A method for analyzing fault transient current in grid-connected converters considering power angle swing

Abstract

The present invention discloses a method for analyzing transient currents in a grid-connected converter fault, taking into account the power angle swing process. This method belongs to the technical field of power system fault analysis and is used to accurately solve the transient current of a grid-connected converter under a three-phase symmetrical grid voltage drop fault. The method comprises the following steps: first, constructing a power angle swing equation based on a virtual synchronous machine control strategy, performing a Taylor series expansion on the nonlinear terms of the equation at the post-fault steady-state equilibrium point, separating the linear oscillation component from the nonlinear perturbation component, and deriving an approximate analytical solution for the power angle; then, establishing a first-order differential equation for the grid-connected current containing the grid impedance based on the circuit topology, substituting the simplified power angle expression into the equation, and obtaining a time-domain analytical expression for the voltage across the grid impedance in a three-phase stationary coordinate system; finally, combining the solution method for the first-order differential equation with the steady-state initial value conditions for the current, establishing an analytical expression for the current throughout the fault transient process.

Description

Technical Field

[0001] The present 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 of renewable energy generation continues to increase in power systems, grid-connected converters, with their ability to independently build grid voltage and maintain synchronous stability, have become a key supporting equipment for these new power systems. In the event of a three-phase symmetrical drop fault in the grid, grid-connected converters must provide the necessary capacity support through rapid current response while strictly meeting the safe operation constraints of power devices. Therefore, their transient current characteristics directly impact the system's fault recovery capabilities and the equipment's safety margins.

[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 using 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. They are also difficult to reveal the universal laws of transient currents and the influence mechanism of multi-physical quantity coupling, resulting in significant obstacles in the design and engineering application of new protection principles.

[0005] In analytical modeling research, current techniques are mostly based on linearized small-signal model analysis. By reducing the order of the converter control equations and the grid circuit equations, an analytical fault current model based on a second-order differential equation is constructed. However, such models often ignore the dynamic changes in the power angle after a fault and fail to account for the dynamic coupling between current oscillation and power angle swing. Furthermore, existing models fail to consider the virtual inertia and damping control mechanisms unique to grid-type converters, which are crucial parameters for improving the transient stability of "low-inertia, weak-damping" systems. Other studies, drawing on the multi-time-scale modeling framework of synchronous generators, divide the fault transient process into "subtransient-transient-steady-state" phases and construct analytical current expressions containing sinusoidal and exponential decay terms. However, key parameters such as the time constant and equivalent output impedance in such expressions are difficult to clearly map to the control and hardware parameters of the grid-type converter. Furthermore, their modeling approach still relies on synchronous generator assumptions, ignoring the fundamental differences of grid-type converters 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] This paper addresses the challenges of the existing technology by providing a method for calculating transient currents in grid-type converters that takes into account power angle swings. By constructing a second-order nonlinear differential equation with a virtual inertia time constant H and a damping coefficient D, this method accurately calculates transient currents in grid-type converters under three-phase symmetrical grid voltage dips.

[0007] The present invention proposes a method for calculating fault transient current of a grid-connected converter taking into account the power angle swing process, comprising the following steps:

[0008] 1) The grid-connected converter is equivalent to a self-synchronous voltage source, and the power angle is defined as the phase angle difference between the converter output voltage and the grid voltage. A second-order nonlinear differential equation with a virtual inertia time constant and damping coefficient is established.

[0009] 2) Perform a Taylor series expansion on the nonlinear terms in the second-order nonlinear differential equation at the post-fault power angle equilibrium point to separate the linear oscillation component from the nonlinear disturbance component. The second-order nonlinear differential equation is linearized into a damped simple harmonic oscillation equation. Combined with the initial power angle before the fault, an approximate analytical expression for the power angle is obtained.

[0010] 3) After the fault, ignoring the tracking process of the voltage and current dual loops, based on Kirchhoff's voltage law and combined with the equivalent circuit after the fault, a first-order differential equation for the grid current including the grid resistance and grid inductance is established. The approximate analytical expression for the power angle from step 2) is substituted into the first-order differential equation for the grid current to obtain a time-domain joint expression for the voltage across the grid resistance and grid inductance, which is then decomposed into a steady-state component and a dynamic component of the fault voltage.

[0011] 4) Determine the homogeneous solution 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 to the form of a superposition of sine and cosine components, substitute it into the differential equation, and obtain the specific analytical expression of the steady-state component through coefficient matching. Then, bring the dynamic component of the fault voltage into the differential equation to obtain the analytical expression of the dynamic component of the current including the decaying oscillation term. Finally, superimpose the homogeneous solution, steady-state component, and dynamic component to establish the analytical expression of the current for the entire transient process of the fault.

[0012] Based on the above technical solution, 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 grid-connected converter under the control of the virtual synchronous machine on the grid-connected current, overcomes the solution obstacles 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 drop fault of the grid voltage.

[0014] (2) The present invention reveals the intrinsic relationship between core control parameters such as virtual inertia H and damping coefficient D and transient current amplitude characteristics, phase characteristics and attenuation laws, providing a direct mathematical tool for the design of improving the overload capacity of grid-type 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 false operation caused by the direct application of traditional synchronous machine protection methods, and significantly improving the grid fault ride-through capability and the coordinated adaptability of the protection system. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 A single-line diagram of a typical grid-connected converter system according to an embodiment of the present invention;

[0016] Figure 2 This is an equivalent circuit diagram of a grid-connected system of a grid-connected converter according to an embodiment of the present invention;

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

[0018] Figure 4 This is a phase A current diagram after the grid voltage drops symmetrically according to an embodiment of the present invention. DETAILED DESCRIPTION

[0019] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0020] Figure 1 This is a typical grid-connected converter system single-line diagram. In terms of circuit topology, the DC side of the grid-connected converter is equivalent to an ideal DC source. , the AC side uses inductance , the capacitance is The filter is connected to the common coupling point; the grid is simplified to have an angular frequency of , an ideal voltage source with an amplitude of E is connected in series with the equivalent grid impedance X g , where X g By grid inductance and grid resistance Composition, covering the transformer impedance X T , transmission line impedance X l and grid impedance X grid Three parts; 、 、 They are the three-phase current on the converter side, the three-phase voltage on the converter side and the grid-side current.

[0021] In terms of control structure, P eand P0 are the output active power and given value of the converter respectively. The outer power loop adopts virtual synchronous machine control. By simulating the synchronous generator rotor motion equation, the virtual inertia time constant H and damping coefficient D are introduced. According to the output active power P e The size of the voltage phase at the output of the converter is adjusted and frequency. 、 、 etc., using The determined rotation angle is transformed into the dq coordinate system through the abc-dq coordinate system. In this coordinate system, the d-axis voltage given value is , the q-axis voltage setting value is 0, the voltage and current dual-loop controller is based on and Equal signal generation modulation voltage command in dq coordinate system The output signal is transformed by dq-abc to obtain a three-phase modulated wave , and finally generate the converter switching signal through PWM modulation. Since the voltage and current dual loop can achieve fast and error-free tracking of the voltage reference, the converter output voltage The amplitude can accurately track the given value , and its phase angle is determined by the output of the virtual synchronizer ring Direct decision.

[0022] The method for analyzing transient current of a grid-type converter fault taking into account the power angle swing process provided by the present invention is mainly used to accurately solve the transient current of a grid-type converter under a three-phase symmetrical voltage drop fault of the power grid, and includes the following steps:

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

[0024] (1)

[0025] The parameter symbols are as defined above.

[0026] Step 2): At the power angle balance point after the fault The nonlinear terms in the second-order nonlinear differential equation are expanded by Taylor series, the linear oscillation component and the nonlinear disturbance component are separated, and the original second-order nonlinear differential equation is linearized into a simple harmonic oscillation equation with damping. The second-order linear homogeneous differential equation solution method is used, combined with the initial power angle before the fault , get the power angle An approximate analytical expression for .

[0027] In step 2), the power angle balance point after the fault And the initial power angle before the fault is Obtained using the following method: Figure 3 The phasor relationship diagram before and after the fault, E and E d are the grid voltage amplitudes before and after the fault, and the initial value at the time of the fault is obtained in the three-phase stationary coordinate system. The power angle before the fault is After the fault, the power angle is dynamically adjusted to reach a new steady-state equilibrium point. The power angle at this equilibrium point is , and satisfy:

[0028] (2)

[0029] In a specific embodiment of the present invention, the process of step 2) is specifically as follows: at the steady-state equilibrium point after the fault The nonlinear terms in the second-order nonlinear differential equation are expanded using Taylor series, the linear vibration part and the nonlinear disturbance part are separated, and the original second-order nonlinear differential equation is linearized into a simple harmonic vibration equation with damping:

[0030] (3)

[0031] in, is the power angle change, and its initial condition is , ; is the free vibration frequency; is the small perturbation parameter; is a nonlinear expansion, specifically:

[0032] ;

[0033] Ignoring the influence of small disturbances on the right side of the equation, the homogeneous solution obtained by the second-order linear homogeneous differential equation solution method is as follows:

[0034] (4)

[0035] in, and are the initial amplitude and initial phase of the power angle variation, t represents time, is the damped vibration frequency, ignoring and The higher order terms of The initial conditions of are obtained as follows:

[0036] (5)

[0037] Then we get the power angle The approximate analytical expression of is:

[0038] (6)

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

[0040] (7)

[0041] The power angle expression in formula (6) Substituting into formula (7), the grid resistance is derived as and inductance The time domain joint expression of the upper voltage is:

[0042] (8)

[0043] Since the interference introduced by the exponential decay term in the power angle expression is small, the trigonometric function of the power angle can be approximately equivalently processed: Approximately equivalent to , Approximately equivalent to Substituting the above equivalent relationship into the time domain joint expression of voltage, the steady-state component of fault voltage is further decomposed to obtain and dynamic components :

[0044] (9)

[0045] (10)

[0046] in: is the dynamic sinusoidal 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 of the first-order differential equation of the grid-connected current ; Based on the steady-state component of the fault voltage Expression structure characteristics, setting the steady-state component of fault current In the form of sine and cosine superposition, it is substituted into the original differential equation and the steady-state solution is obtained by coefficient matching. Then the dynamic component of the fault voltage is Substitute the differential equation and use the integral factor method to obtain the analytical expression of the current dynamic component containing the decay oscillation term Finally, the homogeneous solution, steady-state solution, and dynamic solution are superimposed to establish the current analytical expression of 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 of the first-order differential equation of the grid-connected current is:

[0050] (11)

[0051] Among them, the initial current coefficient C is determined by the initial current at the time of fault OK, that is ;

[0052] Will The corresponding steady-state current solution is expressed in sinusoidal form:

[0053] (12)

[0054] Substituted into equation (7), the steady-state analytical expression of the fault current is obtained by coefficient matching:

[0055] (13)

[0056] Using the integrating factor method to solve the problem of decaying oscillation The corresponding analytical expression of the dynamic part of the fault current is:

[0057] (14)

[0058] in: 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] Adding the homogeneous solution expression, the steady-state analytical expression, and the dynamic analytical expression, we can get 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 grid-type 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 false operation caused by the direct application of traditional synchronous machine protection methods, and significantly improving the grid fault ride-through capability and the coordinated adaptability of the protection system.

[0062] In order 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 grid-connected simulation model of grid-connected converter

[0064]

[0065] Figure 4 The analytical and simulated waveforms of the A-phase grid-connected current are shown when the grid voltage amplitude drops to 0.7 pu at t = 0 s, with a damping coefficient of D = 25 p.u., a virtual inertia time constant of H = 10 s, and other parameters satisfying Table 1. It can be seen that the two waveforms are highly consistent, proving the correctness of the analytical expression for the fault current.

[0066] In order to quantitatively verify the accuracy of the expression, the matching degree (MD) is introduced to represent the similarity. From its expression, we can see that the larger the MD value, the higher the similarity:

[0067] ;

[0068] Among them, I sim and I anl They represent the current simulation and current analysis, respectively. Table 2 shows the MD values ​​under nine test conditions, which are generally higher than 96%, proving the consistency between the current analysis and simulation results and the correctness of the fault transient current calculation method.

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

[0070]

[0071] The above description of the embodiments is intended to facilitate understanding and application of the present invention by those skilled in the art. Those skilled in the art will readily be able to make various modifications to the above embodiments and apply the general principles described herein to other embodiments without requiring inventive effort. Therefore, the present invention is not limited to the above embodiments. Improvements and modifications made by those skilled in the art based on the disclosure of the present invention, such as adopting different converter structures, different current inner loop control methods, etc., should fall within the scope of protection of the present invention.

Claims

1. A method for analyzing transient current of a grid-connected converter fault taking into account the power angle swing process, characterized in that: The following steps are involved: 1) The grid-connected converter is equivalent to a self-synchronous voltage source, and the power angle is defined as the phase angle difference between the converter output voltage and the grid voltage. A second-order nonlinear differential equation with a virtual inertia time constant and damping coefficient is established. 2) Perform a Taylor series expansion on the nonlinear terms in the second-order nonlinear differential equation at the post-fault power angle equilibrium point to separate the linear oscillation component from the nonlinear disturbance component. The second-order nonlinear differential equation is linearized into a damped simple harmonic oscillation equation. Combined with the initial power angle before the fault, an approximate analytical expression for the power angle is obtained. 3) After the fault, ignoring the tracking process of the voltage and current dual loops, based on Kirchhoff's voltage law and combined with the equivalent circuit after the fault, a first-order differential equation for the grid current including the grid resistance and grid inductance is established. The approximate analytical expression for the power angle from step 2) is substituted into the first-order differential equation for the grid current to obtain a time-domain joint expression for the voltage across the grid resistance and grid inductance, which is then decomposed into a steady-state component and a dynamic component of the fault voltage. 4) Determine the homogeneous solution 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, the steady-state component of the fault current is set to the form of sine and cosine superposition, substituted into the differential equation, and the specific analytical expression of the steady-state component is obtained by coefficient matching; Then the dynamic component of the fault voltage is introduced into the differential equation to obtain the analytical expression of the dynamic component of the current including the decay oscillation term. Finally, the homogeneous solution, steady-state component and dynamic component are superimposed to establish the analytical expression of the current of the entire fault transient process.

2. The method for analyzing fault transient current of a grid-connected converter taking into account the power angle swing process according to claim 1 is characterized in that: The fault is a three-phase symmetrical drop fault of the power grid voltage.

3. The method for analyzing transient current of a grid-connected converter fault taking into account the power angle swing process according to claim 2, characterized in that: In step 1), the power angle ,in, is the voltage phase at the output of the converter; is the grid voltage phase; The second-order nonlinear differential equation containing the virtual inertia time constant and the damping coefficient is: ； Where: H is the virtual inertia time constant, D is the damping coefficient, is the converter output active power reference value, is the reference value of the output voltage amplitude, is the grid voltage amplitude, is the equivalent grid impedance, which is determined by the grid inductance and grid resistance constitute.

4. The method for analyzing transient current of a grid-connected converter fault taking into account the power angle swing process according to claim 3 is characterized in that: In step 2), Obtain the initial value at the time of fault in the three-phase stationary coordinate system, and record the initial power angle before the fault as After the fault, the power angle is dynamically adjusted to reach a new steady-state equilibrium point. The power angle at this equilibrium point is , then: ； in, is the grid voltage amplitude after the fault drop.

5. The method for analyzing transient current of a grid-connected converter fault taking into account the power angle swing process according to claim 4, characterized in that: The process of step 2) is specifically as follows: Steady-state equilibrium point after fault The nonlinear terms in the second-order nonlinear differential equation are expanded using Taylor series, the linear vibration part and the nonlinear disturbance part are separated, and the original second-order nonlinear differential equation is linearized into a simple harmonic vibration equation with damping: ； in, is the power angle change, and its initial condition is , ; is the free vibration frequency; is the small perturbation parameter; is a nonlinear expansion, specifically: ； Ignoring the influence of small disturbances, the homogeneous solution obtained by using the second-order linear homogeneous differential equation solution method is: ； in, and are the initial amplitude and initial phase of the power angle variation, t represents time, is the damped vibration frequency, ignoring and The higher order terms of The initial conditions of are obtained as follows: ； Then we get the power angle The approximate analytical expression of is: 。 6. The method for analyzing transient current of a grid-connected converter fault taking into account the power angle swing process according to claim 3, characterized in that: Step 3) The first-order differential equation of the grid-connected current including the grid resistance and grid inductance is: ； Where, is the grid-connected current expression, is the voltage vector at the output of the converter, is the grid voltage vector after a three-phase symmetrical fault drop.

7. The method for analyzing transient current of a grid-connected converter fault taking into account the power angle swing process according to claim 6, characterized in that: In step 3), the tracking process of ignoring the voltage and current dual loops is specifically as follows: after a fault, the voltage amplitude reference value of the converter terminal remains unchanged, the current control link does not perform a limiting operation, and the voltage and current dual loops can quickly and accurately track the reference value.

8. The method for analyzing transient current of a grid-connected converter fault taking into account the power angle swing process according to claim 7, characterized in that: The process of step 3) is specifically as follows: The power angle expression Substituting into the first-order differential equation of the grid current, the grid resistance is derived and grid inductance The time domain joint expression of the upper voltage is: ； Where, is the fundamental angular frequency; Since the interference introduced by the exponential decay term in the power angle expression is small, the trigonometric function of the power angle is approximately equivalent: Approximately equivalent to , Approximately equivalent to ; Substitute the above equivalent relationship into the time domain joint expression of voltage and further decompose to obtain the steady-state component of fault voltage and dynamic components : ； ； in: is the dynamic sinusoidal deviation of the power angle; is the dynamic cosine deviation of the power angle.

9. The method for analyzing transient current of a grid-connected converter fault taking into account the power angle swing process according to claim 8, characterized in that: The process of step 4) is specifically as follows: Homogeneous solution expression of the first-order differential equation of grid-connected current for: ； Among them, the initial current coefficient C is determined by the initial current at the time of fault OK, that is ; Due to the steady-state component of the fault voltage It is a sine-cosine superposition form, so the steady-state component of the fault current is set The form is: ； in, and are the cosine coefficient and 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 by coefficient matching The analytical expression is: ； Then the fault voltage dynamic component Substitute into the differential equation and use the integral factor method to obtain the current dynamic component containing the decay oscillation term The analytical expression is: ； in: 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; Adding the homogeneous solution expression, the steady-state component analytical expression, and the dynamic component analytical expression, we can obtain the complete analytical expression of the fault current: 。

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