CN113657722B - Power plant energy-saving scheduling method based on social spider optimization algorithm - Google Patents
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Abstract
The invention discloses a power plant energy-saving scheduling method based on a social spider optimization algorithm, which is implemented according to the following steps: step 1, taking the lowest total power generation coal consumption of the power system as an optimization target, establishing an objective function, and establishing a power system operation constraint condition; and 2, solving the minimum value of the objective function according to the social spider optimization algorithm under the limit of the established operation constraint condition of the power system to obtain the minimum power generation coal consumption of the power system. According to the power plant energy-saving scheduling method based on the social spider optimization algorithm, the social spider optimization algorithm is utilized, so that the lowest total power generation coal consumption under the safe and reliable operation of a power system is realized.
Description
Technical Field
The invention belongs to the technical field of power dispatching methods, and relates to a power plant energy-saving dispatching method based on a social spider optimization algorithm.
Background
The optimal scheduling of the power system is to ensure that the designed target is optimal through various technical means or reasonable management strategies on the premise of ensuring the safety of power production and the high quality of power quality, and the optimal target generally comprises an economic target, a safety target, an environment-friendly target and the like. Because the system scale is large and constraint conditions are numerous, the complexity of power system scheduling modeling and solving is increased, and the problem becomes an optimization problem with nonlinearity, non-convexity, high dimension and a large number of local extreme points, so that the performance of an optimization algorithm is highly required.
The traditional mathematical programming optimization method requires continuous, conductive and microscopic objective functions, so that the power system optimization scheduling problem containing nonlinear complex constraints is difficult to process, and a large number of intelligent optimization algorithms are used for solving the power system optimization scheduling problem with a plurality of non-smooth objective functions. Unlike mathematical programming, the intelligent algorithm has no special limitation on the model for solving the problem and has stronger global searching capability. However, most intelligent algorithms are based on natural evolution theory, the performance of the algorithm depends on the evolutionary operations such as selection, variation and the like, the population number has obvious influence on iteration speed and frequency, the algorithm is easy to converge in premature, and the selection of key parameters of the algorithm has no clear standard.
The social spider optimization algorithm (social spider optimization, SSO) is a clustered intelligent evolution algorithm, has the advantages of good expansibility, high fault tolerance, strong adaptability, high speed, modular assembly, strong autonomy and the like, is widely used for optimizing problems in communication sensor positioning, pathology recognition and workshop scheduling operation, but has not been widely applied to power system optimization scheduling.
Disclosure of Invention
The invention aims to provide an energy-saving dispatching method for a power plant based on a social spider optimization algorithm, which is used for realizing the lowest total power generation coal consumption under the safe and reliable operation of a power system.
The technical scheme adopted by the invention is that the energy-saving scheduling method of the power plant based on the social spider optimization algorithm is implemented according to the following steps:
step 1, taking the lowest total power generation coal consumption of the power system as an optimization target, establishing an objective function, and establishing a power system operation constraint condition;
and 2, solving the minimum value of the objective function according to the social spider optimization algorithm under the limit of the established operation constraint condition of the power system to obtain the minimum power generation coal consumption of the power system.
The present invention is also characterized in that,
the objective function established in the step 1 is specifically:
step 1.1, calculating a coal consumption characteristic function of the thermal power generating unit, namely a power generation cost function:
wherein: f (F) ti (P Git ) The power generation coal consumption of the thermal power generating unit i is the period t; p (P) Git Active output of the thermal power generating unit i in a period t; a, a i 、b i 、c i The consumption characteristic coefficient of the corresponding unit i;
step 1.2, establishing an objective function:
wherein: t is the total number of scheduling periods, if static scheduling, t=1; n (N) G The total number of the units is set, and the valve point effect is further considered to establish a final objective function:
wherein: e (E) it Is the coal consumption of the ith unit caused by valve point effect in the t period; g i And h i The valve point effect is the corresponding effect coefficient; p (P) Gimin Is the minimum technical output of the ith unit;
and (3) utilizing a penalty function to process constraint conditions, and incorporating related problems of single unit load balance into an objective function of the total unit coal consumption characteristic of the system by a penalty function method, wherein the mathematical expression of the finally obtained objective function is as follows:
wherein: sigma (sigma) 1 Punishment for power balance constraintA penalty factor; sigma (sigma) 2 Penalty factors for inequality constraints; g i (x) For the ith inequality constraint, where n represents the inequality constraint number; h is a j (x) For the j-th equality constraint, where z represents the equality constraint number.
The operation constraint conditions of the electric power system in the step 1 comprise system power balance constraint, network loss constraint, unit operation constraint and unit output climbing constraint;
the system power balance constraint is:
wherein: p (P) Lt Is the total network loss of the system in the t-th period; p (P) Dt Is the total system load during the t-th period;
the network loss constraint is:
wherein: p (P) Gt Is N G An active power vector matrix formed by the generator sets;is P Gt Is a transposed matrix of (a); B. b (B) 0 And B 00 Is the correlation coefficient of the network loss; b is a dimension N G ×N G Is a vector matrix of (a); b (B) 0 Is N G Vector of dimension; b (B) 00 Is a constant coefficient;
the unit operation constraint is as follows:
P Gimin ≤P Git ≤P Gimax ，i＝1,2,3,…,N G (7)
wherein P is Gimin Is the minimum technical output of the ith machine unit, P Gimax Is the upper limit of the active output of the ith unit;
the unit output climbing constraint is as follows:
wherein: u (U) Gi Is the output acceleration extremum of the thermal power unit i, D Gi Is the output deceleration extremum of the thermal power unit i, P Gi(t-1) The active output of the thermal power unit i in the t-1 period is shown;
substituting h in (4) if the system power balance constraint, the network loss constraint, the unit operation constraint and the unit output climbing constraint are equality j (x) If the formula is inequality, substituting g in the formula (4) i (x) Is a kind of medium.
The step 2 is specifically as follows:
step 2.1, setting the number scale N of the spider population S, and determining the number of female and male spider seed populations, wherein the number of female and male individuals is N respectively f 、N m ，N f +N m Randomly initializing female and male population individuals, wherein each spider individual represents a different energy-saving scheduling scheme, setting maximum iteration number Maxiter, wherein the initial iteration number k=0, using the formula (4) as an objective function, and setting a problem dimension, namely the total number of units N G ；
Step 2.2, performing global search, and enabling k=k+1;
step 2.3, calculating the weights of all individuals in the population, sequencing from high to low, and recording the optimal value and position of the individuals with the highest weights;
step 2.4, establishing a female spider cooperation mechanism;
step 2.5, establishing a male spider cooperation mechanism;
step 2.6, performing mutation operation on the re-moved individuals, and performing random mating on the qualified spider individuals according to the mating radius;
step 2.7, reconstructing a female spider population;
step 2.8, if the current iteration number k is less than Maxiter, returning to the step 2.2; otherwise, outputting the current optimal solution and the corresponding objective function value to obtain the energy-saving scheduling scheme with the lowest total power generation coal consumption.
The setting method of the number of the male and female populations in the step 2.1 comprises the following steps:
N f ＝floor[(0.9-rand·0.25)·N]
N m ＝N-N f (9)
wherein: rand is [0,1]Random numbers randomly generated in the range; floor (·) represents the mapping function of the real number domain to the integer domain, N f Represents the number of male spiders, N m Represents the number of male spiders and N represents the number of individuals in the population, i.e. the population size.
The step 2.3 is specifically as follows:
step 2.3.1, calculating weights of all the individual spiders in the population, and weights w of spiders i i Calculated according to the following formula:
wherein: w (w) max Is the maximum value of the weight factors of the individuals of the previous generation; w (w) min Is the minimum value of the weight factors of the individuals of the previous generation; the item is the number of iterations currently being performed; maxiter is the maximum number of iterations; at the first iteration, i.e. when k=1, the initial weight parameters are set manually, randomly at [0,1 using the rand function]Randomly generating 10 groups of data in a range, taking out maximum and minimum values by using max and min functions, completing setting of first weight parameters, and calculating weights of individuals according to a formula (10) in each iteration;
and 2.3.2, after the weights of all the spider individuals are calculated, sorting the weights from high to low, and recording the optimal value and the position of the highest weight individual.
Step 2.4 is specifically: moving female spiders according to a female collaboration mechanism:
wherein alpha, beta and delta are amplification factors; s is S a 、S c 、S d Respectively represent spider a (S a ) Weights of (1), spider b (S) b ) Weight and female spider f (S f ) According to the formula(10) Calculating; i (S) i ) Representing any individual spider i in the population S of spiders; a (S) a ) Represents the distance spider i (S i ) Recently, and weight ratio i (S i ) Heavier spider individuals a; b (S) b ) A spider individual b having an optimal weight in the spider population S; f (S) f ) Representing the distance spider individuals a (S) a ) A nearest female spider individual f; PE is a random number between 0 and 1; k. k+1 each represents the number of iterations; f (f) i k Representing the specific position to which the ith female individual needs to be moved in the kth iteration, f i k+1 Representing the specific location to which the ith female individual needs to be moved in the k+1st iteration, viba i Representing individual a (S) a ) Vibration factor of Vibb i Representing individual b (S) b ) Is a vibration factor of (a);
step 2.5, establishing a male spider cooperation mechanism specifically comprises the following steps:
wherein:represents the specific position of the k+1st generation male individual, < >>Represents the specific location of the kth generation of male individuals; s is S d Representation and i (S) i ) The nearest female spider f (S f ) Weights of (2); />Is a weighted average of the corresponding male population M; />Weights of male individual i and male individual m, respectively, vibf i Representing individual f (S) f ) Is a vibration factor of (a);
the vibration factor is calculated according to the following formula:
(1) distance spider i (S) i ) Recently, and body weight ratio spider i (S i ) Heavier spider a (S a ) The emitted vibration quilt i (S i ) Perceived, individual a (S a ) Viba of vibration factor of (A) i Calculated as follows:
wherein: w (w) a A coefficient less than 1; d, d i,a Is spider i (S) i ) And spider a (S) a ) A two-norm distance therebetween;
(2) spider b (S) with optimal body weight in the population b ) Quilt i (S) i ) Perceived, b (S b ) Vibb of vibration factor (Vibb) i Calculated as follows:
wherein: w (w) b A coefficient less than 1; d, d i,b Is spider b (S) b ) Spider i (S) i ) A two-norm distance therebetween;
(3) distance spider i (S) i ) The nearest female spider f (S f ) Quilt i (S) i ) Perceived, f (S f ) Vibf of vibration factor (Vibf) i Calculated as follows:
wherein: w (w) f A coefficient less than 1; d, d i,f Is female spider f (S) f ) Spider i (S) i ) A two-norm distance therebetween.
Step 2.6 is specifically:
step 2.6.1, performing a mutation operation: the mutation operation is mainly to randomly change the positions of partial individuals in the male and female populations after the step 2.4 and the step 2.5 are performed so as to increase subsequent matingF after mutation operation i k+1 Instead of f in formula (11) i k+1 ；
Wherein: f (f) p ，f q Is any two different individuals in the female sub-population; t is a mutation correlation operator, is set to be dynamically adjusted, and the influence of a T value on mutation operation is positively correlated, so that the T value is changed from small to large in the whole execution process; k is the current iteration number;
step 2.6.2, determining a wedding radius: for a certain spider individual, only the different spider individuals within the radius are considered for wedding, otherwise, the different spider individuals are not considered;
wherein: r represents the mating radius of each individual; p (P) ihigh And P ihigh The upper and lower limits of the female spider perception range corresponding to the ith variable;
step 2.6.3, executing a random mating policy: carrying out random mating policy on individuals meeting marriage after mutation operation, and setting random mating probability P when executing the random mating policy s The male individuals are updated specifically as follows: using P s Multiplying by formula (12)Obtaining a new male individual, and then using the new male individual and the step 2.6.1 to obtain a female individual to mate according to the wedding radius;
wherein, random mating probability P s The calculation is carried out according to the following formula:
wherein: p (P) s Refers to random mating probability; maxiter is the maximum number of iterations.
Step 2.7 is specifically:
after the marriage is finished, new individuals with weight parameters are generated, the individuals subjected to weight sorting in the step 2.3.2 are compared with the new individual weights generated by the marriage, and the individuals with the minimum weights are eliminated; if the weight of the newly generated individuals is smaller, directly eliminating; if the parent individuals are less weighted, the new individuals are substituted and inherit the gender of the original individuals.
Step 2.8 is specifically:
judging whether the current execution iteration number k reaches the maximum iteration number Maxiter or not;
if not, judging the current power generation coal consumption F k Whether or not it is smaller than the power generation coal consumption F of the last iteration k-1 The method comprises the steps of carrying out a first treatment on the surface of the If the current power generation cost is smaller than the power generation coal consumption of the previous iteration, taking the output of each thermal power unit in the scheduling scheme corresponding to the current lowest coal consumption as the initial output of each thermal power unit, and repeating the steps 2.2-2.8; if the current power generation coal consumption F k Greater than the previous iteration of power generation coal consumption F k-1 And taking the constraint output of each thermal power unit corresponding to the power generation coal consumption of the previous iteration as the initial output of each thermal power unit, and repeating the steps 2.2-2.8.
If the current iteration number reaches the maximum iteration number, judging the current power generation coal consumption F k Whether or not it is smaller than the power generation coal consumption F of the last iteration k-1 The method comprises the steps of carrying out a first treatment on the surface of the If the current power generation coal consumption F k Less than the previous iteration of generating coal consumption F k-1 Outputting the current power generation coal consumption as an optimal objective function value, and outputting the output of each thermal power generating unit corresponding to the current lowest power generation coal consumption as an optimal scheduling scheme; if the current power generation coal consumption F k Greater than the previous iteration of power generation coal consumption F k-1 Outputting the lowest power generation coal consumption of the previous iteration as an optimal objective function value, and outputting the power generation coal consumption F of the previous iteration k-1 And the output of each corresponding thermal power generating unit is used as an optimal scheduling scheme.
The beneficial effects of the invention are as follows:
the invention relates to a power plant energy-saving scheduling method based on a social spider optimization algorithm, which optimizes the load distribution of a generator set in a power plant, fits a coal consumption characteristic curve of a total generator set of a power system, establishes an objective function equation, considers valve point effect, improves the capacity of searching a global optimal solution in the scheduling process through the social spider optimization algorithm, accelerates the convergence speed of the algorithm by utilizing linear piecewise weights until the optimal load distribution of each unit is found.
Drawings
FIG. 1 is a diagram of an optimal solution convergence process in a search space when the power plant energy-saving scheduling method based on a social spider optimization algorithm is adopted to perform actual power plant 5-machine static economic scheduling;
FIG. 2 is an iterative convergence graph of a power plant energy-saving scheduling method based on a social spider optimization algorithm for carrying out actual power plant 5-machine static economic scheduling;
FIG. 3 is a diagram of an optimal solution convergence process in a search space when the power plant energy-saving scheduling method based on the social spider optimization algorithm is adopted to perform IEEE10 dynamic economic scheduling;
FIG. 4 is an iterative convergence graph of IEEE10 dynamic economic dispatch by adopting the power plant energy-saving dispatch method based on the social spider optimization algorithm of the invention;
Detailed Description
The invention will be described in detail below with reference to the drawings and the detailed description.
The invention discloses a power plant energy-saving scheduling method based on a social spider optimization algorithm, which is implemented according to the following steps:
step 1, taking the lowest total power generation coal consumption of the power system as an optimization target, establishing an objective function, and establishing a power system operation constraint condition;
the objective function is established specifically as follows:
step 1.1, calculating a coal consumption characteristic function of the thermal power generating unit, namely a power generation cost function:
wherein: f (F) ti (P Git ) The power generation coal consumption of the thermal power generating unit i is the period t; p (P) Git Active output of the thermal power generating unit i in a period t; a, a i 、b i 、c i The consumption characteristic coefficient of the corresponding unit i;
step 1.2, establishing an objective function:
wherein: t is the total number of scheduling periods, if static scheduling, t=1; n (N) G Is the total number of the machine sets,
in the actual operation of each unit of the power plant, as the steam supply quantity is regulated in real time, the corresponding steam regulating valve can cause the loss of the steam quantity at the moment of opening, the fluctuation of up-down waves can appear in the corresponding unit energy consumption characteristic curve, and the phenomenon is the valve point effect, so that the valve point effect is further considered to establish a final objective function:
wherein: e (E) it Is the coal consumption of the ith unit caused by valve point effect in the t period; g i And h i The valve point effect is the corresponding effect coefficient; p (P) Gimin Is the minimum technical output of the ith unit;
and (3) utilizing a penalty function to process constraint conditions, and incorporating related problems of single unit load balance into an objective function of the total unit coal consumption characteristic of the system by a penalty function method, wherein the mathematical expression of the finally obtained objective function is as follows:
wherein: sigma (sigma) 1 Penalty factors for power balance constraints; sigma (sigma) 2 Penalty factors for inequality constraints; g i (x) For the ith inequality constraint, where n represents the inequality constraint number; h is a j (x) For the j-th equality constraint, where z represents the equality constraint number.
The operation constraint conditions of the electric power system in the step 1 comprise system power balance constraint, network loss constraint, unit operation constraint and unit output climbing constraint;
the system power balance constraint is:
wherein: p (P) Lt Is the total network loss of the system in the t-th period; p (P) Dt Is the total system load during the t-th period;
the network loss constraint is:
wherein: p (P) Gt Is N G An active power vector matrix formed by the generator sets;is P Gt Is a transposed matrix of (a); B. b (B) 0 And B 00 Is the correlation coefficient of the network loss; b is a dimension N G ×N G Is a vector matrix of (a); b (B) 0 Is N G Vector of dimension; b (B) 00 Is a constant coefficient;
the unit operation constraint is as follows:
P Gimin ≤P Git ≤P Gimax ，i＝1,2,3,…,N G (7)
wherein P is Gimin Is the minimum technical output of the ith machine unit, P Gimax Is the upper limit of the active output of the ith unit;
the unit output climbing constraint is as follows:
wherein: u (U) Gi Is the output acceleration extremum of the thermal power unit i, D Gi Is the output deceleration extremum of the thermal power unit i, P Gi(t-1) The active output of the thermal power unit i in the t-1 period is shown;
substituting h in (4) if the system power balance constraint, the network loss constraint, the unit operation constraint and the unit output climbing constraint are equality j (x) If the formula is inequality, substituting g in the formula (4) i (x) In (a) and (b);
step 2, solving the minimum value of the objective function according to the social spider optimization algorithm under the limit of the established operation constraint condition of the power system to obtain the minimum power generation coal consumption of the power system; the method comprises the following steps:
in a social spider optimization algorithm, the search space of an optimization problem is formed into a spatial spider web, each position on the spider web represents a scheduling scheme of the optimization problem, the corresponding objective function value is F, and all scheduling schemes have corresponding positions on the spider web. Spider webs are also propagation media of vibration, each spider has its own position on the spider web, and the quality or fitness of the solution directly reflects the merits of objective function values and is expressed as the likelihood of finding a food source at the current position;
step 2.1, setting the number scale N of the spider population S, and determining the number of female and male spider seed populations, wherein the number of female and male individuals is N respectively f 、N m ，N f +N m Randomly initializing female and male population individuals, wherein each spider individual represents a different energy-saving scheduling scheme, setting maximum iteration number Maxiter, wherein the initial iteration number k=0, using the formula (4) as an objective function, and setting a problem dimension, namely the total number of units N G The method comprises the steps of carrying out a first treatment on the surface of the The setting method of the number of the male and female populations comprises the following steps:
N f ＝floor[(0.9-rand·0.25)·N]
N m ＝N-N f (9)
wherein: rand is [0,1]Random numbers randomly generated in the range; floor (·) represents the mapping function of the real number domain to the integer domain, N f Represents the number of male spiders, N m Representing the number of male spiders, N representing the number of individuals in the population, i.e., the population size;
step 2.2, performing global search, and enabling k=k+1;
step 2.3, calculating the weights of all individuals in the population, sequencing from high to low, and recording the optimal value and position of the individuals with the highest weights; the method comprises the following steps:
and 2.3.1, calculating weights of all spider individuals in the population, wherein the weights are indexes for measuring the activity and the viability of the individuals in biology. In the social spider optimization algorithm, each spider is given a weight that characterizes the merits of individual spiders i. In order to further improve the shortcomings of the original algorithm about weight processing, simultaneously meet different requirements of the algorithm on weights in different execution stages and improve the convergence of the algorithm, the invention designs a dynamic weight factor which gradually reduces along with the increase of iteration times to replace a later weight setting method in the original algorithm, and the weight w of the spider i i Calculated according to the following formula:
wherein: w (w) max Is the maximum value of the weight factors of the individuals of the previous generation; w (w) min Is the minimum value of the weight factors of the individuals of the previous generation; the item is the number of iterations currently being performed; maxiter is the maximum number of iterations; at the first iteration, i.e. when k=1, the initial weight parameters are set manually, randomly at [0,1 using the rand function]Randomly generating 10 groups of data in a range, taking out maximum and minimum values by using max and min functions, completing setting of first weight parameters, and calculating weights of individuals according to a formula (10) in each iteration;
the algorithm is to find the optimal value continuously in an iterative mode, and the position of the heaviest individual spider is the solution of the optimization problem. Assuming that the entire search space is a spider network, each potential scheduling scheme F is the location of the spider in the search space. According to the search mechanism of male and female, each individual belongs to two different evolutionary operators, and imitates different cooperative behaviors in a group;
and 2.3.2, after the weights of all the spider individuals are calculated, sorting the weights from high to low, and recording the optimal value and the position of the highest weight individual.
Step 2.4, establishing a female spider cooperation mechanism; the method comprises the following steps: moving female spiders according to a female collaboration mechanism:
wherein alpha, beta and delta are amplification factors; s is S a 、S c 、S d Respectively represent spider a (S a ) Weights of (1), spider b (S) b ) Weight and female spider f (S f ) Is calculated according to formula (10); i (S) i ) Representing any individual spider i in the population S of spiders; a (S) a ) Represents the distance spider i (S i ) Recently, and weight ratio i (S i ) Heavier spider individuals a; b (S) b ) A spider individual b having an optimal weight in the spider population S; f (S) f ) Representing the distance spider individuals a (S) a ) A nearest female spider individual f; PE is a random number between 0 and 1; k. k+1 each represents the number of iterations; f (f) i k Representing the specific position to which the ith female individual needs to be moved in the kth iteration, f i k+1 Representing the specific location to which the ith female individual needs to be moved in the k+1st iteration, viba i Representing individual a (S) a ) Vibration factor of Vibb i Representing individual b (S) b ) Is a vibration factor of (a);
step 2.5, establishing a male spider cooperation mechanism; establishing a male spider collaboration mechanism:
wherein:represents the specific position of the k+1st generation male individual, < >>Represents the specific location of the kth generation of male individuals; s is S d Representation and i (S) i ) The nearest female spider f (S f ) Weights of (2); />Is a weighted average of the corresponding male population M; />Weights of male individual i and male individual m, respectively, vibf i Representing individual f (S) f ) Is a vibration factor of (a);
in female co-operation mechanisms related settings of vibration factors are involved, since the spider web is a propagation medium for vibrations, the spider can move freely on the spider web, but cannot leave the spider web, since areas outside the spider web are not viable solutions to the optimization problem. When a spider moves to a new position, it will generate vibrations and propagate on the spider web, each of which holds information about a spider, and the other spiders can obtain this information after receiving the vibrations, the calculation formula of the vibration factor Vibfi of spider i is as follows:
wherein: w (w) f Is a constant; d, d i,j Is the two-norm distance between spiders i and j;
in order to eliminate excessive schemes which do not need to be considered in actual conditions, the type of the vibration factor is targeted according to an algorithmThe invention is based on the formulaThree vibration conditions are mainly considered:
the vibration factor is calculated according to the following formula:
(1) distance spider i (S) i ) Recently, and body weight ratio spider i (S i ) Heavier spider a (S a ) The emitted vibration quilt i (S i ) Perceived, individual a (S a ) Viba of vibration factor of (A) i Calculated as follows:
wherein: w (w) a A coefficient less than 1; d, d i,a Is spider i (S) i ) And spider a (S) a ) A two-norm distance therebetween;
(2) spider b (S) with optimal body weight in the population b ) Quilt i (S) i ) Perceived, b (S b ) Vibb of vibration factor (Vibb) i Calculated as follows:
wherein: w (w) b A coefficient less than 1; d, d i,b Is spider b (S) b ) Spider i (S) i ) A two-norm distance therebetween;
(3) distance spider i (S) i ) The nearest female spider f (S f ) Quilt i (S) i ) Perceived, f (S f ) Vibf of vibration factor (Vibf) i Calculated as follows:
wherein: w (w) f A coefficient less than 1; d, d i,f Is female spider f (S) f ) Spider i (S) i ) A two-norm distance therebetween.
Step 2.6, performing mutation operation on the re-moved individuals, and performing random mating on the qualified spider individuals according to the mating radius; the method comprises the following steps:
step 2.6.1, performing a mutation operation: the mutation operation is mainly to randomly change the positions of partial individuals in the male and female populations after the steps 2.4 and 2.5 are performed so as to increase a plurality of possible situations of subsequent mating, and f is after the mutation operation i k+1 Instead of f in formula (11) i k+1 ；
Wherein: f (f) p ，f q Is any two different individuals in the female sub-population; t is a mutation correlation operator, is set to be dynamically adjusted, and the influence of a T value on mutation operation is positively correlated, so that the T value is changed from small to large in the whole execution process; k is the current iteration number;
step 2.6.2, determining a wedding radius: for a certain spider individual, only the different spider individuals within the radius are considered for wedding, otherwise, the different spider individuals are not considered;
wherein: r represents the mating radius of each individual; p (P) ihigh And P ihigh The upper and lower limits of the female spider perception range corresponding to the ith variable;
step 2.6.3, executing a random mating policy: carrying out random mating policy on individuals meeting marriage after mutation operation, and setting random mating probability P when executing the random mating policy s The male individuals are updated specifically as follows: using P s Multiplying by formula (12)Obtaining a new male individual, and then using the new male individualAnd step 2.6.1, obtaining female individuals to mate according to the wedding radius;
wherein, random mating probability P s The calculation is carried out according to the following formula:
wherein: p (P) s Refers to random mating probability; maxiter is the maximum number of iterations;
step 2.7, reconstructing a female spider population; the method comprises the following steps:
after the marriage is finished, new individuals with weight parameters are generated, the individuals subjected to weight sorting in the step 2.3.2 are compared with the new individual weights generated by the marriage, and the individuals with the minimum weights are eliminated; if the weight of the newly generated individuals is smaller, directly eliminating; if the parent individuals are less weighted, the new individuals are used for replacing the parent individuals, and the sexes of the original individuals are inherited;
step 2.8, if the current iteration number k is less than Maxiter, returning to the step 2.2; otherwise, outputting the current optimal solution and the corresponding objective function value thereof to obtain an energy-saving scheduling scheme with the lowest total power generation coal consumption, which is specifically as follows:
judging whether the current execution iteration number k reaches the maximum iteration number Maxiter or not;
if not, judging the current power generation coal consumption F k Whether or not it is smaller than the power generation coal consumption F of the last iteration k-1 The method comprises the steps of carrying out a first treatment on the surface of the If the current power generation cost is smaller than the power generation coal consumption of the previous iteration, taking the output of each thermal power unit in the scheduling scheme corresponding to the current lowest coal consumption as the initial output of each thermal power unit, and repeating the steps 2.2-2.8; if the current power generation coal consumption F k Greater than the previous iteration of power generation coal consumption F k-1 And taking the constraint output of each thermal power unit corresponding to the power generation coal consumption of the previous iteration as the initial output of each thermal power unit, and repeating the steps 2.2-2.8.
If the current iteration number reaches the maximum iteration number, judging the current power generation coal consumption F k Whether or not it is smaller than the power generation coal consumption F of the last iteration k-1 The method comprises the steps of carrying out a first treatment on the surface of the If the current power generation coal consumption F k Less than the previous iteration of generating coal consumption F k-1 Outputting the current power generation coal consumption as an optimal objective function value, and outputting the output of each thermal power generating unit corresponding to the current lowest power generation coal consumption as an optimal scheduling scheme; if the current power generation coal consumption F k Greater than the previous iteration of power generation coal consumption F k-1 Outputting the lowest power generation coal consumption of the previous iteration as an optimal objective function value, and outputting the power generation coal consumption F of the previous iteration k-1 And the output of each corresponding thermal power generating unit is used as an optimal scheduling scheme.
The method is implemented by an actual power plant 5 machine system, an IEEE10 dynamic economic dispatch test system and a wind-fire combined power system.
Example 1
And carrying out power plant energy-saving dispatching optimization on an actual power plant 5-machine system by using a social spider optimization algorithm, and comparing the power plant energy-saving dispatching optimization with the existing optimization result, wherein the system data are shown in a table 1. The upper limit of operation of each unit is 600MW, the lower limit is 240MW, and the total load is 2374.63MW, 2469.94MW and 2718.88MW respectively. The embodiment has actual operation data support, and a more accurate fitting cubic function unit consumption characteristic function formula is used for calculation, wherein the formula is as follows:
y i ＝a i P 3 +b i P 2 +c i P+d i (21)
TABLE 1 actual plant 5 machine System related test data
The optimal scheduling schemes for different algorithm solutions are shown in table 2:
table 2 optimization comparison of three loads for three methods
Environmental and economic indicators at 2469.94MW and 2718.88MW loads are shown in Table 3.
Table 3 environmental and economic indicators at 2469.94MW and 2718.88MW loads
As shown in fig. 1-2, respectively, an optimal solution convergence process diagram and an iterative convergence graph diagram in a search space when the power plant energy-saving scheduling method based on the social spider optimization algorithm is adopted to perform the actual power plant 5-machine static economic scheduling, and fig. 1 illustrates a space 3D iterative process of the optimal solution in a population iterative process and a specific space coordinate of the optimal solution finally converged. Fig. 2 illustrates a specific variation curve of the optimal solution as the number of iterations increases, and the convergence effect of the surface of the curve is good and rapid.
Example 2
Taking an IEEE10 machine test system as an example, taking the coupling relation between adjacent time segments of the machine sets into consideration, and taking the valve point effect into consideration, carrying out optimization test on the dynamic economic dispatch of the power system of 10 machine sets. The system technical parameters are shown in tables 4 and 6, and the load requirements are shown in table 5.
TABLE 4 dynamic economic dispatch 10 Unit related parameters
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TABLE 4 dynamic economic dispatch 10 Unit related parameters
Table 56 time period dynamic economic scheduling of individual time period load demands
The optimization result of the method for 6-period dynamic economic dispatch is shown in table 6:
TABLE 6 method 6 time period dynamic economic dispatch optimization results of the invention
TABLE 7 comparison of the optimization results of the inventive method with other algorithms
As shown in fig. 3-4, respectively, an optimal solution convergence process diagram and an iterative convergence graph in a search space when the power plant energy-saving scheduling method based on the social spider optimization algorithm is adopted to perform IEEE10 dynamic economic scheduling, and fig. 3 illustrates a spatial 3D iteration process of the optimal solution in a population iteration process and a specific spatial coordinate of the optimal solution converged finally. Fig. 4 illustrates a specific variation curve of the optimal solution as the number of iterations increases, and the convergence effect of the curve surface is good and rapid.
From tables 2 and 3, it can be analyzed that: under the condition that the three types of load demands are gradually increased, the method has superiority compared with the performance of other two types of optimization algorithms when the load is at the minimum. The optimizing effect is better under the condition of heavier load, and under the condition of heavy load, the optimizing performance even exceeds the unit coal consumption under the condition of low load and medium load, and the optimizing performance curve has outstanding effect under the condition of medium load or heavy load. The method has the advantages that under low load, the large-capacity thermal power generating unit does not need excessive adjustment, the thermal power generating unit needs to be completely output and operated under full load, and a larger adjustment and optimization space is provided under middle load, so that the stronger global searching capability of the method is fully exerted, and a better scheduling scheme is obtained.
Table 7 compares the method of the present invention with the optimized results of MVO algorithm, evolution planning algorithm and sequential quadratic programming method, and the scheduling scheme obtained by the method of the present invention saves 134.3802 tons of coal consumption compared with MVO, 101.7905 tons of coal consumption and 59.0923 tons of coal consumption compared with the evolution planning and sequential quadratic programming methods, respectively. It can be seen that the solution performance of the method of the invention is obviously optimal.
Claims (7)
1. The power plant energy-saving scheduling method based on the social spider optimization algorithm is characterized by comprising the following steps of:
step 1, taking the lowest total power generation coal consumption of the power system as an optimization target, establishing an objective function, and establishing a power system operation constraint condition;
step 2, solving the minimum value of the objective function according to the social spider optimization algorithm under the limit of the established operation constraint condition of the power system to obtain the minimum power generation coal consumption of the power system;
the objective function established in the step 1 specifically comprises the following steps:
step 1.1, calculating a coal consumption characteristic function of the thermal power generating unit, namely a power generation cost function:
wherein: f (F) ti (P Git ) The power generation coal consumption of the thermal power generating unit i is the period t; p (P) Git Active output of the thermal power generating unit i in a period t; a, a i 、b i 、c i The consumption characteristic coefficient of the corresponding unit i;
step 1.2, establishing an objective function:
wherein: t is the total number of scheduling periods, if static scheduling, t=1; n (N) G Is the total number of the machine sets,
further considering the valve point effect, a final objective function is established:
wherein: e (E) it Is the coal consumption of the ith unit caused by valve point effect in the t period; g i And h i The valve point effect is the corresponding effect coefficient; p (P) Gimin Is the minimum technical output of the ith unit;
and (3) utilizing a penalty function to process constraint conditions, and incorporating related problems of single unit load balance into an objective function of the total unit coal consumption characteristic of the system by a penalty function method, wherein the mathematical expression of the finally obtained objective function is as follows:
wherein: sigma (sigma) 1 Penalty factors for power balance constraints; sigma (sigma) 2 Penalty factors for inequality constraints; g i (x) For the ith inequality constraint, where n represents the inequality constraint number; h is a j (x) For the j-th equality constraint, where z represents the equality constraint number;
the operation constraint conditions of the electric power system in the step 1 comprise system power balance constraint, network loss constraint, unit operation constraint and unit output climbing constraint;
the system power balance constraint is:
wherein: p (P) Lt Is the total network loss of the system in the t-th period; p (P) Dt Is the total system load during the t-th period;
the network loss constraint is:
wherein: p (P) Gt Is N G An active power vector matrix formed by the generator sets;is P Gt Is a transposed matrix of (a); B. b (B) 0 And B 00 As phase loss of networkA closing coefficient; b is a dimension N G ×N G Is a vector matrix of (a); b (B) 0 Is N G Vector of dimension; b (B) 00 Is a constant coefficient;
the unit operation constraint is as follows:
P Gimin ≤P Git ≤P Gimax ，i＝1,2,3,…,N G (7)
wherein P is Gimin Is the minimum technical output of the ith machine unit, P Gimax Is the upper limit of the active output of the ith unit;
the unit output climbing constraint is as follows:
wherein: u (U) Gi Is the output acceleration extremum of the thermal power unit i, D Gi Is the output deceleration extremum of the thermal power unit i, P Gi(t-1) The active output of the thermal power unit i in the t-1 period is shown;
substituting h in (4) if the system power balance constraint, the network loss constraint, the unit operation constraint and the unit output climbing constraint are equality j (x) If the formula is inequality, substituting g in the formula (4) i (x) In (a) and (b);
the step 2 specifically comprises the following steps:
step 2.1, setting the number scale N of the spider population S, and determining the number of female and male spider seed populations, wherein the number of female and male individuals is N respectively f 、N m ，N f +N m Randomly initializing female and male population individuals, wherein each spider individual represents a different energy-saving scheduling scheme, setting maximum iteration number Maxiter, wherein the initial iteration number k=0, using the formula (4) as an objective function, and setting a problem dimension, namely the total number of units N G ；
Step 2.2, performing global search, and enabling k=k+1;
step 2.3, calculating the weights of all individuals in the population, sequencing from high to low, and recording the optimal value and position of the individuals with the highest weights;
step 2.4, establishing a female spider cooperation mechanism;
step 2.5, establishing a male spider cooperation mechanism;
step 2.6, performing mutation operation on the re-moved individuals, and performing random mating on the qualified spider individuals according to the mating radius;
step 2.7, reconstructing a female spider population;
step 2.8, if the current iteration number k is less than Maxiter, returning to the step 2.2; otherwise, outputting the current optimal solution and the corresponding objective function value to obtain the energy-saving scheduling scheme with the lowest total power generation coal consumption.
2. The power plant energy-saving scheduling method based on the social spider optimization algorithm according to claim 1, wherein,
the setting method of the number of the male and female populations in the step 2.1 comprises the following steps:
N f ＝floor[(0.9-rand·0.25)·N]
N m ＝N-N f (9)
wherein: rand is [0,1]Random numbers randomly generated in the range; floor (·) represents the mapping function of the real number domain to the integer domain, N f Represents the number of male spiders, N m Represents the number of male spiders and N represents the number of individuals in the population, i.e. the population size.
3. The power plant energy-saving scheduling method based on the social spider optimization algorithm according to claim 1, wherein the step 2.3 is specifically:
step 2.3.1, calculating weights of all the individual spiders in the population, and weights w of spiders i i Calculated according to the following formula:
wherein: w (w) max Is the maximum value of the weight factors of the individuals of the previous generation; w (w) min Is the minimum value of the weight factors of the individuals of the previous generation; the item is the number of iterations currently being performed; maxiter is the maximum iterationThe number of times; at the first iteration, i.e. when k=1, the initial weight parameters are set manually, randomly at [0,1 using the rand function]Randomly generating 10 groups of data in a range, taking out maximum and minimum values by using max and min functions, completing setting of first weight parameters, and calculating weights of individuals according to a formula (10) in each iteration;
and 2.3.2, after the weights of all the spider individuals are calculated, sorting the weights from high to low, and recording the optimal value and the position of the highest weight individual.
4. The power plant energy-saving scheduling method based on the social spider optimization algorithm according to claim 3, wherein the step 2.4 is specifically: moving female spiders according to a female collaboration mechanism:
wherein alpha, beta and delta are amplification factors; s is S a 、S c 、S d Respectively represent spider a (S a ) Weights of (1), spider b (S) b ) Weight and female spider f (S f ) Is calculated according to formula (10); i (S) i ) Representing any individual spider i in the population S of spiders; a (S) a ) Represents the distance spider i (S i ) Recently, and weight ratio i (S i ) Heavier spider individuals a; b (S) b ) A spider individual b having an optimal weight in the spider population S; f (S) f ) Representing the distance spider individuals a (S) a ) A nearest female spider individual f; PE is a random number between 0 and 1; k. k+1 each represents the number of iterations; f (f) i k Representing the specific position to which the ith female individual needs to be moved in the kth iteration, f i k+1 Representing the specific location to which the ith female individual needs to be moved in the k+1st iteration, viba i Representing individual a (S) a ) Vibration factor of Vibb i Representing individual b (S) b ) Is a vibration factor of (a);
the step 2.5 male spider collaboration mechanism:
wherein:represents the specific position of the k+1st generation male individual, < >>Represents the specific location of the kth generation of male individuals; s is S d Representation and i (S) i ) The nearest female spider f (S f ) Weights of (2); />Is a weighted average of the corresponding male population M;weights of male individual i and male individual m, respectively, vibf i Representing individual f (S) f ) Is a vibration factor of (a);
the vibration factor is calculated according to the following formula:
(1) distance spider i (S) i ) Recently, and body weight ratio spider i (S i ) Heavier spider a (S a ) The emitted vibration quilt i (S i ) Perceived, individual a (S a ) Viba of vibration factor of (A) i Calculated as follows:
wherein: w (w) a A coefficient less than 1; d, d i,a Is spider i (S) i ) And spider a (S) a ) A two-norm distance therebetween;
(2) spider b (S) with optimal body weight in the population b ) Quilt i (S) i ) Perceived, b (S b ) Vibb of vibration factor (Vibb) i Calculated as follows:
wherein: w (w) b A coefficient less than 1; d, d i,b Is spider b (S) b ) Spider i (S) i ) A two-norm distance therebetween;
(3) distance spider i (S) i ) The nearest female spider f (S f ) Quilt i (S) i ) Perceived, f (S f ) Vibf of vibration factor (Vibf) i Calculated as follows:
wherein: w (w) f A coefficient less than 1; d, d i,f Is female spider f (S) f ) Spider i (S) i ) A two-norm distance therebetween.
5. The power plant energy-saving scheduling method based on the social spider optimization algorithm according to claim 4, wherein the step 2.6 is specifically:
step 2.6.1, performing a mutation operation: the mutation operation is mainly to randomly change the positions of partial individuals in the male and female populations after the steps 2.4 and 2.5 are performed so as to increase a plurality of possible situations of subsequent mating, and f is after the mutation operation i k+1 Instead of f in formula (11) i k+1 ；
Wherein: f (f) p ，f q Is any two different individuals in the female sub-population; t is a mutation correlation operator, is set to be dynamically adjusted, and the influence of a T value on mutation operation is positively correlated, so that the T value is changed from small to large in the whole execution process; k is the current iteration number;
step 2.6.2, determining a wedding radius: for a certain spider individual, only the different spider individuals within the radius are considered for wedding, otherwise, the different spider individuals are not considered;
wherein: r represents the mating radius of each individual; p (P) ihigh And P ihigh The upper and lower limits of the female spider perception range corresponding to the ith variable;
step 2.6.3, executing a random mating policy: carrying out random mating policy on individuals meeting marriage after mutation operation, and setting random mating probability P when executing the random mating policy s The male individuals are updated specifically as follows: using P s Multiplying by formula (12)Obtaining a new male individual, and then using the new male individual and the step 2.6.1 to obtain a female individual to mate according to the wedding radius;
wherein, random mating probability P s The calculation is carried out according to the following formula:
wherein: p (P) s Refers to random mating probability; maxiter is the maximum number of iterations.
6. The power plant energy-saving scheduling method based on the social spider optimization algorithm according to claim 5, wherein the step 2.7 is specifically:
after the marriage is finished, new individuals with weight parameters are generated, the individuals subjected to weight sorting in the step 2.3.2 are compared with the new individual weights generated by the marriage, and the individuals with the minimum weights are eliminated; if the weight of the newly generated individuals is smaller, directly eliminating; if the parent individuals are less weighted, the new individuals are substituted and inherit the gender of the original individuals.
7. The power plant energy-saving scheduling method based on the social spider optimization algorithm according to claim 6, wherein the step 2.8 is specifically:
judging whether the current execution iteration number k reaches the maximum iteration number Maxiter or not;
if not, judging the current power generation coal consumption F k Whether or not it is smaller than the power generation coal consumption F of the last iteration k-1 The method comprises the steps of carrying out a first treatment on the surface of the If the current power generation cost is smaller than the power generation coal consumption of the previous iteration, taking the output of each thermal power unit in the scheduling scheme corresponding to the current lowest coal consumption as the initial output of each thermal power unit, and repeating the steps 2.2-2.8; if the current power generation coal consumption F k Greater than the previous iteration of power generation coal consumption F k-1 Taking the constraint output of each thermal power generating unit corresponding to the previous iteration of power generation coal consumption as the initial output of each thermal power generating unit, and repeating the steps 2.2-2.8;
if the current iteration number reaches the maximum iteration number, judging the current power generation coal consumption F k Whether or not it is smaller than the power generation coal consumption F of the last iteration k-1 The method comprises the steps of carrying out a first treatment on the surface of the If the current power generation coal consumption F k Less than the previous iteration of generating coal consumption F k- 1, outputting the current power generation coal consumption as an optimal objective function value, and outputting the output of each thermal power generating unit corresponding to the current lowest power generation coal consumption as an optimal scheduling scheme; if the current power generation coal consumption F k Greater than the previous iteration of power generation coal consumption F k-1 Outputting the lowest power generation coal consumption of the previous iteration as an optimal objective function value, and outputting the power generation coal consumption F of the previous iteration k-1 And the output of each corresponding thermal power generating unit is used as an optimal scheduling scheme.
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