Small-interference synchronous stability analysis method for synchronous phase modifier

Abstract

The invention relates to the technical field of power system stability analysis, in particular to a small-interference synchronous stability analysis method for a synchronous phase modifier. On the basis of the actual operation condition of the synchronous phase modifier, a Heffron-Phillips model for analyzing the small interference stability of a power system is simplified and improved, and in combination with a torque analysis method, whether the phase modifier can be kept stable or not is judged according to the numerical values of parameter synchronous torque and damping torque representing the synchronous stability. According to the method, starting from a classic analysis model, the model is improved and simplified based on the actual operation condition, the dynamic behavior of the electromagnetic power of the synchronous phase modifier during the small disturbance period is truly reflected, and the small disturbance instability or stable form of the phase modifier is judged by using specific numerical parameters; and the relationship between excitation system parameter setting and small interference instability forms is clarified, and the method has important significance for reducing the oscillation risk of the synchronous phase modifier.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power system stability analysis, in particular to a small disturbance synchronous stability analysis method of a synchronous phase modifier. BACKGROUND

[0002] With the substantial increase of new energy proportion, the high penetration rate of intermittent power sources such as wind power reduces the risk resistance ability of the power grid. In order to improve the stability of the system, dynamic reactive power compensation equipment needs to be configured. The phase modifier has more advantages in transient voltage support, short-circuit capacity provision, etc. Especially the distributed phase modifier can be deployed in layers to suppress the overvoltage off-grid of new energy and improve the sending capacity due to its small capacity and close electrical distance to new energy.

[0003] The unique advantages of the distributed phase modifier in improving inertia support and improving the frequency and voltage characteristics of new energy make it gradually become a key device to ensure the development of new energy power systems in recent years. The access of the phase modifier also brings new stability problems, such as power angle instability risk and insufficient static stability margin, which need to be analyzed for the actual operation of the phase modifier.

[0004] The existing research has the following shortcomings: the influence of parameter uncertainty on the robustness of the excitation system is not quantified, the analysis of the dynamic characteristics of the excitation system and the electromechanical coupling mechanism of the phase modifier is missing, and the coupling mechanism of the nonlinear dynamics of the excitation system and the low-frequency oscillation is not fully understood, so that the interaction mechanism of the small disturbance stability of the synchronous phase modifier and the excitation system is not fully revealed. SUMMARY

[0005] The purpose of the present application is to overcome the defects of the prior art and provide a small disturbance synchronous stability analysis method of a synchronous phase modifier. In view of the fact that the existing research has not fully revealed the interaction mechanism of the small disturbance stability of the synchronous phase modifier and the excitation system, the present application introduces an improved small disturbance stability analysis model, combines the actual working condition of the synchronous phase modifier with the Heffron-Phillips model, simplifies the expression, and obtains the range of the comprehensive amplification factor of the excitation system; by introducing the torque analysis method, the amplification factor of the excitation system is associated with the synchronous and damping torques, thereby analyzing the small disturbance synchronous stability of the synchronous phase modifier.

[0006] To achieve the above purpose, the following specific technical solutions are adopted in the present application:

[0007] The small disturbance synchronous stability analysis method of the synchronous phase modifier provided by the present application comprises the following steps:

[0008] S1, a synchronous phase modifier model is established; the synchronous phase modifier model adopts a third-order model considering transient electromotive force change, including a rotor motion equation, a differential equation of transient electromotive force change, and an expression of the excitation system equation in time domain;

[0009] S2, synchronous condenser small disturbance analysis model simplification; synchronous condenser is a synchronous generator without prime mover, no active power is emitted, only absorbing or emitting reactive power, the power angle is zero, the small disturbance analysis model of synchronous condenser is simplified;

[0010] S3, torque characteristic analysis; decompose electromagnetic torque component into related power angle increment, use torque analysis method to arrange into complex form, consider synchronous torque coefficient and inherent damping coefficient of synchronous condenser, obtain total synchronous and damping torque coefficient of synchronous condenser;

[0011] S4, stability discrimination; use positive and negative of total synchronous and damping torque coefficient, Routh criterion to judge small disturbance synchronous stability of synchronous condenser;

[0012] S5, parameter interaction analysis, including operation condition of condenser and rotor oscillation frequency.

[0013] Further, in step S1, the synchronous condenser model is as follows:

[0014]

[0015] The first two equations are rotor motion equations, for synchronous condenser ΔP m =0; the third equation is a differential equation of transient electromotive force change, the fourth equation is an expression of the excitation system equation in time domain, and the four equations constitute the synchronous condenser model; the intermediate variables are eliminated, the state variables are reserved, and the state equation is written as follows:

[0016]

[0017] The electromagnetic power is obtained by two parts, one part is the component K1Δδ obtained by the change amount of power angle through coefficient K1, and the other part is the component K2ΔE′ q obtained by the change amount of transient electromotive force through coefficient K2.

[0018]

[0019] Among them, E Q is the virtual electromotive force of salient pole synchronous machine, U is the voltage of infinite bus, U G is the terminal voltage of condenser, U Gq and U Gd are the q-axis component and d-axis component of terminal voltage respectively, δ is the power angle, I q is the q-axis component of system current, x′ d∑ =x′ d +x e , x q∑ =x q +xe , A = r 2 + x' d∑ · x q∑ , is a constant; coefficients K1-K6, except K3, are directly related to the power angle and describe the operating state of the synchronous condenser, K3 is a constant;

[0020] x d is the direct-axis synchronous reactance, x q is the quadrature-axis synchronous reactance, x' d is the direct-axis transient reactance, T j is the inertia time constant, E' q is the transient EMF, E fd is the field voltage, δ is the power angle, T d '0 is the time constant of the field circuit with open stator winding, ω is the angular velocity, U G is the terminal voltage, r e is the total resistance from the condenser outlet to the infinite bus, x e is the total reactance; the transfer function of the field system is G e (s) = K e / 1 + T e s, which is a first-order inertia link; K e is the comprehensive amplification factor of the field system, and its value is closely related to the small-disturbance power angle stability, T e is the time constant of the field system, and is set to 0.01 s.

[0021] Further, in step S2, the synchronous condenser model is simplified as follows:

[0022] When the power angle δ is 0, sin δ = δ, cos δ = 1, U Gd = 0, U G = U Gq , I q = 0, and K1-K6 are simplified as follows:

[0023]

[0024] After simplification, the positive and negative values of K4 and K5 can be determined to determine the torque parameters; for the condenser, the power angle is close to zero, and it is considered that x q∑ δ-r in K4 is approximately -r, so K4 is negative; similarly, it is considered that r-x q∑ δ in K5 is r, so K5 is positive; K3 and K6 are constants.

[0025] Further, in step S3, the torque characteristic analysis is as follows:

[0026] Decompose the electromagnetic torque component K2ΔE' q, the expression is transformed into the power angle increment related by mathematical change In the complex frequency domain, the solution of the state equation is considered as the oscillation frequency ω d , substitute s = jω d , K2ΔE′ q is transformed into complex number form K2ΔE′ q = (ΔK S + jΔK D )Δδ; ΔK S is the additional synchronous torque coefficient, ΔK D is the additional damping torque coefficient; the expressions of the additional synchronous and damping torque coefficients are respectively If the synchronous torque coefficient K1 and the inherent damping coefficient D of the synchronous phase modifier are considered, the total synchronous and damping torque coefficients of the synchronous phase modifier are respectively T S = (K1+ΔK S )Δδ, T D = (ΔK D +D)sΔδ.

[0027] Further, in step S4, the small disturbance synchronous stability of the synchronous phase modifier is judged by the positive and negative of the total synchronous and damping torque coefficients as follows:

[0028] T D <0, it is in the unstable state of power angle increment oscillation; T S <0, it is in the unstable state of power angle monotonic instability; the condition for the phase modifier not to occur periodic power angle instability is T D >0, the condition for not to occur non-periodic power angle instability is T S >0;

[0029] The small disturbance synchronous stability of the synchronous phase modifier is judged by the Routh criterion as follows:

[0030] Rewrite the coefficients of the state equation into the Routh array table, if the coefficients in the first column of the Routh array table are all positive numbers, the system is stable, that is, all roots of the characteristic equation are located in the left half of the root plane; if there are negative numbers in the first column of coefficients, the number of sign changes of the first column of coefficients is equal to the number of roots in the right half plane, and the stability criterion is obtained:

[0031] K1>0;

[0032] K4+K e K5>0;

[0033] K1 / K3-K2K4+K e (K1K6-K2K5)>0;

[0034] The power angle of the phase modifier is zero, K4 is less than zero, K5 is greater than zero; K4+Ke The characteristic curve of K5 is a linear function with a positive coefficient and a negative intercept. The minimum amplification factor K of the excitation system used to maintain the stability of the synchronous condenser is determined by this function. emin K emin =-K4 / K5=(x d -x′ d ) / x′ d ;

[0035] K emin The minimum possible comprehensive amplification factor Ke of the synchronous condenser excitation system determines the magnitude of the additional torque coefficient; K4+K e K5 determines the sign of the additional torque coefficient;

[0036] Magnification greater than K emin At that time, K4+K e K5 is greater than zero. Although the additional synchronous torque is less than zero, its order of magnitude is extremely small compared to the synchronous torque coefficient K1, which can still ensure that the synchronous torque is greater than zero. At the same time, the additional damping torque is also greater than zero, which enhances the inherent damping and allows the synchronous condenser to maintain static stability.

[0037] If the magnification factor is less than the minimum value K emin If the additional synchronous torque coefficient is greater than zero, the additional damping torque will be less than zero; if the inherent damping is zero, the system will oscillate and become unstable due to insufficient damping.

[0038] Furthermore, in step S5, the specific operating conditions of the camera in the parameter interaction influence analysis are as follows:

[0039] The reactive power output of the synchronous condenser changes the additional torque by affecting the size of the synchronous condenser's power angle. The change in the power angle affects K4+K. e The size of K5 decreases as the reactive power output of the synchronous condenser increases, and the power angle decreases.

[0040] K e <K emin At that time, K4+K e The changing trend of K5 is equivalent to U(x) q∑ Multiplying δ-r) / A by a positive coefficient, the additional damping torque decreases as the reactive power output increases, i.e., the power angle decreases, changing from positive to negative; the additional synchronous torque coefficient increases as the reactive power output increases, changing from negative to positive, and the two always have opposite signs.

[0041] K e >K emin At that time, K4+K e The changing trend of K5 is equivalent to U(x) q∑ Multiplying δ-r) / A by a negative coefficient, as the reactive power output increases, the additional damping torque coefficient increases, while the additional synchronous torque coefficient decreases.

[0042] The rotor oscillation frequency is as follows:

[0043] For the additional synchronous torque coefficient, the rotor oscillation frequency ω d Only the denominator of the expression is affected, therefore the additional synchronous torque coefficient varies with ω. d The changes are monotonous; K e <K emin Time follows ω d As K increases, it becomes a negative value; e >K emin Time follows ω d It decreases as it increases, and is a positive value;

[0044] For the additional damping torque coefficient, ω d It simultaneously affects both the numerator and denominator of the expression, and the change is not monotonic; therefore, when K... e <K emin When K is constant, the additional damping torque coefficient is always negative, first decreasing and then increasing, with a minimum value; e >K emin When the value is always positive, it first increases and then decreases, and has a maximum value.

[0045] The present invention can achieve the following technical effects:

[0046] This invention starts from the classical electromechanical transient model and constructs an improved analytical framework by integrating actual synchronous condenser operating constraints to accurately characterize the dynamic characteristics of the electromagnetic power of the synchronous condenser under small disturbances. Quantitative criteria for stable states are established based on key torque parameters, and the interaction mechanism between excitation system parameter configuration and small-disturbance instability modes is revealed. This provides a theoretical basis for the parameter tuning of the synchronous condenser excitation system, enabling the reactive power compensation equipment configuration to follow the dynamic needs of the system and advancing the progress of wide-area collaborative control strategies. Attached Figure Description

[0047] Figure 1 This is a flowchart of a method for analyzing the synchronization stability of a synchronous condenser under small disturbances according to an embodiment of the present invention;

[0048] Figure 2 This is a structural diagram of a synchronous condenser reactive power transmission system independently configured in the sending-end system according to an embodiment of the present invention;

[0049] Figure 3 This is a block diagram of the Heffron-Phillips model provided according to an embodiment of the present invention;

[0050] Figure 4 This is a parameter diagram of the K-coefficient and additional torque coefficient of the synchronous condenser provided according to an embodiment of the present invention;

[0051] Figure 5This is a graph showing the amplification factor and the corresponding system characteristic value, oscillation frequency, and damping ratio data provided according to an embodiment of the present invention;

[0052] Figure 6 This is a graph showing the change of camera power angle over time at different magnifications, provided by an embodiment of the present invention.

[0053] Figure 7 This is a graph showing the change of camera power angle over time when the excitation system amplification factor is 2, with different system resistances.

[0054] Figure 8 This is a graph showing the change of camera power angle over time when the excitation system amplification factor is 20 under different system resistances, according to an embodiment of the present invention.

[0055] Figure 9 This is a graph showing the change of camera power angle over time under different operating conditions when the excitation system amplification factor is 2, according to an embodiment of the present invention.

[0056] Figure 10 This is a graph showing the change of camera power angle over time under different operating conditions when the excitation system amplification factor is 20, according to an embodiment of the present invention. Detailed Implementation

[0057] In the following description, embodiments of the invention will be described with reference to the accompanying drawings. In the description below, the same modules are denoted by the same reference numerals. Where the same reference numerals are used, their names and functions are also the same. Therefore, their detailed description will not be repeated.

[0058] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0059] This invention provides a method for analyzing the synchronization stability of a synchronous condenser under small disturbances, the process of which is as follows: Figure 1 As shown, it includes the following steps:

[0060] S1. Establish a synchronous camera model. Figure 2 This diagram illustrates a synchronous condenser reactive power output system independently configured in the sending-end system. The condenser parameters are as follows: condenser direct-axis synchronous reactance x d quadrature axis synchronous reactance x q Direct-axis transient reactance x′ d Inertial time constant T j Transient potential E′ q Excitation voltage E fdPower angle δ, and the time constant T′ of the excitation circuit when the stator winding is open. d0 Angular velocity ω, terminal voltage U G The system parameters are as follows: total resistance r from the phase converter output to the infinite bus. e Total reactance x e Considering the excitation system, the model is a thyristor fast excitation system, with the transfer function G. e (s)=K e / 1+T e s is a first-order inertial element. Where K... e T represents the overall amplification factor of the excitation system, which is a key parameter tuned in this method. Its value is closely related to the stability of the power angle under small disturbances. e This is the time constant of the excitation system, which is generally set to 0.01s.

[0061] The synchronous condenser model adopts a third-order model that takes into account the transient electromotive force change, and the equation is shown in equation (1):

[0062]

[0063] Among them, the first two equations are the rotor motion equations. For a synchronous condenser, ΔP m =0. The third equation is the differential equation for the transient electromotive force change, and the fourth equation is the time domain expression of the excitation system equation. The four equations constitute the dynamic model of the synchronous condenser. Eliminating the intermediate variables in the equation and retaining the state variables, we write the state equation as shown in equation (2), which is then transformed into a block diagram, as shown in... Figure 3 As shown.

[0064]

[0065] Depend on Figure 3 It can be seen that the increase in electromagnetic power is obtained from two parts: one part is the component K1Δδ obtained by the change in power angle through coefficient K1, and the other part is the component K2ΔE′ obtained by the change in transient electromotive force through coefficient K2. q The expressions for the coefficients K1-K6 are shown in equation (3).

[0066]

[0067] In the formula, E Q U is the virtual electromotive force of the salient-pole synchronous machine, and U is the voltage of the infinite bus. G It's adjusting the camera terminal voltage, U Gq and U Gd These are the q-axis and d-axis components of the terminal voltage, respectively, where δ is the power angle, and I... q It is the q-axis component of the system current, x′ d∑ =x′ d +x ex q∑ =x q +x e A = r 2 +x′ d∑ ·x q∑ K is a constant. Except for K3, all coefficients are directly related to the power angle and describe the operating state of the synchronous condenser. K3 is a constant.

[0068] S2. Simplification of the Synchronous Condenser Model. A synchronous condenser is a synchronous generator without a prime mover; therefore, it does not generate active power, only absorbs or generates reactive power, and its power angle is close to zero. The coefficient expressions are simplified based on actual operating conditions. The specific simplification conditions are as follows: If the power angle δ is approximated as 0, then sinδ = δ, cosδ = 1; furthermore, U... Gd =0, U G =U Gq I q =0. And simplify K1-K6. The simplified expression is shown in equation (4).

[0069]

[0070] After simplification, the torque parameters can be determined by analyzing the positive and negative values ​​of K4 and K5. For a synchronous condenser, the power angle is close to zero, and the term x that determines the sign in K4 is considered to be... q∑ Since δ-r is approximately -r, K4 is negative. Similarly, we consider rx in K5 to be... q∑ Since δ is r, K5 is a positive value. K3 and K6 are both constants.

[0071] S3. Torque Characteristic Analysis. Decompose the electromagnetic torque component K2ΔE′. q The expression is transformed mathematically into one that is related to the increment of the work angle. In the complex frequency domain, the solution to the state equation is considered to be the oscillation frequency ω of the system. d Substituting into s = jω d Using torque analysis, K2ΔE′ q Rearranged into complex form K2ΔE′ q =(ΔK) S +jΔK D )Δδ。 ΔK S It is the additional synchronous torque coefficient, ΔK D This refers to the additional damping torque coefficient. The expressions for the additional synchronization and damping torque coefficients are as follows: Taking into account the synchronous torque coefficient K1 and the inherent damping coefficient D of the synchronous condenser, the total synchronous and damping torque coefficients of the synchronous condenser can be obtained as T. S =(K1+ΔK) S )Δδ,TD =(ΔK) D +D)sΔδ.

[0072] S4. Stability Judgment. The stability of synchronization under small disturbances in synchronous condensers can be judged by the sign of the total synchronization and damping torque coefficients. T D When T < 0, the system is in an unstable state of oscillation with increasing power angle. S When T < 0, the system is in an unstable state of monotonic power angle instability. Therefore, the condition for a synchronous condenser not to experience periodic power angle instability is T. D The condition for T > 0, and for non-periodic power angle instability not to occur, is T S >0.

[0073] The Routh criterion is used to determine the small-perturbation stability of a system expressed by a state equation. The principle of the Routh criterion is as follows: rewrite the coefficients of the state equation as a Routh array. If all coefficients in the first column of the Routh array are positive, then the system is stable, meaning all roots of the characteristic equation lie in the left half-plane of the root plane. If any coefficient in the first column is negative, then the number of sign changes of the coefficients in the first column equals the number of roots in the right half-plane. Using this principle, three stability criteria for third-order state equations are derived:

[0074]

[0075] When adjusting the camera's power angle to near zero, K4 is less than zero, and K5 is greater than zero. K4 + K e The characteristic curve of K5 is a linear function with a positive coefficient and a negative intercept. Criterion 2 describes the criterion that the overall result must be greater than zero when Ke is greater than a certain critical value. This determines the minimum amplification factor Kemin,K of the excitation system used to maintain the stability of the synchronous condenser. emin =-K4 / K5=(x d -x′ d ) / x′ d .

[0076] Kemin is the minimum possible value of the overall amplification factor Ke of the synchronous condenser excitation system, which also determines the magnitude of the additional torque coefficient. In the torque expression, all parameters except K4 are greater than zero. Therefore, K4 + K e The value of K5 determines the sign of the additional torque coefficient.

[0077] When the magnification factor is greater than Kemin, K4+K e K5 is greater than zero. Although the additional synchronous torque is less than zero, its order of magnitude is extremely small compared to the synchronous torque coefficient K1, which still ensures that the synchronous torque is greater than zero. At the same time, the additional damping torque is also greater than zero, which enhances the inherent damping, allowing the synchronous condenser to maintain static stability.

[0078] If the amplification factor is set too small, less than the minimum value Kemin, the additional synchronization torque coefficient will be greater than zero, while the additional damping torque will be less than zero. If the inherent damping is zero, the system will oscillate and become unstable due to insufficient damping.

[0079] The Ke value obtained by criterion 3 should be less than a certain critical value. However, both K1 / K3-K2K4 and K1K6-K2K5 (analysis probability) are greater than zero, making the critical value obtained by criterion 3 less than zero, while Ke is always greater than zero. The determined range of Ke is covered by the range defined by Kemin, so it no longer plays the role of limiting the maximum value of Ke.

[0080] Based on the above analysis, it can be concluded that the overall amplification factor of the synchronous condenser excitation system cannot be too small, otherwise it will cause periodic instability due to insufficient damping.

[0081] S5. Parameter interaction effect analysis.

[0082] (1) Operating conditions of the synchronous condenser

[0083] The reactive power output of the synchronous condenser changes the additional torque by affecting the size of the synchronous condenser's power angle. The change in the power angle affects K4+K. e The size of K5. As the reactive power output of the camera increases, the power angle decreases.

[0084] K e <K emin At that time, K4+K e The changing trend of K5 is equivalent to U(x) q∑ Multiplying δ-r) / A by a positive coefficient, the additional damping torque decreases as the reactive power output increases, i.e., the power angle decreases, changing from positive to negative; the additional synchronous torque coefficient increases as the reactive power output increases, changing from negative to positive, and the two always have opposite signs.

[0085] K e >K emin At that time, K4+K e The changing trend of K5 is equivalent to U(x) q∑ Multiplying δ-r) / A by a negative coefficient, as the reactive power output increases, the additional damping torque coefficient increases, while the additional synchronous torque coefficient decreases.

[0086] (2) Rotor oscillation frequency

[0087] For the additional synchronous torque coefficient, the rotor oscillation frequency ω d Only the denominator of the expression is affected, therefore the additional synchronous torque coefficient varies with ω. d The changes are monotonous. K e <K emin Time follows ω d As K increases, it becomes a negative value; e >K eminTime follows ω d It decreases as it increases, and is a positive value.

[0088] For the additional damping torque coefficient, ω d It simultaneously affects both the numerator and denominator of the expression, and the change is not monotonic; therefore, when K... e <K emin When K is constant, the additional damping torque coefficient is always negative, first decreasing and then increasing, with a minimum value; e >K emin When the value is always positive, it first increases and then decreases, and has a maximum value.

[0089] S6. Measures to improve the damping torque of the synchronous condenser. Based on the above analysis, when the amplification factor is small, the total system resistance can be reduced by optimizing the power grid structure, thereby increasing the damping strength of the synchronous condenser and enhancing system stability.

[0090] The effects of the method of the present invention will be described below with reference to specific embodiments.

[0091] (1) Analysis of Calculation Results

[0092] Assume the camera's parameters are a rated capacity of 50 Mvar, x d =x q =0.88pu, x′ d =0.1163pu,T j = 5.569s, T′ d0 =7.634s, Excitation system comprehensive amplification factor K e =20, system parameter is r e =0.57, x e =0.79. When the synchronous condenser outputs 10 Mvar, let the rotor oscillation frequency ω be... d =10rad / s, the K-coefficient of the camera and the additional torque coefficient, etc., are as follows Figure 4 As shown.

[0093] The maximum amplification factor of the system at this point is calculated to be 6.57. The chosen Ke value of 20 is greater than Kemin. Figure 4 It can be seen that the additional synchronous torque coefficient is less than zero, but much smaller than the synchronous torque coefficient K1, so its influence can be approximately ignored. The additional damping torque coefficient is greater than zero, which improves the damping strength of the synchronous condenser.

[0094] Calculate the characteristic value of the system under this operating condition at different excitation system amplification factors, such as... Figure 5 As shown.

[0095] Depend on Figure 5 It can be seen that as the amplification factor increases from a value less than the critical value to a value greater than the critical value, the pair of conjugate complex roots λ of the system state equation... 1，2As both the real root λ3 and the real root λ3 move towards the left half of the complex plane, the system gradually tends to stabilize, and the degree of stability gradually increases. The damping torque coefficients for the four cases are -7.24 × 10⁻⁶. -4 -2.47×10 -4 The values ​​are 0, 0.0020, and 0.4149, 0.4149, 0.4149, and 0.4144, respectively, which are values ​​greater than zero, because the additional synchronous torque coefficient has a negligible impact on the total synchronous torque coefficient. When the amplification factor is less than the critical value, the damping ratio is negative, indicating that the system is in a weakly damped mode. The corresponding damping torque coefficient is also less than zero, and the system will experience oscillation and instability.

[0096] (2) Analysis of simulation results

[0097] Three sets of simulations were conducted to simulate the dynamic changes of the system after a small disturbance under the same operating condition. The first set was a dynamic simulation of the power angle swing curve of the synchronous condenser under a small disturbance when the system was subjected to different excitation system amplification factors under the same operating condition. The second set was a dynamic simulation of the power angle swing curve of the synchronous condenser under different system resistance values ​​with respect to different excitation system amplification factor levels under the same operating condition. The third set was a dynamic simulation of the power angle swing curve of the synchronous condenser under different operating conditions with different excitation system amplification factor levels, under the condition that the system parameters were the same.

[0098] 1) Group 1

[0099] The curves showing the change of camera power angle over time at different magnifications are as follows: Figure 6 As shown, when the amplification factor is less than the critical value of 6.57, the excitation system provides negative damping for the synchronous condenser, and the power angle oscillates with increasing amplitude over time. The smaller the amplification factor, the greater the amplitude change. When the amplification factor is equal to the critical value, the synchronous condenser is in an undamped state after the disturbance, and the power angle curve oscillates with constant amplitude. When the amplification factor is greater than the critical value, the damping strength can maintain the stability of the power angle, and the power angle curve is a decreasing amplitude oscillation. The larger the amplification factor, the smaller the amplitude of the power angle oscillation.

[0100] 2) Group 2

[0101] The amplification factors were set to 2 and 20 (levels below and above the critical value, respectively), and the change of camera power angle over time under different resistance values ​​was analyzed. The curves showing the change of camera power angle over time under different system resistances when the excitation system amplification factor is 2 are shown below. Figure 7 As shown, the curves of camera power angle changing with time under different system resistances when the excitation system amplification factor is 20 are as follows: Figure 8As shown. When the amplification factor is less than the critical value, the power angle curve exhibits increasing amplitude oscillations. When the system resistance is 0.37 pu, the value is relatively small, and the power angle curve approximates a constant amplitude oscillation. As the resistance increases, the negative damping becomes stronger, and the amplitude of the power angle curve increases. When the amplification factor is greater than the critical value, the power angle curve exhibits decreasing amplitude oscillations. As the resistance increases, the positive damping becomes stronger, and the synchronous condenser's power angle quickly escapes the oscillation state and reaches a stable value.

[0102] 3) Group 3

[0103] The magnification factors were set to 2 and 20 (levels below and above the critical value, respectively), and the change of the camera power angle over time under different operating conditions was analyzed. The curves showing the change of the camera power angle over time under different operating conditions with a magnification factor of 2 for the excitation system are shown below. Figure 9 As shown, the curves of the change in the camera power angle over time under different operating conditions when the excitation system amplification factor is 20 are as follows: Figure 10 As shown, when the magnification is less than the minimum value, the power angle oscillates with increasing amplitude over time after the disturbance. As the output of the synchronous condenser increases, the damping decreases and the oscillation amplitude increases. When the magnification is greater than the minimum value, the power angle oscillates with decreasing amplitude; the greater the reactive power output of the synchronous condenser, the stronger the damping and the smaller the amplitude.

[0104] (3) Comparative effect analysis

[0105] Comparing the conclusions of the mechanism analysis with the results of simulation verification confirms the correctness of this method:

[0106] When the overall amplification factor of the excitation system is less than the critical value, it is equivalent to providing negative damping for the synchronous condenser, which will cause the power angle to oscillate after the disturbance, resulting in periodic instability.

[0107] When the amplification factor is less than the minimum value, the larger system resistance and the reactive power output of the synchronous condenser will enhance the negative damping, thus increasing the amplification of the power angle waveform.

[0108] When the amplification factor is greater than the minimum value, the larger system resistance and the reactive power output of the synchronous condenser will enhance the positive damping, allowing the power angle to escape the oscillation state more quickly and tend to stabilize.

[0109] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0110] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

[0111] The specific embodiments of the present invention described above do not constitute a limitation on the scope of protection of the present invention. Any other corresponding changes and modifications made in accordance with the technical concept of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for analyzing the synchronization stability of a synchronous condenser under small disturbances, characterized in that, Includes the following steps: S1. Establish a synchronous condenser model; the synchronous condenser model adopts a third-order model that takes into account the transient electromotive force change, including the rotor motion equation, the differential equation of transient electromotive force change, and the time domain expression of the excitation system equation. S2. Simplification of the synchronous condenser model: A synchronous condenser is a synchronous generator without a prime mover. It does not generate active power, but only absorbs or generates reactive power. Its power angle is zero. The synchronous condenser model is simplified. S3. Torque characteristic analysis: Decompose the electromagnetic torque components into those related to the power angle increment, and use the torque analysis method to organize them into complex form. Taking into account the synchronous torque coefficient and inherent damping coefficient of the synchronous condenser, the total synchronous and damping torque coefficients of the synchronous condenser are obtained. S4. Stability Judgment: The stability of the synchronous condenser under small disturbances is judged by using the total synchronization, the sign of the damping torque coefficient, and the Routh criterion. S5. Parameter interaction influence analysis, including synchronous condenser operating conditions and rotor oscillation frequency.

2. The method for analyzing the synchronization stability of a synchronous condenser under small disturbances according to claim 1, characterized in that, In step S1, the synchronous camera model is as follows: The first two equations are the rotor motion equations, for the synchronous condenser ΔP m =0; the third equation is the differential equation for the transient electromotive force change, and the fourth equation is the time domain expression of the excitation system equation. These four equations constitute the synchronous condenser model; by eliminating the intermediate variables and retaining the state variables, the state equations are as follows: The increase in electromagnetic power is obtained from two parts: one part is the component K1Δδ obtained from the change in power angle through coefficient K1, and the other part is the component K2ΔE′q obtained from the change in transient electromotive force through coefficient K2. The expressions for coefficients K1-K6 are as follows: Among them, E Q U is the virtual electromotive force of the salient-pole synchronous machine, and U is the voltage of the infinite bus. G It's adjusting the camera terminal voltage, U Gq and U Gd These are the q-axis and d-axis components of the terminal voltage, respectively, where δ is the power angle, and I... q It is the q-axis component of the system current, x′ d∑ =x′ d +x e x q∑ =x q +x e A = r 2 +x′ d∑ ·x q∑ K is a constant; except for K3, all coefficients K1-K6 are directly related to the power angle and describe the operating state of the synchronous condenser. K3 is a constant. x d It is adjusting the camera's direct-axis synchronous reactance, x q It is the quadrature axis synchronous reactance, x′ d It is the direct-axis transient reactance, T j It is the inertial time constant, E′ q It is a transient potential, E fd It is the excitation voltage, δ is the power angle, and T′ is the excitation voltage. d0 U is the time constant of the excitation circuit when the stator winding is open, ω is the angular velocity, and U is the time constant of the excitation circuit. G It is the terminal voltage, r e It is the total resistance from the camera output to the infinite bus, x e It is the total reactance; the transfer function of the excitation system is G. e (s)=K e / 1+T e s is a first-order inertial element; K e T represents the overall amplification factor of the excitation system, and its value is closely related to the stability of the power angle under small disturbances. e Let be the time constant of the excitation system, and let its value be 0.01s.

3. The method for analyzing the synchronization stability of a synchronous condenser under small disturbances according to claim 2, characterized in that, In step S2, the synchronous camera model is simplified as follows: If the work angle δ is 0, then sinδ = δ, cosδ = 1, U Gd =0, U G =U Gq I q =0, and simplify K1-K6 as follows: After simplification, the torque parameters can be determined by analyzing the positive and negative values ​​of K4 and K5; for a synchronous condenser, the power angle is close to zero, and the term x that determines the sign in K4 is considered to be... q∑ δ-r is approximately -r, therefore K4 is negative; similarly, we consider rx in K5 to be... q∑ Since δ is r, K5 is a positive value; K3 and K6 are both constants.

4. The method for analyzing the synchronization stability of a synchronous condenser under small disturbances according to claim 3, characterized in that, In step S3, the torque characteristic analysis is as follows: Decomposition of electromagnetic torque component K2ΔE′ q The expression is transformed mathematically into one that is related to the increment of the work angle. In the complex frequency domain, the solution to the state equation is considered to be the oscillation frequency ω of the system. d Substituting into s = jω d Using torque analysis, K2ΔE′ q Rearranged into complex form K2ΔE′ q =(ΔE) S +jΔK D )Δδ;ΔK S It is the additional synchronous torque coefficient, ΔK D This is the additional damping torque coefficient; the expressions for the additional synchronization and damping torque coefficients are respectively... Taking into account the synchronous torque coefficient K1 and the inherent damping coefficient D of the synchronous condenser, the total synchronous and damping torque coefficients of the synchronous condenser can be obtained as T. S =(K1+ΔK) S )Δδ,T D =(ΔK) D +D)sΔδ.

5. The method for analyzing the synchronization stability of a synchronous condenser under small disturbances according to claim 4, characterized in that, In step S4, the stability of the synchronous condenser under small disturbances is determined by the sign of the total synchronization and damping torque coefficients as follows: T D When <0, it is in an unstable state of oscillation with increasing power angle; T S When T < 0, it is in an unstable state of monotonic instability of the power angle; the condition for the synchronous condenser not to experience periodic power angle instability is T D The condition for T > 0, and for non-periodic power angle instability not to occur, is T S >0; The synchronization stability of a synchronous modulator under small disturbances is determined using the Routh criterion as follows: Using the coefficients of the state equations to form a Routh array, if all coefficients in the first column of the Routh array are positive, then the system is stable, meaning all roots of the characteristic equation lie in the left half-plane of the root plane; if any coefficient in the first column is negative, then the number of sign changes of the coefficients in the first column is equal to the number of roots in the right half-plane, thus obtaining the stability criterion: K1>0； K4+K e K5>0; K1 / K3-K2K4+K e (K1K6-K2K5)>0; When the camera's angle of attack is zero, K4 is less than zero, and K5 is greater than zero; K4+K e The characteristic curve of K5 is a linear function with a positive coefficient and a negative intercept. The minimum amplification factor K of the excitation system used to maintain the stability of the synchronous condenser is determined by this function. emin K emin =-K4 / K5=(x d -x′ d ) / x′ d ; K emin The minimum possible comprehensive amplification factor Ke of the synchronous condenser excitation system determines the magnitude of the additional torque coefficient; K4+K e K5 determines the sign of the additional torque coefficient; Magnification greater than K emin At that time, K4+K e K5 is greater than zero. Although the additional synchronous torque is less than zero, its order of magnitude is extremely small compared to the synchronous torque coefficient K1, which can still ensure that the synchronous torque is greater than zero. At the same time, the additional damping torque is also greater than zero, which enhances the inherent damping and allows the synchronous condenser to maintain static stability. If the magnification factor is less than the minimum value K emin If the additional synchronous torque coefficient is greater than zero, the additional damping torque will be less than zero; if the inherent damping is zero, the system will oscillate and become unstable due to insufficient damping.

6. The method for analyzing the synchronization stability of a synchronous condenser under small disturbances according to claim 5, characterized in that, In step S5, the camera operating conditions are adjusted in the parameter interaction influence analysis as follows: The reactive power output of the synchronous condenser changes the additional torque by affecting the size of the synchronous condenser's power angle. The change in the power angle affects K4+K. e The size of K5 decreases as the reactive power output of the synchronous condenser increases, and the power angle decreases. K e <K emin At that time, K4+K e The changing trend of K5 is equivalent to U(x) q∑ Multiplying δ-r) / A by a positive coefficient, the additional damping torque decreases as the reactive power output increases, i.e., the power angle decreases, changing from positive to negative; the additional synchronous torque coefficient increases as the reactive power output increases, changing from negative to positive, and the two always have opposite signs. K e >K emin At that time, K4+K e The changing trend of K5 is equivalent to U(x) q∑ Multiplying δ-r) / A by a negative coefficient, as the reactive power output increases, the additional damping torque coefficient increases, while the additional synchronous torque coefficient decreases. The rotor oscillation frequency is as follows: For the additional synchronous torque coefficient, the rotor oscillation frequency ω d Only the denominator of the expression is affected, therefore the additional synchronous torque coefficient varies with ω. d The changes are monotonous; K e <K emin Time follows ω d As K increases, it becomes a negative value; e >K emin Time follows ω d It decreases as it increases, and is a positive value; For the additional damping torque coefficient, ω d It simultaneously affects both the numerator and denominator of the expression, and the change is not monotonic; therefore, when K... e <K emin When K is constant, the additional damping torque coefficient is always negative, first decreasing and then increasing, with a minimum value; e >K emin When the value is always positive, it first increases and then decreases, and has a maximum value.

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