Characteristic oscillation frequency early warning method and system for wind turbines
By dividing the wind turbine into combined components and obtaining and analyzing its characteristic frequency, the problem of early warning of characteristic oscillation frequency of wind turbine is solved, and the risk of internal self-excitation oscillation is reduced.
Patent Information
- Application Number
- CN202310292966.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-03-23
- Publication Date
- 2025-02-18
- Estimated Expiration
- 2043-03-23
AI Technical Summary
The prior art is difficult to early warning of the characteristic oscillation frequency of wind turbines, resulting in a high risk of internal self-exciting oscillation of the unit.
By dividing the wind turbine into N combined components, the characteristic frequencies of each combined component are obtained, and the torque excitation source value and characteristic oscillation frequency are determined based on these frequencies, and the early warning is finally made based on these frequencies.
The early warning of the characteristic oscillation frequency of the wind turbine unit is achieved, so that the unit can avoid dangerous frequencies and reduce the risk of internal self-exciting oscillation.
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Figure CN116136206B_ABST
Abstract
Description
Technical Field
[0001] The present application relates to the field of oscillation frequency early warning, and in particular to a characteristic oscillation frequency early warning method and system for a wind turbine generator set. Background Art
[0002] In the design and normal operation of wind turbines, many technical means are used to avoid oscillation during the operation of the turbines. For example, the characteristic frequencies of various components of the wind turbines are detected in advance, and the speeds corresponding to these frequencies are set to the fast transition zone in actual operation to avoid staying in this frequency range for too long; the movement and physical quantity fluctuations of various components of the turbine are monitored in real time during operation, and the turbine is shut down for maintenance as soon as possible when signs of oscillation are found.
[0003] The existing technical solutions are only to avoid the problem in design and operation, and to carry out emergency treatment for the units that have already started to oscillate. However, it is still not possible to give early warning of the characteristic oscillation frequency of the unit, that is, it is not possible to know in advance during operation what frequency signal will stimulate the unit to produce the overall oscillation risk, which makes the risk of internal self-excited oscillation of the unit greater. Summary of the invention
[0004] The present application provides a characteristic oscillation frequency early warning method and system for a wind turbine generator set, so as to at least solve the technical problem that the risk of internal self-excited oscillation of the wind turbine generator set is relatively high.
[0005] The first embodiment of the present application provides a characteristic oscillation frequency early warning method for a wind turbine generator set, the method comprising:
[0006] Divide the wind turbine into N components and obtain the characteristic frequency of each component;
[0007] Determine the torque excitation source value corresponding to each combined component according to the characteristic frequency of each combined component;
[0008] Determine the characteristic oscillation frequency of each combined component according to the torque excitation source value corresponding to each combined component;
[0009] Providing an early warning of the characteristic oscillation frequency of the wind turbine generator system based on the characteristic oscillation frequency of each of the combined components;
[0010] Wherein, N is an integer greater than or equal to 1.
[0011] Preferably, the wind turbine generator set is divided into N combined components, including:
[0012] The wind turbine generator set is divided into N combined components based on the complexity that each component in the wind turbine generator set can bear.
[0013] Preferably, the calculation formula of the torque excitation source value corresponding to each combination component is as follows:
[0014]
[0015] In the formula, x i,t is the torque excitation source value corresponding to the i-th component at time t, F i is the characteristic frequency of the ith component, B j is the value of the jth characteristic frequency multiplier, j∈[1~M], M is the total number of characteristic frequency multipliers.
[0016] Further, the determining of the characteristic oscillation frequency of each combined component according to the torque excitation source value corresponding to each combined component includes:
[0017] Applying torque excitation sources to the rotating shaft of the wind turbine set in sequence, and obtaining a speed value curve of the wind turbine set generator under each torque excitation source value;
[0018] Fourier analysis is performed on the speed curve of the wind turbine generator under each torque excitation source value to obtain the signal amplification factor of each characteristic frequency corresponding to each torque excitation source value;
[0019] Determine the frequency value at each signal amplification factor corresponding to each torque excitation source value according to the signal amplification factor of each characteristic frequency corresponding to each torque excitation source value;
[0020] The characteristic oscillation frequency of each combined component is determined according to the frequency value at each signal amplification factor corresponding to each torque excitation source value.
[0021] Furthermore, the characteristic oscillation frequency of each combined component is determined according to the frequency value at each signal amplification factor corresponding to each torque excitation source value, including:
[0022] The maximum frequency is selected from the frequency values at each signal amplification factor corresponding to each torque excitation source value;
[0023] The maximum frequency value corresponding to each torque excitation source value is taken as the characteristic oscillation frequency of each combined component.
[0024] Preferably, the step of providing an early warning of the characteristic oscillation frequency of the wind turbine generator set based on the characteristic oscillation frequency of each combined component comprises:
[0025] Obtaining the absolute value of the difference between the operating frequency of the wind turbine generator set and the characteristic oscillation frequency of each component;
[0026] When the number of absolute values of the differences that are less than or equal to the preset alarm threshold is greater than or equal to 1, an early warning is issued for the characteristic oscillation frequency of the wind turbine generator set.
[0027] The second embodiment of the present application provides a characteristic oscillation frequency early warning system for a wind turbine generator set, the system comprising:
[0028] A division module is used to divide the wind turbine into N combined components and obtain the characteristic frequency of each combined component;
[0029] A first determination module is used to determine the torque excitation source value corresponding to each combined component according to the characteristic frequency of each combined component;
[0030] A second determination module is used to determine the characteristic oscillation frequency of each combined component according to the torque excitation source value corresponding to each combined component;
[0031] An early warning module, used for issuing an early warning on the characteristic oscillation frequency of the wind turbine generator set based on the characteristic oscillation frequency of each of the combined components;
[0032] Wherein, N is an integer greater than or equal to 1.
[0033] Preferably, the wind turbine generator set is divided into N combined components, including:
[0034] The wind turbine generator set is divided into N combined components based on the complexity that each component in the wind turbine generator set can bear.
[0035] Furthermore, the second determining module includes:
[0036] A first acquisition unit is used to sequentially apply torque excitation sources to the rotating shaft of the wind turbine generator set to obtain a speed value curve of the wind turbine generator set under each torque excitation source value;
[0037] An analysis unit, used to perform Fourier analysis on the speed value curve of the wind turbine generator under each torque excitation source value, and obtain the signal amplification factor of each characteristic frequency corresponding to each torque excitation source value;
[0038] A first determining unit, configured to determine the frequency value at each signal amplification factor corresponding to each torque excitation source value according to the signal amplification factor of each characteristic frequency corresponding to each torque excitation source value;
[0039] The second determination unit is used to determine the characteristic oscillation frequency of each combined component according to the frequency value at each signal amplification factor corresponding to each torque excitation source value.
[0040] Furthermore, the second determining unit includes:
[0041] A screening submodule, used to screen out the maximum frequency value from the frequency values at each signal amplification factor corresponding to each torque excitation source value;
[0042] The determination submodule is used to take the maximum frequency value corresponding to each torque excitation source value as the characteristic oscillation frequency of each combined component.
[0043] The technical solution provided by the embodiments of the present application brings at least the following beneficial effects:
[0044] The present application proposes a characteristic oscillation frequency warning method and system for a wind turbine, the method comprising: dividing the wind turbine into N components and obtaining the characteristic frequency of each component; determining the torque excitation source value corresponding to each component according to the characteristic frequency of each component; determining the characteristic oscillation frequency of each component according to the torque excitation source value corresponding to each component; and issuing an early warning on the characteristic oscillation frequency of the wind turbine based on the characteristic oscillation frequency of each component; wherein N is an integer greater than or equal to 1. The technical solution proposed in the present application obtains a dangerous frequency set of the current unit under the current operating environment for early warning, so that the unit can avoid these frequencies for operation, greatly reducing the risk of internal self-excited oscillation of the unit.
[0045] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through the practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS
[0046] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:
[0047] Figure 1 A flow chart of a characteristic oscillation frequency early warning method for a wind turbine generator set provided according to an embodiment of the present application;
[0048] Figure 2 A structural diagram of a characteristic oscillation frequency warning system for a wind turbine generator set provided according to an embodiment of the present application;
[0049] Figure 3 A structural diagram of a second determination module provided according to an embodiment of the present application;
[0050] Figure 4 A structural diagram of a second determination unit provided according to an embodiment of the present application;
[0051] Figure 5 The figure is a structural diagram of an early warning module provided according to one embodiment of the present application. DETAILED DESCRIPTION
[0052] Embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.
[0053] The characteristic oscillation frequency warning method and system of the wind turbine proposed in the present application include: dividing the wind turbine into N components and obtaining the characteristic frequency of each component; determining the torque excitation source value corresponding to each component according to the characteristic frequency of each component; determining the characteristic oscillation frequency of each component according to the torque excitation source value corresponding to each component; and issuing an early warning on the characteristic oscillation frequency of the wind turbine based on the characteristic oscillation frequency of each component; wherein N is an integer greater than or equal to 1. The technical solution proposed in the present application obtains a set of dangerous frequencies of the current unit under the current operating environment for early warning, so that the unit can avoid these frequencies for operation, greatly reducing the risk of internal self-excited oscillation of the unit.
[0054] The characteristic oscillation frequency early warning method and system of a wind turbine generator system according to an embodiment of the present application will be described below with reference to the accompanying drawings.
[0055] Embodiment 1
[0056] Figure 1 Flow chart of a characteristic oscillation frequency early warning method for a wind turbine generator set provided according to one embodiment of the present application, such as Figure 1 As shown, the method includes:
[0057] Step 1: Divide the wind turbine into N components and obtain the characteristic frequency of each component;
[0058] Wherein, N is an integer greater than or equal to 1.
[0059] In the embodiment of the present disclosure, the wind turbine generator set is divided into N combined components, including:
[0060] The wind turbine generator set is divided into N combined components based on the complexity that each component in the wind turbine generator set can bear.
[0061] Step 2: Determine the torque excitation source value corresponding to each combined component according to the characteristic frequency of each combined component.
[0062] It should be noted that the calculation formula of the torque excitation source value corresponding to each combination component is as follows:
[0063]
[0064] In the formula, x i,t is the torque excitation source value corresponding to the i-th component at time t, F i is the characteristic frequency of the ith component, B j is the value of the jth characteristic frequency multiplier, j∈[1~M], M is the total number of characteristic frequency multipliers.
[0065] Step 3: Determine the characteristic oscillation frequency of each combined component according to the torque excitation source value corresponding to each combined component.
[0066] In the embodiment of the present disclosure, step 3 specifically includes:
[0067] Step 3-1: applying torque excitation sources to the rotating shaft of the wind turbine set in sequence, and obtaining a speed value curve of the wind turbine generator under each torque excitation source value;
[0068] Step 3-2: Perform Fourier analysis on the speed curve of the wind turbine generator under each torque excitation source value to obtain the signal amplification factor of each characteristic frequency corresponding to each torque excitation source value;
[0069] Among them, using the formula Calculate the signal amplification factor of each characteristic frequency, where s(m) is the signal amplification factor of the mth characteristic frequency, and Y(m) is the amplitude of the signal with a frequency of m×Fi after Fourier analysis of the wind turbine generator speed curve.
[0070] Step 3-3: determining the frequency value at each signal amplification factor corresponding to each torque excitation source value according to the signal amplification factor of each characteristic frequency corresponding to each torque excitation source value;
[0071] Step 3-4: Determine the characteristic oscillation frequency of each combined component according to the frequency value at each signal amplification factor corresponding to each torque excitation source value.
[0072] Wherein, the steps 3-4 specifically include:
[0073] Step 3-4-1: Filter out the maximum frequency value from the frequency values at each signal amplification factor corresponding to each torque excitation source value;
[0074] Step 3-4-2: Take the maximum frequency value corresponding to each torque excitation source value as the characteristic oscillation frequency of each combined component.
[0075] The characteristic oscillation frequency refers to the characteristic frequency at which the wind turbine generator set exhibits a strong amplification and amplitude enhancement effect on vibrations of a certain frequency, thereby causing the unit to be in a dangerous operating state.
[0076] Step 4: issuing an early warning on the characteristic oscillation frequency of the wind turbine generator system based on the characteristic oscillation frequency of each combined component.
[0077] It should be noted that the step 4 specifically includes:
[0078] Obtaining the absolute value of the difference between the operating frequency of the wind turbine generator set and the characteristic oscillation frequency of each component;
[0079] When the number of absolute values of the differences that are less than or equal to the preset alarm threshold is greater than or equal to 1, an early warning is issued for the characteristic oscillation frequency of the wind turbine generator set.
[0080] In order to more clearly illustrate the implementation process of a characteristic oscillation frequency warning method for a wind turbine generator set according to an embodiment of the present application, a specific method embodiment is described in detail below:
[0081] 1) Decompose the wind turbine into N components (the decomposition of the components is generally based on the complexity that the system can bear, N can be freely selected, generally 10-100), input the characteristic frequency of each component, a total of N characteristic frequencies, marked as F1-FN;
[0082] 2) Let i = 1;
[0083] 3) Give the wind turbine generator set an independent torque excitation source x i,t :
[0084]
[0085] In the formula, x i,t is the torque excitation source value corresponding to the i-th component at time t, F i is the characteristic frequency of the ith component, B j is the value of the jth characteristic frequency multiplier, j∈[1~M], M is the total number of characteristic frequency multipliers, generally 10-50;
[0086] 4) Detect the wind turbine generator speed value wi(t) curve and perform Fourier analysis on it to obtain the signal amplification factor of each frequency in 1-M, where the signal amplification factor of the mth frequency is calculated as:
[0087]
[0088] Where Y(m) is the amplitude of the signal with a frequency of m×Fi after Fourier analysis of the wi(t) curve;
[0089] 5) Take the frequency value mmax×Fi corresponding to the largest s(mmax) in 1-M as the output frequency value of this cycle.
[0090] 6) Determine whether i is less than N. If yes, set i=i+1 and return to 3); if no, proceed to 7);
[0091] 7) Output all the mmax×Fi frequency value sets formed in the cycle, a total of N elements, as the calculation result output, which is the operating frequency that the wind turbine should avoid in this operation;
[0092] 8) Obtaining the absolute value of the difference between the operating frequency of the wind turbine generator set and the characteristic oscillation frequency of each component in the frequency value set;
[0093] When the number of absolute values of the differences that are less than or equal to the preset alarm threshold is greater than or equal to 1, an early warning is issued for the characteristic oscillation frequency of the wind turbine generator set.
[0094] To summarize, the characteristic oscillation frequency warning method for a wind turbine set proposed in this embodiment analyzes the signal waveforms of the characteristic input and output quantities of the set during the operation of the set, calculates the amplitude amplification of each possible characteristic frequency, and obtains the set of dangerous frequencies of the current set under the current operating environment through analysis and comparison, so that the set can avoid these frequencies for operation, greatly reducing the risk of internal self-oscillation of the set.
[0095] Embodiment 2
[0096] Figure 2 FIG. 1 is a structural diagram of a characteristic oscillation frequency warning system for a wind turbine generator set according to an embodiment of the present application. Figure 2 As shown, the system comprises:
[0097] A division module 100 is used to divide the wind turbine into N combined components and obtain the characteristic frequency of each combined component;
[0098] A first determination module 200 is used to determine the torque excitation source value corresponding to each combined component according to the characteristic frequency of each combined component;
[0099] The second determination module 300 is used to determine the characteristic oscillation frequency of each combined component according to the torque excitation source value corresponding to each combined component;
[0100] An early warning module 400 is used to issue an early warning on the characteristic oscillation frequency of the wind turbine generator system based on the characteristic oscillation frequency of each of the combined components;
[0101] Wherein, N is an integer greater than or equal to 1.
[0102] In the embodiment of the present disclosure, the wind turbine generator set is divided into N combined components, including:
[0103] The wind turbine generator set is divided into N combined components based on the complexity that each component in the wind turbine generator set can bear.
[0104] The calculation formula of the torque excitation source value corresponding to each combination component is as follows:
[0105]
[0106] In the formula, x i,tis the torque excitation source value corresponding to the i-th component at time t, F i is the characteristic frequency of the ith component, B j is the value of the jth characteristic frequency multiplier, j∈[1~M], M is the total number of characteristic frequency multipliers.
[0107] Further, such as Figure 3 As shown, the second determination module 300 includes:
[0108] The first acquisition unit 301 is used to sequentially apply torque excitation sources to the rotating shaft of the wind turbine generator set to obtain a speed value curve of the wind turbine generator set under each torque excitation source value;
[0109] The analysis unit 302 is used to perform Fourier analysis on the speed value curve of the wind turbine generator under each torque excitation source value to obtain the signal amplification factor of each characteristic frequency corresponding to each torque excitation source value;
[0110] A first determining unit 303 is used to determine the frequency value at each signal amplification factor corresponding to each torque excitation source value according to the signal amplification factor of each characteristic frequency corresponding to each torque excitation source value;
[0111] The second determination unit 304 is used to determine the characteristic oscillation frequency of each combined component according to the frequency value at each signal amplification factor corresponding to each torque excitation source value.
[0112] Among them, Figure 4 As shown, the second determining unit 304 includes:
[0113] A screening submodule 3041 is used to screen out the maximum frequency value from the frequency values at each signal amplification factor corresponding to each torque excitation source value;
[0114] The determination submodule 3042 is used to use the maximum frequency corresponding to each torque excitation source value as the characteristic oscillation frequency of each combined component.
[0115] In the embodiments of the present disclosure, Figure 5 As shown, the early warning module 400 includes:
[0116] The second acquisition unit 401 is used to acquire the absolute value of the difference between the operating frequency of the wind turbine and the characteristic oscillation frequency of each component;
[0117] The early warning unit 402 is used to issue an early warning for the characteristic oscillation frequency of the wind turbine generator when the number of absolute values of the differences that are less than or equal to the preset alarm threshold is greater than or equal to 1.
[0118] To sum up, the characteristic oscillation frequency warning system of a wind turbine set proposed in this embodiment, during the operation of the set, analyzes the signal waveforms of the characteristic input and output quantities of the set, calculates the amplitude amplification of each possible characteristic frequency, and obtains the set of dangerous frequencies of the current set under the current operating environment through analysis and comparison, so that the set can avoid these frequencies for operation, greatly reducing the risk of internal self-oscillation of the set.
[0119] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.
[0120] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code comprising one or more executable instructions for implementing the steps of a custom logical function or process, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may not be performed in the order shown or discussed, including performing functions in a substantially simultaneous manner or in the reverse order depending on the functions involved, which should be understood by technicians in the technical field to which the embodiments of the present application belong.
[0121] Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as limitations on the present application. Ordinary technicians in the field can change, modify, replace and modify the above embodiments within the scope of the present application.
Claims
1. A characteristic oscillation frequency early warning method for a wind turbine generator set, characterized in that: The method comprises: Divide the wind turbine into N components and obtain the characteristic frequency of each component; Determine the torque excitation source value corresponding to each combined component according to the characteristic frequency of each combined component; Determine the characteristic oscillation frequency of each combined component according to the torque excitation source value corresponding to each combined component; Providing an early warning of the characteristic oscillation frequency of the wind turbine generator system based on the characteristic oscillation frequency of each of the combined components; Wherein, N is an integer greater than or equal to 1; Wherein, the early warning of the characteristic oscillation frequency of the wind turbine generator set based on the characteristic oscillation frequency of each combined component includes: Obtaining the absolute value of the difference between the operating frequency of the wind turbine generator set and the characteristic oscillation frequency of each component; When the number of absolute values of the differences that are less than or equal to the preset alarm threshold is greater than or equal to 1, an early warning is issued for the characteristic oscillation frequency of the wind turbine generator set.
2. The method according to claim 1, characterized in that The wind turbine generator set is divided into N combined components, including: The wind turbine generator set is divided into N combined components based on the complexity that each component in the wind turbine generator set can bear.
3. The method according to claim 1, characterized in that The calculation formula of the torque excitation source value corresponding to each combination component is as follows: In the formula, x i,t is the torque excitation source value corresponding to the i-th component at time t, F i is the characteristic frequency of the ith component, B j is the value of the jth characteristic frequency multiplier, j∈[1~M], M is the total number of characteristic frequency multipliers.
4. The method according to claim 3, characterized in that The step of determining the characteristic oscillation frequency of each component according to the torque excitation source value corresponding to each component comprises: Applying torque excitation sources to the rotating shaft of the wind turbine set in sequence, and obtaining a speed value curve of the wind turbine set generator under each torque excitation source value; Fourier analysis is performed on the speed curve of the wind turbine generator under each torque excitation source value to obtain the signal amplification factor of each characteristic frequency corresponding to each torque excitation source value; Determine the frequency value at each signal amplification factor corresponding to each torque excitation source value according to the signal amplification factor of each characteristic frequency corresponding to each torque excitation source value; The characteristic oscillation frequency of each combined component is determined according to the frequency value at each signal amplification factor corresponding to each torque excitation source value.
5. The method according to claim 4, characterized in that The method of determining the characteristic oscillation frequency of each combined component according to the frequency value at each signal amplification factor corresponding to each torque excitation source value includes: The maximum frequency is selected from the frequency values at each signal amplification factor corresponding to each torque excitation source value; The maximum frequency value corresponding to each torque excitation source value is taken as the characteristic oscillation frequency of each combined component.
6. A characteristic oscillation frequency early warning system for a wind turbine generator set, characterized in that: The system comprises: A division module is used to divide the wind turbine into N combined components and obtain the characteristic frequency of each combined component; A first determination module is used to determine the torque excitation source value corresponding to each combined component according to the characteristic frequency of each combined component; A second determination module is used to determine the characteristic oscillation frequency of each combined component according to the torque excitation source value corresponding to each combined component; An early warning module, used for issuing an early warning on the characteristic oscillation frequency of the wind turbine generator set based on the characteristic oscillation frequency of each of the combined components; Wherein, N is an integer greater than or equal to 1; Wherein, the early warning module includes: A second acquisition unit is used to acquire the absolute value of the difference between the operating frequency of the wind turbine generator set and the characteristic oscillation frequency of each combined component; The early warning unit is used to issue an early warning for the characteristic oscillation frequency of the wind turbine generator set when the number of absolute values of the differences that are less than or equal to the preset alarm threshold is greater than or equal to 1.
7. The system according to claim 6, characterized in that The wind turbine generator set is divided into N combined components, including: The wind turbine generator set is divided into N combined components based on the complexity that each component in the wind turbine generator set can bear.
8. The system according to claim 7, characterized in that The second determining module includes: A first acquisition unit is used to sequentially apply torque excitation sources to the rotating shaft of the wind turbine generator set to obtain a speed value curve of the wind turbine generator set under each torque excitation source value; An analysis unit, used to perform Fourier analysis on the speed value curve of the wind turbine generator under each torque excitation source value, and obtain the signal amplification factor of each characteristic frequency corresponding to each torque excitation source value; A first determining unit, configured to determine the frequency value at each signal amplification factor corresponding to each torque excitation source value according to the signal amplification factor of each characteristic frequency corresponding to each torque excitation source value; The second determination unit is used to determine the characteristic oscillation frequency of each combined component according to the frequency value at each signal amplification factor corresponding to each torque excitation source value.
9. The system according to claim 8, characterized in that The second determining unit includes: A screening submodule, used to screen out the maximum frequency value from the frequency values at each signal amplification factor corresponding to each torque excitation source value; The determination submodule is used to take the maximum frequency value corresponding to each torque excitation source value as the characteristic oscillation frequency of each combined component.
Citation Information
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