CN115728590A - Power transmission line double-end fault distance measurement method and device using same - Google Patents
Power transmission line double-end fault distance measurement method and device using same Download PDFInfo
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Abstract
The invention discloses a power transmission line double-end fault location method, which aims at the problem that the robustness of a model is poor due to the fact that the traditional deep learning fault location method directly substitutes voltage and current into the model for training, and the invention provides the method for converting the voltage and the current into relative offsets for deep learning, so that the robustness of the model is effectively improved; by the improved wolf algorithm, the ranging precision is effectively improved. Compared with the traditional impedance ranging method, the method provided by the invention can obviously improve the ranging precision, and compared with the traveling wave ranging method, the method can simplify the steps of data acquisition on the premise of ensuring the precision without additionally arranging a traveling wave ranging device, so that the method provided by the invention has great advantages in fault ranging.
Description
Technical Field
The invention relates to the field of line fault location, in particular to a power transmission line double-end fault location method based on fault amount relative offset and GWO-SVR improvement.
Background
The transmission line fault seriously affects the safe and stable operation of the power distribution network, so that various scholars develop various researches on how to accurately perform line fault distance measurement. The impedance ranging method calculates the fault position by measuring the voltage and the current of two end points and utilizing the superposition principle, for example, the applicability of the impedance ranging method is analyzed, and the impedance ranging method is indicated to be greatly influenced by a transition resistor and a fault phase angle in the aspect of precision and difficult to meet the requirement of engineering practice on the precision; the traveling wave ranging method calculates the fault distance by measuring the time or time difference of traveling wave transmitted to the line end point after the fault occurs. If a double-end traveling wave method is adopted for distance measurement, or the accuracy of traveling wave head identification is improved through wavelet transformation, however, the traveling wave distance measurement method has the problems of difficulty in traveling wave measurement, high equipment cost and the like; for this reason, a traveling wave impedance combination fault location method can be adopted, but the limitation of the traveling wave method is not fundamentally solved.
With the development of the smart grid, the deep learning method is applied to fault location, and the established recurrent neural network model is used for fault location; or the voltage amplitude is taken as a fault characteristic and substituted into a Support Vector Regression model for distance measurement, wherein the English name of the Support Vector Regression model is Support Vector Regression. Both of the two methods directly use the measured electric quantity as input, however, if the topology of the line network changes or the normal working voltage fluctuates, the accuracy of the distance measurement is seriously affected.
Disclosure of Invention
In order to solve the problems, the invention provides a fault distance measuring method based on an SVR model, which takes the relative offset of the fault quantity as the fault characteristic.
In order to achieve the purpose, the invention provides a power transmission line double-end fault location method based on fault amount relative offset and GWO-SVR improvement, which comprises the following steps:
s1: establishing a double-end transmission line model, and measuring a first amplitude of voltage and current at two ends of the line during normal work and a second amplitude of voltage and current at two ends of the line during different fault types, different fault positions and different transition resistances;
s2: calculating the relative offset of the voltage fault quantity and the current fault quantity based on the first amplitude and the second amplitude, wherein the relative offset calculation formula of the voltage fault quantity is as follows:
the relative offset calculation formula of the current fault quantity is as follows:
in the formula, subscript m is a, b and c three phases, delta U mf Δ I, a relative shift in the amount of voltage failure mf For relative deviation of fault magnitude of electric current, U m Is the voltage across the line during normal operation, I m Current at both ends of the line, U, during normal operation mf Voltage across the line, I, at different fault types, at different fault locations and at different transition resistances mf The current at two ends of the line is the current at two ends of the line when the fault type is different, the fault position is different and the transition resistance is different;
s3: relative deviation delta U of line head end voltage fault quantity in different fault types, fault positions and transition resistances mf1 Relative deviation Delta I of the amount of current fault at the head end of the line at different fault types, at different fault locations and at different transition resistances mf1 Relative deviation DeltaU of the end-of-line voltage fault quantities at different fault types, at different fault locations and at different transition resistances mf2 Relative deviation Δ I of the end-of-line current fault quantities at different fault types, at different fault locations and at different transition resistances mf2 Taking the fault quantity as a fault characteristic set, and carrying out normalization processing on the fault quantity relative offset in the fault characteristic set to obtain a normalized fault characteristic set;
s4: n sets of samples for the normalized fault signature set { (x) 1 ,y 1 ),(x 2 ,y 2 ),L,(x n ,y n ) And establishing a support vector regression model of the nonlinear soft interval, wherein the mathematical expression of the model is as follows:
in the formula, theta is an input vector, C is a coefficient for controlling the margin width, namely a penalty coefficient, xi i 、
Is a non-negative relaxation variable, ε is a tolerance margin, f (x) i ) Is a function solved by nonlinear regression analysis;
s5: setting an initial parameter penalty coefficient C and a kernel function radius g of the support vector regression model;
s6: inputting the normalized fault feature set into the support vector regression model under the conditions of an initial parameter penalty coefficient C and a kernel function radius g;
s7: solving the support vector regression model to obtain a calculation result, wherein the calculation result is a fault position corresponding to the fault feature, converting the calculation result into a percentage form, performing normalization processing, and calculating the error of the calculation result by using an average percentage error;
s8: selecting three groups of data with the minimum error of the calculation result as input variables;
s9: inputting the input variable into an improved Hurrill algorithm, performing iterative optimization on the initial parameter penalty coefficient C and the kernel function radius g, and obtaining the optimized parameter penalty coefficient C and the optimized kernel function radius g;
s10: replacing the initial parameter penalty coefficient C and the kernel function radius g of the support vector regression model with the optimized parameter penalty coefficient C and the optimized kernel function radius g;
s11: randomly extracting the fault feature set into two parts; one part of the training set is a training set, and the other part of the training set is a testing set;
s12: and training the support vector regression model by using the training set, verifying the accuracy of the support vector regression model by using the test set, wherein the support vector regression model meeting the accuracy requirement is the ranging model.
Preferably, said function f (x) solved by non-linear regression analysis i ) Is generally expressed as：
In the formula, a i 、
Is Lagrange multiplier, b is bias, K (x) i And x) is a kernel function. w is a weight, an intermediate quantity.
In a preferred mode, the improved grey wolf algorithm comprises the following specific steps:
step1: generating an initial population and dividing the level; wherein, the input variables are set as head wolves which are respectively named as alpha, beta and delta, and the other individuals are omega wolves which are guided by the alpha, beta and delta wolves;
step2: hunting and updating the position, the wolves hunting process is described mathematically as follows:
in the formula, X p (t) is a prey position vector, namely a potential optimal solution, X (t) is a current grey wolf population position vector, X (t + 1) is a next grey wolf population position vector, A and C are synergistic coefficient vectors, and D is a distance between a current candidate wolf and a head wolf;
step3: determining the moving positions of the head wolves alpha, beta and delta, wherein the updating formula of the moving positions of the head wolves is as follows:
in the formula, D α Is the distance between the current candidate wolf and the wolf alpha, D β Is the distance between the current candidate wolf and the head wolf beta, D δ Is the distance between the current candidate wolf and the heading wolf delta, X 1 Is the position vector of the first wolf alpha at the next moment, X 2 Is the position vector of the leading wolf beta at the next time, X 3 Is the position vector of the first wolf delta at the next moment, C 1 、C 2 、C 3 、A 1 、A 2 、A 3 Is a vector of cooperative coefficients;
step4: determining the moving position of the grey wolf population according to the moving positions of the alpha, beta and delta of the head wolf, wherein the updating formula of the moving position of the grey wolf population is as follows:
X(t+1)＝w 1 X 1 +w 2 X 2 +w 3 X 3
wherein the contribution weight w i The calculation formula of (2) is as follows:
in a preferred embodiment, the calculation formula of the cooperation coefficient vector a is:
A＝2a·r 1 -a
the calculation formula of the synergy coefficient vector C is as follows:
C＝2·r 2
in the formula, r 1 、r 2 Is a random number between 0 and 1, and a is a convergence factor.
In a preferred mode, a calculation expression of the convergence factor a is provided:
in the formula, F i Is the fitness value of the ith individual, F avg Is the average fitness of the current population, F max As maximum fitness of the current population, F min The minimum fitness of the current population;
when the individual fitness is smaller than the average fitness, the individual is closer to the position of a prey, and the searching range is reduced by adopting an exponential function convergence form; if the individual fitness is larger than the average fitness, the individual performance is considered to be poor, the search range is enlarged, and the position of a hunting object is continuously searched.
The invention has the beneficial effects that: according to the invention, the SVR model parameter selection is optimized through the improved Husky algorithm, and compared with the traditional distance measurement method, the distance measurement method has the advantages of simple electrical quantity measurement, strong robustness, high precision and the like.
Drawings
FIG. 1 is a schematic diagram of a three phase transmission line fault of the present invention;
FIG. 2 is a flow chart of the double-ended fault ranging model of the present invention;
figure 3 is a graph comparing the improvement of the present invention with conventional GWO for initial parameter optimization;
FIG. 4 is a graph of percentage error corresponding to samples under various fault types according to the present invention;
FIG. 5 is a comparison graph of the distance measurement error of the three methods of the present invention.
Detailed Description
The specific embodiment is as follows:
1. principle of fault location
The three-phase transmission line fault model constructed by the invention is shown in figure 1.
The transmission line equation is:
in the formula, R 0 ，L 0 ，G 0 ，C 0 Is a line parameter per kilometer length. Voltage U of transmission line head and tail ends in case of fault 1 ，U 2 And current I 1 ，I 2 Relationship through admittance matrix [16] The determination is as follows:
in the formula, Y i The calculation formula for (i =1,2,3,4) is:
in the formula, Y s The calculation formula of (A) is as follows:
Y s ＝[Y l11 +Y l21 +S] -1 (5)
in formulae (4) and (5), Y l11 ，Y l12 And Y l21 ，Y l22 Are respectively a line l 1 Head end to fault point of transmission line and line 2 Admittance matrix from fault point to end, determined by transmission line parameters and fault point position, Y s It is also affected by the fault-time transition resistance, the element in the matrix S being the inverse of the fault-time transition resistance.
From the expressions (3) to (5), it is understood that there is a correlation between the fault location and the head and tail end voltages and currents. The present invention determines this correlation by a deep learning method.
In the traditional method, three-phase voltage and current at two ends of a line are directly taken as input quantities of a model for deep learning, but the deep learning model can only effectively identify sample data close to a training sample, so that the formed model is only effective for the current line, and therefore, if the voltage level or the line length of a network is changed, the working voltage and current of the line can cause large changes of fault voltage and current at two ends of the line, so that the voltage and current values and the training data generate large deviations at the moment, the accuracy of the model near the sample data is further deteriorated, and the accuracy of distance measurement is seriously influenced, therefore, the invention provides the method for learning by taking the relative deviation of the fault quantities as fault characteristics, namely:
wherein the subscript m is a,b, c triphase, Δ U mf ，ΔI mf For relative deviation of voltage, current fault quantities, U m ，I m The voltage and the current are the voltage and the current in normal operation. The relative offset of the fault quantity comprises voltage and current in normal working, so that the influence on the distance measurement precision caused by factors such as voltage grade, line length change and the like can be avoided, the robustness of the model can be obviously improved, and the offset delta U of the head end is used for solving the problem that the fault quantity has the fault condition of the fault in the normal working mf1 ，ΔI mf1 And end offset Δ U mf2 ，ΔI mf2 And as fault characteristics, the fault characteristics are used as input of the constructed SVR model, and the model is trained.
2. Grey wolf algorithm
2.1 traditional Grey wolf Algorithm
The gray Wolf algorithm is an intelligent algorithm for catching prey by simulating a Wolf group, has the advantages of fast convergence, few parameters and the like, is named as Grey Wolf Optimizer in English and comprises the following specific steps:
(1) Generating an initial population and partitioning the hierarchy
Setting the population number, the initial population position and the like, wherein three individuals with the optimal positions are named as wolfs and are respectively named as alpha, beta and delta, and the other individuals are omega wolfs which are guided by the alpha, beta and delta wolfs.
(2) Trapping preys and updating positions
The mathematical description of the course of hunting a wolf herd is as follows:
D＝C·X p (t)-X(t) (8)
X(t+1)＝X p (t)-A·D (9)
in the formula, X p (t) is a prey position vector, namely a potential optimal solution, X (t) is a current population position vector, A and C are synergistic coefficient vectors, and the calculation formula is as follows:
A＝2a·r 1 -a (10)
C＝2·r 2 (11)
in the formula, r 1 ，r 2 Is a random number between 0 and 1, and the convergence factor a is linearly decreased from 2 to 0,t, t along with the increase of the number of population iterations max Respectively the current iteration number and the maximum iteration number.
(3) Updating the population position according to the positions of alpha, beta and delta of the wolf head
The potential solution positions in the equations (8) to (9) are states to be solved, so the moving direction of the population needs to be determined according to the positions of alpha, beta and delta wolf, and the position updating is as follows:
the update positions of the population are as follows:
2.2 improved Grey wolf Algorithm
The traditional grayish wolf algorithm has the following limitations: (1) The convergence factor a is reduced for any population individuals along with the increase of the iteration times, so that the value range of the synergistic coefficient A is decreased along with the reduction of the convergence factor, and the model solution is easy to fall into local optimum; (2) The convergence factor a is reduced according to a linear rule, but the convergence process of actual iteration is nonlinear, so that a larger search range is required in the initial stage of iteration, and the convergence speed is increased in the later stage of iteration; (3) When the position is updated by the population, the contribution weights of alpha, beta and delta to the position update are different according to the advantages and the disadvantages of the population.
In order to solve the above problems, documents [17-18] propose a self-adaptive convergence strategy, which introduces an average fitness and determines a convergence factor of each individual according to the goodness and badness of the individuals in a population, but the convergence factor range of the convergence strategy is 0-2 for any individual, so that the convergence rate of a model is reduced seriously.
In order to solve the problems of easy falling into local optimum and slow convergence speed, the invention provides a convergence factor expression, namely:
in the formula, F i Is the fitness value of the ith individual, F avg Is the average fitness of the current population, F max As maximum fitness of the current population, F min The minimum fitness of the current population; when the individual fitness is smaller than the average fitness, the individual is closer to the position of the prey, the search range of the individual is reduced by adopting an exponential function convergence mode, if the individual fitness is larger than the average fitness, the individual is considered to be poor in performance, and at the moment, the search range is enlarged, and the position of the prey is continuously searched.
In order to reflect individual goodness and badness of contribution weight in position updating, a dynamic adjustment strategy is introduced [19] Namely:
X(t+1)＝w 1 X 1 +w 2 X 2 +w 3 X 3 (17)
3. ranging model construction
3.1 support vector regression model
The support vector regression model is a derivative of a support vector machine, the support vector regression model is abbreviated as SVR in English, the support vector machine is abbreviated as SVM in English, the fitting function is solved by constructing a minimized loss function, the support vector regression model has the advantages of less required samples, high fitting precision and the like, and considering that the relation between the fault distance and the voltage and the current at two ends is complex and the nonlinearity is strong, the support vector regression model with nonlinear soft intervals is adopted, and for n groups of samples { (x) 1 ,y 1 ),(x 2 ,y 2 ),L,(x n ,y n ) The mathematical model is:
in the formula, theta is an input vector, C is a coefficient for controlling the margin width, namely a penalty coefficient, xi i 、
Is a non-negative relaxation variable,. Epsilon.is a tolerance margin, f (x) i ) The general expression for a function solved by nonlinear regression analysis is:
in the formula, a i 、
Is Lagrange multiplier, b is bias, K (x) i And x) is a kernel function, and the RBF kernel function is adopted in the invention.
The formulas (19) to (21) show that the accuracy of the SVR model depends on the selection of the penalty coefficient C and the kernel function radius g to a great extent, and therefore, the improved Husky algorithm is used for optimizing the initial parameters of the SVR model.
3.2 distance measurement model
The method establishes a double-end fault location model based on the relative offset of the fault quantity and the improved GWOO-SVR.
(1) Converting the voltage and current amplitudes into offsets
And (3) establishing a line model, measuring the amplitude of the voltage and the current in normal work and the amplitudes of the voltage and the current at two ends of the line in different fault types, fault positions and transition resistances, and calculating the relative deviation of the fault quantity by using the formulas (6) to (7).
(2) Determination of initial parameter values using improved graying algorithm
Setting a group of initial parameter values, substituting the initial parameter values into an SVR model, training randomly extracted 70% of data by adopting formulas (19) to (21), normalizing relative offset of fault quantity to be used as model input, converting corresponding fault positions into a percentage form, and then normalizing to be used as model output. And testing the rest 30% of data, measuring the testing error by adopting the average percentage error, selecting three individuals with the minimum error, updating the group of initial parameter values by adopting the formulas (8) to (18) to obtain a new generation of parameter values, and obtaining a final parameter value after iteration is finished.
(3) Obtaining a final ranging model
Substituting the C and g values obtained by optimizing into an SVR model for training to obtain a distance measurement model, and changing the voltage grade and the line length to show the excellent robustness of the model.
4. Simulation example
The invention carries out simulation based on IEEE33 node, builds up a simulation model based on Simulink software, sets the voltage level as 220kV, the frequency as 50Hz, the line length as 200km, the unit length resistance as 0.013 omega/km, the inductance as 9.773 multiplied by 10- 4 H/km, capacitance of 1.27X 10- 8 F/km。
(1) Training data acquisition
According to the invention, a large number of simulation experiments are carried out in Simulink software, the measured voltage and current at different fault positions, fault types and transition resistances are compared and analyzed, the step length of the fault position is finally selected to be 2.5% of the line length, so that 39 line fault positions are selected, the 39 positions do not comprise line end points, the fault types are 10, the number of the fault types is AG, BG, CG, AB, BC, AC, ABG, BCG, ACG and ABC, the range of the transition resistance is 1-301 omega, the step length of the selected transition resistance is 10 omega, 31 groups are provided, as shown in table 1, the measured fault voltage and current amplitude data at two ends are 12090 groups, the measured voltage and current amplitude when the two ends work normally are utilized, and the relative deviation of the fault quantity can be calculated through formulas (6) - (7), and the fault quantity is training data.
TABLE 1 Fault parameter settings
(2) SVR initial parameter optimization
An improved wolf algorithm is adopted, the initial population number is set to be 10, the iteration times are set to be 30, the optimization interval of the C and g parameters is 0-150, the average percentage error of the SVR during each iteration is used as a fitness function for optimization, the optimal C value is calculated to be 99.68, and the g value is 15.34. The parameter optimization process is shown in fig. 3.
As can be seen from fig. 3, the improved grey wolf algorithm is superior to the conventional grey wolf algorithm in convergence speed, and the final fitness function value is also slightly superior to the conventional method.
(3) Error analysis
Substituting the C and g values finally obtained by optimizing into an SVR model, training the SVR model by using 70% of data, testing the SVR model by using 30% of data, wherein the average percentage error of the model testing data is 0.13%, the corresponding percentage error of the sample under each fault type is shown in a figure 4, and the average percentage error of each fault type is shown in a table 2.
In fig. 4, the sections are divided according to the fault types, and samples in the same section are arranged from small to large according to the transition resistance, when a non-single-phase short circuit fault occurs in the line, the error is extremely small, the error is less than 0.2% except for the individual poles, and the precision is high; when a single-phase short-circuit fault occurs in a line, the influence of the transition resistance on the precision is obvious, when the transition resistance is smaller than 200 omega, the error is basically smaller than 1%, but when the transition resistance is larger, the error begins to increase and is smaller than 3% except for poles. The calculation in table 2 shows that the maximum average error is 0.09% and the minimum average error is 0.06% when the single-phase short-circuit fault occurs, the accuracy is high, and when the single-phase short-circuit fault occurs in the line, the maximum average error is 0.36% and the minimum average error is 0.17%, and the normal operation requirement can be met.
TABLE 2 mean percent error under each fault type
The average percentage error of the improved GWO-SVR, SVR and BP neural network ranging is shown in table 3, and taking an a-phase fault as an example, the absolute value of the percentage error corresponding to each sample is shown in fig. 5.
TABLE 3 mean percent error for each ranging model
As can be seen from Table 2, the average percentage error of the ranging method of the present invention is small, 0.13%, while the average percentage error of SVR ranging is 0.19%, and the average percentage error of BP neural network ranging is 0.22%. As can be seen from FIG. 5, taking the phase A fault as an example, it can also be seen that the method of the present invention has higher precision than the other two methods, which indicates that the method of the present invention has certain advantages.
(4) Model robustness analysis
1. Voltage level change
The voltage and current offsets measured when the power supply voltage class is changed into 110kV and 35kV are substituted into the calculation error of the model trained before, as shown in table 4, the fault quantity relative offset can be adopted, so that the trained ranging model can still keep high ranging precision when the voltage class is changed, otherwise, if the voltages and currents at two ends are directly substituted into the ranging model for calculation, after the 220kV data is trained, when the voltage class is changed, the model cannot identify the data at the rest voltage classes, and therefore the robustness is poor.
2. Line length change
The voltage and current offsets measured when the line length is changed to 100km and 50km are substituted into the calculation error of the previously trained model, as shown in table 5, when the line length is changed, the trained ranging model can also maintain high ranging accuracy.
In conclusion, the model of the invention has better robustness, can well adapt to the change of voltage level and line length, and has superiority.
TABLE 4 mean percent error under each fault type when voltage class changes
TABLE 5 mean percent error under each fault type when line length changes
The invention also provides a device for realizing the double-end fault distance measurement of the power transmission line, which comprises the following modules: the system comprises an input module, a deviation calculation module, an optimization model module, a training and testing module and a fault location and error analysis module.
The input module is used for obtaining the amplitude of the voltage and the current at two ends of the line during normal work and the amplitude of the voltage and the current at two ends of the line during different fault types, fault positions and transition resistances based on the double-end transmission line.
The offset calculating module is used for calculating the relative offset of the voltage and current fault quantities based on the relevant amplitude values obtained by the input module; the method comprises the following parameters: relative deviation delta U of line head end voltage fault quantity in different fault types, fault positions and transition resistances mf1 And relative deviation Delta I of the amount of line head end current fault mf1 (ii) a Relative deviation Delta U of line end voltage fault quantity in different fault types, fault positions and transition resistances mf2 And relative deviation of fault magnitude of line end current Δ I mf2 (ii) a As a set of fault signatures.
Wherein, the relative offset calculation formula of the voltage fault quantity is as follows:
the relative offset calculation formula of the current fault quantity is as follows:
in the formula, subscript m is a, b and c three phases, delta U mf Δ I being the relative deviation of the voltage fault magnitude mf For relative deviation of fault magnitude of electric current, U m Is the voltage across the line during normal operation, I m Current at both ends of the line, U, during normal operation mf Voltage across the line, I, at different fault types, at different fault locations and at different transition resistances mf The current at two ends of the line is the current at two ends of the line when the fault type is different, the fault position is different and the transition resistance is different;
the optimization model module is used for establishing and optimizing a support vector regression model, and specifically operates as follows: n groups of samples { (x) based on the fault feature set 1 ,y 1 ),(x 2 ,y 2 ),L,(x n ,y n ) Establishing a support vector regression model of a nonlinear soft interval; setting an initial parameter penalty coefficient C and a kernel function radius g of the support vector regression model; inputting the fault feature set into the support vector regression model according to a preset condition of an initial parameter penalty coefficient C and a kernel function radius g; solving the support vector regression model and obtaining a calculation result, wherein the calculation result is a fault position corresponding to the fault feature; selecting several groups of data with the minimum error of the calculation result as input variables, inputting the input variables into an improved wolf algorithm, and performing iterative optimization on the initial parameter penalty coefficient C and the kernel function radius g; and replacing the initial parameter penalty coefficient C and the kernel function radius g of the support vector regression model by the optimization result.
Firstly, the optimization model module normalizes the relative offset of the fault quantity in the fault feature set to obtain a normalized fault feature set; second, for n sets of samples { (x) of the normalized fault feature set 1 ,y 1 ),(x 2 ,y 2 ),L,(x n ,y n ) And establishing a nonlinear soft interval support vector regression model, wherein the mathematical expression of the model isThe formula is as follows:
in the formula, theta is an input vector, C is a coefficient for controlling the margin width, namely a penalty coefficient, xi i 、
Is a non-negative relaxation variable, ε is a tolerance margin, f (x) i ) Is a function solved by nonlinear regression analysis;
secondly, the optimization model module optimizes the operation: converting the calculation result into a percentage form, carrying out normalization processing, and calculating the error of the calculation result by using the average percentage error; selecting three groups of data with the minimum error of the calculation result as input variables; inputting the input variable into an improved wolf algorithm, performing iterative optimization on the initial parameter penalty coefficient C and the kernel function radius g, and obtaining the optimized parameter penalty coefficient C and the kernel function radius g; and replacing the initial parameter penalty coefficient C and the kernel function radius g of the support vector regression model with the optimized parameter penalty coefficient C and the optimized kernel function radius g.
In addition, the specific steps of the improved wolf algorithm are as follows:
s1: generating an initial population and dividing the level; wherein, the input variables are set as head wolves which are respectively named as alpha, beta and delta, and the other individuals are omega wolves which are guided by the alpha, beta and delta wolves;
s2: hunting and updating the position, the mathematical description of the course of hunting the wolf pack is as follows:
in the formula, X p (t) is a prey position vector, namely a potential optimal solution, X (t) is a current grey wolf population position vector, X (t + 1) is a next grey wolf population position vector, A and C are synergistic coefficient vectors, and D is a distance between a current candidate wolf and a head wolf;
s3: determining the moving positions of the head wolves alpha, beta and delta, wherein the updating formula of the moving positions of the head wolves is as follows:
in the formula D α Is the distance between the current candidate wolf and the head wolf alpha, D β Is the distance between the current candidate wolf and the wolf beta, D δ Is the distance between the current candidate wolf and the head wolf delta, X 1 Is the position vector of the first wolf alpha at the next moment, X 2 Is the position vector of the leading wolf beta at the next time, X 3 Is the position vector of the first wolf delta at the next moment, C 1 、C 2 、C 3 、A 1 、A 2 、A 3 Is a vector of co-operative coefficients;
s4: determining the moving position of the grey wolf population according to the moving positions of the alpha, beta and delta of the head wolf, wherein the updating formula of the moving position of the grey wolf population is as follows:
X(t+1)＝w 1 X 1 +w 2 X 2 +w 3 X 3
wherein the contribution weight w i The calculation formula of (2) is as follows:
the calculation formula of the synergy coefficient vector A is as follows:
A＝2a·r 1 -a
the calculation formula of the synergy coefficient vector C is:
C＝2·r 2
in the formula, r 1 、r 2 Is a random number between 0 and 1, and a is a convergence factor.
A computational expression of convergence factor a:
in the formula, F i Is the fitness value of the ith individual, F avg Is the average fitness of the current population, F max As maximum fitness of the current population, F min The minimum fitness of the current population;
when the individual fitness is smaller than the average fitness, the individual is closer to the position of a prey, and the searching range is reduced by adopting an exponential function convergence form; if the individual fitness is larger than the average fitness, the individual performance is considered to be poor, the search range is enlarged, and the position of a hunting object is continuously searched.
Finally, the training and testing module is used for obtaining a final ranging model; the specific operation is as follows: randomly extracting the fault feature set into two parts; one part of the training set is a training set, and the other part of the training set is a testing set; and training the support vector regression model by using the training set, verifying the accuracy of the support vector regression model by using the test set, and taking the support vector regression model meeting the accuracy requirement as the ranging model. And the fault distance measurement and error analysis module is used for fault distance measurement and error analysis based on the distance measurement model.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein. The scheme in the embodiment of the invention can be realized by adopting various computer languages, such as object-oriented programming language Java and transliterated scripting language JavaScript.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including the preferred embodiment and all changes and modifications that fall within the scope of the invention.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
The above description is only for the 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 able to cover the technical solutions and the inventive concepts of the present invention within the technical scope of the present invention.
Claims (10)
1. A power transmission line double-end fault distance measuring method is characterized by comprising the following steps:
s1: establishing a double-end transmission line, and measuring a first amplitude of voltage and current at two ends of the line during normal work and a second amplitude of voltage and current at two ends of the line during different fault types, different fault positions and different transition resistances;
s2: calculating relative offset of voltage and current fault quantities based on the first amplitude and the second amplitude, and establishing a fault characteristic set;
s3, n groups of samples { (x) according to the fault feature set 1 ,y 1 ),(x 2 ,y 2 ),L,(x n ,y n ) Establishing a support vector regression model of a nonlinear soft interval;
s4: inputting the fault feature set into the support vector regression model according to a preset initial parameter penalty coefficient C and a kernel function radius g of the support vector regression model;
s5: solving the support vector regression model and obtaining a calculation result, wherein the calculation result is a fault position corresponding to the fault feature; performing iterative optimization on the initial parameter penalty coefficient C and the kernel function radius g according to the calculation result and an improved wolf algorithm; replacing an initial parameter penalty coefficient C and a kernel function radius g of the support vector regression model by an optimization result;
s6, randomly extracting the fault feature set into two parts; one part of the training set is a training set, and the other part of the training set is a testing set; training the support vector regression model by using a training set, verifying the accuracy of the support vector regression model by using a test set, and taking the support vector regression model meeting the accuracy requirement as a ranging model; and carrying out fault location based on the location model.
2. The power transmission line double-end fault distance measurement method according to claim 1, wherein the fault feature set in step S2 includes:
relative deviation delta U of line head end voltage fault quantity in different fault types, fault positions and transition resistances mf1 And relative offset Δ I of head end current fault magnitude of line mf1 (ii) a Relative deviation Delta U of line end voltage fault quantity in different fault types, fault positions and transition resistances mf2 And relative deviation of fault magnitude of line end current Δ I mf2 ；
The relative offset calculation formula of the voltage fault quantity is as follows:
the relative offset calculation formula of the current fault quantity is as follows:
in the formula, subscript m is a, b and c three phases, delta U mf Δ I, a relative shift in the amount of voltage failure mf For relative deviation of fault magnitude of electric current, U m Is the voltage across the line during normal operation, I m Current at both ends of the line, U, during normal operation mf Voltage across the line, I, at different fault types, at different fault locations and at different transition resistances mf The current at two ends of the line is the current at two ends of the line when the fault type is different, the fault position is different and the transition resistance is different.
3. The power transmission line double-end fault distance measurement method according to claim 1, wherein the method comprisesCharacterized in that n groups of samples { (x) from the fault feature set 1 ,y 1 ),(x 2 ,y 2 ),L,(x n ,y n ) And establishing a support vector regression model of the nonlinear soft interval, which comprises the following steps:
normalizing the relative deviation of the fault quantity in the fault feature set to obtain a normalized fault feature set;
n sets of samples for the normalized fault signature set { (x) 1 ,y 1 ),(x 2 ,y 2 ),L,(x n ,y n ) And establishing a support vector regression model of the nonlinear soft interval, wherein the mathematical expression of the model is as follows:
in the formula, theta is an input vector, C is a penalty coefficient which is a coefficient for controlling the margin width, and xi i 、
Is a non-negative relaxation variable, ε is a tolerance margin, f (x) i ) Is a function solved by nonlinear regression analysis;
the process of step S5 is: converting the calculation result into a percentage form, carrying out normalization processing, and calculating the error of the calculation result by using the average percentage error; selecting three groups of data with the minimum calculation result error as input variables; and inputting the input variable into an improved wolf algorithm, performing iterative optimization on the initial parameter penalty coefficient C and the kernel function radius g, and replacing the initial parameter penalty coefficient C and the kernel function radius g of the support vector regression model with an optimization result.
4. The double-end fault location method of the power transmission line according to any one of claims 1 to 3Method characterized in that said function f (x) solved by nonlinear regression analysis i ) Is expressed as:
in the formula, a i 、
Is Lagrange multiplier, b is bias, K (x) i And x) is a kernel function.
5. The electric transmission line double-end fault distance measurement method according to claim 4, wherein the specific steps of the improved wolf algorithm are as follows:
step1: generating an initial population and dividing the level; wherein, the input variables are set as head wolves which are respectively named as alpha, beta and delta, and the other individuals are omega wolves which are guided by the alpha, beta and delta wolves;
step2: hunting and updating the position, the mathematical description of the course of hunting the wolf pack is as follows:
in the formula, X p (t) is a prey position vector, namely a potential optimal solution, X (t) is a current grey wolf population position vector, X (t + 1) is a next grey wolf population position vector, A and C are synergistic coefficient vectors, and D is a distance between a current candidate wolf and a head wolf;
step3: determining the moving positions of the head wolves alpha, beta and delta, wherein the updating formula of the moving positions of the head wolves is as follows:
in the formula, D α Is the current candidate wolf and wolf headDistance between alpha, D β Is the distance between the current candidate wolf and the head wolf beta, D δ Is the distance between the current candidate wolf and the head wolf delta, X 1 Is the position vector of the first wolf alpha at the next moment, X 2 Is the position vector, X, of the first wolf beta at the next moment 3 Is the position vector of the first wolf delta at the next moment, C 1 、C 2 、C 3 、A 1 、A 2 、A 3 Is a vector of cooperative coefficients;
step4: determining the moving position of the grey wolf population according to the moving positions of the alpha, beta and delta of the head wolf, wherein the updating formula of the moving position of the grey wolf population is as follows:
X(t+1)＝w 1 X 1 +w 2 X 2 +w 3 X 3
wherein the contribution weight w i The calculation formula of (2) is as follows:
6. the electric transmission line double-end fault distance measurement method according to claim 5, wherein the calculation formula of the cooperative coefficient vector A is as follows:
A＝2a·r 1 -a
the calculation formula of the synergy coefficient vector C is as follows:
C＝2·r 2
in the formula, r 1 、r 2 Is a random number between 0 and 1, and a is a convergence factor.
7. The double-end fault location method of the power transmission line according to claim 6, wherein a calculation expression of a convergence factor a is provided:
in the formula, F i Fitness of ith individualValue, F avg Is the average fitness of the current population, F max As maximum fitness of the current population, F min The minimum fitness of the current population;
when the individual fitness is smaller than the average fitness, the individual is closer to the position of a prey, and the searching range is reduced by adopting an exponential function convergence mode; if the individual fitness is larger than the average fitness, the individual performance is considered to be poor, the search range is enlarged, and the position of a hunting object is continuously searched.
8. A device for implementing double-end fault location of a power transmission line by using the method of the preceding claims, which is characterized by comprising the following modules:
the input module is based on the double-end transmission line and is used for obtaining a first amplitude value of voltage and current at two ends of the line during normal work and a second amplitude value of the voltage and current at two ends of the line during different fault types, different fault positions and different transition resistances;
the offset calculation module is used for calculating the relative offset of the voltage and current fault quantities based on the first amplitude and the second amplitude of the input module so as to establish a fault feature set;
the optimization model module is used for establishing and optimizing a support vector regression model, and specifically comprises the following operations: n sets of samples { (x) from the fault feature set 1 ,y 1 )},(x 2 ,y 2 ),L,(x n ,y n ) Establishing a support vector regression model of a nonlinear soft interval; inputting the fault feature set into the support vector regression model according to a preset initial parameter penalty coefficient C and a kernel function radius g of the support vector regression model; solving the support vector regression model and obtaining a calculation result, wherein the calculation result is a fault position corresponding to the fault feature; performing iterative optimization on the initial parameter penalty coefficient C and the kernel function radius g according to the calculation result and an improved wolf algorithm; replacing an initial parameter penalty coefficient C and a kernel function radius g of the support vector regression model by an optimization result;
the training and testing module is used for obtaining a final ranging model; the specific operation is as follows: randomly extracting the fault feature set into two parts; one part of the training set is a training set, and the other part of the training set is a testing set; training the support vector regression model by using a training set, verifying the accuracy of the support vector regression model by using a test set, and taking the support vector regression model meeting the accuracy requirement as a ranging model;
and the fault location and error analysis module is used for fault location and error analysis based on the location model.
9. The apparatus of claim 8, wherein the means for calculating the set of fault signatures in the migration module comprises:
relative deviation delta U of line head end voltage fault quantity in different fault types, fault positions and transition resistances mf1 And relative offset Δ I of head end current fault magnitude of line mf1 (ii) a Relative deviation Delta U of line end voltage fault quantity in different fault types, fault positions and transition resistances mf2 And relative deviation of fault magnitude of line end current Δ I mf2 ；
The relative offset calculation formula of the current fault quantity is as follows:
in the formula, subscript m is a, b and c three phases, delta U mf Δ I, a relative shift in the amount of voltage failure mf For relative deviation of fault magnitude of electric current, U m Is the voltage across the line during normal operation, I m Current at both ends of the line, U, during normal operation mf Voltage across the line, I, at different fault types, at different fault locations and at different transition resistances mf For different fault types, fault locations and transition resistancesCurrent flows at two ends of the line;
the operation process of the optimization model module is as follows: firstly, normalizing the relative offset of the fault quantity in the fault feature set to obtain a normalized fault feature set; second, for n sets of samples { (x) of the normalized fault feature set 1 ,y 1 ),(x 2 ,y 2 ),L,(x n ,y n ) And establishing a support vector regression model of the nonlinear soft interval, wherein the mathematical expression is as follows:
in the formula, theta is an input vector, C is a coefficient for controlling the margin width, namely a penalty coefficient, xi i 、
Is a non-negative relaxation variable,. Epsilon.is a tolerance margin, f (x) i ) Is a function solved by nonlinear regression analysis;
in the optimization model module, the operation process is as follows: converting the calculation result into a percentage form, carrying out normalization processing, and calculating the error of the calculation result by using the average percentage error; selecting three groups of data with the minimum calculation result error as input variables; inputting the input variable into an improved wolf algorithm, performing iterative optimization on the initial parameter penalty coefficient C and the kernel function radius g, and obtaining the optimized parameter penalty coefficient C and the kernel function radius g; and replacing the initial parameter penalty coefficient C and the kernel function radius g of the support vector regression model with the optimized parameter penalty coefficient C and the optimized kernel function radius g.
10. The apparatus of claim 9, wherein the function solved by nonlinear regression analysisf(x i ) Is expressed as:
in the formula, a i 、
Is Lagrange multiplier, b is bias, K (x) i X) is a kernel function;
the improved gray wolf algorithm comprises the following specific steps:
s1: generating an initial population and dividing the level; wherein, the input variables are set as head wolves which are respectively named as alpha, beta and delta, and the other individuals are omega wolves which are guided by the alpha, beta and delta wolves;
s2: hunting and updating the position, the mathematical description of the course of hunting the wolf pack is as follows:
in the formula, X p (t) is a prey position vector, namely a potential optimal solution, X (t) is a grey wolf population position vector at the current moment, X (t + 1) is a grey wolf population position vector at the next moment, A and C are synergistic coefficient vectors, and D is the distance between the current candidate wolf and the wolf head;
s3: determining the moving positions of the head wolves alpha, beta and delta, wherein the updating formula of the moving positions of the head wolves is as follows:
in the formula, D α Is the distance between the current candidate wolf and the wolf alpha, D β Is the distance between the current candidate wolf and the head wolf beta, D δ Is the distance between the current candidate wolf and the head wolf delta, X 1 Is the position vector of the first wolf alpha at the next moment, X 2 Is the next time pointPosition vector of wolf beta, X 3 Is the position vector of the first wolf delta at the next time, C 1 、C 2 、C 3 、A 1 、A 2 、A 3 Is a vector of co-operative coefficients;
s4: determining the moving position of the grey wolf population according to the moving positions of the alpha, beta and delta of the head wolf, wherein the updating formula of the moving position of the grey wolf population is as follows:
X(t+1)＝w 1 X 1 +w 2 X 2 +w 3 X 3
wherein the contribution weight w i The calculation formula of (c) is:
the calculation formula of the synergy coefficient vector A is as follows:
A＝2a·r 1 -a
the calculation formula of the synergy coefficient vector C is:
C＝2·r 2
in the formula, r 1 、r 2 Is a random number between 0 and 1, and a is a convergence factor.
A computational expression of convergence factor a:
in the formula, F i Is the fitness value of the ith individual, F avg Is the average fitness of the current population, F max Is the maximum fitness of the current population, F min The minimum fitness of the current population;
when the individual fitness is smaller than the average fitness, the individual is closer to the position of a prey, and the searching range is reduced by adopting an exponential function convergence mode; if the individual fitness is larger than the average fitness, the individual is considered to be poor in performance, the search range is enlarged, and the position of the prey is continuously searched.
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