Transient stability analysis method for direct-current bus voltage synchronous network construction type converter

Abstract

The invention discloses a transient stability analysis method for a direct-current bus voltage synchronous grid-forming type converter, relates to the technical field of power electronics, and solves the problem that real-time changes of inertia and potential along with frequency in a converter cannot be accurately described due to constant parameters of an existing transient stability analysis method for the grid-forming type converter. According to the method, nonlinear characteristics of variable inertia and variable internal potential are completely fused into an energy conservation framework for the first time, then explicit expressions of kinetic energy, potential energy and damping work are analyzed and derived, and then an implicit stability boundary equation is solved by adopting an iterative algorithm; by fully utilizing the negative feedback convergence characteristic that the frequency-dependent inertia coefficient and the frequency-dependent internal potential are updated along with the state variable, the accurate capture of the critical stable frequency distribution function is realized. According to the method, constant parameter hypothesis limitation is broken through, the deviation between the theoretical evaluation result and the actual stability boundary of the system is reduced, the analysis precision is improved, and a quantifiable theoretical basis is provided for parameter optimization and robust design of the network-forming converter.

Description

Technical Field

[0001] This invention relates to the field of power electronics technology, and in particular to a transient stability analysis method for DC bus voltage synchronous grid-type converters. Background Technology

[0002] With the rapid increase in the penetration rate of inverter-based integrated power sources (IBRs), represented by wind and solar power, in power systems, the dynamic characteristics of traditional grids dominated by synchronous generators have undergone fundamental changes, posing a severe challenge to the transient stability of power systems. Grid-connected converters (GFMCs), as key equipment providing voltage source support, directly determine the safe operating boundary of renewable energy grid-connected systems based on their transient stability characteristics. Among these, DC voltage synchronization control (DVSC), by revealing the inherent similarity between the dynamics of the DC bus capacitor and the swing equations of synchronous generators, directly utilizes the DC voltage deviation to generate the synchronization frequency. Compared to the traditional cascaded power synchronization control and DC voltage control schemes, it has significant advantages in terms of simpler structure and faster response speed, and has become an important direction in the technological evolution of grid-connected converters. However, the dynamic behavior of DVSC grid-type converters exhibits strong nonlinear characteristics. Their inertial characteristics are coupled with the DC bus voltage in real time, and the frequency feedforward reactive power control (FFIR) introduced to enhance system damping further causes the internal potential to change dynamically with frequency deviation. This frequency-dependent variable inertia and variable internal potential characteristics make the transient response mechanism of the system under large disturbances far more complex than that of traditional synchronous generators, and it is urgent to establish a stability analysis theory that is compatible with it.

[0003] Existing analytical methods for the transient stability of grid-type converters mainly rely on the classical equal area criterion (EAC) and its derived energy function method. However, these methods are all based on the fundamental assumptions of constant inertia coefficient and internal potential, and cannot accurately describe the nonlinear dynamic behavior of inertia and potential changing with frequency in real time in DVSC converters. Specifically, the time-varying characteristics of the DC bus voltage mean that system inertia is no longer a fixed parameter, and the frequency-reactive power coupling effect introduced by FFIR control makes the internal potential a bivariate function of power angle and frequency. If the traditional energy function method ignores the above frequency correlation when deriving kinetic energy, potential energy, and damping work, it will seriously underestimate or overestimate the stability margin of the system, resulting in an evaluation deviation of more than 20% for key indicators such as critical clearing time, which is difficult to meet the accuracy requirements of engineering applications. Due to the lack of analytical tools that can quantify the influence of frequency-related parameters, controller parameter tuning relies on a lot of simulation trial and error, which is not only inefficient, but also cannot theoretically guarantee the stability of the system under the expected set of disturbances. This has become one of the core bottlenecks restricting the large-scale application of DVSC grid-type converters.

[0004] Therefore, a transient stability analysis method for DC bus voltage synchronous grid-type converters is needed. Summary of the Invention

[0005] To address the problem that existing methods for analyzing the transient stability of grid-type converters using constant parameters cannot accurately describe the nonlinear dynamic behavior of inertia and potential changes with frequency in real time in DVSC-type converters, this invention provides a transient stability analysis method for DC bus voltage synchronous grid-type converters. This method can be implemented by constructing a grid-type converter (GFMC) based on DC voltage synchronous control (DVSC) and frequency feedforward reactive power control (FFIR). The method derives analytical expressions for the system kinetic energy, potential energy, and damping work considering the nonlinear DC bus voltage and FFIR. Furthermore, it proposes a numerical method based on an iterative algorithm to evaluate the transient stability boundary of the DVSC-type GFMC. Finally, the analysis results are verified through a power hardware-in-the-loop (PHIL) experiment. The specific technical solution is as follows: A transient stability analysis method for a DC bus voltage synchronous grid-type converter includes the following steps: S1: Establish a mathematical model of a grid-type converter containing DC voltage synchronous control and frequency feedforward reactive power control, and obtain a second-order nonlinear swing equation containing frequency-dependent inertia coefficients and frequency-dependent internal potentials. S2: Based on the law of conservation of energy, derive the kinetic energy of the mathematical model of the grid converter during acceleration and deceleration. E k Potential energy E p and damping work W d The analytical expression for the kinetic energy is obtained by integrating the inertia coefficient with respect to the frequency deviation, and the damping work is obtained by integrating the frequency coupling term introduced by the frequency feedforward reactive control with respect to the work angle. S3: Construct a transient stability criterion and use an iterative algorithm to solve for the critical stable frequency distribution function that satisfies the transient stability criterion; wherein, the transient stability criterion is: the kinetic energy at the fault clearing point is not greater than the sum of the potential energy increment and the damping work increment between the fault clearing point and the unstable equilibrium point; S4: Iteratively solve the trajectory during the fault period based on the energy conservation relationship, and determine the critical clearance angle by the intersection of the trajectory during the fault period and the critical stable frequency distribution function, and then calculate the critical clearance time by power angle path integral.

[0006] Preferably, the expression for the inertia coefficient in step S1 is as follows: in, This is the DC bus capacitance value. These are the instantaneous and reference values ​​of the DC voltage. This is the DVSC proportional gain.

[0007] Preferably, the expression for the internal potential in step S1 is as follows: Among them, coefficient k 1- k 6, φ 1 and φ 2 represents the following: in, , L g and R g For power grid line frequency, inductance, and resistance; R t and L t These represent the sum of the mains resistance and the virtual resistance, and the sum of the mains inductance and the virtual inductance, respectively. L V and R V It is the virtual inductance and resistance of VAC.

[0008] Preferably, the kinetic energy in step S2 E k Potential energy E p and damping work W d The specific parsing expression is as follows: in, C dc For DC bus capacitors, K dc It is the proportional gain of DVSC. V dcref This is a reference value for DC voltage. P e The active power output by the converter. K d It is the proportional gain of frequency feedforward in RPC.

[0009] Preferably, the mathematical expression for the transient stability criterion in step S3 is: in, K dc It is the proportional gain of DVSC. ω max This indicates the frequency deviation at the fault clearing point.

[0010] Preferably, the iterative algorithm in step S3 employs a negative feedback convergence mechanism, and the specific iterative formula is as follows: .

[0011] Preferably, step S4 is as follows: Using an iterative algorithm to quickly approximate the trajectory during the fault period Solution: in, x It represents the upper limit of the integral, and the subscript i indicates the value in the i-th iteration; The critical clearance angle is determined by the intersection of the trajectory during the fault and the critical stable frequency distribution function; Calculate the critical clearance time using the path integral of the power angle: .

[0012] A computer-readable storage medium includes a stored program, wherein, when the program is executed, it controls the device where the computer-readable storage medium is located to perform the transient stability analysis method for a DC bus voltage synchronous grid converter as described above.

[0013] A processor for running a program, wherein the program executes the transient stability analysis method for a DC bus voltage synchronous grid converter as described above.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention constructs an analytical energy function system based on frequency-dependent variable inertia and variable internal potential, and innovatively introduces an iterative approximation mechanism, effectively solving the inherent limitation of traditional methods in transient stability analysis of DVSC-type grid converters. Specifically, this invention, for the first time, fully integrates the nonlinear characteristics of variable inertia and variable internal potential into the energy conservation framework. By analytically deriving explicit expressions for kinetic energy, potential energy, and damping work, it quantitatively reveals the mechanism of frequency coupling effects in the transient energy conversion process. Furthermore, it employs an iterative algorithm to solve the implicit stability boundary equations, fully utilizing the negative feedback convergence characteristics of the frequency-dependent inertia coefficient and the frequency-dependent internal potential as the state variables update, achieving accurate capture of the critical stability frequency distribution function. This method overcomes the constant parameter assumptions of the classical energy function method, reducing the deviation between theoretical evaluation results and the actual stability boundary of the system, significantly improving analytical accuracy. Simultaneously, it transforms the solution of complex nonlinear differential equations into efficient iterative calculations, avoiding the numerical integration burden in time-domain simulations, and improving computational efficiency by more than an order of magnitude. More importantly, this invention establishes a direct theoretical link from controller parameters to stability boundaries, providing a quantifiable theoretical basis for parameter optimization and robust design of grid-type converters. Attached Figure Description

[0015] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0016] Figure 1 This describes the main topology and controller for connecting GFM-VSC based on DVSC to the power grid.

[0017] Figure 2 This is a simplified equivalent circuit for the system.

[0018] Figure 3 This is a second-order nonlinear mathematical model of GFMC based on DVSC.

[0019] Figure 4 For simulation verification of the nonlinear model (10) under large disturbances: (a) Vg drops to 0.55pu; (b) Pin jumps to 1.25pu.

[0020] Figure 5 An illustration of the equal area criterion (EAC) for GFMC based on DVSC under different Kd conditions.

[0021] Figure 6 Let ωcr+ and ωcr- be the iterative solutions for the transient stable boundary.

[0022] Figure 7 This is the convergence mechanism of the proposed iterative method.

[0023] Figure 8 The specific steps for estimating CCA and CCT.

[0024] Figure 9 Simulation verification of the stability boundary when Vg drops to 0.55 pu. (a) Scaled up; (b) Scaled down.

[0025] Figure 10 Simulation verification of the stability boundary when Pin jumps to 1.25 pu. (a) Zoomed in; (b) Zoomed out.

[0026] Figure 11 This is a PHIL experimental platform based on a power amplifier. (a) Schematic diagram of the experimental platform; (b) Specific components of the experimental platform.

[0027] Figure 12 This describes the main topology and control structure of the constant active power output module.

[0028] Figure 13The experimental waveforms for the grid voltage dropping to 0.4 pu are as follows: (a) Tfc = 650 ms = CCT, VSC#1 is stable; (b) Tfc = 680 ms > CCT, VSC#1 is unstable.

[0029] Figure 14 The experimental waveforms are for different Kidc values. (a) When Kidc = 0.3, VSC#1 experiences transient instability; (b) When Kidc = 0.1, VSC#1 remains stable. Detailed Implementation

[0030] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] It should be understood that, when used in this specification and the appended claims, the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0032] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0033] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0034] In one embodiment of the present invention, a transient stability analysis method for a DC bus voltage synchronous grid-type converter based on frequency-dependent variable inertia coefficient and internal potential is provided. This is achieved by constructing a grid-type converter (GFMC) based on DC voltage synchronous control (DVSC) and frequency feedforward reactive power control (FFIR). Analytical expressions for the system kinetic energy, potential energy, and damping work considering the nonlinear DC bus voltage and FFIR are derived. Furthermore, a numerical method based on an iterative algorithm is proposed to evaluate the transient stability boundary of the DVSC-type GFMC. Finally, the analysis results are verified through a power hardware-in-the-loop (PHIL) experiment. Figures 1-14 As shown, the details are as follows: Step 1: First, establish a mathematical model for GFMC access to weak power grid based on DVSC.

[0035] like Figure 1 As shown, its controller includes DVSC, reactive power control (RPC), virtual admittance control (VAC), and vector current control (VCC). A constant power source is used on the DC side. P in Simulating new energy sources such as wind and solar power C dc For DC bus capacitors, P e and Q e These represent the active and reactive power outputs of the converter, respectively. L f For filtering inductors, L g and R g For the inductance and resistance of the power grid lines, V g and θ g For the magnitude and phase of the grid voltage, E DVSC , ω DVSC and θ DVSC The voltage, frequency, and phase of the converter are given. V pcc and θ pcc The voltage magnitude and phase at the point of common coupling (PCC). V pcc The dq axis components are respectively V pccd and V pccq . I g The output current of the GFMC based on DVSC has dq-axis components respectively. I gd and I gq . V dc and V dcref These are the instantaneous and reference values ​​of the DC voltage. K dc It is the proportional gain of DVSC. K d It is the proportional gain of frequency feedforward in RPC (FFIR). K q It is the proportional gain of RPC. E0 and Q ref These are the voltage reference and the reactive power reference, respectively. L V and R V It is the virtual inductance and resistance of VAC, designed to suppress power oscillations. I dref and I qref It is the dq axis current reference.

[0036] The system's virtual power angle δ and frequency deviation ω Defined as the phase difference and frequency difference between the DVSC and the power grid, respectively: (1) (2) Considering the impact of VAC, the output active power of the DVSC-based GFMC P e and reactive power Q e It was deduced that: (3) (4) in, R t and L t These represent the sum of the mains resistance and the virtual resistance, and the sum of the mains inductance and the virtual inductance, respectively. (5) Based on the voltage-current relationship (VCR) of a DC capacitor, a DC capacitor... C dc The dynamic representation is as follows: (6) In practice, the input active power on the DC side P in Adjusted by the front-end converter and approximated as a constant value. Frequency ω DVSC This is generated directly using the DVSC method based on the P controller, also known as matched control. (7) It is noted that the active power balance dynamics of a DC capacitor lack damping, which can lead to severe oscillations. Therefore, frequency feedforward (FFIR) is used in the RPC to introduce an additional damping branch, a method widely used in DVSCs. (8) Combining (1) to (8), we obtain the equivalent second-order nonlinear mathematical model of GFMC based on DVSC, as shown in (9): (9) Combining the expressions for active power and reactive power in (3)-(4), formula (9) is further derived as follows: (10) Where the coefficient k 1- k 6, φ 1 and φ 2 represents the following: (11) Step 2: Based on EAC and the law of conservation of energy, derive the kinetic energy of the system considering the nonlinear DC bus voltage and FFIR. E k Potential energy E p and damping work W d The parsing expression.

[0037] Unlike the swing equations of traditional synchronous generators (SG), the swing equations of GFMC based on DVSC, as shown in (10), have frequency-dependent inertia coefficients. J DVSC and internal potential E DVSC The frequency-dependent inertia coefficient is due to... V dc The nonlinear dynamics (as shown in (6)) are caused by the frequency-dependent internal potential, while the frequency-dependent internal potential is due to the introduction of FFIR. Therefore, the traditional EAC analysis method cannot be directly used to evaluate the stability boundary of GFMC based on DVSC. Therefore, based on the law of energy conservation and the equivalence of EAC, the frequency-dependent inertia coefficient is considered first. J DVSC and internal potential E DVSC The effect of kinetic energy E k Potential energy E p and damping work W d The analytical expression.

[0038] Derivation of kinetic energy, potential energy, and damping work: The essence of a transient process is kinetic energy. E k Potential energy E p and damping work W d The interconversion between these two processes. Therefore, the energy conversion relationships during acceleration and deceleration will be analyzed first. Finally, kinetic energy will be given. E k Potential energy E p and damping work W d The analytical expression is as follows: The specific analysis process is as follows: From... Figure 5 It can be seen that when K d When = 0.1, the acceleration region S acc Equal to S1, and the deceleration region S dec It equals S3 + S4. The expressions for S1 and S3 + S4 are as follows: (12) (13) δ FCP1 This represents the virtual power angle at the fault clearing point (FCP) c1 (d1), such as Figure 5 As shown. δ max This is the virtual power angle at point e1, at which point the operating point decelerates to zero. According to EAC, since the operating point decelerates to e1 after the fault is cleared, therefore... S acc = S dec This means the system is transiently stable. However, when K d When the equilibrium point is 0, the operating point cannot decelerate to zero and eventually exceeds the unstable equilibrium point (UEP), which means that the system experiences transient instability. K d When = 0, S acc It equals S1 + S2, and S dec It equals S3 + S4 + S5. (And) K d Compared to 0.1, the acceleration region increases from S1 to S1+S2. Furthermore, from... δ FCP1,2 arrive δ maxThe deceleration region decreases from S3+S4 to S3. The changes in the acceleration and deceleration regions mentioned above are due to the introduction of FFIR. The decrease in the acceleration region S2 and the increase in the deceleration region S4 related to FFIR are as follows: (14) (15) The damping work introduced by FFIR corresponds to Figure 5 S2 and S4 shown are essentially related to ω The contribution of relevant electromagnetic power components. According to EAC, the criterion for system transient stability is the acceleration region. S acc Less than the maximum deceleration area S dec_max : (16) Combine (10) and (12) to rewrite the acceleration region. S acc As shown below: (17) ω max This represents the frequency deviation at the fault clearing point (FCP), which is the maximum frequency deviation during acceleration. In the derivation of (17), differential substitution is used to express the frequency deviation with respect to the power angle. δ The integral is converted to frequency deviation ω The integral is then obtained. S acc The parsing expression.

[0039] From an energy perspective, (16) illustrates the energy conversion relationship during acceleration. Analogous to the energy function of a classical second-order synchronous generator, the kinetic energy of the system at FCP is obtained: (18) For damping work W d ,from Figure 5 It can be known that, W d This corresponds to the additional acceleration and deceleration area introduced by FFIR. Therefore, during acceleration, the damping work... W d_acc Equal to K d =0, compared to the reduction in acceleration area S2: (19) Substituting (18) and (19) into (17), the energy conversion relationship during the acceleration process is further derived as follows: (20) Potential energy δ SEP Potential energy at the point E p Defined as 0. According to the law of conservation of energy, the transition from SEP to FCP... E p The reduction is equal to the reduction from SEP to FCP. E k and W d Increase: (twenty one) The potential energy at FCP is derived based on (18) and (19): (twenty two) After the fault is cleared, the operating point decelerates to the right. During deceleration, the energy conversion relationship is the reverse of the acceleration process: at FCP... E k ( ω max The energy decreases and is further converted into potential energy. E p and damping work W d The increase. When δ = δ max At that time, the operating point decelerates to zero. Therefore, in δ max At that time, the kinetic energy is equal to zero: (twenty three) from Figure 5 It can be seen that the damping work during deceleration W d Under the influence of S4, the following is added: (twenty four) According to the law of conservation of energy, during deceleration, the decrease in kinetic energy is converted into an increase in potential energy and damping work. (25) Furthermore, according to EAC, S acc = S dec : (26) Combining (25) and (26), we obtain the potential energy. E p ( δ max ): (27) Based on the energy conversion relationships analyzed in (18)-(27), kinetic energy E k Potential energy E p and damping work W d The analytical expression is summarized in (28), where δ and ω The state variables represent the second-order large-signal model of GFMC based on DVSC.

[0040] (28) Step 3: Derive the transient stability boundary using an iterative method. ω cr+ and ω cr- .

[0041] Based on the law of conservation of energy, the transient stability condition is derived as shown in (29). The physical meaning of this condition is as follows: the kinetic energy at FCP is less than the sum of the potential energy increment and the damping work increment from FCP to UEP.

[0042] (29) If (29) is satisfied, the operating point can decelerate to zero before the UEP. Otherwise, the operating point will exceed the UEP, and transient instability will occur. The transient stability condition (29) is of the same nature as (16). However, compared with the transient stability condition (16) derived from EAC, the transient stability condition (29) has a more significant physical meaning. S acc It is derived in (16) as E k(ωmax) , representing the kinetic energy at FCP. S dec_max In equation (16), these are derived as the maximum potential energy increment and damping work increment from FCP to UEP. The transient stability boundary is defined as the set of frequency distribution functions in the critical stable state after fault clearance. Transient stability boundary ω ( x Based on equation (29), we can obtain: (30) in x express δ FCP The alternative variable. As can be seen from equation (30), the transient stability boundary is essentially the frequency deviation. ω Harmony and angle δ The implicit function equation system.

[0043] Further derivation of (30) yields the transient stability boundary of the system: (31) It should be noted that (31) represents the critical stable frequency distribution function during the first right swing. ω cr+ ,Right now ω >0, transient instability mainly occurs during the initial rightward swing. Similarly, the initial leftward swing portion of the critical stability frequency distribution function ( ω <0) is: (32) The third row of formulas (31)-(32) and (10) together form the frequency. ω , angle δ and internal potential E DVSC The implicit functional relationship between them. This invention proposes an iterative method to approximate the aforementioned transient stability boundary through iteration. ω cr+ and ω cr- As shown in equations (33)-(34).

[0044] (33) (34) Subscript i Representing the i The values ​​in this iteration. A detailed flowchart of this iteration is shown below. Figure 6 The core idea is to continuously substitute the result of the previous iteration to achieve a result about... ω cr+ and ω cr- The implicit equations (31) and (32) converge. When the result is within the set threshold... ε The iteration stops when the interface converges.

[0045] Figure 7 The convergence mechanism of the proposed iterative method is shown. When ω cr+ i-1 When the denominator of (31) increases, it leads to ω cr+ i Decrease. According to (9) ω cr+ i-1 The increase will also lead to E DVSC Increase. Increase. E DVSC This will further lead to a larger P eDVSC This also led toω cr+ i Reduced. The above negative feedback mechanism ensures that ω cr+ The iterative convergence is achieved. ω cr- The convergence mechanism is similar and will not be repeated here.

[0046] Step 4: Derive the critical clearing angle (CCA) and critical clearing time (CCT) The critical clearing angle (CCA) is determined by the transient stability boundary. ω cr ( x ) and the fault trace before clearing ω pc ( x The intersection point of the fault is determined. Therefore, in order to accurately identify the fault accretion pathway (CCA) and assess the transient stability of the system, the fault trajectory before clearing is derived. ω pc ( x Potential energy is crucial. Based on the aforementioned energy conversion relationship, during acceleration, potential energy... E p The reduction is converted into kinetic energy E k and damping work W d The increase of . Therefore, we have: (35) The physical meaning of formula (35) is as follows: from SEP to the current working point E p The decrease equals the sum of the increase in kinetic energy and the increase in damping work. Based on (28), further derivation of (35) yields: (36) and ω cr ( x Similar to the estimation of ), an iterative algorithm was constructed to quickly approximate the implicit function (36). ω pc ( δ Solution: (37) in x It is the upper limit of the points, subscript i Indicates the first i The values ​​in the next iteration. It is worth noting that all coefficients in (37) are calculated based on the parameters before the failure. The iteration in (37), aided by matrix operations and pipelined algorithms, is faster than the solution to the time-domain ordinary differential equation in (10). By solving the derived ω cr(x) andω pc ( x The intersection of ) is quickly and accurately estimated by CCA. Furthermore, CCT is calculated as (39), which gives d t Replace with d δ / ω pc ( δ ): (38) The specific steps for estimating CCA and CCT are summarized in Figure 8 According to Figure 8 The proposed method, with CCA and CCT under different disturbances, is listed in Tables 1 and 2. Simulation validation of the proposed CCA and CCT estimation method is performed in... Figure 9 and Figure 10 The solid pink curve represents a stable trajectory, where the fault recovers before the CCT. The dashed blue curve represents an unstable trajectory, where the fault recovers after the CCT. Figure 9 and Figure 10 The conservatism shown is almost negligible, verifying the relatively high accuracy of the proposed method.

[0047] Table 1. CCA and CCT values ​​under different grid voltage sags Table 2. In different P in CCA and CCT values ​​under sudden increase Step 5: Experimental Verification To verify the effectiveness of the proposed iterative transient stability boundary assessment method and its analysis results, a power hardware-in-the-loop (PHIL) experimental platform based on a power amplifier (EGSTON CSU200) and RT-LAB was constructed. The experimental platform consists of three parts: a constant active power output module based on a three-phase AC voltage source and a PWM rectifier VSC#2; a grid-type converter VSC#1 based on a DVSC; and a grid simulation module based on RT-LAB and the power amplifier. The rectifier VSC#2 in the former uses traditional phase-locked loop (PLL) control and vector current control (VCC).

[0048] Figure 13 The accuracy of the proposed transient stability assessment method was verified. During the fault, the grid voltage was set to 0.4 pu. Using the proposed iterative transient stability assessment method, the CCA and CCT were obtained as 1.943 radians and 650 milliseconds, respectively. The fault clearing time was defined as... T fcFirst, to verify the effectiveness of the proposed iterative transient stability evaluation method for GFMC based on DVSC, we conducted separate tests at... T fc =650 milliseconds and T fc The experiment was conducted under the condition of 680 milliseconds. The corresponding experimental waveform is as follows. Figure 13 As shown. Clearly, when T fc At 650 milliseconds, VSC#1 remained stable, while when T fc At 680 milliseconds, VSC#1 experienced transient instability and was eventually locked out by the protection device. These results verify the accuracy of the proposed transient stability assessment method.

[0049] Figure 14 The experimental waveforms are shown when the input power suddenly increases to 2 p.u. Under this condition, the calculated CCA and CCT are 1.72 rad and 390 ms, respectively. T fc =390 milliseconds and T fc The experiment was conducted under the condition of 410 milliseconds. It can be seen that VSC#1... T fc It remains stable under the condition of 390 milliseconds, while when T fc At 410 milliseconds, VSC#1 experienced transient instability. These results validate the accuracy of the proposed transient stability assessment method.

[0050] In summary, this invention effectively addresses the inherent limitations of traditional methods in transient stability analysis of DVSC-type grid converters by constructing an analytical system of energy functions based on frequency-dependent variable inertia and variable internal potential, and innovatively introducing an iterative approximation mechanism. Specifically, this invention, for the first time, fully integrates the nonlinear characteristics of variable inertia and variable internal potential into the energy conservation framework. Through analytical derivation of explicit expressions for kinetic energy, potential energy, and damping work, it quantitatively reveals the mechanism of frequency coupling effects in the transient energy conversion process. Furthermore, it employs an iterative algorithm to solve the implicit stability boundary equations, fully utilizing the negative feedback convergence characteristics of the frequency-dependent inertia coefficient and the frequency-dependent internal potential as the state variables update, achieving accurate capture of the critical stability frequency distribution function. This method overcomes the limitations of the constant parameter assumptions of the classical energy function method, reducing the deviation between theoretical evaluation results and the actual stability boundary of the system, significantly improving analytical accuracy. Simultaneously, it transforms the solution of complex nonlinear differential equations into efficient iterative calculations, avoiding the numerical integration burden in time-domain simulations, and improving computational efficiency by more than an order of magnitude. More importantly, this invention establishes a direct theoretical link from controller parameters to stability boundaries, providing a quantifiable theoretical basis for parameter optimization and robust design of grid-type converters. It fundamentally solves the shortcomings of existing technologies that rely on empirical trial and error and lack analytical evaluation capabilities, opening up a new technical path for transient stability analysis and optimization design of grid-type equipment in high-proportion new energy power systems.

[0051] Those skilled in the art will recognize that the units of the various examples described in connection with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of the invention.

[0052] In the embodiments provided by the present invention, it should be understood that the division of units is only a logical functional division. In actual implementation, there may be other division methods, such as multiple units can be combined into one unit, one unit can be split into multiple units, or some features can be ignored.

[0053] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0054] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.

[0055] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A transient stability analysis method for a DC bus voltage synchronous grid-type converter, characterized in that, Includes the following steps: S1: Establish a mathematical model of a grid-type converter containing DC voltage synchronous control and frequency feedforward reactive power control, and obtain a second-order nonlinear swing equation containing frequency-dependent inertia coefficients and frequency-dependent internal potentials. S2: Based on the law of conservation of energy, derive the kinetic energy of the mathematical model of the grid converter during acceleration and deceleration. E k Potential energy E p and damping work W d The analytical expression for the kinetic energy is obtained by integrating the inertia coefficient with respect to the frequency deviation, and the damping work is obtained by integrating the frequency coupling term introduced by the frequency feedforward reactive control with respect to the work angle. S3: Construct a transient stability criterion and use an iterative algorithm to solve for the critical stable frequency distribution function that satisfies the transient stability criterion; wherein, the transient stability criterion is: the kinetic energy at the fault clearing point is not greater than the sum of the potential energy increment and the damping work increment between the fault clearing point and the unstable equilibrium point; S4: Iteratively solve the trajectory during the fault period based on the energy conservation relationship, and determine the critical clearance angle by the intersection of the trajectory during the fault period and the critical stable frequency distribution function, and then calculate the critical clearance time by power angle path integral.

2. The transient stability analysis method for a DC bus voltage synchronous grid-type converter according to claim 1, characterized in that, The expression for the inertia coefficient in step S1 is as follows: in, This is the DC bus capacitance value. These are the instantaneous and reference values ​​of the DC voltage. This is the DVSC proportional gain.

3. The transient stability analysis method for a DC bus voltage synchronous grid-type converter according to claim 2, characterized in that, The expression for the internal potential in step S1 is as follows: Among them, coefficient k 1- k 6, φ 1 and φ 2 represents the following: in, , L g and R g For power grid line frequency, inductance, and resistance; R t and L t These represent the sum of the mains resistance and the virtual resistance, and the sum of the mains inductance and the virtual inductance, respectively. L V and R V It is the virtual inductance and resistance of VAC.

4. The transient stability analysis method for a DC bus voltage synchronous grid-type converter according to claim 3, characterized in that, Kinetic energy in step S2 E k Potential energy E p and damping work W d The specific parsing expression is as follows: in, C dc For DC bus capacitors, K dc It is the proportional gain of DVSC. V dcref This is a reference value for DC voltage. P e The active power output by the converter. K d It is the proportional gain of frequency feedforward in RPC.

5. The transient stability analysis method for a DC bus voltage synchronous grid-type converter according to claim 4, characterized in that, The mathematical expression for the transient stability criterion in step S3 is: in, K dc It is the proportional gain of DVSC. ω max This indicates the frequency deviation at the fault clearing point.

6. The transient stability analysis method for a DC bus voltage synchronous grid-type converter according to claim 5, characterized in that, In step S3, the iterative algorithm employs a negative feedback convergence mechanism, and the specific iterative formula is as follows: 。 7. The transient stability analysis method for a DC bus voltage synchronous grid-type converter according to claim 6, characterized in that, Step S4 is as follows: Using an iterative algorithm to quickly approximate the trajectory during the fault period Solution: in, x It represents the upper limit of the integral, and the subscript i indicates the value in the i-th iteration; The critical clearance angle is determined by the intersection of the trajectory during the fault and the critical stable frequency distribution function; Calculate the critical clearance time using the path integral of the power angle: 。 8. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored program, wherein, when the program is executed, it controls the device containing the computer-readable storage medium to perform the transient stability analysis method for a DC bus voltage synchronous grid converter as described in any one of claims 1 to 7.

9. A processor, characterized in that, The processor is used to run a program, wherein the program executes the transient stability analysis method for DC bus voltage synchronous grid-type converter according to any one of claims 1 to 7.

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