Application of Singular Value Decomposition (SVD) Theory in Synchronous Motor Parameter Identification by Journal of Changsha University of Electric Power (Jiangsu) In the parameter identification of synchronous motor, this method can obtain the shortest vector solution in the least squares identification algorithm regardless of the singularity of the Jacobian matrix, thus improving the convergence of the identification algorithm and reducing the number of iterations. The parameters of the 200 W turbo generator were successfully identified by the algorithm.
: Singular Value Decomposition Basic Parameter Identification 1 Problem The convergence problem of the algorithm exists by least squares identification (LSE) parameter. Because the least squares equation is used to solve the parameter correction amount X when using the least squares parameter identification, in the above formula, the formed Jacobian matrix (Jaobi k, the condition number is likely to be large, so that the solution The condition of the correction amount X is worse, so that the correction amount X obtained is unreasonable and the identification fails. It has been proved that the singular value decomposition (SVD) theory is applied to the identification process to improve the convergence and reduce the identification of the algorithm. The number of iterations is very advantageous.
2 Usually the method for solving the least squares law equation and the improved method for the Jacobian matrix singularity set the given matrix A ∈R 2 , then the least squares problem is the following special form of minimal problem.
For the sake of simplicity, the problem of least squares is used. The necessary and sufficient condition for ‖AX y‖ to obtain the minimum value is that AX is the orthogonal projection of y on R (A ), that is, X satisfies the normal equation.
For the nonlinear problem, it is obvious that the necessary and sufficient condition for X is the only solution of the equation (5) is that the Jacobian matrix A is a non-singular matrix, ie (A exists. But in the singular case, solving X will fail, resulting in The entire equation of the form is constructed.
To determine X, where U 0 is the damping factor and I is the unit matrix. This method (L-method for short) can play the following two functions: 1) According to the eigenvalue perturbation theorem, when the eigenvalue of the U matrix (AI) Both are greater than zero. Therefore, (A I ) is a symmetric positive definite matrix. Therefore, the equation (6) can be solved by a decomposition method such as holesky.
2) When the Jacobian matrix A condition is large, the iteration can still be performed.
The L-method does make the least squares convergence problem very effective, but it can only be established in purely mathematical sense. Since the introduction of damping with a factor of U does ensure that equation (6) has a solution X, the norm of the solution ‖X ‖ is related to the value of U. Therefore, the X that is often solved does not adapt to a specific physical problem, and the numerical overflow occurs in the mathematical calculation of the specific physical model after the X X is corrected, and the identification fails. However, the (SVD) theory cannot guarantee that the X obtained in each iteration is the most reasonable, but it can guarantee that the obtained X norm ‖X ‖ is the shortest, thus effectively suppressing the overflow problem in the numerical calculation of the physical model.
3 SVD application in synchronous motor parameter identification and the application of 3.1 singular value decomposition theory in identification. The least squares solution is obtained by equation (5). If SVD is used, it is not necessary to invert, and when the matrix is ​​not full rank, Still able to handle. Transform A with an orthogonal matrix, which is known from equation (1).
k , U, V are orthogonal matrices. It is easy to derive the vector Z that minimizes ‖ δ(X ) 由 from equation (11). From this, it is known that r in the system of diagonal equations are accurately solved. Come out, the remaining equations lead to possible non-zero residuals, and it can be seen that when A is not full rank, let ‖δ (the solution with the smallest X is not unique. But in the identification process, I want to get the shortest length. The solution vector, as long as the basic mathematical model of the σ3.2 synchronous motor selects the physical model of the synchronous motor as d and the q-axis each has an equivalent damping loop, then the flux equation is the voltage equation when the excitation winding is ignored. With the mutual leakage resistance between the longitudinal axis damper windings, X ad, r is the resistance value of the stator winding. Therefore, the equations of state and observation equations required for the equations (14) and (15) can be constructed.
Abbreviated as the required observation equation.
Abbreviated as the required state equation, where α=[ X 3 .3SVD applies the algorithm in the parameter identification of synchronous motor to realize the identification of the synchronous motor parameter α. The following steps can be performed: 1) According to the equation of state (19) and the equation of observation (17) ), the law equation that forms the least squares.
Where Y is the calculated output vector calculated by equations (19) and (17), Y is the measured output vector, and R is the diagonal positive weight matrix, representation, and representation. Then, the equation (20) can be rewritten as A 2 ) using the singular value decomposition theory to obtain the shortest solution vector αZ of the correction amount α of the parameter α to be recognized, wherein 3) the parameter correction is performed using α. Because of the shortest solution vector, when i = j, take g 4 ) to make a judgment based on the objective function J (α). Where) is the measured output vector, Y') is the equation (17) to calculate the output vector.
4 Application examples Using the algorithm of this paper, the online parameter identification of the 200 W turbine generator of Tongliao Power Plant was successfully carried out.
The design value of the basic parameters of the unit (*based on experience).
Its identification results.
5 Conclusions For the first time, SVD is applied to the parameter identification of synchronous motors. The algorithm is successfully used to identify the turbo generator (QFSQ 1) compared with the L identification method. The algorithm has fast speed, less iterations and large convergence range. Advantages 2) The parameter X obtained from the identification is smaller than the design value, which is mainly caused by saturation, which is reduced by about 10, and the identification value of the parameter X is larger than the design value, indicating that the design value of the excitation winding and the damper winding leakage reactance is based on experience. Too small, the identification value of T is correspondingly small. 3) Calculating the transient process after the disturbance of the synchronous motor using the parameters identified by the algorithm is closer to the actual measurement process than the design value provided by the manufacturer, and proves that the algorithm is successful.
Grob, Wan Dong Luo. Matrix calculation [ ] . Lian Qingrong translation. Dalian: Dalian University of Technology Press, Gao Jingde, Zhang Linzheng. Basic theory and analysis method of motor process [ ] . Beijing: Science Press, 1985.
Journal of Changsha University of Electric Power (Natural Science Edition) February 2000
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