A method for analyzing transient synchronization characteristics of converters in extremely weak power grids

Abstract

The present invention discloses a method for analyzing the transient synchronization characteristics of a converter under an extremely weak power grid. The method establishes a fourth-order differential equation for transient synchronization of the converter taking into account the dynamics of reactive current, determines the initial value of the fourth-order differential equation according to a control block diagram, further obtains an accurate phase angle response waveform under an extremely weak power grid through a fourth-order model, and determines the instability boundary and parameter sensitivity, thereby improving the transient synchronization analysis method for the converter taking into account the current dynamics under an extremely weak power grid, and providing a reference for improving the transient synchronization stability of the converter under large disturbances.

Description

Technical Field

[0001] The invention belongs to the technical field of converter grid-connected control, and in particular relates to a method for analyzing transient synchronization characteristics of a converter under an extremely weak power grid. Background Art

[0002] With the continuous increase in the penetration rate of new energy, a high proportion of renewable energy and a high proportion of power electronic equipment have significantly affected the transient characteristics of the power system, bringing new problems of power supply security and stability.

[0003] The mainstream solution for connecting new energy power generation systems to the grid is to use a grid-following converter (GFC) to achieve active / reactive power transmission, which requires a phase-locked loop (PLL) to obtain grid frequency and phase information to achieve grid synchronization. Unlike synchronous machines, the transient synchronization characteristics of GFCs are mainly determined by control strategies and control parameters. In recent years, scholars have found that if GFCs are affected by some large disturbances that change the operating point in a weak grid, such as a grid voltage drop, the PLL may not be able to resynchronize during the transient process, resulting in a loss of step fault.

[0004] At present, the following studies have been conducted on the transient synchronization characteristics of GFC at home and abroad: ① The literature [Taul MG, Wang X, Davari P, et al. An Overview of Assessment Methods for Synchronization Stability of Grid-Connected Converters under Severe Symmetrical Grid Faults [J]. IEEE Transactions on Power Electronics, 2019, 34 (10): 9655-9670] determines whether the system is stable by calculating the steady-state operating critical value of GFC. However, in fact, even if the stability judgment conditions are met, a loss-of-step fault may occur. This is because the system has inertia during the transient synchronization process. ② Literature [Chen Junru, Li Guanqun, Liu Muyang, Ye Hua. Influence Mechanism of Grid Impedance Ratio on Synchronous Stability of Grid-following Converter [J]. Proceedings of the CSEE, 2023, 43(06): 2331-2339] uses a quasi-steady-state large signal block diagram to analyze transient synchronization characteristics, which is equivalent to assuming that other links except PLL are in a steady state, and can be extended to the analysis of multi-machine stability; but this is still only a qualitative analysis method, and as the model order increases, the quasi-steady-state large signal block diagram will become complicated. ③ Literature [Shuai Z, Shen C, Liu X, et al. Transient Angle Stability of Virtual Synchronous Generators Using Lyapunov's Direct Method [J]. IEEE Transactions on Smart Grid, 2019, 10(4): 4648-4661] uses Lyapunov's direct method to quantitatively analyze the critical range of out-of-step, but it is difficult to find a suitable potential function in some scenarios.

[0005] The above analysis methods are all based on the assumption that the current loop bandwidth is much larger than the PLL bandwidth. When the d-axis voltage feedforward term is added to further increase the current response speed, the GFC can be regarded as a constant current source in the transient synchronization time scale, and a second-order transient synchronization model can be used to measure whether a step-out fault will occur. However, new energy equipment such as wind turbines may be placed in the open sea or remote mountainous areas. Long-distance transmission lines lead to extremely weak power grid environments with very small short-circuit ratios, thus presenting slower current dynamics. At this time, the current dynamics and transient synchronization dynamics will be coupled. The existing technology lacks a method for analyzing the transient synchronization characteristics of converters under extremely weak power grids. Summary of the invention

[0006] In view of the above, the present invention provides a method for analyzing the transient synchronization characteristics of a converter under an extremely weak power grid, which establishes a fourth-order differential equation and initial value for transient synchronization of the converter considering the dynamics of reactive current, improves the transient synchronization analysis method for the converter considering the current dynamics under an extremely weak power grid, and provides a reference for improving the transient synchronization stability of the converter under large disturbances.

[0007] A method for analyzing transient synchronization characteristics of a converter under an extremely weak power grid comprises the following steps:

[0008] (1) It is verified through simulation that the grid-following converter cannot ignore the reactive current dynamics under extremely weak power grid. The DC side of the grid-following converter is connected to the new energy device, and the AC side is connected to the remote AC grid through the filter inductor and the grid inductor;

[0009] (2) For grid-following converters, a fourth-order differential equation for converter transient synchronization is established taking into account the dynamics of reactive current;

[0010] (3) Determine the system's instability boundary and parameter sensitivity based on the fourth-order differential equation of converter transient synchronization.

[0011] Furthermore, the fourth-order differential equation for transient synchronization of the converter is expressed as follows:

[0012]

[0013] Among them: x1~x4 are the four state variables of the differential equation, which correspond to the phase angle of the grid-type converter, the output reactive current of the grid-type converter, the output angular frequency of the phase-locked loop, and the differential of the output reactive current of the grid-type converter. The superscript ' represents the differential operator, and δ is the output angle of the phase-locked loop θ. PLL Phase angle θ with the remote AC grid voltage GCP The phase angle difference is δ = θ PLL -θ GCP , I q is the q-axis component of the grid-following converter output current, U fault is the voltage amplitude of the remote AC grid under fault, K pp and K ip They are the proportional coefficient and integral coefficient of the PI link in the phase-locked loop, K pc and K ic are the proportional coefficient and integral coefficient of the PI link in the current controller of the grid-following converter, ω g is the grid angular frequency, L g is the grid inductance, L f is the filter inductance value, and They are the output active current reference value and output reactive current reference value of the grid-following converter respectively.

[0014] Furthermore, the dynamic expression of the phase angle difference δ is as follows:

[0015] δ=∫[K pp (-U GCP sinδ+R g I q +ω PLL L g I d +L g I q ′)+K ip ∫(-U GCP sinδ+R g I q +ω PLL L g I d +L g I q ′)] where: U GCP is the voltage amplitude of the remote AC grid, R g is the grid resistance, I d is the d-axis component of the grid-following converter output current, ω PLL is the output angular frequency of the phase-locked loop.

[0016] Furthermore, when the new energy device is subject to a large disturbance, θ PLL With θ PCC are not equal. If the phase difference δ between the two angles exceeds 180°, a loss of step will occur. Therefore, an iterative solution is performed based on the dynamic expression of the phase difference δ. If the phase difference δ converges to a constant, it means that the system has achieved transient synchronous stability. If the phase difference δ cannot converge, it means that the system has a loss of step fault.

[0017] Furthermore, the q-axis component I of the output current of the grid-following converter q It is obtained by the following expression:

[0018]

[0019] Among them: U GCP is the voltage amplitude of the remote AC grid, I d is the d-axis component of the output current of the grid-following converter.

[0020] Furthermore, the initial value expressions of the phase angle difference δ and its differential result δ' are as follows:

[0021]

[0022] Among them: δ0 and δ0' correspond to the initial values ​​of δ and δ' respectively, I max is the maximum current amplitude output by the grid-type converter before the fault, Unom is the voltage amplitude of the remote AC power grid before the fault, I q0 'For I q ''s initial value.

[0023] Furthermore, the grid-following converter outputs a current q-axis component I q And its differential result I q The initial value expression of ' is as follows:

[0024]

[0025] Where: I q0 and I q0 ' respectively correspond to I q and I q ', δ0 and δ0' correspond to the initial values ​​of δ and δ' respectively.

[0026] Compared with the traditional second-order differential equation, the initial value of the fourth-order differential equation has an additional denominator term δ0' And because of the existence of the integral link, the reactive current will not change suddenly at the moment of the fault. If the grid-following converter operates at unity power factor before the fault, then I q0 is 0.

[0027] Furthermore, in step (3), after obtaining the fourth-order differential equation for transient synchronization of the converter, the parameter sensitivity of the system can be analyzed by drawing a stable region diagram under parameter changes. If the phase angle difference δ solved by the equation exceeds 180° 2s after the fault, the system is judged to be out of step; otherwise, it means that the system is in a stable state.

[0028] The present invention establishes a fourth-order differential equation for transient synchronization of the converter taking into account the dynamics of reactive current, determines the initial value of the fourth-order differential equation according to the control block diagram, further obtains the accurate phase angle response waveform under the extremely weak power grid through the fourth-order model, and determines the instability boundary and parameter sensitivity, thus improving the transient synchronization analysis method of the converter taking into account the current dynamics under the extremely weak power grid, and providing a reference for improving the transient synchronization stability of the converter under large disturbances. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Schematic diagram of the control structure of a grid-following converter connected to an extremely weak power grid.

[0030] Figure 2 (a) is the phase angle simulation waveform of the grid-following converter when the voltage drops to 414V under extremely weak grid conditions.

[0031] Figure 2 (b) is the simulated waveform of the output current of the grid-following converter when the voltage drops to 414V under extremely weak grid conditions.

[0032] Figure 3 This is the principle block diagram for calculating the initial values ​​of phase angle and reactive current.

[0033] Figure 4 (a)~ Figure 4 (d) are the phase angle dynamic waveforms at different grid voltage drop depths.

[0034] Figure 5 (a) is the sensitivity analysis diagram of voltage drop depth and grid inductance when reactive current dynamics is ignored.

[0035] Figure 5 (b) is a sensitivity analysis diagram of voltage drop depth and grid inductance considering reactive current dynamics.

[0036] Figure 6 (a) is the sensitivity analysis diagram of the proportional integral gain of the phase-locked loop when the reactive current dynamics is ignored.

[0037] Figure 6 (b) is the sensitivity analysis diagram of the proportional integral gain of the phase-locked loop considering the dynamic reactive current. DETAILED DESCRIPTION

[0038] In order to describe the present invention more specifically, the technical solution of the present invention is described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0039] The method for analyzing transient synchronization characteristics of a converter under an extremely weak power grid of the present invention comprises the following steps:

[0040] (1) Verify that GFC cannot ignore current dynamics in extremely weak power grids.

[0041] A real-time electromagnetic transient (EMT) simulation model of GFC was established in Matlab / Simulink. Figure 1 As shown in the figure, the subscripts d and q represent the variables in the two-phase rotating coordinate system, the superscript ref represents the reference value, and U GFC , U PCC , U GCP Represents the amplitude of GFC output voltage, grid connection point voltage and remote grid voltage, grid inductance L g is 0.808mH(0.8pu),θ PCC and θ GCP Represents the phase angle between the grid connection point voltage and the remote grid voltage, I PCC Represents the three-phase current vector, L f is the filter inductor, ω g =100πrad / s is the reference angular frequency, θ PLL and ω PLL is the PLL output angle and output angular frequency, Vdc is the DC bus voltage, K pp and K ip is the proportional and integral parameter of the PLL, the current loop bandwidth is 1500Hz (the current loop proportional gain K pc =0.5, current loop integral gain K ic =5).

[0042] When a fault occurs, the voltage amplitude of the remote power grid drops from 690V to 414V. The current output criteria for grid connection are as follows:

[0043]

[0044] Among them: U fault is the fault voltage, U nom is the rated voltage.

[0045] According to the grid connection criteria, GFC needs to output 0.8pu reactive current at the moment of fault. max =1p.u., the active current also needs to be reduced to 0.6pu. The EMT simulation waveform during the fault period is as follows Figure 2 (a) and Figure 2 (b) where the phase angle δ = θ PLL -θ GCP It is usually used in existing studies to describe the transient out-of-step process, θ GCP =∫ω g dt. When the new energy device is subject to a large disturbance, the transient process θ PLL With θ PCC are not equal. If δ can eventually converge to a constant, it means that transient synchronous stability has been achieved. If δ cannot converge, it means that the system has a loss of synchronization fault.

[0046] Existing research suggests that the dynamic response time of current is related to the grid inductance and the current loop bandwidth. When the grid inductance increases, the current will reach a steady state more slowly. At this time, it is necessary to increase the current loop bandwidth to improve the current dynamic response speed. Figure 2 (b) It can be found that after using the current controller with a bandwidth of 1500 Hz, the active current can indeed reach a steady state quickly. However, the reactive current still does not fully converge to the current reference value at 0.05 s. Its dynamic time is much longer than that of the active current. Figure 2 The phase angle dynamics in (a) are coupled in time scale, which shows that in extremely weak inductive grids, increasing the current loop bandwidth cannot decouple the phase angle dynamics from the reactive current dynamics, and the reactive current dynamics must be considered.

[0047] (2) Establish the fourth-order differential equation for converter transient synchronization taking into account the reactive current dynamics.

[0048] according to Figure 1 , the GFC circuit equation, control equation and grid connection point voltage expression considering the current dynamics are as follows:

[0049]

[0050]

[0051]

[0052] Combining the above three equations, we can get the following formula:

[0053]

[0054] Then, by taking the derivative of the above formula, we can get:

[0055]

[0056] Finally, the fourth-order differential equation considering the reactive current dynamics can be obtained:

[0057]

[0058] (3) Determine the initial value of the fourth-order differential equation based on the control block diagram.

[0059] Initial phase angle δ during fault period i Usually remains unchanged, but δ i 'Additional L g I qi ' / (1-K pp L g Iref d), I qi and I qi 'Can be passed Figure 3 Obtained, where due to the existence of the integral link, the reactive current will not change suddenly at the moment of the fault. If the GFC operates at unity power factor before the fault, then I qi is 0; in summary, the initial value of the fourth-order differential equation is as follows:

[0060]

[0061] (4) Verify the accuracy of the fourth-order model of converter transient synchronization considering reactive current dynamics.

[0062] In order to verify the accuracy of the fourth-order model of converter transient synchronization considering reactive current dynamics, Figure 4 (a)~ Figure 4 (d) The dynamic waveform diagram of the EMT simulation phase angle under different voltage drop depths is given, and the analytical waveform diagrams of the traditional second-order and fourth-order transient synchronization models of the present invention are given.

[0063] By comparison Figure 4 (a)~ Figure 4 The EMT simulation waveform and the fourth-order transient synchronization model in (d) show that their phase angle dynamic characteristics are completely consistent, which verifies the accuracy of the fourth-order transient synchronization model proposed in the present invention. However, the second-order transient synchronization model has the following problems:

[0064] 1.When U GCP When it drops to 0.6pu, it will output 0.6pu of active current, with an initial value of δ i and the final value δ n Both are 0.927 rad, so the second-order model determines that δ will not fluctuate, but the δ of the EMT simulation waveform fluctuates significantly in the range of [0.34, 1.1].

[0065] 2.When U GCP When falling, the δ of the EMT simulation waveform will first decrease and then increase, and a "reverse run phenomenon" will occur. It will not directly return to the final value δ n movement, but the second-order model cannot predict and explain this phenomenon.

[0066] 3.When U GCP When it drops to 0.7pu or 0.8pu, δ will exceed the limit value δ max , a step-out fault occurs. However, the second-order model believes that δ will converge under these four drop depths.

[0067] For problem 1: Even if the initial value δ i Equal to the final value δ n , the dynamic response process of reactive current cannot be ignored during voltage drop; due to I q There is a coupling relationship between ' and δ', U GCP When it drops to 0.6 pu, I q It will decrease from 0 to -0.8pu, which will cause the fluctuation of δ.

[0068] For question 2: When a step-out fault occurs in an inductive power grid, the final value δ of the second-order model is n It is often larger than the initial value δ i , then ω in the second-order model g L g Iref d is often greater than U fault sinδ i Therefore, the second-order model predicts that δ will increase first after the voltage drop fault; however, the δ in the initial value calculation formula of the fourth-order model i 'Also includes L g I qi ', voltage drop fault I q The decrease of δ i' is negative, which causes the fourth-order model to predict that δ will decrease first after the voltage drop fault, thus causing the "reverse run phenomenon".

[0069] Regarding question 3: The instantaneous increase in reactive power will cause L g I qi The absolute value of ' is very large, so the transient initial velocity of δ is also very large. gcp When it drops to 0.7pu or 0.8pu, δ returns to the initial value δ in 0.012s and 0.009s respectively. i , it can be seen from the enlarged figure that the slope at this time is greater than the initial slope at 0s of the second-order model, so it has a faster moving speed, making it easier to exceed δ max This will cause a step-out fault.

[0070] In summary, the fourth-order transient synchronization model proposed in the present invention can describe the transient synchronization characteristics under extremely weak power grids.

[0071] (5) Determine the system's instability boundary and parameter sensitivity through the fourth-order model.

[0072] After obtaining the accurate fourth-order transient synchronization model of GFC under extremely weak inductive power grid, the parameter sensitivity can be analyzed by drawing the stable region diagram under parameter changes. The device used to solve the differential equation in this implementation is a 1.99GHz, i7-8550U processor, 24GB RAM, 64-bit operating system, Win10 ThinkPad. It takes 5 minutes to test each set of 100×100 data; if the δ solved by the differential equation exceeds 180° at 2s, the system is judged to be out of step, otherwise it means that the system is in a stable state, which is represented by the black area.

[0073] according to Figure 5 (a) and Figure 5 (b) It can be found that with the increase of grid inductance, the second-order transient synchronization model that ignores the reactive current dynamics and the fourth-order transient synchronization model that considers the reactive current dynamics are more likely to have out-of-step faults. The probability of out-of-step faults for both the second-order and fourth-order transient synchronization models is highest when the voltage drops between 0.7pu and 0.8pu. The limiting inductance after considering the reactive current dynamics is 0.78pu, which is lower than 0.82pu after ignoring the reactive current dynamics, resulting in misjudgment of the second-order transient synchronization model.

[0074] Voltage drop in the power grid U fault The grid inductance L is 0.75pu g For 0.8pu, according to Figure 6 (a) and Figure 6(b) It can be found that as the proportional gain of the phase-locked loop decreases and the integral gain of the phase-locked loop increases, the damping ratio of the phase-locked loop will decrease, resulting in an increase in the probability of the system losing step; but after considering the reactive current dynamics, as the proportional gain and integral gain of the phase-locked loop further increase, the system will re-occur out-of-step faults, and the area of ​​the unstable region will also increase. This is because as K pp and K ip The increase of phase angle δ and reactive current I q The coupling degree will also become stronger, resulting in a faster phase angle movement speed δ', making it easier to exceed δ max A step-out fault occurs.

[0075] The above description of the embodiments is to facilitate the understanding and application of the present invention by those skilled in the art. It is obvious that those skilled in the art can easily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative work. Therefore, the present invention is not limited to the above embodiments. Improvements and modifications made by those skilled in the art to the present invention based on the disclosure of the present invention should be within the protection scope of the present invention.

Claims

1. A method for analyzing transient synchronization characteristics of a converter under an extremely weak power grid, comprising the following steps: (1) It is verified through simulation that the grid-following converter cannot ignore the reactive current dynamics under extremely weak power grid. The DC side of the grid-following converter is connected to the new energy device, and the AC side is connected to the remote AC grid through the filter inductor and the grid inductor; (2) For the grid-following converter, the fourth-order differential equation for converter transient synchronization considering the dynamics of reactive current is established as follows: in: x1~x4 are the four state variables of the differential equation, which correspond to the phase angle of the grid-type converter, the output reactive current of the grid-type converter, the output angular frequency of the phase-locked loop, and the differential of the output reactive current of the grid-type converter. The superscript ' represents the differential operator, and δ is the output angle θ of the phase-locked loop. PLL Phase angle θ with the remote AC grid voltage GCP The phase angle difference is δ = θ PLL -θ GCP , I q is the q-axis component of the grid-following converter output current, U fault is the voltage amplitude of the remote AC grid under fault, K pp and K ip They are the proportional coefficient and integral coefficient of the PI link in the phase-locked loop, K pc and K ic are the proportional coefficient and integral coefficient of the PI link in the current controller of the grid-following converter, ω g is the grid angular frequency, L g is the grid inductance, L f is the filter inductance value, and They are the output active current reference value and the output reactive current reference value of the grid-following converter respectively; (3) The instability boundary and parameter sensitivity of the system are determined based on the fourth-order differential equation of transient synchronization of the converter. That is, the parameter sensitivity of the system is analyzed by drawing a stable region diagram under parameter changes. If the phase angle difference δ solved by the equation exceeds 180° 2s after the fault, the system is judged to be out of step. Otherwise, it means that the system is in a stable state.

2. The method for analyzing transient synchronization characteristics of a converter according to claim 1, characterized in that: The dynamic expression of the phase angle difference δ is as follows: δ=∫[K pp (-U GCP sinδ+R g I q +ω PLL L g I d +L g I q ′)+K ip ∫(-U GCP sinδ+R g I q +ω PLL L g I d +L g I q ′)] Among them: U GCP is the voltage amplitude of the remote AC grid, R g is the grid resistance, I d is the d-axis component of the grid-following converter output current, ω PLL is the output angular frequency of the phase-locked loop.

3. The method for analyzing transient synchronization characteristics of a converter according to claim 2, characterized in that: When the new energy device is subject to a large disturbance, θ PLL With θ PCC are not equal. If the phase difference δ between the two angles exceeds 180°, a loss of step will occur. Therefore, an iterative solution is performed based on the dynamic expression of the phase difference δ. If the phase difference δ converges to a constant, it means that the system has achieved transient synchronous stability. If the phase difference δ cannot converge, it means that the system has a loss of step fault.

4. The method for analyzing transient synchronization characteristics of a converter according to claim 1, characterized in that: The q-axis component I of the output current of the grid-following converter q It is obtained by the following expression: Among them: U GCP is the voltage amplitude of the remote AC grid, I d is the d-axis component of the output current of the grid-following converter.

5. The method for analyzing transient synchronization characteristics of a converter according to claim 1, characterized in that: The initial value expressions of the phase angle difference δ and its differential result δ' are as follows: Among them: δ0 and δ0' correspond to the initial values ​​of δ and δ' respectively, I max is the maximum current amplitude output by the grid-type converter before the fault, U nom is the voltage amplitude of the remote AC power grid before the fault, I q0 'For I q 'The initial value of .

6. The method for analyzing transient synchronization characteristics of a converter according to claim 1, characterized in that: The grid-following converter outputs the current q-axis component I q And its differential result I q The initial value expression of ' is as follows: Where: I q0 and I q0 ' respectively correspond to I q and I q ', δ0 and δ0' correspond to the initial values ​​of δ and δ' respectively.

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