CN104217255A - Electrical power system multi-target overhaul optimization method under market environment - Google Patents

Abstract

The invention discloses a multi-objective maintenance optimization method for electric power system under market environment. The present invention includes the following steps: obtaining data of each power generation provider; establishing a multi-objective maintenance optimization model of the power grid in a market environment; encoding the unit output variables and unit maintenance variables in the model with real numbers, and encoding the unit online state variables and unit start-up state variables in the model Carry out 0-1 binary coding, and transform it from an independent variable into a dependent variable represented by the unit output variable and the unit maintenance variable; initialize the unit output variable and the unit maintenance variable; use the obtained variable initialization value as a fast non-dominated The population initialization input of the sorting method is solved to obtain the optimal solution set; the final unit maintenance and output plan is determined from the optimal solution set obtained by using the multi-objective decision-making method. The invention has simple execution and strong expandability, and can be used to solve multi-objective maintenance optimization models of different objective functions and constraint conditions.

Description

A multi-objective maintenance optimization method for electric power system under market environment

technical field

The invention belongs to the technical field of power system optimization, and in particular relates to a multi-objective maintenance optimization method of a power system.

Background technique

Under the electricity market environment, the arrangement of the generator maintenance plan is very different from the traditional generator maintenance plan. In the electricity market environment, each power generation company pursues the maximization of its own interests. At the same time, the system operating organization, such as the power dispatching center, needs to ensure the safety and reliability of the system. Power generators want to arrange their units to be overhauled during low power price periods, while system operators hope to arrange unit overhauls during low-load periods. Since low-power price periods and low-load periods are not exactly the same, power producers and system operators are in the same position. There is a conflict relationship in arranging unit maintenance time slots; on the other hand, because the maximum number of maintenance units and maintenance capacity that can be arranged in low-load periods is limited, there are also conflicts in the interests of various power producers. The existing maintenance plan adjustment mechanism is generally as follows: each power generation company submits the maintenance plan plan to the system operation organization, and the system operation organization uses certain mechanisms, such as incentive/punishment mechanisms, willingness to pay mechanisms, etc., to modify the maintenance plans of power generation companies to achieve system A compromise between safety and reliability and the interests of generators. This mechanism can reach a maintenance plan that satisfies all parties, including power generators and system operators, but it ignores the research on the conflict relationship between the parties and fails to fully understand the relationship between the parties.

Contents of the invention

The purpose of the present invention is to provide a multi-objective maintenance optimization method for electric power system under the market environment in view of the deficiencies in the prior art.

The technical solution adopted by the present invention to solve its technical problems is as follows:

Step (1) Obtain the power generation cost coefficient data C _0ij , C _1ij , C _2ij of each power generation company, the unit is $/MW; the maintenance cost coefficient data The unit is $/MW; unit start-up cost data The unit is $; unit capacity data The unit is MW; the load data P _D (t,s), the unit is MW, and the market electricity price data λ(t,s), the unit is $/MWh;

Step (2) establishing a multi-objective maintenance optimization model of the power grid under the market environment;

Step (3) Carry out real number encoding to the unit output variable and the unit maintenance variable of the model described in step (2), carry out 0-1 binary encoding to the unit online state variable and the unit start-up state variable in the described model, and then the unit The on-line state variables and unit start-up state variables are transformed from independent variables into dependent variables represented by unit output variables and unit maintenance variables;

Step (4) initialize the unit output variable and the unit maintenance variable in the multi-objective maintenance optimization model;

Step (5) using the variable initialization value obtained in step (4) as the population initialization input of the fast non-dominated sorting method, and using NSGA-II to solve the above-mentioned multi-objective maintenance optimization model to obtain the optimal solution set;

Step (6) adopts the multi-objective decision-making method to determine the final unit maintenance and output plan from the obtained optimal solution set.

The objective function of the optimization model in step (2) includes the following three categories: the revenue maximization function of each power generation company, the system reliability maximization function, and the system total power generation cost minimization function;

The constraints of the optimization model include the following five categories: the system reserve is higher than the minimum reserve value required by the system, the total output of the generator set is balanced with the system load, the number of units under maintenance at the same time is less than the upper limit, and the output of the generator set is within its rated output range The inside and the unit cannot be in the inspection and online states at the same time;

The revenue objective function of the i-th power producer is expressed as pf(i), and its expression is shown in formula (1):

In formula (1), G _i represents the unit set of the i-th generator; Indicates the active output of the j unit of the i-th generator in the sub-period s of the period t; T(t,s) indicates the length of the sub-period s of the period t, in hours; y _ij (t,s) indicates the unit , if y _ij (t, s) = 1, it means that the j unit of the i-th generator starts at the beginning of the period t sub-period s, and if y _ij (t, s) = 0, there is no start; x _ij indicates the starting week of the inspection of unit j of the i-th generator; D _ij indicates the continuous inspection duration of unit j of the i-th generator, in weeks; Indicates the maximum capacity of the jth unit of the i-th generator; ∨ indicates logical or; where i and j are natural numbers; m is an integer; T indicates the total number of periods; N indicates the total number of sub-periods;

The reliability index I(t,s) of period t and sub-period s is expressed as the net reserve divided by the gross reserve, the gross reserve is obtained by subtracting the system load from the sum of the capacities of all units, and the net reserve is obtained by subtracting the capacity of the units under maintenance from the gross reserve Obtained, as shown in formula (2), the system reliability objective function is obtained by averaging the reliability indicators I(t, s) of all sub-periods, as shown in formula (3);

$\mathrm{<span\; class="notranslate">\; max</span>}\mathrm{<span\; class="notranslate">\; imize</span>}<span\; class="notranslate">\; :</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

In formula (2), P _D (t, s) represents the system load in sub-period s of time period t;

The objective function of the total power generation cost of the system is expressed as tc, and its expression is shown in formula (4):

The system backup constraints are shown in formula (5):

In formula (5), R ^min (t,s) represents the minimum backup required by the system in sub-period s of time period t;

The constraints on the maximum number of simultaneous maintenance units are shown in formula (6):

In formula (6), N _i (t) represents the maximum number of simultaneous maintenance units allowed by the i-th generator in time period t;

The unit output constraints are shown in formula (7):

${\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}^{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}^{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&ForAll;</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&ForAll;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

In formula (7), Indicates the lower limit of the output of the unit when it is online, v _ij (t, s) indicates the online state variable, 1 for online and 0 for offline;

When the unit is overhauled, the online constraints are not allowed as shown in formula (8):

The system power balance constraints are shown in formula (9):

$\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; I</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&ForAll;</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&ForAll;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span>$

Step (3) specifically comprises the following steps:

3-1. Unit output variable Using real code;

3-2. Unit maintenance variables x _ij are coded by real numbers and then rounded to integers. x _ij represents the start week of unit maintenance of unit j of the i-th generator, and the maintenance duration is represented by D _ij ;

3-3. The unit online state variable v _ij (t, s) is represented by the unit output variable, which is transformed from an independent variable into a dependent variable, as shown in formula (10):

3-4. The start-up state variable y _ij (t, s) of the unit can be represented by the online state variable v _ij (t, s), which is transformed from an independent variable into a dependent variable, as shown in formula (11):

y _ij (t+1,1)=v _ij (t+1,1)-v _ij (t,N)

(11).

y _ij (t,s+1)=v _ij (t,s+1)-v _ij (t,s)

The initialization scheme described in step (4) is as follows:

4-1. Unit maintenance initialization subroutine consists of the following 6 steps:

4-1-1. Input the data np and gidx, let t=0, j=0; where np is the sum of the number of units of all generators, and the array gidx is the number of the units sorted according to the maximum capacity value from large to small order;

4-1-2. Assuming that the unit gidx[j] is under maintenance, judge whether the spare constraint shown in formula (5) and the maximum number of simultaneous maintenance units shown in formula (6) are satisfied at the same time; if formula (5) and formula (6) If both are true at the same time, then the unit gidx[j] will be overhauled; if at least one of formula (5) and formula (6) is not true, then the unit gidx[j] will not be overhauled;

4-1-3. Let j=j+1;

4-1-4. Determine whether j<np is true, if not, jump to step 4-1-6; if true, set t=t+1;

4-1-5. Determine whether t<T is true, if true, execute step 4-1-2; if not, execute step 4-1-6; where T is the total number of weeks considered in the maintenance plan;

4-1-6. Return to the sub-maintenance program, and end the initial subroutine for maintenance;

4-2. The unit output initialization subroutine consists of the following 6 steps:

4-2-1. Let the output of all units be 0, let j=0;

4-2-2. Let k=0;

4-2-3. Make a judgment, if the unit pinc[k] is under inspection, then execute step 4-2-4; if the unit pinc[k] is not under inspection, then execute step 4-2-5;

4-2-4. Make k=k+1; make a judgment, if k<ng is established, then jump to step 4-2-3, if k<ng is not established, then execute step 4-2-6;

4-2-5. Assuming that the output of the unit pinc[k] is at the upper limit of its output, make a judgment, if the output sum of all units is greater than the load, then reduce the unit pinc[k] so that the power balance constraint shown in formula (9) is obtained If it is satisfied, go to step 4-2-6; if the output sum of all units is not greater than the load, then make the unit pinc[k] at its output upper limit, go to step 4-2-4;

4-2-6.j=j+1; make a judgment, if j<nday is established, then jump to step 4-2-2; if j<nday is not established, return to the unit output plan, and end the unit output initialization subroutine ;

Among them, nday is the total number of days considered in the maintenance plan, and its value is T multiplied by 7; the array pinc is the number sequence of the units obtained by sorting the units according to the average energy consumption value of the units from small to large;

4-3. Obtaining the unit maintenance initialization plan and unit output initialization plan consists of the following 7 steps:

4-3-1. Permutation and combination of 1 to I, the total number of permutations and combinations Kinds, execute step 4-3-2 to step 4-3-6 for each permutation and combination scheme;

4-3-2. Record the permutation and combination scheme as (i ₁ ,i ₂ ,…,i _k ,…,i _I ), where i _k represents the i _kth generator;

4-3-3. Let k=1;

4-3-4. Record the number of units owned by the i _kth generator as np, sort these units according to the maximum capacity of the units from large to small, and put the obtained unit numbers in the array gidx; call unit maintenance initialization Subroutine, record the unit maintenance initialization scheme obtained;

4-3-5. Make k=k+1; Make a judgment, if k≤I, jump to execute step 4-3-4; if k>I, then execute step 4-3-6;

4-3-6. merging the maintenance initialization scheme of 1 unit that step 4-3-4 obtains obtains the maintenance initialization scheme of all units;

4-3-7. Call the unit output initialization subroutine to get the unit output initialization scheme.

The fast non-dominated sorting method described in step (5) comprises the following 7 steps:

5-1. Generate an initialization population, the number of individuals in the population is N _pop , the initialization population consists of two parts, the first part is the one described in step (4) A unit maintenance and output initialization scheme; the second part of random generation: set the unit maintenance variable as a randomly generated integer between 1 and T-1, and set the unit output variable as a randomly generated value between the lower limit of the unit output and the upper limit of the unit output a real number;

5-2. Use the current population P _g to generate the offspring population Q _g through the three genetic operators of selection, crossover and mutation, and combine the current population P _g and the offspring population Q _g to obtain the mixed population R _g = P _g ∪ Q _g ;

5-3. Use the fast non-dominated sorting method shown in Table 1 for R _g to obtain a series of Pareto fronts, denoted as F={F ₁ ,F ₂ ,F ₃ ,…,F _n };

5-4. Select N _pop individuals from R _g as the next generation population P _g+1 in the following way: if the number of elements in the Pareto front F ₁ is less than N _pop , then all the elements in F ₁ are put into In P _g+1 ; then compare the next Pareto front F ₂ , if the number of elements in the set P _g+1 ∪ F ₂ is less than N _pop , then all the elements in F ₂ will also be placed in P _g+1 ; and so on, until there is a Pareto frontier F _k , where k∈{1,2,3,…,n}, so that the number of elements in the set P _g+1 ∪F _k is greater than N _pop , then as Calculate the congestion degree I of each element in F _k as shown in Table 2, arrange all the congestion degrees I from large to small, put the arrangement result in F′ _k , and take the first N _pop -|P _g in F′ _{k +1} | elements are put into P _g+1 , that is, P _g+1 ＝P _g+1 ∪F′ _k [1:(N _pop -|P _g+1 |)];

5-5. Use the next-generation population P _g+1 to generate the next-generation offspring population Q _g+1 through the three genetic operators of selection, crossover, and mutation, and merge the next-generation population P _g+1 and the next-generation offspring population Q _g+1 , get the next generation mixed population R _g+1 ＝P _g+1 ∪Q _g+1 ;

5-6. Repeat steps 5-3 to 5-5 until the maximum number of cycles is reached;

5-7. Output the population P _g+1 at the maximum number of cycles, which is the optimal solution set;

Among them, |P _g | represents the number of elements in the set P _g , and P _g+1 ∪ _{F i} represents the union of P _g+1 and F _i ;

Table 1 Pseudo-code list of fast non-dominated sorting method

In Table 1, the description of the symbol < takes multi-objective minimization as an example, that is, the smaller the objective function, the better: the condition for q<p to be established is, if and only if for any i∈{1,2,…,N _obj } have And there exists at least one j∈{1,2,…,N _obj } such that

Table 2 Pseudo-code table for calculating congestion degree program

The multi-objective decision-making method described in step (6) adopts a sorting method approaching the ideal value, and is specifically divided into 5 steps:

6-1. First, calculate the per-unit weighted decision matrix v _ij :

v _ij = ω _i (f _i ⁺ -f _ij )/(f _i ⁺ -f _i ^- ), i=1,2,3,...Nobj,j=1,2,3,...J (12)

Among them, f _ij is the i-th objective function value of the j-th solution in the optimal solution set, N _obj is the number of objectives in multi-objective optimization, J is the number of solutions in the optimal solution set, ${\mathrm{\&omega;}}_i=\frac{1}{N_{\mathrm{obj}}}\underset{j=i}{\overset{N_{\mathrm{obj}}}{\mathrm{\&Sigma;}}}\frac{1}{j},i=\mathrm{1,2,3},...,N_{\mathrm{obj}};$

6-2. Calculate the optimal point separately and least ideal point $A^{-}=\{v_1^{-},v_2^{-},...,v_N^{-}\},$ in, $v_i^{+}=\underset{j}{\max }{v}_{\mathrm{ij}},v_i^{-}=\underset{j}{\min }{v}_{\mathrm{ij}};$

6-3. Calculate the distance D ⁺ from each optimal solution to the most ideal point and the distance D ^- to the least ideal point respectively: ${\mathrm{D.}}_j^{+}=\sqrt{{\mathrm{\&Sigma;}}_{i=1}^N{(v_{\mathrm{ij}}-v_i^{+})}^2},{\mathrm{D.}}_j^{-}=\sqrt{{\mathrm{\&Sigma;}}_{i=1}^N{(v_{\mathrm{ij}}-v_i^{-})}^2},j=\mathrm{1,2,3},...J;$

6-4. Calculate the distance ratio of each optimal solution $R_j={\mathrm{D.}}_j^{-}/({\mathrm{D.}}_j^{-}+{\mathrm{D.}}_j^{+}),j=\mathrm{1,2,3},...J;$

6-5. Select the optimal solution with the largest R _j as the final unit maintenance and output plan.

The beneficial effects of the present invention are:

The invention proposes a multi-objective maintenance optimization method for electric power systems in a market environment. Maintenance under the electricity market is a multi-objective optimization problem. If a single-objective optimization algorithm is used, it is necessary to give the weights of each objective based on experience, and then obtain an optimal solution. By changing the weights of each objective, another optimal solution can be obtained. solution, a series of Pareto (Pareto) optimal solutions can be obtained after so many calculations; while multi-objective optimization methods, such as NSGA-II, do not need to give the weight values of each objective when solving multi-objective optimization problems, and pass a All the Pareto optimal solutions can be obtained through calculation, which is conducive to the study of the relationship between the interests of each power generation company and the reliability of the system in the power market, and a maintenance and output plan that satisfies all parties can be obtained through the final decision . The multi-objective optimization method proposed by the present invention can well solve the problem of generator set maintenance planning under the power market environment, and has the following advantages: (1) carry out real number encoding on the unit output variable and unit maintenance variable of the model, and set the unit online The state variables and unit start-up state variables are transformed from independent variables into dependent variables represented by unit output variables and unit maintenance variables. The coding and conversion processing of the variables can better meet the constraints in the model; (2) NSGA The population initialization performed by -II can solve the multi-objective maintenance optimization model more effectively and obtain a better feasible solution; (3) without giving the weights of each objective, all Pareto optimal models can be obtained through one calculation (4) A maintenance and output plan that satisfies all parties can be obtained through the final decision-making method; (5) The method described is simple to implement and has strong scalability, and can be used to solve multiple problems with different objective functions and constraints. Target overhaul optimization model.

Description of drawings

Fig. 1 is a flow chart of the unit maintenance and output program initialization program used in the present invention.

Fig. 2 is a flow chart of the unit maintenance initialization subroutine used in the present invention.

Fig. 3 is a flow chart of the unit output initialization subroutine used in the present invention.

Fig. 4 is a flowchart of the NSGA-II main loop used in the present invention.

Detailed ways

The present invention will be further described below in conjunction with drawings and embodiments.

A multi-objective maintenance optimization method for power systems in a market environment, specifically comprising the following steps:

Step (1) Obtain the power generation cost coefficient data C _0ij , C _1ij , C _2ij of each power generation company, the unit is $/MW; the maintenance cost coefficient data The unit is $/MW; unit start-up cost data The unit is $; unit capacity data The unit is MW; the load data _PD (t,s), the unit is MW, and the market electricity price data λ(t,s), the unit is $/MWh.

Step (2) establishing a multi-objective maintenance optimization model of the power grid under the market environment;

The objective function of the optimization model includes the following three categories: the revenue maximization function of each power generation company, the system reliability maximization function, and the system total power generation cost minimization function;

The constraints of the optimization model include the following five categories: the system reserve is higher than the minimum reserve value required by the system, the total output of the generator set is balanced with the system load, the number of units under maintenance at the same time is less than the upper limit, and the output of the generator set is within its rated output range The inside and the unit cannot be in the inspection and online states at the same time;

The revenue objective function of the i-th power producer is expressed as pf(i), and its expression is shown in formula (1):

In formula (1), G _i represents the unit set of the i-th generator; Indicates the active output of the j unit of the i-th generator in the sub-period s of the period t; T(t,s) indicates the length of the sub-period s of the period t, in hours; y _ij (t,s) indicates the unit , if y _ij (t, s) = 1, it means that the j unit of the i-th generator starts at the beginning of the period t sub-period s, and if y _ij (t, s) = 0, there is no start; x _ij indicates the starting week of the inspection of unit j of the i-th generator; D _ij indicates the continuous inspection duration of unit j of the i-th generator, in weeks; Indicates the maximum capacity of the jth unit of the i-th generator; ∨ indicates logical or; where i and j are natural numbers; m is an integer; T indicates the total number of periods; N indicates the total number of sub-periods.

The reliability index I(t,s) of period t and sub-period s is expressed as the net reserve divided by the gross reserve, the gross reserve is obtained by subtracting the system load from the sum of the capacities of all units, and the net reserve is obtained by subtracting the capacity of the units under maintenance from the gross reserve Obtained, as shown in formula (2), the system reliability objective function is obtained by averaging the reliability indicators I(t, s) of all sub-periods, as shown in formula (3).

$\mathrm{<span\; class="notranslate">\; max</span>}\mathrm{<span\; class="notranslate">\; imize</span>}<span\; class="notranslate">\; :</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

In formula (2), P _D (t, s) represents the system load of period t sub-period s.

The objective function of the total power generation cost of the system is expressed as tc, and its expression is shown in formula (4):

The system backup constraints are shown in formula (5):

In formula (5), R ^min (t, s) represents the minimum backup required by the system in sub-period s of time period t.

The constraints on the maximum number of simultaneous maintenance units are shown in formula (6):

In formula (6), N _i (t) represents the maximum number of simultaneous maintenance units allowed by the i-th generator in time period t.

The unit output constraints are shown in formula (7):

${\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}^{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}^{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&ForAll;</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&ForAll;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

In formula (7), Indicates the lower limit of the output of the unit when it is online, v _ij (t, s) indicates the online state variable, 1 for online and 0 for offline;

When the unit is overhauled, the online constraint is not allowed as shown in formula (8):

The system power balance constraints are shown in formula (9):

$\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; I</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&ForAll;</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&ForAll;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

Step (3) Carry out real number encoding to the unit output variable and the unit maintenance variable of the model described in step (2), carry out 0-1 binary encoding to the unit online state variable and the unit start-up state variable in the described model, and then the unit The online state variables and unit start-up state variables are transformed from independent variables into dependent variables represented by unit output variables and unit maintenance variables; the specific steps are as follows:

3-1. Unit output variable Using real code;

3-2. Unit maintenance variables x _ij are coded by real numbers and then rounded to integers. x _ij represents the start week of unit maintenance of unit j of the i-th generator, and the maintenance duration is represented by D _ij ;

3-3. The unit online state variable v _ij (t, s) is represented by the unit output variable, which is transformed from an independent variable into a dependent variable, as shown in formula (10):

3-4. The start-up state variable y _ij (t, s) of the unit can be represented by the online state variable v _ij (t, s), which is transformed from an independent variable into a dependent variable, as shown in formula (11):

y _ij (t+1,1)=v _ij (t+1,1)-v _ij (t,N)

  (11)

y _ij (t,s+1)=v _ij (t,s+1)-v _ij (t,s)

Step (4) Initialize the unit output variables and unit maintenance variables in the multi-objective maintenance optimization model. The initialization scheme is as follows:

Here we first describe the unit maintenance initialization subroutine, then describe the unit output initialization subroutine, and finally describe the unit maintenance initialization scheme and unit output initialization scheme obtained by using the first two subroutines.

As shown in Figure 1, the unit maintenance initialization subroutine consists of the following six steps:

4-1-1. Input the data np and gidx, let t=0, j=0; where np is the sum of the number of units of all generators, and the array gidx is the number of the units sorted according to the maximum capacity value from large to small order;

4-1-2. Assuming that the unit gidx[j] is under maintenance, judge whether the spare constraint shown in formula (5) and the maximum number of simultaneous maintenance units shown in formula (6) are satisfied at the same time; if formula (5) and formula (6) If both are true at the same time, then the unit gidx[j] will be overhauled; if at least one of formula (5) and formula (6) is not true, then the unit gidx[j] will not be overhauled;

4-1-3. Let j=j+1;

4-1-4. Determine whether j<np is true, if not, jump to step 4-1-6; if true, set t=t+1;

4-1-5. Determine whether t<T is true, if true, execute step 4-1-2; if not, execute step 4-1-6; where T is the total number of weeks considered in the maintenance plan;

4-1-6. Return to the sub-maintenance program, and end the initial subroutine for maintenance;

As shown in Figure 2, the unit output initialization subroutine consists of the following six steps:

4-2-1. Let the output of all units be 0, let j=0;

4-2-2. Let k=0;

4-2-3. Make a judgment, if the unit pinc[k] is under inspection, then execute step 4-2-4; if the unit pinc[k] is not under inspection, then execute step 4-2-5;

4-2-4. Make k=k+1; make a judgment, if k<ng is established, then jump to step 4-2-3, if k<ng is not established, then execute step 4-2-6;

4-2-5. Assuming that the output of the unit pinc[k] is at the upper limit of its output, make a judgment, if the output sum of all units is greater than the load, then reduce the unit pinc[k] so that the power balance constraint shown in formula (9) is obtained If it is satisfied, go to step 4-2-6; if the output sum of all units is not greater than the load, then make the unit pinc[k] at its output upper limit, go to step 4-2-4;

4-2-6.j=j+1; make a judgment, if j<nday is established, then jump to step 4-2-2; if j<nday is not established, return to the unit output plan, and end the unit output initialization subroutine ;

Among them, nday is the total number of days considered in the maintenance plan, and its value is T multiplied by 7; the array pinc is the unit number sequence obtained by sorting the units according to the average energy consumption value of the units from small to large.

As shown in Figure 3, the method of obtaining the unit maintenance initialization scheme and the unit output initialization scheme consists of the following seven steps:

4-3-1. Permutation and combination of 1 to I, the total number of permutations and combinations Kinds, execute step 4-3-2 to step 4-3-6 for each permutation and combination scheme;

4-3-2. Record the permutation and combination scheme as (i ₁ ,i ₂ ,…,i _k ,…,i _I ), where i _k represents the i _kth generator;

4-3-3. Let k=1;

4-3-4. Record the number of units owned by the i _kth generator as np, sort these units according to the maximum capacity of the units from large to small, and put the obtained unit numbers in the array gidx; call unit maintenance initialization Subroutine, record the unit maintenance initialization scheme obtained;

4-3-5. Make k=k+1; Make a judgment, if k≤I, jump to execute step 4-3-4; if k>I, then execute step 4-3-6;

4-3-6. merging the maintenance initialization scheme of 1 unit that step 4-3-4 obtains obtains the maintenance initialization scheme of all units;

4-3-7. Call the unit output initialization subroutine to get the unit output initialization scheme.

The unit maintenance and output scheme initialization program shown in Figure 3 calls the unit maintenance initialization subroutine shown in Figure 1 and the unit output initialization subroutine shown in Figure 2 successively.

Step (5) Use the variable initialization value obtained in step (4) as the population initialization input of the fast non-dominated sorting method (NSGA-II), and use NSGA-II to solve the above multi-objective maintenance optimization model to obtain the optimal solution set:

As shown in Figure 4, NSGA-II includes the following seven steps:

5-1. Generate an initialization population, the number of individuals in the population is N _pop , the initialization population consists of two parts, the first part is the one described in step (4) A unit maintenance and output initialization scheme; the second part of random generation: set the unit maintenance variable as a randomly generated integer between 1 and T-1, and set the unit output variable as a randomly generated value between the lower limit of the unit output and the upper limit of the unit output a real number.

5-2. Use the current population P _g to generate the offspring population Q _g through the three genetic operators of selection, crossover and mutation, and combine the current population P _g and the offspring population Q _g to obtain the mixed population R _g = P _g ∪ Q _g .

5-3. Use the fast non-dominated sorting method shown in Table 1 to obtain a series of Pareto fronts for R _g , denoted as F={F ₁ , F ₂ , F ₃ ,...,F _n }.

5-4. Select N _pop individuals from R _g as the next generation population P _g+1 in the following way: if the number of elements in the Pareto front F ₁ is less than N _pop , then all the elements in F ₁ are put into In P _g+1 ; then compare the next Pareto front F ₂ , if the number of elements in the set P _g+1 ∪ F ₂ is less than N _pop , then all the elements in F ₂ will also be placed in P _g+1 ; and so on, until there is a Pareto frontier F _k , where k∈{1,2,3,…,n}, so that the number of elements in the set P _g+1 ∪F _k is greater than N _pop , then as Calculate the congestion degree I of each element in F _k as shown in Table 2, arrange all the congestion degrees I from large to small, put the arrangement result in F′ _k , and take the first N _pop -|P _g in F′ _{k +1} |elements are put into P _g+1 , that is, P _g+1 ＝P _g+1 ∪F′ _k [1:(N _pop -|P _g+1 |)].

5-5. Use the next-generation population P _g+1 to generate the next-generation offspring population Q _g+1 through the three genetic operators of selection, crossover, and mutation, and merge the next-generation population P _g+1 and the next-generation offspring population Q _g+1 , to get the next generation mixed population R _g+1 ＝P _g+1 ∪Q _g+1 .

5-6. Repeat steps 5-3 to 5-5 until the maximum number of cycles is reached.

5-7. Output the population P _g+1 at the maximum number of cycles, which is the optimal solution set.

Among them, |P _g | represents the number of elements in the set P _g , and P _g+1 ∪ _{F i} represents the union of P _g+1 and F _i .

Table 1 Pseudo-code list of fast non-dominated sorting method

In Table 1, the description of the symbol < takes multi-objective minimization as an example, that is, the smaller the objective function, the better: the condition for q<p to be established is, if and only if for any i∈{1,2,…,N _obj } have And there exists at least one j∈{1,2,…,N _obj } such that

Table 2 Pseudo-code table for calculating congestion degree program

Step (6) adopts the multi-objective decision-making method to determine the final unit maintenance and output plan from the obtained optimal solution set. The multi-objective decision-making method adopts a sorting method (Technique for Order Preference by Similarity to Ideal Solution, TOPSIS) approaching the ideal value. TOPSIS can be divided into 5 steps:

6-1. First, calculate the per-unit weighted decision matrix vi _j :

v _ij = ω _i (f _i ⁺ -f _ij )/(f _i ⁺ -f _i ^- ), i=1,2,3,...Nobj,j=1,2,3,...J (12)

Among them, f _ij is the i-th objective function value of the j-th solution in the optimal solution set, N _obj is the number of objectives in multi-objective optimization, J is the number of solutions in the optimal solution set, ${\mathrm{\&omega;}}_i=\frac{1}{N_{\mathrm{obj}}}\underset{j=i}{\overset{N_{\mathrm{obj}}}{\mathrm{\&Sigma;}}}\frac{1}{j},i=\mathrm{1,2,3},...,N_{\mathrm{obj}};$

6-2. Calculate the optimal point separately and least ideal point $A^{-}=\{v_1^{-},v_2^{-},...,v_N^{-}\},$ in, $v_i^{+}=\underset{j}{\max }{v}_{\mathrm{ij}},v_i^{-}=\underset{j}{\min }{v}_{\mathrm{ij}}.$

6-3. Calculate the distance D ⁺ from each optimal solution to the most ideal point and the distance D ^- to the least ideal point respectively: ${\mathrm{D.}}_j^{+}=\sqrt{{\mathrm{\&Sigma;}}_{i=1}^N{(v_{\mathrm{ij}}-v_i^{+})}^2},{\mathrm{D.}}_j^{-}=\sqrt{{\mathrm{\&Sigma;}}_{i=1}^N{(v_{\mathrm{ij}}-v_i^{-})}^2},j=\mathrm{1,2,3},...J.$

6-4. Calculate the distance ratio of each optimal solution $R_j={\mathrm{D.}}_j^{-}/({\mathrm{D.}}_j^{-}+{\mathrm{D.}}_j^{+}),j=\mathrm{1,2,3},...J.$

6-5. Select the optimal solution with the largest R _j as the final unit maintenance and output plan.

Step (7) According to the final unit maintenance and output plan in step (6), the power dispatching center sends the maintenance status and output value of each unit to the decentralized control system of the power plant through the information processing and communication device to automatically control the operation of the generator set state and adjust its output.

For the convenience of the following description, first briefly introduce two concepts: power plant distributed control system and automatic power generation control. Power plant distributed control system (Distributed Control System, DCS) is based on microcomputer, according to the concept of system control, it integrates computer technology, control technology, communication technology and graphic display technology to realize centralized management and decentralized control. DCS system has become the main equipment of power plant control and monitoring. Automatic Generation Control (AGC), which is an important part of the energy management system. According to the control target of the power grid dispatching center, the command is sent to the relevant power plant or unit, and the automatic control of the power of the unit is realized through the automatic control and adjustment device of the power plant or unit.

In the power plant network monitoring system, the information processing and communication device D200 is often used. So far, more than 200 power plants in the country, including more than 65% of large power plants, have adopted D200 to realize the AGC control and telecontrol functions of dispatching power plants. These include many power plants with 600MW units, such as Zhejiang Jiaxing Power Plant, Ninghai Power Plant, Sanmenxia Power Plant and so on. The power dispatching center can directly send AGC commands to the DCS system through the information processing and communication device D200, so as to realize the output adjustment of the unit.

According to the final unit maintenance and output plan in step (6), the power dispatching center sends the maintenance status and output value of each unit to the DCS system through the information processing and communication device D200, so as to automatically control the operating status of the generator set and adjust its output . If the unit needs to be overhauled, the power dispatching center will send the automatic shutdown signal to the computer monitoring system of the power plant as an AGC command through the information processing and communication device D200. If the unit does not need maintenance, the power dispatching center can directly send the output value of each unit to the DCS system of the generator set in the form of AGC commands through the information processing and communication device D200, so as to realize automatic control of the output of the generator set. The details are as follows: the power dispatching center obtains the output value of each generating set, and sends it to each power plant with an AGC command through the information processing and communication device D200; the main CPU board of the power plant D200 first receives the AGC command issued by the dispatching center, and then passes The protocol information processing digitizes the AGC command and sends it to the CPU board of the D20C combination board; the D20C combination board converts the received numerical AGC command into the code value corresponding to the 0-100% output of the generator set, and outputs according to this code value The 4-20mA DC analog quantity is sent to the DCS system of the generator set to adjust the output of the generator set.

Example 1

This patent assumes that there are 3 power generators in the electricity market, and according to the arrangement and combination, and according to the sequence of determining the maintenance plans of the power generators, there can be species, namely (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2) and (3,2,1) These 6 kinds. (1,2,3) represents the flow chart of first determining the unit maintenance plan of generator 1, then determining the unit maintenance plan of generator 2, and finally determining the unit maintenance plan of generator 3. The opportunity cost of arranging unit maintenance during low electricity price periods is low. Since the capacity and total number of units to be overhauled at each time period are limited, if the unit maintenance plan of generator 1 is determined first, generator 1’s income will be relatively low. is large; and if the unit maintenance plan of generator 2 is determined first, the revenue of generator 2 will be larger. In this patent, a total of 6 kinds of unit maintenance and output initialization schemes are obtained.

Example 2

The data used in the present invention are based on the power generation costs, maintenance costs, start-up and shutdown costs, unit capacity, and the next 52 weeks, that is, T=52, the market weekly average electricity price and other data obtained in the power system of a certain power market environment. data. Other parameters are set as follows, R ^min (t, s) is taken as 0.05 times of the system load in period t and sub-period s, N _i (t) is taken as 3, sub-period N=7, the number of power suppliers is 3, and there are 32 generating units in total Set, that is, np=32, the number of objective functions N _obj is set to 5, the maximum number of iterations in NSGA-II is set to 1500, and the total number of individuals N _pop in the population is set to 1200.

First of all, in order to verify the encoding conversion processing method described in step (3) and the initialization method described in step (4) in the present invention, use the described NSGA-II algorithm to solve the generator set maintenance under the described power market environment To check the effectiveness of planning problems, we have done four comparative experiments as shown in Table 3, and the solution results are shown in Table 4.

Table 3 Settings of four comparative experiments

Table 4 The results of four comparative experiments

In Table 4, the objective functions f1, f2 and f3 represent the revenues of generators 1, 2 and 3, respectively. The greater the revenue, the better the scheme. Therefore, the objective functions f1, f2 and f3 must be optimized by maximization. Since NSGA-II only Can handle minimization optimization, so in the NSGA-II solution process, we take negative values of f1, f2 and f3, that is, minimize -f1, -f2 and -f3. The objective function f5 represents the system reliability objective function. This function represents the system reserve value. The higher the system reserve value, the better the system stability. Therefore, the objective function f5 must also be optimized by maximization, which is similar to the processing methods of f1, f2 and f3. We take f5 negative, i.e. minimize -f5. The objective function f4 represents the total power generation cost of the system, and the lower the total power generation cost, the better, so the objective function f4 must be minimized and optimized without special treatment.

From Table 4 we can see that NSGA-II-1 and NSGA-II-2 did not use the encoding processing method shown in step (3), and could not obtain a feasible solution; NSGA-II-3 and NSGA-II- In 4, the encoding processing method shown in step (3) is adopted, and the optimal solution set can be obtained smoothly. The optimal value of each objective function in this optimal solution set is shown in Table 4. This shows that the encoding processing shown in step (3) plays a very important role in the smooth solution of the problem.

Comparing NSGA-II-4 with NSGA-II-3, the former includes the initialization in step (4) but the latter does not. The results in Table 4 show that the maximum values of the objective functions f1, f2, f3 and f5 obtained by the former are larger than those obtained by the latter; the minimum value of the objective function f4 obtained by the former is smaller than that obtained by the latter. This shows that the initialization shown in step (4) is beneficial for better solutions. After verification, all the solutions in the optimal solution set obtained by NSGA-II-3 and NSGA-II-4 satisfy the constraint conditions, that is, they are all feasible solutions.

For the convenience of expression, we call the final unit maintenance and output plan determined from the optimal solution set obtained in step (5) by using the multi-objective decision-making method TOPSIS as the final solution. Table 5 shows the values of each objective function of the final solution, and Table 6 shows the unit maintenance plan of the final solution. The output data of the unit in the final solution is relatively large, with 32×364=11648 data, so it is not given. To sum up, NSAG-II, a multi-objective optimization method proposed in the present invention, is effective for solving the maintenance plan of generating units in the electricity market environment.

Table 5 Each objective function value of the final solution

f1/×10 ⁸ $ f2/×10 ⁸ $ f3/×10 ⁸ $ f4/×10 ⁸ $ f5 NSGA-II-4 1.75 1.35 1.99 5.77 0.8715

Table 6 The unit maintenance plan of the final solution

Unit serial number Unit output upper limit Maintenance period/week Unit serial number Unit output upper limit 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 twenty one 155 46-47 6 20 40-41 twenty two 155 44-45 7 76 34-35 twenty three 155 35-36 8 76 43-44 twenty four 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 (6)

1. an electric system multiple goal maintenance optimization method under market environment, is characterized in that comprising the steps:

Step (1) is obtained each Power Generation generating cost coefficient data C _0ij, C _1ij, C _2ij, unit is $/MW; Recondition expense coefficient data unit is $/MW; Unit starting cost data unit is $; Unit capacity data unit is MW; Load data P _d(t, s), unit is MW, and market electricity price data λ (t, s), unit is $/MWh;

Step (2) is set up electrical network multiple goal maintenance Optimized model under market environment;

Step (3) is carried out real coding to unit output variable and the unit maintenance variable of model described in step (2), machine set on line state variable in described model and unit starting state variable are carried out to 0-1 binary coding, then machine set on line state variable and unit starting state variable are transformed into by unit output variable and the represented dependent variable of unit maintenance variable from independent variable;

Step (4) is carried out initialization to unit output variable and unit maintenance variable in multiple goal maintenance Optimized model;

Step (5) adopts the initialization of variable value obtaining in step (4) to input as the initialization of population of quick non-dominated Sorting method, and adopts NSGA-II to solve above-mentioned multiple goal maintenance Optimized model, obtains optimal solution set;

Step (6) adopts Multiobjective Decision Making Method, determines final unit maintenance and the scheme of exerting oneself from the optimal solution set obtaining.

2. electric system multiple goal maintenance optimization method under a kind of market environment as claimed in claim 1, is characterized in that the objective function of the described Optimized model of step (2) comprises following 3 classes: the maximize revenue function of each Power Generation, system reliability maximize function, the system cost minimization function that always generates electricity;

The constraint condition of described Optimized model comprises following 5 classes: system reserve higher than the required minimum backed-up value of system, genset gross capability and system loading balance, overhaul unit number simultaneously and be less than that higher limit, genset are exerted oneself within the scope of its nominal output, unit can not be simultaneously in maintenance and online two states;

The earnings target function representation of i Power Generation is pf (i), and its expression formula is suc as formula shown in (1):

In formula (1), G _irepresent the unit set of i Power Generation; represent that the j platform unit of i Power Generation is in meritorious the exerting oneself of period t sub-period s; T (t, s) represents that the time of period t sub-period s is long, and unit is hour; y _ij(t, s) represents the starting state of unit, if y _ij(t, s)=1 represents that the j platform unit of i Power Generation started in the zero hour of period t sub-period s, if y _ij(t, s)=0 nothing starts; x _ijthe j platform unit maintenance that represents i Power Generation starts week; D _ijthe j platform unit that represents i Power Generation overhauls duration continuously, and unit is week; represent the max cap. of the j platform unit of i Power Generation; ∨ presentation logic or; Wherein i and j are natural number; M is integer; T represents total time hop count; N represents total period of the day from 11 p.m. to 1 a.m hop count;

Reliability index I (the t of period t sub-period s, s) be expressed as clean for subsequent use for subsequent use divided by hair, the hair capacity by all units for subsequent use and deduct system loading and obtain, clean for subsequent usely deduct the capacity of unit in maintenance and obtain by hair is for subsequent use, shown in (2), system reliability goal function is averaged and is obtained by the reliability index I (t, s) of all sub-periods, shown in (3);

In formula (2), P _d(t, s) represents the system loading of period t sub-period s;

The system the goal of cost function representation that always generates electricity is tc, and its expression formula is suc as formula shown in (4):

System reserve constraint condition is suc as formula shown in (5):

In formula (5), R ^min(t, s) represents that the required minimum of period t sub-period s system is for subsequent use;

Maximum is overhauled unit simultaneously and is counted constraint condition suc as formula shown in (6):

In formula (6), N _i(t) maximum that i Power Generation of expression allows at period t is overhauled unit number simultaneously;

Unit output constraint condition is suc as formula shown in (7):

In formula (7), represent the lower limit of exerting oneself when unit is online, v _ij(t, s) is illustrated in line state variable, is 1 online, is not 0 online;

Can not on-line constraints when unit maintenance suc as formula shown in (8):

System power equilibrium constraint is suc as formula shown in (9):

3. electric system multiple goal maintenance optimization method under a kind of market environment as claimed in claim 1, is characterized in that step (3) specifically comprises the steps:

3-1. unit output variable adopt real coding;

3-2. unit maintenance variable x _ijadopt real coding, then round x _ijthe j platform unit maintenance that represents i Power Generation starts week, and maintenance continues duration by D _ijrepresent;

3-3. machine set on line state variable v _ij(t, s) represented by unit output variable, transforms into dependent variable by independent variable, shown in (10):

3-4. unit starting state variable y _ij(t, s) can be by presence variable v _ij(t, s) represents, transforms into dependent variable by independent variable, shown in (11):

y _ij(t+1,1)＝v _ij(t+1,1)-v _ij(t,N)

y _ij(t,s+1)＝v _ij(t,s+1)-v _ij(t,s) (11)。

4. electric system multiple goal maintenance optimization method under a kind of market environment as claimed in claim 1, is characterized in that the described initialization scheme of step (4) is as follows:

4-1. unit maintenance initialization subroutine is made up of following 6 steps:

4-1-1. input data np and gidx, make t=0, j=0; The unit that wherein np is all Power Generations is counted sum, and array gidx is unit according to the maximum capacity unit number order obtaining that sorts from big to small;

4-1-2. hypothesis unit gidx[j] in maintenance, judge that the maximum shown in the Reserve Constraint shown in formula (5) and formula (6) overhauls the constraint of unit number simultaneously and whether meet simultaneously; If formula (5) and formula (6) are all set up simultaneously, make unit gidx[j] overhaul; If formula (5) and formula (6) have at least one to be false, make unit gidx[j] do not overhaul;

4-1-3. makes j=j+1;

4-1-4. judges whether j<np sets up, if be false redirect execution step 4-1-6; Make t=t+1 if set up;

4-1-5. judges whether t<T sets up, and performs step 4-1-2 if set up; Perform step 4-1-6 if be false; Wherein T is total all numbers that turnaround plan is considered;

4-1-6. returns to sub-maintenance scheme, finishes the initial subroutine of maintenance;

4-2. unit output initialization subroutine is made up of following 6 steps:

It is 0 that 4-2-1. makes all unit outputs, makes j=0;

4-2-2. makes k=0;

4-2-3. makes a decision, if unit pinc[k] in maintenance, perform step 4-2-4; If unit pinc[k] not in maintenance, perform step 4-2-5;

4-2-4. makes k=k+1; Make a decision, if k<ng sets up redirect execution step 4-2-3, perform step 4-2-6 if k<ng is false;

4-2-5. hypothesis unit pinc[k] exert oneself in its upper limit of exerting oneself, make a decision, if all unit outputs and be greater than load reduce unit pinc[k] the power-balance constraint shown in formula (9) is met, execution step 4-2-6; If all unit outputs and be not more than load, make unit pinc[k] in its upper limit of exerting oneself, execution step 4-2-4;

4-2-6.j=j+1; Make a decision, if j<nday sets up, redirect execution step 4-2-2; If j<nday is false, return to unit output scheme, finish unit output initialization subroutine;

Wherein, nday is total number of days that turnaround plan is considered, its value is multiplied by 7 for T; Array pinc is unit according to the average power consumption values of the unit unit number order obtaining that sorts from small to large;

4-3. obtains unit maintenance initialization scheme and unit output initialization scheme is made up of following 7 steps:

4-3-1. carries out permutation and combination to 1 to I, and permutation and combination scheme number is total kind, each permutation and combination scheme execution step 4-3-2 is arrived to step 4-3-6;

Permutation and combination scheme is designated as (i by 4-3-2. ₁, i ₂..., i _k..., i _i), i _krepresent i _kindividual Power Generation;

4-3-3. makes k=1;

4-3-4. note i _kthe unit number that individual Power Generation has is np, and these units are sorted from big to small according to unit maximum capacity, and the unit number order obtaining is placed in array gidx; Call unit maintenance initialization subroutine, the unit maintenance initialization scheme that record obtains;

4-3-5. makes k=k+1; Make a decision, if k≤I, redirect execution step 4-3-4; If k > is I, perform step 4-3-6;

The I that 4-3-6. obtains step 4-3-4 unit maintenance initialization scheme merges the maintenance initialization scheme that obtains all units;

4-3-7. calls unit output initialization subroutine, obtains unit output initialization scheme.

5. electric system multiple goal maintenance optimization method under a kind of market environment as claimed in claim 1, is characterized in that described quick non-dominated Sorting method, comprises following 7 steps:

5-1. generate initialization population, in population, number of individuals is N _pop, this initialization population is made up of two parts, and Part I is described in step (4) plant unit maintenance and the initialization scheme of exerting oneself; Part II generates at random: unit maintenance variable is made as to an integer of the random generation between 1 to T-1, unit output variable is made as to the random real number generating between unit output lower limit and the unit output upper limit;

Current population P for 5-2. _ggenerate progeny population Q by selection, these 3 genetic operators of crossover and mutation _g, merge current population P _gwith progeny population Q _gobtain mixed population R _g=P _g∪ Q _g;

5-3. is to R _gquick non-dominated Sorting method shown in employing table 1 obtains a series of Paretos forward position, is designated as F={F ₁, F ₂, F ₃..., F _n;

5-4. is from R _gin select in the following way N _popindividuality is as population P of future generation _g+1if: Pareto forward position F ₁middle element number is less than N _pop, F ₁in all elements all put into P _g+1in; Then more next Pareto forward position F ₂if, set P _g+1∪ F ₂in element number be less than N _pop, F ₂in all elements also all put into P _g+1; By that analogy, until there is a Pareto forward position F _k, wherein k ∈ 1,2,3 ..., n}, makes to gather P _g+1∪ F _kin element number be greater than N _pop, calculating F as shown in table 2 _kin the crowding I of each element, so to crowding I arrange from big to small, rank results is placed in F ' _kin, get F ' _kin front N _pop-| P _g+1| individual element is put into P _g+1in, i.e. P _g+1=P _g+1∪ F ' _k[1:(N _pop-| P _g+1|)];

Population P of future generation for 5-5. _g+1generate progeny population Q of future generation by selection, these 3 genetic operators of crossover and mutation _g+1, merge population P of future generation _g+1with progeny population Q of future generation _g+1, obtain mixed population R of future generation _g+1=P _g+1∪ Q _g+1;

5-6. 5-3 is to 5-5, until reach maximum cycle for circulation execution step;

Population P when 5-7. output maximum cycle _g+1, be optimal solution set;

Wherein, | P _g| represent set P _gthe number of middle element, P _g+1∪ F _irepresent P _g+1with F _iunion;

The pseudo-code table of the quick non-dominated Sorting method program of table 1

In table 1, the explanation of symbol <, is minimised as example with multiple goal, and objective function is the smaller the better: q < p set up condition be, and if only if to any i ∈ 1,2 ..., N _objhave and at least exist a j ∈ 1,2 ..., N _objmake

Table 2 calculates the pseudo-code table of crowding program

6. electric system multiple goal maintenance optimization method under a kind of market environment as claimed in claim 1, is characterized in that the described Multiobjective Decision Making Method of step (6) adopts the sort method that approaches ideal value, is specifically divided into 5 steps:

First 6-1., calculates the weighting decision matrix v of standardization _ij:

v _ij＝ω _i(f _i ⁺-f _ij)/(f _i ⁺-f _i ^-),i＝1,2,3,…Nobj,j＝1,2,3,…J (12)

Wherein, f _ijfor j in optimal solution set i the target function value of separating, n _objfor the number of target in multiple-objection optimization, J is the number of separating in optimal solution set,

6-2. calculates respectively ideal point least ideal point wherein,

6-3. calculate respectively the distance B of each optimum solution to ideal point ⁺with to the distance B of ideal point least ^-:

6-4. calculates the distance ratio of each optimum solution

6-5. is by R _jmaximum optimum solution is chosen as final unit maintenance and the scheme of exerting oneself.