A control performance quantization evaluation method for a network construction converter under stability perspective

Abstract

This invention relates to a quantitative evaluation method for the control performance of grid-connected converters from a stability perspective, belonging to the field of power systems. First, based on a single-phase equivalent model of the grid-connected converter, the modulation voltage is solved. The necessary and sufficient conditions for the existence of real solutions are used to derive the power flow solution boundary, and the voltage over-limit boundary is established in conjunction with modulation ratio constraints, defining the theoretical operating domain of the converter. Based on the theoretical operating domain, a small-signal state-space model is established by combining the main circuit topology and the control system. By analyzing the pole distribution of the converter under different grid impedances, its actual stable operating domain is determined. Finally, by calculating the area ratio of the actual stable operating domain to the theoretical operating domain, a quantitative characterization of the converter's control performance under varying operating conditions is achieved. This method constructs the actual stable operating domain of the grid-connected converter and quantifies the control performance using the area coverage ratio index. This provides a quantitative theoretical benchmark for evaluating its robustness in weak grid environments and guiding parameter optimization design.

Description

Technical Field

[0001] This invention relates to a method for quantitatively evaluating the control performance of grid-connected converters from a stability perspective, belonging to the field of power system technology. Background Technology

[0002] As the proportion of new energy sources in the power system continues to increase, power electronic devices, primarily converters, are largely replacing traditional synchronous generators. This has led to a significant weakening of system inertia and damping characteristics, posing severe challenges to frequency and voltage stability. Grid-based control technology, especially the Virtual Synchronous Generator (VSG), can provide the necessary virtual inertia and damping to the grid by simulating the external characteristics of synchronous generators, becoming crucial for supporting the stable operation of new power systems. However, the randomness of new energy power generation, the volatility of loads, and potential grid fault disturbances make the actual operating conditions of grid-based converters complex and variable. Especially in scenarios with weak grid strength, the complex interaction between the control system and grid impedance can easily lead to instability. Traditional linear stability analysis methods based on specific operating points are insufficient to comprehensively assess the global robustness under a wide range of operating conditions. Therefore, effectively constructing a safe and stable operating domain for the converter in the parameter space is crucial for ensuring system safety and optimizing control design.

[0003] Existing research has focused on deriving theoretical operating boundaries from steady-state power balance equations and physical limits, but this only characterizes the upper limit of the equipment's static capacity and fails to cover the risk of dynamic instability. Due to the interaction of control components in grid-connected converters, some regions within the theoretical operating domain exhibit instability due to control mechanisms. Therefore, a quantitative assessment method that can uniformly consider both steady-state constraints and dynamic stability is urgently needed. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a quantitative evaluation method for the control performance of grid-connected converters from a stability perspective. This method defines the theoretical operating domain of the grid-connected converter and determines its actual stable operating domain by combining small-signal model analysis. Finally, it quantitatively characterizes the control performance by calculating the area ratio of the two domains, i.e., the coverage ratio. This provides a clear quantitative benchmark for objectively evaluating the converter's adaptability under weak grid conditions and guiding its parameter optimization.

[0005] The present invention adopts the following technical solution:

[0006] A method for quantitatively evaluating the control performance of grid-connected converters from a stability perspective includes:

[0007] Step 1: Solve for the modulation voltage based on the single-phase equivalent model of the grid-type converter to determine the power flow solution boundary of the system; determine the voltage limit boundary based on the physical limitation of the modulation ratio; combine the power flow solution boundary and the voltage limit boundary to define the theoretical operating domain of the converter.

[0008] Step 2: Based on the main circuit topology and control system of the grid converter, establish a small-signal state-space model of the grid converter. By analyzing the pole distribution of the grid converter under different grid impedances, determine the actual stable operating domain.

[0009] Step 3: By calculating the area ratio of the theoretical operating domain to the actual stable operating domain, the coverage index is obtained, thereby realizing the quantitative characterization of the control performance of the grid-type converter under various operating conditions.

[0010] In this invention, firstly, the power flow solution boundary is derived based on the steady-state mathematical model of the grid-connected converter. Then, the voltage over-limit boundary of the converter is defined according to physical constraints. These two boundaries together determine the theoretical operating domain of the converter. Secondly, a small-signal model of the grid-connected converter under VSG control is established. Based on the pole distribution under different grid impedances and combined with the theoretical operating domain, its actual stable operating domain is determined. Finally, a coverage index is defined. By calculating the area ratio of the actual operating domain to the theoretical operating domain, a global quantitative index is obtained, thereby achieving an objective and comprehensive evaluation of the adaptability and robustness of the control strategy.

[0011] Preferably, in step 1, based on the single-phase equivalent model of the grid-type converter, the converter output active power equation is as follows:

[0012] (1)

[0013] The converter output reactive power equation is as follows:

[0014] (2)

[0015] The converter output reactive power equation obtained from the control system is as follows:

[0016] (3)

[0017] The reactive power output of the converter is equal to the reactive power output value of the converter obtained from the control system.

[0018] In the formula, For line resistance, For line inductance, This is the real part of the voltage at the point of common coupling (PCC). This represents the imaginary part of the voltage of the PCC. This is the grid voltage. , To output active power and reactive power, This is a reference value for reactive power. The droop coefficient is... This refers to the rated voltage amplitude of the PCC. Let ω be the grid angular frequency; the real part, imaginary part and actual output reactive power of the common coupling voltage of the grid converter can be obtained from equations (1), (2) and (3);

[0019] The modulation voltage equation is established as follows:

[0020] (4)

[0021] In the formula, Modulate the voltage phasor of the converter. For the voltage phasor at the point of common coupling, For grid voltage phasors, The output current phasor on the bridge arm side of the converter. For the line current phasor flowing to the power grid, For the filter branch current phasor, For filtering inductors, For filtering capacitors;

[0022] The modulation voltage based on the grid impedance is By traversing the given range of grid impedance values ​​and discretizing the range of grid impedance values, a global scan of the system's operating state and stability under different operating conditions is achieved. If a stable voltage solution can be obtained by iterative convergence for a certain set of impedance values, then the point is a solvable operating condition; otherwise, if the solution process does not converge or diverges, then the point is an unsolvable boundary point; thus, the solvable boundary of the system's power flow is obtained.

[0023] Preferably, in step 1, the amplitude of the modulation voltage is calculated based on the established modulation voltage equation. ;

[0024] Setting the amplitude of the modulation voltage equal to the upper threshold of the voltage amplitude, we obtain the voltage over-limit boundary with respect to the grid impedance:

[0025] (5)

[0026] In the formula, The upper limit threshold of the voltage amplitude is obtained from equation (6):

[0027] (6)

[0028] In the formula, It is a DC voltage;

[0029] The theoretical operating domain of the grid-type converter is obtained from the power flow solution boundary and the voltage over-limit boundary:

[0030] (7).

[0031] Preferably, the implementation process of step 2 is as follows:

[0032] (2.1) In the dq axis coordinate system, based on Kirchhoff's voltage law and Kirchhoff's current law, establish the nonlinear large-signal differential equation of the converter main circuit;

[0033] (2.2) Integrating the complete control link principle including power calculation, VSG power outer loop, virtual impedance and voltage and current double closed loop, the nonlinear large-signal differential equation of the converter control system is established.

[0034] (2.3) Based on the nonlinear large-signal differential equations of the converter main circuit and control system, the derivative terms of each state variable are set to zero to construct a steady-state algebraic equation system, and the steady-state equilibrium point of the system is determined by solving the equations.

[0035] (2.4) At the steady-state equilibrium point, the nonlinear large-signal differential equation of the converter main circuit is linearized based on the first-order Taylor expansion, thereby obtaining the small-signal state-space equation of the converter main circuit.

[0036] (2.5) At the steady-state equilibrium point, the nonlinear large-signal differential equation of the converter control system is linearized based on the first-order Taylor expansion, thereby obtaining the small-signal state-space equation of the converter control system.

[0037] The linearization process in steps (2.4) and (2.5) specifically refers to: at the obtained steady-state equilibrium point, introducing a small perturbation, applying Taylor series expansion to the nonlinear large-signal differential equation, and truncating and ignoring small nonlinear higher-order terms of second order and above, retaining only the first-order partial derivative terms, thereby transforming the nonlinear differential equation into a linear small-signal state-space equation describing the dynamic characteristics of the system near the steady-state equilibrium point.

[0038] (2.6) By combining the small-signal state-space equations of the main circuit and the control system, the small-signal state-space model of the converter under complete VSG control is obtained as follows:

[0039] (12)

[0040] In the formula, Represents the small-signal state variable at time t. This represents the small-signal input variable at time t. Represents the system matrix. Represents the input matrix;

[0041] The combined small-signal state-space equations of the main circuit and control system are rearranged into standard matrix form, where the small-signal state variables are... The corresponding coefficient matrix is ​​the system state matrix. ;

[0042] The actual stable operating range is determined by the grid resistance R. s With grid inductance L s Within the constructed two-dimensional impedance parameter plane, based on the obtained theoretical operating domain, each impedance operating point in the grid impedance plane is traversed one by one. Then, relying on the constructed small-signal state-space model of the grid-type converter, the system matrix is ​​solved. The characteristic equation is det(λI-A)=0. Several system poles are calculated, and the distribution of system poles corresponding to each impedance operating point is calculated. Where λ represents the system poles and I represents the identity matrix with the same order as the system matrix A.

[0043] Based on the stability criteria of linear systems, operating points with all poles located in the left half of the complex plane are selected and extracted. Finally, the operating points with dynamic stability are mapped in the grid impedance plane to define the actual stable operating domain of the grid converter.

[0044] Preferably, the implementation process of step 3 is as follows:

[0045] (3.1) Define the parameter plane and the operating domain:

[0046] Let the two-dimensional parameter plane be the power grid impedance plane, i.e. , Represents a two-dimensional real number space, at a specified active and reactive power operating point. Let the theoretical operating domain be denoted as The actual stable operating domain is ;

[0047] The theoretical operating domain is It is a closed region enclosed by the power flow solvability boundary and the voltage over-limit boundary at this power point on the grid impedance plane. It represents the range of grid impedance that the converter can connect to under this power output, considering only the steady-state power flow solvability and voltage modulation capability.

[0048] The actual stable operating domain is It is determined by establishing a small-signal state-space model at this power point and analyzing its stability, and includes all grid impedance points that can maintain small-signal stability of the system. The closed region formed represents the range of grid impedance that the converter can stably connect to under this power output, taking into account dynamic stability.

[0049] (3.2) Calculate the operating domain area:

[0050] The area of ​​the theoretical operating domain on the grid impedance plane Defined as:

[0051] (20)

[0052] The area of ​​the actual stable operating region on the grid impedance plane Defined as:

[0053] (twenty one)

[0054] (3.3) Calculate the coverage index:

[0055] Coverage Defined as the ratio of the actual stable operating domain area to the theoretical operating domain area:

[0056] (twenty two)

[0057] The larger the value, the more stable the converter controller can operate over a wider range of grid impedances at a given power point, and the stronger its adaptability and robustness to changes in grid strength.

[0058] For any details not covered in this invention, please refer to the prior art.

[0059] The beneficial effects of this invention are as follows:

[0060] This invention proposes a quantitative evaluation method for the control performance of grid-connected converters from a stability perspective. This method combines power flow solution boundaries and voltage limit boundaries to systematically define the theoretical operating domain of the converter within the grid impedance plane, providing a clear and complete theoretical boundary for its steady-state operating limits. By establishing a unified small-signal state-space model and analyzing the pole distribution of the converter under different grid operating conditions, its actual stable operating domain is determined. Innovatively, coverage rate is introduced as a core quantitative indicator. By calculating the area ratio of the actual stable operating domain to the theoretical operating domain, an objective and quantitative characterization of the controller's global robustness and adaptability to weak grid conditions is achieved. Attached Figure Description

[0061] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments of this application and their descriptions are used to explain this application and do not constitute an undue limitation of this application.

[0062] Figure 1 This is a flowchart illustrating the method for quantitatively evaluating the control performance of grid-connected converters from a stability perspective, as described in this invention.

[0063] Figure 2This is a schematic diagram of the main circuit and control system structure of the grid-type converter of the present invention;

[0064] Figure 3 This is a schematic diagram of the single-phase equivalent model structure of the grid-type converter of the present invention;

[0065] Figure 4 This is a schematic diagram of the theoretical operating domain of the grid-type converter of the present invention;

[0066] Figure 5 This is a schematic diagram of the actual stable operating domain of a grid-type converter. Detailed Implementation

[0067] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. However, this is not the only description; all aspects not described in detail herein are based on conventional techniques in the art.

[0068] Example 1

[0069] A quantitative evaluation method for the control performance of grid-connected converters from a stability perspective, such as Figure 1 As shown, it includes:

[0070] Step 1: Solve for the modulation voltage based on the single-phase equivalent model of the grid-type converter to determine the power flow solution boundary of the system; determine the voltage limit boundary based on the physical limitation of the modulation ratio; combine the power flow solution boundary and the voltage limit boundary to define the theoretical operating domain of the converter.

[0071] Step 2: Based on the main circuit topology and control system of the grid converter, establish a small-signal state-space model of the grid converter. By analyzing the pole distribution of the grid converter under different grid impedances, determine the actual stable operating domain.

[0072] Step 3: By calculating the area ratio of the theoretical operating domain to the actual stable operating domain, the coverage index is obtained, thereby realizing the quantitative characterization of the control performance of the grid-type converter under various operating conditions.

[0073] Example 2

[0074] A method for quantitatively evaluating the control performance of a grid-connected converter from a stability perspective, as shown in Example 1, differs in that, in step 1, based on the single-phase equivalent model of the grid-connected converter, the voltage phasor and power distribution at the point of common coupling (PCC) under steady state are first obtained by decoupling the external transmission characteristics of the converter and the constraints of the control system. Based on this, and further considering the physical correlation of the converter's filter branches, an analytical mapping of the modulation voltage to line impedance changes is established. The converter output active power equation is as follows:

[0075] (1)

[0076] The converter output reactive power equation is as follows:

[0077] (2)

[0078] The converter output reactive power equation obtained from the control system is as follows:

[0079] (3)

[0080] The reactive power output of the converter is equal to the reactive power output value of the converter obtained from the control system.

[0081] In the formula, For line resistance, For line inductance, This is the real part of the voltage at the point of common coupling (PCC). This represents the imaginary part of the voltage of the PCC. This is the grid voltage. , To output active power and reactive power, This is a reference value for reactive power. The droop coefficient is... This refers to the rated voltage amplitude of the PCC. Let ω be the grid angular frequency; the real part, imaginary part and actual output reactive power of the common coupling voltage of the grid converter can be obtained from equations (1), (2) and (3);

[0082] The modulation voltage equation is established as follows:

[0083] (4)

[0084] In the formula, Modulate the voltage phasor of the converter. For the voltage phasor at the point of common coupling, For grid voltage phasors, The output current phasor on the bridge arm side of the converter. For the line current phasor flowing to the power grid, For the filter branch current phasor, For filtering inductors, For filtering capacitors;

[0085] The modulation voltage based on the grid impedance is By traversing the given range of grid impedance values ​​and discretizing the range of grid impedance values, a global scan of the system's operating state and stability under different operating conditions is achieved. If a stable voltage solution can be obtained by iterative convergence for a certain set of impedance values, then the point is a solvable operating condition; otherwise, if the solution process does not converge or diverges, then the point is an unsolvable boundary point; thus, the solvable boundary of the system's power flow is obtained.

[0086] The peak value of the AC-side modulation voltage of the converter is affected by its DC-side voltage. The limitation is that, when using sinusoidal pulse width modulation (SPWM), the maximum output fundamental voltage amplitude is [value missing]. Based on the established modulation voltage equation, the amplitude of the modulation voltage is calculated. Let the amplitude of the modulation voltage be equal to the upper threshold of the voltage amplitude. This yields the voltage over-limit boundary for the grid impedance:

[0087] (5)

[0088] In the formula, The upper limit threshold of the voltage amplitude is obtained from equation (6):

[0089] (6)

[0090] In the formula, It is a DC voltage;

[0091] The power flow solution boundary ensures that for a given operating point, there exists a physically realizable converter modulation voltage that makes the power balance equations valid. Beyond this boundary, the system cannot find a steady-state operating point, meaning it cannot complete the preset power transfer. The voltage limit boundary ensures that the required modulation voltage is within the limits allowed by the converter hardware. Beyond this boundary, the required voltage will exceed the converter's maximum output capacity, leading to control saturation or distortion. Therefore, the theoretical operating domain characterizes the set of all possible static operating points of the converter, determined solely from the existence of a mathematical solution to the steady-state power balance equations and the limits of the physical output capacity of the main circuit, while neglecting dynamic stability.

[0092] The theoretical operating domain of the grid-type converter is obtained from the power flow solution boundary and the voltage over-limit boundary:

[0093] (7).

[0094] This region defines the theoretical maximum permissible operating range of the converter and serves as a benchmark for evaluating its steady-state performance.

[0095] Example 3

[0096] A method for quantitatively evaluating the control performance of grid-connected converters from a stability perspective, as shown in Example 2, differs in that the implementation process of step 2 is as follows:

[0097] (2.1) In the dq-axis coordinate system, based on Kirchhoff's voltage law and current law, the circuit equations are written, and the nonlinear large-signal differential equations of the main circuit of the converter are obtained as follows:

[0098] (8)

[0099] In the formula, Symbols representing differential calculations, This represents the d-axis current at the converter output. This represents the q-axis current at the converter output. This represents the d-axis current at the filter output. This represents the q-axis current at the filter output. This represents the d-axis voltage at the filter output. This represents the q-axis voltage at the filter output. Represents the equivalent d-axis voltage of the power grid. Represents the equivalent grid q-axis voltage. and Representing virtual inductance and virtual resistance, Indicates the inductance of the output filter. This indicates the capacitance of the output filter. This represents the equivalent series resistance of the filter inductor. Indicates the line inductance on the power grid side. Indicates the line resistance on the power grid side. Represents the steady-state value of angular frequency. This indicates the reference amplitude of the filter capacitor voltage. This represents the reference value for reactive power. and These represent the state variables of the d-axis and q-axis voltage regulation integrators in the current loop control, respectively. and These represent the state variables of the d-axis and q-axis current regulation integrators in the voltage loop control, respectively. This represents the state variable of the voltage regulation integrator in the reactive-voltage outer loop control; This indicates the phase angle of the VSG output voltage.

[0100] (2.2) Based on the complete control link principle, which includes power calculation, VSG power outer loop, virtual impedance, and voltage and current double closed loop, the nonlinear large-signal differential equation of the converter control system is obtained as follows:

[0101] (9)

[0102] In the formula, This indicates the angular frequency at the output of the converter. Represents the virtual inertia constant. Indicates the damping coefficient. Indicates the frequency adjustment coefficient. and This represents the proportional and integral coefficients of the reactive-voltage outer loop. and These represent the scaling and integral coefficients of the d-axis current inner loop, while the scaling and integral coefficients of the q-axis current inner loop are the same as those of the d-axis parameters. and The proportional and integral coefficients of the d-axis voltage outer loop are represented by these coefficients, while the proportional and integral coefficients of the q-axis voltage outer loop are the same as those of the d-axis parameters. This represents the reference value for active power. The droop coefficient is... This is the rated voltage amplitude of the PCC.

[0103] (2.3) Based on the nonlinear large-signal differential equations of the converter main circuit and control system, the derivative terms of each state variable are set to zero to construct a steady-state algebraic equation system, and the steady-state equilibrium point of the system is determined by solving the equations.

[0104] (2.4) At the steady-state equilibrium point, the nonlinear large-signal differential equations of the converter main circuit are linearized to obtain the state-space equations of the converter main circuit, i.e., the small-signal state-space equations of the main circuit, as follows:

[0105] (10)

[0106] In the formula, This represents the small-signal disturbance of the converter bridge arm output current on the d-axis. This represents the steady-state value of the converter bridge arm output current on the d-axis. This represents the small-signal disturbance of the converter bridge arm output current on the q-axis. This represents the steady-state value of the converter bridge arm output current on the q-axis. This represents the small-signal disturbance of the filter output voltage on the d-axis. This represents the steady-state value of the filter output voltage on the d-axis. This represents the small-signal disturbance of the filter output voltage on the q-axis. This represents the steady-state value of the filter output voltage on the q-axis. This represents the small-signal disturbance of the filter output current on the d-axis. This represents the steady-state value of the filter output current on the d-axis. This represents the small-signal disturbance in the filter output current on the q-axis. This represents the steady-state value of the filter output current on the q-axis. This represents the small-signal change in the d-axis component of the grid voltage. This represents the small-signal change in the q-axis component of the grid voltage. This represents the small-signal change in the active power reference value. This represents the small-signal change in the reactive power reference value. This indicates the steady-state setting of the reactive power reference value.

[0107] (2.5) At the steady-state equilibrium point, the nonlinear large-signal differential equations of the converter control system are linearized to obtain the state-space equations of the converter control system, i.e., the small-signal state-space equations of the converter control system, as follows:

[0108] (11)

[0109] In the formula, This represents the small-signal change in the active power reference value. This represents the small-signal change in the electrical angular frequency of the VSG output. Represents the steady-state value of angular frequency. This represents the small-signal change in the phase angle of the VSG output voltage. Indicates the initial phase angle. This represents the small signal change in the state of the voltage regulator integrator. This represents the steady-state value of the voltage regulation integrator. This represents the small-signal change in the state of the inner loop integrator of the d-axis current. This represents the steady-state value of the inner loop integrator of the d-axis current. This represents the small-signal change in the state of the inner loop integrator of the q-axis current. This represents the steady-state value of the inner loop integrator of the q-axis current. This represents the small-signal change in the state of the outer loop integrator of the d-axis voltage. This represents the steady-state value of the outer loop integrator of the d-axis voltage. This represents the small-signal change in the state of the outer loop integrator of the q-axis voltage. This represents the steady-state value of the outer loop integrator of the q-axis voltage. and This represents virtual inductance and virtual resistance.

[0110] (2.6) By combining the state-space equations of the main circuit of the converter and the state-space equations of the control system, the state-space equations of the converter under VSG control, i.e., the small-signal state-space model, are obtained as follows:

[0111] (12)

[0112] In the formula, Represents the small-signal state variable at time t. This represents the small-signal input variable at time t. Represents the system matrix. Represent the input matrix; and have:

[0113] (13)

[0114] Based on the mathematical models of the main circuit and control system of the converter, small-signal state variables are extracted. The coefficients are used to obtain the system matrix A; in this embodiment, due to the aforementioned state variables Containing 13 elements, the system matrix A in formula (12) is specifically expanded into a 13th-order square matrix A. 13×13 Specifically:

[0115] (14)

[0116] In the formula:

[0117] (15) (16)

[0118] (17)

[0119] (18)

[0120] (19)

[0121] The actual stable operating range is determined by the grid resistance R. s With grid inductance L s Within the constructed two-dimensional impedance parameter plane, based on the obtained theoretical operating domain, each impedance operating point in the grid impedance plane is traversed one by one. Then, relying on the constructed small-signal state-space model of the grid-type converter, the system matrix A is solved. 13×13 The characteristic equation is det(λI-A) 13×13 =0, calculate several system poles, and calculate the distribution of system poles corresponding to each impedance operating point; where λ represents the system poles, and I represents the identity matrix with the same order as the system matrix A;

[0122] Based on the stability criteria of linear systems, operating points with all poles located in the left half of the complex plane are selected and extracted. Finally, the operating points with dynamic stability are mapped in the grid impedance plane to define the actual stable operating domain of the grid converter.

[0123] Example 4

[0124] A method for quantitatively evaluating the control performance of grid-connected converters from a stability perspective, as shown in Example 3, differs in that the implementation process of step 3 is as follows:

[0125] (3.1) Define the parameter plane and the operating domain:

[0126] Let the two-dimensional parameter plane be the power grid impedance plane, i.e. , Represents a two-dimensional real number space, at a specified active and reactive power operating point. Let the theoretical operating domain be denoted as The actual stable operating domain is ;

[0127] The theoretical operating domain is It is a closed region enclosed by the power flow solvability boundary and the voltage over-limit boundary at this power point on the grid impedance plane. It represents the range of grid impedance that the converter can connect to under this power output, considering only the steady-state power flow solvability and voltage modulation capability.

[0128] The actual stable operating domain is It is determined by establishing a small-signal state-space model at this power point and analyzing its stability, and includes all grid impedance points that can maintain small-signal stability of the system. The closed region formed represents the range of grid impedance that the converter can stably connect to under this power output, taking into account dynamic stability.

[0129] (3.2) Calculate the operating domain area:

[0130] The area of ​​the theoretical operating domain on the grid impedance plane Defined as:

[0131] (20)

[0132] The area of ​​the actual stable operating region on the grid impedance plane Defined as:

[0133] (twenty one)

[0134] (3.3) Calculate the coverage index:

[0135] Coverage Defined as the ratio of the actual stable operating domain area to the theoretical operating domain area:

[0136] (twenty two)

[0137] This metric reflects the proportion of the theoretically feasible operating range that the control system can translate into a truly usable, stable operating range under a given power command. A higher value indicates a wider impedance range that the control system can maintain stability over when responding to changes in grid strength, resulting in stronger dynamic adjustment capabilities, a more sufficient stability margin, and better adaptability and robustness to complex grid environments. Conversely, a lower value indicates a lower stability margin. This value means that the control system can only maintain stability within a narrow impedance range, is more sensitive to changes in operating conditions, and has a narrow stability boundary.

[0138] Coverage transforms the global stability of a control system under multiple operating conditions into an intuitive scalar, providing a quantitative basis for evaluating the strong and weak network adaptability of control strategies, comparing the performance of different control schemes, and guiding the optimization of controller parameters.

[0139] To verify the effectiveness and reliability of the proposed method, based on Figure 2 The detailed topology of the main circuit and control system of the grid-type converter shown is verified by simulation. The specific parameter configuration is shown in Table 1.

[0140] Table 1 Parameters of Grid-type Converters

[0141]

[0142] Figure 2 This diagram illustrates the complete system block diagram of the grid-connected converter used in this embodiment. Its structure can be divided into two main parts: the main circuit and the control system. The main circuit topology includes a three-phase inverter bridge and an output filter, which are connected to the power grid via inductors, forming the physical channel for power transmission. The control system includes Park transformation, power calculation, a power synchronization outer loop, virtual impedance, and voltage / current inner loop components. This block diagram clearly defines the complete control link from power command to bridge arm modulation signal, providing the foundation for establishing a small-signal model, conducting theoretical operating domain analysis, and subsequent stability verification.

[0143] First, based on Figure 3 The single-phase equivalent model of the grid-type converter is shown, and its modulation voltage is established with respect to the output power. and grid impedance The mathematical relationships are determined. By judging the convergence of the iterative solution process of the modulation voltage, the unsolvable region of power flow is accurately identified in the parameter space; simultaneously, based on the physical constraint of the converter's maximum modulation ratio, its voltage over-limit region is determined. Finally, in the selected parameter plane... Above, the region that simultaneously satisfies the power flow solution and voltage amplitude limitation is plotted. This region is the theoretical stable operating domain of the grid-type converter, such as... Figure 4As shown, the system is divided into three regions: the power flow unsolvable region, the voltage over-limit region, and the stable operating region. This figure represents the set of all operating points where the system can theoretically achieve steady-state power balance without exceeding hardware limits under all possible grid impedance conditions.

[0144] Subsequently, combining the main circuit with Figure 2 The VSG control structure shown establishes a complete small-signal state-space model. Under the parameters in Table 1, eigenvalue analysis was used to systematically scan the pole distribution at different grid impedance points, and the system stability was determined accordingly. Finally, on the same parameter plane, the region where the converter can maintain small-signal stability under the actual control strategy was plotted, i.e., as shown in Table 1. Figure 4 The actual stable operating range of the converter shown is Figure 5 The white area in the middle is the overlapping area between the theoretical operating domain and the actual operating domain. It can be seen that there are areas in which the converter is theoretically stable but actually unstable during operation.

[0145] Through calculation Figure 5 The actual stable operating domain area shown is equal to Figure 3 The coverage is obtained by comparing the theoretical operating domain area shown. The success rate of 86.67% is relatively high, indicating that the VSG control strategy can transform most of the theoretically feasible operating range into a practically stable operating region. This fully demonstrates that the method of this invention can not only effectively define the stable operating boundary of grid-type converters, but also provide an objective quantitative evaluation benchmark for the quality of their control performance, thus verifying the correctness of the method of this invention.

[0146] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for quantitatively evaluating control performance of a grid-forming converter under stability perspectives, characterized in that, include: Step 1: Solve for the modulation voltage based on the single-phase equivalent model of the grid-type converter to determine the power flow solution boundary of the system; determine the voltage limit boundary based on the physical limitation of the modulation ratio; combine the power flow solution boundary and the voltage limit boundary to define the theoretical operating domain of the converter. Step 2: Based on the main circuit topology and control system of the grid converter, establish a small-signal state-space model of the grid converter. By analyzing the pole distribution of the grid converter under different grid impedances, determine the actual stable operating domain. Step 3: By calculating the area ratio of the theoretical operating domain to the actual stable operating domain, the coverage index is obtained, thereby realizing the quantitative characterization of the control performance of the grid-type converter under various operating conditions. The implementation process of step 3 is as follows: (3.1) Define the parameter plane and the operating domain: Let the two-dimensional parameter plane be the power grid impedance plane, i.e. , Represents a two-dimensional real number space, at a specified active and reactive power operating point. Let the theoretical operating domain be denoted as The actual stable operating domain is ; The theoretical operating domain is It is a closed region enclosed by the power flow solvability boundary and the voltage over-limit boundary at the power point on the grid impedance plane. It represents the range of grid impedance that the converter can connect to under power output, considering only the steady-state power flow solvability and voltage modulation capability. The actual stable operating domain is It is determined by establishing a small-signal state-space model at the power point and analyzing its stability, and includes all grid impedance points that enable the system to maintain small-signal stability. The closed region formed represents the range of grid impedance that the converter can stably connect to under power output, taking into account dynamic stability. (3.2) Calculate the operating domain area: Area of the theoretical operating domain on the grid impedance plane is defined as: （20） Area of the actual stable operating domain in the impedance plane of the power grid is defined as: （21） (3.3) Calculate the coverage index: Coverage Defined as the ratio of the actual stable operating domain area to the theoretical operating domain area: （22） The larger the value, the more stable the converter controller can operate over a wider range of grid impedances at a given power point, and the stronger its adaptability and robustness to changes in grid strength.

2. The method of claim 1, wherein the control performance of the networked converter is quantitatively evaluated from the stability perspective. In step 1, based on the single-phase equivalent model of the grid-type converter, the converter output active power equation is as follows: （1） The converter output reactive power equation is as follows: （2） The reactive power equation for the converter output obtained from the control system is as follows: （3） In the formula, For line resistance, For line inductance, Let the voltage at the point of common coupling be the real part. The imaginary part of the voltage at the point of common coupling. This is the grid voltage. , To output active power and reactive power, This is a reference value for reactive power. The droop coefficient is... This refers to the rated voltage amplitude of the PCC. Let ω be the grid angular frequency; the real part, imaginary part and actual output reactive power of the common coupling voltage of the grid converter can be obtained from equations (1), (2) and (3); The modulation voltage equation is established as follows: （4） In the formula, Modulate the voltage phasor of the converter. For the voltage phasor at the point of common coupling, For grid voltage phasors, The output current phasor on the bridge arm side of the converter. For the line current phasor flowing to the power grid, For the filter branch current phasor, For filtering inductors, For filtering capacitors; The modulation voltage based on the grid impedance is By traversing the given range of grid impedance values ​​and discretizing the range of grid impedance values, a global scan of the system's operating state and stability under different operating conditions is achieved. If a stable voltage solution can be obtained by iterative convergence for a certain set of impedance values, then the point is a solvable operating condition; otherwise, if the solution process does not converge or diverges, then the point is an unsolvable boundary point; thus, the solvable boundary of the system's power flow is obtained.

3. The method for quantitatively evaluating the control performance of a grid-connected converter from a stability perspective according to claim 2, characterized in that, In step 1, the amplitude of the modulation voltage is calculated based on the established modulation voltage equation. ; Setting the amplitude of the modulation voltage equal to the upper threshold of the voltage amplitude, we obtain the voltage over-limit boundary with respect to the grid impedance: （5） In the formula, is the voltage amplitude upper threshold value, which is obtained from equation (6): （6） In the formula, is a direct current voltage; The theoretical operating domain of the grid-type converter is obtained from the power flow solution boundary and the voltage over-limit boundary: （7）。 4. The method for quantitatively evaluating the control performance of a grid-connected converter from a stability perspective according to claim 3, characterized in that, The implementation process of step 2 is as follows: (2.1) In the dq axis coordinate system, based on Kirchhoff's voltage law and Kirchhoff's current law, establish the nonlinear large-signal differential equation of the converter main circuit; (2.2) Integrating the complete control link principle including power calculation, VSG power outer loop, virtual impedance and voltage and current double closed loop, the nonlinear large-signal differential equation of the converter control system is established. (2.3) Based on the nonlinear large-signal differential equations of the converter main circuit and control system, the derivative terms of each state variable are set to zero to construct a steady-state algebraic equation system, and the steady-state equilibrium point of the system is determined by solving the equations. (2.4) At the steady-state equilibrium point, the nonlinear large-signal differential equation of the converter main circuit is linearized based on the first-order Taylor expansion, thereby obtaining the small-signal state-space equation of the converter main circuit. (2.5) At the steady-state equilibrium point, the nonlinear large-signal differential equation of the converter control system is linearized based on the first-order Taylor expansion, thereby obtaining the small-signal state-space equation of the converter control system. (2.6) By combining the small-signal state-space equations of the main circuit and the control system, the small-signal state-space model of the converter under complete VSG control is obtained as follows: （12） In the formula, Represents the small-signal state variable at time t. This represents the small-signal input variable at time t. Represents the system matrix. Represents the input matrix; The combined small-signal state-space equations of the main circuit and control system are rearranged into standard matrix form, where the small-signal state variables are... The corresponding coefficient matrix is ​​the system matrix mentioned above. ; The actual stable operating range is determined by the grid resistance R. s With grid inductance L s Within the constructed two-dimensional impedance parameter plane, based on the obtained theoretical operating domain, each impedance operating point in the grid impedance plane is traversed one by one. Then, relying on the constructed small-signal state-space model of the grid-type converter, the system matrix is ​​solved. The characteristic equation is det(λI-A)=0. Several system poles are calculated, and the distribution of system poles corresponding to each impedance operating point is calculated. Where λ represents the system poles and I represents the identity matrix with the same order as the system matrix A. Based on the stability criteria of linear systems, operating points with all poles located in the left half of the complex plane are selected and extracted. Finally, the operating points with dynamic stability are mapped in the grid impedance plane to define the actual stable operating domain of the grid converter.

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