained from the power system in a certain power market environment are used in the present invention. The other parameters are set as follows, Rmin(t, s) is 0.05 times the system load of the sub-period s of the period t, Ni(t) is 3, the sub-period N is 7, the number of generators is 3, 32 sets are shared, namely np is 32, and the number of objective functions N isobjThe number of maximum iterations in NSGA-II was taken as 5, and the number of total individuals in the population N was set as 1500popSet to 1200.
First, to verify the effectiveness of the code conversion processing method in step (3) and the initialization method in step (4) in the present invention on solving the generator set maintenance planning problem in the power market environment by using the NSGA-II algorithm, four comparative experiments as shown in table 3 are performed, and the solving results are shown in table 4.
TABLE 3 setup of four comparative experiments
Table 4 results of four comparative experiments
In table 4, the objective functions f1, f2 and f3 represent gains of power generators 1,2 and 3 respectively, the larger the gain is, the better the scheme is, so the objective functions f1, f2 and f3 have to adopt maximum optimization, and since NSGA-II can only deal with minimum optimization, we take negative values of f1, f2 and f3, namely, minimize-f 1, -f2 and-f 3 in the NSGA-II solution process. The objective function f5 represents a system reliability objective function, which represents a system backup value, and the higher the system backup indicates the better system stability, so the objective function f5 also needs to adopt the maximization optimization, similar to the processing of f1, f2 and f3, and we take f5 as a negative value, i.e. minimize-f 5. The objective function f4 represents the total power generation cost of the system, and the lower the total power generation cost is, the better, so the objective function f4 needs to adopt minimum optimization without special treatment.
As can be seen from Table 4, no feasible solution could be obtained by NSGA-II-1 and NSGA-II-2 without the encoding treatment method shown in step (3); the encoding processing method shown in step (3) is employed in both NSGA-II-3 and NSGA-II-4, and an optimal solution set can be obtained smoothly, and the optimal value of each objective function in this optimal solution set is shown in table 4. This indicates that the encoding processing method shown in step (3) plays a very important role in successfully solving the problem.
In NSGA-II-4, the former contains the initialization in step (4) and the latter does not, as compared with NSGA-II-3. The results in table 4 show that the maximum values of the objective functions f1, f2, f3 and f5 obtained in the former are all greater than the corresponding maximum values obtained in the latter; the former obtains a smaller minimum value of the objective function f4 than the latter. This indicates that the initialization shown in step (4) is advantageous for obtaining a better solution. Through verification, all solutions in the optimal solution set obtained by NSGA-II-3 and NSGA-II-4 meet constraint conditions, namely the solutions are feasible solutions.
For convenience of expression, a final unit overhaul and output scheme determined from the optimal solution set obtained in the step (5) by adopting a multi-objective decision method TOPSIS is called as a final solution. Table 5 shows each objective function value of the final solution, and table 6 shows the unit overhaul scheme of the final solution, where the unit output data volume of the final solution is large, and 32 × 364 — 11648 pieces of data are not given. In conclusion, the multi-objective optimization method NSAG-II provided by the invention is effective for solving the maintenance plan of the generator set in the power market environment.
TABLE 5 values of the objective functions of the final solutions
| f5 | |||||
| NSGA-II-4 | 1.75 | 1.35 | 1.99 | 5.77 | 0.8715 |
TABLE 6 final solution for maintenance of units
| Number of units | Upper limit of unit output | Maintenance period/week | Number of units | Upper limit of unit output | Maintenance period/week |
| 1 | 20 | 31-32 | 17 | 12 | 41-42 |
| 2 | 20 | 18-19 | 18 | 12 | 9-10 |
| 3 | 76 | 11-12 | 19 | 12 | 42-43 |
| 4 | 76 | 45-46 | 20 | 155 | 12-13 |
| 5 | 20 | 36-37 | 21 | 155 | 46-47 |
| 6 | 20 | 40-41 | 22 | 155 | 44-45 |
| 7 | 76 | 34-35 | 23 | 155 | 35-36 |
| 8 | 76 | 43-44 | 24 | 350 | 33-34 |
| 9 | 100 | 41-42 | 25 | 400 | 51-52 |
| 10 | 100 | 9-10 | 26 | 400 | 48-49 |
| 11 | 100 | 39-40 | 27 | 50 | 51-52 |
| 12 | 197 | 13-14 | 28 | 50 | 49-50 |
| 13 | 197 | 44-45 | 29 | 50 | 33-34 |
| 14 | 197 | 35-36 | 30 | 50 | 47-48 |
| 15 | 12 | 39-40 | 31 | 50 | 13-14 |
| 16 | 12 | 32-33 | 32 | 50 | 46-47 |
Claims (5)
1. A multi-objective maintenance optimization method for an electric power system in a market environment is characterized by comprising the following steps:
step (1) obtaining power generation cost coefficient data C of each power generator0ij,C1ij,C2ijIn $/MW; maintenance cost coefficient dataThe unit is $/MW; unit start-up cost dataThe unit is $; capacity data of unitThe unit is MW; load data PD(t, s) in MW, and market price data λ (t, s) in $/MWh;
step (2) establishing a power grid multi-target maintenance optimization model in a market environment;
step (3) carrying out real number coding on the unit output variable and the unit overhaul variable of the model in the step (2), carrying out 0-1 binary coding on the unit on-line state variable and the unit starting state variable in the model, and then converting the unit on-line state variable and the unit starting state variable from independent variables into dependent variables represented by the unit output variable and the unit overhaul variable;
initializing a unit output variable and a unit overhaul variable in the multi-target overhaul optimization model;
step (5) adopting the variable initialization value obtained in the step (4) as population initialization input of a rapid non-dominated sorting method, and adopting NSGA-II to solve the multi-target maintenance optimization model to obtain an optimal solution set;
step (6) determining a final unit maintenance and output scheme from the obtained optimal solution set by adopting a multi-objective decision method;
the objective function of the optimization model in the step (2) comprises the following 3 types: the method comprises the following steps of (1) maximizing the profit of each power generator, maximizing the reliability of a system and minimizing the total power generation cost of the system;
the constraints of the optimization model include the following 5 classes: the system standby is higher than the minimum standby value required by the system, the total output of the generator set is balanced with the system load, the number of the simultaneously overhauled generator sets is smaller than the upper limit value, the output of the generator set is within the rated output range of the generator set, and the generator set cannot be in an overhauled state and an online state simultaneously;
the income objective function of the ith generator is expressed as pf (i), and the expression of the income objective function is shown as the formula (1):
in the formula (1), GiA set of units representing the ith generator;the active output of a jth unit of an ith generator in a sub-period s of a period t is represented; t (T, s) represents the time length of the sub-period s of the period T, in hours; y isij(t, s) indicates the starting state of the unit if yijWhen (t, s) ═ 1 indicates that the jth power generator unit of the ith power generator is started at the beginning of the sub-period s of the period t, if yijIf (t, s) is 0, no start is performed; x is the number ofijIndicating the overhaul starting week of the jth unit of the ith generator; dijThe continuous overhaul duration of the jth unit of the ith generator is represented, and the unit is a week;representing the maximum capacity of the jth unit of the ith generator; v represents logic or; wherein i and j are natural numbers; m is an integer; t represents the total number of periods; n represents the total number of subintervals;
the reliability index I (t, s) of the sub-period s in the period t is represented by dividing the net reserve by the gross reserve, the gross reserve is obtained by subtracting the system load from the capacity of all the units, the net reserve is obtained by subtracting the capacity of the unit in maintenance from the gross reserve, as shown in the formula (2), and the system reliability objective function is obtained by averaging the reliability index I (t, s) of all the sub-periods as shown in the formula (3);
in the formula (2), PD(t, s) represents the system load for time period t sub-time period s;
the total power generation cost objective function of the system is represented as tc, and the expression is shown as the formula (4):
the system standby constraint is as shown in equation (5):
in the formula (5), Rmin(t, s) represents the minimum backup required by the system for time period t sub-time period s;
the constraint condition of the maximum simultaneous overhaul unit number is shown as the formula (6):
in the formula (6), Ni(t) represents the maximum number of simultaneous overhaul panels allowed by the ith generator during time period t;
the constraint condition of unit output is shown as formula (7):
in the formula (7), the reaction mixture is,represents the lower limit of the output of the unit when on-line, vij(t, s) represents an online state variable, online is 1, and offline is 0;
the online constraint during unit maintenance is as shown in formula (8):
the system power balance constraint is shown as equation (9):
2. the multi-objective overhaul optimization method for the power system in the market environment as claimed in claim 1, wherein the step (3) specifically comprises the following steps:
3-1. unit output variableReal number coding is adopted;
3-2. unit maintenance variable xijUsing real number encoding, then rounding, xijRepresenting the jth unit maintenance starting week of the ith generator, wherein the maintenance duration is DijRepresents;
3-3. unit on-line state variable vij(t, s) is represented by a unit output variable, and is converted from an independent variable into a dependent variable, as shown in formula (10):
3-4. unit starting state variable yij(t, s) may be represented by an online state variable vij(t, s) is the independent variable converted into the dependent variable, as shown in formula (11):
3. the method for optimizing multi-objective overhaul of a power system in a market environment as claimed in claim 1, wherein the initialization scheme in the step (4) is as follows:
4-1. the set overhaul initialization subprogram consists of the following 6 steps:
4-1-1. input data np and gidx, let t be 0 and j be 0; the np is the sum of the number of the units of all the power generators, and the gidx is the number sequence of the units obtained by sequencing the units from large to small according to the maximum capacity value;
4-1-2, if the unit gidx [ j ] is in maintenance, judging whether the standby constraint shown in the formula (5) and the maximum simultaneous maintenance unit number constraint shown in the formula (6) are simultaneously met; if the formula (5) and the formula (6) are both established at the same time, the unit gidx [ j ] is maintained; if at least one of the formulas (5) and (6) is not established, the unit gidx [ j ] is not maintained;
4-1-3. let j ═ j + 1;
4-1-4, judging whether j < np is true, and if not, skipping to execute the step 4-1-6; if yes, making t equal to t + 1;
4-1-5, judging whether T < T is true, and if so, executing a step 4-1-2; if not, executing the step 4-1-6; wherein T is the total number of weeks considered by the maintenance schedule;
4-1-6, returning to the sub-maintenance scheme, and ending the maintenance initial sub-program;
4-2. the unit output initialization subprogram consists of the following 6 steps:
4-2-1, making the output of all units be 0, and making j be 0;
4-2-2. let k be 0;
4-2-3, judging, and if the unit ping [ k ] is in maintenance, executing the step 4-2-4; if the unit ping [ k ] is not in overhaul, executing the step 4-2-5;
4-2-4. let k be k + 1; judging, if k < ng is true, skipping to execute the step 4-2-3, and if k < ng is not true, executing the step 4-2-6;
4-2-5, assuming that the output of the unit ping [ k ] is in the upper limit of the output, judging, if the sum of the outputs of all the units is greater than the load, reducing the unit ping [ k ] to meet the power balance constraint shown in the formula (9), and executing the step 4-2-6; if the sum of the output power of all the units is not greater than the load, enabling the unit ping [ k ] to be at the upper limit of the output power of the unit ping [ k ], and executing the step 4-2-4;
4-2-6.j ═ j + 1; judging, if j < nday is true, skipping to execute the step 4-2-2; if j < nday is not true, returning to the unit output scheme, and ending the unit output initialization subprogram;
where nday is the total number of days considered by the service plan, and has a value of T multiplied by 7; the multiple pinc groups are the number sequence of the units obtained by the units according to the sequence from small to large of the average energy consumption value of the units;
4-3, the obtained unit maintenance initialization scheme and the unit output initialization scheme consist of the following 7 steps:
4-3-1, permutation and combination are carried out on 1 to I, so that the permutation and combination schemes are totalPerforming steps 4-3-2 to 4-3-6 for each permutation and combination scheme;
4-3-2, the permutation and combination scheme is noted as (i)1,i2,…,ik,…,iI)，ikDenotes the ithkA power generator;
4-3-3. let k be 1;
4-3-4, note ithkThe number of the units owned by each power generator is np, the units are sorted from large to small according to the maximum capacity value of the units, and the obtained unit number sequence is placed in the set gidx; calling a unit maintenance initialization subprogram, and recording the obtained unit maintenance initialization scheme;
4-3-5. let k be k + 1; judging, if k is less than or equal to I, skipping to execute the step 4-3-4; if k is larger than I, executing the step 4-3-6;
4-3-6, combining the I unit maintenance initialization schemes obtained in the step 4-3-4 to obtain maintenance initialization schemes of all the units;
and 4-3-7, calling a unit output initialization subprogram to obtain a unit output initialization scheme.
4. The method for optimizing multi-objective overhaul of the power system in the market environment as claimed in claim 1, wherein the fast non-dominated ranking method comprises the following 7 steps:
5-1, generating an initialization population, wherein the number of individuals in the population is NpopThe initialization population is composed of two parts, the first part is the one described in step (4)A seed unit maintenance and output initialization scheme; and a second part randomly generates: random generation with unit overhaul variable set between 1 and T-1The unit output variable is set as a real number randomly generated between a unit output lower limit and a unit output upper limit;
5-2, using current population PgGeneration of progeny populations Q by selection, crossover and mutation of these 3 genetic operatorsgMerging the current population PgAnd progeny population QgObtaining a mixed population Rg＝Pg∪Qg；
5-3. to RgA series of pareto fronts are obtained by using the fast non-dominated sorting method shown in Table 1, and are marked as F ═ { F }1,F2,F3,…,Fn}；
5-4 from RgWherein N is selected as followspopIndividual as next generation population Pg+1: if pareto front F1The number of the medium elements is less than NpopThen F is1All elements in (1) are put into Pg+1Performing the following steps; the next pareto front F is then compared2If set Pg+1∪F2The number of elements in (1) is less than NpopThen F is2All elements in (A) are also put into Pg+1(ii) a And so on until a pareto front F appearskWhere k ∈ {1,2,3, …, n }, makes the set Pg+1∪FkThe number of elements in (1) is more than NpopThen, F is calculated as shown in Table 2kThe degree of congestion I of each element is arranged from large to small, and the arrangement result is set to F'kMiddle, take F'kFront N inpop-|Pg+1I elements put into Pg+1In (i) Pg+1＝Pg+1∪F′k[1:(Npop-|Pg+1|)]；
5-5, using next generation population Pg+1Generating next generation offspring population Q by selecting, crossing and mutating the 3 genetic operatorsg+1Merging the next generation population Pg+1And the next generation offspring population Qg+1Obtaining the next generation mixed population Rg+1＝Pg+1∪Qg+1；
5-6, circularly executing the steps 5-3 to 5-5 until the maximum circulation times are reached;
5-7, maximum outputPopulation P at cycle timesg+1Namely, the solution is the optimal solution set;
wherein, | PgI represents the set PgNumber of middle elements, Pg+1∪FiRepresents Pg+1And FiA union of (1);
TABLE 1 fast non-dominated sorting method program pseudo-code table
In Table 1, the notation < is given as an example of multi-objective minimization, i.e., the smaller the objective function, the better q < p is satisfied if and only if any of i ∈ {1,2, …, NobjAll have fi q≤fi pAnd at least one j ∈ {1,2, …, N is presentobjMake
Table 2 program pseudo code table for calculating congestion degree
5. The method for optimizing the multi-objective maintenance of the power system in the market environment as claimed in claim 1, wherein the multi-objective decision method in step (6) adopts a ranking method approaching to an ideal value, and the method is specifically divided into 5 steps:
6-1. first, a per-unit weighted decision matrix v is calculatedij：
vij＝ωi(fi +-fij)/(fi +-fi -),i＝1,2,3,…Nobj,j＝1,2,3,…J (12)
Wherein f isijFor the ith objective function value of the jth solution in the optimal solution set, Nobjthe number of targets in the multi-target optimization, J is the number of solutions in the optimal solution set,
6-2, respectively calculating the optimal pointsAnd the most undesirable pointWherein,
6-3, respectively calculating the distance D from each optimal solution to the optimal point+And a distance D to the least ideal point-：
6-4, calculating the distance ratio of each optimal solution
6-5, mixing RjAnd selecting the maximum optimal solution as a final unit overhaul and output scheme.
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