A siso equivalent impedance modeling method and system of a single-phase multi-converter grid-connected system

Abstract

The application discloses a kind of SISO equivalent impedance modeling method and system of single-phase multi-converter grid-connected system, the frequency domain small signal model of single-phase converter main circuit with small signal voltage disturbance existing in alternating current side is established;According to the common-mode relationship of small signal electrical quantity in single-phase converter system, the frequency domain small signal model of dq decoupling current control method of single-phase converter system is established;According to the frequency coupling characteristics, the equivalent circuit model of single-phase converter grid-connected system is established, and finally the SISO equivalent impedance model of the alternating current side port of multiple single-phase voltage source converters under dq decoupling current control is obtained.The SISO equivalent impedance model of single-phase multi-converter grid-connected system established by the application can be used to analyze the stability problem of interconnected system under the scene of multiple locomotives accessing traction power supply system, and is suitable for analyzing the potential resonance risk of system when multiple locomotives access traction power supply arm from the perspective of impedance mechanism, which helps to improve the stability of traction power supply system.

Description

Technical Field

[0001] This invention relates to the field of power electronic system modeling, specifically to a SISO equivalent impedance modeling method and system for a single-phase multi-converter grid-connected system. Background Technology

[0002] In recent years, the continuous development of electrified railways has effectively improved the speed and transport capacity of high-speed rail. With the development of high-speed rail, a large number of single-phase voltage source converters (VSCs) have been applied to railway traction power supply systems, further exacerbating harmonic coupling between locomotives and the traction network. This leads to a series of low-frequency oscillations (LFOs) in the traction network when multiple locomotives are raised and prepared at the same location. Since each locomotive has several power units, and each power unit is typically a dual-quadrant converter structure, the stability problem of multiple locomotives connected to the traction power supply system is essentially a stability problem of a single-phase multi-converter grid-connected system.

[0003] Impedance-based stability analysis methods are commonly used to analyze the stability of interconnected systems. Since single-phase systems lack the concept of phase sequence, improving the accuracy of small-signal impedance models requires considering the more severe frequency coupling issues within single-phase converters. Vehicle-to-grid systems considering frequency coupling are no longer independent single-input single-output (SISO) systems with positive and negative sequences, but rather multiple-input multiple-output (MIMO) systems. However, the increased matrix dimension of MIMO systems makes frequency sweep verification more complex. Furthermore, applying this to stability analysis requires the use of the generalized Nyquist criterion, and the multiple characteristic curves increase the computational burden of stability assessment. Moreover, the stability analysis results are not intuitive and fail to reflect the negative damping characteristics of the converter. Therefore, the established MIMO impedance model is typically transformed into a SISO equivalent impedance model. This simplifies frequency sweep verification while allowing for stability assessment from a Bode plot perspective, analyzing the impact of converter negative damping on system stability. Existing research on converting the MIMO impedance of a single-phase converter to its SISO equivalent impedance typically employs matrix determinant transformations, involving complex mathematical transformations. This approach fails to intuitively reflect the frequency coupling issues present in the system, and the conversion methods are generally applicable to single-converter grid connection or the overall external impedance characteristics of multiple converters in a grid connection. However, for single-phase multi-converter grid-connected systems, simultaneously obtaining the SISO impedance of each individual converter and the overall SISO impedance of all converter ports is crucial for analyzing the impedance characteristics of the converters themselves and the stability of the interconnected system.

[0004] The stability of multiple locomotives connected to the traction power supply system is crucial for the normal operation of high-speed railways. Therefore, it is necessary to establish a SISO equivalent impedance model for a single-phase multi-converter grid-connected system. By analyzing the potential resonance risk of the system when multiple locomotives are simultaneously connected to the traction power supply arm from the perspective of impedance mechanism, it is helpful to improve the stability of the traction power supply system. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a SISO equivalent impedance modeling method for a single-phase multi-converter grid-connected system. The aim is to simultaneously obtain the SISO impedance of a single converter and the SISO impedance of the overall port of the multi-converter system, thereby providing a basis for analyzing the negative damping characteristics of locomotives from the perspective of impedance mechanism and analyzing the stability of the traction power supply system in scenarios where multiple locomotives are simultaneously connected to the traction power supply arm.

[0006] This invention is achieved through the following technical solution:

[0007] A method for SISO equivalent impedance modeling of a single-phase multi-converter grid-connected system includes the following steps:

[0008] Step 1: Establish a frequency domain small-signal model of the main circuit of a single-phase converter with small-signal voltage disturbances on the AC side;

[0009] Step 2: Based on the common-differential mode relationship of small-signal electrical quantities in the single-phase converter system, establish the frequency domain small-signal model of the dq decoupling current control method for the single-phase converter system;

[0010] Step 3: Combine the frequency domain small-signal model of the main circuit of the single-phase converter and the frequency domain small-signal model of the dq decoupling current control method to obtain the AC side MIMO impedance model of the single-phase converter. Combine the transformer ratio and the number of single-phase VSCs of the locomotive to obtain the AC side MIMO impedance model of the locomotive.

[0011] Step 4: Based on the coupling characteristics of the AC side MIMO impedance model of the locomotive, determine the AC side SISO equivalent impedance model when a single-phase VSC system is connected to the grid, and then combine the number of converters to obtain the AC side SISO equivalent impedance model of multiple converters.

[0012] Preferably, the method for establishing the frequency domain small-signal model of the single-phase converter main circuit in step 1 is as follows:

[0013] Based on the main circuit topology of the single-phase converter, the electrical steady-state equations of the single-phase VSC main circuit in the time domain are established.

[0014] By using frequency domain variables in the form of complex Fourier series to perform steady-state linearization and small-signalization on the time-domain steady-state equations, a frequency domain small-signal model of the main circuit of a single-phase converter is obtained.

[0015] Preferably, the expression for the frequency domain small-signal model of the single-phase converter main circuit described in step 1 is as follows:

[0016]

[0017] Among them, M and V dc I s Z represents the steady-state components of the modulating wave, DC voltage, and AC current, respectively. n This is the equivalent impedance of the AC-side transformer.

[0018] Preferably, the method for determining the common difference mode relationship in step 2 is as follows:

[0019] Determine the small-signal electrical quantities of a single-phase VSC system under disturbance conditions, and determine the common-differential mode relationship of the small-signal electrical quantities based on the characteristics of the harmonic flow path of the small-signal electrical quantities.

[0020] Preferably, the method for establishing the frequency domain small-signal model of the dq decoupling current control method in step 2 is as follows:

[0021] The control loops of the dq decoupling current control method for a single-phase VSC system are determined. The multi-harmonic linearization method is used to perform small-signal modeling on each control loop. The small-signal models of each control loop are superimposed to obtain the frequency domain small-signal model of the dq decoupling current control method.

[0022] Preferably, the expression for the frequency domain small-signal model of the dq decoupling current control method is as follows:

[0023]

[0024] Among them, P vdc P i P feed P PLL These are the gain coefficient matrices for the DC voltage loop, current loop, feedforward voltage loop, and phase-locked loop, respectively.

[0025] Preferably, the method for determining the AC-side MIMO impedance model of the locomotive is as follows:

[0026] By combining the frequency domain small-signal model of the main circuit of a single-phase converter and the frequency domain small-signal model of the dq decoupling current control method, the AC side MIMO admittance model of a single-phase converter is obtained.

[0027] Based on the coupling characteristics between AC side voltage, current and converter admittance, the AC side disturbance component of the AC side MIMO admittance model is extracted and combined with the transformer ratio to obtain the AC side MIMO admittance matrix of a single converter. The inverse of the AC side MIMO admittance matrix is ​​then used to obtain the AC side MIMO impedance matrix of a single VSC.

[0028] By combining the transformer turns ratio and the number of single-phase converters in the locomotive, the AC-side MIMO admittance model of the locomotive is obtained. By inverting the AC-side MIMO admittance model of the locomotive, the AC-side MIMO impedance model of the locomotive is obtained.

[0029] Preferably, the expression for the AC port MIMO admittance model of the single VSC is as follows:

[0030]

[0031] Where U is the identity matrix, M, V dc I s Z represents the steady-state components of the modulated wave, DC voltage, and AC current, respectively. n P is the equivalent impedance of the AC-side transformer and line. vdc P i P feed P PLL These are the gain coefficient matrices for the DC voltage loop, current loop, feedforward voltage loop, and phase-locked loop, respectively.

[0032] Preferably, the method for determining the SISO equivalent impedance model of the AC side of the multi-current converter in step 4 is as follows:

[0033] Based on the coupling characteristics in the AC-side MIMO impedance model, an equivalent circuit model for a single VSC connected to the grid is established.

[0034] The equivalent impedance model of the AC side SISO when a single-phase VSC is connected to the grid is determined based on the equivalent circuit model.

[0035] The equivalent impedance model of AC side SISO is converted to determine the equivalent impedance model of AC side of a single-phase VSC when multiple converters are connected to the grid. The equivalent impedance model of AC side SISO of multiple converters is obtained by combining the number of converters.

[0036] A system for SISO equivalent impedance modeling of a single-phase multi-converter grid-connected system includes,

[0037] The main circuit module is used to establish a frequency domain small-signal model of the main circuit of a single-phase converter with small-signal voltage disturbances on the AC side.

[0038] The control system module is used to establish a frequency domain small-signal model of the dq decoupling current control method of the single-phase converter system based on the common-differential mode relationship of the small-signal electrical quantities in the single-phase converter system.

[0039] The MIMO impedance model module is used to combine the frequency domain small-signal model of the main circuit of a single-phase converter with the frequency domain small-signal model of the dq decoupling current control method to obtain the AC side MIMO impedance model of the single-phase converter. Combined with the transformer ratio and the number of single-phase VSCs of the locomotive, the AC side MIMO impedance model of the locomotive is obtained.

[0040] The SISO impedance model construction module is used to determine the AC-side SISO equivalent impedance model when a single-phase VSC system is connected to the grid, based on the coupling characteristics of the locomotive's AC-side MIMO impedance model. Then, combined with the number of converters, the AC-side SISO equivalent impedance model of multiple converters is obtained.

[0041] Compared with the prior art, the present invention has the following beneficial technical effects:

[0042] This invention discloses a SISO equivalent impedance model for a single-phase multi-converter grid-connected system. It fully considers the time-varying nonlinear elements in the single-phase voltage source converter controller system, the dynamic coupling characteristics of internal electrical quantities caused by asymmetrical control, and the more complex harmonic coupling problem caused by the grid-side equivalent inductance. Based on the established MIMO impedance model of the single-phase voltage source converter using dq decoupling current control, an equivalent circuit model of the single-phase converter grid-connected system is established by combining frequency coupling characteristics. Finally, the SISO equivalent impedance model of the AC side ports of multiple single-phase voltage source converters under dq decoupling current control is obtained, and the correctness of the established model is verified. The accurate SISO equivalent impedance model of the single-phase multi-converter grid-connected system established in this invention can be used to analyze the stability problem of interconnected systems in scenarios where multiple locomotives are connected to the traction power supply system. It can reflect the negative damping characteristics of the AC side ports of a single converter as well as the negative damping characteristics of the AC side ports of multiple locomotives. It is suitable for explaining the potential resonance risk of the system when multiple locomotives are simultaneously connected to the traction power supply arm from the perspective of impedance mechanism, and helps to improve the stability of the traction power supply system. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the vehicle-network coupling system for multiple CRH5 locomotives connected to the traction network, as studied in this invention.

[0044] Figure 2 This is the main circuit topology of a single CRH5 locomotive according to the present invention;

[0045] Figure 3 This is a block diagram of the control system under the dq decoupling current control mode of the present invention;

[0046] Figure 4 The disturbance frequency f is given by the present invention when a single VSC is connected to the grid. p A schematic diagram of the equivalent circuit model;

[0047] Figure 5 The coupling frequency f is the same as that of a single VSC connected to the grid in this invention. p A schematic diagram of the equivalent circuit model of -2f1;

[0048] Figure 6 The coupling frequency f is the same as that of a single VSC connected to the grid in this invention. p A schematic diagram of the equivalent circuit model of +2f1;

[0049] Figure 7 This is a schematic diagram of the frequency sweeping method used in this invention;

[0050] Figure 8 This is a comparison chart showing the calculated small-signal SISO equivalent impedance of a single VSC AC side port when the multi-converter of this invention is connected to the grid, and the measured value obtained by the frequency sweep method.

[0051] Figure 9 This is a comparison chart showing the calculated small-signal SISO equivalent impedance of the AC side port of the multi-converter of this invention and the measured value obtained by the frequency sweep method. Detailed Implementation

[0052] The present invention will now be described in further detail with reference to the accompanying drawings. These descriptions are intended to explain the invention and not to limit it.

[0053] A SISO equivalent impedance system for a single-phase multi-converter grid-connected system is presented, taking the scenario of multiple CRH5 locomotives simultaneously connected to the traction power supply system for pantograph raising preparation as an example. A schematic diagram of the vehicle-grid coupling system of multiple CRH5 locomotives connected to the traction grid is shown below. Figure 1 As shown, the V / V traction transformer converts the three-phase public power grid into two 27.5kV single-phase power supplies to form a traction power supply system, which supplies power to the L and R side power supply arms respectively. Since the two power supply arms are completely symmetrical, this invention will focus on a scenario where multiple CRH5 locomotives are connected to the traction network under the R side power supply arm.

[0054] A method for modeling the SISO equivalent impedance of a single-phase multi-converter grid-connected system is established, including the following steps:

[0055] Step 1: Taking the CRH5 locomotive as the research object, establish a frequency domain small-signal model of the main circuit of the single-phase converter under the condition of small-signal voltage disturbance on the AC side.

[0056] S1.1 Based on the main circuit topology of a single-phase VSC, Kirchhoff's constant voltage and current law equations are written, and then the electrical steady-state equations of the single-phase VSC main circuit in the time domain are established.

[0057] The main circuit topology of the CRH5 locomotive is as follows: Figure 2 As shown, where L n R n For the equivalent inductance and resistance of the vehicle-mounted transformer, Cd For DC-side capacitor, Z g The equivalent impedance on the traction network side is the inverter and motor load connected to the DC side of the rectifier when the locomotive is in pantograph raising preparation mode, which is equivalent to a resistive load R. d A single CRH5 locomotive contains five power units, each of which adopts a dual-quadrant converter structure, meaning a single CRH5 locomotive contains ten single-phase VSCs.

[0058] Taking a single-phase VSC as an example, the time-domain electrical steady-state equation of the main circuit is established as follows:

[0059]

[0060] S1.2 The main circuit is modeled using a multi-harmonic linearization method. The established time-domain steady-state equation is linearized and converted to a small-signal form using a frequency domain variable in the form of a complex Fourier series, resulting in a frequency domain small-signal model of the single-phase converter main circuit.

[0061] To establish a single-phase VSC AC side impedance model considering frequency coupling effects, assume that the AC side port simultaneously has frequencies fi and fj. p -2f1、f p and f p +2f1 small signal disturbance voltage The specific expression is:

[0062]

[0063] Among them, V1, V represents the amplitude and phase of the AC side fundamental frequency voltage. p-2 V p V p+2 and They are frequencies f p -2f1、f p f p The amplitude and initial phase of the AC side voltage disturbance of +2f1.

[0064] By using frequency domain variables in the form of complex Fourier series to perform steady-state linearization and small-signal transformation on the established time-domain steady-state equations, the frequency domain small-signal model of the main circuit under single-phase VSC frequency domain conditions with AC side disturbances is finally obtained as follows:

[0065]

[0066] Among them, M and V dc I s The Toeplitz forms of the modulated wave, DC voltage, and AC current steady-state components are respectively, Z. n This is the equivalent impedance of the AC-side transformer.

[0067] Step 2: Determine the common-differential mode relationship of small-signal electrical components in a single-phase VSC system.

[0068] S2.1 Analyze the small-signal electrical quantities existing inside the single-phase VSC system under disturbance conditions.

[0069] If the AC port in a single-phase system has a frequency of f p Small-signal voltage disturbances, influenced by time-varying nonlinear elements, asymmetric control elements, and equivalent inductance on the grid side in the locomotive controller system, cause steady-state components and small-signal disturbance components to couple with each other, generating a series of frequencies with frequency f. p Small-signal harmonic components of ±kf1 (k=0,1,2,3…,n). In establishing the small-signal impedance model, the impedance model established considering the third harmonic component has sufficiently high accuracy; that is, the highest-order small-signal quantity considered in subsequent modeling is f. p ±3f1, the steady-state components are all 7×7 matrices.

[0070] S2.2 Determine the common-mode relationship of harmonic electrical quantities based on the characteristics of the harmonic flow path of small-signal electrical quantities in a single-phase system.

[0071] When the highest harmonic component is considered up to the 3rd order, in a three-phase grid-connected system, if the PCC point has a frequency of f... p The voltage disturbance will eventually couple out a frequency f at the grid connection point. p and f p The disturbance voltage and current are -2f1. However, single-phase systems lack the concept of phase sequence; if an AC port has a frequency f... p Small-signal voltage disturbances, where k is even, all harmonic components flow into the AC side; where k is odd, all harmonic components flow into the DC side. Therefore, the frequency coupling problem becomes more complex, meaning a single-phase system will simultaneously couple out harmonics with frequency f. p -2f1 and f p The disturbance voltage and disturbance current of +2f1.

[0072] Step 3: Establish the frequency domain small-signal model of the dq decoupling current control method for a single-phase VSC system based on the common-differential mode relationship.

[0073] S3.1 Determine each control loop of the dq decoupling current control method.

[0074] The single-phase VSC in the CRH5 locomotive uses dq decoupling current control, and the control block diagram is as follows: Figure 3 As shown, it consists of a DC voltage outer loop, a feedforward voltage loop, a current inner loop, a second-order generalized integrator (SOGI), a phase-locked loop, and a modulation stage. The DC-side voltage setpoint of the converter, v dc This is the actual value of the DC-side voltage, v ac i ac H represents the actual values ​​of the AC side voltage and current of the converter. v (s) is the transfer function of the voltage outer loop controller, i d i q These are single-phase alternating currents i ac The d-axis and q-axis components in the dq coordinate system obtained after SOGI and coordinate transformation. and H represents the given values ​​of the d-axis and q-axis components of the alternating current in the dq coordinate system, respectively. i (s) is the transfer function of the current inner loop controller, K id This is the decoupling coefficient for the inner current loop.

[0075] S3.2 The multi-harmonic linearization method is used to perform small-signal modeling of each control loop of the control system, and the frequency domain small-signal model of the dq decoupled current control method is obtained.

[0076] The small-signal model of the modulated wave, formed by the superposition of small-signal models of different control elements, can be expressed as:

[0077]

[0078] Among them, P vdc P i P feed P PLL These are the gain coefficient matrices for the DC voltage loop, current loop, feedforward voltage loop, and phase-locked loop, respectively. Harmonic components up to the third order are considered during modeling, and all the above coefficient matrices are 7×7 square matrices.

[0079] Taking the DC voltage outer loop as an example, the small-signal model of the control system is derived. The derivation approach for other control loops is the same and will not be repeated here. The DC voltage loop controls the DC-side voltage, and only the common-mode component of the harmonic components is output to the DC side. Therefore, the outer loop controller only controls the frequency f. p Small voltage disturbances of ±(2k+1)·f1, k=0,1,2… take effect. Assume the frequency is f. p The small-signal component of the DC voltage of +f1 The dq-axis small-signal modulated wave generated after DC voltage outer loop, current inner loop, and coordinate transformation is:

[0080]

[0081] Using the measured initial phase as a reference angle, the phase generated by the angle generator includes the initial phase of the fundamental frequency voltage. That is, the phase corresponding to the dq / αβ transformation is Therefore, the transformation matrix is:

[0082]

[0083] The α-axis small-signal modulated wave can be obtained by transforming the dq-axis small-signal modulated wave into dq / αβ coordinates. The expression is:

[0084]

[0085] From equation (7), it can be seen that after coordinate transformation, the amplitude of the small signal modulation wave becomes half of its original value, and the frequency increases by f1 and decreases by f1, respectively. Substituting equation (5), we can obtain the frequency f. p The small-signal component of the DC voltage of +f1 Modulated wave via voltage outer loop The specific expression for the effect is:

[0086]

[0087] The matrix form expression is:

[0088]

[0089] The analog frequency is f p The small-signal component of the DC voltage of +f1 Modulated wave via voltage outer loop The effect is generated when the harmonic components are considered up to the third order, resulting in the DC voltage loop gain coefficient matrix P. vdc The expression is:

[0090]

[0091] P vdc Internal elements can be specifically represented as:

[0092]

[0093] Step 4: Combine the frequency domain small-signal model of the main circuit of the single-phase converter and the frequency domain small-signal model of the dq decoupling current control method to obtain the AC side MIMO impedance model of the single-phase VSC. Combine the transformer ratio and the number of single-phase VSCs in the locomotive to obtain the AC side MIMO impedance model of the locomotive.

[0094] S4.1 The single-phase VSC AC side MIMO impedance model is obtained by combining the main circuit frequency domain small-signal model and the control system frequency domain small-signal model.

[0095] By combining the frequency domain small-signal main circuit model (3) of the single-phase converter under the condition of disturbance on the AC side established in step 1 with the frequency domain small-signal model (4) of the dq decoupling current control method established in step 3, the AC port MIMO admittance model of a single VSC can be obtained. The expression is:

[0096]

[0097] When considering the third order harmonics of steady-state electrical quantities, if there is a frequency f on the AC side of a single-phase system... p Small signal voltage disturbance At that time, the AC side grid connection point of a single-phase system will have a frequency of f. p Small signal voltage disturbance and current disturbance And couples out a frequency of f p -2f1 and f p +2f1 disturbance voltage and disturbance current The coupling characteristics between AC side voltage, current, and converter admittance can be expressed as:

[0098]

[0099] The admittance model established by considering the third order of steady-state electrical quantity harmonics is sufficiently accurate, and the coupling characteristic relationship (13) is used to extract... The intermediate frequency is f p -2f1、f p f p By considering the AC-side disturbance component of +2f1 and the transformer turns ratio K, the MIMO admittance matrix Y of a single VSC AC-side can be obtained. VSC (s) is:

[0100]

[0101] Inverting matrix (14) yields the impedance matrix Z of a single VSC AC-side MIMO. VSC (s).

[0102] S4.2 takes into account the transformer turns ratio and the number of power units contained in the locomotive to obtain the AC side MIMO impedance model of a single CRH5 locomotive.

[0103] Considering the transformer turns ratio K and the number of single-phase VSCs in a single CRH5 locomotive power unit, the AC port MIMO admittance model of a single CRH5 locomotive can be obtained. The expression is:

[0104]

[0105] The MIMO admittance matrix Y on the AC side of a single CRH5 locomotive can be obtained. CRH5 The expression for (s) is:

[0106]

[0107] Inverting matrix (16) yields the AC-side MIMO impedance matrix Z of a single CRH5 locomotive. CRH5 (s).

[0108] Step 5: Based on the coupling characteristics of the AC side MIMO impedance model of the locomotive, establish the AC side SISO equivalent impedance model when a single-phase VSC system is connected to the grid. Then, combine the number of converters to obtain the AC side SISO equivalent impedance model of the CRH5 locomotive with multiple converters.

[0109] S5.1 Establish the equivalent circuit model of a single VSC when connected to the grid based on the coupling characteristics in the MIMO impedance.

[0110] The coupling characteristics between AC side voltage, current, and converter admittance are shown in equation (13). To obtain the SISO equivalent impedance model of a single-phase multi-converter grid-connected system, based on the frequency coupling characteristics in the MIMO impedance (13), the equivalent circuit model for a single VSC grid connection is first established. When there is a frequency f on the AC side... p Small signal voltage disturbance At that time, the current expression at the grid connection point is:

[0111]

[0112] The frequency at the grid connection point is retained as f. p Small signal voltage disturbance Will and Both are equivalent to current sources, and the grid-side admittance Y is also considered. g Taking (s) into account, the equivalent circuit model can be obtained as follows: Figure 4 As shown. Similarly, combining equation (13), the frequency at the grid connection point is retained as f. p -2f1、f p +2f1 small-signal voltage disturbance and The coupling frequency f can be obtained. p The equivalent circuit model corresponding to -2f1 is as follows: Figure 5 As shown, the coupling frequency is f p The equivalent circuit model corresponding to +2f1 is as follows: Figure 6 As shown.

[0113] S5.2 Derive the AC side SISO equivalent impedance model when a single-phase VSC is connected to the grid based on the equivalent circuit model.

[0114] by Figures 4-6 Based on the equivalent circuit model, the frequency f is derived. p Corresponding disturbance current and disturbance voltage The expression for the ratio yields the equivalent admittance model of the SISO at a single VSC AC side port under the dq decoupling current control mode. right The SISO equivalent admittance model can be obtained by inverting the equation.

[0115] Depend on Figure 4 It can be seen that the frequency is f p Corresponding disturbance current and disturbance voltage The ratio expression is:

[0116]

[0117] Y4, Y5, and Y6 are all known quantities; the key lies in deriving them. and The expression.

[0118] Depend on Figure 5 It can be known

[0119]

[0120] The equivalent admittance Y on the network side g (f p -2f) taken into account, for By making the substitution, we can obtain

[0121]

[0122] Same reason Figure 6 It can be known

[0123]

[0124] The equivalent admittance Y on the network side g (f p Taking +2f) into account, for By making the substitution, we can obtain

[0125]

[0126] Solving the system of equations consisting of equations (20) and (22) simultaneously yields the result. and The expression.

[0127] The system of equations to be solved is as follows:

[0128]

[0129] Ultimately obtain

[0130]

[0131] Substituting equation (24) into equation (18) yields the SISO equivalent admittance model for a single-phase VSC. The expression is:

[0132]

[0133] Inverting equation (25) yields the SISO equivalent impedance model expression for a single-phase VSC.

[0134] S5.3 calculates the equivalent impedance on the grid side, derives the equivalent impedance model of the AC side of a single-phase VSC when multiple converters are connected to the grid, and obtains the equivalent impedance model of the AC side of multiple converters by combining the number of converters. The stability of the interconnected system when multiple locomotives are connected to the traction power supply system is analyzed by using the equivalent impedance model of the AC side of multiple converters.

[0135] Considering the scenario of multiple converters connected to the grid, it is necessary to perform an equivalent conversion of the grid-side impedance. Let the AC port current be i when a single voltage source converter is connected to the grid. vsc The coupling voltage generated by the flow through the grid-side impedance is i vsc ·Z g When N converters are connected to the grid, the AC port current is N·i vsc The coupling voltage generated by the current flowing through the grid-side impedance is N·i vsc ·Z g That is, when N converters are connected to the grid, the grid-side equivalent impedance is N times that when a single converter is connected to the grid, and the equivalent admittance relationship is 1 / N.

[0136] Based on the principle of grid-side impedance reduction, the SISO equivalent admittance model of a single VSC AC side port when multiple converters are connected to the grid can be obtained from the SISO equivalent admittance model of a single-phase VSC (25). The expression is:

[0137]

[0138] Inverting equation (26) yields the equivalent impedance model expression for the SISO of a single VSC AC side port when multiple converters are connected to the grid.

[0139] Based on the equivalent admittance model (26) of the SISO of a single VSC AC side port when multiple converters are connected to the grid, multiplying it by the number of multiple converters N yields the equivalent admittance model of the overall AC side port SISO of the multiple converters. The specific expression is:

[0140]

[0141] Inverting equation (27) yields the expression for the SISO equivalent impedance model of the overall AC side port of the multi-converter.

[0142] Step 6: Verify the accuracy of the established impedance model using the frequency sweep method.

[0143] S6.1 Determine the frequency sweeping scheme based on the working principle of the frequency sweeping method.

[0144] When multiple CRH5 locomotives are connected to the traction network, such as Figure 7 As shown, when multiple converters are connected to the grid, a frequency of f is added to the traction network side. p Small signal voltage disturbance Extract the frequency f from the traction network side port, i.e., measure port 1. p Corresponding small-signal current response A single VSC AC side port, i.e., measuring port 2 frequency f p Corresponding small-signal voltage response Current response By calculating the frequency f p voltage disturbance With current disturbance The ratio of these two values ​​yields the overall small-signal SISO equivalent impedance sweep value for the AC side ports of the multi-converter. This is obtained by calculating the frequency f. p voltage disturbance With current disturbance The ratio of these two values ​​yields the small-signal SISO equivalent impedance sweep value of a single VSC AC side port when multiple converters are connected to the grid. Changing the disturbance frequency f... p By iterating through 1Hz-100Hz and repeating step 5 and the frequency sweep process, the small-signal impedance model calculation value and frequency sweep value of a single VSC AC side port and the overall AC side port of the multi-converter in the case of grid connection of multiple converters can be obtained.

[0145] S6.2 Compare the amplitude and phase errors of the calculated values ​​and the swept-frequency values ​​of the small-signal impedance model to verify the high accuracy of the established impedance model.

[0146] Taking the grid connection of two CRH5 locomotives as an example, the frequency sweep values ​​of a single VSC AC side port and the overall AC side port of multiple converters, the calculated values ​​of the SISO equivalent impedance model, and the comparison results of directly taking the middle element Z(4,4) of the MIMO impedance matrix as the SISO impedance calculation value without considering frequency coupling are as follows: Figure 8 , Figure 9As shown in the results, the amplitude and phase of the calculated value of the SISO equivalent impedance model small-signal impedance model and the sweep frequency value are in good agreement, and the model accuracy is high. However, without considering the frequency coupling effect, directly taking Z(4,4) as the calculated value of SISO impedance and the sweep frequency value have a large error. This further verifies the importance of considering the frequency coupling effect and analyzing the MIMO and SISO conversion process in this invention.

[0147] This invention also provides a system for SISO equivalent impedance modeling of a single-phase multi-converter grid-connected system, comprising,

[0148] The main circuit module is used to establish a frequency domain small-signal model of the main circuit of a single-phase converter with small-signal voltage disturbances on the AC side.

[0149] The control system module is used to establish a frequency domain small-signal model of the dq decoupling current control method of the single-phase converter system based on the common-differential mode relationship of the small-signal electrical quantities in the single-phase converter system.

[0150] The MIMO impedance model module is used to combine the frequency domain small-signal model of the main circuit of a single-phase converter with the frequency domain small-signal model of the dq decoupling current control method to obtain the AC side MIMO impedance model of the single-phase converter. Combined with the transformer ratio and the number of single-phase VSCs of the locomotive, the AC side MIMO impedance model of the locomotive is obtained.

[0151] The SISO impedance model construction module is used to determine the AC-side SISO equivalent impedance model when a single-phase VSC system is connected to the grid, based on the coupling characteristics of the locomotive's AC-side MIMO impedance model. Then, combined with the number of converters, the AC-side SISO equivalent impedance model of multiple converters is obtained.

[0152] This invention discloses a SISO equivalent impedance model for a single-phase multi-converter grid-connected system. It fully considers the time-varying nonlinear elements in the single-phase VSC controller system, the dynamic coupling characteristics of internal electrical quantities caused by asymmetrical control, and the more complex harmonic coupling problem caused by the grid-side equivalent inductance. A high-precision MIMO impedance model is established. Based on this, an equivalent circuit model is established according to the frequency coupling characteristics. Finally, the SISO equivalent impedance model of a single VSC AC side port and the overall AC side port SISO equivalent impedance model of the multi-converter are derived. The established model has… The modeling results are highly accurate, reflecting coupling characteristics and simultaneously demonstrating the impedance characteristics of a single VSC and the overall port impedance characteristics of multiple converters. The established accurate SISO equivalent impedance model for a single-phase multi-converter grid-connected system can be used to analyze the stability of interconnected systems when multiple locomotives are connected to the traction power supply system. It can reflect the negative damping characteristics of the AC side port of a single converter as well as the negative damping impedance characteristics of the AC side ports of multiple locomotives. It is suitable for explaining the potential resonance risk of the system when multiple locomotives are simultaneously connected to the traction power supply arm from the perspective of impedance mechanism, which helps to improve the stability of the traction power supply system.

[0153] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A SISO equivalent impedance modeling method for a single-phase multi-converter grid-connected system, characterized in that, Includes the following steps: Step 1: Establish a frequency domain small-signal model of the main circuit of a single-phase converter with small-signal voltage disturbances on the AC side; Step 2: Based on the common-differential mode relationship of small-signal electrical quantities in the single-phase converter system, establish the frequency domain small-signal model of the dq decoupling current control method for the single-phase converter system; Step 3: Combine the frequency domain small-signal model of the main circuit of the single-phase converter and the frequency domain small-signal model of the dq decoupling current control method to obtain the AC side MIMO impedance model of the single-phase converter. Combine the transformer ratio and the number of single-phase VSCs of the locomotive to obtain the AC side MIMO impedance model of the locomotive. Step 4: Based on the coupling characteristics in the AC side MIMO impedance model of the locomotive, establish the equivalent circuit model when a single VSC is connected to the grid, and determine the AC side SISO equivalent impedance model when a single single-phase VSC is connected to the grid based on the equivalent circuit model. The grid-side equivalent admittance is converted to Yg / n according to the number of grid-connected VSCs n. The conversion result is substituted into the AC-side SISO equivalent impedance model when a single-phase VSC is connected to the grid. The AC-side SISO equivalent impedance model is converted to determine the AC-side SISO equivalent impedance model of a single-phase VSC when multiple converters are connected to the grid. The AC-side SISO equivalent impedance model of multiple converters is obtained by combining the number of converters.

2. The SISO equivalent impedance modeling method for a single-phase multi-converter grid-connected system according to claim 1, characterized in that, The method for establishing the frequency domain small-signal model of the single-phase converter main circuit in step 1 is as follows: Based on the main circuit topology of the single-phase converter, the electrical steady-state equations of the single-phase VSC main circuit in the time domain are established. By using frequency domain variables in the form of complex Fourier series to perform steady-state linearization and small-signalization on the time-domain steady-state equations, a frequency domain small-signal model of the main circuit of a single-phase converter is obtained.

3. The SISO equivalent impedance modeling method for a single-phase multi-converter grid-connected system according to claim 1, characterized in that, The expression for the frequency domain small-signal model of the single-phase converter main circuit described in step 1 is as follows: in, M , V dc , I s These are the steady-state components of the modulating wave, DC voltage, and AC current, respectively. Z n This is the equivalent impedance of the AC-side transformer.

4. The SISO equivalent impedance modeling method for a single-phase multi-converter grid-connected system according to claim 1, characterized in that, The method for determining the common difference mode relationship in step 2 is as follows: Determine the small-signal electrical quantities of a single-phase VSC system under disturbance conditions, and determine the common-differential mode relationship of the small-signal electrical quantities based on the characteristics of the harmonic flow path of the small-signal electrical quantities.

5. The SISO equivalent impedance modeling method for a single-phase multi-converter grid-connected system according to claim 1, characterized in that, The method for establishing the frequency domain small-signal model of the dq decoupling current control method in step 2 is as follows: The control loops of the dq decoupling current control method for a single-phase VSC system are determined. The multi-harmonic linearization method is used to perform small-signal modeling on each control loop. The small-signal models of each control loop are superimposed to obtain the frequency domain small-signal model of the dq decoupling current control method.

6. The SISO equivalent impedance modeling method for a single-phase multi-converter grid-connected system according to claim 5, characterized in that, The expression for the frequency domain small-signal model of the dq decoupling current control method is as follows: in, P vdc , P i , P feed , P PLL These are the gain coefficient matrices for the DC voltage loop, current loop, feedforward voltage loop, and phase-locked loop, respectively.

7. The SISO equivalent impedance modeling method for a single-phase multi-converter grid-connected system according to claim 1, characterized in that, The method for determining the AC-side MIMO impedance model of the locomotive is as follows: By combining the frequency domain small-signal model of the main circuit of a single-phase converter and the frequency domain small-signal model of the dq decoupling current control method, the AC side MIMO admittance model of a single-phase converter is obtained. Based on the coupling characteristics between AC side voltage, current and converter admittance, the AC side disturbance component of the AC side MIMO admittance model is extracted and combined with the transformer ratio to obtain the AC side MIMO admittance matrix of a single converter. The inverse of the AC side MIMO admittance matrix is ​​then used to obtain the AC side MIMO impedance matrix of a single VSC. By combining the transformer turns ratio and the number of single-phase converters in the locomotive, the AC-side MIMO admittance model of the locomotive is obtained. By inverting the AC-side MIMO admittance model of the locomotive, the AC-side MIMO impedance model of the locomotive is obtained.

8. The SISO equivalent impedance modeling method for a single-phase multi-converter grid-connected system according to claim 7, characterized in that, The AC port MIMO admittance model of a single VSC Y MIMO VSC ( s The expression for ) is as follows: in, U It is the identity matrix. M , V dc , I s These are the steady-state components of the modulating wave, DC voltage, and AC current, respectively. Z n The equivalent impedance of the AC-side transformer and line. P vdc , P i , P feed , P PLL These are the gain coefficient matrices for the DC voltage loop, current loop, feedforward voltage loop, and phase-locked loop, respectively.

9. A system for implementing the SISO equivalent impedance modeling method for a single-phase multi-converter grid-connected system according to any one of claims 1-8, characterized in that, include, The main circuit module is used to establish a frequency domain small-signal model of the main circuit of a single-phase converter with small-signal voltage disturbances on the AC side. The control system module is used to establish a frequency domain small-signal model of the dq decoupling current control method of the single-phase converter system based on the common-differential mode relationship of the small-signal electrical quantities in the single-phase converter system. The MIMO impedance model module is used to combine the frequency domain small-signal model of the main circuit of a single-phase converter with the frequency domain small-signal model of the dq decoupling current control method to obtain the AC side MIMO impedance model of the single-phase converter. Combined with the transformer ratio and the number of single-phase VSCs of the locomotive, the AC side MIMO impedance model of the locomotive is obtained. The SISO impedance model construction module is used to determine the AC-side SISO equivalent impedance model when a single-phase VSC system is connected to the grid, based on the coupling characteristics of the locomotive's AC-side MIMO impedance model. Then, combined with the number of converters, the AC-side SISO equivalent impedance model of multiple converters is obtained.

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