Resonance suppression and stability analysis method of lcl grid-connected inverter based on vsg under weak grid

Abstract

This invention discloses a method for resonance suppression and stability analysis of VSG-based LCL grid-connected inverters in weak grid environments. The method involves: establishing the open-loop transfer function of the VSG controller system's inner current loop; determining the optimal combination of the proportional parameters of the PR controller and the active damping feedback coefficient by combining resonance suppression, gain margin, phase margin, and steady-state error constraints; and solving for the optimal value of the resonance coefficient. Considering the influence of the VSG active power controller, reactive power controller, inner current loop, and active damping, and taking into account the dynamic characteristics of the reactive power controller, a system sequence impedance model containing the active damping component is established using the harmonic linearization method, combined with the VSG harmonic small-signal model. The stability of the grid-connected system after resonance suppression is analyzed using the established sequence impedance model, the grid impedance model, and the Nyquist stability criterion. This invention effectively suppresses the harmonic components of the LCL filter's resonant frequency, reduces the distortion rate of the grid-connected current, ensures the stability of the LCL filter as a grid-connected interface, and provides a model for small-disturbance stability analysis in scenarios such as inverters connected to microgrids and new energy power plants, which is beneficial for the promotion and application of VSG.

Description

Technical Field

[0001] This invention relates to the field of DC-AC converter technology for power conversion devices, and in particular to a method for resonance suppression and stability analysis of VSG-based LCL grid-connected inverters suitable for weak power grids. Background Technology

[0002] Grid-connected inverters serve as the interface between renewable energy generation and the power grid. On one hand, they significantly impact the efficiency and development prospects of renewable energy generation systems; on the other hand, to minimize the adverse effects of renewable energy integration on the main power grid, they themselves must meet grid connection standards, making their research essential. LCL filters possess low-pass, third-order filtering characteristics. When harmonic standards and switching frequencies are the same, smaller filter inductors can be designed, reducing losses and size. However, LCL filters inevitably suffer from resonance problems, affecting system stability. Previous research has extensively addressed this, summarizing numerous methods to achieve the aforementioned goals. Passive damping is the simplest method, involving adding a resistor in series in the filter circuit to increase system damping. However, increasing the damping resistor can not only reduce harmonic filtering performance but also increase system losses and reduce system efficiency. Especially in high-power environments, resistor heating is significant. Therefore, active control strategies that replace actual damping resistors through control are the mainstream research direction in academia.

[0003] Due to factors such as the inverse distribution of renewable energy resources and loads in some regions, and weak grid structures, the power grid exhibits characteristics of high inductance and weak grid resistance, affecting the operation, control, and stability of grid-connected inverters. Therefore, it is necessary to establish an accurate impedance model of the virtual synchronous machine, and then study its interaction stability with the power grid, providing theoretical and technical support for the promotion and application of virtual synchronous machine technology. Summary of the Invention

[0004] The purpose of this invention is to provide a damping control method based on VSG, which is suitable for resonance suppression strategies under weak grid conditions. It can suppress resonance in LCL grid-connected inverters and perform stability analysis on the grid-connected system after resonance suppression.

[0005] The technical solution of this invention is: a resonance suppression method for VSG-based LCL grid-connected inverters under weak grid conditions, comprising the following steps:

[0006] Step S1, Sampling and Transformation: Sample the grid-side current to obtain the three-phase inverter-side currents i of phases a, b, and c. 2a i 2b i 2c and for i 2a i 2b i 2c Perform Clark transformation to obtain i 2αi 2β The voltage of the three-phase capacitors a, b, and c is obtained by sampling the grid-side voltage. a u b u c and for u a u b u c Perform Clark transformation to obtain u α u β ;

[0007] Step S2, VSG power loop: Based on the sampled grid-side voltage and current, perform power calculation, and obtain the current reference signal of the inner current loop through the virtual synchronous machine active-frequency loop and reactive-voltage loop and stator electrical equations;

[0008] Step S3, Resonance Suppression: Establish the open-loop transfer function of the inner current loop of the VSG system after adding an active damping element in the s domain. Combine the LCL resonance suppression, system gain margin and phase margin, and steady-state error constraints to select the optimal control parameters.

[0009] Step S4, Inner Current Loop: The VSG power loop output is used as the current reference signal, and the grid-side current is used as the feedback quantity. After passing through the PR controller and the active damping circuit, it is then transformed by Clark to output a three-phase modulated wave signal.

[0010] Step S5, Modulation Drive: The three-phase modulation wave signal obtained in step S4 is used to generate a pulse width modulation signal through a sinusoidal pulse width modulation unit. The pulse width modulation signal controls the working state of the inverter switching transistor through the drive circuit.

[0011] Furthermore, the constraint condition for harmonic suppression at the resonant frequency of the LCL filter in step S3 is as follows: The actual resonant frequency ω of the LCL filter res An offset will occur after using an active damping control loop; the resonant frequency after the offset is ω. res The resonance suppression constraint conditions are as follows:

[0012] ;

[0013] Furthermore, step S3 imposes the following constraints on the system's gain margin and phase margin:

[0014]

[0015] ;

[0016] Furthermore, in step S3, the optimal control parameter ω c The selection criteria are as follows:

[0017]

[0018] In the formula, ;

[0019] Furthermore, the selection of the optimal control parameters for the resonance coefficient in step S3 is as follows:

[0020]

[0021] in, .

[0022] A stability method for VSG-based LCL grid-connected inverters applicable to weak grid conditions includes the following steps:

[0023] Step S1: In the time domain, a positive-sequence small-signal voltage disturbance is added to the VSG network side to obtain the expressions for the three-phase output voltage and output current of the inverter in the time domain, and then transformed to the frequency domain to obtain v. a [f] and i a [f];

[0024] Step S2: Based on instantaneous power theory and using the frequency domain convolution theorem, calculate the output active power and reactive power of the virtual synchronous machine in the frequency domain as P0 and P1, respectively. e [f] and Q e [f];

[0025] Step S3: Combining the active-frequency loop and reactive-voltage loop of the VSG, the output phase angle θ[f] and output voltage amplitude E[f] can be obtained; combining the VSG output phase angle θ[f] and output voltage amplitude E[f], the internal electromotive force e of the VSG can be obtained. a [f],e b [f],e c [f], obtained by Clark transformation, is e. α [f];

[0026] Step S4: After applying the virtual impedance stator electrical equations, the current reference signal i of the inner current loop is obtained. α [f];

[0027] Step S5: After passing through the current loop PR controller, active damping, and voltage feedforward, the modulated wave u is obtained. α [f], and after inverse Clark transformation, the bridge arm voltage response signal V is obtained. ia [f];

[0028] Step S6: Combining the small-signal harmonic model of the main circuit, obtain the positive-sequence impedance Z of the VSG containing the source damping element. vp [f], Z vn[f]; Draw the Bode plots of the positive and negative sequence impedances of the VSG containing the source damping element and the positive and negative sequence impedances of the grid. Based on the Nyquist stability criterion, analyze the stability of the grid-connected system after resonance suppression.

[0029] Further, step S2 obtains the output power of the VSG as follows:

[0030]

[0031] Furthermore, step S3 takes into account the influence of reactive power dynamic characteristics, as follows:

[0032]

[0033]

[0034]

[0035] Furthermore, step S6 utilizes the small-signal model of the main circuit, as follows:

[0036]

[0037] Using the impedance Bode plot and the Nyquist stability criterion, specifically as follows: Draw the Bode plots of the VSG system with source damping and the grid sequence impedance model, and perform stability analysis using the Nyquist stability criterion. When the grid impedance changes, the grid-connected system after resonance suppression is stable only when both the positive sequence impedance ratio and the negative sequence impedance ratio satisfy the Nyquist stability criterion.

[0038] Compared with the prior art, the significant advantages of this invention are: (1) considering the sampling delay, calculating the delay and modulation delay in one step, using active damping through grid-side current feedback, and simplifying the design process, thus realizing LCL resonance suppression control; (2) considering the influence of the dynamic characteristics of the VSG reactive power controller, establishing a system sequence impedance model containing the active damping element, finding that the impedance model established at low frequencies is more accurate, and using the impedance model to perform small-signal stability analysis on the grid-connected system after resonance suppression. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the structure of an LCL grid-connected inverter under weak grid conditions.

[0040] Figure 2 This is a schematic diagram of the VSG power loop and virtual stator electrical equation control.

[0041] Figure 3 This is a control block diagram for the inner current loop containing a source damping element.

[0042] Figure 4 The main circuit is a harmonicized small-signal model.

[0043] Figure 5 The simulation waveforms are shown after adding active damping under ideal power grid conditions.

[0044] Figure 6 For the inductor L in a weak grid g The simulation waveform after adding active damping at 3mH.

[0045] Figure 7 The positive sequence impedance Bode plot and simulation diagram are provided to consider the dynamic characteristics of the reactive power loop.

[0046] Figure 8 The following are Bode plots of the sequence impedance of a VSG system with source damping: (a) is the positive sequence impedance Bode plot; (b) is the negative sequence impedance Bode plot. Detailed Implementation

[0047] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0048] Combination Figure 1 This invention is adapted to the resonance suppression of LCL grid-connected inverters under weak grid conditions. It collects three-phase voltage and current signals from the LCL filter grid side for power calculation; obtains the VSG internal potential from the virtual synchronous active and reactive power loops, and obtains the current reference for the inner current loop through the virtual stator electrical equations; using the grid-side current as feedback, after passing through the PR controller and active damping circuit, a modulation wave is generated and sent to the sinusoidal pulse width modulation unit. The output of the sinusoidal pulse width modulation unit is connected to each switch of each phase arm of the three-level inverter via a drive circuit.

[0049] Combination Figure 1 This invention is adapted to the stability analysis of LCL grid-connected inverters under weak grid conditions. In the time domain, a positive-sequence small-signal voltage disturbance is added to the grid side of the virtual synchronous machine to obtain the expressions for the three-phase output voltage and output current of the inverter in the time domain, and then transformed to the frequency domain. According to the instantaneous power theory, the active and reactive power outputs of the virtual synchronous machine in the frequency domain are calculated using the frequency domain convolution theorem. Combining the active-frequency loop and reactive-voltage loop of the VSG, the internal potential of the VSG is obtained. After passing through the virtual impedance stator electrical equations, the current reference signal of the inner current loop is obtained. After passing through the current loop PR controller, active damping, and voltage feedforward, a modulation wave is generated, and the bridge arm voltage response signal can be obtained. Figure 3 The small-signal model of the road harmonics is used to obtain the positive and negative sequence impedances of the VSG system with source damping. Bode plots of the positive and negative sequence impedances of the VSG system with source damping and the positive and negative sequence impedances of the grid are drawn. Based on the Nyquist stability criterion, the stability of the grid-connected system after resonance suppression is analyzed.

[0050] The present invention will now be described in further detail with reference to the embodiments.

[0051] This invention addresses resonance suppression in LCL grid-connected inverters operating under weak grid conditions, and includes the following steps:

[0052] Step S1, Sampling and Transformation: Sample the grid-side current to obtain the three-phase inverter-side currents i of phases a, b, and c. 2a i 2b i 2c and for i 2a i 2b i 2c Perform Clark transformation to obtain i 2α i 2β The voltage of the three-phase capacitors a, b, and c is obtained by sampling the grid-side voltage. a u b u c and for u a u b u c Perform Clark transformation to obtain u α u β ;

[0053] Step S2, VSG power loop: Based on the sampled grid-side voltage and current, perform power calculation, and obtain the current reference signal of the inner current loop through the virtual synchronous machine active-frequency loop and reactive-voltage loop and stator electrical equations;

[0054] Step S3, Resonance Suppression: Establish the open-loop transfer function of the VSG system current inner loop after adding an active damping element in the s domain, and select the optimal control parameters by combining LCL resonance suppression, system magnitude margin and phase margin, and stability error constraints.

[0055] Active damping controller:

[0056] The total delay introduced by digital control in the system can be expressed as:

[0057] The controlled object LCL filter considers L g Post-transfer function:

[0058] Current controller G PR The form of (s) is:

[0059] The open-loop transfer function expression of the current control system of the LCL grid-connected inverter under weak grid conditions is as follows:

[0060]

[0061] To ensure the system's resonance suppression effect, the gain of the system's open-loop transfer function at the resonant frequency needs to be suppressed to below 0dB, that is:

[0062]

[0063] The current controller parameter K can be obtained. p and active damping controller parameter k ad The following conditions must be met:

[0064]

[0065] In the formula

[0066]

[0067] To ensure that the system's gain margin GM meets the requirements, assuming the ideal gain margin is GM0 (usually taken as 3dB), we can obtain:

[0068]

[0069] To ensure the weak grid L g In 0 ≤ L g ≤ L g_max Within the specified range, the grid-connected inverter system satisfies the phase margin requirement PM≥PM0, because at frequencies equal to or below the cutoff frequency ω... c In the frequency band where the filter capacitor C has a small effect, it can be approximated as C=0. Therefore, the active damping controller parameter k... ad Required to satisfy the following formula:

[0070]

[0071] ω c_max The solution to the quartic equation in one variable:

[0072]

[0073] In the formula,

[0074] ω c_max Substituting into the following formula, we can obtain the optimal current controller parameter K. p_opt The expression:

[0075]

[0076] To effectively reduce the steady-state error of the grid-connected current, the system loop gain must have sufficient amplitude-frequency gain at the fundamental frequency, thus T f ≥T f0 (T is usually taken as T) f0 =73dB), to make 0 ≤ L g≤ L g_max Since the requirements are met within the specified range, we can conclude that:

[0077]

[0078] In the formula, ;

[0079] Step S4, Inner Current Loop: The VSG power loop output is used as the current reference signal, and the grid-side current is used as the feedback quantity. After passing through the PR controller and the active damping circuit, it is then transformed by Clarke to output a three-phase modulated wave signal.

[0080] Step S5, Modulation Drive: The three-phase modulation wave signal obtained in step S4 is used to generate a pulse width modulation signal through a sinusoidal pulse width modulation unit. The pulse width modulation signal controls the working state of the inverter switching transistor through the drive circuit.

[0081] A stability method for VSG-based LCL grid-connected inverters applicable to weak grid conditions includes the following steps:

[0082] Step S1: In the time domain, a positive-sequence small-signal voltage disturbance is added to the VSG network side to obtain the expressions for the three-phase output voltage and output current of the inverter in the time domain, and then transformed to the frequency domain to obtain v. a [f] and i a [f];

[0083]

[0084] In the formula: .

[0085] Step S2: Based on instantaneous power theory and using the frequency domain convolution theorem, calculate the output active power and reactive power of the VSG in the frequency domain as P0, respectively. e [f] and Q e [f];

[0086]

[0087] Step S3, combining the active-frequency loop of the VSG, yields the output phase angle θ[f];

[0088]

[0089] By combining the reactive-voltage loop of the VSG, the output voltage amplitude E[f] can be obtained;

[0090]

[0091] By combining the output phase angle θ[f] and output voltage amplitude E[f] of the VSG, the three-phase internal electromotive force e of the VSG can be obtained. a [f],eb [f],e c [f], obtained by Clark transformation, is e. α [f];

[0092] Step S4: After applying the virtual impedance stator electrical equations, the current reference signal i of the inner current loop is obtained. α [f];

[0093]

[0094] Step S5: After passing through the current loop PR controller, active damping, and voltage feedforward, the modulated wave u is obtained. α [f], and after inverse Clark transformation, the bridge arm voltage response signal V is obtained. ia [f];

[0095]

[0096] Step S6, combining the main circuit harmonic small-signal model Figure 4 The positive sequence impedance Z of the VSG system containing the source damping element is obtained. vp [f],Z vn [f];

[0097]

[0098]

[0099] Plot the positive and negative sequence impedances of the VSG system with source damping and the positive and negative sequence impedances of the grid. Analyze the stability of the grid-connected system after resonance suppression based on the Nyquist stability criterion.

[0100] According to the Nyquist criterion, for a system to be stable, then at Z... gpn (s) and Z vpn The phase margin (PM) at the intersection of (s) must be positive. The phase margin PM can be expressed as:

[0101]

[0102] Example 1

[0103] This embodiment is built based on MATLAB / Simulink, as follows: Figure 1 The system simulation model shown is suitable for LCL grid-connected inverters under weak grid conditions. The DC power is inverted by a three-level inverter circuit after passing through the DC bus capacitor, and then output as a three-phase voltage after passing through an LCL filter circuit. The output is a stable three-phase sinusoidal voltage.

[0104] Table 1

[0105] parameter numerical values <![CDATA[Inductance value L1 on the inverter side]]> 2mH <![CDATA[Inductance value L2 of the grid side inductor]]> 1mH Filter capacitor value C 50uF <![CDATA[Sampling frequency f s > 20kHz <![CDATA[Switching frequency f sw > 20kHz <![CDATA[Maximum inductance L of weak grid g_max > 3mH Gauss Margin GM 3dB Phase margin PM 45deg <![CDATA[Inverter transfer function K PWM > 150

[0106] According to the simulation parameters in Table 1, K can be obtained. p K r and k ad The value can be:

[0107]

[0108] Figure 5 The waveforms are simulated under ideal power grid conditions after adding active damping. Figure 6 The simulation waveform diagram is shown after adding active damping when the inductance Lg=3mH of the weak grid. It can be seen that the resonance suppression method of LCL grid-connected inverter adapted to weak grid conditions in this invention suppresses the resonant frequency subharmonics in the grid-side current and reduces the total harmonic distortion rate of the current. Figure 7 The positive-sequence impedance Bode plot and simulation diagram considering the dynamic characteristics of the VSG reactive loop verify the accuracy of the established model. Comparative analysis shows that the impedance model of the system at low frequencies is more accurate when considering the dynamic characteristics of the VSG reactive loop. Figure 8 It is VSG and power grid L g When the sequence impedance Bode plot is 3mH, the phase margin at the intersection of the VSG system with the grid Bode plot containing the source damping element is 0. Therefore, it can be concluded that the grid-connected system after resonance suppression can operate stably under weak grid conditions.

Claims

1. A method for suppressing resonance in VSG-based LCL grid-connected inverters under weak grid conditions, characterized in that, Resonance suppression is achieved using the inner current loop of the VSG system, and the process includes the following steps: Step S1, Sampling and Transformation: Sample the grid-side current to obtain the three-phase inverter-side currents i of phases a, b, and c. 2a i 2b i 2c and for i 2a i 2b i 2c Perform Clark transformation to obtain i 2α i 2β The voltage of the three-phase capacitors a, b, and c is obtained by sampling the grid-side voltage. a u b u c and for u a u b u c Perform Clark transformation to obtain u α u β ; Step S2, VSG power loop: Based on the sampled grid-side voltage and current, perform power calculation, and obtain the current reference signal of the inner current loop through the virtual synchronous machine active-frequency loop and reactive-voltage loop and stator electrical equations; Step S3, Resonance Suppression: Establish the open-loop transfer function of the system after adding an active damping element in the s-domain, and select the optimal control parameters by combining the LCL resonance suppression condition, the system gain margin and phase margin constraints, and the steady-state error constraints. Step S4, Inner Current Loop: The VSG power loop output is used as the current reference signal, and the grid-side current is used as the feedback quantity. After passing through the PR controller and the active damping circuit, it is then transformed by Clark to output a three-phase modulated wave signal. Step S5, Modulation Drive: The three-phase modulation wave signal obtained in step S4 is used to generate a pulse width modulation signal through a sinusoidal pulse width modulation unit. The pulse width modulation signal controls the working state of the inverter switching transistor through the drive circuit. Step S3 imposes the following constraints on the system's gain margin and phase margin: In the formula, Among them, K p k is the proportional element coefficient of the PR controller. ad L1 is the active damping feedback coefficient, L2 is the inductance value of the LCL filter on the inverter side, C1 is the capacitance value of the LCL filter on the grid side, and L is the capacitance value of the LCL filter. g Here, GM is the inductance value of the weak grid, PM0 is the system's gain margin, and ω is the system's phase margin. c T is the cutoff frequency of the system's open-loop transfer function. s K is the switching period of the system. PWM Inverter gain; Step S3 imposes the following constraints on harmonic suppression at the resonant frequency of the LCL filter: the actual resonant frequency ω of the LCL filter. res An offset will occur after using an active damping control loop; the resonant frequency after the offset is ω. res The resonance suppression constraint conditions are as follows: Among them, G op (s) is the open-loop transfer function of the system, ω res ' is the resonant frequency after offset; Step S3: ω of the optimal control parameter c The selection is as follows: In the formula, Among them, L g_max This is the inductance value of the weak grid corresponding to a short-circuit ratio (SCR) of 10. Step S3 involves selecting the optimal control parameters for the PR controller's resonance coefficient, as follows: In the formula, , Where, k ad_opt For the optimal parameters of active damping, K p_opt K is the optimal parameter for the proportion. r_opt ω0 is the optimal resonant parameter and the fundamental frequency.

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