Variable coefficient equivalent SISO model based stability analysis method for grid-connected converter system

Abstract

Disclosed in the present invention is a variable coefficient equivalent SISO model based stability analysis method for a grid-connected converter system, comprising the following steps: constructing a variable coefficient equivalent SISO model; obtaining a complex space vector open-loop transfer function on the basis of the variable coefficient equivalent SISO model; and obtaining Nyquist curves under different current loop parameters or phase-locked loop parameters on the basis of the complex space vector open-loop transfer function. If the Nyquist curves surround point (-1,0), the grid-connected converter system is stable; and if the Nyquist curves do not surround point (-1,0), the grid-connected converter system is unstable. The present invention performs small disturbance modeling on the grid-connected converter system, considers the influence of mutual coupling between the phase-locked loop and the inner current loop, and derives a variable coefficient SISO open-loop transfer function capable of characterizing an MIMO system. Compared with the technical solution in the prior art that actual working conditions are not considered, the method disclosed in the present invention can more accurately analyze the system stability of the system under variable working conditions and variable parameters.

Description

Stability Analysis Method of Grid-Connected Converter System Based on Variable Coefficient Equivalent SISO Model Technical Field

[0001] The present invention relates to the technical field of power systems, and in particular to a stability analysis method for a grid-connected power conversion system based on a variable coefficient equivalent SISO model. Background Art

[0002] Actively developing renewable energy, represented by wind and photovoltaic power, and accelerating the green, low-carbon transformation of the energy system are the unanimous choices for addressing energy crises, environmental pollution, and enhancing energy security. Grid-connected converters, serving as the interface between renewable energy generation units and the power grid, have gained widespread application. However, due to the relatively remote locations of renewable energy sources, line impedance cannot be ignored, resulting in weak grid characteristics. Under weak grid conditions, the dynamic performance of converters has attracted widespread attention, as it impacts renewable energy absorption and can even endanger grid operation.

[0003] The current control loop and phase-locked loop (PLL) are key control elements in converters, characterized by their high speed and small timescale. However, PI regulation exhibits a certain degree of hysteresis, which affects the system's dynamic response speed. Furthermore, in weak grid environments, the intercoupling between the converter's various control elements can affect the PLL's phase output. The PLL's negative impedance characteristic can reduce the output phase angle, impacting system stability and even causing grid-connected current distortion and power oscillation, compromising the stable operation of the grid-connected converter system.

[0004] When modeling grid-connected systems in existing technologies, most focus is placed solely on the rated operating point, ignoring the actual operating conditions. Once the system operating environment deviates from the fixed operating conditions, the existing grid-connected control model may not be applicable to the new operating conditions, making it difficult to make timely adjustments based on the actual operating conditions, thereby affecting the stability analysis of the grid-connected converter system.

[0005] Summary of the Invention

[0006] In view of this, the present invention provides a grid-connected converter system stability analysis method based on a variable coefficient equivalent SISO model, which is used to at least solve the problem that the existing technology does not consider the actual operating conditions when modeling, resulting in inaccurate stability analysis of the grid-connected converter system.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] The stability analysis method of the grid-connected converter system based on the variable coefficient equivalent SISO model includes the following steps:

[0009] Constructing a variable coefficient equivalent SISO model, obtaining a complex space vector open-loop transfer function based on the variable coefficient equivalent SISO model, and obtaining a Nyquist curve under different current loop parameters or phase-locked loop parameters based on the complex space vector open-loop transfer function. If the Nyquist curve surrounds the (-1, 0) point, the grid-connected power conversion system is stable; if not, the grid-connected power conversion system is unstable.

[0010] The specific steps of constructing a variable coefficient equivalent SISO model include:

[0011] S1. According to the grid-connected converter system structure, a dual-input single-output DISO model is established, where the two input quantities are the voltage disturbance at the PCC point under the synchronous reference frame. and “*” indicates conjugate, and the output is the small current disturbance

[0012] S2. Simplify the DISO model and, based on the circuit topology, convert the two input quantities in the DISO model into equivalent small current disturbance quantities to obtain an equivalent transformed DISO model;

[0013] S3. Eliminate the conjugate part of the small current disturbance, convert the equivalent transformed DISO model into a single-input single-output model based on the input-output relationship in the equivalent transformed DISO model, and further obtain the open-loop transfer function of the system.

[0014] Preferably, the specific content of S1 includes:

[0015] S11. According to the linearization relationship in the phase-locked loop during the dynamic adjustment process of the phase-locked loop, the phase-locked loop output position angle θ is p The dq coordinate system is the control reference system, and the actual position angle θ of the PCC voltage s The dq coordinate system is a synchronous reference system, and θ is obtained. p and θ s There is a deviation angle Δθ between:

[0016] Among them, g p (s)=F PLL (s) / (s+U t0 F PLL (s)), F PLL (s) = k pp +k ip / s is the phase-locked loop PI controller, k pp and k ip are the proportional coefficient and integral coefficient of the phase-locked loop, U t0 is the steady-state voltage value at PCC point;

[0017] S12. Obtain the relationship between the voltage small disturbance and the current small disturbance in the two reference frames of the current control circuit respectively. According to the conversion relationship between the control reference frame and the synchronous reference frame, obtain the converter output voltage small disturbance Δe in the current control circuit in the synchronous reference frame. s Small current disturbance The relationship between:

[0018] Among them, G de (s) is the time delay introduced by the digital control system, G C (s) is the current loop PI controller, the current reference value disturbance Δi dqr ,i L0 is the steady-state value of the current, and E0 is the steady-state value of the converter output voltage;

[0019] S13. Obtain the voltage small disturbance Δe in the power circuit under the synchronous reference frame s and respectively with the current small disturbance The relationship between and S12 is combined to obtain the current small disturbance value. The expression is:

[0020] S14. Combine the deviation angle Δθ expression to eliminate small current disturbances The deviation angle Δθ in the current reference value is set to Δi dqr =0, the dual-input single-output DISO model is obtained as:

[0021] Preferably, the current loop PI controller G c (s) is: G c (s) = k pc +k ic / s (7)

[0022] Among them, k pc and k ic They are the proportional gain coefficient and the integral gain coefficient in the current loop PI controller respectively.

[0023] Preferably, the specific content in S12 includes:

[0024] The relationship between the voltage small disturbance and the current small disturbance in the two reference frames of the current control circuit is:

[0025] The conversion relationship between the control reference frame and the synchronization reference frame is: Δx c =Δx s-jx0Δθ (9)

[0026] where x0 = x d0 +jx q0 , is the steady-state value of the variable x;

[0027] Will According to the conversion relationship, it is converted into The voltage small disturbance Δe in the current control circuit under the synchronous reference frame is obtained s Small current disturbance The relationship between them.

[0028] Preferably, the specific content of S13 includes:

[0029] Small voltage disturbance Δe in power circuit under synchronous reference frame s and respectively with the current small disturbance The relationship between them is:

[0030] Among them, since the grid voltage is an ideal voltage source, the grid voltage small disturbance ΔU g Ignore, ΔU g =0; Z f (s) is the filter impedance in the control reference frame, Z g (s) is the grid impedance in the synchronous reference frame:

[0031] Substituting equations (10) and (11) into equation (2), we can obtain the current small disturbance

[0032] Preferably, the specific content of S2 includes:

[0033] Using the circuit topology, the PCC voltage disturbance ΔU t Grid current disturbance Replace, eliminate ΔU t and Get the DISO model after equivalent transformation:

[0034] Among them, Z g (s) is the grid impedance in the synchronous reference frame.

[0035] Preferably, the specific content of S3 includes:

[0036] Eliminate the conjugate part of the small current disturbance in the DISO model after equivalent transformation:

[0037] In the calculation of the conjugate of the complex transfer function, s is considered to be a real number, so the conjugate is solved as follows when calculating the full frequency response:

[0038] Where ω is the angular frequency;

[0039] Substituting Equation (14) into the DISO model after equivalent transformation, we obtain a single-input single-output model:

[0040] Therefore, the complex space vector open-loop transfer function of the system G s (s) is:

[0041] Among them, Z g (s) is the grid impedance in the synchronous reference frame.

[0042] It can be seen from the above technical solution that, compared with the prior art, the present invention discloses a stability analysis method for a grid-connected converter system based on a variable coefficient equivalent SISO model, which has the following beneficial effects:

[0043] The present invention performs small-disturbance modeling on the grid-connected power conversion system, considers the influence of the mutual coupling between the phase-locked loop and the current inner loop, and obtains a variable-coefficient SISO open-loop transfer function that can characterize the MIMO system. Compared with the technical solutions in the prior art that do not consider the actual operating conditions, the method disclosed in the present invention can more accurately analyze the system stability under varying operating conditions and varying parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0045] FIG1 is a topology and control block diagram of a three-phase grid-connected converter provided by an embodiment of the present invention;

[0046] FIG2 is an SRF-PLL linearization model provided by an embodiment of the present invention;

[0047] FIG3 illustrates the establishment of a complex space vector equivalent SISO model according to an embodiment of the present invention; (a) a complex space vector DISO model; (b) a complex space vector DISO model after equivalent transformation; (c) a complex space vector equivalent SISO model;

[0048] FIG4 is a Nyquist curve of a complex transfer function provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0049] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0050] The present invention provides a grid-connected converter system stability analysis method based on a variable coefficient equivalent SISO model, wherein the grid-connected converter system topology and control module are shown in FIG1. ​​Ignoring the voltage fluctuation on the DC side of the converter, an ideal DC source V dc Replace; L f and R L Respectively represent the inductance and parasitic resistance of the filter; L g and R g Represent the equivalent reactance and equivalent resistance of the power grid respectively, and the power grid impedance is compared with the ideal voltage source U g Series simulated weak power grid; e is the converter output voltage vector, U t is the voltage vector at the point of common coupling (PCC), i L is the grid current vector; G de represents the delay link, i dr 、i qr are the current d and q axis component command values ​​respectively.

[0051] The current is controlled based on the PI controller in the dq coordinate system, as shown in Figure 1. The current loop PI controller can be expressed as: G c (s) = k pc +k ic / s (19)

[0052] The time delay G introduced by the digital control system de (s) can be expressed as:

[0053] Where T s =1 / f s is the sampling period, in the present invention, t=T s .

[0054] In order to obtain the phase information of the grid voltage in real time, a synchronous reference frame-PLL (SRF-PLL) based on a synchronous reference frame is used, and the control structure is shown in Figure 1. p is the phase-locked loop output angle, F PLL(s) = k pp +k ip / s is the phase-locked loop PI controller. The SRF-PLL linearization model is shown in Figure 2, where Δθ p and Δθ s are the small disturbance of the phase angle of the phase-locked loop output and the small disturbance of the actual voltage phase angle of the PCC point, U t0 is the steady-state voltage value at PCC point, ΔU tq is the q-axis component disturbance of the voltage at the PCC point.

[0055] The open-loop transfer function expression of the phase-locked loop is:

[0056] The method provided by the present invention comprises the following steps:

[0057] Constructing a variable coefficient equivalent SISO model, obtaining a complex space vector open-loop transfer function based on the variable coefficient equivalent SISO model, and obtaining a Nyquist curve under different current loop parameters or phase-locked loop parameters based on the complex space vector open-loop transfer function. If the Nyquist curve surrounds the (-1, 0) point, the grid-connected power conversion system is stable; if not, the grid-connected power conversion system is unstable.

[0058] The specific steps of constructing a variable coefficient equivalent SISO model include:

[0059] S1. According to the grid-connected converter system structure, a dual-input single-output DISO model is established, where the two input quantities are the voltage disturbance at the PCC point under the synchronous reference frame. and “*” indicates conjugate, and the output is the small current disturbance

[0060] S2. Simplify the DISO model and, based on the circuit topology, convert the two input quantities in the DISO model into equivalent small current disturbance quantities to obtain an equivalent transformed DISO model;

[0061] S3. Eliminate the conjugate part of the small current disturbance, convert the equivalent transformed DISO model into a single-input single-output model based on the input-output relationship in the equivalent transformed DISO model, and further obtain the open-loop transfer function of the system.

[0062] In order to further implement the above technical solutions, the specific contents of S1 include:

[0063] S11. According to the linearization relationship in the phase-locked loop during the dynamic adjustment process of the phase-locked loop, the phase-locked loop output position angle θ is p The dq coordinate system is the control reference system, and the actual position angle θ of the PCC voltage sThe dq coordinate system is a synchronous reference system, and θ is obtained. p and θ s There is a deviation angle Δθ between:

[0064] Among them, g p (s)=F PLL (s) / (s+U t0 F PLL (s)), F PLL (s) = k pp +k ip / s is the phase-locked loop PI controller, k pp and k ip are the proportional coefficient and integral coefficient of the phase-locked loop, U t0 is the steady-state voltage value at PCC point;

[0065] S12. Obtain the relationship between the voltage small disturbance and the current small disturbance in the two reference frames of the current control circuit respectively. According to the conversion relationship between the control reference frame and the synchronous reference frame, obtain the converter output voltage small disturbance Δe in the current control circuit in the synchronous reference frame. s Small current disturbance The relationship between:

[0066] Among them, G de (s) is the time delay introduced by the digital control system, G C (s) is the current loop PI controller, the current reference value disturbance Δi dqr ,i L0 is the steady-state value of the current, and E0 is the steady-state value of the converter output voltage;

[0067] S13. Obtain the voltage small disturbance Δe in the power circuit under the synchronous reference frame s and respectively with the current small disturbance The relationship between and S12 is combined to obtain the current small disturbance value. The expression is:

[0068] S14. Combine the deviation angle Δθ expression to eliminate small current disturbances The deviation angle Δθ in the current reference value is set to Δi dqr =0, the dual-input single-output DISO model is obtained as:

[0069] The dual-input single-output model is shown in Figure 3(a). The two input quantities of the system are ΔUt and The output is Δi L .

[0070] In order to further implement the above technical solution, the current loop PI controller G C (s) is: G c (s) = k pc +k ic / s (7)

[0071] Among them, k pc and k ic They are the proportional gain coefficient and the integral gain coefficient in the current loop PI controller respectively.

[0072] In order to further implement the above technical solution, the specific contents of S12 include:

[0073] The relationship between the voltage small disturbance and the current small disturbance in the two reference frames of the current control circuit is:

[0074] The conversion relationship between the control reference frame and the synchronization reference frame is: Δx c =Δx s -jx0Δθ (9)

[0075] where x0 = x d0 +jx q0 , is the steady-state value of the variable x;

[0076] Will According to the conversion relationship, it is converted into The voltage small disturbance Δe in the current control circuit under the synchronous reference frame is obtained s Small current disturbance The relationship between them.

[0077] It should be noted that:

[0078] During the dynamic adjustment of the phase-locked loop, due to the voltage fluctuation at the PCC point, the phase-locked loop output position angle q p The actual position angle θ with the PCC voltage s There will be a deviation angle Δθ between p =θ s +Δθ. In order to distinguish the corresponding dq coordinate systems of the two, θ p The dq coordinate system is defined as the control reference system, and the superscript is represented by "c"; θ s The dq coordinate system is a synchronous reference system, represented by the superscript "s". For the operating point variable x, the small disturbance quantity in different reference systems satisfies the following relationship:

[0079] Among them, x d0 、x q0 are the steady-state values ​​of the dq-axis components of the variable x, respectively.

[0080] Formula (4) can be rewritten as formula (5) in plural form.

[0081] In order to further implement the above technical solution, the specific contents of S13 include:

[0082] Small voltage disturbance Δe in power circuit under synchronous reference frame s and respectively with the current small disturbance The relationship between them is:

[0083] Among them, since the grid voltage is an ideal voltage source, the grid voltage small disturbance ΔU g Ignore, ΔU g =0; Z f (s) is the filter impedance in the control reference frame, Z g (s) is the grid impedance in the synchronous reference frame:

[0084] Substituting equations (10) and (11) into equation (2), we can obtain the current small disturbance

[0085] In order to further implement the above technical solutions, the specific contents of S2 include:

[0086] Using the circuit topology, the PCC voltage disturbance ΔU t Grid current disturbance Replace, eliminate ΔU t and The DISO model after equivalent transformation is obtained, as shown in Figure 3.(b):

[0087] Among them, Z g (s) is the grid impedance in the synchronous reference frame.

[0088] To further implement the above technical solutions, the specific contents of S3 include:

[0089] Eliminate the conjugate part of the small current disturbance in the DISO model after equivalent transformation:

[0090] In the calculation of the conjugate of the complex transfer function, s is considered to be a real number, so the conjugate is solved as follows when calculating the full frequency response:

[0091] Where ω is the angular frequency;

[0092] Substituting Equation (14) into the DISO model after equivalent transformation, we obtain a single-input single-output model, as shown in Figure 3.(c):

[0093] Therefore, the complex space vector open-loop transfer function of the system G s (s) is:

[0094] Among them, Z g (s) is the grid impedance in the synchronous reference frame.

[0095] Compared with the classical frequency domain modeling, the complex transfer function includes the coupling relationship between dq, and its frequency domain response usually has the characteristics of positive and negative frequency domain asymmetry, that is, the response of ω>0 is usually not the conjugate of the response of ω<0, as shown in Figure 4. Its stability criterion is also the Nyquist theorem, but there is only one Nyquist curve. By analyzing G s If (s) surrounds (-1, 0), the stability of the system can be determined.

[0096] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the scope of protection of the present application.

Claims

1. A stability analysis method for grid-connected power conversion systems based on a variable coefficient equivalent SISO model, characterized in that: The following steps are involved: Constructing a variable coefficient equivalent SISO model, obtaining a complex space vector open-loop transfer function according to the variable coefficient equivalent SISO model, and obtaining a Nyquist curve under different current loop parameters or phase-locked loop parameters according to the complex space vector open-loop transfer function, if the Nyquist curve surrounds the (-1, 0) point, the grid-connected power conversion system is stable, if not, the grid-connected power conversion system is unstable; The specific steps of constructing the variable coefficient equivalent SISO model include: S1. According to the grid-connected converter system structure, a dual-input single-output DISO model is established, where the two input quantities are the voltage disturbance at the PCC point under the synchronous reference system. and "*" indicates conjugation, and the output is the small current disturbance S2. Simplify the DISO model, and according to the circuit topology, convert the two input quantities in the DISO model into small current disturbance quantities to obtain the DISO model after equivalent transformation; S3. Eliminate the conjugate part of the small current disturbance, convert the DISO model after equivalent transformation into a single-input single-output model based on the input-output relationship in the DISO model after equivalent transformation, and further obtain the open-loop transfer function of the system.

2. The grid-connected converter system stability analysis method based on the variable coefficient equivalent SISO model according to claim 1 is characterized in that: The specific contents of S1 include: S11. According to the linearization relationship in the phase-locked loop during the dynamic adjustment process of the phase-locked loop, the phase-locked loop output position angle θ p The dq coordinate system is the control reference system, and the actual position angle θ of the PCC voltage s The dq coordinate system is the synchronous reference system, and θ is obtained. p With θ s There is a deviation angle Δθ between: Among them, g p (s) = F PLL (s) / (s+U t0 F PLL (s)), F PLL (s) = k pp +k ip / s is the phase-locked loop PI controller, k pp and k ip are the proportional coefficient and integral coefficient of the phase-locked loop, U t0 is the steady-state value of the voltage at the PCC point; S12. Obtain the voltage small disturbance and current small disturbance in the two reference systems of the current control circuit respectively According to the conversion relationship between the control reference system and the synchronous reference system, the small disturbance Δe of the converter output voltage in the current control circuit under the synchronous reference system is obtained. s Small current disturbance The relationship between: Among them, G de (s) is the time delay introduced by the digital control system, G C (s) is the current loop PI controller, the current reference value disturbance Δi dqr ,i L0 is the steady-state value of current, E0 is the steady-state value of the converter output voltage; S13. Obtain the voltage small disturbance Δe in the power circuit under the synchronous reference frame s and The current small disturbance The relationship between and S12 is combined to obtain the current small disturbance value. The expression is: S14. Combine the deviation angle Δθ expression to eliminate small current disturbances The deviation angle Δθ in the current reference value is set to Δi dqr = 0, the dual-input single-output DISO model is obtained as:

3. The grid-connected converter system stability analysis method based on the variable coefficient equivalent SISO model according to claim 2 is characterized in that: Current loop PI controller G C (s) is: G c (s) = k pc +k ic / s (7) Among them, k pc and k ic They are respectively the proportional gain coefficient and the integral gain coefficient in the current loop PI controller.

4. The grid-connected converter system stability analysis method based on the variable coefficient equivalent SISO model according to claim 2 is characterized in that: The specific contents of S12 include: The relationship between voltage small disturbance and current small disturbance in the two reference frames of the current control circuit is: The conversion relationship between the control reference system and the synchronization reference system is: Δx c =Δx s -jx0Δθ (9) where x0 = x d0 +jx q0 , is the steady-state value of variable x; Will According to the conversion relationship, it is converted to The voltage small disturbance Δe in the current control circuit under the synchronous reference system is obtained s Small current disturbance The relationship between.

5. The grid-connected converter system stability analysis method based on the variable coefficient equivalent SISO model according to claim 4 is characterized in that: The specific contents of S13 include: Small voltage disturbance Δe in power circuit under synchronous reference frame s and The current small disturbance The relationship between them is: Among them, since the grid voltage is an ideal voltage source, the small disturbance of the grid voltage ΔU g Ignore, ΔU g =0; Z f (s) is the filter impedance in the control reference frame, Z g (s) is the grid impedance in the synchronous reference system: Substituting equations (10) and (11) into equation (2), we can obtain the current small disturbance 6. The grid-connected converter system stability analysis method based on the variable coefficient equivalent SISO model according to claim 2 is characterized in that: The specific contents of S2 include: Using the circuit topology relationship, the PCC voltage disturbance ΔU t Grid current disturbance Replace, eliminate ΔU t and ΔU t * , and get the DISO model after equivalent transformation: Among them, Z g (s) is the grid impedance in the synchronous reference system.

7. The grid-connected converter system stability analysis method based on the variable coefficient equivalent SISO model according to claim 2 is characterized in that: The specific contents of S3 include: Eliminate the conjugate part of the small current disturbance in the DISO model after equivalent transformation: In the calculation of the conjugate of the complex transfer function, s is considered to be a real number, so the conjugate is solved as follows when calculating the full frequency response: Where ω is the angular frequency; Substituting the formula into the DISO model after equivalent transformation, we obtain a single-input single-output model: Therefore, the complex space vector open-loop transfer function of the system G s (s) is: Among them, Z g (s) is the grid impedance in the synchronous reference frame.

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