CN111144623B - Fixed value tuning method based on self-adaptive learning factor particle swarm - Google Patents
Fixed value tuning method based on self-adaptive learning factor particle swarm Download PDFInfo
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Abstract
The invention relates to a fixed value tuning method based on a self-adaptive learning factor particle swarm, which comprises the following steps of: establishing a mathematical model of timing time delay protection, and performing weighting and model solving on constraint conditions in the model through subjective weighting and objective weighting. The invention overcomes the defect of a single weighting method, ensures that the determination of the weight is more reasonable, and ensures the objectivity and scientificity of the scheme. The final protection scheme can be closer to the solution required by the practical problem, the particle swarm optimization enhances global search in the early stage by improving the learning factor, so that the particle swarm optimization is not easy to fall into local optimum, and the local search capability is enhanced in the later stage, so that a more accurate global optimum solution can be quickly obtained.
Description
Technical Field
The invention relates to a tuning method, in particular to a constant value tuning method based on self-adaptive learning factor particle swarm.
Background
At present, with the electric power system becoming more and more extensive and complicated, the importance of safe and stable operation of the electric power system is promoted. In order to obtain a set of fixed values which can meet the expectations of most users in a power grid and have the optimal protection effect of the whole power grid, the current mainstream research method is to transform a complex and continuous setting calculation problem into a multivariable, multi-target and multi-constraint simple and discrete global optimization problem and solve a model by combining an intelligent algorithm.
Generally, the quality of a protection scheme is judged in terms of the protection effect of the solution on the entire power system. Therefore, most of research on optimization of relay protection setting values focuses on global optimization of power system relay protection setting values. At present, a mainstream research algorithm is based on a genetic algorithm or a particle swarm algorithm, a mathematical model is established according to four basic requirements of relay protection of a power system, and intelligent tuning is performed by combining constraint conditions in the relay protection field such as power flow constraint, selective constraint, sensitivity constraint and level difference constraint. Such methods of tuning the fixed value suffer from the following problems:
1. in the process of setting the constraint conditions by establishing the mathematical model, the selection of the weight of the constraint conditions can directly influence the tuning result of the tuning algorithm on the relay protection type of the power system. The vulnerability of the grid and the user expectations vary in different areas, resulting in different primary emphasis on relay protection.
2. In the iterative process of intelligent tuning, the problems of local optimization, low convergence speed and the like inevitably occur in standard intelligent optimization algorithms such as heredity, particle swarm and the like.
Disclosure of Invention
In order to solve the technical problem, in the process of designing a model, the shortest time of all protection setting actions is taken as an objective function, and the constraint conditions such as sensitivity, selectivity and the like are expressed in the form of a penalty function. And in view of different requirements of different protections on the constraint conditions, weighting the constraint conditions by a method of combining subjective and objective weights. Meanwhile, aiming at the problems of local optimization, low convergence speed and the like which inevitably occur in the solving process, a particle swarm algorithm of a self-adaptive learning factor is designed, wherein the learning factor c 1 、c 2 Mainly influences the consciousness and individual behavior of particle swarm in the particle swarm algorithm, and is aligned to c at different stages 1 And c 2 And correcting to ensure that the optimization iteration process is not easy to fall into local optimization, thereby obtaining a more accurate global optimal solution and achieving the purpose of accelerating convergence.
The technical scheme of the invention is as follows:
a constant value tuning method based on adaptive learning factor particle swarm comprises the following steps:
step (1) establishing a mathematical model for timing time-delay protection
And (3) establishing a mathematical model of the timing time-limited delay protection by taking the shortest setting time of the protection delay period in the whole system as a target function:
in the formula, M is the setting time of the protection delay period; t is t ij To protect the jth delay action time; alpha, beta, chi and delta are respectively the weight of the level difference constraint, the sensitivity constraint, the selectivity constraint and the load constraint; f. of int (t)、f sen (t)、f sel (t)、f load (t) penalty functions of level difference constraint, sensitivity constraint, selectivity constraint and load constraint with respect to time are respectively provided, and k is a constant;
step (2) weighting constraint conditions in the model through subjective weighting and objective weighting
2.1, objective empowerment
For a strongly-connected power grid structure, when a protection scheme is prepared, the priority of the sensitivity is greater than the selectivity; in the weakly-connected power grid structure, the priority of selectivity is greater than the sensitivity; for being at n i Protection i in a simple loop, the line to which the bus to which it is connected has l i The grid vulnerability factors are as follows:
η i ＝1/(n i ×l i ) (2)
wherein eta is the grid vulnerability coefficient, and the objective weights of the sensitivity and the selectivity constraint are as follows:
wherein c and d are constants, v βij 、v χij Respectively representing the sensitivity of the ith protection time period and the weight of the selective constraint;
2.2 subjective empowerment
Grading all constraint conditions of different protections, and carrying out subjective empowerment on the constraint conditions in the model by considering the subjective intention of a user; establishing an AHP judgment matrix R = [ R ] mn ]Wherein r is mn The importance of the principle m is equal to that of the principle n, the greater the value is, the greater the importance of the principle m is, the weight value of each index is calculated according to the matrix R, and the following steps are carried out:
wherein: omega m When m =1, the weight is a sensitivity constraint weight; when m =2, the value is a selective constraint weight value; k is the number of the setting principles of protection;
2.3 subjective and objective combination empowerment
Combining the objective weight and the subjective weight obtained in the step 2.1 and the step 2.2, combining the objective weight and the subjective weight through the following formula to obtain a final weight:
wherein, ω is l Subjective weights obtained for the ith constraint, i.e., the results of equations (4) and (5); v. of l The objective weight obtained for the ith constraint, i.e., the result of equation (6); a is l The final weight obtained for the ith constraint;
step (3) model solving
And (3) taking the formula (1) as an objective function, and solving the model by adopting a particle swarm optimization method of the self-adaptive learning factor.
Further, in the step (3), a concrete process of model solution is as follows:
and (3) taking the setting scheme of the protection as a particle to carry out cyclic solution, wherein the particle speed is represented as the following formula:
wherein the learning factor c 1 、c 2 Influence independent awareness and population awareness of particles; making c earlier in the iteration 1 The size is relatively larger, the independence of the particles is enhanced, and therefore the global search capability is enhanced; iterative late stage of c 2 Relatively larger, enhances the group consciousness of particles, strengthens the capability of local search, improves the convergence rate of the algorithm and learns the factor c 1 、c 2 Is determined by the following formula:
c 1 ＝a+b cos(kπ/itermax) (9)
c 2 ＝c-d cos(kπ/itermax) (10)
wherein k is the current iteration number, itermax is the maximum iteration number, and a, b, c, d are constants.
Further, in the step (3), firstly, a binary character string coding method is adopted to re-read the matching mode between each two adjacent line protection, and the method can be divided into three modes according to different actual sizes, wherein the three modes comprise matching with a first section of adjacent line distance protection, matching with a second section of adjacent line distance protection and sensitivity setting related to the line fault;
judging whether the position of the setting result meets the selective constraint or the sensitivity constraint; when the setting result does not satisfy the selectivity constraint or the sensitivity constraint, the penalty function f (t) = Δ t of the selectivity constraint or the sensitivity constraint in the equation (1), otherwise f (t) =0.
Further, in formula (1), α =0 and δ =0. For timing margin backup protection, the step difference constraint is subject to the selectivity constraint, so α is taken to be 0 here, and the load constraint is generally satisfied for setting calculation, so δ is 0 here.
Compared with the traditional method, the method has the following advantages:
1. the invention utilizes a mathematical method to combine subjective weighting and objective weighting to weight the constraint conditions in the model, overcomes the defect of a single weighting method, ensures more reasonable weight determination and ensures the objectivity and scientificity of the scheme. The final protection scheme can be closer to the solution needed by the practical problem
2. According to the invention, through improvement of the learning factor, the particle swarm optimization enhances global search in the early stage, so that the particle swarm optimization is not easy to fall into local optimum, and enhances the local search capability in the later stage, so that a more accurate global optimum solution can be rapidly obtained.
Drawings
FIG. 1 is a flow chart of weight assignment to constraint conditions using a combination of objective and subjective weights method of the present invention;
FIG. 2 is a code pattern of the present invention that matches a segment of protection according to distance from an adjacent line;
FIG. 3 is a code pattern for two-stage protection according to the distance to adjacent lines in accordance with the present invention;
FIG. 4 is a code map of the present invention tuned in accordance with sensitivity associated with a present line fault;
fig. 5 is a flowchart for solving the model by the particle swarm optimization method of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention, and it is obvious that the described embodiments are only a part of examples of the present invention, and not all examples. All other embodiments, which can be obtained by a person skilled in the art without inventive effort based on the embodiments of the present invention, are within the scope of the present invention.
The fixed value tuning method based on the adaptive learning factor particle swarm of the embodiment comprises the following steps:
step (1) establishing a mathematical model of timing time-delay protection
And (3) establishing a mathematical model of the timing time-limited delay protection by taking the shortest setting time of the protection delay period in the whole system as a target function:
wherein M is a protectionSetting time in a time delay manner; t is t ij The jth delay action time is protected; alpha, beta, chi and delta are respectively the weight of the level difference constraint, the sensitivity constraint, the selectivity constraint and the load constraint; f. of int (t)、f sen (t)、f sel (t)、f load And (t) penalty functions of level difference constraint, sensitivity constraint, selectivity constraint and load constraint with respect to time are respectively set, and k is a constant. For timing margin backup protection, the step difference constraint is subject to the selectivity constraint, so α is taken to be 0 here, and the load constraint is generally satisfied for setting calculation, so δ is 0 here.
Step (2), the constraint conditions in the model are weighted through subjective weighting and objective weighting
2.1 Objective empowerment
In order to reduce the occurrence probability of power grid accidents, different protection schemes are made aiming at the problem of different network vulnerabilities of different structures. For a strongly-connected power grid structure, the priority of the sensitivity is greater than the selectivity when a protection scheme is prepared; in the weakly-connected power grid structure, the priority of selectivity is greater than the sensitivity; for being at n i Protection i in a simple loop, the line to which the bus to which it is connected has l i The grid vulnerability factors are as follows:
η i ＝1/(n i ×l i ) (2)
wherein eta is the grid vulnerability coefficient, and the objective weights of the sensitivity and the selectivity constraint are as follows:
wherein c and d are constants, v βij 、v χij Respectively representing the sensitivity of the ith protection time period and the weight of the selective constraint;
2.2 subjective empowerment
Grading all constraint conditions of different protections, and carrying out subjective empowerment on the constraint conditions in the model by considering the subjective intention of a user; establishing an AHP judgment matrix R = [ R ] mn ]Wherein r is mn The principle m and n are equal in importance, the greater the numerical value is, the greater the importance of the principle m and n is, the weighted value of each index is calculated according to the matrix R, and the method is carried out according to the following formula:
wherein: omega m When m =1, the weight is a sensitivity constraint weight; when m =2, the value is a selective constraint weight value; k is the number of the setting principles of protection;
2.3 subjective and objective combination empowerment
As shown in fig. 1, combining the objective weight and the subjective weight obtained in step 2.1 and step 2.2, the objective weight and the subjective weight are combined by the following formula to obtain a final weight:
wherein, ω is l Subjective weights obtained for the ith constraint, i.e., the results of equations (4) and (5); v. of l The objective weight obtained for the ith constraint, i.e., the result of equation (6); a is a l The final weight obtained for the ith constraint;
step (3) model solving
And (3) taking the formula (1) as an objective function, and solving the model by adopting a particle swarm optimization method of the self-adaptive learning factor. The concrete process of model solution is as follows:
firstly, a binary character string coding method is adopted to re-interpret the matching mode between each protection, according to the protection matching principle, Z0 is expressed as matching with a first section of adjacent line distance protection, Z1 is expressed as matching with a second section of adjacent line distance protection, zlm is expressed as setting according to the sensitivity related to the line fault, and the method can be divided into three modes according to different actual sizes, namely, model1, model2 and model3, and the code diagram is shown in FIGS. 2-4.
And if the time constant value is t0 or t1, the setting result is matched with the adjacent protection I section when being positioned on the left side of the matching point (Z0, t 0), and the setting result is matched with the adjacent protection II section when being positioned on the left side of the matching point (Z1, t 1), so that the selective constraint is met. And the sensitivity constraint is met when the setting result is positioned at the right side of the matching points (Zlm, t 0) and (Zlm, t 1). When the setting result does not satisfy the selectivity constraint or the sensitivity constraint, a penalty function f (t) = Δ t of the selectivity constraint or the sensitivity constraint in equation (1), otherwise f (t) =0.
At present, in most studies on constant value tuning, a mainstream study mode is to convert a continuity problem into a discreteness problem, and in this embodiment, the model is solved by using the equation (1) as an objective function and using a particle swarm optimization method of an adaptive learning factor.
And (3) taking the setting scheme of the protection as a particle to carry out cyclic solution, wherein the particle speed is represented as the following formula:
the coordinates of the particle in the D-dimensional space may represent one potential solution to the problem, and by tracking the historical optimal and global optimal positions of the particle locations, the optimal position of the particle, i.e., the optimal solution to the problem, may be found. Wherein, the position of the ith particle in the D-dimensional search space (i.e. the coordinates of the D-dimensional space) can be expressed as: x i ＝(x i1 ,x i2 ...x iD ) (ii) a The optimal point of the history is P i ＝(p i1 ,p i2 ,...p iD ) (ii) a The velocity of the ith particle is expressed as: v i ＝(v i1 ，v i2 ...v iD ) (ii) a The historical optimal points of the whole particle swarm are as follows: p g ＝(p g1 ,p g2 ,...p gD )。
Wherein i =1,2 … n; d =1,2 … D; w is the inertial weight, which acts to balance the global search and the local search; and rand () represents random numbers evenly distributed in [0,1 ].
In the embodiment, the solution is carried out by adopting a particle swarm method of the adaptive learning factor, wherein the learning factor c 1 、c 2 Influence independent awareness and population awareness of particles; making c earlier in the iteration 1 The size is relatively larger, the independence of the particles is enhanced, and therefore the global search capability is enhanced; iterative late stage c 2 Relatively larger, enhances the group consciousness of particles, strengthens the capability of local search, improves the convergence rate of the algorithm and learns the factor c 1 、c 2 Is determined by the following formula:
c 1 ＝a+bcos(kπ/itermax) (9)
c 2 ＝c-dcos(kπ/itermax) (10)
wherein k is the current iteration number, itermax is the maximum iteration number, and a, b, c, d are constants.
As shown in fig. 3, the adaptive learning factor particle swarm optimization solving steps of this embodiment are as follows: and (1) representing the matching state of each protection by using binary character strings in combination with a code graph, and connecting the binary character strings of each protection to form a particle, wherein the particle represents a set of possible fixed values of the whole network protection device. And (2) loading initial data, including a network structure, an action fixed value, time and particle swarm algorithm parameters, initializing a particle swarm for protection codes by using a binary string, and endowing an initial position and a speed to each particle.
Step (3) calculating the fitness value of each particle according to the formula (1)
Step (4), updating the position, speed and learning factor of the particle
Compared with the historical optimal particles and the global optimal particles, the particle speed, the position and the learning factor are updated according to the formulas (8), (9) and (10).
Step (5) iteration: and determining whether the iteration is finished according to the constraint conditions, the fitness value, the iteration times and the like. If yes, turning to the step (6); if not, go to step (3).
And (6) stopping iteration and outputting a global optimal fitness value and a protection scheme.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and should not be taken as limiting the scope of the present invention, which is intended to cover any modifications, equivalents, improvements, etc. within the spirit and scope of the present invention.
Claims (4)
1. A constant value tuning method based on self-adaptive learning factor particle swarm is characterized in that: the method comprises the following steps:
step (1) establishing a mathematical model of timing time-delay protection
And (3) establishing a mathematical model of the timing time-limited delay protection by taking the shortest setting time of the protection delay period in the whole system as a target function:
in the formula, M is the setting time of the protection delay period; t is t ij To protect the jth delay action time; alpha, beta, chi and delta are respectively the weight of the level difference constraint, the sensitivity constraint, the selectivity constraint and the load constraint; f. of int (t)、f sen (t)、f sel (t)、f load (t) penalty functions of level difference constraint, sensitivity constraint, selectivity constraint and load constraint with respect to time are respectively set, and k is a constant;
step (2), the constraint conditions in the model are weighted through subjective weighting and objective weighting
2.1 Objective empowerment
For a strongly-connected power grid structure, the priority of the sensitivity is greater than the selectivity when a protection scheme is prepared; in the weakly-connected power grid structure, the priority of selectivity is greater than the sensitivity; for being at n i Protection i in a simple loop, the line to which the bus to which it is connected has l i The grid vulnerability factors are as follows:
η i ＝1/(n i ×l i ) (2)
wherein eta is a power grid vulnerability coefficient, and objective weights of sensitivity and selectivity constraints are as follows:
wherein c and d are constants, v βij 、v χij Respectively representing the sensitivity of the ith protection time period and the weight of the selective constraint;
2.2 subjective empowerment
Grading all constraint conditions of different protections, and carrying out subjective empowerment on the constraint conditions in the model by considering the subjective intention of a user; establishing an AHP judgment matrix R = [ R ] mn ]Wherein r is mn The principle m and n are equal in importance, the greater the numerical value is, the greater the importance of the principle m and n is, the weighted value of each index is calculated according to the matrix R, and the method is carried out according to the following formula:
wherein: omega m When m =1, the weight is a sensitivity constraint weight; when m =2, the value is a selective constraint weight value; k is the number of the setting principles of protection;
2.3 subjective and objective combination empowerment
Combining the objective weight and the subjective weight obtained in the step 2.1 and the step 2.2, and combining the objective weight and the subjective weight through the following formula to obtain a final weight:
wherein, ω is l The subjective weight obtained for the ith constraint, i.e., the result of equation (6); v. of l The objective weights obtained for the ith constraint, i.e., the results of equations (4) and (5); a is l The final weight obtained for the ith constraint;
step (3) model solving
And (3) taking the formula (1) as an objective function, and solving the model by adopting a particle swarm optimization method of the self-adaptive learning factor.
2. The adaptive learning factor particle population-based fixed-value tuning method according to claim 1, wherein: in the step (3), the concrete process of model solution is as follows:
and (3) taking the setting scheme of the protection as a particle to carry out cyclic solution, wherein the particle speed is represented as the following formula:
wherein the position of the ith particle in the D-dimensional search space is represented as: x i ＝(x i1 ,x i2 ...x iD ) (ii) a The historical optimum point is P i ＝(p i1 ,p i2 ,...p iD ) (ii) a The velocity of the ith particle is expressed as: v i ＝(v i1 ，v i2 ...v iD ) (ii) a The historical optimum points of the whole particle swarm are as follows: p g ＝(p g1 ,p g2 ,...p gD )；
Wherein i =1,2 … n; d =1,2 … D; w is the inertial weight, balancing the global search and the local search; rand () represents random numbers evenly distributed in [0,1 ];
wherein the learning factor c 1 、c 2 Influence independent awareness and population awareness of particles; making c earlier in the iteration 1 The size is relatively larger, the independence of the particles is enhanced, and therefore the global search capability is enhanced; iterative late stage of c 2 Relatively larger, enhances the group consciousness of particles, enhances the local search capability, andhigh convergence rate of algorithm, learning factor c 1 、c 2 Determined by the following formula:
c 1 ＝a+b cos(kπ/itermax) (9)
c 2 ＝c-d cos(kπ/itermax) (10)
wherein k is the current iteration number, itermax is the maximum iteration number, and a, b, c, d are constants.
3. The adaptive learning factor particle population-based fixed-value tuning method according to claim 1, wherein: in the step (3), firstly, a binary character string coding method is adopted to re-read the matching mode between each two adjacent line protection, and the matching mode can be divided into three modes according to different actual sizes, wherein the three modes comprise matching with a first section of adjacent line distance protection, matching with a second section of adjacent line distance protection and sensitivity setting related to the line fault;
judging whether the position of the setting result meets the selective constraint or the sensitivity constraint; when the setting result does not satisfy the selectivity constraint or the sensitivity constraint, the penalty function f (t) = Δ t of the selectivity constraint or the sensitivity constraint in the equation (1), otherwise f (t) =0.
4. The adaptive learning factor particle population-based fixed-value tuning method according to claim 1, wherein: in formula (1), α =0 and δ =0.
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