Transient power angle stability prediction method for large-scale wind power grid-connected system based on voltage-speed response characteristics

Abstract

The application discloses a large-scale wind power grid-connected system transient power angle stability prediction method based on voltage-speed response characteristics, which comprises the following steps: analyzing the variation law of the node voltage amplitude of the wind power grid-connected system; determining the relationship between the generator voltage and speed and the system transient power angle stability; analyzing the key stability characteristics of the voltage-speed phase plane trajectory; combining the node voltage amplitude variation law after the fault, constructing a transient power angle stability prediction starting criterion; using the variation rate of the machine terminal bus voltage amplitude, constructing a fast identification criterion of the seriously disturbed machine group; based on the key stability characteristics of the voltage-speed phase trajectory, constructing a transient power angle stability identification criterion suitable for the wind power grid-connected system. The method can effectively realize the transient power angle stability discrimination of the wind power grid-connected system, has strong adaptability, and can obtain more time for subsequent emergency control.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of new energy grid-connected system protection and stability control, and particularly relates to a large-scale wind power grid-connected system transient power angle stability prediction method based on voltage-speed response characteristics. BACKGROUND

[0002] The proportion of wind power in the energy structure of the power system continues to increase. Due to the typical reverse distribution of wind power resources and power load, wind power transmission often adopts a long-distance centralized delivery mode, and wind power output has the characteristics of intermittency and volatility. After large-scale wind power is connected to the power grid, the system inertia and disturbance resistance are reduced, which brings severe challenges to the transient power angle stability of the system.

[0003] In recent years, in order to achieve the goal of "real-time decision and real-time control" of modern power grids, there are rich research results on transient stability discrimination methods based on response information. For example, the corresponding relationship between the detailed analysis of transient loss of step process and phase trajectory motion characteristics based on generalized angular velocity-angular acceleration is analyzed, and the change characteristics of the tangent intercept of the extended phase trajectory are used to discriminate transient stability. As recorded in document [1]: Ma Shying, Zhu Cunhao, Zheng Chao, et al. Analysis of extended phase trajectory characteristics and transient stability discrimination method [J]. Proceedings of the Chinese Electrical Engineering Society, 2020, 40(20): 6516-6526.

[0004] However, these methods all involve derivative operation of response information, and the accuracy of the transient stability criterion is easily affected by the quality of the measured data. Some scholars based on random matrix theory proposed a transient power angle stability discrimination method based on the time series spectrum distribution characteristics of the measured data. As recorded in document [2]: Sun Hui, Sun Baoshuo, Gao Zhengnan, et al. Online discrimination of power system transient power angle stability based on time series spectrum distribution characteristics of measured data [J]. Power Grid Technology, 2023, 47(3): 1107-1116.

[0005] Some scholars also proposed a transient stability discrimination method based on the relative power angle MLE estimation by analyzing the relationship between the motion characteristics of each unit and the maximum Lyapunov exponent (MLE). As recorded in document [3]: Wei SP, Yang M, Qi JJ, et al. Model-free MLE estimation for online rotor angle stability assessment with PMU data [J]. IEEE Transactions on Power Systems, 2018, 33(3): 2463-2476.

[0006] However, the calculation process of the above method is relatively complex in actual application, and the influence of new energy grid connection is not considered, so it is difficult to guarantee the reliability and adaptability of transient stability identification. SUMMARY

[0007] In order to solve the problem that the transient power angle stability is difficult to effectively identify due to the decrease of system inertia and anti-disturbance ability after the wind power is connected to the power grid, the application provides a transient power angle stability prediction method for a large-scale wind power grid-connected system based on voltage-speed response characteristics. First, the equivalent external characteristics of the wind power plant are analyzed, and the node voltage amplitude variation law of the wind power grid-connected system is studied based on the equivalent external characteristics; second, the relationship between the generator voltage and speed and the system transient power angle stability is found out by combining the voltage amplitude variation law and the equivalent power angle characteristics; then, a transient power angle stability identification method suitable for a large-scale wind power grid-connected system is provided according to the voltage-speed phase trajectory motion characteristics, and the method is extended to a multi-machine system for application. The method can effectively identify the transient power angle stability of the wind power grid-connected system, has strong adaptability, and can provide more time for subsequent emergency control.

[0008] The technical scheme adopted by the application is as follows:

[0009] The transient power angle stability prediction method for a large-scale wind power grid-connected system based on voltage-speed response characteristics comprises the following steps:

[0010] Step 1: analyze the variation law of the node voltage amplitude of the wind power grid-connected system;

[0011] Step 2: determine the relationship between the generator voltage and speed and the system transient power angle stability;

[0012] Step 3: analyze the key stability characteristics of the voltage-speed phase plane trajectory;

[0013] Step 4: combine the node voltage amplitude variation law after the fault to construct a transient power angle stability prediction starting criterion;

[0014] Step 5: use the machine terminal bus voltage amplitude variation rate to construct a disturbed serious machine group fast identification criterion;

[0015] Step 6: based on the key stability characteristics of the voltage-speed phase trajectory in step 3, a transient power angle stability identification criterion suitable for the wind power grid-connected system is constructed.

[0016] In step 1, the equivalent external characteristics of the wind power are closely related to the control strategy. Since the control strategy of the double-fed wind turbine realizes the decoupling of active power and reactive power, the equivalent external characteristics can be equivalent to a parallel negative resistance r and a negative reactance x connected to the ground, as shown in formula (1):

[0017]

[0018] In formula (1): U s is the wind turbine outlet bus voltage; P e and Q e are the active and reactive power generated by the wind turbine respectively.

[0019] In a single-machine infinite system, the wind farm is connected to the source-side bus, and are the equivalent potentials of the synchronous generator and the infinite system respectively; r and x are the equivalent resistance and reactance of the wind farm respectively;

[0020] The equivalent external characteristics of the doubly-fed wind turbine are equivalent to the system on the right side of the source-side bus by Thevenin equivalent, and the voltage vector of the source-side bus is calculated by the superposition theorem, as shown in formula (2):

[0021]

[0022] In formula (2): is the grid-connected point voltage vector; X1 and X2 are the equivalent reactances of the generator and the grid-connected point and the grid-connected point and the infinite system respectively; δ is the angle difference between E G and E S ; E G and E S are the equivalent potential amplitudes of the synchronous generator and the infinite system respectively; is the equivalent admittance of the DFIG; e jδ is a complex exponential function.

[0023] During system oscillation, the active output of the wind turbine is limited, resulting in a small value of 1 / r, so formula (2) can be rewritten as:

[0024]

[0025] In formula (3): x is the equivalent reactance of the wind farm;

[0026] According to formula (3), the analytical expression of the bus node voltage amplitude U m is calculated, as shown in formula (4):

[0027]

[0028] As can be seen from formula (4), when the wind power output is any value, with the increase of δ, the bus voltage amplitude first decreases and then increases, and the voltage amplitude reaches a minimum when δ is 180°; in addition, the minimum value of the bus voltage amplitude continuously rises with the increase of the wind power output, but the trend of the voltage amplitude is not affected by the wind power output. Specifically as follows:

[0029] Let Q eThe power supply voltage amplitude E varies in the interval 0.3-1.0 G = E S = 1.0, X1=0.1, X2=0.5, the bus voltage amplitude variation law calculated by substituting formula (4) is shown in FIG. 2(a) and FIG. 2(b). As shown in FIG. 2(a), when the wind power output is any value, with the increase of δ, the bus voltage amplitude first decreases and then increases, and the voltage amplitude reaches the minimum when δ is 180°. According to FIG. 2(b), the minimum value of the bus voltage amplitude continuously rises with the increase of the wind power output, but the voltage amplitude variation trend is not affected by the wind power output.

[0030] In step 2, it is assumed that the generator is a second-order classical model, and its differential equation is shown in formula (5) (without considering the damping coefficient):

[0031]

[0032] In formula (5), δ is the angle difference between E G and E S , that is, the power angle; ω is the speed deviation; T J is the inertia time constant; P m is the mechanical power; P e ' is the electromagnetic power of the generator after the wind power is connected to the grid.

[0033] In step 2, combined with the generator power angle curve of the wind power connected system, when the system is stable, in the process of crossing the stable equilibrium point, the generator speed decreases to the minimum value and then increases, and the speed minimum point will appear at the stable equilibrium point. At the same time, combined with the voltage amplitude variation law in step 1, since the power angle continuously decreases in the process of crossing the stable equilibrium point, the voltage amplitude increases accordingly. Therefore, when the system is stable, the speed minimum point will appear at the stable equilibrium point, and the voltage near the speed minimum point continuously increases. Specifically as follows:

[0034] When the system is stable, the wind power active power restores to the initial power at a certain rate, and the generator power angle curve is shown in FIG. 4(a). After the fault is cleared, the generator operating point jumps from point c to point e, and moves to point f with the restoration of the wind power active power. When the operating point reaches point g at the synchronous speed of the generator, the power angle begins to decrease, and the operating point moves along the power angle curve P3" from point g to the stable equilibrium point a. According to formula (5), in the process of crossing the stable equilibrium point a, the generator speed decreases to the minimum value and then increases, and the speed minimum point will appear at the stable equilibrium point. At the same time, combined with the voltage amplitude variation law in step 1, since the power angle continuously decreases in the process of crossing the stable equilibrium point a, the voltage amplitude increases accordingly. Therefore, when the system is stable, the speed minimum point will appear at the stable equilibrium point, and the voltage near the speed minimum point continuously increases.

[0035] When the system is unstable, the generator speed also decreases to a minimum value and then increases during the process of crossing the unstable equilibrium point, and the speed minimum point will also appear at the unstable equilibrium point. However, according to the voltage amplitude variation law in step 1, the power angle continuously increases and the voltage amplitude continuously decreases during the process of crossing the unstable equilibrium point. Therefore, when the system is unstable, the speed minimum point will appear at the unstable equilibrium point, and the voltage near the speed minimum point continuously decreases. Specifically as follows:

[0036] When the system is unstable, the wind power only outputs reactive power under the control of the fault ride-through strategy, and the generator power angle curve is shown in Fig. 4(b). After the fault is cleared, the generator operating point jumps from point c to point e, and then moves along the power angle curve P3' to the unstable equilibrium point u. According to equation (5), during the process of crossing the unstable equilibrium point u, the generator speed also decreases to a minimum value and then increases, and the speed minimum point will also appear at the unstable equilibrium point. However, according to the voltage amplitude variation law in step 1, the power angle continuously increases and the voltage amplitude continuously decreases during the process of crossing the unstable equilibrium point. Therefore, when the system is unstable, the speed minimum point will appear at the unstable equilibrium point, and the voltage near the speed minimum point continuously decreases.

[0037] In step 3, the voltage and speed operating trajectories of the system in stable and unstable states are plotted in the phase plane with speed as the horizontal axis and generator voltage as the vertical axis, as shown in Figs. 5(a) and 5(b). By comparing Figs. 5(a) and 5(b), it can be seen that when the system is stable, the U-w phase trajectory gradually converges to a certain stable point, while when the system is unstable, the U-w phase trajectory gradually diverges, indicating that the dynamic characteristics of the U-w phase trajectory are closely related to the transient stability of the system, and the transient power angle stability discrimination problem can be converted into the identification of the key characteristics of the U-w phase trajectory.

[0038] In addition, whether the system is stable or not, the U-w phase trajectory will have a speed minimum point in a short time, and after passing through the speed minimum point, the convergence and divergence characteristics of the U-w phase trajectory gradually appear. At the same time, the voltage near the speed minimum point always shows obvious differences in stable and unstable states, i.e., the voltage near the speed minimum point continuously increases in stable state, and the voltage near the speed minimum point continuously decreases in unstable state, as shown in Fig. 5(c). Figure 6

[0039] In step 4, after the fault is cleared, the generator voltage shows different trends after a short time of recovery, and the stability prediction program is started by monitoring the voltage when it reaches a maximum value, i.e.,

[0040]

[0041] ​In equation (6): U(k) represents the voltage amplitude at the k-th sampling time; U(k-1) represents the voltage amplitude at the (k-1)-th sampling time; η represents a sufficiently small positive real number; ΔT represents the sampling interval; U(ki) represents the voltage amplitude at the (ki)-th sampling time; U(ki-1) represents the voltage amplitude at the (ki-1)-th sampling time; k represents the k-th sampling time; i represents the i-th sampling time in the neighborhood before the voltage maximum point; M is the number of sampling points in the neighborhood before the voltage maximum point, and it is recommended to take M = 3.

[0042] In step 5, in a multi-generator system, severely disturbed generators (SDGs) are distinguished based on the severity of changes in the generator terminal bus voltage amplitude. The specific criteria are as follows:

[0043] 1) Collect the amplitude U of the generator terminal bus voltage of each generator after the fault is cleared. n n = 1, 2, ..., N G N G This represents the number of generators.

[0044] 2) Calculate the rate of change of voltage amplitude ΔU at the generator terminal bus of each generator in real time according to the following formula. n :

[0045]

[0046] In equation (7): U n (k) represents the voltage amplitude of the nth generator at the kth sampling time; U n (k-1) represents the voltage amplitude of the nth generator at the (k-1)th sampling time; △T represents the sampling interval.

[0047] 3) Let △U * =max{△U n}, △U * This represents the maximum value among the rate of change of voltage amplitude at each generator bus; max{ΔU n} represents the maximum value function, which is used to obtain the maximum value among the rate of change of voltage amplitude of each generator bus.

[0048] Will satisfy △U n / △U * Generators with a value greater than σ are classified into an SDG set. Here, σ is the SDG identification threshold, which is recommended to be 0.8.

[0049] In step 6, the transient stability determination method for wind power grid-connected systems based on generator voltage and speed response characteristics has the following specific criteria:

[0050] |ω(k)-ω(k-1)|≤η△T (8);

[0051] ω(ki)-ω(ki-1)<0,i=0,1,2,…,N (9);

[0052] U(k)-U(k-1)<0 (10);

[0053] In the formula: ω(k) represents the generator speed at the k-th sampling time; ω(k-1) represents the generator speed at the (k-1)-th sampling time; ω(ki) represents the generator speed at the (ki)-th sampling time; ω(ki-1) represents the generator speed at the (ki-1)-th sampling time. △T represents the sampling interval; k represents the k-th sampling time; η is a sufficiently small positive real number; N is the number of sampling points in the neighborhood before the speed minimum point. To balance the speed minimum point identification speed, this invention uses η = 0.001 and N = 5.

[0054] This invention provides a method for predicting transient power angle stability in large-scale wind power grid-connected systems based on voltage-speed response characteristics. The technical advantages are as follows:

[0055] 1) Based on the analysis of the equivalent external characteristics of wind farms, the present invention shows that the connection of wind farms only changes the node voltage level and does not affect the trend of voltage amplitude change.

[0056] 2) Based on the clear transient stability and instability characteristics of the voltage after a fault, and combined with the equivalent power angle characteristics of the wind power grid-connected system, this invention explores the mapping relationship between generator voltage and speed and transient power angle stability. That is, when the system is stable, the voltage at the speed minimum point continues to increase, and when the system is unstable, the voltage near the speed minimum point continues to decrease.

[0057] 3) When the method of this invention is extended to multi-machine systems, the rate of change of the amplitude of the bus voltage at the machine terminal can be used to achieve rapid and accurate identification of severely disturbed machine groups.

[0058] 4) The method of this invention is not affected by the system network structure, model, and parameters, and has the advantages of requiring less monitoring information and having a fast calculation speed. Furthermore, under different wind power penetration rates, this method can predict system instability earlier, demonstrating strong adaptability and allowing more time for subsequent emergency control. Attached Figure Description

[0059] The present invention will be further described below with reference to the accompanying drawings and examples;

[0060] Figure 1(a) is a schematic diagram of a wind farm connected to a single-unit infinite bus system;

[0061] Figure 1(b) is the equivalent system diagram of wind power grid connection;

[0062] Figure 1(c) is a Thevenin equivalent system diagram.

[0063] Figure 2(a) is a variation law of bus voltage amplitude when power angle swings (U-w phase trajectory variation law when power angle swings). m In δ - Q e variation law in space) ;

[0064] Figure 2(b) is a variation law of bus voltage amplitude when power angle swings (voltage variation law when wind power output changes).

[0065] Figure 3 is a generator terminal voltage amplitude curve when the system is stable and unstable.

[0066] Figure 4(a) is a generator power angle curve when the system is stable;

[0067] Figure 4(b) is a generator power angle curve when the system is unstable.

[0068] Figure 5(a) is a U-w phase trajectory curve when the system is stable;

[0069] Figure 5(b) is a U-w phase trajectory curve when the system is unstable.

[0070] Figure 6 is a U-w phase trajectory comparison diagram when stable and unstable.

[0071] Figure 7 is a transient stability pre-judgment flowchart based on U-w phase trajectory characteristics

[0072] Figure 8(a) is a stable working condition transient response characteristic curve (generator voltage amplitude curve) ;

[0073] Figure 8(b) is a stable working condition transient response characteristic curve (generator speed curve).

[0074] Figure 8(c) is a stable working condition transient response characteristic curve (U-w phase trajectory).

[0075] Figure 8(d) is a stable working condition transient response characteristic curve (generator power angle curve).

[0076] Figure 9(a) is an unstable working condition transient response characteristic curve (generator voltage amplitude curve) ;

[0077] Figure 9(b) is an unstable working condition transient response characteristic curve (generator speed curve) ;

[0078] Figure 9(c) is an unstable working condition transient response characteristic curve (U-w phase trajectory) ;

[0079] Figure 9(d) is an unstable working condition transient response characteristic curve (generator power angle curve).

[0080] Figure 10The U-w phase trajectory under different wind power penetration rates in stable operating conditions.

[0081] Figure 11 The U-w phase trajectory under different wind power penetration rates in unstable operating conditions.

[0082] FIG. 12(a) is a transient response curve (relative power angle curve of each generator) of the IEEE39 system in stable operating conditions;

[0083] FIG. 12(b) is a transient response curve (voltage amplitude curve of each generator) of the IEEE39 system in stable operating conditions;

[0084] FIG. 12(c) is a transient response curve (rotational speed curve of generator G38) of the IEEE39 system in stable operating conditions;

[0085] FIG. 12(d) is a transient response curve (U-w phase trajectory of generator G38) of the IEEE39 system in stable operating conditions.

[0086] FIG. 13(a) is a transient response (relative power angle curve of each generator) of the IEEE39 system in unstable operating conditions;

[0087] FIG. 13(b) is a transient response (voltage amplitude curve of each generator) of the IEEE39 system in unstable operating conditions;

[0088] FIG. 13(c) is a transient response (rotational speed curve of generator G38) of the IEEE39 system in unstable operating conditions;

[0089] FIG. 13(d) is a transient response (U-w phase trajectory of generator G38) of the IEEE39 system in unstable operating conditions. DETAILED DESCRIPTION

[0090] The method is based on the voltage-rotational speed response characteristics of a large-scale wind power grid-connected system. The method is aimed at the problem that the inertia and anti-disturbance capacity of the system are reduced after the wind power is connected to the grid, which makes it difficult to effectively identify the transient power angle stability. The method is based on the movement characteristics of the generator voltage-rotational speed phase trajectory, and constructs a transient power angle stability identification criterion suitable for large-scale wind power grid-connected systems.

[0091] The method combines the equivalent external characteristics of the wind farm to analyze the change law of the node voltage amplitude of the wind power grid-connected system, determines the relationship between the generator voltage and rotational speed and the transient power angle stability of the system, excavates the key stability characteristics of the voltage-rotational speed phase trajectory, constructs a transient power angle stability pre-judgment starting criterion combined with the change law of the node voltage amplitude, constructs a fast identification criterion for seriously disturbed machine groups by using the change rate of the machine terminal bus voltage amplitude, and constructs a transient power angle stability identification criterion suitable for wind power grid-connected systems based on the key characteristics of the voltage-rotational speed phase trajectory.

[0092] The method has the advantages of simple principle, less monitoring information, fast calculation speed, etc. Meanwhile, the method can predict system instability earlier under different wind power penetration rates, has strong adaptability, and can gain more time for subsequent emergency control.

[0093] Specifically, the method comprises the following steps:

[0094] Step one: analyze the change rule of the node voltage amplitude of the wind power grid-connected system:

[0095] The equivalent external characteristic of wind power is closely related to its control strategy. Since the control strategy of the doubly-fed wind turbine realizes the decoupling of active power and reactive power, its equivalent external characteristic can be equivalent to a parallel negative resistance r and a negative reactance x grounded, as shown in formula (1).

[0096]

[0097] Wherein: U s is the outlet bus voltage of the wind turbine; P e and Q e are the active and reactive power generated by the wind turbine, respectively.

[0098] In the single-machine infinite system, the wind farm is connected to the source-side bus, and the system structure is shown in FIG. 1(a). and are the equivalent potentials of the synchronous generator and the infinite system, respectively. The equivalent system of the wind power grid connection is shown in FIG. 1(b), is the grid-connected point voltage vector, r and x are the equivalent resistance and reactance of the wind farm, X1 and X2 are the equivalent reactances of the generator and the grid-connected point and the grid-connected point and the infinite system, respectively. δ is the angle difference between E G and E S . The equivalent external characteristic of the doubly-fed wind turbine is equivalent to the right side system of the source-side bus by Thevenin equivalent, as shown in FIG. 1(c). The voltage vector of the source-side bus is calculated by using the superposition theorem, as shown in formula (2).

[0099]

[0100] Wherein: E G and E S are the equivalent potential amplitudes of the synchronous generator and the infinite system, respectively; is the equivalent admittance of the DFIG; e jδ is a complex exponential function.

[0101] During system oscillation, the active output of the wind turbine is limited, resulting in a small value of 1 / r, so formula (2) can be rewritten as:

[0102]

[0103] The bus node voltage amplitude U is calculated according to equation (3). m The analytical expression for is shown in equation (4).

[0104]

[0105] Under fault ride-through control, the wind farm only outputs reactive power. To study the impact of different wind power outputs on the bus voltage amplitude, let Q... e =0.3~1.0, power supply voltage amplitude E G =E S =1.0, X1=0.1, X2=0.5, substituting into equation (4), the bus voltage amplitude variation law is shown in Figure 2(a) and Figure 2(b). As can be seen from Figure 2(a), when the wind power output is arbitrary, the bus voltage amplitude first decreases and then increases with the increase of δ, and the voltage amplitude reaches the minimum when δ is 180°, indicating that the bus voltage amplitude decreases when the power angle difference increases. According to Figure 2(b), the minimum value of the bus voltage amplitude increases continuously with the increase of wind power output, but the trend of voltage amplitude variation is not affected by wind power output.

[0106] Step 2: Determine the relationship between generator voltage and speed and the system's transient power angle stability:

[0107] Assuming the generator is a second-order classical model, its differential equation is as follows (neglecting the damping coefficient):

[0108]

[0109] Where: δ is the power angle; ω is the speed deviation; T J P is the inertial time constant; m P represents mechanical power. e ′ represents the electromagnetic power of the generator after the wind power is connected to the grid.

[0110] Figure 3 The generator terminal voltage amplitude trajectories are presented for a three-phase short-circuit fault occurring at the midpoint of a single-circuit line at 0.2s, with the fault cleared at 0.37s (critical stability) and 0.38s (critical instability), respectively. Figure 3 It can be seen that the voltage U after the fault m The differences are evident after a short recovery. In a stable system scenario, the post-fault voltage gradually recovers to a stable value after decreasing to a minimum; however, in an unstable system, the post-fault voltage continues to decrease and oscillates significantly. Therefore, the post-fault voltage exhibits distinct dynamic characteristics after a short recovery, corresponding to the transient stability of the system.

[0111] With the generator power angle curve of the wind power grid-connected system, the wind power active power is restored to the initial power at a certain rate when the system is stable, and the generator power angle curve is shown in Fig. 4(a). After the fault is cleared, the generator operating point jumps from point c to point e, and then moves to point f with the restoration of the wind power active power. When the operating point reaches point g at the synchronous speed of the generator, the power angle starts to decrease, and the operating point moves from point g to the stable equilibrium point a along the power angle curve P3". According to formula (5), during the process of passing through the stable equilibrium point a, the generator speed decreases to the minimum value and then starts to increase. At the stable equilibrium point, the speed minimum point will appear. At the same time, according to the voltage amplitude variation law in step 1, since the power angle decreases during the process of passing through the stable equilibrium point a, the voltage amplitude increases accordingly. Therefore, at the stable equilibrium point, the speed minimum point will appear, and the voltage near the speed minimum point will continuously increase.

[0112] When the system is unstable, the wind power only outputs reactive power under the control of the fault ride-through strategy, and the generator power angle curve is shown in Fig. 4(b). After the fault is cleared, the generator operating point jumps from point c to point e, and then moves to the unstable equilibrium point u along the power angle curve P3'. According to formula (5), during the process of passing through the unstable equilibrium point u, the generator speed also decreases to the minimum value and then starts to increase. At the unstable equilibrium point, the speed minimum point will also appear. However, according to the voltage amplitude variation law in step 1, during the process of passing through the unstable equilibrium point, the power angle continuously increases, and the voltage amplitude decreases accordingly. Therefore, at the unstable equilibrium point, the speed minimum point will appear, and the voltage near the speed minimum point will continuously decrease.

[0113] Step three: excavating the key stability characteristics of the voltage-speed phase plane trajectory:

[0114] The operating trajectory is drawn in the phase plane with the speed as the horizontal axis and the generator voltage as the vertical axis. By adjusting the fault clearance time, the generator voltage and speed phase trajectories are obtained when the system is stable and unstable, as shown in Fig. 5(a) and Fig. 5(b). As shown in Fig. 5(a) and Fig. 5(b), when the system is stable, the U-w phase trajectory converges to a certain stable point; when the system is unstable, the U-w phase trajectory diverges, indicating that the dynamic characteristics of the U-w phase trajectory are closely related to the transient stability of the system, and the transient power angle stability discrimination problem can be converted into the identification of the key characteristics of the U-w phase trajectory.

[0115] In addition, regardless of whether the system is stable or not, the U-w phase trajectory will have a speed minimum point in a short time. After passing through the speed minimum point, the convergence and divergence characteristics of the U-w phase trajectory gradually appear. At the same time, the voltage near the speed minimum point always shows obvious differences between stability and instability, i.e., the voltage near the speed minimum point continuously increases when the system is stable, and the voltage near the speed minimum point continuously decreases when the system is unstable, as shown in Fig. 5(a) and Fig. 5(b). Figure 6The voltage variation characteristics near the minimum point of the rotational speed in the U-w phase trajectory are used to determine the transient stability of the wind power grid-connected system.

[0116] Step four: constructing a transient power angle stability pre-determination starting criterion:

[0117] After the fault is cleared, the generator voltage shows different trends after a short recovery. The stability pre-determination program is started by monitoring the voltage when it reaches the maximum value, that is:

[0118]

[0119] In the formula: U(k) represents the voltage amplitude at the kth sampling time; U(k-1) represents the voltage amplitude at the (k-1)th sampling time; η represents a sufficiently small positive real number; △T represents the sampling interval; U(k-i) represents the voltage amplitude at the (k-i)th sampling time; U(k-i-1) represents the voltage amplitude at the (k-i-1)th sampling time; k represents the kth sampling time; i represents the ith sampling time in the neighborhood before the voltage maximum point; M is the number of sampling points in the neighborhood before the voltage maximum point, and is recommended to be M=3.

[0120] Step five: when extended to multi-machine system application, construct a severely disturbed generator group rapid identification criterion:

[0121] In a multi-machine system, the present application distinguishes the severely disturbed generator group (SDG) according to the severity of the change in the generator terminal bus voltage amplitude, and the specific criterion is as follows:

[0122] 1) Collect the generator terminal bus voltage amplitude U n n=1,2,…,N G , N G is the number of generators.

[0123] 2) Calculate the voltage amplitude change rate △U n of each generator in real time according to the following formula:

[0124]

[0125] In the formula: U n (k) represents the voltage amplitude of the nth generator at the kth sampling time; U n (k-1) represents the voltage amplitude of the nth generator at the (k-1)th sampling time; △T represents the sampling interval.

[0126] 3) Let △U * = max{△U n}, and the condition △U n / △U * The generators are divided into SDG sets, wherein, △U * represents the maximum value in the amplitude variation rate of each generator bus voltage; max{△U n} represents a maximum function for obtaining the maximum value in the amplitude variation rate of each generator bus voltage; and sigma is an SDG identification threshold, preferably 0.8.

[0127] Step six: constructing a transient power angle stability identification criterion suitable for a wind power grid-connected system:

[0128] The transient stability identification method for the wind power grid-connected system based on the generator voltage and speed response characteristics is shown in the following formula (8)-(10). Therefore, when the system satisfies the criterion, the system is determined to be transient power angle instability; otherwise, the system is determined to be transient power angle stability.

[0129] |ω(k)-ω(k-1)|≤η△T (8);

[0130] ω(k-i)-ω(k-i-1)<0,i=0,1,2,…,N (9);

[0131] U(k)-U(k-1)<0 (10);

[0132] In the formula, ω(k) represents the generator speed at the kth sampling time; ω(k-1) represents the generator speed at the (k-1)th sampling time; ω(k-i) represents the generator speed at the (k-i)th sampling time; ω(k-i-1) represents the generator speed at the (k-i-1)th sampling time; △T represents a sampling interval; k represents the kth sampling time; η is a sufficiently small positive real number; and N is the number of sampling points in the neighborhood before the speed minimum point. In order to balance the rapidity and accuracy of the speed minimum point identification, the present application takes η=0.001 and N=5, respectively.

[0133] The specific process of the transient power angle stability pre-judgment method for the large-scale wind power grid-connected system based on the voltage-speed response characteristics is shown in Figure 7 .

[0134] Simulation verification:

[0135] In order to verify the effectiveness of the method, a wind farm connected to a single-end power transmission system model as shown in Fig. 1(a) is built in PSCAD. The synchronous generator adopts a sub-transient model of a hidden pole machine, and the excitation machine and the speed regulator are recorded as V G =18kV, the equivalent reactance X d ′=0.382p.u.; the transformer ratio is 31.18kV / 220kV, and the short-circuit reactance X T= 0.1 p.u.; the length of the double-circuit transmission line is 200 km, and its unit reactance X L = 0.472 Ω / km; the receiving-end system is an infinite grid with a rated voltage of 220 kV; the capacity of the wind farm is 100 MVA (20 units of 5 MW doubly-fed wind turbines), the doubly-fed units adopt maximum power tracking control mode, and the wind power penetration is 25%.

[0136] (1) System transient stability simulation example:

[0137] Suppose that a three-phase short circuit occurs at 50% of one of the lines at 1 s, and the fault is cleared at 1.15 s, the transient response characteristics of the wind power grid-connected system are shown in FIG. 8. As shown in FIG. 8(a), the generator voltage reaches a maximum value at t1=1.32 s for the first time, satisfying equation (6), and the transient stability is pre-judged. According to FIG. 8(b), the generator speed reaches a minimum point at t2=1.90 s, satisfying equations (8) and (9), and the speed minimum point is accurately identified. In combination with the generator voltage curve, it can be seen that the voltage at t2 keeps rising, so it is judged that the transient power angle is stable. Figures 8(a) to 8(d)

[0138] The U-w phase trajectory in a period of time after the fault is cleared corresponds to FIG. 8(c), and the voltage of the U-w phase trajectory near the speed minimum point shows a sustained increasing characteristic. According to the criterion of the present application, the U-w phase trajectory of the generator satisfies the transient stability criterion at 0.75 s after the fault is cleared, and it is determined that the system is transiently stable. At the same time, as shown in FIG. 8(d), the generator power angle finally tends to be stable after attenuation oscillation, which is consistent with the result obtained by the criterion of the present application.

[0139] (2) System transient instability simulation example:

[0140] Suppose that a three-phase short circuit occurs at 50% of one of the lines at 1 s, and the fault is cleared at 1.16 s, the transient response characteristics of the system are shown in FIG. 9. As shown in FIG. 9(a), the generator voltage reaches a maximum value at t1=1.28 s for the first time, and the transient stability is pre-judged. According to FIG. 9(b), the generator speed reaches a minimum point at t2=1.46 s, satisfying equations (8) and (9), and the speed minimum point is accurately identified. In combination with the generator voltage curve, it can be seen that the voltage at t2 keeps falling, so it is judged that the transient power angle is unstable. Figures 9(a) to 9(d)

[0141] ​​The Uw phase trajectory after the fault is cleared corresponds to Figure 9(c). The voltage of the Uw phase trajectory near the minimum speed exhibits a continuous decrease. Using the criterion of this invention, it can be seen that 0.30s after the fault is cleared, the generator's Uw phase trajectory satisfies the transient instability criterion, and the system is determined to be transiently unstable. Meanwhile, as shown in Figure 9(d), the generator power angle continuously increases after the fault is cleared, until it reaches 180° at 1.67s, at which point the system becomes unstable, consistent with the result obtained from the criterion of this invention.

[0142] (3) Reliability analysis under different wind power penetration rates:

[0143] To verify the reliability of this invention under different wind power penetration rates, the wind power penetration rate was varied by changing the number of connected wind turbines. Under the premise of ensuring the same fault conditions, the generator Uw phase trajectories under stable system conditions were obtained for wind power penetration rates of 0%, 14.3%, 25%, and 50%, respectively. Figure 10 As shown. By Figure 10 It can be seen that the voltage of the Uw phase trajectory near the minimum rotational speed under different wind power penetration rates all show a continuous increase, which satisfies the transient stability criterion proposed in this invention, indicating that the method can still correctly judge transient stability under different wind power penetration rates.

[0144] Similarly, under the premise of ensuring the same fault conditions, the system instability conditions under different wind power penetration rates were obtained, and their Uw phase trajectories are as follows: Figure 11 As shown. From Figure 11 It can be seen that the key transient stability characteristics of the Uw phase trajectory still exist under different wind power penetration rates. The voltage near the minimum rotational speed exhibits a continuous decrease, satisfying the transient instability criterion proposed in this invention. Therefore, the method of this invention is still applicable to systems with different wind power penetration rates.

[0145] (4) Simulation of a doubly fed wind farm connected to a 10-unit, 39-bus system:

[0146] To further verify the effectiveness of the method of this invention in a multi-machine system, a 600MW doubly-fed induction generator (DFIG) wind farm was connected to the grid at nodes 25 and 18 of the IEEE 39-node system, respectively. All generators were modeled using a classical second-order model, with generator G31 serving as the reference generator, and all loads using a constant impedance model. It was assumed that a three-phase short-circuit fault occurred on line 27-17 at 2 seconds, and the fault was cleared after 0.152 seconds, indicating critical system stability; if the fault was cleared after 0.153 seconds, the system was critically unstable.

[0147] Under the system stable scenario, the relative power angle curves of each generator with respect to generator G31 and the generator terminal voltage amplitude are shown in FIG. 12(a) and FIG. 12(b) respectively. As shown in FIG. 12(a) and FIG. 12(b), the relative power angle and the voltage amplitude are damped oscillation after the fault is cleared, and finally tend to be stable. At the same time, according to the SDG fast identification method, the generator G38 has the most severe oscillation of the generator terminal voltage amplitude, that is, G38 is the severely disturbed unit, and its speed curve and U-w phase trajectory are shown in FIG. 12(c) and FIG. 12(d) respectively. As shown in FIG. 12(c) and FIG. 12(d), the generator speed first appears a minimum point at t2=3.576s, and the voltage of the U-w phase trajectory near the minimum point of the speed presents a feature of continuously increasing. According to the criterion of the present application, it is determined that the system is transiently stable 1.424s after the fault is cleared.

[0148] Under the system unstable scenario, the relative power angle curves of each generator with respect to generator G31 and the generator terminal voltage amplitude are shown in FIG. 13(a) and FIG. 13(b) respectively. As shown in FIG. 13(a) and FIG. 13(b), the relative power angle δ 38-31 After the fault is cleared, the relative power angle δ At the same time, according to the SDG fast identification method, the generator G38 has the most severe oscillation of the generator terminal voltage amplitude, that is, G38 is the severely disturbed unit, and its speed curve and U-w phase trajectory are shown in FIG. 13(c) and FIG. 13(d) respectively. As shown in FIG. 13(c) and FIG. 13(d), the generator speed first appears a minimum point at t2=2.784s, and the voltage of the U-w phase trajectory near the minimum point of the speed presents a feature of continuously decreasing. According to the criterion of the present application, it is determined that the system is transiently unstable 0.631s after the fault is cleared. Compared with the engineering power angle difference (δ>180°) criterion, the present application can realize transient instability discrimination 0.568s in advance, and the rapidity is effectively improved.

Claims

1. A method for transient power angle stability prediction of a large-scale wind power grid-connected system based on voltage-speed response characteristics, characterized in that The method comprises the following steps: Step 1: analyze the variation law of the node voltage amplitude of the wind power grid-connected system; Step 2: determine the relationship between the generator voltage and the speed and the transient stability of the system; Step 3: analyze the key stability characteristics of the voltage-speed phase plane trajectory; Step 4: in combination with the variation law of the node voltage amplitude after the fault, a transient stability pre-judgment starting criterion is constructed; Step 5: a disturbed serious machine group fast identification criterion is constructed by using the variation rate of the terminal bus voltage amplitude; Step 6: based on the key stability characteristics of the voltage-speed phase trajectory in step 3, a transient stability identification criterion suitable for the wind power grid-connected system is constructed; The specific transient stability identification criterion is shown in the following formula: （8）； （9）； （10）； In the formula: This represents the voltage amplitude at the k-th sampling time. This represents the voltage amplitude at the (k-1)th sampling time. Indicates the first k Generator speed at each sampling time; Indicates the first k Generator speed at -1 sampling time; Indicates the first k - i Generator speed at each sampling time; Indicates the first k - i Generator speed at -1 sampling time; Indicates the sampling interval; k Indicates the first k Each sampling time; It is a sufficiently small positive real number; N This represents the number of sampling points in the neighborhood before the point of minimum rotational speed; When the system satisfies the criterion, it is judged that the system is transiently unstable; otherwise, it is judged that the system is transiently stable. 2.The method for transient power angle stability pre-judgment of large-scale wind power grid-connected system based on voltage-speed response characteristic according to claim 1, characterized in that: In step 1, since the active power and the reactive power are decoupled by the doubly-fed fan control strategy, the equivalent external characteristics can be equivalent to parallel negative resistance r and negative reactance x grounded, as shown in equation (1): （1）； In formula (1): Vout is the wind turbine generator outlet bus voltage; and Pout and Qout are the active and reactive power generated by the wind turbine generator, respectively. In the single-machine infinite system, the source-side bus is connected with the wind farm, the equivalent external characteristics of the doubly-fed wind turbine are equivalent to the system on the right side of the source-side bus, the superposition theorem is used to calculate the source-side bus voltage vector, and the formula (2) is shown as follows: （2）； In formula (2): is the grid-connected point voltage vector; X 1、 X 2are the equivalent reactances of the generator and the grid-connected point, and the grid-connected point and the infinite system, respectively; is E G is the angle difference between E S and are the equivalent potential amplitudes of the synchronous generator and the infinite system, respectively; is the DFIG equivalent admittance; is the complex exponential function;​ The active output of the fan is limited during system oscillation, which leads to 1 / r The numerical value is small, so equation (2) can be rewritten as: （3）； In formula (3): x X is the equivalent reactance of the wind farm. The bus node voltage amplitude is calculated according to formula (3) An analytical expression of the bus node voltage amplitude, as shown in formula (4): （4）； Analysis of equation (4) shows that when the wind power output is any value, as... With the increase of [variable name], the bus voltage amplitude first decreases and then increases, and [variable name]... The voltage amplitude reaches its minimum at 180°. In addition, the minimum value of the bus voltage amplitude increases with the increase of wind power output, but the trend of voltage amplitude change is not affected by wind power output. 3.The method for transient power angle stability pre-judgment of large-scale wind power grid-connected system based on voltage-speed response characteristic according to claim 2, characterized in that: In the step 2, the generator is a second-order classical model, and the differential equation is shown in the following formula (5): （5）； The angle difference between the two lines in the formula (5) is the power angle. The angle difference between the two lines in the formula (5) is the power angle. E G The angle difference between the two lines in the formula (5) is the power angle. E S The angle difference between the two lines in the formula (5) is the power angle. The angle difference between the two lines in the formula (5) is the power angle. The angle difference between the two lines in the formula (5) is the power angle. The angle difference between the two lines in the formula (5) is the power angle. The angle difference between the two lines in the formula (5) is the power angle.

4. The method of claim 3, wherein the method is characterized by: In step 2, in combination with the generator power angle curve of the wind power grid-connected system, when the system is stable, the generator speed decreases to a minimum value and then increases in the process of passing through the stable equilibrium point, and the speed minimum point appears at the stable equilibrium point; at the same time, in combination with the voltage amplitude variation law in step 1, since the power angle continuously decreases in the process of passing through the stable equilibrium point, the voltage amplitude increases; therefore, when the system is stable, the speed minimum point appears at the stable equilibrium point, and the voltage near the speed minimum point continuously increases; When the system is unstable, the generator speed also decreases to a minimum value and then increases in the process of passing through the unstable equilibrium point, and the speed minimum point also appears at the unstable equilibrium point; according to the voltage amplitude variation law in step 1, in the process of passing through the unstable equilibrium point, the power angle continuously increases, and the voltage amplitude continuously decreases; therefore, when the system is unstable, the speed minimum point appears at the unstable equilibrium point, and the voltage near the speed minimum point continuously decreases.

5. The method of claim 1, wherein the method is characterized by: In the step 3, in the phase plane with the speed as the horizontal axis and the generator voltage as the vertical axis, the operating trajectories of the voltage U and the speed w are drawn when the system is stable and unstable respectively; when the system is stable, the U-w phase trajectory gradually converges to a certain stable point; when the system is unstable, the U-w phase trajectory gradually diverges, which shows that the dynamic characteristics of the U-w phase trajectory are closely related to the transient stability of the system, and the transient stability discrimination problem can be converted into the identification of the key characteristics of the U-w phase trajectory; In addition, whether the system is stable or not, the U-w phase trajectory will appear a speed minimum point in a short time, and after passing through the speed minimum point, the convergence and divergence characteristics of the U-w phase trajectory gradually appear; at the same time, the voltage near the speed minimum point always shows obvious differences in stability, that is, the voltage near the speed minimum point continuously increases when the system is stable, and the voltage near the speed minimum point continuously decreases when the system is unstable. 6.The method for transient power angle stability pre-judgment of large-scale wind power grid-connected system based on voltage-speed response characteristic according to claim 1, characterized in that: In step 4, after the fault is cleared, the generator voltage shows different trends after a short recovery, and the stability prediction program is started by monitoring the voltage when it reaches a maximum value, that is: （6） In formula (6), denotes the voltage amplitude at the kth sampling time; denotes the voltage amplitude at the (k-1)th sampling time; denotes a sufficiently small positive real number; denotes the sampling interval; denotes the voltage amplitude at the (k-i)th sampling time; denotes the voltage amplitude at the (k-i-1)th sampling time; k denotes the kth sampling time; i denotes the ith sampling time in the neighborhood before the voltage maximum point; M is the number of sampling points in the neighborhood before the voltage maximum point. 7.The method for transient power angle stability pre-judgment of large-scale wind power grid-connected system based on voltage-speed response characteristic according to claim 1, characterized in that: In step 5, in a multi-machine system, the severity of the disturbance is determined according to the severity of the change in the bus voltage amplitude, and the specific criterion is as follows: 1) Collect the amplitude of the bus voltage at the generator terminals after the fault is cleared , , is the number of generators; 2) Real-time calculation of the generator terminal bus voltage magnitude rate of change according to the following formula : （7）； In formula (7): represents the voltage amplitude of the first generator at the n first sampling time point; k represents the voltage amplitude of the first generator at the -1 sampling time point; n represents the voltage amplitude of the first generator at the k -1 sampling time point; represents the sampling interval; 3) Let , denotes the maximum value in the rate of change of the voltage amplitude of each generator busbar; denotes the maximum function for obtaining the maximum value in the rate of change of the voltage amplitude of each generator busbar; The generators satisfying are divided into a set of SDGs; wherein, is an SDG identification threshold.

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