A centralized active damping control method for grid-connected inverters of multi-circuit lines based on π-type lines

Abstract

The application discloses a kind of multi-loop line grid-connected inverter centralized active damping control methods based on π type line, comprising the following steps: S1, establish π type line impedance model;S2, implement centralized parallel active damping stability promotion strategy, construct parallel active damping branch at point of common coupling, reshape system output impedance and inhibit resonance instability by virtual damping current;S3, implement centralized parallel adaptive active damping control strategy based on phase margin constraint, according to phase margin, the dormancy or activation state of damping branch is judged, and virtual resistance is adaptively optimized, the present application breaks through the limitation that traditional fixed damping parameter cannot consider short line low loss and long line high stability, by real-time sensing system phase margin, virtual resistance resistance value is adaptively adjusted, and the stability and economy of multi-loop line parallel system under full line length working condition are effectively balanced.

Description

Technical Field

[0001] This invention belongs to the field of grid-connected inverter stability control technology, and relates to a centralized active damping control method for multi-circuit grid-connected inverters based on π-type lines. Background Technology

[0002] With the large-scale integration of new energy power generation, distributed power sources, and energy storage conversion systems, grid-connected inverters have become crucial interface devices in power electronic systems. In practical engineering, multiple grid-connected inverters are often connected to the point of common coupling (PCC) via their respective independent transmission lines, and then connected to the grid via the common grid impedance. While this type of multi-line grid-connected structure offers strong engineering adaptability, it also creates complex coupling between the inverter output impedance, line impedance, and grid impedance, making it prone to inducing resonance instability under weak grid conditions or long-distance transmission.

[0003] In existing grid-connected inverter stability analyses, transmission lines are typically simplified to an R+L line model consisting of a resistor and an inductor in series. This model is suitable for short-distance transmission or scenarios where high-frequency characteristics are not critical. However, under long-line operating conditions, the influence of the line-to-ground distributed capacitance cannot be ignored. If the traditional R+L model is still used, it will be difficult to accurately reflect the high-frequency resonance peaks, phase changes, and impedance interaction characteristics caused by long lines, thus affecting the accuracy of system stability assessment.

[0004] To suppress resonance in grid-connected inverter systems, existing methods often employ strategies such as feedforward control, active damping, or virtual impedance control. However, feedforward control has limited ability to suppress external resonance at the point of common coupling caused by line impedance; directly paralleling physical damping resistors generates fundamental active power losses, reducing system operating efficiency; while fixed-parameter active damping can improve stability under certain operating conditions, it struggles to adapt to variations in line length and grid weakness. A key challenge is how to accurately consider the impact of distributed parameters on long lines, adaptively adjust the damping strength based on system stability margin, and balance the stability and operational economy of multi-line grid-connected inverter systems. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a centralized active damping control method for multi-circuit grid-connected inverters based on π-type lines, so as to solve the problem that traditional fixed damping parameters in the prior art cannot simultaneously take into account low loss of short lines and high stability of long lines.

[0006] To solve the above technical problems, the technical solution adopted by this invention is: a centralized active damping control method for multi-circuit grid-connected inverters based on π-type lines, comprising the following steps: S1. Establish a π-type line impedance model to accurately characterize the line distributed parameter characteristics and complex impedance interaction mechanism in a multi-circuit grid-connected inverter system. S2. Implement a centralized parallel active damping stability enhancement strategy, construct a parallel active damping branch at the common connection point, and reshape the system output impedance and suppress resonance instability through virtual damping current. S3. Implement a centralized parallel adaptive active damping control strategy based on phase margin constraints. Determine the dormant or active state of the damping branch according to the phase margin and adaptively optimize the virtual resistance.

[0007] Preferably, in step S1, in scenarios with short-distance power transmission or low requirements for high-frequency characteristics, the line-to-ground distributed capacitance is ignored, and the transmission line is equivalent to an R+L line model consisting of a resistor and an inductor connected in series; when the first i The length of the line is l i At that time, its equivalent resistance, equivalent inductance, line impedance, and total equivalent output impedance after a single inverter is connected to the grid are respectively: in, l i For the first i The length of the transmission line, R 0、 L 0 represents the resistance and inductance per unit length of the power distribution line, respectively. Z load ( s () represents the original output impedance of a single inverter.

[0008] Preferably, in step S1, the π-type line impedance model is a classic equivalent model used in power systems to characterize distributed parameter lines. It approximates the distributed characteristics of the line through lumped parameters. A single π-type line segment comprises two parts: Series impedance: Parallel admittance at both ends: in, R 0 represents the line resistance. L 0 represents the line inductance. C 0 represents the distributed capacitance of the line.

[0009] Preferably, in step S1, in a multi-machine parallel scenario, each line connecting the inverter or the inverter to the grid can be equivalent to a π-type network. By combining series impedance and parallel admittance at both ends, the distributed parameter effect of the line can be accurately reproduced, providing a more realistic line model basis for impedance interaction analysis of multi-machine systems. When multiple π-type equivalent circuits are used in series to simplify the modeling of the distribution line, the parameters of the π-type equivalent circuit are calculated as follows: in,R 0、 L 0、 C 0 represents the resistance, inductance, and capacitance per unit length of the power distribution line. l 0 represents the length of a single π-type circuit.

[0010] Preferably, in step S1, under weak grid conditions, multiple inverters are often distributed to the public grid via independent transmission lines as multiple circuits. The parallel topology of multiple circuits fits the distributed access scenario of the project. In the model, each inverter corresponds to an independent transmission line, and all circuits are connected to the public grid through impedance Z. gep Connected to the mains voltage source V g Each line branch is equivalent to a Norton model of an inverter consisting of a current source, output impedance, and π-type line impedance. This model retains the practicality of the engineering topology while simplifying the analysis complexity through the lumped parameters of the π-type line. Under this model, the output impedance of a single inverter after paralleling the line impedance is: in, l i This is the length of the line.

[0011] Preferably, in step S2, a centralized parallel active damping branch is constructed at the point of common coupling (PCC) of the multi-line grid-connected inverter system. The centralized parallel active damping branch includes a PCC voltage sampling stage, a high-pass filter stage, and a virtual resistance stage. The high-pass filter stage uses a first-order high-pass filter with the following transfer function: in, ω c The cutoff angular frequency of the high-pass filter is designed between the fundamental frequency and the resonant frequency to ensure that the fundamental signal is effectively attenuated or filtered out, while the high-frequency resonant signal can pass through smoothly.

[0012] Preferably, the centralized parallel active damping branch generates a virtual damping current based on the point of common coupling voltage, and the virtual damping current is expressed in the complex frequency domain as: in, v pcc ( s () represents the voltage at the point of common coupling. R p The virtual resistance is used; from the perspective of port characteristics, the centralized parallel active damping branch is equivalent to the frequency-dependent virtual admittance at the common connection point, and the virtual admittance is: At the fundamental frequency ,but At the resonant frequency ,but This provides positive real-part damping for the system.

[0013] Preferably, after adding a centralized parallel active damping branch, the reshaped output impedance of the system is: in, Z out-line ( s ) The inverter output impedance after taking line impedance into account. Z p This is the virtual impedance corresponding to the parallel active damping branch.

[0014] Preferably, in step S3, the system phase margin is used as the criterion for whether the centralized parallel active damping branch is activated; the system phase margin after adding the parallel active damping is expressed as: Right now: The output impedance of a single inverter is decomposed into its real and imaginary parts: in, PM For the system phase margin, To reshape the output impedance of the system after adding parallel active damping, Z g ( jw () represents the power grid impedance. l This represents the line length.

[0015] Preferably, in step S3, the equivalent impedance after transmission via the π-type line is set as follows: The four key coefficients A, B, C, and D are the corresponding transmission transformation parameters, and their fully analytical expansion is as follows: This yields the real part of the natural impedance of a system containing lines. R out-line and the virtual part X out-line for: The real and imaginary parts of the virtual admittance are obtained from the virtual admittance model as follows: The line-side admittance component is: Real part of total system admittance G' out and the virtual part B' out for: The global equivalent resistance and equivalent reactance of the system are obtained from the real and imaginary parts of the total system admittance, and their expressions are as follows: Substituting the system's global equivalent resistance and equivalent reactance into the phase margin expression, the system phase margin under different line lengths and virtual resistance conditions is obtained, and the operating state of the centralized parallel active damping branch is determined based on the system phase margin. When the system phase margin PM is detected to be ≥ 45°, the system is determined to be in a naturally stable state, and the virtual resistance R is adjusted accordingly. p The value is set to infinity, putting the centralized parallel active damping branch in a dormant state. When the system phase margin PM is detected to be less than 45°, the centralized parallel active damping branch is activated, and parameter optimization is performed on the virtual resistance. The mathematical model for parameter optimization is as follows: Among them, PM(R) p , l ( ) is the given line length l and virtual resistance R p Below, the phase margin of the system loop gain, PM th The set stability threshold is 45°. (R p.min ,R p.max () represents the adjustable range of the virtual resistance to prevent parameters from exceeding limits.

[0016] Compared with existing technologies, the centralized active damping control method for multi-circuit grid-connected inverters based on π-type lines provided by this invention achieves at least the following beneficial effects: 1. This invention introduces a π-type line impedance model, which can simultaneously consider the effects of line resistance, line inductance, and distributed capacitance to ground. Compared with the traditional R+L line model, it can more accurately reflect the high-frequency impedance characteristics and resonance mechanism under long line conditions.

[0017] 2. This invention constructs a centralized parallel active damping branch at the common connection point, and reshapes the system output impedance through virtual damping current, which can reduce the resonant peak value and improve the stability margin of multi-line grid-connected inverter systems.

[0018] 3. This invention designs the sleep and activation control logic based on phase margin constraints and performs adaptive optimization on the virtual resistor, so that the damping branch sleeps when the stability margin is sufficient and activates when the stability margin is insufficient, which can take into account both system stability and operating economy. Attached Figure Description

[0019] Figure 1 This is the overall flowchart of the present invention.

[0020] Figure 2 It is a π-type circuit model.

[0021] Figure 3 A multi-circuit model that takes into account line impedance.

[0022] Figure 4 Bode plot for sensitivity analysis of feedforward control parameters considering line impedance.

[0023] Figure 5 This is a diagram of a parallel active damping structure.

[0024] Figure 6 The main topology and control block diagram of the parallel active damping system are shown.

[0025] Figure 7 This is the equivalent model after adding the parallel module.

[0026] Figure 8 (a) A complete comparison Bode plot of no control and active damping control; Figure 8 (b) is an enlarged view of the intersection point.

[0027] Figure 9 The flowchart is for adaptive active damping control.

[0028] Figure 10 A comparison of the virtual resistance adaptive adjustment trajectory and phase margin under different control strategies; Figure 10 (a) is the adaptive adjustment trajectory of Rp within the set line length range; Figure 10 (b) is a magnified view of the active area data; Figure 10 (c) is a comparison diagram of the system phase margin under the three cases.

[0029] Figure 11 Line length l =6km phase voltage and current waveforms at PCC point.

[0030] Figure 12 The waveforms of phase voltage and current before and after the parallel active damping are shown.

[0031] Figure 13 For fixed R p =50Ω active damped phase voltage and current waveform.

[0032] Figure 14 The phase voltage and current waveforms after adding adaptive active damping. Detailed Implementation

[0033] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0034] like Figure 1 As shown, the centralized active damping control method for multi-circuit grid-connected inverters based on π-type lines includes the following steps: 1. Establish a π-type line impedance model to accurately characterize the line distributed parameter characteristics and complex impedance interaction mechanism in a multi-circuit grid-connected inverter system; In scenarios involving short-distance power transmission or where high-frequency characteristics are not critical, the line-to-ground capacitance is ignored, and the transmission line is equivalent to an R+L line model consisting of a resistor and an inductor connected in series; when the first i The length of the line is l i At that time, its equivalent resistance, equivalent inductance, line impedance, and total equivalent output impedance after a single inverter is connected to the grid are respectively: in, l i For the first i The length of the transmission line, R 0、 L 0 represents the resistance and inductance per unit length of the power distribution line, respectively. Z load ( s () represents the original output impedance of a single inverter.

[0035] As system scale increases and analytical precision improves, especially in multi-machine parallel scenarios, considering only series impedance is insufficient to accurately characterize system features. To compensate for the limitations of a single R+L model and more accurately reproduce the distributed parameter effects of the line, a π-type line impedance model needs to be introduced.

[0036] The π-type line impedance model is a classic equivalent model used in power systems to characterize lines with distributed parameters. It can approximate the distributed characteristics of the line through "lumped parameters." The specific model is as follows: Figure 2 As shown.

[0037] from Figure 2 As can be seen, a single π-type circuit consists of two parts: 1. Series impedance Z L = R 0+ jωL 0 (of which) R 0 represents the line resistance; L 0 is the line inductance); 2 is the parallel admittance at both ends.Y l / 2= jωC 0 / 2 (where C 0 represents the distributed capacitance of the line.

[0038] In multi-machine parallel scenarios, each line connecting the inverter or the inverter to the grid can be equivalently represented as a π-type network. By combining series impedance and parallel admittance at both ends, the distributed parameter effect of the line can be accurately reproduced, providing a more realistic line model basis for impedance interaction analysis of multi-machine systems. When multiple π-type equivalent circuits are used in series to simplify the modeling of the distribution line, the parameters of the π-type equivalent circuit are calculated as follows: in, R 0、 L 0、 C 0 represents the resistance, inductance, and capacitance per unit length of the power distribution line. l 0 represents the length of a single π-type circuit.

[0039] In weak power grids, multiple inverters are often distributed and connected to the public power grid via independent transmission lines (multiple circuits). To accurately characterize the impedance interaction characteristics of multi-circuit systems, a system such as... Figure 3 The model shown is a multi-line parallel connection model that considers line impedance.

[0040] In a multi-circuit parallel topology application scenario for distributed power grid connection, each inverter in the model corresponds to an independent transmission line, and all circuits pass through the public grid with impedance Z. gep Connected to the mains voltage source V g Each line branch can be equivalently represented as a combination of the inverter Norton model (current source + output impedance + π-type line impedance), which retains the practicality of the engineering topology while simplifying the analysis complexity through the lumped parameters of the π-type line. Under this model, the output impedance of a single inverter after paralleling the line impedance is: in, l i This is the length of the line.

[0041] 2. Implement a centralized parallel active damping stability enhancement strategy, construct a parallel active damping branch at the common connection point, and reshape the system output impedance and suppress resonance instability through virtual damping current; As the length of the power distribution line increases, the impedance characteristics at the PCC point of the system change, causing the Nyquist curve to encircle the point (-1, j0), thus inducing high-frequency resonance instability. The first consideration is to optimize the feedforward coefficients to improve system stability. The feedforward coefficients are selected as follows: k q The impedance Bode plot results for the three operating conditions of 0.8, 0.5, and 0.2 are as follows: Figure 4 As shown.

[0042] from Figure 4 It can be seen that, considering line impedance, the intersection of grid impedances has shifted to the high-frequency band, regardless of how the feedforward coefficient is changed. k q The magnitude of the voltage has almost no effect on the phase margin. Therefore, while grid voltage feedforward control can suppress resonance caused by parallel inverters, its ability to suppress external resonance at the PCC point caused by line impedance is limited. Furthermore, while directly connecting a physical resistor in parallel at the PCC point can provide sufficient damping, it would cause significant fundamental active power loss, making it impractical in engineering.

[0043] Therefore, a centralized parallel active damping control strategy is adopted. Based on the original structure, a parallel virtual impedance branch is added, as shown in the following figure. Figure 5 As shown. Among them Z * ln This is the sum of the inverter's output impedance and the line impedance. The topology and control block diagram of the active damping section are shown below. Figure 6 As shown.

[0044] Figure 6 The middle harmonic module high-pass filter (HPF) adopts a first-order form, and its transfer function is: in, ω c The cutoff angular frequency of a high-pass filter is typically designed between the fundamental frequency and the resonant frequency to ensure that the fundamental signal is effectively attenuated or filtered out, while the high-frequency resonant signal can pass through smoothly.

[0045] according to Figure 6 The control block diagram in the figure shows the virtual damping current generated by the parallel branches. In the complex frequency domain, it can be represented as: From the perspective of circuit port characteristics, this control loop is equivalent to connecting a frequency-dependent virtual admittance in parallel at the PCC point: As can be seen from the above equation: at the fundamental frequency ,but At this point, the virtual resistor is equivalent to an open circuit, consuming no active power and solving the problem of high power loss associated with physical resistance. At the resonant frequency... ,but At this point, the control loop is equivalent to having a resistor R connected in parallel at point PCC. p This provides positive real part damping for the system.

[0046] After introducing this strategy, the Norton equivalent impedance model of the inverter grid-connected system is as follows: Figure 7 As shown. After adding parallel active damping control, the reshaped output impedance of the system is... for: To verify the effectiveness of the proposed active damping control strategy, the positive-sequence output impedance of the system before and after the improved control was analyzed, and the impedance Bode plot is shown below. Figure 8 As shown in the figure. The figure illustrates the operation of a long line in a weak power grid (line length...). l =20km), comparison of positive sequence impedance without damping (blue solid line) and with active damping control (red dashed line).

[0047] from Figure 8 As can be seen from the amplitude-frequency response curve of the complete Bode plot in (a), in the undamped case, the inverter output impedance exhibits a resonant peak with an amplitude exceeding 50dB at a frequency of approximately 2000Hz. Correspondingly, after introducing active damping, the amplitude decreases by approximately 30dB.

[0048] Depend on Figure 8 As shown in the magnified diagram of the intersection point in (b), under undamped conditions, due to the influence of high-frequency resonance, the system impedance phase at the impedance intersection point of 2282Hz is approximately -86.6°. According to the stability criterion, the phase margin at this point is only 3.4°, far below the stable operation requirements of the project. In contrast, after adding active damping, the intersection frequency of the system impedance and the grid impedance shifts from a high frequency to approximately 293Hz. At this new intersection frequency, the system impedance phase is approximately 35°, increasing the phase margin to 55.0°, which is higher than the stability margin standard, ensuring the robustness of the system.

[0049] Therefore, it can be seen that by adjusting R p The resistance value can significantly reduce the resonant peak value at the PCC point. The centralized parallel active damping stability improvement strategy effectively provides physical damping, changes the interaction frequency between the system and the power grid, and brings it back to the low-to-medium frequency band with better phase characteristics within the control bandwidth, thereby solving the system resonance instability problem under long-line weak power grid conditions.

[0050] A centralized parallel adaptive active damping control strategy based on phase margin constraints is implemented. The dormant or active state of the damping branch is determined according to the phase margin, and the virtual resistance is adaptively optimized.

[0051] The control logic employed is always-on, meaning that regardless of the system's current stability state, the control algorithm consistently outputs a virtual resistance value to maintain a fixed phase margin target. However, this approach suffers from over-control issues under short-line or high-voltage grid conditions. When transmission lines are short, the initial phase margin of the system may be far higher than the design target. In such cases, adding a parallel virtual resistor would increase the system's control burden, violating the principles of green and energy-saving control. Therefore, a centralized parallel adaptive active damping control strategy based on phase margin constraints is implemented.

[0052] The system phase margin is used as the criterion for whether the centralized parallel active damping branch should be activated; the system phase margin after adding parallel active damping is expressed as: Right now: The output impedance of a single inverter is decomposed into its real and imaginary parts: in, PM For the system phase margin, To reshape the output impedance of the system after adding parallel active damping, Z g ( jw () represents the power grid impedance. l This represents the line length.

[0053] Let the equivalent impedance after transmission via a π-type line be: The four key coefficients A, B, C, and D are the corresponding transmission transformation parameters, and their fully analytical expansion is as follows: This yields the real part of the natural impedance of a system containing lines. R out-line and the virtual part X out-line for: The real and imaginary parts of the virtual admittance are obtained from the virtual admittance model as follows:

[0054] The line-side admittance component is: The real part of the total admittance of the system, G' out and the imaginary part B' out for: The global equivalent resistance and equivalent reactance of the system are obtained from the real and imaginary parts of the total system admittance, and their expressions are as follows: The core of this strategy lies in threshold discrimination. If PM > 45° is detected, the system is determined to be in a natural steady state. At this time, the control algorithm will adjust the virtual resistance R. p The value is set to infinity (open circuit), meaning active damping control is not activated to achieve near-zero additional damping loss operation. If PM < 45°, it is determined that the system will be unable to maintain stability on its own as the line length continues to increase. At this point, the adaptive algorithm is immediately activated, automatically optimizing and calculating the R required to maintain PM = 45°. p * Implement precise damping injection.

[0055] The above adaptive tuning process can be abstracted as a constrained optimization problem. The transmission line length is... l Let the objective function be to maximize the virtual resistance R. p The constraint is that the system phase margin PM is not lower than the design threshold PM. th .

[0056] Its mathematical model is as follows: PM(R p , l ( ) is the given line length l and virtual resistance R p Below, the phase margin of the system loop gain; PM th The set stability threshold is 45°; (R) p.min ,R p.max () represents the adjustable range of the virtual resistance to prevent parameters from exceeding limits.

[0057] To solve the optimization problem, a binary search method is used to optimize the virtual resistance parameters. The specific process is as follows: Figure 9 As shown. After entering activation mode, the algorithm searches within the preset resistance range [R]. min , R max ] Perform an iterative search within the current search interval, taking the midpoint R of the current search interval at each step. mid Substitute into the impedance model and calculate the corresponding system phase margin. PM. When PM < 45° When PM > 45°, it indicates that the current virtual resistance is too large and the damping is insufficient. The upper limit of the resistance search should be lowered to enhance the damping effect. If the current damping meets the stability requirements, the lower limit of the resistance search is increased to find a larger feasible resistance value. This process is repeated until the difference between the upper and lower limits of the search interval is less than a preset accuracy threshold, at which point the optimal virtual resistance R is finally output. p * .

[0058] To verify the effectiveness of the aforementioned piecewise adaptive active damping control strategy and to explore the specific impact of line impedance variations on control parameters, a full-condition simulation of the algorithm was performed in Matlab. The simulation was set with the transmission line length varying from 2km to 80km, and the target phase margin set to PM=45°. The results are as follows: Figure 10 As shown.

[0059] Figure 10 (a) shows R within the specified line length range p The adaptive adjustment trajectory is determined. Based on the initial system margin, the control strategy clearly presents two distinct operating ranges. In the region with a shorter transmission line (shown as green dots in the figure), the initial system margin is greater than 45°. The algorithm determines that the system's own physical damping is sufficient to maintain stability, requiring no additional intervention. Therefore, the controller outputs R... p Maintain at the preset upper limit value (R) p =4000Ω, approximately open circuit). When the increase in line length causes PM to fall below the 45° threshold, the algorithm immediately switches to the active state (shown by the red dot in the figure), initiates bisection optimization, calculates and outputs the precise damping value R required to maintain system stability. p * .

[0060] Figure 10 (b) is a magnified view of the active region data. The curve shows that as the transmission line length increases, the optimal virtual resistance R... p * It exhibits a monotonically decreasing and asymptotically converging trend. When the line length exceeds 60km, the curve tends to flatten out and eventually converges to approximately 20Ω.

[0061] Figure 10 (c) is a comparison of the system phase margin under three conditions. In the uncontrolled state (blue dashed line), as the line length increases, the system phase margin drops sharply, rapidly falling below 10°, indicating that the system faces extremely high oscillation and instability risk under long-line conditions in weak power grids. A fixed resistance value (R) is used. pWhile the active damping control (red dashed line) with impedance ≈ 50Ω improves system stability to some extent, it exhibits significant limitations. When the transmission line is short, the phase margin is much higher than 45°, indicating that the damping is too strong, resulting in unnecessary waste of control resources despite ensuring stability. When the line length exceeds 30km, the phase margin continuously decreases to less than 30°, meaning that a single fixed damping parameter cannot accommodate a wide range of line impedance variations, and instability risks remain in long-distance transmission scenarios. In contrast, after implementing the adaptive control proposed in this paper (red solid line), the system can adjust R in real time according to the current line impedance characteristics. p The size of the line length is such that the phase margin of the system is always not less than 45°, regardless of how the line length changes.

[0062] 4. Verify the control strategy through simulation.

[0063] A dual-machine grid-connected system model was built on the Matlab / Simulink simulation platform. The theoretical analysis conclusions were verified one by one by comparing the simulation waveforms under different operating conditions.

[0064] (1) Simulation verification of the effect of line length on system stability First, regarding the impact of line length on system stability, this paper selects a typical instability condition from the Nyquist analysis mentioned earlier (line length parameter). l The verification was conducted at 6km, and the results are as follows: Figure 11 As shown.

[0065] Depend on Figure 11 It can be seen that the grid-connected voltage waveform amplitude is superimposed with significant periodic high-frequency fluctuations. Simultaneously, the current waveform amplitude fluctuates back and forth without any convergence trend, indicating system instability. This verifies the analysis of the unstable region in the Nyquist plot.

[0066] (2) Simulation verification of system stability by parallel active damping To verify the improvement in system stability brought about by the active damping strategy, the transmission line length was set. l Simulation verification was conducted at a distance of 20km. The simulation settings included applying a fixed damping resistor R at 1.0s. p =50Ω active damping control. The waveforms of the PCC point voltage and grid-connected current are as follows. Figure 12 As shown.

[0067] As can be seen from the figure, the grid-connected current amplitude fluctuates severely before 1.0s, at which point the system is in an unstable state.

[0068] At t=1.0s, after the control system activated the parallel active damping strategy, the current oscillation rapidly decayed. After a settling time of approximately 0.1s, the waveform recovered to a smooth and stable sine wave, with the amplitude stabilizing within the rated range.

[0069] This dynamic process intuitively verifies that adding parallel active damping effectively improves the stability of the parallel system.

[0070] (3) Simulation verification of system stability by adaptive active damping To further verify the robustness of the centralized parallel adaptive active damping strategy based on phase margin constraints under long-distance transmission lines, this invention selects the transmission line length... l The simulation was conducted on a typical long-distance line with a length of 40km to verify the effectiveness of fixed parameter control and adaptive control. Figure 13 and Figure 14 The following demonstrates the use of fixed-parameter active damping control (R) under this operating condition. p The system waveforms of (50Ω) and the adaptive active damping control proposed in this paper.

[0071] like Figure 13 As shown, when the transmission line length increases to 40km, the fixed resistance value R changes significantly due to the significant change in line impedance. p A system with a voltage rating of 50Ω could no longer meet the system's phase margin requirements, and the voltage waveform exhibited obvious oscillating instability characteristics with severe waveform distortion. This severe system instability verified that a single fixed parameter cannot accommodate a wide range of line variations. In contrast, Figure 14 The system waveforms after adaptive control were demonstrated. Despite the same long-line operating conditions, both voltage and current waveforms remained stable within the rated range.

[0072] Simulation results show that, as the transmission line length changes, the adaptive control strategy can adjust the virtual resistance in real time according to the changes in the system phase margin, keeping the system phase margin near the preset stability threshold. Compared with fixed-parameter active damping control, this method can reduce unnecessary damping input under short-line conditions and enhance the damping effect under long-line weak grid conditions, thereby achieving a balance between system stability and operational economy.

[0073] The above embodiments are not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the technical solution of the present invention are also within the protection scope of the present invention.

Claims

1. A centralized active damping control method for multi-circuit grid-connected inverters based on π-type lines, characterized in that: Includes the following steps: S1. Establish a π-type line impedance model to accurately characterize the line distributed parameter characteristics and complex impedance interaction mechanism in a multi-circuit grid-connected inverter system. In step S1, under weak grid conditions, multiple inverters are often distributed to the public grid via independent transmission lines as multiple circuits. This multi-circuit parallel topology aligns with the distributed grid connection scenario. In the model, each inverter corresponds to an independent transmission line, and all circuits are connected to the grid voltage source Vg via the public grid impedance Zgep. Each circuit branch is equivalent to a Norton inverter model composed of a current source, output impedance, and π-type line impedance. Under this model, the output impedance of a single inverter after paralleling the line impedance is: in, l i This is the length of the line at this station; S2. Implement a centralized parallel active damping stability enhancement strategy, construct a parallel active damping branch at the common connection point, and reshape the system output impedance and suppress resonance instability through virtual damping current. In step S2, a centralized parallel active damping branch is constructed at the point of common coupling (PCC) of the multi-line grid-connected inverter system. This centralized parallel active damping branch includes a PCC voltage sampling stage, a high-pass filter stage, and a virtual resistance stage. The high-pass filter stage uses a first-order high-pass filter with the following transfer function: in, ω c The cutoff angular frequency of the high-pass filter is designed between the fundamental frequency and the resonant frequency to ensure that the fundamental signal is effectively attenuated or filtered out, while the high-frequency resonant signal can pass through smoothly. The centralized parallel active damping branch generates a virtual damping current based on the common coupling point voltage. This virtual damping current is expressed in the complex frequency domain as: in, v pcc ( s () represents the voltage at the point of common coupling. R p The virtual resistance is used; from the perspective of port characteristics, the centralized parallel active damping branch is equivalent to the frequency-dependent virtual admittance at the common connection point, and the virtual admittance is: At the fundamental frequency ,but At the resonant frequency ,but This provides positive real-part damping for the system; After adding the centralized parallel active damping branch, the reshaped output impedance of the system is: in, Z out-line ( s This refers to the inverter output impedance after considering line impedance. Z p This is the virtual impedance corresponding to the parallel active damping branch; S3. Implement a centralized parallel adaptive active damping control strategy based on phase margin constraints, determine the dormant or active state of the damping branch according to the phase margin, and adaptively optimize the virtual resistance. In step S3, the system phase margin is used as the criterion for whether the centralized parallel active damping branch is activated; the system phase margin after adding parallel active damping is expressed as: Right now: The output impedance of a single inverter is decomposed into its real and imaginary parts: in, PM For the system phase margin, To reshape the output impedance of the system after adding parallel active damping, For grid impedance, l This represents the line length.

2. The centralized active damping control method for multi-circuit grid-connected inverters based on π-type lines according to claim 1, characterized in that: In step S1, in scenarios where short-distance power transmission or high-frequency characteristics are not required, the line-to-ground distributed capacitance is ignored, and the power transmission line is equivalent to an R+L line model consisting of a resistor and an inductor connected in series. When the i The length of the line is l i At that time, its equivalent resistance, equivalent inductance, line impedance, and total equivalent output impedance after a single inverter is connected to the grid are respectively: in, l i For the first i The length of the transmission line, R 0、 L 0 represents the resistance and inductance per unit length of the power distribution line, respectively. Z load ( s () represents the original output impedance of a single inverter.

3. The centralized active damping control method for multi-circuit grid-connected inverters based on π-type lines according to claim 1, characterized in that: In step S1, the π-type line impedance model is a classic equivalent model used in power systems to characterize distributed parameter lines. It approximates the distributed characteristics of the line through lumped parameters. A single π-type line segment consists of two parts: Series impedance: Parallel admittance at both ends: in, R 0 represents the line resistance. L 0 represents the line inductance. C 0 represents the distributed capacitance of the line.

4. The centralized active damping control method for multi-circuit grid-connected inverters based on π-type lines according to claim 3, characterized in that: In step S1, in a multi-machine parallel scenario, each line connecting the inverter or the inverter to the grid can be equivalent to a π-type network. By combining series impedance and parallel admittance at both ends, the distributed parameter effect of the line is accurately reproduced, providing a more realistic line model basis for impedance interaction analysis of multi-machine systems. When multiple π-type equivalent circuits are used in series to simplify the modeling of the distribution line, the parameters of the π-type equivalent circuit are calculated as follows: in, R 0、 L 0、 C 0 represents the resistance, inductance, and capacitance per unit length of the power distribution line. l 0 represents the length of a single π-type circuit.

5. The centralized active damping control method for multi-circuit grid-connected inverters based on π-type lines according to claim 1, characterized in that: In step S3, the equivalent impedance after transmission via the π-type line is assumed to be: The four key coefficients A, B, C, and D are the corresponding transmission transformation parameters, and their fully analytical expansion is as follows: This yields the real part of the natural impedance of a system containing lines. R out-line and the virtual part X out-line for: The real and imaginary parts of the virtual admittance are obtained from the virtual admittance model as follows: The line-side admittance component is: Real part of total system admittance G' out and the virtual part B' out for: The global equivalent resistance and equivalent reactance of the system are obtained from the real and imaginary parts of the total system admittance, and their expressions are as follows: Substituting the system's global equivalent resistance and equivalent reactance into the phase margin expression, the system phase margin under different line lengths and virtual resistance conditions is obtained, and the operating state of the centralized parallel active damping branch is determined based on the system phase margin. When the system phase margin PM is detected to be ≥ 45°, the system is determined to be in a naturally stable state, and the virtual resistance R is adjusted accordingly. p The value is set to infinity, putting the centralized parallel active damping branch in a dormant state. When the system phase margin PM is detected to be less than 45°, the centralized parallel active damping branch is activated, and parameter optimization is performed on the virtual resistance. The mathematical model for parameter optimization is as follows: Among them, PM(R) p , l ( ) is the given line length l and virtual resistance R p Below, the phase margin of the system loop gain, PM th The set stability threshold is 45°, (R) p.min ,R p.max () represents the adjustable range of the virtual resistance to prevent parameters from exceeding limits.

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