A method for modeling the third-order admittance of inverter considering frequency coupling effect

Abstract

The present invention discloses a third-order admittance modeling method of an inverter considering the frequency coupling effect. First, the main circuit structure and control strategy of the inverter grid-connected system are established; secondly, the dq-axis frequency domain expressions of various electrical quantities of the inverter main circuit are derived under the condition of considering the small disturbance of the phase angle of the phase-locked loop output; thirdly, a simplified modeling method based on the superposition theorem is used to establish a second-order admittance model of the inverter considering only the frequency coupling effect on the AC side; finally, the frequency coupling between the AC side and the DC side of the inverter is considered to further construct a third-order admittance matrix model of the grid-connected inverter. This inverter third-order admittance modeling method considers the third-order admittance matrix model of the LCL type grid-connected inverter with the AC side of the inverter and the AC-DC frequency coupling, which can improve the accuracy of the stability analysis of the inverter grid-connected system.

Description

Technical Field

[0001] The invention belongs to the technical field of distributed renewable energy grid-connected power generation, and relates to a third-order admittance modeling method of an inverter taking frequency coupling effect into consideration. Background Art

[0002] With the widespread application of distributed generation technology, a large number of renewable energy sources are interconnected with the power system through power electronic devices. As the main interface unit, the inverter connected to the grid is responsible for transmitting the power generated by distributed generation sources to the grid. However, the interaction between the inverter and the grid poses a threat to the stability and power quality of the power system.

[0003] So far, researchers have conducted in-depth studies on the stability of grid-connected inverters based on sequence impedance modeling, considering the frequency coupling effect on the AC side. These studies usually assume that the DC bus capacitance is infinite and the DC voltage is constant. However, with the continuous development of distributed generation technology, the complex dynamics of the DC side of the inverter may lead to complex frequency coupling effects between the AC and DC sides of the inverter. When the inverter adopts bus voltage outer loop control, disturbances on the DC side may cause current resonance, endangering the overall stability of the grid-connected system. In addition, in order to optimize costs, some inverter manufacturers reduce the DC side bus capacitance, exacerbating the AC-DC frequency coupling. This may cause current resonance and pose a threat to the overall stability of the inverter.

[0004] Distributed power sources are usually connected to the grid via three-phase grid-connected inverters with LCL filters. Due to the complex control circuit of three-phase grid-connected inverters with LCL filters, there is currently a lack of models that simultaneously consider the frequency coupling between the AC side and the AC and DC sides. Therefore, when the frequency coupling between the AC and DC sides of the system is strong, there is a lack of appropriate stability analysis standards. Summary of the invention

[0005] The purpose of the present invention is to provide a third-order admittance modeling method for an inverter taking into account the frequency coupling effect, which takes into account the third-order admittance matrix model of an LCL-type grid-connected inverter with AC side of the inverter and AC-DC frequency coupling, and can improve the accuracy of stability analysis of the inverter grid-connected system.

[0006] In order to achieve the above object, the solution of the present invention is:

[0007] A method for modeling the third-order admittance of an inverter considering frequency coupling effect comprises the following steps:

[0008] Step S1, establishing the main circuit structure and control strategy of the inverter grid-connected system;

[0009] Step S2, deriving the dq-axis frequency domain expressions of various electrical quantities of the inverter main circuit under the condition of considering the small disturbance of the phase angle of the phase-locked loop output;

[0010] Step S3, using a simplified modeling method based on the superposition theorem, to establish a second-order admittance model of the inverter that only considers the frequency coupling effect on the AC side;

[0011] Step S4: Considering the frequency coupling between the AC side and the DC side of the inverter, a third-order admittance matrix model of the grid-connected inverter is further constructed.

[0012] After adopting the above scheme, compared with the prior art, the present invention first establishes the main circuit structure and control strategy of the inverter grid-connected system; secondly, considering the small disturbance of the phase angle of the phase-locked loop output, the dq-axis frequency domain expression of each electrical quantity of the inverter main circuit is derived; then, using the simplified modeling method based on the superposition theorem, a second-order admittance model of the inverter that only considers the frequency coupling benefit of the AC side is established; finally, considering the frequency coupling between the AC side and the DC side of the inverter, the third-order admittance matrix model of the grid-connected inverter is further constructed. The model constructed by the present invention can reveal the influence of the AC side and AC / DC frequency coupling effect of the inverter on the stability of the grid-connected system, and is used for the stability analysis of various types of distributed new energy grid-connected systems through inverters, thereby improving the accuracy of stability analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is the main circuit diagram of the three-phase LCL inverter grid-connected system;

[0014] Figure 2 This is the internal and external loop control block diagram of a three-phase LCL inverter;

[0015] Figure 3 It is a block diagram of phase-locked loop control of synchronous rotating coordinate system;

[0016] Figure 4 It is a schematic diagram of the measurement method of the admittance of the grid-connected inverter;

[0017] Figure 5 It is the simulation verification diagram of each element of the inverter second-order admittance matrix;

[0018] Figure 6 is the third-order admittance matrix element Y of the inverter 13 , Y 23 Simulation verification diagram of

[0019] Figure 7 is the third-order admittance matrix element Y of the inverter 31 , Y 32 Simulation verification diagram. DETAILED DESCRIPTION

[0020] The following will be combined with the accompanying drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the present invention, they all belong to the scope of protection of the present invention.

[0021] The present invention provides a method for modeling a third-order admittance of an inverter considering a frequency coupling effect, comprising the following steps:

[0022] S1. Establish the main circuit structure and control strategy of the inverter grid-connected system;

[0023] Figure 1 The main circuit diagram of the three-phase LCL inverter grid-connected system, the inner and outer loop control block diagrams are shown in Figure 2 As shown in the figure, the inverter outer loop adopts bus voltage control, and the inner loop adopts capacitor current and inductor current feedback control. The control is implemented in the dq coordinate system, using Figure 3 The synchronous reference frame phase-locked loop (SRF-PLL) shown in FIG. 1 obtains the phase-locked angle θ required for Park coordinate transformation. PLL .

[0024] S2. Considering the small disturbance of the phase angle of the phase-locked loop output, derive the dq-axis frequency domain expressions of the electrical quantities of the inverter main circuit;

[0025] The grid voltage u of phase a at the PCC is known. ga and grid current i ga The time domain expression of is:

[0026]

[0027]

[0028] Among them, V1, V p 、V po Respectively represent the amplitudes of the fundamental frequency component, disturbance component and coupling component of the grid voltage; I1, I p ,I po They represent the amplitudes of the fundamental frequency component, disturbance component and coupling component of the grid-connected current respectively; f p and f po are the frequencies of disturbance and coupling, respectively, satisfying f po0 =f p -2f1; is the initial phase angle of each time domain component. ga and i ga After Fourier transform, the frequency domain expressions of phase a grid-connected voltage and phase a grid-connected current are obtained: and

[0029]

[0030]

[0031] in Similarly, the grid-connected voltage u of phases b and c can be obtained: gb ,u gc and grid current i gb ,i gc Frequency domain expression of and

[0032] When considering a small disturbance in the phase angle of the phase-locked loop output, the output phase angle of the PLL is θ PLL =θ0+Δθ, where θ0 represents the phase angle of the fundamental frequency voltage of phase a, and Δθ represents the phase angle small signal disturbance corresponding to the disturbance voltage of phase a. Park coordinate transformation matrix T dq / abc (θ PLL )satisfy:

[0033] T dq / abc (θ PLL )=T dq / abc (Δθ)·T dq / abc (θ0)

[0034] Among them, T dq / abc (θ0) represents the Park transformation matrix without considering the phase angle disturbance, and T dq / abc (Δθ) is the additional transformation matrix introduced when considering the phase angle perturbation Δθ, and their expressions are:

[0035]

[0036]

[0037] Three-phase grid-connected voltage u at PCC ga ,u gb ,u gc After Park transformation matrix T dq / abc (θ PLL ) to obtain the grid voltage dq axis component u when considering phase angle disturbance gd ,u gq In the frequency domain, Park transformation can be used to obtain the grid voltage dq axis component u gd ,u gq Frequency domain expression of and

[0038]

[0039]

[0040] in is the frequency domain component of the small phase angle perturbation Δθ, satisfying:

[0041]

[0042] Among them, H PLL (s) is the transfer function of the PLL. Similarly, the grid current i gabc The frequency domain expression of the dq axis is for:

[0043]

[0044]

[0045] The capacitor current i of the LCL filter gabc The frequency domain expression of the dq axis is for:

[0046]

[0047]

[0048] Among them, I c1 and are the fundamental frequency amplitude and phase of the capacitor current, They are the disturbance component and coupling component of the capacitor current respectively.

[0049] S3. Using a simplified modeling method based on the superposition theorem, a second-order admittance model of the inverter is established that only considers the frequency coupling effect on the AC side;

[0050] Without considering the DC bus voltage disturbance, the dq-axis frequency domain expression of the bridge arm voltage is for:

[0051]

[0052]

[0053] Among them, D0 and Q0 represent the steady-state value of the inverter bridge arm output voltage, which is:

[0054]

[0055] Traditional modeling methods directly Performing the inverse Park transform, we get the expression of the bridge arm voltage. However, since multiplication in the time domain corresponds to convolution in the frequency domain, direct Performing the inverse Park transform will result in a complex convolution operation. The disturbance component in includes the disturbance element These dq axis components are converted from the components in the abc coordinate system and then converted back to the abc reference coordinate system, resulting in redundant calculations. The complete steady-state and disturbance components are included in Their corresponding components in the abc coordinate system can be written directly. To achieve this, the present invention applies the superposition theorem to Divided into and Two parts:

[0056]

[0057]

[0058]

[0059]

[0060] in,

[0061]

[0062]

[0063] because The steady-state and disturbance components of There is no perturbation component, so it is easy to get their components in the abc coordinate system respectively:

[0064]

[0065]

[0066] According to the main circuit structure of the inverter, assuming that L1 and L2 are the inductors on the inverter side and the grid side of the LCL filter respectively, and C is the filter capacitor, we can know that:

[0067]

[0068] The second-order admittance matrix expression of the inverter is:

[0069]

[0070] Combining the above formulas, we can derive the admittance elements Y of the second-order matrix 11 (s),Y 12 (s),Y 21 (s),Y 22 (s). The model was built using the PSCAD simulation software platform. Figure 4The measured values ​​of each element of the second-order admittance matrix obtained by the method shown are compared with the theoretical values ​​obtained by MATLAB drawing. Figure 5 As shown, the theory is consistent with the simulation, which verifies the correctness of the model.

[0071] S4. Considering the frequency coupling between the AC side and the DC side of the inverter, a third-order admittance matrix model of the grid-connected inverter is further constructed.

[0072] When considering the disturbance on the DC side of the inverter, the DC bus voltage U dc , bus current I dc The frequency domain expression of is:

[0073]

[0074] Among them U dc0 ,I dc0 and U dc ,I dc Steady-state component and disturbance component in frequency domain. The third-order admittance matrix expression of the inverter is:

[0075]

[0076] When considering the bus voltage external loop disturbance, can be rewritten as:

[0077]

[0078]

[0079] Compared with the original formula, The following additional components have been added

[0080]

[0081]

[0082] in It is the disturbance component transmitted to the AC side through the bus voltage outer loop control. It is the disturbance transmitted from the inverter main circuit to the AC side through PWM modulation. U′ d0 and U q '0 is the steady-state value of the dq-axis component of the bridge arm voltage. Containing only the perturbation component, their Park inverse transform results are as follows:

[0083]

[0084] The output voltage of the inverter bridge arm includes three different components. According to the superposition theorem, combined with the inverter main circuit structure:

[0085]

[0086] Based on this, the admittance element Y in the third-order admittance matrix of the inverter can be derived 13 (s),Y 23 (s) is the expression of Y 13 (s),Y 23 The simulation verification of (s) is as follows Figure 6 shown.

[0087] Then, consider the impact of AC side disturbance on DC side. Considering the power conservation principle on both sides of the inverter, we get:

[0088]

[0089] where U′ d ,U q ′,I′ d ,I q ′ is the steady-state value of the inverter bridge arm output voltage and current in the dq coordinate system. In the frequency domain, the voltage and current across the inverter satisfy:

[0090]

[0091] in U′ d ,U q ′,I′ d ,I q Ignoring the small disturbance of the phase angle of the phase-locked loop output, we get:

[0092]

[0093] According to the characteristics of the LCL circuit, the disturbance component and coupling component of the bridge arm voltage The disturbance component and coupling component of the bridge arm current Can be used express:

[0094]

[0095]

[0096]

[0097]

[0098] Known satisfy Combining the above equations, the admittance element Y in the inverter third-order admittance matrix can be derived: 31 ,Y 32 ,Y 33 The expression of 31 ,Y 32 The simulation verification is as follows Figure 7 The model constructed by the present invention can reveal the influence of the AC side of the inverter and the AC / DC frequency coupling effect on the stability of the grid-connected system, and improve the accuracy of the stability analysis of various types of distributed new energy grid-connected systems via inverters.

[0099] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes. The schemes in the embodiments of the present invention may be implemented in various computer languages, for example, object-oriented programming language Java and literal scripting language JavaScript, etc.

[0100] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0101] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0102] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0103] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0104] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A method for modeling the third-order admittance of an inverter considering the frequency coupling effect, characterized in that The steps include: Step S1, establishing the main circuit structure and control strategy of the inverter grid-connected system; Step S2, deriving the dq-axis frequency domain expressions of various electrical quantities of the inverter main circuit under the condition of considering the small disturbance of the phase angle of the phase-locked loop output; Step S3, using a simplified modeling method based on the superposition theorem, to establish a second-order admittance model of the inverter that only considers the frequency coupling effect on the AC side; Step S4, considering the frequency coupling between the AC side and the DC side of the inverter, further constructing a third-order admittance matrix model of the grid-connected inverter; In step S4, when the DC side disturbance of the inverter is considered, the DC bus voltage U dc , bus current I dc The frequency domain expression of is: Among them U dc0 ,I dc0 and U dc ,I dc Steady-state component and disturbance component in the frequency domain; the third-order admittance matrix expression of the inverter is: When considering the bus voltage external loop disturbance, Rewritten as: Compared with the original formula, The following additional components have been added in It is the disturbance component propagated to the AC side through the bus voltage outer loop control; is the disturbance transmitted from the inverter main circuit to the AC side through PWM modulation; U′ d0 and U q ′0 is the steady-state value of the dq-axis component of the bridge arm voltage; Containing only the perturbation component, their Park inverse transform results are as follows: The output voltage of the inverter bridge arm includes three different components, which are combined with the inverter main circuit structure: Based on this, the admittance element Y in the third-order admittance matrix of the inverter is derived 13 (s),Y 23 (s) expression; Then, considering the power conservation principle on both sides of the inverter, we get: where U′ d ,U q ′,I′ d ,I q ′ is the steady-state value of the inverter bridge arm output voltage and current in the dq coordinate system; in the frequency domain, the voltage and current at both ends of the inverter satisfy: in U′ d ,U q ′,I′ d ,I q ′ frequency domain expression; ignoring the small disturbance of the phase angle of the phase-locked loop output, we get: According to the characteristics of the LCL circuit, the disturbance component and coupling component of the bridge arm voltage The disturbance component and coupling component of the bridge arm current use express: Known satisfy Combining the above equations, the admittance element Y in the inverter third-order admittance matrix is ​​derived: 31 ,Y 32 ,Y 33 expression.

2. The method according to claim 1, characterized in that: In step S1, the outer loop of the inverter grid-connected system adopts bus voltage control, and the inner loop adopts capacitor current and inductor current feedback control.

3. The method according to claim 1, characterized in that: In step S2, it is known that the grid voltage u of phase a at the grid connection point ga and grid current i ga The time domain expression of is: Among them, V1, V p 、V po Respectively represent the amplitudes of the fundamental frequency component, disturbance component and coupling component of the grid voltage; I1, I p ,I po They represent the amplitudes of the fundamental frequency component, disturbance component and coupling component of the grid-connected current respectively; f p and f po are the frequencies of disturbance and coupling, respectively, satisfying f po =f p -2f1; is the initial phase angle of each time domain component; u ga and i ga After Fourier transform, the frequency domain expressions of phase a grid-connected voltage and phase a grid-connected current are obtained: and in Assume that the grid-connected voltage u of phases b and c is gb ,u gc and grid current i gb ,i gc Frequency domain expression of and When considering a small disturbance in the phase angle of the phase-locked loop output, the output phase angle of the PLL is θ PLL =θ0+Δθ, where θ0 represents the phase angle of the fundamental frequency voltage of phase a, and Δθ represents the phase angle small signal disturbance corresponding to the disturbance voltage of phase a; Park coordinate transformation matrix T dq / abc (θ PLL )satisfy: T dq / abc (i PLL )=T dq / abc (Δθ)·T dq / abc (θ0) Among them, T dq / abc (θ0) represents the Park transformation matrix without considering the phase angle disturbance, and T dq / abc (Δθ) is the additional transformation matrix introduced when considering the phase angle perturbation Δθ, and their expressions are: Three-phase grid-connected voltage u at the grid-connected point ga ,u gb ,u gc After Park transformation matrix T dq / abc (θ PLL ) to obtain the grid voltage dq axis component u when considering phase angle disturbance gd ,u gq ; In the frequency domain, Perform Park transformation to obtain the grid voltage dq axis component u gd ,u gq Frequency domain expression of and in is the frequency domain component of the small phase angle perturbation Δθ, satisfying: Among them, H PLL (s) is the transfer function of PLL; grid-connected current i gabc The frequency domain expression of the dq axis is for: The capacitor current i of the LCL filter gabc The frequency domain expression of the dq axis is for: Among them, I c1 and are the fundamental frequency amplitude and phase of the capacitor current, They are the disturbance component and coupling component of the capacitor current respectively.

4. The method according to claim 1, characterized in that: In step S3, without considering the DC bus voltage disturbance, the dq axis frequency domain expression of the bridge arm voltage is for: Among them, D0 and Q0 represent the steady-state value of the inverter bridge arm output voltage, which is: Will Divided into and Two parts: in, Get the components in the abc coordinate system: According to the main circuit structure of the inverter, L1 and L2 are respectively the inductances of the LCL filter inverter side and the grid side, and C is the filter capacitor: The second-order admittance matrix expression of the inverter is: Thus, the admittance elements Y of the second-order matrix are derived 11 (s),Y 12 (s),Y 21 (s),Y 22 (s).

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