Transient stability analysis method for hybrid synchronous control network-forming inverter considering damping influence

Abstract

The invention discloses a method for analyzing transient stability of a hybrid synchronous control grid-forming inverter considering damping influence, and belongs to the field of DC / AC converters, the method comprises the following steps: dividing a power angle interval to be analyzed into a plurality of sub-intervals, constructing an explicit damping-power angle function in each sub-interval, further quantifying the damping influence, and calculating the transient stability of the hybrid synchronous control grid-forming inverter. And depicting a transient stability boundary of the network-constructing inverter system. According to the method, the damping influence is quantified, the defect that a traditional equal-area method is too conservative is overcome, meanwhile, compared with a traditional transient stability analysis method needing iteration, the method does not need to solve a nonlinear differential equation through complex numerical iteration, an explicit transient stability boundary can be obtained, and the method is suitable for being used for transient stability analysis. And the method is also used for the grid-forming inverter with droop control and virtual synchronous machine control of a linear damping item, and an effective method with high analyzability and low complexity is provided for transient stability analysis of the grid-forming inverter. And the method has good practical application value.

Description

Technical Field

[0001] This invention belongs to the field of DC / AC converters, and more specifically, relates to a transient stability analysis method for hybrid synchronous control grid-type inverters that takes into account the damping effect. Background Technology

[0002] In recent years, with the continuous increase in the penetration rate of renewable energy based on inverters, grid-connected inverters with virtual inertia have become a research hotspot due to their excellent voltage and frequency support capabilities. However, these inverters face severe transient stability problems. Hybrid synchronous control methods have shown great application potential in addressing this issue. Hybrid synchronous control introduces additional nonlinear damping terms, effectively improving the transient stability of grid-connected inverter systems. However, the presence of nonlinear damping terms further exacerbates the nonlinear characteristics of the system, making transient stability analysis more complex. While time-domain numerical analysis can realistically reflect the system's operating trajectory, the extensive numerical calculations make the determination of the stability boundary dependent on exhaustive search, making quantitative analysis difficult. Traditional equal-area rule analysis simplifies the analysis, but neglecting the damping term leads to overly conservative calculation results, limiting practical analysis and design. While iterative equal-area rule analysis can account for damping effects through iteration and achieves high computational accuracy, the lack of explicit calculation processes results in low accuracy at low iteration counts and convergence problems. At high iteration counts, the calculation becomes more complex, reducing computational speed and weakening analytical capabilities.

[0003] The three main methods for transient stability analysis currently available include time-domain simulation, manifold analysis, and energy methods. While time-domain simulation, such as time-domain numerical methods, is simple to implement and can realistically reflect the system's trajectory and intuitively determine its transient stability, it relies heavily on numerical calculations. Its physical meaning is unclear, obscuring the impact of various parameters on performance and making it difficult to fundamentally analyze the system's transient stability mechanism. Furthermore, the determination of the stability boundary essentially relies on exhaustive search, which is insufficient for guiding practical design. Although manifold analysis can study transient stability by analyzing the system's attraction domain boundaries, bifurcation analysis involves very in-depth mathematical analysis, making it overly complex in practical applications. For the reasons mentioned above, the energy method is currently the main method used to analyze the transient and steady-state properties of grid-connected inverters. The energy method mainly includes the classical equal-area method, which is essentially an extension of Lyapunov's second method. It uses a suitable energy function to characterize the transient behavior of the system. Compared with the time-domain simulation method, it has an explicit energy function, which is more convenient for quantitative analysis. Compared with the manifold analysis method, the energy method has a clear physical meaning and can convert the mathematical model of the grid-connected inverter into a dynamic system, making the analysis simpler and more intuitive.

[0004] However, compared to traditional synchronous generators, grid-connected inverters are characterized by high damping and low inertia. If energy methods (such as the classical equal-area method) that neglect damping effects are used to analyze transient stability, the results are overly conservative, limiting practical analysis and design to some extent. Hybrid synchronous control, compared to traditional grid-connected control (such as droop control and virtual synchronous machine control), introduces additional nonlinear damping terms, further exacerbating the aforementioned problems. Although some methods exist to improve upon this by considering damping effects, such as the iterative equal-area method, which estimates the damping effect and solves the system stability boundary through continuous iteration, achieving high computational accuracy at higher iteration counts, the lack of an explicit computational process limits this approach: insufficient accuracy and convergence issues at low iteration counts, and computational complexity and speed reduction at high iteration counts, while also weakening the analytical nature of energy methods to some extent. Summary of the Invention

[0005] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a transient stability analysis method for hybrid synchronous control grid-type inverters that takes into account the damping effect. This method quantifies the damping effect to a certain extent, eliminates the need for complex numerical iteration to solve nonlinear differential equations, and obtains explicit transient stability boundaries. This enables accurate, reliable, and convenient solution and characterization of the transient stability boundaries of hybrid synchronous control grid-type inverters that take into account the damping effect.

[0006] To achieve the above objectives, according to a first aspect of the present invention, a transient stability analysis method for a grid-type inverter with hybrid synchronous control taking into account damping effects is provided, comprising: S1, the power angle range to be analyzed for the grid-type inverter is... Divide into n groups of length. subinterval ;in, , , The initial angle of attack, The work angle at an unstable equilibrium point; S2, the angle of attack The value is The speed of the grid-type inverter As the initial velocity, the estimation, neglecting damping, is performed in the sub-interval. The velocity distribution function of the grid-type inverter described above ,right The product of the damping term of the grid-type inverter in the sub-interval Integrating the damping term yields the deceleration effect. The potential energy term of the grid-type inverter in the sub-interval Integrating the potential energy term yields the acceleration / deceleration effect. ,Will and Substitute into the formula get The value is The speed of the grid-type inverter Use a linear function to perform the operation. and By performing a linear approximation, we obtain the subintervals. The transient stability boundary of the grid-type inverter described in the article By sequentially iterating through the various values ​​of k, the transient stability boundary of the grid-type inverter within each sub-interval is obtained; where k = 1, 2, ..., n. ; S3, perform stability analysis of the grid-type inverter based on the transient stability boundary of the grid-type inverter in each sub-interval.

[0007] According to a second aspect of the present invention, an electronic device is provided, comprising: a computer-readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method as described in the first aspect.

[0008] According to a third aspect of the invention, a computer-readable storage medium is provided, the computer-readable storage medium storing computer instructions for causing a processor to perform the method as described in the first aspect.

[0009] According to a fourth aspect of the invention, a computer program product is provided, comprising a computer program or instructions that, when executed by a processor, implement the method described in the first aspect.

[0010] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects: The method provided by this invention utilizes the traditional equal-area method to construct an explicit damping-work angle function within each calculation interval to quantify the effect of the damping term. This function is then used to modify the classical equal-area method, thereby estimating the velocity distribution within each calculation interval. This yields an estimate of the transient stability boundary of the hybrid synchronous control grid-type inverter system, taking into account the damping effect, which serves as the basis for judging the system's transient stability. On one hand, by considering the damping effect, the conservatism of the analysis is reduced, improving the accuracy of the transient stability boundary solution. On the other hand, while optimizing accuracy, the results still retain a moderate degree of conservatism compared to the true stability boundary, ensuring the reliability of the analytical conclusions. Furthermore, the explicit solution process avoids complex iterative operations, simplifies the analysis process, and maintains the good analytical performance of the energy method. Ultimately, this achieves a more accurate, reliable, and convenient solution and characterization of the transient stability boundary of the grid-type inverter system.

[0011] In summary, the method provided by this invention can effectively consider the damping effect, thereby improving the accuracy of the characterized transient stability boundary; it eliminates the need for complex numerical iteration to solve nonlinear differential equations and can obtain explicit transient stability boundaries, making it more convenient for practical research and application; it has good versatility and is applicable not only to grid-type inverters with linear damping droop control and virtual synchronous machine control, but also to grid-type inverters with nonlinear damping hybrid synchronous control. Attached Figure Description

[0012] Figure 1 This is the topology and control block diagram of a hybrid synchronous control grid-type inverter system; Figure 2 This is a control block diagram of a hybrid synchronous control loop; Figure 3 This is one of the flowcharts of the transient stability analysis method for hybrid synchronous control grid inverters that takes into account the damping effect provided in the embodiments of the present invention; Figure 4 This is the second flowchart of the transient stability analysis method for hybrid synchronous control grid inverters that takes into account the damping effect provided in the embodiments of the present invention; Figure 5 This is a schematic diagram of the transient stability boundary corresponding to different n under the virtual synchronous machine control (K=0) and D=3p.u. provided in the embodiments of the present invention; Figure 6 This is a schematic diagram of the transient stability boundary corresponding to different n under the virtual synchronous machine control (K=0) and D=35p.u. provided in the embodiments of the present invention; Figure 7 This is a schematic diagram of the transient stability boundary corresponding to different n under the condition of hybrid synchronous control, D=20p.u., K=0.2., KPLL=10, using the method provided in the embodiments of the present invention; Figure 8 This is a schematic diagram of the transient stability boundary corresponding to different n under the condition of hybrid synchronous control, D=20p.u., K=0.8., KPLL=10, using the method provided in the embodiments of the present invention; Figure 9 This is a schematic diagram of the transient stability boundary corresponding to different n under the condition of hybrid synchronous control, D=20p.u., K=0.2., KPLL=30, using the method provided in the embodiments of the present invention. Detailed Implementation

[0013] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0014] The topology and control block diagram of a hybrid synchronous control grid-type inverter system are as follows: Figure 1 As shown, it consists of a grid-connected inverter and a power grid. The grid-connected inverter comprises a main power topology and a control section. Its main power topology includes a three-phase inverter bridge and an LC filter, the LC filter including a filter inductor. L f and filter capacitor C f Its control section includes a hybrid synchronous control loop and virtual reactors. X v Voltage and current control circuits, pulse width modulation module. The power grid includes an ideal AC voltage source and a grid inductor. L g In the picture v a , v b , v c Indicates the voltage at the point of common coupling. i a , i b , i c Indicates the current at the point of common coupling. v ga , v gb , v gc The grid voltage, after undergoing the Parker transformation, yields... dq Voltage and current at the common coupling point of the coordinate system v d , v d ,i d , i q The actual power output of the inverter is calculated, and the inverter electromotive force angle reference is obtained through the hybrid synchronous control loop. θ The voltage amplitude reference is a constant value. E Considering that the bandwidth of the voltage control loop and the current control loop is much larger than that of the hybrid synchronous control module, the dynamics of the voltage and current control loops and the LC filter are ignored.

[0015] The control block diagram of the hybrid synchronous control loop is as follows: Figure 2 As shown, its core is the output voltage angular frequency error. It is obtained by weighting the outputs of the virtual synchronous machine control and the phase-locked loop. P ref This represents the reference value for active power. J and D Let 1 represent the inertia coefficient and damping coefficient of the virtual synchronous machine control, respectively. K and K These represent the weighting coefficients for the virtual synchronous machine control and the phase-locked loop (PLL); the PLL uses a proportional gain... K PLL The first order is achieved dq - Phase-locked loop (PLL). ω 0 represents the angular frequency reference value. ω This is the angular frequency of the output voltage. ω The electromotive force angle reference is obtained through integration. θ , P This represents the actual active power output of the inverter. v q PCC voltage q To prevent excessive negative damping introduced by the hybrid synchronous control from causing the total damping to be negative, which would severely compromise the system's transient stability, the shaft component is designed... K PLL The time should satisfy the formula ,in V ge Indicates the rated grid voltage amplitude. X Σ This represents the total reactance, which is the sum of the grid reactance and the virtual reactance. X Σ = X g + X v , grid reactance X g =j ω 0 L g ).

[0016] Taking damping effects into account and quantifying these effects to simplify the analysis method is currently key to improving transient stability analysis methods. Based on this, this invention provides a transient stability analysis method for a hybrid synchronous control grid-type inverter that takes damping effects into account, including: S1, the power angle range to be analyzed for the grid-type inverter is... Divide into n groups of length. subinterval ;in, The initial power angle of the system is determined by the initial operating state of the system. The work angle at an unstable equilibrium point is calculated using the following formula: , , , j=1,2,…,n+1; S2, the angle of attack The value is The speed of the grid-type inverter As the initial velocity, the estimation, neglecting damping, is performed in the sub-interval. The velocity distribution function of the grid-type inverter described above ,right The product of the damping term of the grid-type inverter in the sub-interval Integrating the damping term yields the deceleration effect. The potential energy term of the grid-type inverter in the sub-interval Integrating the potential energy term yields the acceleration / deceleration effect. ,Will and Substitute into the formula get The value is The speed of the grid-type inverter Use a linear function to perform the operation. and By performing a linear approximation, we obtain the subintervals. The transient stability boundary of the grid-type inverter described in the article ; sequentially traverse each value of k to obtain the transient stability boundary of the grid-type inverter in each sub-interval; where k=1,2,…,n; S3, perform stability analysis of the grid-type inverter based on the transient stability boundary of the grid-type inverter in each sub-interval.

[0017] Specifically, such as Figure 3 As shown, the method provided in this embodiment of the invention includes the following steps: 1. System structure of grid-type inverter based on hybrid synchronous control: Establish the dynamic model of grid-type inverter with hybrid synchronous control, the expression of which is: (1) 0 ≤ K ≤ 1. This means that when K = 0, it can be equivalent to virtual synchronous machine control; when K = 1, it can be equivalent to phase-locked loop (PLL) control; and when 0 < K < 1, it can be equivalent to a combination of virtual synchronous machine control and PLL control. Furthermore, to avoid ambiguity, this invention specifies... The direction of increase is positive, and the descriptions of acceleration and deceleration effects are consistent with the actual physical process, namely equation (1).

[0018] 2. Based on the above mathematical model, considering that the critical stability boundary of the system is composed of the stable manifold of the unstable equilibrium point, the system's trajectory can be deduced from the unstable equilibrium point as the transient stability boundary of the system. By changing the sign of the damping term in equation (1), the inverse trajectory dynamic model is obtained to describe the trajectory, as shown in equation (2).

[0019] (2) 3. Definition δ The power angle of the system ( δ=θ - ω 0 t ), Δ ω The system velocity (Δ) ω = ω - ω 0), Set the range of the angle to be analyzed. Given the number of subintervals n, the interval Divided into n subintervals The length of each subinterval is ,in, , , j=1,2,…,n+1; Assume If the system is in a critically stable state, then δ The speed of the system at point 1 is .

[0020] Understandably, the number of subintervals, n, can be arbitrarily set as the number of solutions. Higher values ​​of n result in higher computational accuracy, while lower values ​​of n reduce computational complexity.

[0021] 4. For example Figure 4 As shown, the system is calculated using the equal area rule when damping is neglected. Exercise velocity distribution function during the process As shown in the following formula, .

[0022] (3) Understandably, this formula is essentially derived from the system's... Exercise The final state of the process ( , The velocity distribution function is obtained by inversely calculating the trajectory. Since damping is neglected, according to the dynamic model of the inverse trajectory, the velocity distribution function solved by this formula is lower than the true value, and therefore has a certain degree of conservatism.

[0023] 5. The velocity distribution function calculated using equation (3) Calculation in the system by Exercise The damping-work angle function is used to quantify the deceleration effect produced by the damping term during the process.

[0024] (4) Since the velocity distribution function calculated using formula (3) has a certain degree of conservatism, the calculation result of formula (4) also has a degree of conservatism.

[0025] 6. Utilizing the traditional equal area rule, the area of ​​the system can be directly and accurately calculated. Exercise The acceleration and deceleration effects generated by the potential energy term during the process.

[0026] (5) Understandably, in Within the interval, the potential energy term produces an accelerating effect. Within the interval, the potential energy term produces a deceleration effect; therefore, the potential energy term is defined as producing an acceleration or deceleration effect, i.e., acceleration and / or deceleration. Wherein, The formula for calculating the work angle at the stable equilibrium point is as follows: .

[0027] 7. Calculate the deceleration effect using the estimated damping term and the acceleration / deceleration effect using the potential energy term. The speed of the system .

[0028] (6) Since the deceleration effect of the damping term estimated by formula (4) is somewhat conservative, the calculation result of formula (6) is also conservative.

[0029] 8. Repeat steps 4-7. Note that the velocity distribution function should be solved using the equal area method in subsequent calculations. When (k=2,3,4…n), the system has The initial velocity is shown in the following formula, and the rest of the process is the same as above.

[0030] (7) Understandably, this formula is essentially derived from the system's... Exercise The final state of the process ( , This is obtained by inverse calculation using the inverse trajectory. Therefore, in estimation... The time used is .

[0031] Since damping is ignored, according to the inverse trajectory dynamics model, the velocity distribution function solved by this formula is lower than the true value, and therefore has a certain degree of conservatism.

[0032] 9. The solution can be obtained through the above calculations. velocity at that point , ,…, , ,…, By using a linear approximation with a linear function, the transient stability boundary of the system in different computational intervals can be obtained.

[0033] (8) For interval The transient stability boundary of the internal system.

[0034] Considering the conservatism of the previous steps, the final calculated transient stability boundary is also conservative, ensuring the reliability of the method in the analysis.

[0035] 10. Based on the transient stability boundary of the system, the transient stability is determined. When the system trajectory (which can be obtained by solving equation (1) using the ode45 function in Matlab) exceeds the transient stability boundary, the system is unstable; otherwise, it is stable.

[0036] Figure 5 The method provided in the embodiments of this invention is used in hybrid synchronous control ( K =0, which can be equivalent to virtual synchronous machine control). D =3p.u., schematic diagram of transient stability boundary corresponding to different n in the case, since DThe method proposed in this invention uses a linearized approximation for the transient stable boundary, which adds a degree of conservatism to the calculation. This makes the estimation deviation using the classical equal area rule smaller than the estimation deviation for n=2 (the minimum number of intervals). When n=3, the method proposed in this invention is superior to the classical equal area rule. As n increases, the estimation deviation of the method proposed in this invention decreases, and when n=10, the estimated boundary almost coincides with the true boundary.

[0037] Figure 6 The method provided in the embodiments of this invention is used in hybrid synchronization control. K =0, which can be equivalent to virtual synchronous machine control). D =35p.u., schematic diagram of transient stability boundary corresponding to different n in the case, since D The large area of ​​the curve leads to a significant estimation error in the transient stable boundary calculated by the classical equal area rule. Compared with the classical equal area rule, the estimation error of the method proposed in this invention is significantly reduced. When n=2, the method proposed in this invention is superior to the classical equal area rule. As n increases, the estimation error of the method proposed in this invention decreases, and when n=10, the estimated boundary deviates very little from the true boundary.

[0038] Figure 7 The method provided in the embodiments of this invention is used in hybrid synchronous control. D =20p.u., K =0.2. K PLL =10, the schematic diagram of the transient stability boundary corresponding to different n. The hybrid synchronous control introduces an additional damping term, which further increases the influence of damping. At this time, the transient stability boundary calculated by the classical equal area method has a large estimation error. As n increases, the estimation error of the method proposed in this invention decreases. Compared with the traditional equal area method, the estimation error of the method proposed in this invention is significantly reduced. Figure 8 The method provided in the embodiments of this invention is used in hybrid synchronous control. D =20p.u., K =0.8. K PLL =10, schematic diagram of transient stability boundary corresponding to different n; hybrid synchronous control introduces an additional damping term, and as... K As n increases, the additional damping term also increases, leading to a greater impact of damping. In this case, the transient stability boundary calculated using the classical equal-area method has a significant estimation error. However, as n increases, the estimation error of the method proposed in this invention decreases. Compared to the traditional equal-area method, the estimation error of the method proposed in this invention is significantly reduced. Figure 9The method provided in the embodiments of this invention is used in hybrid synchronous control. D =20p.u., K =0.2. K PLL =30, schematic diagram of transient stability boundary corresponding to different n; hybrid synchronous control introduces an additional damping term, and as... K PLL As n increases, the additional damping term also increases, leading to a greater impact of damping. In this case, the transient stability boundary calculated using the classical equal-area rule has a significant estimation error. However, as n increases, the estimation error of the method proposed in this invention decreases. Compared to the traditional equal-area rule, the estimation error of the method proposed in this invention is significantly reduced.

[0039] This invention provides an electronic device, including: a computer-readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method as described in any of the above embodiments.

[0040] This invention provides a computer-readable storage medium storing computer instructions that cause a processor to perform the method described in any of the above embodiments.

[0041] This invention provides a computer program product, including a computer program or instructions, which, when executed by a processor, implement the method described in any of the above embodiments.

[0042] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A transient stability analysis method for a grid-type inverter with hybrid synchronous control taking into account damping effects, characterized in that, include: S1, the power angle range to be analyzed for the grid-type inverter is... Divide into n groups of length. subintervals ;in, , , The initial angle of attack, The work angle at an unstable equilibrium point; S2, the angle of attack The value is The speed of the grid-type inverter As the initial velocity, the estimation, neglecting damping, is performed in the sub-interval. The velocity distribution function of the grid-type inverter described above ,right The product of the damping term of the grid-type inverter in the sub-interval Integrating the damping term yields the deceleration effect. The potential energy term of the grid-type inverter in the sub-interval Integrating the potential energy term yields the acceleration / deceleration effect. ,Will and Substitute into the formula get The value is The speed of the grid-type inverter Use a linear function to perform the operation. and By performing a linear approximation, we obtain the subintervals. The transient stability boundary of the grid-type inverter described in the article By sequentially iterating through the various values ​​of k, the transient stability boundary of the grid-type inverter within each sub-interval is obtained; where k = 1, 2, ..., n. , , These are the inertia coefficient and weighting coefficient for virtual synchronous machine control, respectively. S3, perform stability analysis of the grid-type inverter based on the transient stability boundary of the grid-type inverter in each sub-interval.

2. The method as described in claim 1, characterized in that, The calculation formula is: in, This is a reference value for active power. The damping coefficient for virtual synchronous machine control. For total reactance, and These are the weighting coefficients for virtual synchronous machine control and phase-locked loop, respectively. For virtual reactance, This represents the current grid voltage amplitude. This is a reference value for voltage amplitude. For total reactance, This is the proportional gain of the phase-locked loop.

3. The method as described in claim 1 or 2, characterized in that, The potential energy term of the grid-type inverter is: ; This is a reference value for active power. The damping coefficient for virtual synchronous machine control. For total reactance, and These are the weighting coefficients for virtual synchronous machine control and phase-locked loop, respectively. For virtual reactance, This represents the current grid voltage amplitude. This is a reference value for voltage amplitude. For total reactance, This is the proportional gain of the phase-locked loop.

4. The method as described in claim 1 or 2, characterized in that, The damping term of the grid-type inverter is: ; This is a reference value for active power. and These are the inertia coefficient and damping coefficient of the virtual synchronous machine control, respectively. For total reactance, and These are the weighting coefficients for virtual synchronous machine control and phase-locked loop, respectively. For virtual reactance, This represents the current grid voltage amplitude. This is a reference value for voltage amplitude. For total reactance, For the phase-locked loop proportional gain, For the output voltage angular frequency error, , The output voltage angular frequency, This is the reference value for angular frequency.

5. An electronic device, characterized in that, include: Computer-readable storage media and processors; The computer-readable storage medium is used to store executable instructions; The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method as described in any one of claims 1-4.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for causing a processor to perform the method as described in any one of claims 1-4.

7. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by a processor, they implement the method as described in any one of claims 1-4.

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