A transient power angle stability analysis method for virtual synchronous generator with virtual speed regulator

Abstract

A method for analyzing the transient power angle stability of a virtual synchronous generator containing a virtual speed regulator relates to the field of microgrid technology. The method includes: constructing a large signal reduced-order model of a virtual synchronous generator containing a low-pass filter type virtual speed regulator; qualitatively analyzing the large signal reduced-order model based on the extended equal-area rule to determine the stability of the transient power angle of the virtual synchronous generator containing the low-pass filter type virtual speed regulator; based on the qualitative analysis, quantitatively analyzing the large signal reduced-order model using a phase diagram method to determine the influence of different control parameters on the transient power angle stability performance of the virtual synchronous generator containing the low-pass filter type virtual speed regulator; determining the transient stability parameter range of the virtual synchronous generator containing the low-pass filter type virtual speed regulator. The method of the present invention can not only improve the comprehensiveness and accuracy of the analysis and reduce the conservatism of the analysis, but also effectively evaluate the stability domain of the speed regulator based on the analysis method.

Description

Technical Field

[0001] The present invention relates to the technical field of microgrids, and in particular to a method for analyzing transient power angle stability of a virtual synchronous generator containing a virtual speed regulator. Background Art

[0002] In order to solve the energy crisis and environmental pollution problems, a large number of new energy sources such as solar energy and wind energy have been widely adopted and connected to the power grid through power electronic converters. At the same time, the large-scale access of new energy sources and their power electronic converters will cause a significant reduction in the inertia level of the power grid. In order to compensate for the inertia loss, converters based on virtual synchronous generators have received widespread attention in recent years. Virtual synchronous generators (VSGs) are mainly composed of rotor motion loops, virtual speed regulator loops, and reactive power control loops. They can imitate the output characteristics of traditional synchronous generators, so that virtual synchronous generators have inertial support, frequency regulation, and voltage control capabilities. However, similar to synchronous generators, under large disturbances such as short circuits and grid voltage sags, virtual synchronous generators often suffer from serious transient stability problems due to the imbalance between mechanical power and output electromagnetic power, which causes the acceleration area to be larger than the deceleration area.

[0003] Domestic and foreign scholars have conducted a lot of research on the transient stability of virtual synchronous generators. From the perspective of transient stability analysis methods, existing methods include numerical time domain analysis, Lyapunov energy function method, phase diagram method and equal area method. From the perspective of transient stability mechanism, a large number of studies are devoted to the study of rotor motion loop, reactive power control loop and current limiting control of virtual synchronous generators. However, the virtual speed regulator, as an important component of the virtual synchronous generator, is often overlooked. It plays a vital role in effectively regulating the input mechanical power. Its parameters not only affect the system frequency and parallel power distribution, but also have an important influence on maintaining the transient power angle stability of the virtual synchronous generator. The influence of the virtual speed regulator on the transient power angle stability of the virtual synchronous generator needs to be studied.

[0004] As we all know, as the primary frequency regulation link of traditional synchronous generators, speed regulators play an important role in the safe and stable operation of the system. At the same time, the influence of speed regulators on stability in traditional synchronous generators has been widely studied. Compared with traditional synchronous generators, the control of virtual synchronous generators is more flexible and diverse. Therefore, by reasonably designing the structure and parameters of virtual speed regulators, virtual synchronous generators can more easily achieve transient stability under large disturbances. At present, typical virtual speed regulators mainly include high-pass filter type and low-pass filter type. Among them, the virtual synchronous generator with low-pass filter type virtual speed regulator is more similar to the traditional synchronous generator in structure, making its dynamic response closer to that of the traditional synchronous generator, which is conducive to the stable operation of the synchronous generator and virtual synchronous generator parallel system. However, the existing literature only studies the system modeling after adding this virtual speed regulator and the dynamic characteristics under load power changes, and does not analyze the deep-level influence mechanism of dynamic characteristics. At the same time, it also does not consider the influence of this virtual speed regulator on the transient power angle stability of the virtual synchronous generator under large disturbances. At the same time, in order to solve the influence of low-pass filter virtual speed regulator on the transient power angle stability of virtual synchronous generator under large disturbance, some literatures have proposed to use equal area rule and Lyapunov energy function to evaluate the transient stability of the system. However, these analysis methods generally have shortcomings such as incomplete and unclear analysis of the influencing mechanism and overly conservative analysis results. Summary of the invention

[0005] The method for analyzing the transient power angle stability of a virtual synchronous generator containing a virtual speed regulator provided by the present invention can effectively solve the problems of incomplete analysis, low accuracy and strong conservatism in the existing method for analyzing the transient power angle stability of a virtual synchronous generator containing a virtual speed regulator.

[0006] In order to solve the above technical problems, the present invention adopts the following technical method: a method for analyzing transient power angle stability of a virtual synchronous generator containing a virtual speed regulator, comprising the following steps:

[0007] S1, construct a large signal reduced-order model of a virtual synchronous generator with a low-pass filter virtual speed regulator;

[0008] S2, based on the extended equal area rule, the large signal reduced-order model is qualitatively analyzed to determine the stability of the transient power angle of the virtual synchronous generator containing the low-pass filter type virtual speed regulator;

[0009] S3, based on the qualitative analysis in step S2, using a phase diagram method to quantitatively analyze the large signal price reduction model to determine the influence of different control parameters on the transient power angle stability performance of the virtual synchronous generator with a low-pass filter type virtual speed regulator;

[0010] S4, determining the transient stability parameter range of the virtual synchronous generator including the low-pass filter type virtual speed regulator.

[0011] Furthermore, in step S1, the method for constructing the large signal reduced-order model is as follows:

[0012] S11, combining the characteristics of the virtual synchronous generator rotor motion loop, reactive power control loop and low-pass filter type virtual speed regulator, determine the expression of the virtual synchronous generator with low-pass filter type virtual speed regulator;

[0013] S12, using the coupling relationship between the active power and reactive power transmitted between the virtual synchronous generator and the power grid to determine the relationship between the active power and the power angle considering the reactive power control loop;

[0014] S13, according to the expression of the virtual synchronous generator obtained in step S11 and the relationship between the active power and the power angle obtained in step S12, an equivalent circuit model of the virtual synchronous generator is established to obtain a large signal reduced-order model of the virtual synchronous generator.

[0015] Furthermore, in step S11:

[0016] The expression of the rotor motion loop of the virtual synchronous generator is as follows:

[0017]

[0018]

[0019] In the formula, J and D P are the virtual inertia coefficient and virtual damping coefficient of VSG respectively; ω represents the virtual angular frequency of VSG, ω 0 is the system angular frequency setting value; δ represents the VSG output voltage phase angle θ ref and the grid voltage phase angle θ g The phase angle difference between them is defined as the power angle; ω g is the grid angular frequency, and ω 0 Equal; P * and P are the reference active power and actual output active power of the virtual speed regulator respectively;

[0020] The expression of the reactive power control loop of the virtual synchronous generator is as follows:

[0021] U ref =U 0 +D q (Q 0 -Q) (3)

[0022] Where U 0 is the VSG output voltage setting value; D q represents the QV droop coefficient; Q 0and Q are the VSG output reference reactive power and actual output reactive power respectively; due to the use of fast internal voltage and current control, U ref is the actual output voltage amplitude of VSG;

[0023] The expression of the low-pass filter type virtual speed regulator of the virtual synchronous generator is as follows:

[0024]

[0025] Where P 0 is the VSG output active power setting value; G is the gain, ω c is the cut-off angular frequency, s is the Laplace operator;

[0026] Combining the above expressions (1), (2), (3) and (5), the expression of the virtual synchronous generator with a low-pass filter type virtual speed regulator is obtained as follows.

[0027]

[0028] Furthermore, in step S12, when determining the relationship between the active power and the power angle considering the reactive power control loop:

[0029] First, the grid voltage U gabc As a reference, let the grid voltage phase θ g =0°, then θ ref =δ, the expressions of active power P and reactive power Q transmitted between the virtual synchronous generator and the power grid are shown in the following equations (7) and (8), respectively:

[0030]

[0031]

[0032] From equations (7) and (8), we can determine that P and Q are related to each other through δ and U ref Mutual coupling;

[0033] Finally, combining equations (8), (3), and (7), we obtain the P-δ relationship considering the reactive power control loop, as follows.

[0034]

[0035] A=1.5D q U g (m 1 cosδ+m 2 sinδ) (10)

[0036] B=6m 1 D q (U 0 +Dq Q 0 ) (11)

[0037]

[0038]

[0039] Furthermore, in step S13, after the equivalent circuit model of the virtual synchronous generator is established, let x 3 =Gδs / (s+ω c ), x=[x 1 ,x 2 ,x 3 ] T , where x 1 represents the power angle δ, x 2 The angular frequency difference Δω=ω-ω g , while ignoring the influence of the voltage and current inner loop with a smaller time scale, the expression of the large signal reduced-order model of the virtual synchronous generator is obtained as follows.

[0040]

[0041] Furthermore, in step S2, when the large signal reduced-order model is qualitatively analyzed based on the extended equal-area rule:

[0042] First, the main influencing factors of the dynamic characteristics of the virtual synchronous generator with a low-pass filter virtual speed regulator are determined based on the large signal reduction model. The main influencing factors are the gain G and the cutoff angular frequency ω. c ;

[0043] Then the stability criterion of the system is determined based on the virtual synchronous generator, as follows:

[0044]

[0045] Where P n =P 0 –(G / (s+ω c )+D p )sδ; A a is the acceleration area, A dmax is the maximum deceleration area, δ 0 is the power angle under normal operation, δ U is the unstable power angle under fault;

[0046] Finally, the influence of various influencing factors on the transient power angle stability of the virtual synchronous generator is analyzed. For the virtual synchronous generator with a low-pass filter virtual speed regulator, increasing G can reduce the acceleration area and increase the maximum deceleration area, which is beneficial to the stability of the transient power angle. cIt will be counterproductive and worsen the system power angle stability.

[0047] Furthermore, in step S3, when the large signal price reduction model is quantitatively analyzed, the gain G and the cutoff angular frequency ω in the virtual speed regulator are determined. c Impact on the transient power angle stability performance of virtual synchronous generator.

[0048] Furthermore, in step S3, when determining the influence of the gain G in the virtual speed regulator on the transient power angle stability performance of the virtual synchronous generator, the system parameters are first used, and the plane diagram of the relationship between the power angle and the angular frequency deviation is drawn using expression (14), and then the dynamic response under the large disturbance of voltage drop is observed. Finally, it is obtained that as the gain G gradually increases, the maximum values ​​of the power angle overshoot and the angular frequency difference gradually decrease, the transient power angle stability margin continues to increase, and the transient stability of the system continues to increase.

[0049] Furthermore, in step S3, the cutoff angular frequency ω in the virtual speed regulator is determined. c When considering the influence of transient power angle stability of virtual synchronous generator, we first use system parameters and use expression (14) to draw a plane diagram of the relationship between power angle and angular frequency deviation, then observe the dynamic response under large voltage drop disturbance, and finally obtain the relationship between the cutoff angular frequency ω and the transient power angle stability of virtual synchronous generator. c With the increase of , the transient power angle stability of the virtual synchronous generator containing the low-pass filter type virtual speed regulator will decrease.

[0050] Preferably, in step S4, the process of determining the transient stability parameter range of the virtual synchronous generator including the low-pass filter type virtual speed regulator is as follows:

[0051] S41, scan and check the gain G and cutoff angular frequency ω with small change steps c , the gain G and the cutoff frequency ω are determined based on a compromise between accuracy and computer calculation burden c The calculation step size is 1 p.u. and 0.05 rad / s;

[0052] S42, according to each specified cutoff angular frequency ω c Get multiple gain G values ​​for stable operation;

[0053] S43, repeat step S42 to obtain the gain G and the cutoff angular frequency ω c Stable area composed of:

[0054] In ω c When <1.2rad / s, no matter what value G takes in (0,50]pu, the system can maintain transient stability;

[0055] When cWhen the value is between [1.2,3.4]rad / s, if G≥2p.u., the system can maintain transient power angle stability, otherwise transient instability will occur;

[0056] In ω c When >3.4rad / s, G≥3p.u. can keep the system stable.

[0057] The method for analyzing the transient power angle stability of a virtual synchronous generator containing a virtual speed regulator involved in the present invention can effectively solve the problems of incomplete analysis, low precision, and strong conservatism of existing methods. Specifically, the present invention constructs a large price reduction signal model of a virtual synchronous generator containing a low-pass filter type virtual speed regulator, and based on this model, uses the extended equal area rule and the phase diagram method to perform qualitative and quantitative analysis on the transient power angle stability of the virtual synchronous generator containing the virtual speed regulator. Not only is the analysis comprehensive, the accuracy of the analysis can be improved, and the conservatism of the analysis can be reduced, but the stability domain of the speed regulator can also be effectively evaluated based on the analysis method. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a flow chart of the method for analyzing transient power angle stability of a virtual synchronous generator including a virtual speed regulator according to the present invention;

[0059] Figure 2 is a control structure diagram of a virtual synchronous generator in an embodiment of the present invention (wherein, Figure 2 a is a typical topology and control structure diagram of energy storage VSG connected to a three-phase power grid; Figure 2 b is the control structure diagram of the virtual speed regulator);

[0060] Figure 3 is a control structure diagram of a virtual speed regulator transfer function in an embodiment of the present invention;

[0061] Figure 4 It is a structural diagram of an equivalent circuit model of a virtual synchronous generator including a low-pass filter type virtual speed regulator in an embodiment of the present invention;

[0062] Figure 5 : is a power angle variation curve diagram of a virtual synchronous generator including a low-pass filter type virtual speed regulator in an embodiment of the present invention (wherein, Figure 5 a is a graph showing the change in power angle under the influence of gain; Figure 5 b is a curve diagram of the power angle change under the influence of the cut-off frequency);

[0063] Figure 6 A plane diagram showing the relationship between the power angle and the angular frequency difference under the influence of different gains in an embodiment of the present invention;

[0064] Figure 7A plane diagram showing the relationship between the power angle and the angular frequency difference under the influence of different cut-off angular frequencies in an embodiment of the present invention;

[0065] Figure 8 A flow chart of obtaining a gain value by specifying a cutoff angular frequency in an embodiment of the present invention;

[0066] Fig. 9 A stable region diagram of the cutoff angular frequency and gain components in an embodiment of the present invention;

[0067] Fig.10 is a curve diagram of system transient stability under different control parameters in the implementation mode of the present invention (wherein, Fig.10 a is the influence of different control parameters on frequency deviation, Fig.10 b is the influence of different control parameters on the power angle);

[0068] Fig.11 is a curve diagram of system transient stability under parameter optimization in an embodiment of the present invention (wherein, Fig.11 a is the effect of parameter optimization on frequency deviation, Fig.11 b is the effect of parameter optimization on the power angle). DETAILED DESCRIPTION

[0069] In order to facilitate the understanding of those skilled in the art, the present invention is further described below in conjunction with embodiments and drawings. The contents mentioned in the implementation modes are not intended to limit the present invention.

[0070] In order to better understand the present invention, the structure of the virtual synchronous generator is first explained before the present invention is described below. Figure 2 (a) shows the typical topology and control structure of energy storage VSG connected to a three-phase grid. It uses pulse width modulation to transfer power from the DC side to the AC side, and L f , C f and L l1 The LCL filter is used to reduce the output current and output voltage ripple. T is the transformer equivalent inductance, R g and L l2 Represent the line resistance and inductance respectively, and L l1 , L T and L l2 Together they form the equivalent inductance L of the line g Here U abc and U gabc Represent the VSG output voltage and grid voltage respectively, P and Q are the VSG output active and reactive power, i abcRepresents the VSG output current flowing into the grid. VSG control mainly consists of three parts: rotor motion loop, reactive power control loop and virtual speed regulator loop. The rotor motion loop and reactive power control loop are used to generate the VSG output voltage phase angle θ ref and amplitude U ref , together constitute the internal output voltage of VSG; the virtual speed regulator mainly adjusts the reference active power P through the transfer function X (LPF or HPF) according to the system angular frequency difference * ,like Figure 2 (b) shown and Figure 3 Considering that transient stability is mainly determined by the power control loop and the virtual speed regulator, the present invention adopts fast dynamic internal voltage and current control to ensure U abc Accurately track U ref .

[0071] A method for analyzing transient power angle stability of a virtual synchronous generator containing a virtual speed regulator includes four major steps, which are specifically as follows.

[0072] The first step is to construct a large signal reduced-order model of a virtual synchronous generator with a low-pass filtering virtual speed regulator.

[0073] S11, combining the characteristics of the virtual synchronous generator rotor motion loop, reactive power control loop and low-pass filter type virtual speed regulator, determine the expression of the virtual synchronous generator with a low-pass filter type virtual speed regulator.

[0074] The expression of the rotor motion loop of the virtual synchronous generator is as follows:

[0075]

[0076]

[0077] In the formula, J and D P are the virtual inertia coefficient and virtual damping coefficient of VSG respectively; ω represents the virtual angular frequency of VSG, ω 0 is the system angular frequency setting value; δ represents the VSG output voltage phase angle θ ref and the grid voltage phase angle θ g The phase angle difference between them is defined as the power angle; ω g is the grid angular frequency, and ω 0 Equal; P * and P are the reference active power and actual output active power output by the virtual speed regulator respectively.

[0078] The expression of the reactive power control loop of the virtual synchronous generator is as follows:

[0079] U ref =U 0 +D q(Q 0 -Q) (3)

[0080] Where U 0 is the VSG output voltage setting value; D q represents the QV droop coefficient; Q 0 and Q are the VSG output reference reactive power and actual output reactive power respectively; due to the use of fast internal voltage and current control, U ref is the actual output voltage amplitude of VSG.

[0081] The virtual speed regulator expression is shown in formula (4):

[0082] P * =P 0 -X(ω-ω 0 ) (4)

[0083] Where X is the transfer function of the virtual speed regulator; P 0 Set the active power output of the VSG.

[0084] The expression of the low-pass filter type virtual speed regulator of the virtual synchronous generator is as follows:

[0085]

[0086] Where G is the gain, ω c is the cut-off angular frequency, s is the Laplace operator;

[0087] Combining the above expressions (1), (2), (3) and (5), the expression of the virtual synchronous generator with a low-pass filter type virtual speed regulator is obtained as follows.

[0088]

[0089] S12, using the coupling relationship between the active power and reactive power transmitted between the virtual synchronous generator and the power grid to determine the relationship between the active power and the power angle considering the reactive power control loop.

[0090] First, the grid voltage U gabc As a reference, let the grid voltage phase θ g =0°, then θ ref =δ, the expressions of active power P and reactive power Q transmitted between the virtual synchronous generator and the power grid are obtained as shown in the following equations (7) and (8), respectively.

[0091]

[0092]

[0093] From equations (7) and (8), we can determine that P and Q are related to each other through δ and U ref Mutual coupling.

[0094] Finally, combining equations (8), (3), and (7), we obtain the P-δ relationship considering the reactive power control loop, as follows.

[0095]

[0096] A=1.5D q U g (m 1 cosδ+m 2 sinδ) (10)

[0097] B=6m 1 D q (U 0 +D q Q 0 ) (11)

[0098]

[0099]

[0100] S13, according to the expression of the virtual synchronous generator obtained in step S11 and the relationship between the active power and the power angle obtained in step S12, an equivalent circuit model of the virtual synchronous generator is established, such as Figure 4 As shown, for Figure 4 In the equivalent circuit model, let x 3 =Gδs / (s+ω c ), x=[x 1 ,x 2 ,x 3 ] T , where x 1 represents the power angle δ, x 2 The angular frequency difference Δω=ω-ω g , while ignoring the influence of the voltage and current inner loop with a smaller time scale, the expression of the large signal reduced-order model of the virtual synchronous generator is obtained as follows.

[0101]

[0102] In the second step, based on the extended equal-area rule, the large-signal reduced-order model obtained above is qualitatively analyzed to determine the stability of the transient power angle of the virtual synchronous generator with a low-pass filter virtual speed regulator.

[0103] The extended equal area rule can be used to qualitatively analyze the transient power angle stability of VSG. The extended equal area rule is more suitable for qualitative analysis of the transient angle stability of the system to avoid the extremely conservative judgment problem caused by the traditional equal area rule because it does not consider damping. According to expression (14), it can be concluded that the dynamic characteristics of the virtual synchronous generator with a low-pass filter virtual speed regulator are mainly determined by the gain G and the cutoff angular frequency ω c Decide.

[0104] According to expression (6), let the equivalent active power reference value P n =P 0 –(G / (s+ω c )+D p )sδ, the active power control expression of the virtual synchronous generator with low-pass filter virtual speed regulator is as follows:

[0105] Js 2 δ=P n -P (15)

[0106] The system stability criteria meet:

[0107]

[0108] Where: A a is the acceleration area, A dmax is the maximum deceleration area, δ 0 is the power angle under normal operation, δ U is the unstable power angle under fault.

[0109] At the grid voltage U g When the power angle curve of the virtual synchronous generator with low-pass filter virtual speed regulator drops from 1.0pu to 0.6pu, the power angle curve of the virtual synchronous generator with low-pass filter virtual speed regulator is as follows: Figure 5 As shown, curve I is the power angle curve before the fault, and curve II is the power angle curve during the fault. It can be found that when a fault occurs, the operating point will jump from point O to point C. At this time, P <P n , as the fault persists, P increases, P n Decrease, in the acceleration stage, δ continues to increase until P ≥ P n It enters the deceleration stage when δ slows down. It can be seen from expression (15) that during the acceleration and deceleration process, due to the influence of the virtual speed regulator gain G and the cutoff angular frequency ω c The influence of P n It changes dynamically and different dynamic situations will occur.

[0110] In G = G 0 (G 0 When taking 0p.u.), due to A a (The solid line part S1 )≥A dmax (The dashed line part S 3 ), causing the transient process power angle to exceed δ U , the system eventually loses transient stability, such as Figure 5 As shown in (a), at this time A dmax With A a Very close; at G>G 0 When A a For S 1 -S 2 (dotted line part), and A dmax For S 3 +S 4 (point part), at this time A a dmax , the system will be S Keep the transient power angle stable. c =ω c0 (ω c0 When A is 0.5 rad / s, a For S 1 , A dmax For S 3 , now there is A a dmax , the system will maintain a stable transient power angle, such as Figure 5 (b) is shown by the solid line; c >ω c0 When A a For S 1 +S 2 (Point part))>A dmax (The dashed line part S 3 ), which will cause the system to become unstable. In summary, for LPF-VG-VSG, increasing G can reduce the acceleration area and increase the maximum deceleration area, which is beneficial to the stability of the transient power angle, while increasing ω c It will be counterproductive and worsen the system power angle stability.

[0111] The third step is to use the phase diagram method to quantitatively analyze the large signal price reduction model based on the aforementioned qualitative analysis of transient power angle stability based on the extended equal area rule to determine the influence of different control parameters on the transient power angle stability performance of the virtual synchronous generator with a low-pass filter virtual speed regulator.

[0112] Based on the large signal model constructed in the first step, the phase diagram method is used in this step to solve this problem. The influence of different control parameters (gain and cutoff angular frequency of the virtual speed regulator) on the transient power angle stability performance of the virtual synchronous generator with a low-pass filter virtual speed regulator is studied by comparing the δ-Δω plane diagram.

[0113] Table 1 System parameters​​

[0114]

[0115] In order to determine the influence of the gain G in the virtual speed regulator on the transient power angle stability, other parameters except the G parameter in Table 1 are used to draw the δ-Δω plane diagram using expression (14), as shown in Figure 6 As shown. Figure 6 The dynamic response under large disturbances such as voltage drop can be observed intuitively. When Δω>0, δ increases; when Δω<0, δ decreases. If Δω drops to zero before the unstable equilibrium point U (hollow ellipse) (the corresponding equilibrium point is S (solid ellipse) at this time), δ will converge to the new stable equilibrium point, otherwise it will diverge, resulting in transient power angle instability, such as G=0p.u. (that is, the virtual speed regulator link is not used or the virtual speed regulator link fails). Although there is an equilibrium point at this time, transient stability may still be lost.

[0116] (1) Gain influence: From Figure 6 It can be seen that when the gain G = 2p.u., the system can ensure the stability of the transient power angle, and the stable equilibrium point is [1.3025,0] T ,like Figure 6 In this embodiment, the power angle overshoot is represented by σ δi_X %=(δ mi -δ e ) / δ e , the maximum angular frequency difference is expressed as maxΔω i_X =Δω mi -Δω e For LPF-VG-VSG, there is σ δ4_L % = (1.6643-1.3025) / 1.3025 = 27.78%, while maxΔω 4_L =1.91rad / s. When the gain G = 10p.u., the system can ensure transient stability, but exhibits different dynamic characteristics, such as Figure 6 As shown by the dotted line in the figure. maxΔω 3_L =1.8686rad / s,σ δ3_L %=20.67%, and its stable equilibrium point is the same as when the gain G=2p.u.. At this time, the system has the lowest overshoot characteristic and shows a larger transient power angle stability margin. When the gain G=30p.u., when the grid voltage drops, the system has a smaller power angle overshoot σ δ2_L % = 11.07%. When the gain G = 40 p.u., the power angle overshoot of the system at this time is σ δ1_L % = 7.49%, maximum angular frequency difference maxΔω 1_L=1.786rad / s. In general, as the gain G of LPF-VG-VSG gradually increases, the power angle overshoot and the maximum value of the angular frequency difference gradually decrease, the transient power angle stability margin continues to increase, and the transient stability of the system continues to strengthen. The detailed comparison of the transient power angle stability of the system under different gains G is shown in Table 2. From Table 2, it can be concluded that the increase of G is conducive to the transient power angle stability of LPF-VG-VSG.

[0117] Table 2 Effect of gain G on VSG transient power angle stability

[0118]

[0119] (2) Influence of cut-off angular frequency: Different cut-off angular frequencies ω c It will also affect the stability of the system transient power angle. c For other parameters other than the parameter, the δ-Δω plane graph is plotted using expression (14), as Figure 7 As shown. Figure 7 It can be seen that as ω c As the system transient power angle stability margin decreases, it may even become unstable. c =0.5rad / s, the transient power angle of the virtual synchronous generator with low-pass filter virtual speed regulator is stable, where σ δ1_L % = 26.60% and maxΔω 1_L =1.915rad / s; when ω c =1.5rad / s, the virtual synchronous generator with low-pass filter virtual speed regulator still maintains transient stability. δ2_L % increased to 28.980%, while maxΔω 2_L Almost unchanged. c When =4.5rad / s, the virtual synchronous generator containing low-pass filter virtual speed regulator loses transient power angle stability.

[0120] Different cutoff angular frequencies ω c The detailed comparison of the transient power angle stability of the system under the above conditions is shown in Table 3. From Table 3, it can be concluded that as ω c As the value of φm increases, the transient power angle stability of the virtual synchronous generator containing the low-pass filter type virtual speed regulator decreases.

[0121] Table 3 Cut-off angular frequency ω c Impact on system transient power angle stability

[0122]

[0123]

[0124] The fourth step is to determine the transient stability parameter range of the virtual synchronous generator with a low-pass filter virtual speed regulator.

[0125] In this embodiment, the gain G and the cutoff angular frequency ω are c To improve the transient stability of the system, it is necessary to find G and ω c The allowable parameter range is also the basis for actual engineers to determine the transient stability margin of the system.

[0126] To find G and ω c The transient power angle stability region of the virtual synchronous generator with a low-pass filter type virtual speed regulator under simultaneous changes needs to be scanned and checked for ω with a small change step size. c and G, G and ω are determined based on a trade-off between accuracy and computer computational burden c The calculation step size is set to 1p.u. and 0.05rad / s, respectively, for each specified cutoff angular frequency ω c , you can use Figure 8 The method shown above yields multiple values ​​of gain G for stable operation. Repeating this method yields ω c and G form a stable region, such as Fig. 9 As shown in the figure, the midpoint area and the enclosed area are stable areas, and the white area is the unstable operation area. Fig. 9 It can be obtained that in ω c <1.2rad / s, no matter what value G takes in (0,50]pu, it can maintain transient stability. c When the value is between [1.2,3.4]rad / s, if G≥2p.u., the system can maintain transient power angle stability, otherwise transient instability will occur. c >3.4rad / s, G≥3p.u. can keep the system stable. c The smaller the value, the larger the allowed range of G.

[0127] In order to demonstrate the effectiveness of the transient power angle stability analysis method of the virtual synchronous generator with a virtual speed regulator proposed in the present invention, it is verified from two aspects as follows.

[0128] 1) Comparative analysis of transient power angle stability of virtual synchronous generator with low-pass filter virtual speed regulator under different control parameters, such as Fig.10 As shown, the frequency deviation Δω is shown from top to bottom. 0 and power angle δ. Fig.10 It can be seen that in ω c=1.5rad / s, with the continuous increase of G, the large signal stability of the system is enhanced, the power angle overshoot and angular frequency deviation are significantly reduced, and the transient power angle stability margin is continuously improved, which is conducive to maintaining the transient power angle stability of the system. At the same time, the oscillation attenuation is significantly weakened, and both can eventually reach the same stable state, which means that the virtual speed regulator only increases the transient damping during the transient process, and will not change the stable equilibrium point of the system. Under G = 2p.u., with ω c Increase, such as ω c =4.5rad / s, the system will experience low-frequency oscillation, which means that transient power angle instability has occurred. This is consistent with the analysis in the second and third steps above.

[0129] 2) In order to solve the instability problem and consider the optimization of transient power angle stability, the gain G can be reselected according to Table 4. In order to verify the correctness of the parameter design optimization, G = 4p.u. is taken for the test. The experimental results are as follows Fig.11 As shown. G = 2p.u. and ω c =4.5rad / s is also included in the instability case Fig.11 In comparison, from Fig.11 It can be seen that when ω c =4.5rad / s, taking G=4p.u. can ensure that the system can recover the transient power angle stability, further verifying the analysis of step 4. From the above analysis, it can be seen that the method proposed in the present invention can better perform transient power angle stability analysis on the virtual synchronous generator containing a low-pass filter type virtual speed regulator.

[0130] Table 4 Optimal design of parameters of VSG_LPF_VG

[0131]

[0132] The above embodiments are preferred implementation schemes of the present invention. In addition, the present invention can also be realized in other ways. Any obvious replacement without departing from the concept of the present technical solution is within the protection scope of the present invention.

[0133] In order to make it easier for ordinary technicians in the field to understand the improvements of the present invention over the prior art, some drawings and descriptions of the present invention have been simplified, and for the sake of clarity, some other elements are omitted in this application document. Ordinary technicians in the field should realize that these omitted elements may also constitute the content of the present invention.

Claims

1. A method for analyzing transient power angle stability of a virtual synchronous generator containing a virtual speed regulator, characterized in that: The steps include: S1, construct a large signal reduced-order model of a virtual synchronous generator with a low-pass filter virtual speed regulator; S11, combining the characteristics of the virtual synchronous generator rotor motion loop, reactive power control loop and low-pass filter type virtual speed regulator, determine the expression of the virtual synchronous generator with low-pass filter type virtual speed regulator; The expression of the rotor motion loop of the virtual synchronous generator is as follows: In the formula, J and D P are the virtual inertia coefficient and virtual damping coefficient of VSG respectively; ω represents the virtual angular frequency of VSG, ω0 is the system angular frequency setting value; δ represents the VSG output voltage phase angle θ ref and the grid voltage phase angle θ g The phase angle difference between them is defined as the power angle; ω g is the grid angular frequency, which is equal to ω0; P * and P are the reference active power and actual output active power of the virtual speed regulator respectively; The expression of the reactive power control loop of the virtual synchronous generator is as follows: U ref =U0+D q (Q0-Q) (3) Where, U0 is the VSG output voltage setting value; D q represents the QV droop coefficient; Q0 and Q are the VSG output reference reactive power and actual output reactive power respectively; due to the use of fast internal voltage and current control, U ref is the actual output voltage amplitude of VSG; The expression of the low-pass filter type virtual speed regulator of the virtual synchronous generator is as follows: Where P0 is the VSG output active power setting value; G is the gain, ω c is the cut-off angular frequency, s is the Laplace operator; Combining the above expressions (1), (2), (3) and (5), the expression of the virtual synchronous generator with a low-pass filter type virtual speed regulator is obtained as follows: S12, using the coupling relationship between the active power and reactive power transmitted between the virtual synchronous generator and the power grid to determine the relationship between the active power and the power angle considering the reactive power control loop; First, the grid voltage U gabc As a reference, let the grid voltage phase θ g =0°, then θ ref =δ, the expressions of active power P and reactive power Q transmitted between the virtual synchronous generator and the power grid are shown in the following equations (7) and (8), respectively: From equations (7) and (8), we can determine that P and Q are related to each other through δ and U ref Mutual coupling; Finally, combining equations (8), (3), and (7), we get the P-δ relationship considering the reactive power control loop, as follows: A=1.5D q U g (m1cosδ+m2sinδ) (10) B=6m1D q (U0+D q Q0) (11) S13, firstly establish the equivalent circuit model of the virtual synchronous generator according to the expression of the virtual synchronous generator obtained in step S11 and the relationship between the active power and the power angle obtained in step S12, and then set x3 = Gδs / (s+ω c ), x=[x1,x2,x3] T , where x1 represents the power angle δ, and x2 represents the angular frequency difference Δω=ω-ω g , ignoring the influence of the voltage and current inner loop with a smaller time scale, the expression of the large signal reduced-order model of the virtual synchronous generator is obtained as follows: S2, based on the extended equal area rule, the large signal reduced-order model is qualitatively analyzed to determine the stability of the transient power angle of the virtual synchronous generator containing the low-pass filter type virtual speed regulator; First, the main influencing factors of the dynamic characteristics of the virtual synchronous generator with a low-pass filter virtual speed regulator are determined based on the large signal reduction model. The main influencing factors are the gain G and the cutoff angular frequency ω. c ; Then the stability criterion of the system is determined based on the virtual synchronous generator, as follows: Where P n =P0–(G / (s+ω c )+D p )sδ; A a is the acceleration area, A dmax is the maximum deceleration area, δ0 is the power angle under normal operation, δ U is the unstable power angle under fault; Finally, the influence of various influencing factors on the transient power angle stability of the virtual synchronous generator is analyzed. For the virtual synchronous generator with a low-pass filter virtual speed regulator, increasing G can reduce the acceleration area and increase the maximum deceleration area, which is beneficial to the stability of the transient power angle. c It will be counterproductive and worsen the system power angle stability; S3, based on the qualitative analysis in step S2, using a phase diagram method to quantitatively analyze the large signal reduced-order model to determine the influence of different control parameters on the transient power angle stability performance of the virtual synchronous generator with a low-pass filter type virtual speed regulator; S4, determining the transient stability parameter range of the virtual synchronous generator including the low-pass filter type virtual speed regulator.

2. The method for analyzing transient power angle stability of a virtual synchronous generator with a virtual speed regulator according to claim 1, characterized in that: In step S3, when the large signal reduced-order model is quantitatively analyzed, the gain G and the cutoff angular frequency ω in the virtual speed regulator are determined. c Impact on the transient power angle stability performance of virtual synchronous generator.

3. The method for analyzing transient power angle stability of a virtual synchronous generator with a virtual speed regulator according to claim 2 is characterized in that: In step S3, when determining the influence of the gain G in the virtual speed regulator on the transient power angle stability performance of the virtual synchronous generator, the system parameters are first used, and the plane diagram of the relationship between the power angle and the angular frequency deviation is drawn using expression (14), and then the dynamic response under the large disturbance of voltage drop is observed. Finally, it is found that as the gain G gradually increases, the power angle overshoot and the maximum value of the angular frequency difference gradually decrease, the transient power angle stability margin continues to increase, and the transient stability of the system continues to increase.

4. The method for analyzing transient power angle stability of a virtual synchronous generator with a virtual speed regulator according to claim 3 is characterized in that: In step S3, the cutoff angular frequency ω in the virtual speed regulator is determined c When considering the influence of transient power angle stability of virtual synchronous generator, we first use system parameters and use expression (14) to draw a plane diagram of the relationship between power angle and angular frequency deviation, then observe the dynamic response under large voltage drop disturbance, and finally obtain the relationship between the cutoff angular frequency ω and the power angle. c With the increase of , the transient power angle stability of the virtual synchronous generator containing the low-pass filter type virtual speed regulator will decrease.

5. The method for analyzing transient power angle stability of a virtual synchronous generator with a virtual speed regulator according to claim 4, characterized in that: In step S4, the process of determining the transient stability parameter range of the virtual synchronous generator including the low-pass filter type virtual speed regulator is as follows: S41, scan and check the gain G and cutoff angular frequency ω with small change steps c , the gain G and the cutoff frequency ω are determined based on a compromise between accuracy and computer calculation burden c The calculation step size is 1 p.u. and 0.05 rad / s; S42, according to each specified cutoff angular frequency ω c Get multiple gain G values ​​for stable operation; S43, repeat step S42 to obtain the gain G and the cutoff angular frequency ω c Stable area composed of: In ω c When <1.2rad / s, no matter what value G takes in (0,50]pu, the system can maintain transient stability; When c When the value is between [1.2,3.4]rad / s, if G≥2p.u., the system can maintain transient power angle stability, otherwise transient instability will occur; In ω c When >3.4rad / s, G≥3p.u. can keep the system stable.

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