CN112016207B - Economic load distribution optimization method for generator set - Google Patents

Economic load distribution optimization method for generator set Download PDF

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CN112016207B
CN112016207B CN202010882769.6A CN202010882769A CN112016207B CN 112016207 B CN112016207 B CN 112016207B CN 202010882769 A CN202010882769 A CN 202010882769A CN 112016207 B CN112016207 B CN 112016207B
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李玲玲
郑胜杰
王汝靖
张淇瑞
郑颖
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Abstract

The invention aims to overcome the defects of the prior art and provides an economic load distribution optimization method of a generator set, wherein the constraint conditions in the economic load distribution problem of the generator set comprise the following steps: the method comprises the following steps of power balance constraint, generator set output power constraint, slope rate constraint, forbidden operation area constraint and the like, wherein under the combined action of the constraints, the problem of economic load distribution optimization of the generator set is changed into a complex multi-constraint problem, and the difficulty of economic load distribution of the generator set is increased; the method adopts the improved manta ray foraging algorithm to solve the problem of economic load distribution of a complex and high-dimensional generator set, is not limited by the dimension of a target function, and can solve the optimization problems of nonlinearity, non-convexity, discontinuity and infinitesimal property; the inertial weight w is introduced into the classic bat ray foraging algorithm, the sine and cosine self-adaptation and differential variation strategies are improved, and compared with other optimization methods, the optimization capability, the convergence speed and the quality of the optimal solution of the improved bat ray foraging algorithm are improved, the power generation cost is minimized, and the resource utilization rate is improved.

Description

Economic load distribution optimization method for generator set
Technical Field
The invention belongs to the technical field of power systems, and particularly relates to an economic load distribution optimization method for a generator set.
Background
The economic load distribution optimization method is a distribution optimization method which distributes power generation tasks to each power generator on the premise of meeting various constraint conditions so as to minimize the power generation cost.
With the rapid increase of world economy, the demand of various industries on electric energy is increasing day by day, the installed capacity of the generator set of the power system is increasing continuously, and the reasonable distribution of the economic load of the power system has important significance for improving the resource utilization rate, reducing the operation cost of the power system and protecting the environment. The reasonable load distribution and the unit power generation task arrangement in the power system can not only reduce the economic cost, but also improve the production efficiency, and the larger the system scale is, the more obvious the improvement degree is. In the early economic load distribution, a provincial dispatching mechanism transmits a power generation requirement to a generator set according to the available capacity of a power plant, the maintenance condition of the generator set, the preparation condition of power generation raw materials such as coal and the like, the economic performance of the generator set and other practical conditions. After the electric power production is marketized, the load distribution mode becomes more flexible, and meanwhile, the difficulty of reasonable load distribution is increased due to the problems of valve point effect, slope rate constraint, forbidden operation area constraint and the like involved in the load distribution. For this reason, economic load distribution can be regarded as a multi-constraint optimization problem whose optimization goal is to minimize the total generation cost of the electrical energy production unit.
The economic load distribution problem is a complex multidimensional problem, and is converted into a multidimensional, non-convex, discontinuous and non-differentiable multi-constraint problem due to the combined action of conditions such as a generator set valve point effect, slope rate limitation, operation forbidden areas and the like, so that the difficulty in solving the economic load distribution is increased. At present, two main ways for solving the economic load distribution are provided, one is a traditional optimization method, the traditional mathematical optimization method is used for solving by simplifying an economic load distribution objective function and constraint conditions, and the other is a method for solving the complex multidimensional economic load distribution problem by using a meta-heuristic algorithm. The traditional optimization method is to simplify the cost function of economic load distribution into a quadratic function and ignore the sinusoidal component in the cost function, so that the complex, non-convex and discontinuous cost function is converted into a smooth cost function, and the smooth cost function can be solved by using mathematical methods such as an iteration method, a gradient method, a quadratic programming method and the like. The metaheuristic algorithm has excellent optimization capability and is not limited by the dimension of the target function, and can solve the problems of non-linearity, non-convexity and non-differentiable optimization. These advantages of the meta-heuristic algorithm can make up for the disadvantages of the conventional optimization method, so that the meta-heuristic algorithms such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), etc. are gradually applied to the problem of economic load distribution. However, the meta-heuristic algorithm has a good or bad optimizing result when solving the economic load distribution problem with different constraints, so the algorithm needs to be improved, so that the algorithm can be suitable for the economic load distribution problem under various constraint conditions.
In summary, for the different types of economic load distribution problems, whether the optimization capability of the traditional optimization algorithm or the meta-heuristic algorithm is good or bad, it is very unfavorable for protecting the environment, improving the resource utilization rate and reducing the operation cost of the power system.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an economic load distribution optimization method of a generator set, wherein the constraint conditions in the economic load distribution problem of the generator set comprise the following steps: the method comprises the following steps of power balance constraint, generator set output power constraint, slope rate constraint, forbidden operation area constraint and the like, wherein the economic load optimization problem is changed into a complex multi-constraint problem under the combined action of the constraints, so that the difficulty of economic load distribution is increased; the method adopts the improved manta ray foraging algorithm to solve the problem of complex and high-dimensional economic load distribution, is not limited by the dimension of a target function, and can solve the optimization problems of nonlinearity, non-convexity, discontinuity and infinitesimal property; the inertial weight w, sine and cosine adaptive factors and a differential variation strategy are introduced into the classic manta ray foraging algorithm to be improved, and compared with other optimization methods, the optimization capability, the convergence speed and the quality of the optimal solution of the improved manta ray foraging algorithm are improved, the power generation cost is minimized, and the resource utilization rate is improved.
The technical scheme adopted by the invention for solving the technical problem is as follows: an economic load distribution optimization method for a generator set comprises the following steps:
step one, establishing a normal operation constraint condition of a generator set according to the operation requirement of a power system
(1.1) establishing equality constraint of normal operation of the generator set
Figure BSA0000217970560000021
Wherein d is the number of generators in the generator set, PiThe output power of the ith generator is in the dimension of MW; pjThe output power of the jth generator is MW; pDThe dimension of the total load demand of the power system is MW; pLLine loss of power system is measured in MW, PLThe method is mainly determined by the output power of a generator set and a topological structure of a power transmission network; b isij、B0i、B00The system power transmission loss coefficient;
here, the total output power of the generator set
Figure BSA0000217970560000022
Should correspond to the total load P of the power system in the distribution rangeDAnd line loss PLMatching, so the equation of equilibrium for power shown in equation (1) belongs to the equality constraint;
(1.2) establishing three inequality constraints of the generator set on the output power, the slope rate of the generator set and the forbidden operation area
An inequality constraint of the output power of the generator set is established, and the method comprises the following steps:
Figure BSA0000217970560000023
in the formula (I), the compound is shown in the specification,
Figure BSA0000217970560000024
is the minimum output power, P, of the ith generatoriIs the output power of the ith generator,
Figure BSA0000217970560000025
the maximum output power of the ith generator;
the generator set output power constraint shown in the formula (2) belongs to inequality constraint, because the output power of each generator in normal operation must be between the maximum value and the minimum value, and the aging of the generator is accelerated when the output power exceeds the maximum value, so that the service life of the generator is shortened; the generator with too low output power is not fully utilized, so that resource waste is caused;
establishing a slope rate constraint of the output power of the generator set, wherein the method comprises the following steps:
Figure BSA0000217970560000031
in the formula, PiFor the output power of the ith generator at the current moment,
Figure BSA0000217970560000032
is the output power of the ith generator at the last moment, d is the number of generators in the generator set, URiRepresents the upper limit of the increase of the generated power of the ith generator per unit time, DRiAn upper limit of the reduction amount of the generated power of the ith generator in unit time;
establishing the forbidden operation area constraint of the output power of the generator set, wherein the method comprises the following steps:
Figure BSA0000217970560000033
in the formula, NPZiThe number of the operation forbidden areas of the ith generator in the generator set, d is the number of the generators in the generator set,
Figure BSA0000217970560000034
for the lower bound of the jth forbidden operating zone for the ith generator in the genset,
Figure BSA0000217970560000035
the upper boundary of the jth operation forbidden area of the ith generator in the generator set is set;
the constraint of the forbidden operation area of the output power of each generator in the generator set shown in the formula (4) belongs to inequality constraint, because the forbidden operation area is set for protecting bearings of the generator or relevant auxiliary equipment, and the like, the generator is prevented from running in the forbidden operation area in order to prolong the service life of the generator;
step two, establishing an economic load distribution model of the power system generator set
Selecting the power generation cost of a power system as a target function, considering a valve point effect caused when an air inlet valve of a generator is suddenly opened, and generating the power generation cost under the condition of nonlinear output of the generator as shown in the formula (5):
Figure BSA0000217970560000036
in the formula, FtRepresenting the cost function of the electricity generated by the generator set, PiRepresents the output power of the ith generator,
Figure BSA0000217970560000037
represents the minimum output power of the ith generator, ai、bi、ci、eiAnd fiRepresenting the fuel cost coefficient of the ith generator, wherein the first three coefficients form a smooth unary quadratic function, and the last two coefficients form an irreducible and non-convex function related to sine;
Figure BSA0000217970560000038
denotes fiAnd
Figure BSA0000217970560000039
the multiplication of (1);
step three, improving the foraging algorithm of the classical manta ray
The classic manta ray foraging algorithm comprises three foraging operations of linkage foraging, whirlwind foraging and tendon-turning foraging, the classic manta ray foraging algorithm is improved, a nonlinear inertia weight w, a self-adaptive change and a differential variation strategy are introduced on the basis of the classic algorithm, and the improvement method comprises the following steps:
(3.1) in the chain foraging operation, the current position of the manta ray individual is jointly determined by the positions of the previous generation individual and the current optimal individual, and the expression is as follows:
Figure BSA00002179705600000310
in the formula (I), the compound is shown in the specification,
Figure BSA00002179705600000311
and
Figure BSA00002179705600000312
the t generation and the t +1 generation of the individual bat ray xiA position parameter on d dimension, wherein the position of each individual bat ray is jointly determined by the d parameters; in the economic load distribution problem of the generating set, the position parameter of each individual manta ray represents an alternative solution of the problem, the dimension of each alternative solution is d, and
Figure BSA0000217970560000041
and
Figure BSA0000217970560000042
representing the output power of d generators in the generator set in t times and t +1 times of iterative calculations when the problem adopts an improved manta ray foraging algorithm;
Figure BSA0000217970560000043
the method is characterized in that the method is an optimal solution of an improved manta ray foraging algorithm in the position parameters of the t-th generation of the optimal manta ray individual, namely the t-th iterative calculation of the economic load distribution problem of a generator set; r is a real number interval [0, 1]]A random number of (c); n is the population scale of the improved manta ray foraging algorithm, namely the number of alternative solutions of the economic load distribution problem of the generator set; a isdFor chain foraging operation
Figure BSA0000217970560000044
And
Figure BSA0000217970560000045
right of connectionA weight coefficient of which the formula is
Figure BSA0000217970560000046
(3.2) the cyclonic foraging operation comprises: pure whirlwind foraging operation and exploration search space operation
The pure whirlwind foraging operation is that the modern individual bat ray follows the last individual bat ray in the bat population and moves to the current optimal individual, and the expression is as follows:
Figure BSA0000217970560000047
in the formula, betadFor simple whirlwind foraging operation
Figure BSA0000217970560000048
And
Figure BSA0000217970560000049
the connection weight coefficient of (2) is calculated as:
Figure BSA00002179705600000410
wherein r is a random number in a real number interval [0, 1], T is the current iterative computation time of the improved manta ray foraging algorithm, and T is the maximum iterative computation time;
the method is characterized in that nonlinear inertia weight w is introduced to improve the search space exploration operation, and comprises the following steps:
Figure BSA00002179705600000411
in the formula (I), the compound is shown in the specification,
Figure BSA00002179705600000412
to search for a random position in space, βdOperating to explore search spaces
Figure BSA00002179705600000413
And
Figure BSA00002179705600000414
r is [0, 1]]W is a nonlinear inertial weight and is expressed as:
Figure BSA00002179705600000415
wherein T and T are the current iteration number and the maximum iteration number, wminAnd wmaxFor the lower and upper limits of the inertial weight, the invention sets wmin0.2 and wmaxWhen 0.7, formula (10) is embodied as:
Figure BSA00002179705600000416
introducing a nonlinear inertia weight w in the exploration search space operation, and improving the global search capability and convergence accuracy of the algorithm through continuous adjustment of the nonlinear inertia weight w;
(3.3) introducing sine and cosine adaptive factors in the clamshell foraging operation to enhance the adaptive capacity of the improved manta ray foraging algorithm;
Figure BSA00002179705600000417
wherein C is a cosine adaptive factor, S is a sine adaptive factor, r1、r2、r3And r*Is [0, 1]]A random number in between;
(3.4) introducing a differential variation strategy, and performing variation, difference and selection operations on the obtained individual manta ray in each iteration process to obtain a new individual manta ray for next iteration calculation, so as to enhance the global optimization capability of the algorithm;
for the t generation of the optimal individual bat ray
Figure BSA0000217970560000051
Using a mutation vector
Figure BSA0000217970560000052
Making it generate variation for generating new individual bat ray x'i d(t) the method comprises:
Figure BSA0000217970560000053
in formula (II), x'i d(t) is a new individual bat ray generated by variation operation;
Figure BSA0000217970560000054
and
Figure BSA0000217970560000055
is a random individual in the t generation, r4And r5The random number is a maximum value of the population size N and a minimum value of 1;
Figure BSA0000217970560000056
is the optimal individual of the bat ray in the t generation; f is the scaling factor, F is [0.2, 0.8 ]]A random number in between;
an individual x 'of fresh manta ray generated after the mutation operation'i d(t) and individuals
Figure BSA0000217970560000057
Performing binomial cross operation to increase the population diversity, wherein the method comprises the following steps:
Figure BSA0000217970560000058
in the formula, x ″)i d(t) is an individual bat ray obtained after binomial cross operation; CR is cross probability and has a value range of [0, 1]]；r6Is [0, 1]]A random number in between; r is7Is a random number, the maximum value of which is the problem dimensionNumber d, minimum value 1;
constructing a fitness function, and converting the target function into the fitness function, wherein the method comprises the following steps:
Figure BSA0000217970560000059
in the formula (I), the compound is shown in the specification,
Figure BSA00002179705600000510
the position parameter of each individual bat ray is an alternative solution of the economic load distribution of a generator set for the ith individual bat ray in the tth generation;
Figure BSA00002179705600000511
the generating cost of the generating set is obtained by using the alternative solution corresponding to the ith individual bat ray in the tth generation;
Figure BSA00002179705600000512
generating set power generation cost maximum value corresponding to alternative solutions for all the individual bat ray in the tth generation;
selecting the optimal individual to reserve according to the fitness function value, wherein the method comprises the following steps:
Figure BSA00002179705600000513
in the formula (I), the compound is shown in the specification,
Figure BSA00002179705600000514
and f (x ″)i d(t)) is an individual bat ray calculated according to the formula (15)
Figure BSA00002179705600000515
And x ″)i d(t) fitness value;
step four, optimizing the load distribution of the generator set by adopting an improved manta ray foraging algorithm
(4.1) initializing the population position of the improved manta ray foraging algorithm, and setting the population size N to be 100 and the maximumThe large iteration number T is 1000, the cross probability CR is 0.2, and the upper and lower limits w of the inertia weightmax＝0.7、wmin＝0.2；
(4.2) starting iteration, generating a random number between [0, 1] by the Rand, and if the Rand is more than 0.5, executing the chain foraging operation by the current population according to the formula (6); if Rand is less than 0.5, generating a random number between [0, 1] by Rand, if T/T is greater than Rand, executing pure cyclone foraging operation according to formula (7) by the current population, and if T/T is less than Rand, executing exploration search space operation according to formula (9) by the current population; after one of a chain foraging operation, a simple cyclone foraging operation or a search space searching operation is executed, calculating individual fitness values in the bat ray population according to a formula (15), and selecting an individual with the largest fitness value as a current optimal individual;
(4.3) executing a tendon-turning foraging operation on the bat ray population according to the formula (12), calculating individual fitness values in the bat ray population according to the formula (15), and selecting the individual with the largest fitness value as a global optimal individual;
(4.4) carrying out differential variation operation on the obtained optimal individuals according to the formulas (13), (14) and (16), then calculating the fitness value of the individual of the bat ray population according to the formula (15), and selecting the individual with the maximum fitness value as a global optimal individual;
(4.5) judging whether the iteration times meet the requirements, namely judging whether T is more than or equal to T, if not, adding 1 to the iteration times T, and returning to the step (4.2) to enter the next iteration; if T is more than or equal to T, exiting iteration and outputting an optimal solution of the economic load distribution of the generator set;
the method of inputting data into a computer in the above-described steps is a known method; the computers, displays and MATLAB computer software used were all commercially available.
The invention has the beneficial effects that:
(1) the economic load distribution optimization method for the generator set can solve the problem of economic load distribution under various constraint conditions such as power balance constraint, output power constraint, slope rate constraint, forbidden operation area constraint and the like, the adaptive capacity, the local optimization capacity and the global optimization capacity of the improved manta ray foraging algorithm are improved, and compared with the existing method, the method has the advantages of higher convergence speed and better optimal solution quality.
(2) The method models the economic load distribution of the generator set in reality, solves the optimization problems of high dimension, nonlinearity, non-convexity and infinitesimal by using the meta-heuristic intelligent algorithm, and provides an effective solution for the economic load distribution of the generator set.
(3) According to the method, sine and cosine adaptive factors, nonlinear inertia weight w and a differential variation strategy are introduced on the basis of a classic manta ray foraging algorithm, so that the method is more suitable for the optimization problem of economic load distribution of a generator set. The inertia weight is introduced to improve the exploration search space operation, so that the global search capability of the algorithm is improved, and the convergence precision is improved; sine self-adaptation and cosine self-adaptation enhancement algorithm adaptation capacity is added in the process of the tumbling foraging; and finally introducing a differential variation strategy to perform variation, intersection and selection on the bat ray group in each iteration, so that the diversity of the group is enhanced, and the global search capability of the algorithm is improved. The improvements enable the improved manta ray foraging algorithm to have higher convergence speed and higher accuracy of solving the optimal solution compared with other meta-heuristic algorithms, are beneficial to economic load distribution of a generator set, reduce power generation cost and improve resource utilization rate.
Drawings
The invention is further illustrated with reference to the following figures and examples.
FIG. 1 is a schematic flow chart of an economic load distribution optimization method for a generator set according to the present invention.
Fig. 2 is a comparison graph of convergence curves of an improved manta ray foraging algorithm (IMRFO), a classical manta ray foraging algorithm (MRFO) and a Particle Swarm Optimization (PSO) in example 1.
Detailed Description
Fig. 1 shows that the program flow of the method for optimizing the economic load distribution of the generator set of the present invention is as follows: starting → establishing a constraint expression according to actual requirements → establishing an economic load distribution objective function → inputting a modified manta ray foraging algorithm parameter, a generator set parameter → starting iteration → Rand < 0.5? → N, performing chain foraging operation on the bat ray population; y, T/T < rand? → N, carrying out simple whirlwind foraging operation on the manta ray population; y, after performing one of exploration search space operation → performing chain foraging operation, exploration search space operation and simple whirlwind foraging operation on the bat ray population, calculating the fitness of individuals in the bat ray population, updating the optimal individuals → performing tendon-turning and fighting foraging operation on the bat ray population → introducing a differential variation strategy, performing variation, intersection and selection operation on the optimal individuals and updating individual values of the bat ray → calculating the individual fitness of the bat ray population and updating a global optimal value → T is more than or equal to T? → N, the number of iterations t plus 1, and the next iteration starts; and Y, finishing and outputting an optimization result.
Example 1
Economic load distribution optimization problem of generator set of medium-sized power system containing 15 thermal power generators
Step one, establishing a normal operation constraint condition of a generator set according to the operation requirement of a power system
(1.1) establishing equality constraint of normal operation of the generator set
Figure BSA0000217970560000071
In the formula, PiIs the output power of the ith generator, PDThe value for the total load demand is 2630MW, PLIs the line loss, P, of the power systemLMainly determined by the output power of the generator set and the topological structure of the power transmission network, Bij、B0i、B00Represents the system power transmission loss coefficient, wherein BijIs a 15 x 15 dimensional matrix, B0iIs a 1 × 15 dimensional matrix, B00Is a constant;
(1.2) establishing three inequality constraints of the generator set on the output power, the slope rate of the generator set and the forbidden operation area
An inequality constraint of the output power of the generator set is established, and the method comprises the following steps:
Figure BSA0000217970560000072
in the formula (I), the compound is shown in the specification,
Figure BSA0000217970560000073
is the minimum output power, P, of the ith generatoriIs the output power of the ith generator,
Figure BSA0000217970560000074
the maximum output power of the ith generator; the output power of each generator in normal operation must be between the maximum value and the minimum value, and the aging of the generator is accelerated when the output power exceeds the maximum value, so that the service life of the generator is shortened; the generator with too low output power is not fully utilized, so that resource waste is caused;
establishing a slope rate constraint of the output power of the generator set, wherein the method comprises the following steps:
Figure BSA0000217970560000075
in the formula, PiFor the output power of the ith generator at the current moment,
Figure BSA0000217970560000076
output power of the i-th generator at the previous moment, URiRepresents the upper limit of the increase of the generated power of the ith generator per unit time, DRiAn upper limit of the reduction amount of the generated power of the ith generator in unit time;
establishing the forbidden operation area constraint of the output power of the generator set, wherein the method comprises the following steps:
Figure BSA0000217970560000077
in the formula, NPZiThe number of forbidden operating regions for the ith generator in the generator set,
Figure BSA0000217970560000078
for the lower bound of the jth forbidden operating zone for the ith generator in the genset,
Figure BSA0000217970560000079
the upper boundary of the jth operation forbidden area of the ith generator in the generator set is set; the operation forbidden region is set for protecting a motor bearing or relevant auxiliary equipment and the like, and the generator is prevented from running in the operation forbidden region in order to prolong the service life of the generator;
step two, establishing an economic load distribution model of the power system generator set
The power generation cost of the power system is selected as an objective function, a valve point effect caused when an air inlet valve of the generator is suddenly opened is considered, and the power generation cost under the condition of nonlinear output of the generator can be expressed as follows:
Figure BSA0000217970560000081
in the formula, FtRepresenting the cost function of the electricity generated by the generator set, PiRepresents the output power of the ith generator,
Figure BSA0000217970560000082
represents the minimum output power of the ith generator, ai、bi、ci、eiAnd fiRepresenting the fuel cost coefficient of the ith generator, wherein the first three coefficients form a smooth unary quadratic function, and the last two coefficients form an irreducible and non-convex function related to sine;
Figure BSA0000217970560000083
denotes fiAnd
Figure BSA0000217970560000084
the multiplication of (1);
step three, improving the foraging algorithm of the classical manta ray
The classic manta ray foraging algorithm comprises three foraging operations of linkage foraging, whirlwind foraging and tendon-turning foraging, the classic manta ray foraging algorithm is improved, a nonlinear inertia weight w, a self-adaptive change and a differential variation strategy are introduced on the basis of the classic algorithm, and the improvement method comprises the following steps:
(3.1) in the chain foraging operation, the current position of the manta ray individual is jointly determined by the positions of the previous generation individual and the current optimal individual, and the expression is as follows:
Figure BSA0000217970560000085
in the formula (I), the compound is shown in the specification,
Figure BSA0000217970560000086
and
Figure BSA0000217970560000087
the t generation and the t +1 generation of the individual bat ray xiA position parameter in 15 dimensions, wherein the position of each individual bat ray is jointly determined by 15 parameters; the position parameter of each individual manta ray in the economic load distribution problem of the generating set represents an alternative solution of the problem, the dimension of each alternative solution is 15, and
Figure BSA0000217970560000088
and
Figure BSA0000217970560000089
representing the output power of 15 generators in the generator set in t times and t +1 times of iterative calculations when the problem adopts an improved manta ray foraging algorithm;
Figure BSA00002179705600000810
the method is characterized in that the method is an optimal solution of an improved manta ray foraging algorithm in the position parameters of the t-th generation of the optimal manta ray individual, namely the t-th iterative calculation of the economic load distribution problem of a generator set; r is a real number interval [0, 1]]A random number of (c); the population scale of the improved manta ray foraging algorithm is 100, namely the number of alternative solutions of the economic load distribution problem of the generator set; a is15For chain foraging operation
Figure BSA00002179705600000811
And
Figure BSA00002179705600000812
is calculated as
Figure BSA00002179705600000813
(3.2) the cyclonic foraging operation comprises: pure whirlwind foraging operation and exploration search space operation
The pure whirlwind foraging operation is that the modern individual bat ray follows the last individual bat ray in the bat population and moves to the current optimal individual, and the expression is as follows:
Figure BSA00002179705600000814
in the formula, beta15For simple whirlwind foraging operation
Figure BSA00002179705600000815
And
Figure BSA00002179705600000816
the connection weight coefficient of (2) is calculated as:
Figure BSA00002179705600000817
wherein r is a random number in a real number interval [0, 1], and t is the current iterative computation times of the improved manta ray foraging algorithm;
the method is characterized in that nonlinear inertia weight w is introduced to improve the search space exploration operation, and comprises the following steps:
Figure BSA00002179705600000818
in the formula (I), the compound is shown in the specification,
Figure BSA00002179705600000819
to search for a random position in space, β15Operating to explore search spaces
Figure BSA00002179705600000820
And
Figure BSA00002179705600000821
r is [0, 1]]W is a nonlinear inertial weight and is expressed as:
Figure BSA0000217970560000091
where t is the current iteration number, wminAnd wmaxFor the lower and upper limits of the inertial weight, w is set in this embodimentmin0.2 and wmax0.7, the nonlinear inertial weight w expression is embodied as:
Figure BSA0000217970560000092
introducing a nonlinear inertia weight w in the exploration search space operation, and improving the global search capability and convergence accuracy of the algorithm through continuous adjustment of the nonlinear inertia weight w;
(3.3) introducing sine and cosine adaptive factors in the clamshell foraging operation to enhance the adaptive capacity of the improved manta ray foraging algorithm;
Figure BSA0000217970560000093
wherein C is a cosine adaptive factor, S is a sine adaptive factor, r1、r2、r3And r*Is [0, 1]]A random number in between;
(3.4) introducing a differential variation strategy, and performing variation, difference and selection operations on the obtained individual manta ray in each iteration process to obtain a new individual manta ray for next iteration calculation, so as to enhance the global optimization capability of the algorithm;
for the t generation of the optimal individual bat ray
Figure BSA0000217970560000094
Using a mutation vector
Figure BSA0000217970560000095
Making it generate variation for generating new individual bat ray x'i 15(t) the method comprises:
Figure BSA0000217970560000096
in formula (II), x'i 15(t) is a new individual bat ray generated by variation operation;
Figure BSA0000217970560000097
and
Figure BSA0000217970560000098
is a random individual in the t generation, r4And r5The random number has the maximum value of 100 population numbers and the minimum value of 1;
Figure BSA0000217970560000099
is the optimal individual of the bat ray in the t generation; f is the scaling factor, F is [0.2, 0.8 ]]A random number in between;
an individual x 'of fresh manta ray generated after the mutation operation'i 15(t) and individuals
Figure BSA00002179705600000910
Performing binomial cross operation to increase the population diversity, wherein the method comprises the following steps:
Figure BSA00002179705600000911
in the formula, x ″)i 15(t) is an individual bat ray obtained after binomial cross operation; r is6Is [0, 1]]A random number in between; r is7Is a random number, the maximum value of which is the problem dimension 15 and the minimum value of which is 1;
constructing a fitness function, and converting the target function into the fitness function, wherein the method comprises the following steps:
Figure BSA00002179705600000912
in the formula (I), the compound is shown in the specification,
Figure BSA00002179705600000913
the position parameter of each individual bat ray is an alternative solution of the economic load distribution of a generator set for the ith individual bat ray in the tth generation;
Figure BSA00002179705600000914
the generating cost of the generating set is obtained by using the alternative solution corresponding to the ith individual bat ray in the tth generation;
Figure BSA0000217970560000101
generating set power generation cost maximum value corresponding to alternative solutions for all the individual bat ray in the tth generation;
selecting the optimal individual to reserve according to the fitness function value, wherein the method comprises the following steps:
Figure BSA0000217970560000102
in the formula (I), the compound is shown in the specification,
Figure BSA0000217970560000103
and f (x ″)i 15(t)) is an individual bat ray
Figure BSA0000217970560000104
And x ″)i 15(t) fitness value;
step four, optimizing the load distribution of the generator set by adopting an improved manta ray foraging algorithm
(4.1) initializing population position of improved manta ray foraging algorithm and settingThe population size N is 100, the maximum iteration number T is 1000, the cross probability CR is 0.2, and the upper and lower limits w of the inertia weightmax＝0.7、wminInputting the parameters of the generator set which are 0.2, wherein the parameters of the generator set are shown in a table 1;
TABLE 1 Generator set parameters
Figure BSA0000217970560000105
(4.2) starting iteration, generating a random number between [0, 1] by the Rand, and if the Rand is more than 0.5, executing the chain foraging operation by the current population according to the formula (6); if Rand is less than 0.5, generating a random number between [0, 1] by Rand, if T/T is greater than Rand, executing pure cyclone foraging operation according to formula (7) by the current population, and if T/T is less than Rand, executing exploration search space operation according to formula (9) by the current population; after one of a chain foraging operation, a simple cyclone foraging operation or a search space searching operation is executed, calculating individual fitness values in the bat ray population according to a formula (15), and selecting an individual with the largest fitness value as a current optimal individual;
(4.3) executing a tendon-turning foraging operation on the bat ray population according to the formula (12), calculating individual fitness values in the bat ray population according to the formula (15), and selecting the individual with the largest fitness value as a global optimal individual;
(4.4) carrying out differential variation operation on the obtained optimal individuals according to the formulas (13), (14) and (16), then calculating the fitness value of the individual of the bat ray population according to the formula (15), and selecting the individual with the maximum fitness value as a global optimal individual;
(4.5) judging whether the iteration times meet the requirements, namely judging whether T is more than or equal to T, if not, adding 1 to the iteration times T, and returning to the step (4.2) to enter the next iteration; if T is more than or equal to T, exiting iteration, outputting an optimal solution of the economic load distribution of the generator set, and comparing the optimal solution with an optimized result of the economic load distribution of the generator set solved by adopting a Particle Swarm Optimization (PSO) and a classical bat ray foraging algorithm (MRFO), wherein the result comparison is shown in tables 2 and 3; wherein the parameter setting population size N of the particle swarm algorithm is 100, the maximum iteration number T is 1000, and the acceleration factor C11, acceleration factor C21.318, inertia weight w is 1; setting a population scale N of 100, a maximum iteration time T of 1000 and a tendon-turning factor S of 2 for the cray ray foraging operation according to the classic parameter setting; a convergence curve comparison graph of three algorithms of an improved manta ray foraging algorithm (IMRFO), a classical manta ray foraging algorithm (MRFO) and a Particle Swarm Optimization (PSO) is shown in FIG. 2;
TABLE 2 Particle Swarm Optimization (PSO), classical manta ray foraging algorithm (MRFO), and improved manta ray foraging algorithm (IMRFO) optimization results
Figure BSA0000217970560000111
The numbers in Table 2 represent the economic load distribution results, units (MW) of the generator set
TABLE 3 comparison of results optimized by three algorithms
Figure BSA0000217970560000112
It can be seen from table 3 that when the load is 2630MW and the power balance is satisfied, the fuel cost, i.e., the power generation cost, of the power generating set in the optimization result of the improved bat ray foraging algorithm is smaller than that of the particle swarm algorithm and the classic bat ray foraging algorithm, and the optimal power generation cost ratio of the particle swarm algorithm (PSO), the classic bat ray foraging algorithm (MRFO) and the improved bat ray foraging algorithm (IMRFO) is 1: 0.9953: 0.9951, which indicates that the optimal solution capability of the improved bat ray foraging optimization algorithm is stronger, and the effect of the improved bat ray foraging algorithm is more obvious when the improved bat ray foraging algorithm is applied to a larger-scale load distribution optimization problem, which is beneficial to protecting the environment and improving the energy utilization rate. Further illustrates that the invention is very effective in generating the economic load distribution of the generator set under the situation of containing complex equality constraint and inequality constraint.
Fig. 2 shows iterative convergence curve comparison graphs of the improved manta ray foraging algorithm (IMRFO), the classical manta ray foraging algorithm (MRFO) and the particle swarm algorithm (PSO) when solving the economic load distribution optimization problem of a medium-sized power system generator set including 15 thermoelectric generators, and it can be seen that the improved manta ray foraging algorithm (IMRFO) adopted in the economic load distribution optimization method of the generator set has a faster convergence speed, a better optimal solution and a smoother convergence curve, thereby proving that the economic load distribution optimization method of the generator set of the present invention has advantages when solving the economic load distribution problem of the generator set under the situations including complex equality constraints and inequality constraints.
In all the above embodiments, the method for inputting data into the computer is a known method; the computer, display and MATLAB computer software were all commercially available.
The above is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered as the technical solutions and the inventive concepts of the present invention within the technical scope of the present invention.

Claims (2)

1. An economic load distribution optimization method of a generator set is characterized in that the economic load distribution optimization method of the generator set based on an improved manta ray foraging algorithm comprises the following steps:
step one, establishing a normal operation constraint condition of a generator set according to the operation requirement of a power system
(1.1) establishing equality constraint of normal operation of the generator set
Figure FSA0000217970550000011
Wherein d is the number of generators in the generator set, PiThe output power of the ith generator is in the dimension of MW; pjThe output power of the jth generator is MW; pDThe dimension of the total load demand of the power system is MW; pLLine loss of power system is measured in MW, PLThe method is mainly determined by the output power of a generator set and a topological structure of a power transmission network; b isij、B0i、B00The system power transmission loss coefficient;
here, the total output power of the generator set
Figure FSA0000217970550000012
Should correspond to the total load P of the power system in the distribution rangeDAnd line loss PLMatching, so the equation of equilibrium for power shown in equation (1) belongs to the equality constraint;
(1.2) establishing three inequality constraints of the generator set on the output power, the slope rate of the generator set and the forbidden operation area
An inequality constraint of the output power of the generator set is established, and the method comprises the following steps:
Figure FSA0000217970550000013
in the formula (I), the compound is shown in the specification,
Figure FSA0000217970550000014
is the minimum output power, P, of the ith generatoriIs the output power of the ith generator,
Figure FSA0000217970550000015
the maximum output power of the ith generator;
the generator set output power constraint shown in the formula (2) belongs to inequality constraint, because the output power of each generator in normal operation must be between the maximum value and the minimum value, and the aging of the generator is accelerated when the output power exceeds the maximum value, so that the service life of the generator is shortened; the generator with too low output power is not fully utilized, so that resource waste is caused;
establishing a slope rate constraint of the output power of the generator set, wherein the method comprises the following steps:
Figure FSA0000217970550000016
in the formula, PiFor the output power of the ith generator at the current moment,
Figure FSA0000217970550000017
is the output power of the ith generator at the last moment, d is the number of generators in the generator set, URiAn upper limit of an increase amount of generated power of the ith generator per unit time, DRiAn upper limit of the reduction amount of the generated power of the ith generator in unit time;
establishing the forbidden operation area constraint of the output power of the generator set, wherein the method comprises the following steps:
Figure FSA0000217970550000021
in the formula, NPZiThe number of the operation forbidden areas of the ith generator in the generator set, d is the number of the generators in the generator set,
Figure FSA0000217970550000022
for the lower bound of the jth forbidden operating zone for the ith generator in the genset,
Figure FSA0000217970550000023
the upper boundary of the jth operation forbidden area of the ith generator in the generator set is set;
the constraint of the forbidden operation area of the output power of each generator in the generator set shown in the formula (4) belongs to inequality constraint, because the forbidden operation area is set for protecting bearings of the generator or relevant auxiliary equipment, and the like, the generator is prevented from running in the forbidden operation area in order to prolong the service life of the generator;
step two, establishing an economic load distribution model of the power system generator set
Selecting the power generation cost of a power system as a target function, considering a valve point effect caused when an air inlet valve of a generator is suddenly opened, and generating the power generation cost under the condition of nonlinear output of the generator as shown in the formula (5):
Figure FSA0000217970550000024
in the formula, FtRepresenting the cost function of the electricity generated by the generator set, PiRepresents the output power of the ith generator,
Figure FSA0000217970550000025
represents the minimum output power of the ith generator, ai、bi、ci、eiAnd fiRepresenting the fuel cost coefficient of the ith generator, wherein the first three coefficients form a smooth unary quadratic function, and the last two coefficients form an irreducible and non-convex function related to sine;
Figure FSA0000217970550000026
denotes fiAnd
Figure FSA0000217970550000027
the multiplication of (1);
step three, improving the foraging algorithm of the classical manta ray
The classic manta ray foraging algorithm comprises three foraging operations of linkage foraging, whirlwind foraging and tendon-turning foraging, the classic manta ray foraging algorithm is improved, a nonlinear inertia weight w, a self-adaptive change and a differential variation strategy are introduced on the basis of the classic algorithm, and the improvement method comprises the following steps:
(3.1) in the chain foraging operation, the current position of the manta ray individual is jointly determined by the positions of the previous generation individual and the current optimal individual, and the expression is as follows:
Figure FSA0000217970550000028
in the formula (I), the compound is shown in the specification,
Figure FSA0000217970550000029
and
Figure FSA00002179705500000210
the t generation and the t +1 generation of the individual bat ray xiA position parameter on d dimension, wherein the position of each individual bat ray is jointly determined by the d parameters; in the economic load distribution problem of the generating set, the position parameter of each individual manta ray represents an alternative solution of the problem, the dimension of each alternative solution is d, and
Figure FSA00002179705500000211
and
Figure FSA00002179705500000212
representing the output power of d generators in the generator set in t times and t +1 times of iterative calculations when the problem adopts an improved manta ray foraging algorithm;
Figure FSA00002179705500000213
the method is characterized in that the method is an optimal solution of an improved manta ray foraging algorithm in the position parameters of the t-th generation of the optimal manta ray individual, namely the t-th iterative calculation of the economic load distribution problem of a generator set; r is a real number interval [0, 1]]A random number of (c); n is the population scale of the improved manta ray foraging algorithm, namely the number of alternative solutions of the economic load distribution problem of the generator set; a isdFor chain foraging operation
Figure FSA00002179705500000214
And
Figure FSA00002179705500000215
is calculated as
Figure FSA00002179705500000216
(3.2) the cyclonic foraging operation comprises: pure whirlwind foraging operation and exploration search space operation
The pure whirlwind foraging operation is that the modern individual bat ray follows the last individual bat ray in the bat population and moves to the current optimal individual, and the expression is as follows:
Figure FSA0000217970550000031
in the formula, betadFor simple whirlwind foraging operation
Figure FSA0000217970550000032
And
Figure FSA0000217970550000033
the connection weight coefficient of (2) is calculated as:
Figure FSA0000217970550000034
wherein r is a random number in a real number interval [0, 1], T is the current iterative computation time of the improved manta ray foraging algorithm, and T is the maximum iterative computation time;
the method is characterized in that nonlinear inertia weight w is introduced to improve the search space exploration operation, and comprises the following steps:
Figure FSA0000217970550000035
in the formula (I), the compound is shown in the specification,
Figure FSA0000217970550000036
to search for a random position in space, βdOperating to explore search spaces
Figure FSA0000217970550000037
And
Figure FSA0000217970550000038
r is [0, 1]]A random number in between, w is a nonlinear inertiaThe sex weights and their expressions are:
Figure FSA0000217970550000039
wherein T and T are the current iteration number and the maximum iteration number, wminAnd wmaxFor the lower and upper limits of the inertial weight, the invention sets wmin0.2 and wmaxWhen 0.7, formula (10) is embodied as:
Figure FSA00002179705500000310
introducing a nonlinear inertia weight w in the exploration search space operation, and improving the global search capability and convergence accuracy of the algorithm through continuous adjustment of the nonlinear inertia weight w;
(3.3) introducing sine and cosine adaptive factors in the clamshell foraging operation to enhance the adaptive capacity of the improved manta ray foraging algorithm;
Figure FSA00002179705500000311
wherein C is a cosine adaptive factor, S is a sine adaptive factor, r1、r2、r3And r*Is [0, 1]]A random number in between;
(3.4) introducing a differential variation strategy, and performing variation, difference and selection operations on the obtained individual manta ray in each iteration process to obtain a new individual manta ray for next iteration calculation, so as to enhance the global optimization capability of the algorithm;
for the t generation of the optimal individual bat ray
Figure FSA00002179705500000312
Using a mutation vector
Figure FSA00002179705500000313
To make it generate variation for generating new individual bat ray
Figure FSA00002179705500000314
The method comprises the following steps:
Figure FSA0000217970550000041
in the formula (I), the compound is shown in the specification,
Figure FSA0000217970550000042
a new manta ray individual generated by variation operation;
Figure FSA0000217970550000043
and
Figure FSA0000217970550000044
is a random individual in the t generation, r4And r5The random number is a maximum value of the population size N and a minimum value of 1;
Figure FSA0000217970550000045
is the optimal individual of the bat ray in the t generation; f is the scaling factor, F is [0.2, 0.8 ]]A random number in between;
generating a new individual bat ray after the mutation operation
Figure FSA0000217970550000046
With individuals
Figure FSA0000217970550000047
Performing binomial cross operation to increase the population diversity, wherein the method comprises the following steps:
Figure FSA0000217970550000048
in the formula (I), the compound is shown in the specification,
Figure FSA0000217970550000049
is an individual bat ray obtained after binomial cross operation; CR is cross probability and has a value range of [0, 1]]；r6Is [0, 1]]A random number in between; r is7The problem dimension d is the maximum value of the random number, and the minimum value is 1;
constructing a fitness function, and converting the target function into the fitness function, wherein the method comprises the following steps:
Figure FSA00002179705500000410
in the formula (I), the compound is shown in the specification,
Figure FSA00002179705500000411
the position parameter of each individual bat ray is an alternative solution of the economic load distribution of a generator set for the ith individual bat ray in the tth generation;
Figure FSA00002179705500000412
the generating cost of the generating set is obtained by using the alternative solution corresponding to the ith individual bat ray in the tth generation;
Figure FSA00002179705500000413
generating set power generation cost maximum value corresponding to alternative solutions for all the individual bat ray in the tth generation;
selecting the optimal individual to reserve according to the fitness function value, wherein the method comprises the following steps:
Figure FSA00002179705500000414
in the formula (I), the compound is shown in the specification,
Figure FSA00002179705500000415
and
Figure FSA00002179705500000416
the bat ray individual calculated by the formula (15)
Figure FSA00002179705500000417
And
Figure FSA00002179705500000418
a fitness value;
step four, optimizing the load distribution of the generator set by adopting an improved manta ray foraging algorithm
(4.1) initializing the population position of the improved manta ray foraging algorithm, and setting the population size N to 100, the maximum iteration time T to 1000, the cross probability CR to 0.2, and the upper and lower limits w of the inertia weightmax＝0.7、wmin＝0.2；
(4.2) starting iteration, generating a random number between [0, 1] by the Rand, and if the Rand is more than 0.5, executing the chain foraging operation by the current population according to the formula (6); if Rand is less than 0.5, generating a random number between [0, 1] by Rand, if T/T is greater than Rand, executing pure cyclone foraging operation according to formula (7) by the current population, and if T/T is less than Rand, executing exploration search space operation according to formula (9) by the current population; after one of a chain foraging operation, a simple cyclone foraging operation or a search space searching operation is executed, calculating individual fitness values in the bat ray population according to a formula (15), and selecting an individual with the largest fitness value as a current optimal individual;
(4.3) executing a tendon-turning foraging operation on the bat ray population according to the formula (12), calculating individual fitness values in the bat ray population according to the formula (15), and selecting the individual with the largest fitness value as a global optimal individual;
(4.4) carrying out differential variation operation on the obtained optimal individuals according to the formulas (13), (14) and (16), then calculating the fitness value of the individual of the bat ray population according to the formula (15), and selecting the individual with the maximum fitness value as a global optimal individual;
(4.5) judging whether the iteration times meet the requirements, namely judging whether T is more than or equal to T, if not, adding 1 to the iteration times T, and returning to the step (4.2) to enter the next iteration; if T is more than or equal to T, exiting iteration and outputting an optimal solution of the economic load distribution of the generator set;
the method of inputting data into a computer in the above-described steps is a known method; the computers, displays and MATLAB computer software used were all commercially available.
2. The economic load distribution optimization method of the generator set according to claim 1, characterized in that: the generator set operation parameters are obtained according to generator set power balance constraint, generator set output power constraint, ramp rate constraint, forbidden operation area constraint and the like in an actual power system.
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