Frequency Domain Modal Method for Determining Stability of Vehicle-to-Grid Oscillations in New Energy Vehicles Applicable to Converter Impedance Measurement

Abstract

This invention discloses a frequency-domain modal method for determining the stability of vehicle-to-grid oscillations in new energy systems, applicable to converter impedance measurement. Specifically, it involves: acquiring the topology and component parameters of an electrified railway traction power supply system; performing frequency scanning on the single-input single-output frequency-domain impedance obtained through measurement or mathematical modeling in the frequency band to be analyzed, forming the system frequency-domain node admittance matrix at each frequency; performing eigenvalue decomposition to obtain the amplitude-frequency curve of the modal admittance or modal impedance; determining the oscillation frequency based on the extreme values ​​of the curve; determining the system stability based on the real and imaginary parts of the modal admittance or impedance at the oscillation frequency; and calculating the participation factor of each node in the unstable oscillation mode. This invention is applicable to low-frequency oscillation stability analysis of traction power supply systems with arbitrary topologies that do not contain three-phase converters. The SISO frequency-domain impedance of the single-phase voltage source converter interface power supply and locomotive load can be directly measured through impedance scanning without the need for dq-domain conversion.

Description

Technical Field

[0001] This invention belongs to the field of low-frequency oscillation in traction power supply systems, and particularly relates to a frequency domain modal method for determining the stability of vehicle-grid new energy oscillations, applicable to converter impedance measurement. Background Technology

[0002] Currently, the main methods for studying low-frequency oscillations in traction power supply systems include the eigenvalue method using state-space models, the s-domain modal method (complex frequency domain modal method), and the frequency impedance method. While the eigenvalue method and s-domain modal method of state-space models can accurately reflect the oscillations of the system, these methods require detailed system information, making system modeling challenging in practical applications. Furthermore, the dimensionality of the state-space model increases with the number of converters, leading to the "curse of dimensionality" when studying large-scale systems. Increased dimensionality of the state-space model introduces numerical problems, issues with ultra-large system models, and irrelevant results. The frequency impedance method can obtain the impedance of components in the dq domain without knowing their parameters. However, the frequency impedance method requires clearly dividing the system into "active" and "passive" parts, which is often difficult to distinguish directly due to the complex topology of large-scale systems.

[0003] In summary, it is necessary to find a new research method to analyze the low-frequency oscillation stability of traction power supply systems containing new energy sources that have complex topologies and whose system component parameters are difficult to obtain. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a frequency domain modal method for determining the stability of vehicle-to-grid new energy oscillations, applicable to converter impedance measurement.

[0005] The present invention provides a frequency domain modal method for determining the stability of vehicle-to-grid new energy oscillations, applicable to converter impedance measurement, comprising the following steps:

[0006] Step 1: Obtain the topology and component parameters of the electrified railway traction power supply system.

[0007] Step 2: For locomotive, new energy or energy storage single-phase converter interface components for which parameters cannot be obtained, the single-input single-output SISO frequency scanning impedance is obtained by measurement based on the range P of the oscillation frequency band to be analyzed.

[0008] Step 3: Based on the topology and component parameters from Step 1, and combined with the SISO frequency domain impedance Z obtained through mathematical modeling of the converter, SISO (jω) or the SISO frequency scanning impedance of the converter interface element obtained in step 2, is used to form the frequency ω of each frequency through frequency scanning. i ω i The system frequency domain node admittance matrix Y(jω) ∈Pi ), Y(jω i ) is a constant matrix, where the scanning frequency when forming the nodal admittance matrix is ​​less than the scanning frequency when measuring.

[0009] Step 4: For the Y(jω) obtained in Step 3... i Eigenvalue decomposition yields an eigenvalue matrix, whose diagonal elements are called modal admittances. Inverting the eigenvalue matrix yields its diagonal elements, which are called modal impedances.

[0010] Step 5: When the modal admittance amplitude-frequency curve is at frequency ω j There is a minimum value at ω, or the amplitude-frequency curve of the modal impedance has a minimum value at frequency ω. j When there is a maximum value at ω, through ω j The stability of a mode is determined by the sign of the real part of the modal admittance or the slope of the imaginary part; the corresponding oscillation frequency f j By ω j To obtain.

[0011] Step 6: If any mode is unstable, the system is unstable; calculate the participation factor for each unstable mode. The larger the participation factor, the stronger the participation of the components connected to that node in the unstable mode.

[0012] Furthermore, the SISO frequency domain impedance Z obtained from the mathematical modeling in step 3... SISO (jω) is:

[0013] SISO complex frequency domain impedance Z SISO (s) is

[0014] ;

[0015] in

[0016] ,

[0017] ω N It is the power frequency angular frequency, Z. dd Z dq Z qd and Z qq The element's dq complex frequency domain impedance model Z ldq Elements in (s):

[0018] ,

[0019] Let Z SISO In (s), s=jω, which gives the SISO frequency domain impedance Z. SISO (jω).

[0020] Furthermore, step 5 uses modal admittance to determine the system stability criterion as follows:

[0021] The amplitude-frequency curve of modal admittance at frequency ω j It has a local minimum at ω, and at frequency ω j If the product of the slopes of the real and imaginary parts of the modal admittance is greater than 0, then the mode is stable; at frequency ω... j If the product of the slopes of the real part and the imaginary part of the modal admittance is less than 0, then the mode is unstable.

[0022] Furthermore, the criterion for determining system stability in step 5 using modal impedance is:

[0023] The amplitude-frequency curve of modal impedance at frequency ω j It has a maximum value at ω, and at frequency ω j If the product of the slopes of the real and imaginary parts of the modal impedance is less than 0, then the mode is stable; at frequency ω... j If the product of the slopes of the real part and the imaginary part of the modal impedance is greater than 0, then the mode is unstable.

[0024] Furthermore, the oscillation frequency f in step 5 j The calculation is as follows:

[0025]

[0026] Let the steady-state power frequency be f0, then the DC-side oscillation frequency of the converter is... .

[0027] The beneficial technical effects of this invention compared to the prior art are as follows:

[0028] 1. Compared to the eigenvalue method of state-space models, this invention does not significantly increase the dimension of the nodal admittance matrix when the system contains multiple power electronic components, thus avoiding problems such as the "curse of dimensionality." Furthermore, this invention can generate the nodal admittance matrix by directly measuring the frequency domain impedance model of the components without knowing the component parameters in the system, making it suitable for systems where the component parameters are actually unknown.

[0029] 2. Compared with the s-domain modal method, this invention does not require knowledge of the component parameters in the system. It can obtain the impedance model of the component directly by measurement to form the nodal admittance matrix, which is suitable for systems with unknown component parameters.

[0030] 3. Compared to the frequency impedance method, this invention does not require explicitly dividing the system into "active" and "passive" parts. Furthermore, it can obtain the participation factor of each node in the oscillation mode. Moreover, this invention obtains the actual impedance by directly measuring the components, eliminating the need for dq-domain conversion. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the frequency scanning method in an embodiment of the present invention.

[0032] Figure 2 This is a schematic diagram of a traction power supply system incorporating new energy photovoltaics in an embodiment of the present invention.

[0033] Figure 3 This is a simplified structural diagram of a traction power supply system incorporating new energy photovoltaics in an embodiment of the present invention.

[0034] Figure 4 , Figure 5 , Figure 6 This is a modal impedance-frequency curve diagram of calculation example 1 in the embodiment of the present invention.

[0035] Figure 7 , Figure 8 , Figure 9 This is a modal admittance-frequency curve diagram of Example 1 in the embodiments of the present invention.

[0036] Figure 10 This is a graph showing the results of the participation factor for mode 5 in Example 1 of this invention.

[0037] Figure 11 , Figure 12 , Figure 13 This is the modal impedance-frequency curve of example 2 in the embodiments of the present invention.

[0038] Figure 14 , Figure 15 , Figure 16 This is a modal admittance-frequency curve diagram for example 2 in this embodiment of the invention.

[0039] Figure 17 This is a graph showing the results of the participation factor for mode 5 in example 2 of this invention.

[0040] Figure 18 This is a graph showing the results of the participation factor of mode 3 in example 2 of the present invention.

[0041] Figure 19 The train simulation waveforms for examples 1 and 2 in this embodiment of the invention are shown.

[0042] Figure 20 The image shows the photovoltaic simulation waveform of Example 2 in this embodiment of the invention. Detailed Implementation

[0043] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0044] This invention provides a frequency domain modal method for determining the stability of vehicle-to-grid oscillations in new energy systems, applicable to converter impedance measurement. Specifically, it involves: acquiring the topology and component parameters of an electrified railway traction power supply system; performing frequency scanning on the single-input, single-output frequency domain impedance obtained through measurement or mathematical modeling in the frequency band to be analyzed, forming the system's frequency domain node admittance matrix at each frequency; performing eigenvalue decomposition to obtain the amplitude-frequency curve of the modal admittance or modal impedance; determining the oscillation frequency based on the extreme values ​​of the curve; determining the system stability based on the real and imaginary parts of the modal admittance or impedance at the oscillation frequency; and calculating the participation factor of each node in the unstable oscillation mode. The specific steps include:

[0045] Step 1: Obtain the topology and component parameters of the electrified railway traction power supply system.

[0046] Step 2: For locomotive, new energy or energy storage single-phase converter interface components for which parameters cannot be obtained, the single-input single-output SISO frequency scanning impedance is obtained by measurement based on the range P of the oscillation frequency band to be analyzed.

[0047] Step 3: Based on the topology and component parameters from Step 1, and combined with the SISO frequency domain impedance Z obtained through mathematical modeling of the converter, SISO (jω) or the SISO frequency scanning impedance of the converter interface element obtained in step 2, is used to form the frequency ω of each frequency through frequency scanning. i ω i The system frequency domain node admittance matrix Y(jω) ∈P i ), Y(jω i ) is a constant matrix, where the scanning frequency when forming the nodal admittance matrix is ​​less than the scanning frequency when measuring.

[0048] SISO frequency domain impedance Z obtained from mathematical modeling SISO (jω) is:

[0049] SISO complex frequency domain impedance Z SISO (s) is

[0050] ;

[0051] in

[0052] ,

[0053] ω N It is the power frequency angular frequency, Z. dd Z dq Z qd and Z qq The element's dq complex frequency domain impedance model Z ldq Elements in (s):

[0054] ,

[0055] Let Z SISO In (s), s=jω, which gives the SISO frequency domain impedance Z. SISO (jω).

[0056] Step 4: For the Y(jω) obtained in Step 3... i Eigenvalue decomposition yields an eigenvalue matrix, whose diagonal elements are called modal admittances. Inverting the eigenvalue matrix yields its diagonal elements, which are called modal impedances.

[0057] Step 5: When the modal admittance amplitude-frequency curve is at frequency ω j There is a minimum value at ω, or the amplitude-frequency curve of the modal impedance has a minimum value at frequency ω. j When there is a maximum value at ω, through ω j The stability of a mode is determined by the sign of the real part of the modal admittance or the slope of the imaginary part; the corresponding oscillation frequency f j By ω j To obtain.

[0058] The criterion for judging the stability of a system by modal admittance is:

[0059] The amplitude-frequency curve of modal admittance at frequency ω j It has a local minimum at ω, and at frequency ω j If the product of the slopes of the real and imaginary parts of the modal admittance is greater than 0, then the mode is stable; at frequency ω... j If the product of the slopes of the real part and the imaginary part of the modal admittance is less than 0, then the mode is unstable.

[0060] The criterion for determining system stability is:

[0061] The amplitude-frequency curve of modal impedance at frequency ω j It has a maximum value at ω, and at frequency ω j If the product of the slopes of the real and imaginary parts of the modal impedance is less than 0, then the mode is stable; at frequency ω... j If the product of the slopes of the real part and the imaginary part of the modal impedance is greater than 0, then the mode is unstable.

[0062] Oscillation frequency f j The calculation is as follows:

[0063]

[0064] Let the steady-state power frequency be f0, then the DC-side oscillation frequency of the converter is... .

[0065] Step 6: If any mode is unstable, the system is unstable; calculate the participation factor for each unstable mode. The larger the participation factor, the stronger the participation of the components connected to that node in the unstable mode.

[0066] Example:

[0067] The detailed process of designing small-disturbance measurements to obtain the frequency domain impedance of power electronic interface loads or power sources such as locomotives, single-phase converter interfaces, and new energy sources is as follows:

[0068] like Figure 1 As shown. The frequency scanning method first requires injecting a disturbance voltage source into the system, and then measuring the disturbance voltage and the response current at the same frequency at the interface. After Fast Fourier Transform analysis, the corresponding components in the frequency domain can be obtained. Finally, the impedance at the corresponding frequency can be calculated using the following formula. It is important to note that the disturbance amplitude needs to be very small when injecting the voltage source disturbance to ensure that the steady-state operating point of the original system is not disturbed.

[0069]

[0070] Among them, U t and I t These are represented as voltage and current vectors at a certain frequency, respectively. E l The steady-state operating voltage is the point of steady-state operation, typically around 25000V. p This indicates a small disturbance voltage source with an amplitude set to 250V.

[0071] A schematic diagram of a traction power supply system including new energy photovoltaic power is shown in the example. Figure 2 As shown, the simplified structure diagram is as follows: Figure 3 As shown in Table 1.

[0072] Table 1 System Parameter Table

[0073]

[0074] Calculation example 1:

[0075] The five trains run at a distance of 10km, and there are no trains at node 9.

[0076] Based on the topology of Example 1, the system frequency domain nodal admittance matrix Y(jω) can be obtained as follows:

[0077]

[0078] in,

[0079]

[0080]

[0081]

[0082] Calculation example 2:

[0083] Five trains operate at a distance of 10km from each other, with no trains running at node 9. Meanwhile, the photovoltaic power generation system is connected to node 3 on the low-voltage side.

[0084] Based on the topology of Example 2, the system frequency domain nodal admittance matrix Y(jω) can be obtained as follows:

[0085]

[0086] In matrix D 11 =Y T +Y q1 +Y q4 +Y pvl The remaining matrices and elements are the same as those in Example 1.

[0087] Among them, Y li (i=1,2,3,4,5) is the measured train admittance, Y pvl It is the admittance of the photovoltaic power generation system as measured.

[0088] The results obtained using the frequency domain scanning calculation example 1 of this invention are as follows: Figures 4-6 and Figures 7-9 As shown, the impedance amplitude of mode 5 has a maximum at 57.7 Hz, and the product of the slopes of the real and imaginary parts of the mode impedance is less than 0 at this point. The admittance amplitude of mode 5 has a minimum at 57.7 Hz, and the product of the slopes of the real and imaginary parts of the mode admittance is greater than 0 at this point. Therefore, mode 5 is stable at this point, with an oscillation frequency of 7.7 Hz. The results of the factor analysis are as follows... Figure 10 As shown in the figure. The participation factor analysis results show that nodes 4 to 9 have relatively large participation factors, indicating that the oscillation mode is dominated by the train.

[0089] The results obtained using the frequency domain scanning calculation example 2 of this invention are as follows: Figures 11-13 and Figures 14-16As shown, the impedance amplitude of mode 5 has a maximum at 57.3 Hz, and the product of the slopes of the real and imaginary parts of the mode impedance is greater than 0 at this point. The admittance amplitude of mode 5 has a minimum at 57.3 Hz, and the product of the slopes of the real and imaginary parts of the mode admittance is less than 0 at this point. Therefore, mode 5 is unstable at this point, with an oscillation frequency of 7.3 Hz. The impedance amplitude of mode 3 has a maximum at 65.9 Hz, and the product of the slopes of the real and imaginary parts of the mode impedance is less than 0 at this point. The admittance amplitude of mode 5 has a minimum at 65.9 Hz, and the product of the slopes of the real and imaginary parts of the mode admittance is greater than 0 at this point. Therefore, mode 3 is stable at this point, with an oscillation frequency of 15.9 Hz. The factor analysis results for mode 5 are as follows: Figure 17 As shown, the results of the modality 3 participation factor analysis are as follows: Figure 18 As shown in the figure. The participation factor analysis results for mode 5 show that the participation factors of nodes 4 to 9 are relatively large, indicating that the oscillation mode is dominated by the train. The participation factor analysis results for mode 3 show that the participation factor of node 3 is relatively large, indicating that the oscillation mode is dominated by the photovoltaic.

[0090] To verify the accuracy of the present invention, a simulation model was built in MATLAB / SIMULINK, and the simulation results were analyzed using Esprit. The calculation results and simulation analysis results of the present invention are shown in Table 2. Simulation waveforms are shown below. Figure 19 and Figure 20 As shown.

[0091] Table 2. Calculation results and simulation analysis results of the present invention.

[0092]

[0093] The simulation results are consistent with the calculation results of the present invention, demonstrating the accurate nature of the present invention.

Claims

1. A frequency domain modal method for determining the stability of vehicle-to-grid new energy oscillations, applicable to converter impedance measurement, characterized in that, Includes the following steps: Step 1: Obtain the topology and component parameters of the electrified railway traction power supply system; Step 2: For locomotive, new energy or energy storage single-phase converter interface components for which parameters cannot be obtained, the single-input single-output SISO frequency scanning impedance is obtained by measurement based on the range P of the oscillation frequency band to be analyzed. Step 3: Based on the topology and component parameters from Step 1, and combined with the SISO frequency domain impedance Z obtained through mathematical modeling of the converter, SISO (jω) or the SISO frequency scanning impedance of the converter interface element obtained in step 2, is used to form the frequency ω of each frequency through frequency scanning. i ω i The system frequency domain node admittance matrix Y(jω) ∈P i ), Y(jω i ) is a constant matrix, where the scanning frequency when forming the nodal admittance matrix is ​​less than the scanning frequency when measuring; Step 4: For Y(jω) obtained in Step 3... i Eigenvalue decomposition yields an eigenvalue matrix, whose diagonal elements are called modal admittances. Inverting the eigenvalue matrix yields diagonal elements called modal impedances. Step 5: When the modal admittance amplitude-frequency curve is at frequency ω j There is a minimum value at ω, or the amplitude-frequency curve of the modal impedance has a minimum value at frequency ω. j When there is a maximum value at ω, through ω j The stability of a mode is determined by the sign of the real part of the modal admittance or the slope of the imaginary part; the corresponding oscillation frequency f j By ω j Seek; Step 6: If any mode is unstable, the system is unstable; calculate the participation factor for each unstable mode. The larger the participation factor, the stronger the participation of the components connected to that node in the unstable mode.

2. The frequency domain modal method for determining the stability of vehicle-to-grid new energy oscillations, applicable to converter impedance measurement, as described in claim 1, is characterized in that... The SISO frequency domain impedance Z obtained from the mathematical modeling in step 3 SISO (jω) is: SISO complex frequency domain impedance Z SISO (s) is ； in ， ω N It is the power frequency angular frequency, Z. dd Z dq Z qd and Z qq The element's dq complex frequency domain impedance model Z ldq Elements in (s): ， Let Z SISO In (s), s=jω, which gives the SISO frequency domain impedance Z. SISO (jω).

3. The frequency domain modal method for determining the stability of vehicle-to-grid new energy oscillations, applicable to converter impedance measurement, as described in claim 1, is characterized in that... The criterion for determining system stability in step 5 using modal admittance is: The amplitude-frequency curve of modal admittance at frequency ω j It has a local minimum at ω, and at frequency ω j If the product of the slopes of the real and imaginary parts of the modal admittance is greater than 0, then the mode is stable; at frequency ω... j If the product of the slopes of the real part and the imaginary part of the modal admittance is less than 0, then the mode is unstable.

4. The frequency domain modal method for determining the stability of vehicle-to-grid new energy oscillations, applicable to converter impedance measurement, as described in claim 1, is characterized in that... The criterion for determining system stability in step 5 using modal impedance is: The amplitude-frequency curve of modal impedance at frequency ω j It has a maximum value at ω, and at frequency ω j If the product of the slopes of the real and imaginary parts of the modal impedance is less than 0, then the mode is stable; at frequency ω... j If the product of the slopes of the real part and the imaginary part of the modal impedance is greater than 0, then the mode is unstable.

5. The frequency domain modal method for determining the stability of vehicle-to-grid new energy oscillations, applicable to converter impedance measurement, as described in claim 1, is characterized in that... The oscillation frequency f in step 5 j The calculation is as follows: ； Let the steady-state power frequency be f0, then the DC-side oscillation frequency of the converter is... .

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