Method for analyzing fault transient current of network-forming converter in consideration of power angle swing process

Abstract

The invention discloses a fault transient current analysis method of a network-forming converter considering a power angle swing process. The method belongs to the technical field of power system fault analysis, is used for realizing accurate solution of transient current of a network-forming converter under a three-phase symmetric drop fault of power grid voltage, and comprises the following steps: firstly, constructing a power angle swing equation based on a virtual synchronous machine control strategy; taylor series expansion is carried out on an equation nonlinear term at a steady-state equilibrium point after the fault, a linear oscillation component and a nonlinear disturbance component are separated, and a power angle approximate analytical solution is derived; secondly, establishing a grid-connected current first-order differential equation containing power grid impedance based on circuit topology, and substituting the simplified power angle expression to obtain a time domain analytical expression of voltage on the power grid impedance under a three-phase static coordinate system; and finally, in combination with a solving method of a first-order differential equation and a current steady-state initial value condition, establishing a current analytical expression of the whole fault transient process.

Description

Technical Field

[0001] The invention belongs to the technical field of power system fault analysis, and in particular relates to a method for analyzing transient current of a grid-connected converter fault taking into account a power angle swing process. Background Art

[0002] As the penetration rate of renewable energy generation in the power system continues to increase, the grid-type converter has become a key supporting equipment for the new power system with its technical characteristics of autonomously building grid voltage and maintaining synchronous stability. When a three-phase symmetrical drop fault occurs in the power grid, the grid-type converter needs to provide the necessary capacity support through fast current response under the premise of strictly meeting the safe operation constraints of power devices, so its transient current characteristics directly affect the system fault recovery capability and equipment safety margin.

[0003] In the field of power system fault analysis, the fault response mechanism of traditional synchronous generators has formed a complete theoretical system. However, there are still technical bottlenecks in the accurate modeling of transient currents in grid-connected converters: the strong coupling characteristics of its nonlinear control link and grid fault parameters make it difficult to accurately characterize the amplitude, phase and attenuation characteristics of transient currents through traditional linearization methods.

[0004] Early research mainly relied on electromagnetic transient simulation or experimental testing to analyze the dynamic characteristics of faults. Although such methods can obtain transient data under specific working conditions, they have high computational costs and long simulation times. In addition, they are difficult to reveal the universal laws of transient currents and the influence mechanism of the coupling of multiple physical quantities, resulting in significant obstacles in the design and engineering application of new protection principles.

[0005] In the field of analytical modeling research, current technologies are mostly based on linearized small signal model analysis methods. By reducing the order of the converter control equation and the grid circuit equation, a fault current analytical model with a second-order differential equation as the core is established. However, this type of model usually ignores the dynamic change process of the power angle after the fault, and cannot reflect the dynamic coupling relationship between current oscillation and power angle swing. In addition, the existing model does not consider the virtual inertia and damping control links unique to the grid-type converter, which are the core parameters used to improve the transient stability of the "low inertia-weak damping" system. Other studies draw on the multi-time scale modeling framework of synchronous machines, divide the fault transient process into "sub-transient-transient-steady state" stages, and construct current analytical expressions containing sinusoidal terms and exponential decay terms. However, key parameters such as time constants and equivalent output impedance in such expressions are difficult to establish clear mathematical mappings with the control and hardware parameters of the grid-type converter, and their modeling ideas still continue the synchronous machine assumptions, ignoring the essential differences of the grid-type converter in terms of frequency component distribution and attenuation characteristics. Furthermore, if the relay protection setting method based on the characteristics of the synchronous machine is directly used, it may cause the protection in the grid-type converter system to fail to operate or malfunction, posing a safety hazard. Summary of the Invention

[0006] Aiming at the problems existing in the prior art, the present invention provides a method for calculating the fault transient current of a network-forming converter considering the power angle swing process. This method realizes the accurate solution of the transient current of the network-forming converter under the three-phase symmetrical voltage dip fault of the power grid by constructing a second-order nonlinear differential equation containing the virtual inertia time constant H and the damping coefficient D.

[0007] A method for calculating the fault transient current of a network-forming converter considering the power angle swing process proposed by the present invention includes the following steps:

[0008] 1) Equivalent the network-forming converter to a self-synchronous voltage source, define the power angle as the phase angle difference between the voltage at the output end of the converter and the grid voltage; establish a second-order nonlinear differential equation containing the virtual inertia time constant and the damping coefficient;

[0009] 2) Perform Taylor series expansion on the nonlinear terms in the second-order nonlinear differential equation at the power angle equilibrium point after the fault, separate the linear oscillation component and the nonlinear perturbation component, linearize the second-order nonlinear differential equation into a damped harmonic vibration equation, and combine the initial power angle before the fault to solve for the approximate analytical expression of the power angle;

[0010] 3) After the fault, ignore the tracking process of the voltage and current double loops, based on Kirchhoff's voltage law, combine the equivalent circuit after the fault, and establish a first-order differential equation of the grid-connected current containing the grid resistance and the grid inductance; substitute the approximate analytical expression of the power angle in step 2) into the first-order differential equation of the grid-connected current to obtain the time-domain joint expression of the voltages on the grid resistance and the grid inductance, and decompose it into the steady-state component and the dynamic component of the fault voltage;

[0011] 4) Determine the homogeneous solution expression of the first-order differential equation of the grid-connected current based on the initial fault current; according to the structural characteristics of the steady-state component expression of the fault voltage, set the steady-state component of the fault current as the form of the superposition of sine and cosine, substitute it into the differential equation, and obtain the specific analytical expression of the steady-state component through coefficient matching; then substitute the dynamic component of the fault voltage into the differential equation to obtain the analytical expression of the current dynamic component containing the decaying oscillation term, and finally superimpose the homogeneous solution, the steady-state component, and the dynamic component to establish the current analytical expression for the entire process of the fault transient state.

[0012] Based on the above technical solutions, the present invention has the following beneficial technical effects:

[0013] (1) The present invention fully considers the influence of the power angle swing characteristics of the network-forming converter under virtual synchronous machine control on the grid-connected current, overcomes the solution obstacle brought by the nonlinear terms in the active power control equation, and realizes the accurate solution of the transient current under the three-phase symmetrical voltage dip fault of the power grid.

[0014] (2) The present invention reveals the internal relationships between core control parameters such as virtual inertia H and damping coefficient D and the transient current amplitude characteristics, phase characteristics, and attenuation laws, providing a direct mathematical tool for the design of improving the overload capacity of grid-forming converters; at the same time, it provides a theoretical basis for the adaptive adjustment of relay protection strategies in new power systems, avoiding the risk of misoperation caused by directly applying traditional synchronous machine protection methods, and significantly improving the coordination and adaptability between the grid fault ride-through ability and the protection system. Description of the Drawings

[0015] Figure 1 It is a single-line diagram of the grid-connected system of the typical grid-forming converter described in the embodiment of the present invention;

[0016] Figure 2 It is the equivalent circuit diagram of the grid-connected system of the grid-forming converter in the embodiment of the present invention;

[0017] Figure 3 It is the phasor relationship diagram before and after the fault in the embodiment of the present invention;

[0018] Figure 4 It is the phase A current diagram after the grid voltage symmetrically drops in the embodiment of the present invention. Detailed Embodiment

[0019] In order to make the objectives, technical solutions, and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0020] Figure 1 It is a single-line diagram of the grid-connected system of the typical grid-forming converter. In terms of circuit topology, the DC side of the grid-forming converter is equivalent to an ideal DC source , and the AC side is connected to the point of common coupling through a filter with an inductor of and a capacitor of ; the power grid is simplified to an ideal voltage source with an angular frequency of and an amplitude of E in series with an equivalent grid connection impedance X g , where X g is composed of the grid inductor and the grid resistance , covering three parts: the transformer impedance X T , the transmission line impedance X l and the grid impedance X grid ; , , are the three-phase currents on the converter side, the three-phase voltages on the converter side, and the grid-side current respectively.

[0021] In terms of the control structure, P e$P$ and $P_0$ are the active power output and the given value of the converter respectively. The outer power loop adopts virtual synchronous machine control. By simulating the rotor motion equation of a synchronous generator, the virtual inertia time constant $H$ and the damping coefficient $D$ are introduced. According to the magnitude of the output active power $P$, e the phase of the voltage at the output terminal of the converter is adjusted. and the frequency. The collected , , and other AC side measurements are transformed from the abc-dq coordinate system to the dq coordinate system using the rotation angle determined by . In this coordinate system, the given value of the d-axis voltage is , the given value of the q-axis voltage is 0, and the voltage-current double-loop controller generates the modulation voltage command in the dq coordinate system according to signals such as . The output signal is transformed back from the dq-abc coordinate system to obtain the three-phase modulation wave , and finally the converter switching signal is generated through PWM modulation. Since the voltage-current double-loop can achieve fast and error-free tracking of the voltage reference, the amplitude of the voltage at the output terminal of the converter can accurately track the given value , while its phase angle is directly determined by output by the virtual synchronous machine loop.

[0022] The analytical method for the transient current of a network-forming converter considering the power angle swing process provided by the present invention is mainly used for accurately solving the transient current of a network-forming converter under a three-phase symmetrical voltage dip fault of the power grid. It includes the following steps:

[0023] Step 1): Figure 2 is the equivalent circuit diagram of the network-forming converter grid-connected system of the present invention. First, based on the virtual synchronous machine control strategy, the network-forming converter is equivalent to a self-synchronous voltage source. Taking the power grid phase as the reference, the power angle is defined as the phase angle difference between the voltage at the output terminal of the converter and the power grid voltage, where is the phase of the voltage at the output terminal of the converter; is the power grid voltage phase. Taking the power grid voltage as the reference, that is, the power grid voltage phase , then the output terminal of the converter . Based on the circuit topology and control structure of the network-forming converter grid-connected system, a second-order nonlinear differential equation related to the power angle containing the virtual inertia time constant $H$ and the damping coefficient $D$ is obtained:

[0024] (1)

[0025] The parameter symbols in the formula are as defined above.

[0026] Step 2): At the post-fault power angle equilibrium point , perform Taylor series expansion on the non-linear terms in the second-order non-linear differential equation, separate the linear oscillation component and the non-linear perturbation component, linearize the original second-order non-linear differential equation into a damped simple harmonic vibration equation, and use the solution method of the second-order linear homogeneous differential equation, combined with the initial power angle before the fault, to obtain an approximate analytical expression for the power angle.

[0027] In Step 2), the post-fault power angle equilibrium point and the initial power angle before the fault are obtained by the following method: Figure 3 is the phasor relationship diagram before and after the fault. E and E d are the grid voltage amplitudes before and after the fault respectively. Obtain the initial values at the fault moment in the three-phase stationary coordinate system. The power angle before the fault is , and the power angle after the fault reaches a new steady-state equilibrium point after dynamic adjustment. The power angle at this equilibrium point is , and it satisfies:

[0028] (2)

[0029] In a specific embodiment of the present invention, the process of Step 2) is specifically as follows: At the post-fault steady-state equilibrium point , perform Taylor series expansion on the non-linear terms in the second-order non-linear differential equation, separate the linear vibration part and the non-linear perturbation part, and linearize the original second-order non-linear differential equation into a damped simple harmonic vibration equation:

[0030] (3)

[0031] where, is the power angle change amount, and its initial condition is , ; is the free vibration frequency; is the small perturbation parameter; is the non-linear expansion formula, specifically:

[0032] ;

[0033] Ignoring the influence of the small perturbation on the right side of the equation, use the solution method of the second-order linear homogeneous differential equation to obtain the form of the homogeneous solution as:

[0034] (4)

[0035] where, and are the initial amplitude and initial phase of the power angle change, respectively, t represents time, is the damping vibration frequency, ignoring and higher-order terms, and obtaining its expression through the initial conditions as:

[0036] (5)

[0037] Furthermore, the power angle approximate analytical expression is obtained as:

[0038] (6)

[0039] Step 3): After the fault, ignoring the tracking process of the voltage and current double loops, based on Kirchhoff's voltage law and combining with the equivalent circuit after the fault, establish a first-order differential equation of the grid-connected current containing the grid resistance and inductance :

[0040] (7)

[0041] Substitute the power angle expression in Equation (6) into Equation (7), and derive the time-domain joint expression of the voltages on the grid resistance and inductance :

[0042] (8)

[0043] Since the interference introduced by the exponential decay term in the power angle expression is small, an approximate equivalent treatment can be performed on the trigonometric function of the power angle: approximate as approximately equivalent to , as approximately equivalent to . Substitute the above equivalent relationship into the time-domain joint expression of the voltage, and further decompose it to obtain the steady-state component and the dynamic component of the fault voltage:

[0044] (9)

[0045] (10)

[0046] where: is the dynamic sine deviation of the power angle; is the dynamic cosine deviation of the power angle.

[0047] Step 4): Based on the initial fault current determine the homogeneous solution expression ; According to the steady-state component of the fault voltage Based on the structural characteristics of the expression, set the steady-state component of the fault current in the form of a superposition of sine and cosine, substitute it into the original differential equation, and obtain the analytical expression of the steady-state solution through coefficient matching; then substitute the dynamic component of the fault voltage into the differential equation, and use the integrating factor method to obtain the analytical expression of the current dynamic component with decaying oscillation terms , and finally superimpose the homogeneous solution, steady-state solution, and dynamic solution to establish the analytical expression of the current during the entire fault transient process.

[0048] In a specific embodiment of the present invention, the process of step 4) is specifically as follows:

[0049] The homogeneous solution expression of the first-order differential equation of the grid-connected current is:

[0050] (11)

[0051] where the initial current coefficient C is determined by the initial current at the fault moment , that is ;

[0052] Substitute The corresponding particular steady-state current solution is expressed in sine form:

[0053] (12)

[0054] Substitute it into equation (7), and obtain the analytical expression of the steady-state part of the fault current through coefficient matching:

[0055] (13)

[0056] Use the integrating factor method to solve the corresponding analytical expression of the dynamic part of the fault current with decaying oscillation terms:

[0057] (14)

[0058] where: is the exponential factor; and are the high-frequency angular frequency and high-frequency phase difference respectively; and are the low-frequency angular frequency and low-frequency phase difference respectively;

[0059] Add the homogeneous solution expression, the analytical expression of the steady-state part, and the analytical expression of the dynamic part to obtain the complete analytical expression of the fault current:

[0060] (15)

[0061] The method of the present invention provides a direct mathematical tool for the design of improving the overload capacity of the network-forming converter; meanwhile, it provides a theoretical basis for the adaptive adjustment of relay protection strategies in the new power system, avoiding the risk of misoperation caused by directly applying traditional synchronous machine protection methods, and significantly improving the grid fault ride-through ability and the coordination and adaptability of the protection system.

[0062] To verify the accuracy of the current analytical expression, simulation verification was carried out on the Matlab / Simulink platform. The main electrical and control parameters in the simulation model are shown in Table 1.

[0063] Table 1 - Parameters of the network-forming converter grid-connected simulation model

[0064]

[0065] Figure 4 It shows the analytical and simulation waveforms of the grid-connected current of phase A after the grid voltage amplitude drops to 0.7 p.u. at t = 0 s when the damping coefficient D = 25 p.u., the virtual inertia time constant H = 10 s and other parameters meet the requirements of Table 1. It can be seen that the coincidence degree between the two is relatively high, which proves the correctness of the fault current analytical expression.

[0066] To quantitatively verify the accuracy of the expression, the matching degree (MD) is introduced to represent the similarity. From its expression, it can be seen that the larger the MD value, the higher the similarity:

[0067] ;

[0068] where I sim and I anl represent the current simulation quantity and the current analytical quantity respectively. Table 2 shows the MD values under nine test conditions, which are basically all higher than 96%, proving the consistency between the analytical and simulation results of the current again, and proving the correctness of the fault transient current calculation method.

[0069] Table 2 - Matching degree analysis under different conditions

[0070]

[0071] The above description of the embodiments is to facilitate the understanding and application of the present invention by those of ordinary skill in the art. Those skilled in the art can obviously make various modifications to the above embodiments easily and apply the general principles described herein to other embodiments without creative labor. Therefore, the present invention is not limited to the above embodiments, and the improvements and modifications made by those skilled in the art to the present invention should be within the protection scope of the present invention, such as using different converter structures, different current inner-loop controls, etc.

Claims

1. An analytical method for the transient current of a network-forming converter considering the power angle swing process, characterized in that It includes the following steps: 1) Equivalent the grid-forming converter to a self-synchronous voltage source, and define the power angle as the phase angle difference between the voltage at the output terminal of the converter and the grid voltage; establish a second-order nonlinear differential equation containing the virtual inertia time constant and damping coefficient; 2) At the power angle equilibrium point after the fault, perform Taylor series expansion on the nonlinear terms in the second-order nonlinear differential equation, separate the linear oscillation component and the nonlinear perturbation component, linearize the second-order nonlinear differential equation into a damped simple harmonic vibration equation, and combine with the initial power angle before the fault to solve and obtain an approximate analytical expression of the power angle; 3) After the fault, ignore the tracking process of the voltage and current double loops. Based on Kirchhoff's voltage law, combine with the equivalent circuit after the fault to establish a first-order differential equation of the grid-connected current containing the grid resistance and grid inductance; substitute the approximate analytical expression of the power angle in step 2) into the first-order differential equation of the grid-connected current to obtain the time-domain joint expression of the voltages on the grid resistance and grid inductance, and decompose it into the steady-state component and the dynamic component of the fault voltage; 4) Determine the homogeneous solution expression of the first-order differential equation of the grid-connected current based on the initial current at the fault; According to the structural characteristics of the steady-state component expression of the fault voltage, set the steady-state component of the fault current in the form of a superposition of sine and cosine, substitute it into the differential equation, and obtain the specific analytical expression of the steady-state component through coefficient matching; Then substitute the dynamic component of the fault voltage into the differential equation to obtain the analytical expression of the current dynamic component containing the decaying oscillation term. Finally, superimpose the homogeneous solution, the steady-state component, and the dynamic component to establish the analytical expression of the current during the entire fault transient process.

2. The analytical method for the fault transient current of a network-forming converter considering the power angle swing process according to claim 1, characterized in that: The fault is a three-phase symmetrical voltage dip fault of the grid.

3. The transient current analysis method of the network-forming converter fault considering the power angle swing process according to claim 2, characterized in that: In step 1), the power angle , where is the voltage phase at the output terminal of the converter; is the grid voltage phase. The second-order nonlinear differential equation containing the virtual inertia time constant and damping coefficient is: ； Where: H is the virtual inertia time constant, D is the damping coefficient, and are the reference values of the active power output and the voltage amplitude at the output terminal of the converter respectively, is the grid voltage amplitude, is the equivalent grid impedance, which consists of the grid inductance and the grid resistance constitute.

4. The analytical method for the fault transient current of the network-forming converter considering the power angle swing process according to claim 3, wherein: In step 2), Obtain the initial value at the fault moment in the three-phase static coordinate system. Denote the initial power angle before the fault as , after the fault, the power angle reaches a new steady-state equilibrium point through dynamic regulation, and the power angle at this equilibrium point is , then we have: ； Among them, is the grid voltage amplitude after the fault drops.

5. The analytical method for the transient fault current of a network-forming converter considering the power angle swing process according to claim 4, characterized in that The process of step 2) is specifically: At the steady-state equilibrium point after a fault Perform a Taylor series expansion on the nonlinear term in the second-order nonlinear differential equation, separate the linear vibration part and the nonlinear perturbation part, and linearize the original second-order nonlinear differential equation into a simple harmonic vibration equation with damping: ； Among them, is the power angle variation, and its initial condition is , ; is the free vibration frequency; is the small perturbation parameter; is the nonlinear expansion, specifically: ； Ignore the influence of small perturbations, and use the solution method of the second-order linear homogeneous differential equation to obtain the form of the homogeneous solution as: ； Among them, and are the initial amplitude and initial phase of the power angle change respectively, t represents time, is the damped vibration frequency, ignoring and high-order terms, and its expression is obtained through the initial conditions of as follows: ； Thus, the power angle has an approximate analytical expression as follows: 。 6. The transient current analysis method of the network-forming converter fault considering the power angle swing process according to claim 3, characterized in that The first-order differential equation of the grid-connected current containing the grid resistance and grid inductance in step 3) is: ； In the formula, is the grid-connected current expression, is the voltage vector at the output terminal of the converter, is the grid voltage vector after a three-phase symmetrical fault drops out.

7. The analytical method for the fault transient current of a network-forming converter considering the power angle swing process according to claim 6, characterized in that In step 3), the ignoring of the tracking process of the voltage and current double loops is specifically: after the fault, the reference value of the converter terminal voltage amplitude remains unchanged, the current control link does not perform the limiting operation, and the voltage and current double loops can quickly and accurately track the reference value.

8. The transient current analysis method for a network-forming converter fault considering the power angle swing process according to claim 7, characterized in that The process of step 3) is specifically: Substitute the power angle expression into the first-order differential equation of the grid-connected current, and derive the time-domain joint expression of the voltage across the grid resistance and the grid inductance: ； In the formula, is the fundamental angular frequency; Since the interference introduced by the exponential decay term in the power angle expression is small, an approximate equivalent treatment is performed on the trigonometric function of the power angle: Substitute with an approximate equivalent of , with an approximate equivalent of ; Substitute the above equivalent relationship into the time-domain joint expression of the voltage, and further decompose it to obtain the steady-state component and the dynamic component : ； ； Wherein: is the dynamic sine deviation of the power angle; is the dynamic cosine deviation of the power angle.

9. The analytical method for the fault transient current of a network-forming converter considering the power angle swing process according to claim 8, characterized in that The process of step 4) is specifically: Homogeneous solution expression of the first-order differential equation of grid-connected current is as follows: ； Among them, the initial current coefficient C is determined by the initial current at the fault moment That is ; Due to the steady-state component of the fault voltage being in the form of a sine-cosine superposition, the steady-state component of the fault current is set in the form of: ； Among them, and are the cosine coefficient and the sine coefficient respectively; Bring back the first-order differential equation of the grid-connected current, and obtain the steady-state component of the fault current through coefficient matching The analytical expression is as follows: ； Then bring the dynamic component of the fault voltage into the differential equation, and by using the integrating factor method, obtain the dynamic component of the current containing a decaying oscillation term The analytical expression is as follows: ； Wherein: is the exponential factor; and are the high-frequency angular frequency and the high-frequency phase difference, respectively; and are the low-frequency angular frequency and the low-frequency phase difference, respectively; Add the homogeneous solution expression, the steady-state component analytical expression, and the dynamic component analytical expression to obtain the complete analytical expression of the fault current: 。

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