Method and system for small-signal stability analysis of power plant containing grid-forming converters

Abstract

Disclosed in the present invention are a method and system for small-signal stability analysis of a power plant containing grid-forming converters. The method comprises: establishing a grid-following converter impedance model; establishing a grid-forming converter impedance model; constructing a new energy power plant grid-connected system model containing grid-following converters and grid-forming converters; establishing a simplified equivalent circuit of a power plant grid-connected system; establishing a small-signal stability Nyquist criterion for a grid-connected new energy power plant containing grid-forming converters; and using a Nyquist plot to analyze the small-signal stability characteristics of the power plant grid-connected system. According to the present invention, the problem in the prior art of lacking quantitative and effective analysis of small-signal stability in new energy power plants containing grid-following converters and grid-forming converters is solved, and establishing a small-signal stability criterion for the power plants on the basis of established small-signal models enables quantitative analysis of the small-signal stability characteristics of a new energy power plant containing grid-forming converters under low grid strength conditions, and compared with conventional impedance modeling methods for new energy power plants, the impact of grid-forming converter integration on the small-signal stability of the new energy power plants is better reflected.

Description

A small disturbance stability analysis method and system for a grid-type converter station Technical Field

[0001] The present invention relates to a stability analysis method and system for a transformer station, and in particular to a small disturbance stability analysis method and system for a station containing a grid-type converter. Background Art

[0002] When traditional renewable energy stations are connected to the main grid via long-distance lines and multi-stage transformers, the grid-following converter control system is susceptible to coupling with the grid impedance. This coupling can increase the risk of oscillations at low short-circuit ratios, seriously impacting the safe and stable operation of the system. As the installed capacity of traditional grid-following converters in renewable energy stations increases, the problem of subsynchronous oscillations in weak grid scenarios becomes increasingly prominent. Currently, most literature on small-disturbance stability research focuses on the grid-connected stability of a single type or single-device inverter in weak grid conditions. However, relatively little research has been conducted on the small-disturbance stability analysis of traditional grid-following renewable energy multi-stations connected to grid-forming converters.

[0003] Small-signal modeling methods for grid-connected converters can be primarily categorized into the impedance method and the state-space method. The state-space method establishes a linearized small-disturbance dynamic model of the system at its static operating point, calculates the system's state-space matrix, and then solves for the eigenvalues ​​and eigenvectors of the system's state matrix to determine system stability. However, the state-space method relies on a deep understanding of the system's internal mechanisms, including various electrical quantities and control parameters, which are often difficult to obtain directly or remain confidential. The impedance method, based on frequency-domain analysis, can be used to directly model the system using control structures and parameters, or to characterize the system's dynamic behavior by measuring the impedance characteristics between system ports. This method does not require a detailed understanding of the system's internal structure and parameters, and is therefore known as a "black-box" model. The application of the impedance method is not only of great theoretical value but also demonstrates its practicality in practical engineering applications.

[0004] Summary of the Invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a small-disturbance stability analysis method and system for a station containing a grid-type converter, which can better reflect the small-disturbance stability characteristics of the station grid-connected system under a scenario with weak grid strength, and solve the problem in the prior art of lack of quantitative and effective analysis of the small-disturbance stability of new energy stations containing grid-type converters.

[0006] Technical solution: The present invention includes: establishing a grid-following converter impedance model; establishing a grid-forming converter impedance model; constructing a grid-connected system model of a new energy station including grid-following and grid-forming types; establishing a simplified equivalent circuit of the station grid-connected system: converting the system model into a circuit model, converting the grid-following converter into a controlled current source model, converting the grid-forming converter into a controlled voltage source model, performing circuit equivalent calculations on the circuit model, controlled current source model and controlled voltage source model of the system model, and solving the station grid-connected system. An equivalent circuit model of the grid system is used for small-disturbance stability analysis, and the impedance of the new energy station is aggregated to simplify the equivalent circuit of the station in the equivalent circuit model; the Nyquist criterion for small-disturbance stability of the grid-connected new energy station containing the grid-forming type is established: combining the impedance model of the grid-following converter and the grid-forming converter with the line impedance, the transfer relationship between the grid connection point current and each power source is derived, and the small-disturbance stability criterion of the new energy station grid-connected system is solved by the transfer relationship; the Nyquist diagram is used to analyze the small-disturbance stability characteristics of the station grid-connected system.

[0007] The specific steps of establishing the grid-connected converter impedance model are as follows: deriving each link of the small disturbance transmission in the new energy station grid-connected system, and obtaining the grid-connected converter output impedance model that takes into account the phase-locked loop, the current inner loop, and the DC voltage outer loop. The analytical expression is as follows:

[0008] Where Z1=G id (I+G del G ci G vdc G vd ) -1 G del Z2=(G dei -G ci )G pll_i -G ci G vdc G ve +G pll_d +G pll_v

[0009] Among them: G ci is the PI link of the current loop, G vdc is the voltage outer loop PI link, G dei is the current loop decoupling matrix, G del is the transfer function matrix considering sampling delay; G pll_v , G pll_i and G pll_d is the transfer function of voltage, current and duty cycle from system coordinates to control system coordinates through the phase-locked loop; G id : small disturbance transfer matrix from duty cycle vector to grid-side current vector in system synchronous coordinates; G vd: small perturbation transfer matrix from duty cycle vector to DC voltage vector;

[0010] The output admittance is: Y out =Z out -1 .

[0011] The specific steps of establishing the grid-connected converter impedance model are as follows: based on the main circuit small signal model and the small signal transmission relationship in the controller coordinates in the new energy station grid-connected system, an analytical expression for the external impedance of the self-synchronous voltage source under virtual synchronous control is obtained:

[0012] Among them: G voio and G vovc is the main circuit transformation matrix; I is the unit matrix; s is the complex variable in the transfer function;

[0013] G vio and G vvc is the small signal linearization transfer function of the reactive loop;

[0014] G ωio and G ωvc is the small signal linearization transfer function of the active loop;

[0015] G Lf and G Cf are the LC filter transfer functions of the main circuit; G ωLf and G ωCf It is the transfer function from the active loop output phase angle small signal to the main circuit; T1=G Lf ·G Cf T2=-(G Cf ·G Lf -1 ·G ωLf +G Cf -1 ·G ωCf ) T3=-G Cf K=(I-T1·G vvc -T2·G ωvc ) -1 ·(T1·G vio +T2·G ωio +T3)

[0016] T s is the rotation matrix; T v and T c It is the small signal linearization transfer matrix for transforming the voltage and current controller coordinates to the system coordinate system.

[0017] The system model consists of multiple grid-following converters connected via line impedance Z lAt the point of common coupling, it is connected in parallel with the voltage source and connected to the grid via the line impedance Z g Connected in series with the ideal source; among them, the grid-following converter keeps synchronization with the main grid through a phase-locked loop, and the grid-building converter adopts a virtual synchronization control strategy.

[0018] The grid-following converter adopts unified parameters, and multiple grid-following converters form a converter string through a tie line. The tie line impedance is preset, and multiple strings of converters are connected to the infinite power grid through the line impedance Zg at the common grid connection point PCC; the grid-forming converter adopts unified parameters, and multiple grid-forming converters are connected to the infinite power grid through the line impedance Zg at the common grid connection point PCC through the tie line impedance.

[0019] The Nyquist criterion for small-disturbance stability of grid-connected new energy stations is established as follows: based on the simplified equivalent circuit of the grid-connected system, V PCC and I PCC are the voltage and current at the grid connection point respectively; I GFM with I GFL are the output currents of the grid-forming converter and the grid-following converter respectively; Z g is the line impedance, V Grid is the grid-side power supply; calculate I PCC The transfer function relationship between each power supply can be obtained from the equivalent impedance network model topology:

[0020] Among them, I S2 is the current source after being equal to the grid-type converter; Y GFM and Y GFL are the output admittances of the network-building type and the network-following type respectively; the expressions of H1(s), H2(s) and H3(s) are as follows: H2(s)=Y GFM H3(s)=Y GFM +Y GFL

[0021] Among them, V s1 is a voltage source, H1(s) is related to the equivalent impedance of the grid-type converter, the equivalent impedance of the grid-type converter and the line impedance, H2(s) is only related to the impedance of the grid-type converter itself, and H3(s) is related to the equivalent impedance of the grid-type converter and the equivalent impedance of the grid-type converter; for H1(s) and H3(s), H1(s) and H1(s)·H3(s) can be regarded as two closed-loop transfer functions and Its stability depends on its open-loop transfer function Z g ·(Y GFM +Y GFL ).

[0022] The small perturbation stability criterion is: when H2(s) does not have a positive real part pole and Z g ·(Y GFM +Y GFL ) satisfies the Nyquist criterion: when Z = N + P = 0, the new energy station grid-connected system is stable; where Z is the number of closed-loop positive real part poles; N is the number of cycles of the Nyquist diagram clockwise surrounding the point (-1,0); and P is the number of open-loop positive real part poles.

[0023] The Nyquist diagram is used to analyze the small disturbance stability characteristics of the station grid-connected system. Specifically, the Nyquist diagram under different parameters is drawn using the stability criterion to analyze the small disturbance stability of the new energy station grid-connected system.

[0024] The above-mentioned method of using stability criterion to draw Nyquist diagrams under different parameters and analyze the small disturbance stability of the new energy station grid-connected system specifically includes: when the stability criterion: L = Z g ·(Y GFM +Y GFL ) must satisfy the Nyquist criterion and obtain its eigenvalues ​​l1 and l2:

[0025] Where L is the defined loop matrix; L dd , L dq , L qd and L qq are the four elements of the loop matrix L; l1 and l2 are the two characteristic roots of the matrix;

[0026] Draw the Nyquist plots for l1 and l2 respectively and judge the stability.

[0027] A small-disturbance stability analysis system for a station containing a grid-forming converter comprises: a grid-following converter impedance model, a grid-forming converter impedance model, a grid-connected system model for new energy stations containing both grid-following and grid-forming types, a simplified equivalent circuit model for the grid-connected system for new energy stations, a Nyquist criterion model for small-disturbance stability of grid-connected new energy stations containing grid-forming types, and a model for analyzing the small-disturbance stability characteristics of the station grid-connected system.

[0028] Beneficial effects: The present invention solves the problem in the prior art of lack of quantitative and effective analysis of the small-disturbance stability of new energy stations containing grid-following and grid-forming converters. Based on the established small signal model, a small-disturbance stability criterion for the station is established, which can quantitatively analyze the small-disturbance stability characteristics of new energy stations containing grid-forming converters under low grid strength scenarios; compared with the traditional impedance modeling method for new energy stations, it can better reflect the impact of grid-forming access on the small-disturbance stability of new energy stations. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] FIG1 is a flow chart of the present invention;

[0030] FIG2 is a topological diagram of the main circuit of the present invention;

[0031] FIG3 is a diagram showing the main circuit topology and control links of the grid-connected converter of the present invention;

[0032] FIG4 is a block diagram of an output impedance model of a grid-connected converter according to the present invention;

[0033] FIG5 is a diagram showing the main circuit topology and control links of the grid-connected converter of the present invention;

[0034] FIG6 is a block diagram of an output impedance model of a grid-connected converter of the present invention;

[0035] FIG7 is an impedance equivalent circuit model of a new energy station after equivalent replacement of the impedance model of the present invention;

[0036] FIG8 is an impedance equivalent circuit model of a new energy station according to the present invention;

[0037] FIG9 is a diagram of a frequency sweep test of the output admittance of a grid-connected converter according to the present invention;

[0038] FIG10 is a diagram of a frequency sweep test of the output admittance of a grid-connected converter according to the present invention;

[0039] FIG11 is a Nyquist diagram of the characteristic root l2 of the grid-type converter of the present invention;

[0040] FIG12 is the grid-connected current I of the present invention. dq Simulation waveform. DETAILED DESCRIPTION

[0041] The present invention will be further described below with reference to the accompanying drawings.

[0042] As shown in FIG1 , the small disturbance stability analysis method of the grid-type converter station of the present invention includes the following steps:

[0043] S1. Establishing the impedance model of grid-following converter;

[0044] The grid-connected angle in the grid-connected converter control is detected through a phase-locked loop (PLL), and then generates a drive signal after passing through the current loop. The grid-connected control link is shown in Figure 3. By deducing the various links of small disturbance transmission, we can obtain the output impedance model of the grid-connected converter that takes into account the PLL, the inner current loop, and the outer DC voltage loop. The small signal block diagram is shown in Figure 4, and the analytical expression is shown as follows:

[0045] Where Z1=G id (I+G del G ci G vdc G vd ) -1G del Z2=(G dei -G ci )G pll_i -G ci G vdc G ve +G pll_d +G pll_v

[0046] Among them: G ci is the PI link of the current loop, G vdc is the voltage outer loop PI link, G dei is the current loop decoupling matrix, G del is the transfer function matrix considering sampling delay; G pll_v , G pll_i and G pll_d is the transfer function of voltage, current and duty cycle from system coordinates to control system coordinates through the phase-locked loop; G id : small disturbance transfer matrix from duty cycle vector to grid-side current vector in system synchronous coordinates; G vd : small perturbation transfer matrix from duty cycle vector to DC voltage vector;

[0047] The output admittance is: Y out =Z out -1 (11)

[0048] S2. Establishing a grid-type converter impedance model;

[0049] The main circuit topology and control links of the grid-type converter are shown in Figure 5. The grid-type converter considers the power outer loop, and the voltage amplitude and phase angle are generated by the power loop.

[0050] The small signal model of the main circuit and the small signal transfer relationship under the controller coordinates are shown in Figure 6. The analytical expression of the external impedance of the self-synchronous voltage source under virtual synchronous control can be obtained:

[0051] Among them: G voio and G vovc is the main circuit transformation matrix; I is the unit matrix; s is the complex variable in the transfer function;

[0052] G vio and G vvc is the small signal linearization transfer function of the reactive loop;

[0053] G ωio and G ωvc is the small signal linearization transfer function of the active loop;

[0054] G Lf and G Cfare the LC filter transfer functions of the main circuit; G ωLf and G ωCf It is the transfer function from the active loop output phase angle small signal to the main circuit; T1=G Lf ·G Cf T2=-(G Cf ·G Lf -1 ·G ωLf +G Cf -1 ·G ωCf ) T3=-G Cf K=(I-T1·G vvc -T2·G ωvc ) -1 ·(T1·G vio +T2·G ωio +T3)

[0055] T s is the rotation matrix; T v and T c It is the small signal linearization transfer matrix for transforming the voltage and current controller coordinates to the system coordinate system.

[0056] S3. Construct a grid-connected system model for new energy stations with both grid-following and grid-building types;

[0057] The system model consists of multiple grid-following converters connected via line impedance Z l At the point of common coupling (PCC), it is connected in parallel with the voltage source and connected to the grid via the line impedance Z g Connected in series with the ideal source, the system topology is shown in Figure 2. The grid-following converter is synchronized with the main grid through a phase-locked loop, and the grid-forming converter adopts a virtual synchronization control strategy.

[0058] The grid-following converter adopts unified parameters. Multiple grid-following converters form a converter string via tie lines. Tie line impedance can be set separately. Multiple converter strings are connected to the infinite grid via line impedance Zg at the common grid connection point PCC. The grid-forming converter adopts unified parameters. Multiple grid-forming converters are connected to the infinite grid via line impedance Zg at the common grid connection point PCC via tie line impedance.

[0059] S4. Establish a simplified equivalent circuit for the station grid-connected system: convert the system model into a circuit model, apply Norton's theorem to convert the grid-connected converter into a controlled current source model, apply Thevenin's theorem to construct the grid-connected converter into a controlled voltage source model, perform circuit equivalent calculations on the circuit model, controlled current source model, and controlled voltage source model of the system model, and solve the equivalent circuit model of the station grid-connected system for small disturbance stability analysis; aggregate the output impedance of the new energy station after equivalent, and simplify the station equivalent circuit in the equivalent circuit model.

[0060] The external characteristics of the grid-type converter are shown as a current source, and the external characteristics of the grid-type converter are shown as a voltage source. The grid-type converter uses a current source I S1 Parallel equivalent admittance Y GFL1 The Norton equivalent circuit is replaced by the grid-type converter using a voltage source V S1 With the series equivalent impedance Z GFM The Thevenin equivalent circuit is replaced with the equivalent circuit shown in Figure 7. Furthermore, the Norton circuit of multiple grid-type converters is simplified to a Norton circuit consisting of a current source and its external output impedance in parallel. This circuit is connected to the grid side to form a grid. The equivalent current source can be directly calculated by multiplying the number of converters N. The output impedance is calculated by opening the current source and performing series and parallel calculations. The impedance aggregation of the grid-type converter is shown as follows:

[0061] S5. Establish the Nyquist criterion for small-disturbance stability of grid-connected new energy stations: Combine the dq output impedance model of the grid-following converter and the grid-connecting converter with the line impedance, derive the transfer relationship between the grid-connected point current and each power source, and solve the small-disturbance stability criterion of the system based on the transfer relationship.

[0062] The simplified equivalent circuit of the grid-connected system obtained based on S4 is shown in Figure 8. PCC and I PCC are the voltage and current at the grid connection point respectively; I GFM with I GFL are the output currents of the grid-forming converter and the grid-following converter respectively; Z g is the line impedance, V Grid is the grid-side power supply. Calculate I PCC The transfer function relationship between each power supply can be obtained from the equivalent impedance network model topology:

[0063] Among them, I S2 is the current source after being equal to the grid-type converter; Y GFM and Y GFL are the output admittances of the network-building type and the network-following type respectively; the expressions of H1(s), H2(s) and H3(s) are as follows: H2(s)=Y GFM (16) H3(s)=Y GFM +Y GFL (17)

[0064] Among them, V s1 is a voltage source, H1(s) is related to the equivalent impedance of the grid-type converter, the equivalent impedance of the grid-type converter and the line impedance, H2(s) is only related to the impedance of the grid-type converter itself, and H3(s) is related to the equivalent impedance of the grid-type converter and the equivalent impedance of the grid-type converter. For H1(s) and H3(s), H1(s) and H1(s)·H3(s) can be regarded as two closed-loop transfer functions and Its stability depends on its open-loop transfer function Z g ·(Y GFM +Y GFL ). Therefore, the small disturbance stability criterion of the station is: when H2(s) does not have a positive real part pole and Z g ·(Y GFM +Y GFL ) satisfies the Nyquist criterion: Z = N + P = 0, and the grid-connected renewable energy station system is stable. Here, Z is the number of positive real poles in the closed loop; N is the number of cycles of the Nyquist plot clockwise around the point (-1, 0); and P is the number of positive real poles in the open loop.

[0065] S6. Use Nyquist diagram to analyze the small disturbance stability characteristics of the station grid-connected system: Using the stability criterion in S5, draw Nyquist diagrams under different parameters to analyze the small disturbance stability of the new energy station grid-connected system.

[0066] Stability criterion obtained from S5: L = Z g ·(Y GFM +Y GFL ) must satisfy the Nyquist criterion,

[0067] Find its eigenvalues ​​l1 and l2:

[0068] Where L is the defined loop matrix; L dd , L dq , L qd and L qq are the four elements of the loop matrix L; l1 and l2 are the two characteristic roots of the matrix;

[0069] Draw the Nyquist plots for l1 and l2 respectively and judge the stability.

[0070] Example

[0071] The small disturbance stability analysis method for a grid-connected converter station of this embodiment is applicable to grid-connected and grid-connected converter new energy stations, specifically including:

[0072] Step 1: Construct a grid-following converter impedance model;

[0073] The open-loop output impedance of the converter without considering the phase-locked loop:

[0074] Where L and R are the line impedances before the grid connection point, ω is the system angular frequency, and s is a complex variable in the frequency domain.

[0075] The transfer function matrix between the duty cycle vector and the grid-side current vector is:

[0076] Where V dc is the DC side voltage; R L is the line resistance, which is the same as R.

[0077] The output angle formula under small disturbance of the phase-locked loop PLL is:

[0078] is the output angle small disturbance, is the small disturbance of q-axis voltage;

[0079] in:

[0080] where k p_PLL 、k i_PLL is the phase-locked loop PI control parameter;

[0081] The transfer function relationship between the phase-locked loop output angle and the system q-axis voltage is:

[0082] where tf PLL is the phase-locked loop transfer function; V d s is the d-axis component of the voltage in the grid-side synchronous rotating coordinate system; It is the voltage q-axis small signal quantity under the grid-side synchronous rotating coordinate.

[0083] Definition G PLL for:

[0084] but

[0085] Substitute it into formula 2-1-11,

[0086] in It is the voltage d-axis small signal quantity under the synchronous rotating coordinate of the controller; It is the voltage q-axis small signal quantity under the synchronous rotating coordinate of the controller.

[0087] Get G pll_v :

[0088] Similarly, we get G pll_i and G pll_d :

[0089] Each control link:

[0090] G ci The current loop PI link, where K p_I , K i_I is the current loop PI control parameter, G dei is the current loop decoupling matrix, G del G is the transfer function matrix considering sampling delay, LPF is the first-order low-pass filter of the feedforward voltage, where T del is the unit sampling time.

[0091] Considering the non-ideal source of the DC side power supply, when there is disturbance:

[0092] in, D d and D q are the d-axis and q-axis components of the duty cycle respectively; i dref and i qref are the d-axis and q-axis current command values ​​respectively; Δi d and Δi q are the current changes of d-axis and q-axis respectively; Δd d s and Δd q s are the d-axis and q-axis components of the duty cycle disturbance under the grid-side coordinates; Z dc is the DC side impedance; R dc and C dc are the DC side resistance and capacitance respectively; Δu dc is the DC voltage change.

[0093] The small disturbance transfer matrix from the duty cycle vector to the grid-side current vector in the system synchronous coordinates is:

[0094] Among them, G id is the small perturbation transfer matrix of the grid-side current vector; Z out d c To consider the open-loop output impedance of the DC loop; U dcis the DC side voltage; I d s and I q s They are the d-axis and q-axis components of the output current in the grid-side rotating coordinate system respectively.

[0095] The small perturbation transfer matrix from the duty cycle vector to the DC voltage vector is shown below:

[0096] By deducing each link of small disturbance transmission, we can obtain the output impedance model of the grid-connected converter taking into account the phase-locked loop (PLL), the current inner loop, and the DC voltage outer loop:

[0097] Where Z1=G id (I+G del G ci G vdc G vd ) -1 G del Z2=(G dei -G ci )G pll_i -G ci G vdc G ve +G pll_d +G pll_v Y out =Z out -1 (37)

[0098] Substitute the grid-following converter parameters into the table 1.

[0099] Table 1 Parameters of grid-following converter

[0100] Figure 9 shows the theoretical output impedance of a grid-connected converter, taking into account the phase-locked loop (PLL), the inner current loop, and the outer DC voltage loop, along with a frequency sweep test. The solid line represents the theoretically calculated value, while the scattered dots represent the results of a frequency sweep calculation over a frequency range of 20 Hz to 600 Hz. The frequency sweep results show that the theoretical impedance calculations for the grid-connected converter are consistent with the frequency sweep results, demonstrating the accuracy of the impedance model.

[0101] Step 2: Constructing a grid-type converter impedance model;

[0102] Main circuit transformation matrix:

[0103] Where R C , L C is the impedance of the tie line to the grid connection point, ω s is the grid side angular frequency.

[0104] Reactive loop small signal linearization transfer function:

[0105] Among them, V Cdqc and I odqc is the steady-state output voltage and current of the converter under the controller rotation coordinate, K is the virtual inertia, D q is the virtual damping, V Cq c and V Cd c are the steady-state q-axis and d-axis output voltages of the converter under the controller rotation coordinates, I oq c and I od c are the steady-state q-axis and d-axis output currents of the converter under the rotating coordinates of the controller, respectively.

[0106] Active loop small signal linearization transfer function:

[0107] Among them, V Cdqc and I odqc is the steady-state output voltage and current of the converter under the rotating coordinate of the controller, J is the virtual inertia, D p is the virtual damping.

[0108] The filtering process is shown as follows:

[0109] Among them, Ω c Indicates the steady-state value of the controller coordinate rotation angular frequency, L f is the filter inductor, I Lq c and I Ld c are the q-axis and d-axis steady-state current values ​​of the filter inductor controller coordinates, V Cq c and V Cd c are the steady-state q-axis and d-axis output voltages of the converter under the rotating coordinates of the controller, respectively. and and The transfer relationship can be expressed as follows:

[0110] Where: T1=G Lf ·G Cf T2=-(G Cf ·G Lf -1 ·G ωLf +G Cf -1 ·G ωCf) T3=-G Cf

[0111] Furthermore, by connecting the power outer loop, we can get the controller rotation coordinate and The transitive relationship: K=(I-T1·G vvc -T2·G ωvc ) -1 ·(T1·G vio +T2·G ωio +T3) (50)

[0112] The rotation matrix is ​​shown as:

[0113] v Cdq and i odq The transformation relationship between the two coordinate systems is: Cdq s =T s ·v Cdq c (52) i odq c =T s -1 ·i odq s (53)

[0114] Perform small signal linearization on the above two equations:

[0115] Where Δ is the steady-state value of the phase angle difference between the two coordinates, is the phase angle difference between the system rotation coordinate and the controller rotation coordinate, T v and T c are the transfer functions of the phase angle difference small signal quantity to the output voltage and output current respectively. In summary, by substituting the small signal transfer relationship of the main circuit small signal model and the controller coordinate, the analytical expression of the external impedance of the self-synchronous voltage source under virtual synchronous control can be obtained:

[0116] Substitute the grid-type converter parameters into Table 2:

[0117] Table 2 Parameters of grid-type converter

[0118] Figure 10 shows a frequency sweep test of the output impedance of a grid-connected converter, including only the active and reactive power outer loop. The solid line represents the theoretically calculated value, and the scattered dots represent the results of the frequency sweep calculation. The frequency sweep range is 10 Hz to 800 Hz. The frequency sweep results show that the theoretical impedance calculation of the grid-connected converter is consistent with the frequency sweep results, verifying the accuracy of the impedance model.

[0119] Step 3: Establish a system model that includes both grid-following and grid-building new energy stations connected to the infinite power grid;

[0120] The system model consists of multiple grid-following converters connected via line impedance Z l At the point of common coupling (PCC), it is connected in parallel with the voltage source and connected to the grid via the line impedance Z g The grid-following converter is synchronized with the main grid through a phase-locked loop, while the grid-forming converter adopts a virtual synchronization control strategy.

[0121] Step 4: Establish a simplified equivalent circuit of the station grid-connected system;

[0122] The external characteristics of the grid-type converter are shown as a current source, and the external characteristics of the grid-type converter are shown as a voltage source. The grid-type converter uses a current source I S1 Parallel equivalent admittance Y GFL1 The Norton equivalent circuit is replaced by the grid-type converter using a voltage source V S1 With the series equivalent impedance Z GFM The Thevenin equivalent circuit is replaced. Furthermore, the Norton circuit of multiple grid-connected converters is simplified to a Norton circuit consisting of a current source and its output impedance in parallel, which is then connected to the grid. The equivalent current source can be directly calculated by multiplying the number of converters N. The output impedance is calculated by opening the current source and performing series and parallel calculations. The aggregate impedance of the grid-connected converter is shown in the equation below.

[0123] Step 5: Establish the Nyquist criterion for small-disturbance stability of grid-connected new energy stations;

[0124] Based on the simplified equivalent circuit of the grid-connected system obtained in step 4, V PCC and I PCC are the voltage and current at the grid connection point respectively; I GFM with I GFL are the output currents of the grid-forming converter and the grid-following converter respectively; Z g is the line impedance, V Grid is the grid-side power supply. Calculate I PCC The transfer function relationship between each power supply can be obtained from the equivalent impedance network model topology: I GFL =I S2 -V PCC ·Y GFL (59) V PCC =I PCC ·Z g +VGrid (60)

[0125] Substituting the above formula into the combination, we can get:

[0126] in, H2(s)=Y GFM (63) H3(s)=Y GFM +Y GFL (64)

[0127] Among them, H1(s) is related to the equivalent impedance of the grid-type and grid-forming converters and the line impedance, H2(s) is only related to the impedance of the grid-forming converter itself, and H3(s) is related to the equivalent impedance of the grid-type and grid-forming converters. For H1(s) and H3(s), H1(s) and H1(s)·H3(s) can be regarded as two closed-loop transfer functions and Its stability depends on its open-loop transfer function Z g ·(Y GFM +Y GFL ). Therefore, the small disturbance stability criterion of the station is: when H2(s) does not have a positive real part pole and Z g ·(Y GFM +Y GFL ) satisfies the Nyquist criterion: Z = N + P = 0, the output system is stable. Here, Z is the number of closed-loop positive real poles; N is the number of clockwise cycles of the Nyquist plot around the point (-1, 0); and P is the number of open-loop positive real poles.

[0128] Step 6: Use Nyquist diagram to analyze the small disturbance stability characteristics of the station grid-connected system;

[0129] The stability criterion obtained from step 5: L = Z g ·(Y GFM +Y GFL ) must satisfy the Nyquist criterion,

[0130] Find its eigenvalues ​​l1 and l2:

[0131] Draw the Nyquist plots for l1 and l2 respectively and judge the stability.

[0132] For a system consisting of five grid-following converters in series and one grid-forming converter, the Nyquist diagram is shown in Figure 11.

[0133] Figure 12 shows the PCC current I at the grid connection point. dqSimulation waveform. At 1.75s, the line impedance Lg switches from 0.03mH to 0.05mH, and at 3.5s it switches to 0.06mH. It can be seen that I dq When switching from steady state to a lower grid strength, the grid stabilizes after the damping oscillation caused by the switching, which is consistent with the Nyquist stability analysis results.

[0134] The small-disturbance stability analysis system of a station containing a grid-forming converter of the present invention comprises: a grid-following converter impedance model, a grid-forming converter impedance model, a grid-connected system model of new energy stations containing both grid-following and grid-forming types, a simplified equivalent circuit model of the new energy station grid-connected system, a Nyquist criterion model for the small-disturbance stability of the grid-connected new energy stations containing the grid-forming type, and a model for analyzing the small-disturbance stability characteristics of the station grid-connected system.

[0135] In another implementation example, the above-mentioned small-disturbance stability analysis system for a station containing a grid-connected converter includes: a processor, wherein the processor is used to execute the above-mentioned program model stored in the memory, including: a grid-following converter impedance model, a grid-connected converter impedance model, a grid-connected system model of new energy stations containing grid-following and grid-connected types, a simplified equivalent circuit model of a new energy station grid-connected system, a Nyquist criterion model for small-disturbance stability of a grid-connected new energy station containing a grid-connected type, and an analysis model of the small-disturbance stability characteristics of the station grid-connected system.

Claims

1. A small disturbance stability analysis method for a grid-type converter station, characterized in that: include: Establish the impedance model of grid-following converter; establish the impedance model of grid-forming converter; Construct a grid-connected system model for new energy stations, including both grid-following and grid-building types; Establish a simplified equivalent circuit for the station grid-connected system: convert the system model into a circuit model, convert the grid-following converter into a controlled current source model, and convert the grid-connecting converter into a controlled voltage source model. Perform circuit equivalent calculations on the circuit model, controlled current source model, and controlled voltage source model of the system model to obtain the equivalent circuit model for the station grid-connected system used for small-disturbance stability analysis. Aggregate the impedance of the new energy station and simplify the station equivalent circuit in the equivalent circuit model. Establish the Nyquist criterion for small-disturbance stability of grid-connected new energy stations: Combine the impedance models of grid-following and grid-connecting converters with the line impedance to derive the transfer relationship between the grid connection point current and each power source. From this transfer relationship, solve the small-disturbance stability criterion of the grid-connected new energy station system. The Nyquist diagram is used to analyze the small disturbance stability characteristics of the station grid-connected system.

2. A small disturbance stability analysis method for a grid-type converter station according to claim 1, characterized in that: The specific steps of establishing the grid-connected converter impedance model are as follows: deriving each link of the small disturbance transmission in the new energy station grid-connected system, and obtaining the grid-connected converter output impedance model that takes into account the phase-locked loop, the current inner loop, and the DC voltage outer loop. The analytical expression is as follows: Where, Z1=G id (I+G del G ci G vdc G vd ) -1 G del Z2=(G dei -G ci )G pll_i -G ci G vdc G ve +G pll_d +G pll_v Among them: G ci is the PI link of the current loop, G vdc is the voltage outer loop PI link, G dei is the current loop decoupling matrix, G del is the transfer function matrix considering sampling delay; G pll_v , G pll_i and G pll_d is the transfer function of voltage, current and duty cycle from system coordinates to control system coordinates through the phase-locked loop; G id : small disturbance transfer matrix from duty cycle vector to grid-side current vector in system synchronous coordinates; G vd : small perturbation transfer matrix from duty cycle vector to DC voltage vector; The output admittance is: Y out =Z out -1 。 3. The small disturbance stability analysis method of a grid-type converter station according to claim 1 is characterized in that: The specific steps of establishing the grid-connected converter impedance model are as follows: based on the main circuit small signal model and the small signal transmission relationship in the controller coordinates in the new energy station grid-connected system, an analytical expression for the external impedance of the self-synchronous voltage source under virtual synchronous control is obtained: Among them: G voio and G vovc is the main circuit transformation matrix; I is the unit matrix; s is the complex variable in the transfer function; G vio and G vvc is the small signal linearization transfer function of the reactive loop; G ωio and G ωvc is the small signal linearization transfer function of the active loop; G Lf and G Cf are the LC filter transfer functions of the main circuit; G ωLf and G ωCf It is the transfer function from the active loop output phase angle small signal to the main circuit; T1=G Lf ·G Cf T2=-(G Cf ·G Lf -1 ·G ωLf +G Cf -1 ·G ωCf ) T3=-G Cf K=(I-T1·G vvc -T2·G ωvc ) -1 ·(T1·G vio +T2·G ωio +T3) T s is the rotation matrix; T v and T c It is the small signal linearization transfer matrix for transforming the voltage and current controller coordinates to the system coordinate system.

4. The small disturbance stability analysis method of a grid-type converter station according to claim 1 is characterized in that: The system model consists of multiple grid-following converters connected via line impedance Z l At the point of common coupling, it is connected in parallel with the voltage source and connected to the grid via the line impedance Z g Connected in series with the ideal source; among them, the grid-following converter keeps synchronization with the main grid through a phase-locked loop, and the grid-building converter adopts a virtual synchronization control strategy.

5. The small disturbance stability analysis method of a grid-type converter station according to claim 4 is characterized in that: The grid-following converter adopts unified parameters, and multiple grid-following converters form a converter string through a tie line. The tie line impedance is preset, and multiple strings of converters are connected to the infinite power grid through the line impedance Zg at the common grid connection point PCC; the grid-forming converter adopts unified parameters, and multiple grid-forming converters are connected to the infinite power grid through the line impedance Zg at the common grid connection point PCC through the tie line impedance.

6. The small disturbance stability analysis method of a grid-type converter station according to claim 1 is characterized in that: The Nyquist criterion for small-disturbance stability of grid-connected new energy stations is established as follows: based on the simplified equivalent circuit of the grid-connected system, V PCC and I PCC are the voltage and current at the grid connection point respectively; I GFM with I GFL are the output currents of the grid-forming converter and the grid-following converter respectively; Z g is the line impedance, V Grid is the grid-side power supply; calculate I PCC The transfer function relationship between each power supply can be obtained from the equivalent impedance network model topology: Among them, I S2 is the current source after being equal to the grid-type converter; Y GFM and Y GFL are the output admittances of the network-building type and the network-following type respectively; the expressions of H1(s), H2(s) and H3(s) are as follows: H2(s)=Y GFM H3(s)=Y GFM +Y GFL Among them, V s1 is a voltage source, H1(s) is related to the equivalent impedance of the grid-type converter, the equivalent impedance of the grid-type converter and the line impedance, H2(s) is only related to the impedance of the grid-type converter itself, and H3(s) is related to the equivalent impedance of the grid-type converter and the equivalent impedance of the grid-type converter; for H1(s) and H3(s), H1(s) and H1(s)·H3(s) are regarded as two closed-loop transfer functions and Its stability depends on its open-loop transfer function Z g ·(Y GFM +Y GFL ).

7. A small disturbance stability analysis method for a grid-type converter station according to claim 6, characterized in that: The small perturbation stability criterion is: when H2(s) does not have a positive real part pole and Z g ·(Y GFM +Y GFL ) satisfies the Nyquist criterion: when Z = N + P = 0, the new energy station grid-connected system is stable; where Z is the number of closed-loop positive real part poles; N is the number of cycles of the Nyquist diagram clockwise surrounding the point (-1,0); and P is the number of open-loop positive real part poles.

8. The small disturbance stability analysis method of a grid-type converter station according to claim 1 is characterized in that: The Nyquist diagram is used to analyze the small disturbance stability characteristics of the station grid-connected system. Specifically, the Nyquist diagram under different parameters is drawn using the stability criterion to analyze the small disturbance stability of the new energy station grid-connected system.

9. A small disturbance stability analysis method for a grid-type converter station according to claim 8, characterized in that: The use of stability criteria to draw Nyquist diagrams under different parameters and analyze the small disturbance stability of the new energy station grid-connected system specifically includes: When stability criterion: L=Z g ·(Y GFM +Y GFL ) must satisfy the Nyquist criterion and obtain its eigenvalues ​​l1 and l2: Where L is the defined loop matrix; L dd , L dq , L qd and L qq are the four elements of the loop matrix L; l1 and l2 are the two characteristic roots of the matrix; Draw the Nyquist plots for l1 and l2 respectively and judge the stability.

10. A small disturbance stability analysis system for a grid-type converter station, characterized in that: include: Impedance model of grid-following converter, impedance model of grid-forming converter, grid-connected system model of new energy stations including grid-following and grid-forming types, simplified equivalent circuit model of new energy station grid-connected system, Nyquist criterion model for small-disturbance stability of grid-connected new energy stations including grid-forming type, and model for analyzing small-disturbance stability characteristics of station grid-connected system.

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