Wideband oscillation s-domain modal analysis method for traction power supply system

Abstract

The invention discloses a broadband oscillation s-domain modal analysis method for a traction power supply system. The method specifically comprises the following steps: acquiring a topological structure and element parameters of an electrified railway traction power supply system; a single-input single-output s-domain (complex frequency domain) impedance model is formed based on a small-disturbance dq impedance model of power electronic interface loads or power supplies such as locomotive and single-phase converter interface new energy; forming a system s domain node admittance matrix Y (s); in a to-be-analyzed frequency band, performing s-domain scanning on the Y (s) to obtain a system oscillation mode; calculating a damping ratio and an oscillation frequency of the oscillation mode, and a participation factor of each node to the oscillation mode; the method is suitable for broadband oscillation stability analysis of any complex topology traction power supply system containing a single-phase voltage source type converter interface power supply (new energy, energy storage and the like) and an external power system power supply. The system does not need to be divided into an active system and a passive system, and compared with a state space model, the dimensionality is low, and the engineering feasibility is good.

Description

Technical Field

[0001] The present invention belongs to the field of broadband oscillation of the traction power supply system, and particularly relates to a method for analyzing the s-domain mode of broadband oscillation of the traction power supply system. Background Art

[0002] In recent years, with the rapid development of the social economy and the continuous improvement of people's living standards, the demand for high-speed and heavy-haul electrified railway transportation has shown a significant growth trend. The continuous growth of this demand has promoted the rapid development of electrified railways, resulting in the continuous expansion of railway operating mileage and the increasing perfection of the high-speed rail network. Facing the severe challenges of global resource shortage, climate change, and environmental pollution, the collaborative carbon reduction and decarbonization of the energy supply side and the load demand side have become the key measures to address these challenges. To respond to these measures, integrating new energy into the traction power supply system has currently become the mainstream trend of the greening of rail transit.

[0003] With more and more new energy power generation equipment connected to the traction power supply system, the stability problem of the traction power supply system has become increasingly serious. After new energy is connected to the system, there are a large number of converters in the system. The interaction between converters and the interaction between converters and the power grid will deteriorate the stability of the system.

[0004] Currently, the methods for studying the broadband oscillation of the traction power supply system mainly include the eigenvalue method of the state-space model and the frequency impedance method. Although the eigenvalue method of the state-space model can accurately reflect the oscillation situation of the system, this method requires detailed system information, so it is challenging to model large-scale systems in practical applications. At the same time, the dimension of the state-space model will increase with the increase of converters. When studying large-scale systems, the method based on the state-space model will face the "curse of dimensionality". When the dimension of the state-space model increases, numerical problems, ultra-large system models, and irrelevant results will occur. The frequency impedance method needs to clearly divide the system into two parts: "active system" and "passive system", and it is often difficult to directly distinguish the complex topological structure of large-scale systems.

[0005] In summary, it is necessary to find a new research method to analyze the broadband oscillation stability of the traction power supply system with new energy and a complex topological structure. Summary of the Invention

[0006] In view of the above problems, the present invention provides a method for analyzing the s-domain mode of broadband oscillation of the traction power supply system.

[0007] A method for analyzing the s-domain mode of broadband oscillation of the traction power supply system according to the present invention includes the following steps:

[0008] Step 1: Obtain the topology and component parameters of the electrified railway traction power supply system (including external equivalent power sources), as well as the main circuit and control system parameters of the power electronic components.

[0009] Step 2: Based on the small disturbance dq impedance model of the power electronic interface load or power supply of locomotive, single-phase converter interface new energy, form its single-input single-output s-domain (complex frequency domain) impedance model.

[0010] Step 3: Based on the topology and component parameters from Step 1, and the single-input single-output s-domain impedance model and its parameters of the power electronic components from Step 2, form the system s-domain node admittance matrix Y(s).

[0011] Step 4: In the oscillation frequency band to be analyzed, perform an s-domain scan of Y(s), and obtain the system oscillation mode s by finding that the determinant of Y(s) is equal to zero. i The set of: , where the real part α of the oscillation mode i This reflects the attenuation performance, with the imaginary part ω. i It reflects the oscillation frequency.

[0012] Step 5: If a certain oscillation mode exists, its actual part α i Greater than zero or damping ratio ξ i If the damping ratio is less than 0, the system is considered unstable; this mode is a negatively damped oscillation mode. A damping ratio greater than 0 and less than a given value indicates a weakly damped oscillation mode; the corresponding oscillation frequency f... i From the imaginary part ω of the oscillation mode i To obtain.

[0013] Step 6: For each negatively damped or weakly damped oscillation mode, calculate the participation factor of the node in that oscillation mode; the element directly connected to the node with the largest participation factor has the greatest impact on the oscillation and is considered to be the oscillation mode dominated by that node, providing a basis for oscillation suppression.

[0014] Furthermore, the single-input single-output s-domain impedance model in step 2 is as follows:

[0015]

[0016] in:

[0017]

[0018] Where, ω N It is the power frequency angular frequency, Z. dd Z dq Z qd and Z qq The element's dq impedance model Z ldq Elements in (s):

[0019]

[0020] Furthermore, in step 5, the damping ratio ξ i and oscillation frequency f i The calculation is as follows:

[0021]

[0022] Let the steady-state power frequency be f0, then the DC-side oscillation frequency of the converter is... .

[0023] Furthermore, in step 5, the damping ratio is given as 0.05.

[0024] Furthermore, the calculation process for the participation factor of the node pair in step 6 is as follows:

[0025]

[0026] Here, Λ represents the eigenvalue matrix, and there exists an eigenvalue λ. q =0; L and T are the left and right eigenvector matrices, respectively, L=T -1 ; n is the order of the nodal admittance matrix.

[0027] Node j, j=1,2,….n pairs of oscillation modes s i Participating factor PF jq for:

[0028]

[0029] Among them, L jq T represents the element in the j-th row and q-th column of the left eigenvector matrix L. qj This represents the element in the q-th row and j-th column of the right eigenvector matrix T.

[0030] The beneficial technical effects of this invention compared with the prior art are as follows:

[0031] 1. Compared with the eigenvalue method of the state-space model, the present invention does not cause a significant increase in the dimension of the node admittance matrix when the system contains multiple power electronic components, and does not cause problems such as the "curse of dimensionality".

[0032] 2. Compared with the frequency impedance method, this invention does not require the system to be explicitly divided into "active system" and "passive system". At the same time, it can give the damping ratio and stability margin of the oscillation mode and obtain the participation factor of each node in the oscillation mode. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of a traction power supply system incorporating new energy photovoltaics in an embodiment of the present invention.

[0034] Figure 2 This is a simplified structural diagram of a traction power supply system incorporating new energy photovoltaics in an embodiment of the present invention.

[0035] Figure 3 This is a diagram showing the specific control structure of the train in an embodiment of the present invention.

[0036] Figure 4 This is a specific control structure diagram of photovoltaic in an embodiment of the present invention.

[0037] Figure 5 This is a detailed control structure diagram of the photovoltaic boost circuit module in an embodiment of the present invention.

[0038] Figure 6 The diagram shows the calculation results of the oscillation mode in Example 1 of this invention.

[0039] Figure 7 This is a graph showing the oscillation mode participation factor results for Example 1 in this embodiment of the invention.

[0040] Figure 8 The diagram shows the calculation results of the oscillation mode in Example 2 of this invention.

[0041] Figure 9 This is a graph showing the oscillation mode participation factor results on the left side of Example 2 in this embodiment of the invention.

[0042] Figure 10 This is a graph showing the oscillation mode participation factor results on the right side of example 2 in this embodiment of the invention.

[0043] Figure 11 The train simulation waveforms for examples 1 and 2 in this embodiment of the invention are shown.

[0044] Figure 12 The image shows the photovoltaic simulation waveform of Example 2 in this embodiment of the invention. Detailed Implementation

[0045] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0046] This invention provides a broadband oscillation S-domain modal analysis method for traction power supply systems. The method obtains the topology and component parameters of the electrified railway traction power supply system; based on the small-disturbance dq impedance model of the locomotive, single-phase converter interface, and new energy power electronic interface loads or power sources, it forms a single-input single-output S-domain (complex frequency domain) impedance model; it forms the system S-domain node admittance matrix Y(s); in the frequency band to be analyzed, it performs an S-domain scan of Y(s) to obtain the system oscillation modes; and it calculates the damping ratio, oscillation frequency, and participation factor of each node in the oscillation mode. Specifically, it includes the following steps:

[0047] Step 1: Obtain the topology and component parameters of the electrified railway traction power supply system (including external equivalent power sources), as well as the main circuit and control system parameters of the power electronic components.

[0048] Step 2: Based on the small disturbance dq impedance model of the new energy power electronic interface load or power supply of the locomotive and single-phase converter interface, form its single-input single-output s-domain (complex frequency domain) impedance model.

[0049] The single-input single-output s-domain impedance model is as follows:

[0050]

[0051] in:

[0052]

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

[0054]

[0055] Step 3: Based on the topology and component parameters from Step 1, and the single-input single-output s-domain impedance model and its parameters of the power electronic components from Step 2, form the system s-domain node admittance matrix Y(s).

[0056] Step 4: In the oscillation frequency band to be analyzed, perform an s-domain scan of Y(s), and obtain the system oscillation mode s by finding that the determinant of Y(s) is equal to zero. i The set of: , where the real part α of the oscillation mode i This reflects the attenuation performance, with the imaginary part ω. i It reflects the oscillation frequency.

[0057] Step 5: If a certain oscillation mode exists, its actual part α i Greater than zero or damping ratio ξ i If the damping ratio is less than 0, the system is considered unstable, and this mode is a negatively damped oscillation mode; a mode with a damping ratio greater than 0 and less than a certain given value (here, 0.05) is a weakly damped oscillation mode; the corresponding oscillation frequency f i From the imaginary part ω of the oscillation mode i To obtain.

[0058] Damping ratio ξ i and oscillation frequency f i The calculation is as follows:

[0059]

[0060] Let the steady-state power frequency be f0, then the DC-side oscillation frequency of the converter is... .

[0061] Step 6: For each negatively damped or weakly damped oscillation mode, calculate the participation factor of the node in that oscillation mode; the element directly connected to the node with the largest participation factor has the greatest impact on the oscillation and is considered to be the oscillation mode dominated by that node, providing a basis for oscillation suppression.

[0062] The calculation process for the participation factor of a node in an oscillation mode is as follows:

[0063]

[0064] Here, Λ represents the eigenvalue matrix, and there exists an eigenvalue λ. q =0; L and T are the left and right eigenvector matrices, respectively, L=T -1 ; n is the order of the nodal admittance matrix.

[0065] Node j, j=1,2,….n pairs of oscillation modes s i Participating factor PF jq for:

[0066]

[0067] Example

[0068] A schematic diagram of a traction power supply system including new energy photovoltaic power is shown in the example. Figure 1 As shown, the simplified structure diagram is as follows: Figure 2 As shown in Table 1.

[0069] Table 1 System Parameter Table

[0070]

[0071] The specific control structure of the train is as follows Figure 3 As shown in Table 2, the specific parameters are as follows.

[0072] Table 2 Train-related parameters

[0073]

[0074] The specific control structure of photovoltaics is as follows: Figure 4 and Figure 5 As shown in Table 3, the specific parameters are as follows.

[0075] Table 3. Photovoltaic Relevant Parameters

[0076]

[0077] Calculation example 1:

[0078] The five trains run at a distance of 10km, and there are no trains at node 9.

[0079] Based on the topology of Example 1, the admittance matrix Y(s) of the system s-domain nodes can be obtained as follows:

[0080]

[0081] in,

[0082]

[0083]

[0084]

[0085] Calculation example 2:

[0086] 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.

[0087] Based on the topology of Example 2, the nodal admittance matrix Y(s) of the system in the s-domain can be obtained as follows:

[0088]

[0089] 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.

[0090] The results obtained using the s-domain scan calculation example 1 of this invention are as follows: Figure 6 As shown, the results of the factor analysis are as follows: Figure 7 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.

[0091] The results obtained using the s-domain scan calculation example 2 of this invention are as follows: Figure 8 As shown, the results of the participation factor analysis for the left-hand pattern are as follows: Figure 9 As shown in the figure. The participation factor analysis results show that node 3 has a larger participation factor, indicating that this oscillation mode is dominated by photovoltaics; the participation factor analysis results for the right-hand mode are shown in the figure. 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.

[0092] 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 4. Simulation waveforms are shown below. Figure 11 and Figure 12 As shown.

[0093] Table 4. Calculation results and simulation analysis results of the present invention.

[0094]

[0095] The simulation results are consistent with the calculation results of the present invention, demonstrating the accurate nature of the present invention.

Claims

1. A method for broadband oscillation S-domain modal analysis of a traction power supply system, characterized in that, Includes the following steps: Step 1: Obtain the topology and component parameters of the electrified railway traction power supply system, as well as the main circuit and control system parameters of the power electronic components; Step 2: Based on the small disturbance dq impedance model of the locomotive, single-phase converter interface, and new energy power electronic interface load or power supply, form its single-input single-output s-domain impedance model; Step 3: Based on the topology and component parameters in Step 1, and the single-input single-output s-domain impedance model and its parameters of the power electronic components in Step 2, form the system s-domain node admittance matrix Y(s). Step 4: In the oscillation frequency band to be analyzed, perform an s-domain scan of Y(s), and obtain the system oscillation mode s by finding that the determinant of Y(s) is equal to zero. i The set of: , where the real part α of the oscillation mode i This reflects the attenuation performance, with the imaginary part ω. i It reflects the oscillation frequency; Step 5: If a certain oscillation mode exists, its actual part α i Greater than zero or damping ratio ξ i If the damping ratio is less than 0, the system is considered unstable; this mode is a negatively damped oscillation mode. A damping ratio greater than 0 and less than a given value indicates a weakly damped oscillation mode; the corresponding oscillation frequency f... i From the imaginary part ω of the oscillation mode i Seek; Step 6: For each negatively damped or weakly damped oscillation mode, calculate the participation factor of the node in that oscillation mode; the element directly connected to the node with the largest participation factor has the greatest impact on the oscillation and is considered to be the oscillation mode dominated by that node, providing a basis for oscillation suppression.

2. The method for broadband oscillation S-domain modal analysis of a traction power supply system according to claim 1, characterized in that, The single-input single-output s-domain impedance model in step 2 is as follows: in: ; where ω N It is the power frequency angular frequency, Z. dd Z dq Z qd and Z qq The element's dq impedance model Z ldq Elements in (s): .

3. The method for broadband oscillation S-domain modal analysis of a traction power supply system according to claim 1, characterized in that, In step 5, the damping ratio ξ i and oscillation frequency f i The calculation is as follows: Let the steady-state power frequency be f0, then the DC-side oscillation frequency of the converter is... .

4. The method for broadband oscillation S-domain modal analysis of a traction power supply system according to claim 1, characterized in that, In step 5, the damping ratio is given as 0.

05.

5. The method for broadband oscillation S-domain modal analysis of a traction power supply system according to claim 1, characterized in that, The calculation process for the participation factor of the node pair in the oscillation mode in step 6 is as follows: ； Here, Λ represents the eigenvalue matrix, and there exists an eigenvalue λ. q =0; L and T are the left and right eigenvector matrices, respectively, L=T -1 n is the order of the nodal admittance matrix; Node j, j=1,2,….n pairs of oscillation modes s i Participating factor PF jq for: ; Among them, L jq T represents the element in the j-th row and q-th column of the left eigenvector matrix L. qj This represents the element in the q-th row and j-th column of the right eigenvector matrix T.

Images