Robust stability analysis method for grid-connected rectifier under weak power grid

Abstract

The invention discloses a robust stability analysis method for a grid-connected rectifier under a weak power grid, and the method comprises the following steps: S1, building a differential equation for connecting the grid-connected rectifier to the weak power grid, and describing the dynamic behavior of a system; s2, obtaining a disturbance model of the system by using a structure disturbance theory; s3, under different disturbance levels, solving Hopf bifurcation points of the system by using a bifurcation theory and constructing a bifurcation diagram; s4, aiming at Hopf bifurcation points under different disturbance levels, adopting a singular perturbation theory to track an evolution law of a limit cycle; and S5, visually displaying the instability path of the grid-connected rectifier under the weak power grid by analyzing the bifurcation diagram and the phase diagram corresponding to the limit cycle. According to the method, the instability mechanism of the grid-connected rectifier under the weak power grid condition can be accurately analyzed, and theoretical support is provided for system design and operation.

Description

Technical Field

[0001] The present invention relates to the technical field of distributed energy grid connection, and in particular to a robust stability analysis method of a grid-connected rectifier under a weak power grid. Background Art

[0002] With the continuous increase in the penetration rate of new energy, the access of intermittent energy such as wind power and photovoltaics has significantly changed the dynamic characteristics of traditional power grids, making the power grid show more and more significant "weak" characteristics, including high impedance, low short-circuit ratio, low inertia and other problems. Under weak grid conditions, the complex nonlinear interaction between the grid-connected rectifier and the grid may cause system instability. Therefore, studying the robust stability and instability path of the grid-connected rectifier under weak grid conditions can provide effective guidance for system parameter adjustment.

[0003] In existing research, in order to simplify the analysis process, the dynamic characteristics of the grid-connected rectifier current loop are usually ignored, and linear analysis methods such as small signal analysis and impedance analysis are mainly used. However, these methods fail to fully reveal the nonlinear characteristics in the system, resulting in limitations in the assessment of system stability and difficulty in accurately identifying the formation mechanism of the instability path. The limitations of the above analysis methods significantly restrict the effectiveness of system design and operation optimization, and it is difficult to meet the needs of grid-connected rectifier stability and reliability assessment under weak grid conditions. Summary of the invention

[0004] In order to solve the problem of evaluating the stability and reliability of a grid-connected rectifier under weak power grid conditions, the present invention proposes a robust stability analysis method for a grid-connected rectifier under weak power grid conditions to solve the above problem.

[0005] The present application discloses a robust stability analysis method for a grid-connected rectifier under a weak power grid, comprising the following steps: S1. Establish the differential equation of the grid-connected rectifier connected to the weak grid to describe the dynamic behavior of the system; S2. Based on the differential equation of the grid-connected rectifier connected to the weak power grid, the disturbance model of the system is obtained using the structural disturbance theory; S3. Under different disturbance levels, the bifurcation theory is used to solve the Hopf bifurcation point of the system and construct the bifurcation diagram; S4. For Hopf bifurcation points under different disturbance levels, singular perturbation theory is used to track the evolution of limit cycles; S5. By analyzing the bifurcation diagram and the phase diagram corresponding to the limit cycle, the instability path of the grid-connected rectifier under a weak power grid is intuitively displayed, and the robustness of the system is directly determined.

[0006] Preferably, the S1 comprises the following steps: S11. Build a phase-locked loop model:

[0007] in, , and is the state variable of the phase-locked loop, and is the PI control coefficient of the phase-locked loop, is the q-axis component of the voltage at the PCC point, is the AC grid frequency, is the ideal value of AC grid frequency; S12. Construct a model of the voltage loop:

[0008] in, is the DC voltage on the rectifier side, For voltage The reference value of is the state variable of the voltage controller, is the d-axis component of the rectifier side voltage, is the q-axis component of the rectifier side voltage, is the d-axis component of the current flowing through the filter inductor, is the q-axis component of the current flowing through the filter inductor, is the DC bus capacitance of the grid-connected rectifier, is the DC bus load resistance of the grid-connected rectifier; S13. Construct a model of the current loop:

[0009]

[0010] in, and is the state variable of the current controller, for The d-axis component of the current, for The q-axis component of the current, for The reference value of for The reference value of , and is the PI control coefficient of voltage control, is the voltage on the rectifier side The reference value of is the voltage on the rectifier side The reference value of and is the PI control coefficient of voltage control; S14. Construct the dynamic model of delay module, LCL filter and grid impedance:

[0011]

[0012]

[0013]

[0014] in, is the delay period, is the filter inductance, is the filter capacitance, for The stray resistance of is the d-axis component of the filter capacitance and stray resistance voltage, is the q-axis component of the filter capacitor and stray resistance voltage, is the d-axis component of the filter capacitor voltage, is the q-axis component of the filter capacitor voltage, and is the line inductance, for The corresponding resistor, for The corresponding resistor, is the d-axis component of the weak AC grid voltage, is the q-axis component of the weak AC grid voltage; S15. Combining S11-S14, we get the differential equation of the grid-connected rectifier connected to the weak grid, where the state vector is:

[0015] The differential equation of the grid-connected rectifier connected to a weak grid is:

[0016] in, is the state matrix of the system.

[0017] Preferably, the disturbance model of the system is:

[0018] Among them, the matrix is the structured perturbation of the differential equation of the grid-connected rectifier connected to the weak grid, the matrix and All of them reflect the structural information of the perturbation, and the matrix represents an unknown disturbance; If the system has multiple disturbances , then the disturbance model of the system is:

[0019] like , , , then The perturbation model and formula shown The perturbation models shown are of the same form.

[0020] Preferably, S3 comprises the following steps: Assumptions is a parameter disturbance degree measurement indicator, using the formula Or Constructing a grid-connected rectifier to access a weak grid , and disturbance model for disturbance levels; against , and The disturbance model of the disturbance level uses bifurcation theory to detect the location of the Hopf bifurcation point and construct the bifurcation diagram of the system based on it.

[0021] Preferably, the detecting the position of the Hopf bifurcation point by using bifurcation theory comprises the following steps: Formula (10) can be expressed as ,in represents the bifurcation parameter, when When, meet There exists a pair of purely imaginary eigenvalues ​​in and , then the system is at point A Hopf bifurcation occurs. represents the eigenvalue, is the imaginary part of the eigenvalue.

[0022] Preferably, S4 comprises the following steps: Taking the Hopf bifurcation point as the starting point, the singular perturbation theory is used to analyze the evolution process of the limit cycle under parameter changes, further revealing the dynamic characteristics of the limit cycle.

[0023] Preferably, the evolution process of the limit cycle of the system under parameter changes using singular perturbation theory is shown in the following formula:

[0024] in, is the amplitude of the limit cycle, and is the partial derivative with respect to the time scale, is a small parameter, .

[0025] Preferably, S5 comprises the following steps: Under a certain disturbance level, the instability path of the system is revealed by combining the changing trend of the limit cycle generated by the Hopf bifurcation and the stability of the limit cycle; By comparing and analyzing the bifurcation diagrams of the system under different disturbance levels, the robust stability of the system can be further judged, thus providing effective guidance for the adjustment of system parameters.

[0026] Beneficial effects of the present invention: (1) The present invention fully considers the interaction between dynamic links when the grid-connected rectifier is connected to a weak power grid system. Combining bifurcation theory and structural perturbation theory, the robust stability characteristics of the system are systematically studied, the influence of parameters on system stability is clarified, and a comprehensive and specific guiding basis is provided for optimizing system parameter adjustment.

[0027] (2) Through bifurcation analysis and limit cycle tracking, the present invention intuitively demonstrates the instability path of the grid-connected rectifier under weak grid conditions, clearly reveals the dynamic evolution law during the system instability process, and provides scientific and reliable theoretical support for the optimal control design of the system and the in-depth understanding of the instability mechanism. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 A flowchart of a robust stability analysis method for a grid-connected rectifier under a weak power grid according to an embodiment of the present invention; Figure 2 A structural diagram of a grid-connected rectifier connected to a weak power grid system according to an embodiment of the present invention; Figure 3 is a system bifurcation diagram of an embodiment of the present invention; Figure 4 1 is a bifurcation diagram under different disturbance levels of an embodiment of the present invention; Figure 5 is a phase diagram of a system limit cycle of an embodiment of the present invention; Figure 6 is a stable region phase diagram of an embodiment of the present invention; Figure 7 It is a time domain diagram of a stable region according to an embodiment of the present invention; Figure 8 This is a phase diagram of the unstable limit cycle region of an embodiment of the present invention. DETAILED DESCRIPTION

[0029] In order to make the objectives, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below with reference to the accompanying drawings and examples.

[0030] The embodiment of the present invention discloses a robust stability analysis method for a grid-connected rectifier under a weak power grid. The structure of the grid-connected rectifier connected to the weak power grid system is as follows: Figure 2 As shown, Figure 2 middle is the AC grid voltage, is the impedance, is the PCC point voltage, for and The voltage, is the damping resistor. Figure 1 The steps shown are used to analyze the system. The specific steps are as follows: S1. System modeling: Establish the differential equation of the grid-connected rectifier connected to the weak power grid to describe the dynamic behavior of the system.

[0031] S11. Build a phase-locked loop model:

[0032] in, , and is the state variable of the phase-locked loop, and is the PI control coefficient of the phase-locked loop, is the q-axis component of the voltage at the PCC point, is the AC grid frequency, is the ideal value of the AC grid frequency.

[0033] S12. Construct a model of the voltage loop:

[0034] in, is the DC voltage on the rectifier side, For voltage The reference value of is the state variable of the voltage controller, is the d-axis component of the rectifier side voltage, is the q-axis component of the rectifier side voltage, is the d-axis component of the current flowing through the filter inductor, is the q-axis component of the current flowing through the filter inductor, is the DC bus capacitance of the grid-connected rectifier, is the DC bus load resistance of the grid-connected rectifier.

[0035] S13. Construct a model of the current loop:

[0036]

[0037] in, and is the state variable of the current controller, for The d-axis component of the current, for The q-axis component of the current, for The reference value of for The reference value of , and is the PI control coefficient of voltage control, is the voltage on the rectifier side The reference value of is the voltage on the rectifier side The reference value of and is the PI control coefficient of voltage control.

[0038] S14. Construct the dynamic model of delay module, LCL filter and grid impedance:

[0039]

[0040]

[0041]

[0042] in, is the delay period, is the filter inductance, is the filter capacitance, for The stray resistance of is the d-axis component of the filter capacitance and stray resistance voltage, is the q-axis component of the filter capacitor and stray resistance voltage, is the d-axis component of the filter capacitor voltage, is the q-axis component of the filter capacitor voltage, and is the line inductance, for The corresponding resistor, for The corresponding resistor, is the d-axis component of the weak AC grid voltage, is the q-axis component of the weak AC grid voltage.

[0043] S15. Combining S11-S14, we get the differential equation of the grid-connected rectifier connected to the weak grid, where the state vector is:

[0044] The differential equation of the grid-connected rectifier connected to a weak grid is:

[0045] in, is the state matrix of the system.

[0046] S2. Disturbance modeling: Based on the differential equation of the grid-connected rectifier connected to the weak grid, the disturbance model of the system is obtained using the structural disturbance theory as follows:

[0047] Among them, the matrix is the structured perturbation of the differential equation of the grid-connected rectifier connected to the weak grid, the matrix and All of them reflect the structural information of the perturbation, and the matrix represents an unknown disturbance; If the system has multiple disturbances , then the disturbance model of the system, that is, equation (11), can be expressed as:

[0048] like , , , then The perturbation model and formula shown The perturbation models shown are of the same form.

[0049] S3. Solve the bifurcation diagram based on bifurcation theory: Under different disturbance levels, use the bifurcation theory to solve the Hopf bifurcation point of the system and construct the bifurcation diagram.

[0050] Assumptions is a parameter disturbance degree measurement indicator, using the formula Or Constructing a grid-connected rectifier to access a weak grid , and disturbance model for disturbance levels; against , and The disturbance model of the disturbance level uses bifurcation theory to detect the location of the Hopf bifurcation point, and constructs the bifurcation diagram of the system based on it. Using bifurcation theory to detect the location of the Hopf bifurcation point includes the following steps: Formula (10) can be expressed as ,in represents the bifurcation parameter, when When, meet There exists a pair of purely imaginary eigenvalues ​​in and , then the system is at point A Hopf bifurcation occurs. represents the eigenvalue, is the imaginary part of the eigenvalue. In this embodiment, the system bifurcation diagram drawn by combining S1, S2 and S3 is as follows Figure 3 , Figure 4 shown.

[0051] S4. Evolution law of limit cycles: For Hopf bifurcation points under different perturbation levels, the singular perturbation theory is used to track the evolution law of limit cycles.

[0052] Taking the Hopf bifurcation point as the starting point, the singular perturbation theory is used to analyze the evolution of the limit cycle under parameter changes, further revealing the dynamic characteristics of the limit cycle. The evolution process of the limit cycle is shown in the following formula:

[0053] in, is the amplitude of the limit cycle, and is the partial derivative with respect to the time scale, is a small parameter, .

[0054] Based on the bifurcation diagram of the system drawn by S3, the limit cycle traced by singular perturbation theory is obtained as follows Figure 5 shown.

[0055] S5. Analyze robust stability and instability path: By analyzing the bifurcation diagram and the phase diagram corresponding to the limit cycle, the instability path of the grid-connected rectifier under a weak power grid is intuitively displayed, and the robustness of the system is directly determined. For a certain disturbance level, the instability path of the system is revealed by combining the change trend of the limit cycle generated by the Hopf bifurcation and the stability of the limit cycle; then, by comparing and analyzing the bifurcation diagrams of the system under different disturbance levels, the robust stability of the system is further determined, thereby providing effective guidance for the adjustment of system parameters. Specifically, the following steps are included: Bifurcation analysis and stability study: In the AC power grid connected to the grid-connected system, the line inductance This will weaken the stability of the AC power grid. To analyze its impact, in this embodiment, the line inductance As the key control variable of bifurcation analysis, the results are as follows Figure 3 As shown: when When , the system will undergo Hopf bifurcation; when When , the system will have Saddle-node bifurcation; The above bifurcation behaviors reveal the significant impact of parameter changes on system stability and dynamic behavior, and provide a theoretical basis for optimizing the operation of grid-connected rectifiers.

[0056] Robust stability analysis: This embodiment is based on the structural perturbation theory and focuses on line inductance. exist , and Under the three disturbance levels, the corresponding disturbance models were constructed and the following plots were made: Figure 4 The bifurcation diagram of the system shown is given by Figure 4 It can be seen that: As the disturbance level increases, the DC bus load resistance of the grid rectifier The stability range of is gradually reduced. In particular, when the disturbance level reaches When , the system adds two new Hopf bifurcation points, which significantly complicates the bifurcation characteristics of the system. This shows that the sensitivity of the system to structural disturbances significantly affects its stability and dynamic behavior. In order to improve the robustness of the system, it can be combined with Figure 3 and Figure 4 Based on the analysis results in , the system parameters are optimized and adjusted to make it run in the stable area, thus achieving the coordination of stability and robustness.

[0057] Instability path analysis: Figure 5 In this embodiment, Figure 3 The limit cycle of the Hopf bifurcation point shown is traced and analyzed. The following results are obtained: The stable limit cycle of the system extends to the unstable region. After extending to a certain region, the system undergoes period-doubling bifurcation, and the stable limit cycle transforms into an unstable limit cycle. Finally, after two folding bifurcations, the limit cycle of the system disappears completely. Figure 3 , Figure 5 The analysis can intuitively reveal the instability path of the system and its dynamic evolution characteristics, providing an important basis for system operation optimization.

[0058] Typical scenario verification: Figure 6 , Figure 7 and Figure 8 Corresponding to Figure 3 There are three typical cases of bifurcation diagrams, specifically: Figure 6 (L s =7.7mH): the system is in a stable state; Figure 7 (L s =8.5mH): The system converges to the stable limit cycle after a certain oscillation; Figure 8 (L s =10.3mH): The system loses stability after oscillation.

[0059] The analysis results of the above typical scenarios further prove that Figure 3 The accuracy and effectiveness of the bifurcation analysis in this paper support the comprehensive description of the system dynamics characteristics in this application.

[0060] In summary, this application fully considers the interaction between dynamic links when the grid-connected rectifier is connected to a weak power grid system, and combines bifurcation theory and structural perturbation theory to systematically study the robust stability characteristics of the system. Through analysis, the influence of parameters on system stability is clarified, providing a comprehensive and specific guidance basis for optimizing system parameter adjustment. At the same time, this application intuitively shows the instability path of the grid-connected rectifier under weak power grid conditions through bifurcation analysis and limit cycle tracking, clearly reveals the dynamic evolution law during the system instability process, and provides scientific and reliable theoretical support for the optimal control design of the system and the in-depth understanding of the instability mechanism.

[0061] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A robust stability analysis method for a grid-connected rectifier under a weak power grid, characterized in that: The following steps are involved: S1. Establish the differential equation of the grid-connected rectifier connected to the weak grid to describe the dynamic behavior of the system; S2. Based on the differential equation of the grid-connected rectifier connected to the weak power grid, the disturbance model of the system is obtained using the structural disturbance theory; S3. Under different disturbance levels, the bifurcation theory is used to solve the Hopf bifurcation point of the system and construct the bifurcation diagram; S4. For Hopf bifurcation points under different disturbance levels, singular perturbation theory is used to track the evolution of limit cycles; S5. By analyzing the bifurcation diagram and the phase diagram corresponding to the limit cycle, the instability path of the grid-connected rectifier under a weak power grid is intuitively displayed, and the robustness of the system is directly determined.

2. The robust stability analysis method of a grid-connected rectifier under a weak power grid according to claim 1, characterized in that: The S1 comprises the following steps: S11. Build a phase-locked loop model: in, , and is the state variable of the phase-locked loop, and is the PI control coefficient of the phase-locked loop, is the q-axis component of the voltage at the PCC point, is the AC grid frequency, is the ideal value of AC grid frequency; S12. Construct a model of the voltage loop: in, is the DC voltage on the rectifier side, For voltage The reference value of is the state variable of the voltage controller, is the d-axis component of the rectifier side voltage, is the q-axis component of the rectifier side voltage, is the d-axis component of the current flowing through the filter inductor, is the q-axis component of the current flowing through the filter inductor, is the DC bus capacitance of the grid-connected rectifier, is the DC bus load resistance of the grid-connected rectifier; S13. Construct a model of the current loop: in, and is the state variable of the current controller, for The d-axis component of the current, for The q-axis component of the current, for The reference value of for The reference value of , and is the PI control coefficient of voltage control, is the voltage on the rectifier side The reference value of is the voltage on the rectifier side The reference value of and is the PI control coefficient of voltage control; S14. Construct the dynamic model of delay module, LCL filter and grid impedance: in, is the delay period, is the filter inductance, is the filter capacitance, for The stray resistance of is the d-axis component of the filter capacitance and stray resistance voltage, is the q-axis component of the filter capacitor and stray resistance voltage, is the d-axis component of the filter capacitor voltage, is the q-axis component of the filter capacitor voltage, and is the line inductance, for The corresponding resistor, for The corresponding resistor, is the d-axis component of the weak AC grid voltage, is the q-axis component of the weak AC grid voltage; S15. Combining S11-S14, we get the differential equation of the grid-connected rectifier connected to the weak grid, where the state vector is: The differential equation of the grid-connected rectifier connected to a weak grid is: in, is the state matrix of the system.

3. The robust stability analysis method of a grid-connected rectifier under a weak power grid according to claim 2, characterized in that: The disturbance model of the system is: Among them, the matrix is the structured perturbation of the differential equation of the grid-connected rectifier connected to the weak grid, the matrix and All of them reflect the structural information of the perturbation, and the matrix represents an unknown disturbance; If the system has multiple disturbances , then the disturbance model of the system is: like , , , then The perturbation model and formula shown The perturbation models shown are of the same form.

4. The robust stability analysis method of a grid-connected rectifier under a weak power grid according to claim 3, characterized in that: The S3 comprises the following steps: Assumptions is a parameter disturbance degree measurement indicator, using the formula Or Constructing a grid-connected rectifier to access a weak grid , and disturbance model for disturbance levels; against , and The disturbance model of the disturbance level uses bifurcation theory to detect the location of the Hopf bifurcation point and construct the bifurcation diagram of the system based on it.

5. The robust stability analysis method of a grid-connected rectifier under a weak power grid according to claim 4, characterized in that: The method of detecting the position of the Hopf bifurcation point by using bifurcation theory comprises the following steps: Formula (10) can be expressed as ,in represents the bifurcation parameter, when When, meet There exists a pair of purely imaginary eigenvalues ​​in and , then the system is at point A Hopf bifurcation occurs. represents the eigenvalue, is the imaginary part of the eigenvalue.

6. The robust stability analysis method of a grid-connected rectifier under a weak power grid according to claim 5, characterized in that: The S4 comprises the following steps: Taking the Hopf bifurcation point as the starting point, the singular perturbation theory is used to analyze the evolution process of the limit cycle under parameter changes, further revealing the dynamic characteristics of the limit cycle.

7. The robust stability analysis method of a grid-connected rectifier under a weak power grid according to claim 6, characterized in that: The evolution process of the limit cycle of the system under parameter changes using singular perturbation theory is shown in the following formula: in, is the amplitude of the limit cycle, and is the partial derivative with respect to the time scale, is a small parameter, .

8. The robust stability analysis method of a grid-connected rectifier under a weak power grid according to claim 7, characterized in that: The S5 comprises the following steps: Under a certain disturbance level, the instability path of the system is revealed by combining the changing trend of the limit cycle generated by the Hopf bifurcation and the stability of the limit cycle; By comparing and analyzing the bifurcation diagrams of the system under different disturbance levels, the robust stability of the system can be further judged, thus providing effective guidance for the adjustment of system parameters.

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