CN105808967B - Exciter saturation coefficient computational methods based on secant iterative method - Google Patents
Exciter saturation coefficient computational methods based on secant iterative method Download PDFInfo
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Abstract
The present invention provides a kind of exciter saturation coefficient computational methods based on secant iterative method, by the progressive fitting exciter no-load curve of secant iterative method, to reach the purpose for calculating saturation coefficient.This method avoids error caused by manually recognizing, and it is suitable for the test data containing interference.The present invention has the result of calculation more more precisely consistent than artificial interpretation, the problem of avoiding different artificial sentence read result difference, suitable for the exciter saturation coefficient calculating based on exciter no-load characteristic.
Description
Technical Field
The invention relates to the technical field of generator excitation systems, in particular to a method for calculating saturation coefficients of an exciter based on a secant iteration method.
Background
Exciter saturation coefficient C in parameter calculation of excitation system of large-scale single-machine excitation generator set 1 And C 2 Is a key parameter, which is defined as follows:
in which I Ef After the no-load characteristic of the exciter is tested, the per unit value, U, of the exciting current of the exciter is measured fd The per unit value of the exciting voltage is measured after the no-load characteristic of the exciter is tested.
The parameter directly influences the dynamic characteristics of the generator excitation system and is one of the key parameters of the generator excitation system. The accurate calculation of the saturation coefficient by the exciter no-load curve is the key for accurately calculating the parameters of the generator excitation system.
The widely applied calculation method at present only uses an exciter air gap line and a no-load saturation curve, and calculates exciter exciting current values at 0.75 times and 1 time of maximum exciting voltage values by solving the following equation sets:
in which I fB 、I fJ Is the exciting current value at the position of the exciter air gap line corresponding to 1 time and 0.75 time of the maximum exciting voltage value respectively, I f0 、I fK Is the exciting current value, U, at the position corresponding to the maximum voltage value of 1 time and 0.75 time on the no-load curve of the exciter fM Is the maximum excitation voltage.
The saturation coefficient is determined by an exciter no-load characteristic test curve according to the formula, but the test result of the exciter no-load curve in the actual field test is influenced by various interference factors in the environment and often contains certain disturbance. And saturation factor pair I f0 、I fK The numerical value of (2) is high in requirement, large errors can occur when identification is carried out by means of manual experience, and the consistency of different interpretation results is difficult to guarantee.
Disclosure of Invention
The invention provides an exciter saturation coefficient calculation method based on a secant iteration method, aiming at a no-load curve obtained in a no-load characteristic test, the saturation coefficient can be calculated under the condition of containing interference data, the accurate interpretation of the test data is realized, and an accurate basis is provided for the parameter calculation of a generator excitation system.
An exciter saturation coefficient calculation method based on a secant iteration method comprises the following steps:
(1) Through the no-load characteristic test of the exciter, a group of no-load test data of the exciter are obtained:
X＝{I i ,U i },i＝1,2,…,m；
wherein U is i For measured excitationMagnetic voltage value, I i M is a positive integer greater than or equal to 2 for the measured exciter exciting current value;
(2) The following set of iterative equations is established by the principle of least squares:
wherein C 1 And C 2 The exciter saturation coefficient can be obtained by the principle of least square method, and the saturation coefficient C satisfying the above formula 1 And C 2 The fitted curve has the minimum mean square error;
(3) From variable C 2 To a certain initial value C 2,1 Starting from the first two formulas of the step (2), solving the variable C 1 Two initial values of C 1,1 (1) And C 1,1 (2) ：
(4) Two C to be solved 1 Substituting the initial values into the discriminant together:
F 1 ＝C 1,1 (1) -C 1,1 (2)
(5) If the result of the above-mentioned discriminant is greater than 0, C is decreased 2 Is such that it is C 2,2 (ii) a If the result is less than 0, increase C 2 Is such that it is C 2,2 ：
C 2,2 ＝C 2,1 -0.1,if(C 1,1 (1) -C 1,1 (2) )>0，
C 2,2 ＝C 2,1 +0.1,if(C 1,1 (1) -C 1,1 (2) )<0，
(6) Using C obtained in step (5) 2 New value of C 2,2 Repeating the formula of steps (3) - (4) to obtain a new value F 2 ：
(7) Calculating C by using a secant iteration formula 2 Correction value of (C) 2,3 ：
(8) And (5) repeating the steps (6) to (7) and performing iterative solution:
(9) When the absolute value of the third equation in step (8) is less than 10 -9 Then, the saturation coefficient C satisfying the condition can be obtained 1 And C 2 In which C is 1 Take the last calculation C 1 (1) And C 1 (2) Average value of (a).
The invention has the beneficial effects that:
1. the method has more accurate and consistent calculation results than manual interpretation, and avoids the problem of different manual interpretation results;
2. fitting is carried out based on the principle of a least square method, and the mean square error of a fitting curve is minimum;
3. the used secant iteration method can obtain the calculation result in limited iteration times.
Drawings
FIG. 1 is a schematic representation of test data employed in the present invention;
FIG. 2 is a saturation coefficient C calculated using the present invention 2 Schematic diagram of the iteration.
Detailed Description
The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings and specific examples.
The no-load characteristic curve obtained by measuring the no-load characteristic test of a certain synchronous generator exciter is shown in figure 1. Reading the test data to obtain a set of no-load characteristic data as follows:
where U is the measured excitation voltage value and I is the measured exciter excitation current value.
Given saturation coefficient C 2,1 Initial value of (C) 2,1 =1, substituting the first and second equations of the iterative equation set:
can be solved to obtain the saturation coefficient C 1 Two initial values of C 1,1 (1) And C 1,1 (2) ：
And (3) calculating a discriminant:
F 1 ＝C 1,1 (1) -C 1,1 (2) ＝-1.97×10 -7
the discriminant is less than 0, and C is increased 2 The numerical value of (A):
C 2,2 ＝1+0.1＝1.1
will C 2,2 Substituting the iteration equation set to continuously calculate C 1 ：
And (3) calculating a discriminant:
F 2 ＝C 1,2 (1) -C 1,2 (2) ＝-4.51×10 -8
calculating C by secant formula 2 ：
The iterative loop calculation is entered, and the results are shown in the following table:
when iterating to the fifth time, the absolute value of the discriminant is less than 10 -9 And ending iteration, wherein the obtained saturation coefficient is as follows:
saturation coefficient C 2 The iterative process of (a) is shown in figure 2.
Comparing the variance of the algorithm of the present invention with the conventional algorithm, the test data can be read:
solving the following equation set to obtain C 1 And C 2 ：
Obtaining by solution:
the variance comparing the conventional algorithm to the inventive cut-line iteration is as follows:
therefore, the variance of the secant iteration method is far smaller than that of the conventional algorithm, and the fitting precision is higher.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are also within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (1)
1. An exciter saturation coefficient calculation method based on a secant iteration method is characterized by comprising the following steps of:
(1) Through the no-load characteristic test of the exciter, a group of no-load test data of the exciter are obtained:
X＝{I i ,U i },i＝1,2,…,m；
wherein U is i For measured excitation voltage value, I i M is a positive integer greater than or equal to 2 for the measured exciter exciting current value;
(2) The following set of iterative equations is established by the principle of least squares:
wherein C 1 And C 2 For the exciter saturation systemNumber, as known from the principle of least squares, the saturation coefficient C satisfying the above formula 1 And C 2 The fitted curve has the minimum mean square error;
(3) From variable C 2 To a certain initial value C 2,1 Starting from the first two formulas of the step (2), solving the variable C 1 Two initial values of (C) 1,1 (1) And C 1,1 (2) ：
(4) Two C to be solved 1 The initial values are substituted into the discriminant together:
F 1 ＝C 1,1 (1) -C 1,1 (2)
(5) If the result of the above-mentioned discriminant is greater than 0, C is decreased 2 Is such that it is C 2,2 (ii) a If the result is less than 0, increase C 2 Is such that it is C 2,2 ：
C 2,2 ＝C 2,1 -0.1,if(C 1,1 (1) -C 1,1 (2) )>0，
C 2,2 ＝C 2,1 +0.1,if(C 1,1 (1) -C 1,1 (2) )<0，
(6) Using C obtained in step (5) 2 New value of (C) 2,2 Repeating the formula of steps (3) - (4) to obtain a new value F 2 ：
(7) Calculating C by using a secant iteration formula 2 Correction value of (C) 2,3 ：
(8) And (5) repeating the steps (6) to (7) and performing iterative solution:
(9) When the absolute value of the third equation in step (8) is less than 10 -9 Then, the saturation coefficient C satisfying the condition can be obtained 1 And C 2 In which C is 1 Take the last calculation C 1 (1) And C 1 (2) Average value of (a).
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101272116A (en) * | 2008-04-30 | 2008-09-24 | 山东电力研究院 | Modeling method of generator excitation system |
| CN104135018A (en) * | 2014-08-04 | 2014-11-05 | 东南大学 | Distribution method for angular speed non-linear excitation controllers |
| CN105403800A (en) * | 2015-12-30 | 2016-03-16 | 华北电力科学研究院有限责任公司 | Electric power system parameter determination method and device |
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| KR100794245B1 (en) * | 2006-08-22 | 2008-01-11 | 한국전기연구원 | An intelligent monitoring system of the reactive power limit of generator using machine model parameters and method the same |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN101272116A (en) * | 2008-04-30 | 2008-09-24 | 山东电力研究院 | Modeling method of generator excitation system |
| CN104135018A (en) * | 2014-08-04 | 2014-11-05 | 东南大学 | Distribution method for angular speed non-linear excitation controllers |
| CN105403800A (en) * | 2015-12-30 | 2016-03-16 | 华北电力科学研究院有限责任公司 | Electric power system parameter determination method and device |
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