Electromagnetic release optimization method based on whale algorithm

Abstract

The invention relates to the technical field of electromagnetic release structure optimization, and discloses an electromagnetic release optimization method based on a whale algorithm, and the method comprises the steps: solving an optimal structure parameter through the whale algorithm, taking a position with the maximum counterforce as a design point, and taking the maximum electromagnetic suction value of the point as an optimization target, according to the national standard requirement, the condition that tripping is not carried out when the test current is equal to 80% of the short circuit setting current serves as the constraint condition, and mathematical modeling is carried out on the relation between the structure parameters and the electromagnetic attraction through SPSS analysis software. And then the whale algorithm and the optimization result of the orthogonal test are compared and analyzed, so that the rapid breaking of the electromagnetic release is better realized, and the short-circuit protection reliability of the electromagnetic release is improved.

Description

Technical Field

[0001] The invention relates to the technical field of electromagnetic release structure optimization, and in particular to an electromagnetic release optimization method based on a whale algorithm. Background Art

[0002] With the continuous development of DC system research, key DC equipment and related technologies used in DC systems need to achieve new breakthroughs. DC circuit breakers play an indispensable role in achieving fault tripping and protecting other DC power equipment. Therefore, in recent years, the exploration of new technologies for DC circuit breakers has gradually attracted the attention of scholars.

[0003] According to the different breaking currents and topological structures, DC circuit breakers can generally be divided into solid-state circuit breakers, mechanical circuit breakers and hybrid circuit breakers. Compared with solid-state circuit breakers with large conduction losses and high-cost hybrid circuit breakers, traditional mechanical circuit breakers have the advantages of mature technology, stable operation, small conduction losses and low costs. Therefore, in low-voltage DC power supply and distribution systems, mechanical DC circuit breakers still occupy a huge application market.

[0004] However, the switching speed of mechanical circuit breakers is limited by the mechanical switch, so the breaking speed is relatively slow. And because DC current has no zero-crossing point, a zero-crossing environment must be created when it is applied, so in terms of limiting the fault current, DC current has more stringent requirements on related technologies.

[0005] In the traditional electrical appliance optimization design method, orthogonal experiment is widely used. However, from the final optimization result, the selected parameter combination has limitations. The selected parameter combination is limited to a limited number of levels, making it difficult to find the global optimal value, and it is also inconvenient to consider the constraints on the optimization target. With the continuous development of intelligent optimization algorithms, more and more intelligent optimization algorithms are applied to the optimization design of low-voltage electrical appliances, such as genetic algorithms, simulated annealing methods, and gray wolf algorithms. Those skilled in the art proposed to use artificial fish swarm algorithms to optimize the dynamic process of a certain type of intelligent AC contactor, ensuring the rapid release of the mechanism and realizing dynamic optimization control of the pull-in process. In addition, it is also proposed to use genetic algorithms to optimize the design of the shunt release, so that its structural dimensions are optimal, and at the same time, it also satisfies the constraints of electromagnetic force and temperature rise limit. At the same time, the prior art also discloses the use of orthogonal experiments to optimize the structural parameters of the electromagnetic system of the AC contactor, reduce the collision loss between the moving and static iron cores, and improve the mechanical life of the contactor.

[0006] However, when studying the small-scale optimization problem of electromagnetic release structural parameter optimization, the above algorithm converges slowly, takes more time, and the results are not accurate. In addition, when setting the optimization parameters, only weighted summation is used to construct an extreme value function, which is not comprehensive. Summary of the invention

[0007] The purpose of the present invention is to solve the above problems and to design an electromagnetic release optimization method based on the whale algorithm.

[0008] To achieve the above-mentioned purpose, the technical solution of the present invention is a method for optimizing an electromagnetic release based on a whale algorithm, which comprises:

[0009] Step 1: Select the structural parameters of the electromagnetic release, establish a mathematical model through SPSS analysis software, obtain the functional relationship between each structural parameter and the electromagnetic suction force, and use the functional relationship as the design basis of the structural parameters of the electromagnetic release;

[0010] Step 2: Take the current as 8I N The value of electromagnetic suction force is less than the value of spring pre-compression reaction force as a constraint condition, and then the whale algorithm is used to optimize the structural parameters of the electromagnetic release;

[0011] In step three, the static and dynamic characteristics of the electromagnetic release were analyzed to verify the applicability of the whale optimization algorithm in the optimization design of low-voltage electrical appliances.

[0012] The structural parameters of the electromagnetic release in step 1 include: the cross-sectional radius of the moving iron core, the thickness of the yoke iron and the height of the static iron core.

[0013] The construction process of the functional relationship in step 1 is:

[0014] According to Maxwell's theory, the calculation formula of the electromagnetic attraction on the moving iron core can be obtained as shown in formula (1):

[0015]

[0016] Among them, F x is the electromagnetic attraction of the moving iron core, A is the cross-sectional area of ​​the moving iron core, R is the cross-sectional radius of the moving iron core, B is the working air gap magnetic flux density, μ 0 is the vacuum permeability, K l is the solenoid force coefficient;

[0017] From formula (1), it can be seen that the electromagnetic release should optimize the moving iron core cross-sectional radius, yoke iron thickness, and static iron core height as the main structural parameters;

[0018] Assume the radius of the moving iron core is a 1 、a 2 、a 3 , static core height b, yoke thickness c, in the orthogonal table, A, B, C, D, E represent a 1 、a 2 、a 3 , b, c; in the fitted function, x 1 、x2 、x 3 、x 4 、x 5 Represents a 1 、a 2 、a 3 , b, c;

[0019] The optimization objectives and constraints established are as follows:

[0020]

[0021] In the formula, F x1 The air gap is 1.3mm and the current is 10I N The value of electromagnetic attraction when F x2 The air gap is 3.7mm and the current is 8I N The value of electromagnetic attraction, F f is the spring pre-compression reaction force value;

[0022] The data in the table were fitted with curves using the statistical software SPSS to obtain the relationship between the structural parameters and the electromagnetic suction force F. x1 、F x2 The functional relationship between them is shown in formula (3) and formula (4) respectively.

[0023]

[0024]

[0025] After obtaining the functional relationship, in order to verify the accuracy of the fitting curve, the determination coefficient of the fitting curve is calculated using formula (5), which reflects the proportion of the total variation of the dependent variable that can be explained by the independent variable through the regression relationship.

[0026]

[0027] where y i is the true measurement value, y is the average value of the true measurement value, is the predicted value.

[0028] The process of optimizing the structural parameters of the electromagnetic release using the whale algorithm in step 2 is as follows:

[0029] First, the whales surround the prey. Assume that in the d-dimensional space, the current best whale individual X * Location is The position of the individual whale X j for Then the whale individual X j In the best whale individual X * The next position under the influence of is calculated as follows:

[0030]

[0031]

[0032] in is the spatial coordinate X jnew The kth component of ;

[0033] C 1 =2r 2

[0034] A 1 =2a·r 1 -a

[0035] where r 1 、r 2 is a random number in (0, 1), and a decreases linearly from 2 to 0 as the number of iterations increases. The expression is as follows:

[0036]

[0037] Where t represents the current iteration number, T max is the maximum number of iterations;

[0038] According to the hunting behavior of humpback whales, they swim towards their prey in a spiral motion, so the mathematical model of hunting behavior is established as follows:

[0039]

[0040]

[0041] Where b is the logarithmic spiral shape constant, l is a random number between (-1, 1);

[0042] In order to increase the global search capability, the mathematical model of whales searching for prey is established as follows:

[0043]

[0044]

[0045] Where X rand is a randomly selected whale position vector;

[0046] That is, a random array is created to replace the whale's position, forcing the whale to deviate from the prey and find a more suitable prey. The exploration ability of the algorithm is enhanced so that the whale algorithm can perform a global search. The convergence speed is adjusted by adjusting the weights of surrounding prey and searching prey. The optimization goal and constraints of the whale algorithm are shown in formula (2). The optimal value is continuously iterated within the limited search range, and the various structural parameters when the optimal result is obtained.

[0047] The process of analyzing the static characteristics of the electromagnetic release in step 3 is as follows:

[0048] The static characteristic analysis model of electromagnetic release is established by using ANSYS analysis software. The electromagnetic field units selected are SOLID96 and SOURC36, which are used to establish the dynamic and static cores, yoke iron and electromagnetic coils respectively. The SOLID96 unit is a commonly used unit for three-dimensional magnetic field modeling, and the SOURC36 unit is a current source unit, which is used to specify the position, shape and total current size of the current source.

[0049] The relative magnetic permeability of air is set to 1.0. The moving core, stationary core and yoke iron are made of electrical pure iron, which is a nonlinear ferromagnetic material. In order to ensure the accuracy of electromagnetic simulation, the saturation characteristics of the magnetization process need to be taken into account. Therefore, the material properties are input through the BH value of electrical pure iron.

[0050] Then the different parts were meshed. Due to the symmetry of the structure and magnetic circuit of the electromagnetic release, and in order to save computer resources, only a quarter of the model was established in ANSYS, and the differential scalar potential method (DSP) was used for electromagnetic solution.

[0051] The process of analyzing the dynamic characteristics of the electromagnetic release in step 3 is as follows:

[0052] A simulation model was built using ADAMS analysis software to analyze dynamic characteristics. After the physical model was built in ADAMS, the mechanical motion equation of the electromagnetic release during the closing process was solved using the measured electromagnetic suction force data.

[0053] After the mechanical system model is established in ADAMS, the Lagrangian motion equation of the system is established. For each component, the Lagrangian equation with multipliers and the corresponding constraint equations are listed. The listed equations are shown in equation (15):

[0054]

[0055] Where K is the kinetic energy of the system; q j To describe the generalized coordinates of the system, Φ i is the constraint equation of the system; i is the Lagrange multiplier; F j is the generalized force in the generalized coordinate direction;

[0056] The electromagnetic force, tripping force and spring reaction force of the electromagnetic release are measured experimentally, and a unidirectional force is established on the moving iron core in the direction of the moving iron core suction. The two-dimensional static suction data is input into ADAMS and the data is curve fitted through the AKISPL function. The AKISPL function can fit the experimentally measured data into a smooth curve and generate a driving function and substitute it into the model to simulate the driving effect of the electromagnetic suction on the moving iron core. At the same time, the spring reaction force and tripping force are also reasonably added to the model to form a dynamic simulation model of the electromagnetic release.

[0057] Compared with the prior art, the present invention has the following advantages:

[0058] 1. This application uses the whale algorithm to achieve an optimization process with high optimization accuracy, fast convergence speed, few required control parameters, and easy implementation for the structural parameters of the electromagnetic release. It is more applicable when solving multi-dimensional small-scale optimization problems, and by considering the influence of different structural parameters of the electromagnetic release on its electromagnetic suction, the radius of the moving iron core, the height of the static iron core, and the thickness of the yoke iron are taken as key structural parameters;

[0059] 2. In order to improve the breaking capacity of the circuit breaker for short-circuit current and prevent the electromagnetic release from malfunctioning due to excessive optimized electromagnetic attraction, the SPSS software is used to perform curve fitting on the data in the orthogonal table, and the function expression between each structural parameter and the electromagnetic attraction is obtained;

[0060] 3. This application uses ANSYS and ADAMS analysis software to model the electromagnetic release and study its static and dynamic characteristics. After optimizing the structural parameters, the electromagnetic attraction value of the electromagnetic release increased by 13.05%, and the tripping time was shortened to varying degrees at different short-circuit currents, which can cut off the short-circuit current more quickly. Then, the traditional orthogonal design experiment optimization method was used for design. The electromagnetic attraction value only increased by 11.31%, and the disconnection time at different short-circuit currents was worse than the result after WOA optimization. By comparing the two, the applicability of the whale algorithm optimization method is further proved. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a flow chart of an electromagnetic release optimization method based on a whale algorithm according to the present invention;

[0062] Figure 2 It is a logo diagram of the structural parameters of the electromagnetic release of the present invention;

[0063] Figure 3 It is a simulation model diagram of the static characteristics of the electromagnetic release of the present invention;

[0064] Figure 4 It is a simulation model diagram of the dynamic characteristics of the electromagnetic release of the present invention;

[0065] Figure 5 is a graph showing the change of the air gap over time according to the present invention;

[0066] Figure 6 It is the protection characteristic curve diagram of the electromagnetic release before and after optimization of the present invention;

[0067] Figure 7 is the orthogonal test factor and level table of the present invention;

[0068] Figure 8 It is the orthogonal test table of five factors and four levels of the present invention;

[0069] Fig. 9 are the structural parameter values ​​before and after the whale algorithm optimization of the present invention;

[0070] Fig.10 It is a parameter table of the SOLID96 unit and the SOURC36 unit described in the present invention;

[0071] Fig.11 is a comparison table of the tripping time of the electromagnetic release before and after the optimization of the present invention;

[0072] Fig.12 It is the electromagnetic attraction extreme difference analysis table of the present invention;

[0073] Fig.13 It is a comparison table of the structural parameter values ​​of the electromagnetic release optimized by the whale algorithm and the orthogonal design method of the present invention;

[0074] Fig.14 It is a comparison table of the tripping time of the electromagnetic release under the whale algorithm and the orthogonal design method of the present invention;

[0075] Fig.15 It is a structural diagram of the solenoid type electromagnetic release of the present invention. DETAILED DESCRIPTION

[0076] The embodiments of the present invention are described in detail below with reference to the accompanying drawings:

[0077] Example 1

[0078] like Figure 1-15 As shown;

[0079] This application uses a plastic case circuit breaker with a rated current of 63A and an instantaneous setting current of 10IN. When a short circuit occurs, the electromagnetic release drives the traction rod to complete the contact disconnection. Its internal structure is as follows: Fig.15 shown.

[0080] The electromagnetic release is an important component of the low voltage DC circuit breaker to complete the instantaneous breaking task when the short circuit current passes through it. According to its different structural types, it can be divided into a snap-on type and a solenoid type. The circuit breaker studied in this application is a solenoid type electromagnetic release, and its structure diagram is as follows Fig.15 As shown in the figure, it is mainly composed of a moving iron core, a static iron core, a reaction spring, an electromagnetic coil, a yoke, a guide sleeve, etc. It is essentially an electromagnet with a special structure, and its action process is based on electromagnetic theory.

[0081] According to Maxwell's theory, the calculation formula for the electromagnetic attraction on the moving iron core can be obtained as shown in formula (1).

[0082]

[0083] Among them, F x is the electromagnetic attraction of the moving iron core, A is the cross-sectional area of ​​the moving iron core, R is the cross-sectional radius of the moving iron core, B is the working air gap magnetic flux density, μ 0 is the vacuum permeability, k l is the solenoid force coefficient.

[0084] From the relationship between various physical quantities, it can be obtained that the electromagnetic attraction of the moving iron core is in a quadratic function relationship with the cross-sectional radius of the moving iron core and the main magnetic flux of the electromagnetic release. Since the main magnetic flux of the electromagnetic release forms a closed loop through the moving iron core, yoke iron, static iron core, and working air gap, the thickness of the yoke iron will directly affect the distribution of the magnetic field, and then affect the electromagnetic attraction of the moving iron core. The height of the static iron core will affect the magnetic flux passing through the moving iron core, and will also indirectly affect the electromagnetic attraction of the moving iron core.

[0085] The suction force of the solenoid electromagnet can be divided into two parts: end suction force and solenoid force. The end suction force refers to the suction force generated by the main magnetic flux between the end faces of the moving iron core and the static iron core; the solenoid force refers to the suction force generated by the leakage magnetic flux between the armature and the shell. When the air gap is small, as the height of the static iron core increases, the value of the electromagnetic suction force under the same air gap also increases, but when the air gap is large, as the height of the static iron core increases, the value of the electromagnetic suction force under the same air gap decreases instead. When the air gap is large, the decrease in the height of the static iron core is equivalent to the increase in the length of the moving iron core from the initial position to the inside of the coil. In this way, the leakage magnetic flux between the side surface of the moving iron core and the yoke increases, thereby increasing the solenoid force and the total electromagnetic suction force. When the air gap is small, the proportion of the solenoid force is small, and the electromagnetic suction force is mainly the suction force between the surfaces of the moving and static iron cores. Therefore, if the height of the static core is reduced, it is equivalent to increasing the leakage flux, which increases the magnetic pressure drop in the non-working air gap and the magnetic conductor, and decreases the magnetic pressure drop in the working air gap, thereby reducing the electromagnetic attraction. When the thickness of the yoke increases, the magnetic resistance of the magnetic conductor decreases, which increases the magnetic flux density B in the working air gap and the electromagnetic attraction. Therefore, the radius of the moving core section, the thickness of the yoke, and the height of the static core are optimized as the main structural parameters.

[0086] Since the moving iron core is composed of three parts, and the cross-sectional radius of each part is different, five optimization parameters are selected, namely: moving iron core radius a 1 、a 2 、a 3 , static core height b, yoke iron thickness c, the specific meaning of the selected parameters are as follows Figure 2 In the following analysis, for convenience, A, B, C, D, and E are used to represent a in the orthogonal table. 1 、a 2 、a 3 , b, c; in the fitted function, x 1 、x 2 、x 3 、x 4 、x 5 Represents a 1 、a 2 、a 3 , b, c.

[0087] When the moving iron core is moved by the electromagnetic suction force, it will be subjected to the reverse force of the internal spring and the traction rod, that is, the tripping reaction force. Through the measurement of the tripping reaction force, it is found that when the air gap is 1.3mm, the tripping reaction force on the moving iron core is the largest. Therefore, the electromagnetic suction force under this air gap is selected as the optimization target. When the electromagnetic suction force increases, the moving iron core movement speed is also accelerated, that is, the short-circuit current is cut off in a shorter time, so as to achieve the purpose of optimizing the performance of the electromagnetic release.

[0088] However, the greater the electromagnetic attraction, the better. When the test current is equal to 80% of the short-circuit setting current, the electromagnetic release should be guaranteed not to operate according to national standards. N Therefore, when optimizing the structural parameters, it is necessary to ensure that the electromagnetic suction force at the initial position is less than the tripping reaction force value, so as to ensure that the electromagnetic release will not trip under this current excitation. The reaction force value of the spring pre-compression at the initial position is 2.3544N through measurement, that is, the electromagnetic suction force value should be less than 2.3544N. Therefore, the optimization objectives and constraints established are as follows:

[0089]

[0090] Among them, F x1 The air gap is 1.3mm and the current is 10I N The value of electromagnetic attraction when F x2 The air gap is 3.7mm (at the initial position) and the current is 8I N The value of electromagnetic attraction, F f is the spring pre-compression reaction force value.

[0091] Combined with the value range of each parameter, each parameter is set to 4 levels. The designed factor levels are as follows: Figure 7 shown.

[0092] according to Figure 7 It can be seen that this experiment involves 5 factors, each factor has 4 levels, so L is selected. 16 (4 5 ) orthogonal table, the designed five-factor four-level orthogonal test table is as follows Figure 8 shown.

[0093] According to the designed orthogonal test table, the data in the table are fitted with curves using the data statistics software SPSS to obtain the relationship between the structural parameters and the electromagnetic suction force F. x1 、F x2 The functional relationship between them is shown in formula (3) and formula (4) respectively.

[0094]

[0095]

[0096] After obtaining the functional relationship, in order to verify the accuracy of the fitting curve, the determination coefficient of the fitting curve is calculated using formula (5), which reflects the proportion of the total variation of the dependent variable that can be explained by the independent variable through the regression relationship.

[0097]

[0098] where y iis the true measurement value, y is the average value of the true measurement value, is the predicted value.

[0099] The determination coefficient R of formula (3) and formula (4) is calculated 2 They are 0.953 and 0.981 respectively. It can be seen that the curve fitting effect is ideal and the obtained mathematical model is relatively accurate.

[0100] The Whale Optimization Algorithm (WOA) is a new heuristic optimization algorithm that imitates the hunting behavior of humpback whales. It uses fitness to judge the quality of the solution sought, and achieves the purpose of searching for the optimal solution through the process of whale group searching, surrounding, chasing and attacking prey. First, the whale surrounds the prey. Assume that in the d-dimensional space, the current best whale individual X * Location is The position of the individual whale X j for Then the whale individual X j In the best whale individual X * The next position under the influence of is calculated as follows:

[0101]

[0102]

[0103] in is the spatial coordinate X jnew The kth component of ;

[0104] C 1 =2r 2

[0105] A 1 =2a·r 1 -a

[0106] where r 1 、r 2 is a random number in (0, 1), and a decreases linearly from 2 to 0 as the number of iterations increases. The expression is as follows:

[0107]

[0108] Where t represents the current iteration number, T max is the maximum number of iterations.

[0109] According to the hunting behavior of humpback whales, they swim towards their prey in a spiral motion, so the mathematical model of hunting behavior is established as follows:

[0110]

[0111]

[0112] Where b is the logarithmic spiral shape constant, and l is a random number between (-1, 1).

[0113] In order to increase the global search capability, the mathematical model of whales searching for prey is established as follows:

[0114]

[0115]

[0116] Where X rand is a randomly chosen whale position vector.

[0117] That is, a random array is created to replace the whale's position, forcing the whale to deviate from the prey and thereby find a more suitable prey, thereby enhancing the algorithm's exploration ability and enabling the WOA algorithm to perform a global search.

[0118] The whale algorithm can adjust the convergence speed by adjusting the weights of surrounding prey and searching prey, avoiding falling into the local optimal solution too early while also having good convergence. For the optimization of the structural parameters of the electromagnetic release, the optimization objectives and constraints are clear, and the solution range is small. The whale algorithm has the advantages of easy implementation, fast convergence speed and high accuracy, so it is more applicable in solving this problem.

[0119] The initial structural parameters of the electromagnetic release are obtained through test measurement. In the process of optimizing the structural parameters, not only the maximization of performance should be considered, but also the limitation of the structural size of the electrical appliance itself should be considered. Therefore, the optimization range is set as follows: 2.6≤x 1 ≤3.5; 3.9≤x 2 ≤4.8; 2.4≤x 3 ≤3.6; 2.4≤x 4 ≤2.7; 0.9≤x 5 ≤2.7.

[0120] When the whale algorithm is used for iterative solution, its optimization objective and constraints are shown in Formula 2. The optimal value is continuously solved iteratively within the limited search range, and the structural parameters of the optimal result are obtained. After iterative calculation, the structural parameter values ​​before and after optimization are as follows: Fig. 9 shown.

[0121] The static characteristic analysis model of the electromagnetic release is established using ANSYS analysis software. In order to correctly complete the electromagnetic simulation, it is necessary to reasonably select the units that simulate the electromagnetic phenomenon. The electromagnetic field units selected in this application are SOLID96 and SOURC36, which are used to establish the dynamic and static iron cores, yoke irons, and electromagnetic coils, respectively. The SOLID96 unit is a commonly used unit for three-dimensional magnetic field modeling, and the SOURC36 unit is a current source unit, which is used to specify the position, shape, and total current of the current source. The parameters of the two units are as follows Fig.10 shown.

[0122] The relative magnetic permeability of air is set to 1.0. The moving iron core, the stationary iron core and the yoke iron are made of electrical pure iron, which is a nonlinear ferromagnetic material. In order to ensure the accuracy of electromagnetic simulation, it is necessary to take into account the saturation characteristics during the magnetization process, so its material properties are input through the BH value of electrical pure iron. Then the different parts are meshed. Since the structure and magnetic circuit of the electromagnetic release are symmetrical, and in order to save computer resources, only one-quarter of the model is established in ANSYS. The model is appropriately simplified without affecting the accuracy of the calculation. The model after meshing and applying boundary conditions is shown in the figure below. Figure 3 As shown, finally, the differential scalar potential method (DSP) is used for electromagnetic solution.

[0123] The optimized structural parameters were brought into the electromagnetic release model established in ANSYS, and simulation was performed under the conditions of 10 times the rated current and 1.3mm air gap. The optimized electromagnetic suction force value was solved to be 16.2792N, which was 13.05% higher than the 14.4N before optimization. According to the results of static characteristics, the optimized data has a more ideal effect.

[0124] After optimizing the structural parameters of the electromagnetic release, in order to verify whether the tripping time is effectively shortened, a simulation model was built using ADAMS analysis software for dynamic characteristic analysis. After building a physical model in ADAMS, the measured electromagnetic suction data was used to solve the mechanical motion equation of the electromagnetic release during the closing process. After establishing the mechanical system model in ADAMS, the Lagrangian motion equation of the system was established, and the Lagrangian equation with multipliers and the corresponding constraint equations were listed for each component. The listed equations are shown in formula (11).

[0125]

[0126] Where K is the kinetic energy of the system; q j To describe the generalized coordinates of the system, φ i is the constraint equation of the system; i is the Lagrange multiplier; F jis the generalized force in the generalized coordinate direction.

[0127] When establishing the model, since the influence of the yoke on the dynamic characteristics is only reflected in the influence on the electromagnetic suction force, the influence of the yoke on the dynamic characteristics can be indirectly reflected by importing the electromagnetic suction force data, so the yoke model can be omitted. In addition, since the value of the electromagnetic suction force is smaller than the spring reaction force at the beginning, a block is fixed above the moving iron core to block the moving iron core to prevent it from moving in the opposite direction due to the spring reaction force. After constraints and contact are imposed on each component, the load is applied. The electromagnetic force, tripping force, spring reaction force and other data of the electromagnetic release are measured experimentally, and a unidirectional force is established on the moving iron core in the direction of the moving iron core attraction. The two-dimensional static suction data is input into ADAMS and the data is curve fitted through the AKISPL function. The AKISPL function can fit the experimentally measured data into a smooth curve, and generate a driving function and substitute it into the model, thereby simulating the driving effect of the electromagnetic suction force on the moving iron core. At the same time, the spring reaction force and the tripping force are also reasonably added to the model. The dynamic simulation model of the electromagnetic release established is as follows: Figure 4 shown.

[0128] In order to verify that the optimized electromagnetic release can be disconnected more quickly under different short-circuit currents, the present application sets the short-circuit current to 1kA-3.4kA, and the current increment is 0.3kA. As mentioned above, when the electromagnetic attraction of the moving iron core is input into ADAMS through the AKISPL function, since the first variable of the function is the short-circuit current, in order to simulate the change of the short-circuit current over time when a short-circuit fault occurs during the simulation process, it is necessary to input the expression of the short-circuit current in the ADAMS model. According to relevant national standards, taking the expected short-circuit current of 1kA as an example, the function expression of the short-circuit current in ADAMS is shown in formula (12):

[0129]

[0130] Through simulation analysis, the motion curve of the moving iron core of the electromagnetic release under different short-circuit currents can be obtained, such as Figure 5 As shown. The tripping time refers to the time from the moment the disconnection operation starts to the moment the disconnection command becomes irreversible. When the moving iron core moves to the point where the air gap exceeds 0.7mm, it will drive the tripping rod to rotate and cut off the short-circuit current. Therefore, "the moment the disconnection command becomes irreversible" occurs when the air gap is 0.7mm. Therefore, when analyzing the dynamic characteristics of this application, the time point when the moving iron core moves to the air gap of 0.7mm is taken as the end point.

[0131] Take the expected short-circuit current of 1kA as an example for analysis: 0-4.9ms is the triggering stage. During this period, the short-circuit current gradually increases, but does not reach the tripping current. The electromagnetic suction force generated is less than the reaction force of the spring in the initial position, and the moving iron core will not move. After 4.9ms is the movement stage. As the short-circuit current gradually increases, the electromagnetic suction force on the moving iron core after 4.9ms is greater than the reaction force of the spring. The moving iron core begins to accelerate and move toward the static iron core. It can be seen that when the expected short-circuit current is 1kA, the tripping time of the electromagnetic release is 8.7ms. Under other short-circuit current conditions, the movement process of the moving iron core is generally the same, except for the triggering time and the tripping time.

[0132] The dynamic characteristic model is modified by using the optimized structural parameter values, and the electromagnetic attraction value of the moving iron core under different currents and air gaps is updated to the calculated value of the optimized static characteristic model, and the tripping time and change rate of the electromagnetic release before and after optimization are obtained as follows: Fig.11 As shown in the figure, the protection characteristic curve is compared with Figure 6 shown.

[0133] After optimization, the tripping time of the electromagnetic releaser under different short-circuit currents has been reduced to a certain extent compared with before optimization. It can be seen that the optimization of structural parameters is more conducive to the breaking of the electromagnetic releaser, reducing the tripping time and improving its breaking capacity.

[0134] In order to further verify the rationality of the structural parameters optimized by the whale algorithm, the optimization results of the traditional orthogonal test were compared and analyzed. Figure 8 The orthogonal test table listed in the above is further analyzed and calculated to obtain the range analysis table as shown in Fig.12 shown.

[0135] Where T ij is the sum of the electromagnetic attraction of a factor at level i; M ij is the average electromagnetic attraction of a factor at level i; R j is the extreme difference, that is, M ij The difference between the maximum and minimum values ​​of . Fig.12 The maximum M under each factor ij By permuting and combining the values, the optimal combination of structural parameters optimized by the orthogonal test method can be obtained, that is, A 4 -B 1 -C 4 -D 1 -E 2 The structural parameters obtained by the two optimization methods are as follows Fig.13 shown.

[0136] The structural parameters obtained by the orthogonal test were corrected, and the electromagnetic suction force of the electromagnetic release under the parameters was calculated to be 16.028N under the conditions of 10 times the rated current and an air gap of 1.3mm, which was 11.31% higher than the 14.4N before optimization, but less than the value after optimization by the whale algorithm. It can be seen that in terms of static characteristics, the method selected in this application has high feasibility.

[0137] The structural parameters obtained from the orthogonal test were introduced into the ADAMS model, and the dynamic characteristics of the results obtained by the two optimization methods were compared and analyzed. The results are as follows: Fig.14 shown.

[0138] pass Fig.14 It can be seen that compared with the traditional orthogonal experimental optimization method, the optimization result obtained by the whale optimization algorithm has a shorter tripping time and can cut off the short-circuit current more quickly. From the overall level, the optimization result of the whale algorithm is more optimistic.

[0139] It should be noted that, in this application, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions. The sentence "includes an element defined by ... does not exclude the existence of other identical elements in the process, method, article or device including the element".

[0140] The above technical solutions only reflect the preferred technical solutions of the technical solutions of the present invention. Some changes that may be made to certain parts thereof by technicians in this technical field all reflect the principles of the present invention and fall within the protection scope of the present invention.

Claims

1. An electromagnetic release optimization method based on whale algorithm, characterized in that: It includes: Step 1: Select the structural parameters of the electromagnetic release, establish a mathematical model through SPSS analysis software, obtain the functional relationship between each structural parameter and the electromagnetic suction force, and use the functional relationship as the design basis of the structural parameters of the electromagnetic release; Step 2: Take the current as 8I N The value of electromagnetic suction force is less than the value of spring pre-compression reaction force as a constraint condition, and then the whale algorithm is used to optimize the structural parameters of the electromagnetic release; In step three, the static and dynamic characteristics of the electromagnetic release were analyzed to verify the applicability of the whale optimization algorithm in the optimization design of low-voltage electrical appliances.

2. The electromagnetic release optimization method based on the whale algorithm according to claim 1 is characterized in that: The structural parameters of the electromagnetic release in step 1 include: the cross-sectional radius of the moving iron core, the thickness of the yoke iron and the height of the static iron core.

3. The electromagnetic release optimization method based on the whale algorithm according to claim 1 is characterized in that: The construction process of the functional relationship in step 1 is: According to Maxwell's theory, the calculation formula of the electromagnetic attraction on the moving iron core can be obtained as shown in formula (1): Among them, F x is the electromagnetic attraction of the moving iron core, A is the cross-sectional area of ​​the moving iron core, R is the cross-sectional radius of the moving iron core, B is the working air gap magnetic flux density, μ0 is the vacuum permeability, K l is the solenoid force coefficient; From formula (1), it can be seen that the electromagnetic release should optimize the moving iron core cross-sectional radius, yoke iron thickness, and static iron core height as the main structural parameters; Assume that the radius of the moving iron core is a1, a2, a3, the height of the stationary iron core is b, and the thickness of the yoke is c. In the orthogonal table, A, B, C, D, and E represent a1, a2, a3, b, and c respectively; in the fitted function, x1, x2, x3, x4, and x5 represent a1, a2, a3, b, and c respectively; The optimization objectives and constraints established are as follows: In the formula, F x1 The air gap is 1.3mm and the current is 10I N The value of electromagnetic attraction when F x2 The air gap is 3.7mm and the current is 8I N The value of electromagnetic attraction, F f is the spring pre-compression reaction force value; The data in the table were fitted with curves using the statistical software SPSS to obtain the relationship between the structural parameters and the electromagnetic suction force F. x1 、F x2 The functional relationship between them is shown in formula (3) and formula (4) respectively; After obtaining the functional relationship, in order to verify the accuracy of the fitting curve, the determination coefficient of the fitting curve is calculated using formula (5), which reflects the proportion of the total variation of the dependent variable that can be explained by the independent variable through the regression relationship; where y i is the true measurement value, y is the average value of the true measurement value, is the predicted value.

4. The electromagnetic release optimization method based on the whale algorithm according to claim 1 is characterized in that: The process of optimizing the structural parameters of the electromagnetic release using the whale algorithm in step 2 is as follows: First, the whales surround the prey. Assume that in the d-dimensional space, the current best whale individual X * Location is The position of the individual whale X j for Then the whale individual X j In the best whale individual X * The next position under the influence of is calculated as follows: in is the spatial coordinate x jnew The kth component of ; C1＝2r2 A1=2a·r1-a Where r1 and r2 are random numbers in (0, 1), and a decreases linearly from 2 to 0 as the number of iterations increases. The expression is as follows: Where t represents the current iteration number, T max is the maximum number of iterations; According to the hunting behavior of humpback whales, they swim towards their prey in a spiral motion, so the mathematical model of hunting behavior is established as follows: Where b is the logarithmic spiral shape constant, l is a random number between (-1, 1); In order to increase the global search capability, the mathematical model of whales searching for prey is established as follows: Where X rand is a randomly selected whale position vector; That is, a random array is created to replace the whale's position, forcing the whale to deviate from the prey and find a more suitable prey. The exploration ability of the algorithm is enhanced so that the whale algorithm can perform a global search. The convergence speed is adjusted by adjusting the weights of surrounding prey and searching prey. The optimization goal and constraints of the whale algorithm are shown in formula (2). The optimal value is continuously iterated within the limited search range, and the various structural parameters when the optimal result is obtained.

5. The electromagnetic release optimization method based on the whale algorithm according to claim 1 is characterized in that: The process of analyzing the static characteristics of the electromagnetic release in step 3 is as follows: The static characteristic analysis model of electromagnetic release is established by using ANSYS analysis software. The electromagnetic field units selected are SOLID96 and SOURC36, which are used to establish the dynamic and static cores, yoke iron and electromagnetic coils respectively. The SOLID96 unit is a commonly used unit for three-dimensional magnetic field modeling, and the SOURC36 unit is a current source unit, which is used to specify the position, shape and total current size of the current source. The relative magnetic permeability of air is set to 1.

0. The moving core, stationary core and yoke iron are made of electrical pure iron, which is a nonlinear ferromagnetic material. In order to ensure the accuracy of electromagnetic simulation, the saturation characteristics of the magnetization process need to be taken into account. Therefore, the material properties are input through the BH value of electrical pure iron. Then the different parts were meshed. Due to the symmetry of the structure and magnetic circuit of the electromagnetic release, and in order to save computer resources, only a quarter of the model was established in ANSYS, and the differential scalar potential method (DSP) was used for electromagnetic solution.

6. The electromagnetic release optimization method based on the whale algorithm according to claim 1 is characterized in that: The process of analyzing the dynamic characteristics of the electromagnetic release in step 3 is as follows: A simulation model was built using ADAMS analysis software to analyze dynamic characteristics. After the physical model was built in ADAMS, the mechanical motion equation of the electromagnetic release during the closing process was solved using the measured electromagnetic suction force data. After the mechanical system model is established in ADAMS, the Lagrangian motion equation of the system is established. For each component, the Lagrangian equation with multipliers and the corresponding constraint equations are listed. The listed equations are shown in equation (15): Where K is the kinetic energy of the system; q j To describe the generalized coordinates of the system, Φ i is the constraint equation of the system; i is the Lagrange multiplier; F j is the generalized force in the generalized coordinate direction; The electromagnetic force, tripping force and spring reaction force of the electromagnetic release are measured experimentally, and a unidirectional force is established on the moving iron core in the direction of the moving iron core suction. The two-dimensional static suction data is input into ADAMS and the data is curve fitted through the AKISPL function. The AKISPL function can fit the experimentally measured data into a smooth curve and generate a driving function and substitute it into the model to simulate the driving effect of the electromagnetic suction on the moving iron core. At the same time, the spring reaction force and tripping force are also reasonably added to the model to form a dynamic simulation model of the electromagnetic release.

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