A visual quantitative analysis method for transient damping energy of grid-connected converters

Abstract

The present invention discloses a method for visualizing and quantitatively analyzing transient damping energy of a grid-connected converter, which belongs to the field of power electronic control technology. In view of the challenge that the traditional energy function analysis method is difficult to consider the energy dissipation effect of the damping torque, a D p The energy consumed in the work done in the transient process of the damping torque is mapped to the area of ​​the phase plane. The area of ​​the right triangle is used to approximate the actual damping area. The influence of the transient damping energy during the fault duration and after the fault is cleared is quantitatively characterized, and the transient stability boundary of the grid-type converter taking into account the large damping effect and the quantitative calculation of the critical fault clearance angle are achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of power electronic control, and in particular relates to a method for visualizing and quantitatively analyzing transient damping energy of a grid-connected converter. Background Art

[0002] The grid-type control strategy simulates the active power and reactive power regulation characteristics of synchronous generators, which can provide voltage and frequency support for the system, enhance the stability of the power system, and become a forward-looking technology for new power systems. However, unlike synchronous generators, grid-type control usually has a large equivalent damping torque, resulting in energy dissipation related to the motion trajectory. The influence mechanism of this damping effect on the transient characteristics of the grid-type converter is still unclear, which brings great challenges to the grid-connected transient stability analysis of the grid-type converter and the system relay protection setting.

[0003] The traditional quantitative analysis method is mainly the energy function method, which can perform intuitive and quantitative analysis on the kinetic energy and potential energy conversion process of the virtual rotor. However, it is difficult to consider the energy dissipation effect of the damping torque, resulting in unclear transient stability boundaries of the grid-type converter and the inability to quickly calculate the critical fault clearance angle of the grid-type converter. Summary of the invention

[0004] In order to quantitatively analyze the influence of damping torque on the transient process of grid-type converter, this paper proposes a visualization quantitative analysis method of transient damping energy of grid-type converter. This paper introduces a customized phase diagram to realize the visualization analysis of energy dissipation caused by damping torque work, and proposes a transient damping area approximation method to quantitatively characterize the influence of transient damping energy. Furthermore, this method is linked with the traditional energy function method to realize the quantitative characterization of transient stability boundary of grid-type converter taking into account large damping effect and quantitative calculation of critical fault clearance angle.

[0005] The method for visualizing and quantitatively analyzing transient damping energy of a grid-connected converter proposed in the present invention specifically comprises the following steps:

[0006] 1) The power angle swing equation of the grid-connected converter is expressed as follows:

[0007] Hδ″=P0-P e -D p δ′

[0008] Among them, δ′ and δ″ are the first and second derivatives of the power angle, respectively, P0, P e , D p and H represent active power reference value, active power output, damping coefficient and virtual inertia time constant respectively;

[0009] 2) When a fault occurs in the power system, the initial power angle of the grid-connected converter is δ0, and the power angle at the time of fault clearing is δc , the relative speed of the rotor is δ′ c ;

[0010] 3) After the fault is cleared, when the grid-connected converter power angle is δ and its derivative is δ′, the total transient energy of the virtual rotor is V pf (δ,δ′), so when the fault is cleared, the total transient energy is V pf (δ c ,δ′ c ); In the critical stability case, the virtual rotor reaches the unstable equilibrium position δ eu At this point, the relative speed of the rotor is 0 and the total transient energy is V pf (δ eu ,0);

[0011] 4) The damping torque D p δ′ integrates δ to obtain the expression of damping torque work in transient process

[0012]

[0013] According to this expression, the D with the vertical axis δ′ is customized p times, and the horizontal axis is δ, and then the energy consumed by the damping torque in the process of the power angle changing from δ1 to δ2 is mapped to the area enclosed by the phase trajectory and the horizontal axis in the angle range in the phase plane diagram;

[0014] 5) The critical value of transient damping energy consumed after the fault is cleared is S DM , using the phase plane diagram (δ c ,0)、(δ c ,δ′ cca ) and (δ eu ,0) is the area of ​​the right triangle S DA Instead of S DM , the transient stability boundary of the system can be directly obtained according to the following algebraic equation:

[0015] V pf (δ c ,δ′ cca )-S DA =V pf (δ eu ,0)

[0016] Among them, δ′ cca is the fault clearing angle δ c The critical virtual rotor relative speed at DA The expression is

[0017] S DA =|D p δ′ cca |(δeu -δ c ) / 2

[0018] 6) During the fault period, the total transient energy of the virtual rotor is V df (δ,δ′), the transient damping energy consumed is S C , using the phase plane diagram (δ0,0), (δ cm ,δ′ cm ) and (δ cm ,0) is the area of ​​the right triangle S CA Instead of S C , the critical fault clearance angle can be directly solved according to the following algebraic equations:

[0019]

[0020] Among them, δ cm is the critical fault clearing angle, δ c ′ m is the relative speed of the rotor corresponding to the critical clearance angle, S DA and S CA The expression is

[0021]

[0022] Among them, δ0 is the initial power angle of the virtual rotor.

[0023] Based on the above technical solution, the present invention has the following beneficial technical effects:

[0024] (1) The present invention adopts a customized phase plane and intuitively displays the significant damping effect existing in the grid-type converter in the phase plane, thereby overcoming the defect that existing transient analysis tools are difficult to intuitively analyze the damping dissipation energy.

[0025] (2) The present invention adopts an approximate solution in which the transient damping energy represented by the area of ​​the right triangle in the phase plane diagram replaces the transient damping energy after the actual fault is cleared, thereby realizing a quantitative analytical characterization of the transient stability boundary of the grid-type converter taking into account the large damping effect. This method has the advantages of fast solution speed and high accuracy, and can realize a rapid assessment of the transient stability of the equipment.

[0026] (3) The present invention extends the transient damping energy approximation scheme to the transient energy analysis during the fault duration, simplifies the iterative solution calculation process of the critical fault clearance angle into the direct quantitative solution of the algebraic equation group, and can realize the online calculation of the critical fault clearance angle of the network-type equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is a schematic diagram of the grid-type control structure and the equivalent circuit of the grid-connected converter;

[0028] Figure 2 Customized phase diagrams for transient damping energy visualization;

[0029] Figure 3 This is the approximate scheme diagram of transient damping energy after fault clearing;

[0030] Figure 4 The transient stability boundary comparison diagram of the grid-type converter;

[0031] Figure 5 This is an approximate diagram of transient damping energy during the fault duration. DETAILED DESCRIPTION

[0032] To explain the present invention in more detail, the present invention is further described in detail below by taking a grid-type converter with constant terminal voltage control under a grid voltage drop fault as an example, in combination with the accompanying drawings and embodiments. It should be noted that the method of the present invention is applicable to grid-type converters with constant terminal voltage control and reactive voltage control.

[0033] Figure 1 This is a schematic diagram of the grid-type control structure and the equivalent circuit of the grid-connected converter. The converter adjusts the active power output by adjusting the output voltage phase. f The amplitude of is its reference value U0, the phase is θ, the amplitude of the grid voltage E is E, and the phase is θ g , the output power angle δ is the phase difference between the two voltages δ = θ-θ g The power angle swing equation and power transmission equation of the grid-connected converter are expressed as follows:

[0034]

[0035] Among them, δ, δ′ and δ″ are the power angle and its first-order derivative and second-order derivative respectively, P0, P e , D p and H represent active power reference value, active power output, damping coefficient and virtual inertia time constant respectively, X ge is the equivalent impedance of the power grid.

[0036] When a fault occurs in the power system, the initial power angle of the grid-connected converter is δ0, and the power angle at the time of fault clearing is δ c , the relative speed of the rotor is δ′ c .against Figure 1 For the system in Figure 1, after the fault is cleared, when the power angle is δ and its derivative is δ′, the total transient energy of the virtual rotor is V pf (δ,δ′) can be written as

[0037]

[0038] Among them, E pf is the grid voltage amplitude after the fault is cleared, E0 is a constant representing the potential energy reference value, and the unstable equilibrium position δ eu is the zero potential energy surface, then E0 is

[0039]

[0040] Substituting the corresponding power angle δ and rotor relative speed δ′, at the moment of fault clearing, the transient total energy is V pf (δ c ,δ′ c ); In the critical stability case, the virtual rotor reaches the unstable equilibrium position δ eu At the position where the relative speed of the rotor is 0, the critical transient total energy V pf (δ eu ,0)=0.

[0041] During the fault period, since the transient energy does not change suddenly, there is V df (δ c ,δ′ c )=V pf (δ c ,δ′ c ), so the total transient energy of the virtual rotor V df (δ,δ′) can be written as

[0042]

[0043] Among them, E df is the grid voltage amplitude during the fault duration. p δ′ integrates δ to obtain the expression of excess electromagnetic torque work in the transient process:

[0044]

[0045] According to this expression, the custom vertical axis is δ ′ D p times, with the horizontal axis being δ, such as Figure 2 As shown, the energy E consumed by the damping torque in the process of changing the power angle from δ1 to δ2 d Map the area S enclosed by the phase trajectory and the horizontal axis in this angle range into the phase plane diagram.

[0046] After the fault is cleared, the critical stability condition of the system is that the total energy at the moment of fault clearing is equal to the unstable equilibrium position δ eu The sum of the potential energy at and the energy consumed by the damping torque, that is,

[0047] V pf (δ c ,δc ′ ca )=S DM

[0048] Among them, the critical value of transient damping energy consumed after the fault is cleared is S DM ,like Figure 3 (a) is shown. Figure 3 (b) (δ c ,0)、(δ c ,δ c ′ ca ) and (δ eu ,0) is the area of ​​the right triangle S DA Instead of S DM , substituting into each part of the expression, the critical stability condition of the system after the fault is cleared is

[0049]

[0050] Among them, δ c ′ ca is the fault clearing angle δ c The critical virtual rotor relative speed at can be solved according to the above formula as follows: Figure 4 The transient stability boundary is shown by the dashed line.

[0051] During the fault period, further Figure 5 (b) (δ0,0), (δ cm ,δ c ′ m ) and (δ cm ,0) is the area of ​​the right triangle S CA replace Figure 5 The actual damping area S in (a) C , and considering the damping energy approximation after fault clearance, the critical fault clearance angle δ cm It can be obtained according to the following formula

[0052]

[0053] Among them, δ cm is the critical fault clearing angle, δ c ′ m is the rotor relative speed corresponding to the critical clearance angle, substitute S DA and S CA The specific expression of the equation can be written as

[0054]

[0055] for Figure 1 The schematic diagram of the grid-type control structure and the grid-connected converter equivalent circuit shown in the figure is verified using the following normalized parameter settings: the grid voltage amplitude E is rated at 1.0 pu and drops to E during the fault duration. df =0, after the fault is cleared, it will return to E pf =0.6pu, grid equivalent impedance X ge is 0.5pu, the equivalent damping coefficient D p It is 25p.u, the inertia time constant H is 5.0s, the converter terminal voltage reference value U0 is 1.0pu, and the active power output reference value P0 is 1.0pu.

[0056] If only the transient damping energy after fault clearance is used, the solution is: Figure 4 The transient stability boundary shown by the dashed line is closer to the actual stability boundary shown in the figure than the boundary shown by the dotted line without considering the damping effect. The accuracy of different transient stability boundaries can be quantitatively measured by using the critical fault clearance angle as an indicator. When the fault occurs, the power angle δ0 is 0.1667πrad, and the actual critical fault clearance angle δ of the system is cm_r is 0.3945πrad. According to the transient stability boundary obtained by the traditional energy function method without considering the damping effect, the critical fault clearance angle δ cm_t The error with the actual result is as high as 79.4%. According to the transient stability boundary obtained by the proposed method, the critical fault clearance angle δ cm_p The error is reduced to 3.6% from the actual result.

[0057] If the transient damping energy approximation is used both during the fault continuation stage and after the fault is cleared, and the critical fault clearance angle is directly calculated using an algebraic equation, its value δ can be obtained by solving cm_dp The error is 0.3678πrad, which is 11.7%, still much smaller than the 79.8% of the traditional method.

[0058] The above analysis results verify the effectiveness and advantages of the proposed transient damping energy visualization quantitative analysis method.

[0059] 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. The 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 scope of protection of the present invention, such as in Figure 1 The control structure shown takes into account reactive power control, adopts different fault types for analysis, etc. Therefore, the claims are intended to cover all modifications that come within the true spirit and scope of the invention.

Claims

1. A method for visualizing and quantitatively analyzing transient damping energy of a grid-connected converter, characterized in that: The following steps are involved: 1) The power angle swing equation of the grid-connected converter is expressed as follows: Hδ″=P0-P e -D p d′ Among them, δ′ and δ″ are the first and second derivatives of the power angle, respectively, P0, P e , D p and H represent active power reference value, active power output, damping coefficient and virtual inertia time constant respectively; 2) When a fault occurs in the power system, the initial power angle of the grid-connected converter is δ0, and the power angle at the time of fault clearing is δ c , the relative speed of the rotor is δ′ c ; 3) After the fault is cleared, when the grid-connected converter power angle is δ and its derivative is δ′, the total transient energy of the virtual rotor is V pf (δ,δ′), so when the fault is cleared, the total transient energy is V pf (δ c ,δ′ c ); In the critical stability case, the virtual rotor reaches the unstable equilibrium position δ eu At this point, the relative speed of the rotor is 0 and the total transient energy is V pf (δ eu ,0); 4) The damping torque D p δ′ integrates δ to obtain the expression of damping torque work in transient process According to this expression, the custom vertical axis is δ ′ D p times, and the horizontal axis is δ, and then the energy consumed by the damping torque in the process of the power angle changing from δ1 to δ2 is mapped to the area enclosed by the phase trajectory and the horizontal axis in the angle range in the phase plane diagram; 5) The critical value of transient damping energy consumed after the fault is cleared is S DM , using the phase plane diagram (δ c ,0)、(δ c ,δ′ cca ) and (δ eu ,0) is the area of ​​the right triangle S DA Instead of S DM , the transient stability boundary of the system can be directly obtained according to the following algebraic equation: V pf (d c ,d′ cca )-S DA =V pf (d eu ,0) Among them, δ′ cca is the fault clearing angle δ c The critical virtual rotor relative speed at DA The expression is S DA =|D p d′ cca |(d eu -d c ) / 2 6) During the fault period, the total transient energy of the virtual rotor is V df (δ,δ ′ ), the transient damping energy consumed is S C , using the phase plane diagram (δ0,0), (δ cm ,δ c ′ m ) and (δ cm ,0) is the area of ​​the right triangle S CA Instead of S C , the critical fault clearance angle can be directly solved according to the following algebraic equations: Among them, δ cm is the critical fault clearing angle, δ c ′ m is the relative speed of the rotor corresponding to the critical clearance angle, S DA and S CA The expression is

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