Small signal resonance analysis method and system for grid-connected inverter based on impedance model

Abstract

A method for analyzing small-signal resonance of a grid-connected inverter based on an impedance model includes: calculating the output impedance of a harmonically linearized inverter; the output impedance of the inverter includes: positive-sequence impedance and negative-sequence impedance; calculating the equivalent grid impedance at the connection point between the inverter and the grid; judging whether the Nyquist stability criterion is satisfied based on the output impedance of the inverter and the grid impedance; if the Nyquist stability criterion is satisfied, the small-signal resonance of the parallel system is stable; otherwise, the small-signal resonance is unstable; if the small-signal resonance of the parallel system is stable, calculating the relationship between the inverter voltage and current based on the output impedance of the inverter; and establishing a Bode diagram based on the relationship between the inverter voltage and current to obtain the characteristics of the transformer self-resonance, mutual resonance, and grid resonance. The present invention establishes an inverter impedance model that considers the VSG as a power loop. The inverter impedance model does not change with changes in the system circuit topology and has high scalability.

Description

Technical Field

[0001] The present invention belongs to the field of renewable energy power generation systems, and more specifically, relates to a small-signal resonance analysis method and system for a grid-connected inverter based on an impedance model. Background Art

[0002] With the increasing adoption of renewable energy generation technologies, a large number of renewable energy generators and energy storage components are connected to the grid through inverters. Inverters, as power electronic converters, lack the mechanical inertia of traditional rotating motors. To increase the inertia of grids with high renewable energy penetration and reduce the frequency change rate after grid faults, virtual synchronous generators (VSGs) are widely used in inverter control. By simulating the motion equations of a rotating synchronous machine rotor, the VSG enables the inverter to simulate the inertia of the synchronous machine.

[0003] With the widespread application of virtual synchronous machine control in inverters, the need to study their resonant stability issues arises. When multiple inverters are connected in parallel in a power system, the resonance characteristics of the inverters themselves, between inverters, and in the power grid need to be considered to suppress the system's resonance and optimize control parameters. Summary of the Invention

[0004] In order to solve the deficiencies in the prior art, the present invention aims to provide an impedance model-based small signal resonance analysis method for a grid-connected inverter, targeting the small signal resonance stability problem of a virtual synchronous machine.

[0005] The present invention adopts the following technical solutions.

[0006] A small signal resonance analysis method for a grid-connected inverter based on an impedance model includes the following steps:

[0007] Step 1: Calculate the output impedance of the harmonic linearized inverter. The output impedance of the inverter includes: positive sequence impedance Z p (s) and negative sequence impedance Z n (s);

[0008] Step 2: Calculate the equivalent grid impedance at the connection point between the inverter and the grid;

[0009] Step 3: Determine whether the Nyquist stability criterion is met based on the output impedance of the inverter and the grid impedance; if the Nyquist stability criterion is met, the small signal resonance of the parallel system is stable; otherwise, the small signal resonance is unstable;

[0010] Step 4: If the small signal resonance of the parallel system is stable, calculate the relationship between the inverter voltage and current based on the output impedance of the inverter;

[0011] Step 5: Based on the relationship between the inverter voltage and current, a Bode diagram is established to obtain the characteristics of the transformer's self-resonance, mutual resonance, and grid resonance.

[0012] Further,

[0013]

[0014]

[0015] in, is the frequency f p The positive sequence voltage small signal disturbance, is the frequency f n The negative sequence voltage small signal disturbance, and The frequencies f p and f n The disturbance current response of p is the frequency of the preset positive sequence small signal disturbance, f n is the frequency of the preset negative sequence small signal disturbance; s is the Laplace operator, E m is the output voltage amplitude of the inverter, P is the active power output by the inverter, M(s)=1 / (Js 2 +D p s), J is the moment of inertia, D p is the active power droop coefficient, ω n is the system frequency, D q is the reactive droop control coefficient, K is the reactive inertia coefficient; is the initial value of the fundamental current phase angle, f1 is the fundamental frequency, V1 and I1 are the fundamental amplitudes of the output voltage and current respectively, j is the imaginary unit, and L1 is the filter inductor of the inverter.

[0016] Furthermore, the inverter output voltage amplitude E m As shown below:

[0017]

[0018] Among them, Q is the reactive power output by the inverter, Q set are the set values ​​of the inverter reactive power, θ is the inverter output voltage phase angle, V is the actual value of the inverter output voltage, V n is the system voltage rating.

[0019] Furthermore, the filter inductor L1 of the inverter is as follows:

[0020]

[0021] e=Em cosθ

[0022]

[0023] Where i, v are the inverter output current and voltage with small signal disturbance, θ is the inverter output voltage phase angle, P set is the set value of the inverter active power, and t is the time.

[0024] Furthermore, the grid impedance Z g (s) is:

[0025] Z g (s)=sL g / / (R f +1 / (sC f )) / / Z s1 (s) / / … / / Z sn (s)

[0026] Among them, Z s1 (s) is the output impedance of the first inverter, Z sn (s) is the output impedance of the nth inverter, n is the number of inverters, L g For the connection line series inductance, R f is the parasitic resistance of the filter inductor, C f is the filter capacitor, and s is the Laplace operator.

[0027] Furthermore, in step 3, judging whether the Nyquist stability criterion is satisfied based on the output impedance of the inverter and the grid impedance specifically includes:

[0028] Calculate Z p (s) / Z gp (s) and Z n (s) / Z gn (s), by analyzing Z p (s) / Z gp (s) and Z n (s) / Z gn (s) whether it satisfies the Nyquist stability criterion; where Z gp (s) and Z gn (s) are the grid impedance Z g (s) positive sequence impedance and negative sequence impedance, and satisfy Z g (s)=Z gp (s)=Z gn (s).

[0029] Furthermore, the relationship between the inverter voltage and current is shown below:

[0030]

[0031] Among them, A ii Reflects the output voltage U of the i-th inverter si The output current I of the i-th inverter caused by i Harmonic characteristics of A ij Reflects the output voltage U of the jth inverter sj The output current I of the i-th inverter caused by i Harmonic characteristics of B i Indicates the grid voltage U g The output current I of the i-th inverter i The harmonic characteristics of i is the fundamental amplitude of the output current of the i-th inverter, where i=1, 2, ..., n; n is the number of inverters.

[0032] Further,

[0033]

[0034]

[0035]

[0036] Among them, Z si =Z p (s), Z ci is the filter capacitor impedance of inverter i, Z ti is the line impedance at the connection point between the inverter and the grid of inverter i, Z ei =Z ti +Z g / / Z1 / / … / / Z i-1 / / Z i+1 / / … / / Z N , Z i =Z ti +Z si / / Z ci , / / means parallel connection, i, j = 1, 2, ..., N; if i = j, then Z ti =Z tj And Z ei =Z ej ; Z g is the grid impedance, and N is the number of inverters.

[0037] Furthermore, step 5 specifically includes:

[0038] If there is a resonance peak in the Bode diagram, there is resonance at the frequency of the resonance peak, and the gain of the resonance peak reflects the size of the resonance; if there is no resonance peak or the peak gain is small, the resonance of the inverter is small; the maximum amplitude and the frequency at the maximum amplitude point in the Bode diagram reflect the resonance size and the resonance frequency respectively; Among them, the Bode diagram is A ii Bode plot of A ij Bode plot and B i Any one of the Bode plots of ii Bode plot of A ij Bode plot and B i The Bode diagrams are used to analyze transformer self-resonance, mutual resonance and grid resonance.

[0039] A small signal resonance analysis system for a grid-connected inverter based on an impedance model, the system comprising: a calculation module, a Nyquist module, and a Bode diagram analysis module;

[0040] The calculation module is used to calculate the output impedance of the harmonic linearized inverter, the equivalent grid impedance at the connection point between the inverter and the grid, and the relationship between the voltage and current of the inverter;

[0041] The Nyquist module is used for Nyquist stability criterion;

[0042] The Bode diagram analysis module is used to create a Bode diagram to obtain the characteristics of transformer self-resonance, mutual resonance and grid resonance.

[0043] The beneficial effects of the present invention are that, compared with the prior art, the present invention has the following advantages:

[0044] (1) An inverter impedance model considering VSG as the power loop is established. The inverter impedance model will not change with the change of the system circuit topology and has high scalability.

[0045] (2) The criterion for small signal stability and resonance analysis method of the system are given when multiple inverters are connected in parallel in the system, which is suitable for the resonance stability analysis of multiple inverters running in parallel. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a flow chart of the resonance analysis method of the present invention.

[0047] Figure 2 It is a control block diagram of the virtual synchronous machine of the present invention.

[0048] Figure 3 It is a schematic diagram of the resonance analysis circuit of the present invention. DETAILED DESCRIPTION

[0049] The present application will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present application.

[0050] A small signal resonance analysis method for a grid-connected inverter based on an impedance model includes the following steps:

[0051] Step 1: Calculate the equivalent output impedance of the harmonic linearized inverter (also referred to as the inverter output impedance). The positive sequence impedance is defined as:

[0052]

[0053] Its negative sequence impedance is defined as,

[0054]

[0055] in, is the frequency f p The positive sequence voltage small signal disturbance, is the frequency f n The negative sequence voltage small signal disturbance, and The frequencies f p and f n The disturbance current response of p is the frequency of the preset positive sequence small signal disturbance, f n is the frequency of the preset negative sequence small signal disturbance.

[0056] For virtual synchronous machine (VSG) control, the control block diagram is as follows Figure 2 As shown, active power control and reactive power control are shown in (3) and (4) respectively.

[0057]

[0058]

[0059] Where, s is the Laplace operator, θ is the inverter output voltage phase angle, E m is the output voltage amplitude of the inverter, P and Q are the active power and reactive power output by the inverter respectively, P set and Q set are the set values ​​of the inverter active power and reactive power, M(s)=1 / (Js 2 +D p s), J is the moment of inertia, D p is the active power droop coefficient, V is the actual value of the inverter output voltage, ω n and V n are the system frequency and voltage ratings, Dq is the reactive droop control coefficient, and K is the reactive inertia coefficient.

[0060] The frequency domain expression of the sine value of the inverter output voltage phase angle can be obtained from formula (3):

[0061]

[0062] Among them, V1 and I1 are the fundamental amplitudes of the output voltage and current respectively. M(s-j2πf1)=1 / [J(s-j2πf1) 2 +D p (s-j2πf1)], M(s+j2πf1)=1 / [J(s+j2πf1) 2 +D p (s+j2πf1)]. Assume that E in formula (4) m is a constant value, and the inverter electromotive force e=E m cosθ, substitute

[0063]

[0064] Where L1 is the filter inductor of the inverter, i and v are the output current and voltage of the inverter with small signal disturbances. The sequence impedance of the virtual synchronous machine is:

[0065]

[0066]

[0067] is the initial value of the fundamental current phase angle, f1 is the fundamental frequency, and j is the imaginary unit. The output impedance of the inverter shown in (7) and (8) does not include the filter capacitor.

[0068] It should be noted that since there are n inverters, the formula in step 1 only calculates the output voltage and current of inverter 1. Therefore, the variables "V1" and "I1" in step 1 more accurately refer to the fundamental amplitudes of the output voltage and current of inverter 1.

[0069] Step 2: Calculate the equivalent grid impedance at the common connection point; wherein the common connection point is the connection point between the inverter and the grid.

[0070] Its grid impedance Z g (s) is expressed as:

[0071] Z g (s)=Z gp (s)=Z gn (s)≈sLg / / (R f +1 / (sC f )) (9)

[0072] The positive and negative sequence impedances of the power grid are equal, where L g For the connection line series inductance, R f is the parasitic resistance of the filter inductor, C f is the filter capacitor. It should be noted that Z gp (s) and Z gn (s) are the grid impedance Z g (s) positive sequence impedance and negative sequence impedance.

[0073] When there are other inverters at the common connection point, the grid impedance Z g (s) is:

[0074] Z g (s)=sL g / / (R f +1 / (sC f )) / / Z s1 (s) / / … / / Z sn (s) (10)

[0075] Among them, Z s1 (s) is the output impedance of the first inverter, Z sn (s) is the output impedance of the n-th inverter, which can be obtained by equations (7) and (8), that is, Z sn (s)=Z p (s) or Z sn (s)=Z n (s).

[0076] Step 3: Calculate the ratio of the inverter output impedance to the positive sequence impedance (and negative sequence impedance) of the grid impedance, and the values ​​are Z p (s) / Z gp (s) and Z n (s) / Z gn (s). By analyzing Z p (s) / Z gp (s) and Z n (s) / Z gn (s) satisfies the Nyquist stability criterion, and the small signal resonance stability of the inverter system can be analyzed. p (s) / Z gp and Z n (s) / Z gn If the Nyquist stability criterion is met, the small signal resonance of the parallel system is stable, otherwise the small signal resonance is unstable.

[0077] Step 4: Based on the small signal resonance stability criterion in step 3, if the parallel system has stable small signal resonance, a parallel circuit model is established based on the output impedance of the inverter to calculate the relationship between the inverter voltage and current.

[0078] Inverter multi-machine parallel circuit topology Figure 3 As shown, according to Kirchhoff's voltage-current theorem, the relationship between the inverter voltage and current is shown in the formula.

[0079]

[0080] Among them A ii Reflects the output voltage U of the i-th inverter si The output current I of the i-th inverter caused by i Harmonic characteristics of A ij Reflects the output voltage U of the jth inverter sj The output current I of the i-th inverter caused by i Harmonic characteristics of B i Indicates the grid voltage U g The output current I of the i-th inverter i It is understandable that I i is the fundamental amplitude of the output current of the i-th inverter, where i=1, 2, ..., n; n is the number of inverters.

[0081] in,

[0082]

[0083]

[0084]

[0085] Among them, Z si The output impedance of inverter i is Z calculated by formula (7) si =Z p (s), Z ci is the filter capacitor impedance of inverter i, Z ti is the line impedance of the common connection point of inverter i, Z ei =Z ti +Z g / / Z1 / / … / / Z i-1 / / Z i+1 / / … / / Z N , Z i =Z ti +Z si / / Z ci , i, j = 1, 2, ..., N; if i = j, then Z ti =Ztj And Z ei =Z ej ;N is the number of inverters. / / indicates parallel connection. It can be understood that the above i and j represent the numbers of the inverters (i.e. inverter i, inverter j). Therefore, the variable Z ei With Z ej It should be understood as the same character, and accordingly, the variable Z tj With variable Z ti It should also be understood as the same character.

[0086] Step 5: Establish the transfer function A between voltage and current ii , A ij and B i The Bode diagram can be used to analyze the characteristics of the inverter's self-resonance, mutual resonance and grid resonance.

[0087] Among them, the three resonance characteristics of transformer self-resonance, mutual resonance and grid resonance correspond to A ii , A ij and B i These three transfer functions. For example, for A ii The Bode diagram of A is analyzed to obtain the self-resonance characteristics of the i-th inverter. ij By analyzing the Bode diagram of , we can get the mutual resonance characteristics of the j-th inverter to the i-th inverter. i The Bode diagram of is analyzed to obtain the grid resonance characteristics of the grid to the i-th inverter.

[0088] Specifically, for any of the three resonant characteristics, if a resonant peak is present in the Bode plot, resonance exists at the frequency of the peak, and the gain of the peak reflects the magnitude of the resonance. If the peak is absent or the gain of the peak is small, the inverter's resonance is small. The maximum amplitude and the frequency at the maximum amplitude point in the Bode plot reflect the magnitude and frequency of the resonance, respectively.

[0089] It should be noted that the impedance mentioned in this article (for example, Z p ) and the s-domain impedance (e.g., Z p (s)) should be considered the same thing. It's just that the mathematical expression is different. You can refer to the relationship between polar coordinates and rectangular coordinates.

[0090] Accordingly, the present invention also proposes a small signal resonance analysis system for a grid-connected inverter based on an impedance model, comprising: a calculation module, a Nyquist module and a Bode diagram analysis module;

[0091] The calculation module is used to calculate the output impedance of the harmonic linearized inverter, the equivalent grid impedance at the connection point between the inverter and the grid, and the relationship between the voltage and current of the inverter;

[0092] The Nyquist module is used for Nyquist stability criterion;

[0093] The Bode diagram analysis module is used to create a Bode diagram to obtain the characteristics of transformer self-resonance, mutual resonance and grid resonance.

[0094] The applicant of the present invention has made a detailed explanation and description of the implementation examples of the present invention in conjunction with the drawings in the specification. However, those skilled in the art should understand that the above implementation examples are only preferred implementation plans of the present invention, and the detailed description is only to help readers better understand the spirit of the present invention, and is not a limitation on the scope of protection of the present invention. On the contrary, any improvements or modifications based on the inventive spirit of the present invention should fall within the scope of protection of the present invention.

Claims

1. A small signal resonance analysis method for a grid-connected inverter based on an impedance model, characterized in that: The steps include: Step 1: Calculate the output impedance of the harmonic linearized inverter. The output impedance of the inverter includes: positive sequence impedance Z p (s) and negative sequence impedance Z n (s); in, is the frequency f p The positive sequence voltage small signal disturbance, is the frequency f n The negative sequence voltage small signal disturbance, and The frequencies f p and f n The disturbance current response of p is the frequency of the preset positive sequence small signal disturbance, f n is the frequency of the preset negative sequence small signal disturbance; s is the Laplace operator, E m is the output voltage amplitude of the inverter, P is the active power output by the inverter, M(s)=1 / (Js 2 +D p s), J is the moment of inertia, D p is the active power droop coefficient, ω n is the system frequency, D q is the reactive droop control coefficient, K is the reactive inertia coefficient; is the initial value of the fundamental current phase angle, f1 is the fundamental frequency, V1 and I1 are the fundamental amplitudes of the output voltage and current respectively, j is the imaginary unit, and L1 is the filter inductance of the inverter; Step 2: Calculate the equivalent grid impedance at the connection point between the inverter and the grid; Step 3: Determine whether the Nyquist stability criterion is met based on the output impedance of the inverter and the grid impedance; if the Nyquist stability criterion is met, the small signal resonance of the parallel system is stable; otherwise, the small signal resonance is unstable; Step 4: If the small signal resonance of the parallel system is stable, calculate the relationship between the inverter voltage and current based on the output impedance of the inverter; Step 5: Based on the relationship between the inverter voltage and current, a Bode diagram is established to obtain the characteristics of the transformer's self-resonance, mutual resonance, and grid resonance.

2. The method for analyzing small signal resonance of a grid-connected inverter based on an impedance model according to claim 1, wherein: Inverter output voltage amplitude E m As shown below: Among them, Q is the reactive power output by the inverter, Q set are the set values ​​of the inverter reactive power, θ is the inverter output voltage phase angle, V is the actual value of the inverter output voltage, V n is the system voltage rating.

3. The method for analyzing small signal resonance of a grid-connected inverter based on an impedance model according to claim 1, wherein: The filter inductor L1 of the inverter is shown below: and=And m cosθ Where i, v are the inverter output current and voltage with small signal disturbance, θ is the inverter output voltage phase angle, P set is the set value of the inverter active power, and t is the time.

4. The method for analyzing small signal resonance of a grid-connected inverter based on an impedance model according to claim 1, wherein: Grid impedance Z g (s) is: Z g (s)=sL g / / (R f +1 / (sC f )) / / Z s1 (s) / / … / / Z sn (s) Among them, Z s1 (s) is the output impedance of the first inverter, Z sn (s) is the output impedance of the nth inverter, n is the number of inverters, L g For the connection line series inductance, R f is the parasitic resistance of the filter inductor, C f is the filter capacitor, and s is the Laplace operator.

5. The method for analyzing small signal resonance of a grid-connected inverter based on an impedance model according to claim 1, wherein: In step 3, judging whether the Nyquist stability criterion is satisfied based on the output impedance of the inverter and the grid impedance includes: Calculate Z p (s) / Z gp (s) and Z n (s) / Z gn (s), by analyzing Z p (s) / Z gp (s) and Z n (s) / Z gn (s) whether it satisfies the Nyquist stability criterion; where Z gp (s) and Z gn (s) are the grid impedance Z g (s) positive sequence impedance and negative sequence impedance, and satisfy Z g (s)=Z gp (s)=Z gn (s).

6. The method for analyzing small signal resonance of a grid-connected inverter based on an impedance model according to claim 1, wherein: The relationship between the inverter voltage and current is shown below: Among them, A ii Reflects the output voltage U of the i-th inverter si The output current I of the i-th inverter caused by i Harmonic characteristics of A ij Reflects the output voltage U of the jth inverter sj The output current I of the i-th inverter caused by i Harmonic characteristics of B i Indicates the grid voltage U g The output current I of the i-th inverter i The harmonic characteristics of i is the fundamental amplitude of the output current of the i-th inverter, where i = 1, 2, …, n; n is the number of inverters.

7. The method for analyzing small signal resonance of a grid-connected inverter based on an impedance model according to claim 6, wherein: Among them, Z si =Z p (s), Z ci is the filter capacitor impedance of inverter i, Z ti is the line impedance at the connection point between the inverter and the grid of inverter i, Z ei =Z ti +Z g / / Z1 / / … / / Z i-1 / / Z i+1 / / … / / Z N , Z i =Z ti +Z si / / Z ci , / / indicates parallel connection, i,j=1,2,…,N; if i=j, then Z ti =Z tj And Z ei =Z ej ; Z g is the grid impedance, and N is the number of inverters.

8. The method for analyzing small signal resonance of a grid-connected inverter based on an impedance model according to claim 7, wherein: Step 5 specifically includes: If there is a resonance peak in the Bode diagram, there is resonance at the frequency of the resonance peak, and the gain of the resonance peak reflects the size of the resonance; the maximum amplitude and the frequency at the maximum amplitude point in the Bode diagram reflect the size of the resonance and the resonance frequency respectively; Among them, the Bode diagram is A ii Bode plot of A ij Bode plot and B i Any one of the Bode plots of ii Bode plot of A ij Bode plot and B i The Bode diagrams are used to analyze transformer self-resonance, mutual resonance and grid resonance.

9. A small signal resonance analysis system for a grid-connected inverter based on an impedance model, used to execute the method according to any one of claims 1 to 8, characterized in that: The system includes: calculation module, Nyquist module and Bode diagram analysis module; The calculation module is used to calculate the output impedance of the harmonic linearized inverter, the equivalent grid impedance at the connection point between the inverter and the grid, and the relationship between the voltage and current of the inverter; The Nyquist module is used for Nyquist stability criterion; The Bode diagram analysis module is used to create a Bode diagram to obtain the characteristics of transformer self-resonance, mutual resonance and grid resonance.

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