A Method for Evaluating the Interaction Stability between SVC and Power Grid and Its Application

Abstract

The present invention discloses a method for evaluating the interaction stability between SVC and the power grid and its application, including: 1. constructing a dynamic harmonic domain model of a thyristor controlled reactor considering the influence of conduction angle and phase-locked loop; 2. constructing a dynamic harmonic domain model of a power system with a static var compensator for a thyristor controlled reactor and a fixed capacitor type static var compensator; 3. determining the system state matrix related to the interaction stability between the static var compensator and the power grid; 4. calculating the eigenvalues of the system state matrix and evaluating the interaction stability between the static var compensator and the power grid by using the eigenvalue analysis method; 5. determining the optimization of the controller parameters based on the influence of the controller parameters of the static var compensator on the interaction stability. The modeling method based on the dynamic harmonic domain equation of the present invention can realize the calculation of the multi-harmonic dynamic characteristics and coupling effects of the static var compensator, so as to accurately evaluate the interaction stability between SVC and the power grid and improve the design efficiency of the control system.

Description

Technical Field

[0001] The present invention relates to the technical field of power system modeling for flexible power transmission and distribution, and more specifically, to a method for evaluating the interaction stability between an SVC and a power grid and its application. Background Art

[0002] With the continuous expansion of the scale of China's power transmission and distribution network and the rapid increase of various electricity loads, in order to ensure the power quality of electricity, the demand for system reactive power optimization and reactive power compensation is also increasing. As a typical flexible AC transmission equipment, the static var compensator can achieve the advantages of optimal reactive power compensation of the power grid, suppressing voltage fluctuations, and improving the voltage stability of the system, and is widely used in the field of flexible power transmission and distribution of power systems. However, during the operation of the static var compensator, a large amount of harmonic current is injected into the power grid, resulting in the deterioration of power quality and even the occurrence of system oscillation instability. Therefore, it is necessary to accurately evaluate the interaction stability between the static var compensator and the power grid.

[0003] At present, the grid connection research of the static var compensator as a flexible power transmission and distribution equipment mainly focuses on the suppression strategy of subsynchronous oscillation of the power system with series capacitor compensation by using it. However, the fast response ability of the SVC itself will have an obvious coupling effect with the power grid, resulting in oscillation problems of the system. Regarding the stability evaluation problem of the SVC connected to the power grid, the existing research mainly discusses the existence of low-frequency oscillation phenomena based on RTDS simulation records, but no specific theoretical analysis is given. At the same time, the establishment of an accurate model of the SVC is the premise for evaluating the interaction stability between the SVC and the power grid. Most literatures equivalent the static var compensator to a fundamental frequency linearized model, and fail to analyze the interaction stability between the SVC and the power grid from the harmonic coupling characteristics, ignoring the dynamic characteristics of multiple harmonics and the harmonic coupling effect inside the system. Although a few related literatures have established an open-loop DHD model of the SVC and verified the step response of the model under disturbances, the model does not involve the influence of the conduction angle of the TCR and the phase-locked loop on the model, and the model does not involve the control link. Summary of the Invention

[0004] In order to overcome the above deficiencies in the prior art, the present invention provides an evaluation method for the interaction stability between an SVC and a power grid and its application, aiming to establish a dynamic harmonic domain model of a thyristor-controlled reactor considering the influence of the conduction angle and the phase-locked loop, and to establish a closed-loop DHD model of a power system containing a static var compensator, so as to accurately evaluate the interaction stability problem between the SVC and the power grid, improve the design efficiency of the SVC control system, and further improve the reliability of the power transmission and distribution network.

[0005] In order to achieve the above object, the technical solutions adopted by the present invention are as follows:

[0006] The method for evaluating the interaction stability between SVC and power grid according to the present invention is characterized in that it includes:

[0007] Step 1: Construct a dynamic harmonic domain model of a thyristor-controlled reactor considering the influence of conduction angle and phase-locked loop;

[0008] Step 2: For the thyristor-controlled reactor and the fixed capacitor type static var compensator, construct a dynamic harmonic domain model of the power system containing the static var compensator;

[0009] Step 3: According to the dynamic harmonic domain model, determine the system state matrix related to the interaction stability between the static var compensator and the power grid;

[0010] Step 4: Calculate the eigenvalues of the system state matrix, and use the eigenvalue analysis method to evaluate the interaction stability between the static var compensator and the power grid.

[0011] The method for evaluating the interaction stability between SVC and power grid according to the present invention is also characterized in that the Step 1 includes:

[0012] Step 1.1 Use Equation (1) and Equation (2) to construct the dynamic harmonic domain equation of the main circuit topology of the thyristor-controlled reactor:

[0013]

[0014]

[0015] In Equation (1) and Equation (2), X1 represents the column vector of reactor current, represents the differential of X1, I AB 、I BC 、I CA are the currents flowing through the inductors of the AB, BC, and CA branches in the thyristor-controlled reactor respectively, U represents the column vector of the phase voltage of the thyristor-controlled reactor, V A 、V B 、V C are the phase voltages of phases A, B, and C in the thyristor-controlled reactor respectively, and A1 and B1 are parameter matrices;

[0016] Step 1.2 Use Equation (3) to establish the relationship of the actual conduction angle σ of the three-phase thyristors in the thyristor-controlled reactor for solving the accurate conduction angle σ * :

[0017]

[0018] In Equation (3), x represents the set of AB, BC, and CA phase branches of the thyristor-controlled reactor, t0 is the moment corresponding to the trigger angle of the thyristor-controlled reactor, t represents time, V x(t) is the time-domain function of the branch terminal voltage of the thyristor-controlled reactor, V x,k is the terminal voltage vector of the k-th harmonic, represents the conjugate vector of the terminal voltage vector of the k-th harmonic, θ x represents the phase angles of the branch sets of phases AB, BC, and CA, and θ x = 0, -2π / 3, 2π / 3; N is a positive integer, ω0 is the fundamental angular frequency, e is the natural constant, and j is the imaginary unit;

[0019] Step 1.3 Use Equation (4) to determine the phase angle θ of the phase-locked loop output of the terminal voltage of the thyristor-controlled reactor v :

[0020]

[0021] In Equation (4), V A,1 is the fundamental frequency voltage component of phase A in the thyristor-controlled reactor, and angle(·) represents obtaining the phase angle of the vector.

[0022] The said Step 2 includes:

[0023] Step 2.1 Equivalently represent the AC power grid, transformer, and transmission line in the power system with a static var compensator as an equivalent resistance R s and an equivalent inductance L s , for the thyristor-controlled reactor and the fixed capacitor type static var compensator, with the voltage of the fixed capacitor C and the current of the system equivalent inductance L s as state variables, use Equation (5) and Equation (6) to construct the dynamic harmonic domain equation of the main circuit topology in the power system with a static var compensator except for the thyristor-controlled reactor:

[0024]

[0025]

[0026] In Equation (5) and Equation (6), X2 represents the column vector of the equivalent inductance current, represents the differential of X2, I a 、I b 、I c are the currents flowing through the equivalent inductances L s of phases A, B, and C of the power grid respectively, U g represents the column vector of the power grid voltage, V a 、V b 、V c are the power grid voltages of phases A, B, and C respectively, and A2, B2 are parameter matrices;

[0027] Step 2.2 Determine the differential-algebraic equations of the static var compensator control part using Equations (7) and (8):

[0028]

[0029]

[0030] In Equations (7) and (8): X c represents the control part state column vector, represents the derivative of X c , X V is the intermediate output of the cascaded second-order low-pass filter link, V rms is the per-unit value of the rms bus voltage, X B is the integral output in PI control, U c represents the control part input column vector, V rmsf is for V rms the filtered rms voltage, V ref is the voltage reference value, B n is the command susceptance, A c , B c , C c , D c are parameter matrices;

[0031] Step 2.3 Combine the main circuit topology part and the control part in the power system with a static var compensator, and thus determine the dynamic harmonic domain model of the system in the constant voltage control mode using Equations (9) and (10):

[0032]

[0033]

[0034] In Equations (9) and (10): X s represents the system state column vector, represents the derivative of X s , U s represents the system input column vector, A s , B s , C s , D s are parameter matrices.

[0035] The said Step 3 is to obtain the state matrix characterizing the system stability using Equation (11):

[0036]

[0037] In Equation (11), A is the state matrix of the system.

[0038] The said Step 4 includes:

[0039] Derive the system state matrix of the system dynamic harmonic domain model according to Equation (11), and obtain the distribution of the dominant eigenvalue λ1 of the state matrix in the complex plane, so as to judge the system stability by using the Lyapunov criterion:

[0040] If the real part of λ1 is negative, it means that the power system with static var compensator is small-signal stable;

[0041] If the real part of λ1 is positive, it means that the power system with static var compensator is small-signal unstable;

[0042] If the real part of λ1 is 0, it means that the power system with static var compensator is critically stable.

[0043] In step 1.2, the precise conduction angle σ is solved according to the following process * :

[0044] S1.2.1. When the firing angle of the thyristor controlled reactor is α0, assume that the initial value of the conduction angle of the thyristor switching function is σ0 = 2π - 2α0, then derive the Toeplitz matrix formed by the switching function;

[0045] S1.2.2. According to the Toeplitz matrix obtained from the current conduction angle, combined with the dynamic harmonic domain equations under the steady state of the three-phase system derived from Equation (12), calculate the harmonic components of the terminal voltage of the three-phase thyristor controlled reactor TCR;

[0046] 0 = A1X1 + B1U (12)

[0047] In Equation (12), 0 represents the zero matrix;

[0048] S1.2.2. Use Equation (3) to obtain the time-domain function V x (t) of the branch terminal voltage of the thyristor controlled reactor. According to the principle that the integral of the terminal voltage of the thyristor controlled reactor within the conduction time is zero, combined with Equation (3), numerically integrate the time-domain function V x (t) to obtain the conduction angle σ of the thyristor controlled reactor;

[0049] S1.2.3. Substitute the conduction angle σ into step S1.2.2 for iteration until the conduction angle σ meets the convergence criterion, and obtain the precise conduction angle σ * .

[0050] The calculation process of the control part of the static var compensator in step 2.2 is as follows:

[0051] Step 2.2.1. According to the relationship between the fundamental frequency component of the bus voltage and the effective value of the bus voltage in the dynamic harmonic domain model, use Equation (13) to determine the per-unit value V of the effective value of the bus voltagerms :

[0052]

[0053] In Equation (13), V A,1 , V A,-1 are respectively the two fundamental frequency voltage vectors of the bus voltage V A , and V base is the reference effective value of the voltage;

[0054] Step 2.2.2: Use a second-order low-pass filter to filter out the harmonic components in V rms , and use Equation (14) to determine the effective value V rmsf of the filtered bus voltage:

[0055]

[0056] In Equation (14), represents the differential of X v , represents the differential of V rmsf , and T1 and T2 are the time constants of the second-order low-pass filter;

[0057] Step 2.2.3: Under the constant AC voltage control mode, the control part of the static var compensator adopts PI control, so as to use Equation (15) to determine the calculation formula of PI control:

[0058]

[0059] In Equation (15), represents the differential of X B , B t is the output susceptance, and k pv , k iv are respectively the proportional and integral coefficients of PI control.

[0060] The feature of a method for evaluating the interaction stability between SVC and power grid according to the present invention is that: based on the method for evaluating the interaction stability between SVC and power grid, it is applied to optimize the PI control parameters:

[0061] When the system operates stably under the constant AC voltage control mode, with the current proportional coefficient k pv and integral coefficient k iv of PI control as the reference, increase k pv , and at the same time keep k iv unchanged, draw the motion trajectory of the dominant eigenvalue λ2 of the system state matrix, and then, increase k iv , and at the same time keep k pvRemain unchanged, plot the trajectory of the dominant eigenvalue λ2 of the system state matrix, and thus determine the PI control parameters k according to the trajectories of the dominant eigenvalue λ2 in the two cases using the Lyapunov criterion pv and k iv stable region, so as to realize the optimization of the PI control parameters.

[0062] Compared with the prior art, the beneficial effects of the present invention are reflected in:

[0063] 1. The present invention proposes a method for analyzing and quantifying the interaction stability assessment between SVC and the power grid, and establishes a mathematical model of thyristor-controlled reactor considering the influence of conduction angle and phase-locked loop module based on the dynamic harmonic domain equation. This model takes into account the coupling effect of each harmonic in the thyristor-controlled reactor of power electronic equipment, and accurately reflects the dynamic characteristics of the thyristor-controlled reactor and the transient and steady-state characteristics of each harmonic, and can intuitively interpret the unstable phenomena generated between SVC and the power grid from the harmonic coupling characteristics.

[0064] 2. Based on the dynamic harmonic domain model of the power system containing SVC, the present invention uses the eigenvalue analysis method to realize the effective discrimination and quantification of the interaction stability assessment between SVC and the power grid, and is easy to be extended to complex actual systems, providing a new method for the stability analysis of flexible transmission and distribution power grid systems.

[0065] 3. The present invention separately proposes that the interaction stability assessment method between SVC and the power grid can be used to analyze the influence of controller parameters on the system stability, effectively improving the design efficiency of the control system. Brief Description of the Drawings

[0066] Figure 1 is a schematic diagram of the equivalent circuit of the power system containing SVC;

[0067] Figure 2 is the waveform of the instantaneous terminal voltage and phase current of the reactor in the thyristor-controlled reactor;

[0068] Figure 3 is the characteristic root distribution diagram of the harmonic transfer matrix of the reference PI parameters of the SVC controller of the present invention;

[0069] Figure 4 is the controller parameter K of the present invention PV step V rmsf change curve;

[0070] Figure 5 is the controller parameter K of the present invention IV step V rmsf change curve. Detailed Embodiment

[0071] In this embodiment, a thyristor-controlled reactor and a fixed capacitor type static var compensator are taken as the research objects. When the static var compensator is incorporated into the power grid, the power system containing SVC is simplified and equivalent to two subsystems: a power source and a load. Figure 1 The following shows the schematic diagram of the equivalent circuit of a three-phase power system containing SVC in the present invention, where only three-phase symmetrical conditions are considered for the parameters in the power grid. A method for evaluating the interaction stability between SVC and the power grid is carried out according to the following steps:

[0072] Step 1: Construct a dynamic harmonic domain model of the thyristor-controlled reactor considering the influence of the conduction angle and the phase-locked loop;

[0073] Step 1.1 Taking the current I AB of the reactor in phase A in the TCR and the capacitor voltage V A as state variables, we get:

[0074]

[0075] In Equation (1), R L is the equivalent resistance of the reactor, I AB is the system line current, and S(t) is the switching function;

[0076] Using Equation (2), the Fourier expansion of the switching function S(t) can be obtained:

[0077]

[0078] In Equation (2), σ is the conduction angle of the TCR, is the phase angle of the fundamental frequency component in the voltage at the TCR terminal, and S(t) is determined by σ, .

[0079] Using Equation (3) and Equation (4), the dynamic harmonic domain equation of the main circuit topology of the thyristor-controlled reactor is constructed:

[0080]

[0081]

[0082] In Equation (3) and Equation (4), represents the differential operation on X1, I AB , I BC , I CA are the currents flowing through the inductors of the AB, BC, and CA branches in the TCR respectively, V A , V B , V C are the voltages of phases A, B, and C in the TCR respectively, and A1, B1 are parameter matrices;

[0083] Step 1.2 Use Equation (5) to determine the actual conduction angle σ of the three-phase thyristors in the thyristor-controlled reactor:

[0084]

[0085] In Equation (5), x represents the AB, BC, and CA phase branches of the thyristor, t0 is the moment corresponding to the trigger delay angle of the thyristor-controlled reactor, V x (t) is the time-domain function of the branch terminal voltage of the thyristor-controlled reactor, V x,k is the kth harmonic terminal voltage vector, represents the conjugate vector of the kth harmonic terminal voltage vector, θ x represents the phase angles of the AB, BC, and CA phase branches, which are 0, -2π / 3, and 2π / 3 respectively, N is a positive integer, represents the summation of terms from k = 0 to N, ω0 is the fundamental angular frequency, e is the natural constant, and j is the imaginary unit;

[0086] S1.2.1. When the trigger angle of the thyristor-controlled reactor is α0, assume that the initial value of the conduction angle of the thyristor switch function is σ0 = 2π - 2α0, then derive the Toeplitz matrix formed by the switch function;

[0087] S1.2.2. According to the Toeplitz matrix obtained from the current conduction angle and combined with the dynamic harmonic domain equations under the steady state of the three-phase system derived from Equation (6), calculate the harmonic components of each order of the terminal voltage of the three-phase thyristor-controlled reactor TCR;

[0088] 0 = A1X1 + B1U (6)

[0089] In Equation (12), 0 represents the zero matrix.

[0090] S1.2.2. Use Equation (3) to obtain the time-domain function V x (t) of the branch terminal voltage of the thyristor-controlled reactor. According to the principle that the integral of the terminal voltage of the thyristor-controlled reactor within the conduction time is zero, combined with Equation (3), numerically integrate the time-domain function V x (t) to obtain the conduction angle σ of the thyristor-controlled reactor;

[0091] S1.2.3. Substitute the conduction angle σ into Step S1.2.2 for iteration until the conduction angle σ meets the convergence criterion to obtain the accurate conduction angle σ * .

[0092] The principle for solving the conduction angle of the thyristor-controlled reactor in the present invention is as Figure 2 shown.

[0093] Step 1.3 Use Equation (7) to determine the phase angle θ of the phase-locked loop output of the thyristor terminal voltage v :

[0094]

[0095] In Equation (7), V A,1 is the fundamental frequency component of the A-phase voltage in the TCR of the model, and angle(·) represents obtaining the phase angle of the vector.

[0096] Step 2: Construct the dynamic harmonic domain model of the power system with a static var compensator;

[0097] Step 2.1 For the thyristor-controlled reactor and fixed capacitor type static var compensator, with the voltage of the fixed capacitor C and the current of the equivalent inductor L s of the system as the state variables, use Equations (5) and (6) to construct the dynamic harmonic domain equations of the main circuit topology in the three-phase system except for the thyristor-controlled reactor:

[0098]

[0099]

[0100] In Equations (8) and (9), represents the differential operation on X2, and I a , I b , I c are the currents flowing through the equivalent inductors L s of the A, B, and C phases of the power grid respectively, and V a , V b , V c are the grid voltages of the A, B, and C phases respectively, and A2, B2 are parameter matrices;

[0101] Step 2.2 Construct the differential-algebraic equations of the control part of the static var compensator;

[0102] Step 2.2.1: According to the relationship between the fundamental frequency component of the bus voltage and the effective value of the bus voltage in the dynamic harmonic domain model, use Equation (10) to determine the per-unit value V rms of the effective value of the bus voltage:

[0103]

[0104] In Equation (10), V A,1 , V A,-1 are the two fundamental frequency voltage vectors of the bus voltage V c,A , and V base is the reference effective value of the voltage;

[0105] Step 2.2.2: Use a second-order low-pass filter to filter out the harmonic components in V rms , and use Equation (11) to determine the effective value V rmsf of the filtered bus voltage:

[0106]

[0107] In Equation (11), represents the differential of X v , represents the differential of V rmsf , and T1 and T2 are the time constants of the second-order low-pass filter;

[0108] Step 2.2.3: Under the fixed AC voltage control mode, the controller of the SVC adopts PI control, and the calculation formula for the PI control of the system is determined using Equation (12):

[0109]

[0110] In Equation (12), k pv , k iv are the proportional and integral coefficients of the PI control respectively, and B t is the output susceptance;

[0111] Let the susceptance B t be multiplied by -ωL for normalization and a limit of 0 to 1 is applied, as shown in Equation (13):

[0112]

[0113] In Equation (13), B n is the commanded susceptance;

[0114] From Equations (10) - (13), the differential-algebraic equation of the static var compensator control part can be obtained:

[0115]

[0116]

[0117] In Equations (14) and (15): represents the differential operation on X c , X v is the intermediate output of the cascaded second-order low-pass filter link, V rms is the per-unit value of the effective value of the bus voltage, X B is the integral output in the PI control, V rmsf is V rms the effective value of the filtered voltage, V ref is the voltage reference value, A c , B c , C c , D c are the parameter matrices;

[0118] The firing angle α and Bn Denoted as α(B n ), as shown in Equation (16):

[0119]

[0120] Equation (16) is an overdetermined equation, but the unique α can be obtained from B in the equation. n

[0121] Step 2.3 combines the main circuit topology part and the control part in the system, so as to determine the dynamic harmonic domain model of the system under the constant voltage control mode by using Equations (9) and (10):

[0122]

[0123]

[0124] In Equations (17) and (18): Denotes the differential operation on X s , A s , B s , C s , D s are parameter matrices;

[0125] Step 3: Based on this model, determine the system state matrix that characterizes the interaction stability evaluation between the static var compensator and the power grid;

[0126] According to the dynamic harmonic domain model of the power system with a static var compensator, the state matrix characterizing the system stability is obtained by using Equation (19):

[0127]

[0128] In Equation (19), A is the state matrix of the system.

[0129] Step 4: Calculate the eigenvalues of the system state matrix, and use the eigenvalue analysis method to evaluate the interaction stability between the static var compensator and the power grid;

[0130] According to Equation (19), the system state matrix of the system dynamic harmonic domain model is derived, and the distribution of the dominant eigenvalue λ1 of the state matrix in the complex plane is calculated, so as to judge the system stability by using the Lyapunov criterion:

[0131] If the real part of λ1 is negative, it means that the power system with a static var compensator is small-signal stable;

[0132] If the real part of λ1 is positive, it means that the power system with a static var compensator is small-signal unstable;

[0133] ​If the real part of λ1 is 0, it means that the power system with static var compensator is critically stable;

[0134] Step 5: Based on the influence of the static var compensator controller parameters on the dominant eigenvalues characterizing the interaction stability, determine the optimization of the static var compensator controller parameters.

[0135] When the system operates stably in the constant AC voltage control mode, taking the current PI controller k pv 、k iv values as a reference, now increase k pv while keeping the reference k iv unchanged, plot the motion trajectory of the dominant eigenvalue λ2 of the system state matrix. In addition, now increase k iv while keeping the reference k pv unchanged, plot the motion trajectory of the dominant eigenvalue of the system state matrix. After obtaining the motion trajectories of the dominant eigenvalue λ2 in the above two cases, the Lyapunov criterion can be used to determine the stable regions of the parameters k pv and k iv :

[0136] If the real part of λ2 is negative, it means that the power system with static var compensator is small-signal stable;

[0137] If the real part of λ2 is positive, it means that the power system with static var compensator is small-signal unstable;

[0138] If the real part of λ2 is 0, it means that the power system with static var compensator is critically stable;

[0139] According to the stable regions of the parameters k pv and k iv , it provides a basis for improving the design efficiency of the control system.

[0140] Step 6: Simulation analysis

[0141] The present invention takes the equivalent circuit of the three-phase power system with SVC shown in Figure 1 as an example, and the harmonic order in the constructed dynamic harmonic domain model is selected as the 11th harmonic. According to the application of a method for evaluating the interaction stability between SVC and the power grid introduced above, Matlab / Simulink is used for simulation analysis, and the results are as shown in Figure 3 、 Figure 4 、 Figure 5 :

[0142] Figure 3For the eigenvalues of the state matrix of the small-signal model based on the dynamic harmonic domain equation of the present invention, the eigenvalues corresponding to odd harmonics (h = 1, 3, 5, 7, 9) are mainly shown in the figure. Among them, the imaginary parts of the eigenvalues in the left circular region are ±hω0, and the imaginary parts of the eigenvalues in the right circular region are ±ω n ±hω0, ω n is the equivalent inductance L of the AC system s and the natural frequency of the fixed capacitor C. The remaining eigenvalues correspond to the characteristic roots of the low-pass filter and the PI controller. Among them, the conjugate eigenvalues corresponding to the 5th harmonic are the dominant eigenvalues, as shown in Figure 4 the small square box area in

[0143] Figure 4 is the controller parameter K of the present invention pv V during the step rmsf variation curve. In Simulink, when t = 1.0 s, K pv has a step from 40 to 70, and the low-frequency components in the filtered voltage V rmsf gradually increase and are in a stable oscillation state. At t = 2.8 s, K pv is reduced back to 40. After the oscillation condition of the low-frequency components of the system is not satisfied, it rapidly decays due to the damping effect and reaches a stable state again. Therefore, the Simulink simulation results verify the correctness of judging the system stability by calculating the eigenvalue distribution of the state matrix corresponding to this dynamic harmonic domain model

[0144] Figure 5 is the controller parameter K of the present invention iv V during the step rmsf variation curve. In Simulink, when t = 1.0 s, K IV has a step from 400 to 600, and the low-frequency components in the filtered voltage V rmsf gradually increase and are in a stable oscillation state. At t = 2.8 s, K PV is reduced back to 400. After the oscillation condition of the low-frequency components of the system is not satisfied, it rapidly decays due to the damping effect and reaches a stable state again. Therefore, the Simulink simulation results verify the correctness of judging the system stability by calculating the eigenvalue distribution of the state matrix corresponding to this DHD model

[0145] Through the above simulations, the following conclusions can be drawn:

[0146] 1. The present invention proposes a method for analyzing and quantifying the interaction stability evaluation between the SVC and the power grid, and establishes a mathematical model of the thyristor-controlled reactor considering the influence of the conduction angle and the phase-locked loop module based on the dynamic harmonic domain equation. This model considers the coupling effect of each harmonic in the thyristor-controlled reactor of the power electronic device, and accurately reflects the dynamic characteristics of the thyristor-controlled reactor and the transient and steady-state characteristics of each harmonic

[0147] The present invention realizes an effective discrimination and quantification of the interaction stability evaluation between the SVC and the power grid, and is easy to be extended to complex actual systems, providing a new method for the stability analysis of flexible transmission and distribution power grid systems.

[0148] The present invention separately proposes an SVC and power grid interaction stability evaluation method, which can be used to analyze the influence of controller parameters on system stability, and can effectively improve the control system design efficiency.

Claims

1. A method for evaluating the interaction stability between SVC and the power grid, characterized in that, Including: Step 1: Construct a dynamic harmonic domain model of a thyristor-controlled reactor considering the conduction angle and the influence of the phase-locked loop; Step 1.1: Use Equations (1) and (2) to construct the dynamic harmonic domain equation of the main circuit topology of the thyristor-controlled reactor: (1) (2) In Formula (1) and Formula (2), represents the column vector of the reactor current, represents the differential of, are the currents flowing through the inductances of the AB, BC, and CA branches in the thyristor controlled reactor respectively, represents the column vector of the phase voltage of the thyristor controlled reactor, are the phase voltages of phases A, B, and C in the thyristor controlled reactor respectively, and A1 and B1 are parameter matrices; Step 1.2 Establish the relationship of the actual conduction angles of the three-phase thyristors in the thyristor controlled reactor by using Equation (3) for solving the accurate conduction angles : for solving the accurate conduction angles (3) In Equation (3), x represents the set of AB, BC, and CA phase branches of the thyristor-controlled reactor, is the corresponding moment of the firing angle of the thyristor-controlled reactor, represents time, V x (t) is the time-domain function of the branch terminal voltage of the thyristor-controlled reactor, is the terminal voltage vector of the k-th harmonic, represents the conjugate vector of the terminal voltage vector of the k-th harmonic, represents the phase angles of the set of AB, BC, and CA phase branches, and = 0, , ; N is a positive integer, is the fundamental angular frequency, e is the natural constant, and j is the imaginary unit; Step 1.3 Determine the phase angle output of the phase-locked loop for the terminal voltage of the thyristor-controlled reactor using Equation (4) :[[]]END]] (4) In formula (4), V A,1 is the fundamental frequency voltage component of phase A in the thyristor controlled reactor, represents obtaining the phase angle of the vector; Step 2: For the thyristor-controlled reactor and the fixed capacitor type static var compensator, construct a dynamic harmonic domain model of the power system containing the static var compensator; Step 2.1 Equivalently represent the AC power grid, transformer, and transmission line in the power system with static var compensator as equivalent resistance and equivalent inductance . For the thyristor-controlled reactor and fixed capacitor type static var compensator, taking the voltage of the fixed capacitor C and the current of the system equivalent inductance as state variables, use Equation (5) and Equation (6) to construct the dynamic harmonic domain equation of the main circuit topology in the power system with static var compensator, excluding the thyristor-controlled reactor: (5) (6) In Equations (5) and (6), represents the equivalent inductor current column vector, represents the differential of, are the currents flowing through the equivalent inductors of power grids A, B, and C respectively respectively, represents the power grid voltage column vector, are the power grid voltages of phases A, B, and C respectively, and A2 and B2 are parameter matrices; Step 2.2: Use Equations (7) and (8) to determine the differential-algebraic equations of the control part of the static var compensator; (7) (8) In formulas (7) and (8): represents the control part status column vector, represents the differential of, is the intermediate output of the cascaded second-order low-pass filter section, is the per-unit value of the effective bus voltage, is the integral output in PI control, represents the control part input column vector, V rmsf is the filtered effective voltage, V ref is the voltage reference value, B n is the command susceptance, A c , B c , C c , D c are parameter matrices; Step 2.3: Combine the main circuit topology part and the control part in the power system containing the static var compensator, so as to use Equations (9) and (10) to determine the dynamic harmonic domain model of the system under the constant voltage control mode: (9) (10) In Equations (9) and (10): represents the system state column vector, represents the differential of, represents the system input column vector, A s , B s , C s , D s are parameter matrices; Step 3: According to the dynamic harmonic domain model, determine the system state matrix related to the interaction stability between the static var compensator and the power grid; Step 4: Calculate the eigenvalues of the system state matrix, and use the eigenvalue analysis method to evaluate the interaction stability between the static var compensator and the power grid.

2. The method for evaluating the interaction stability between SVC and power system according to claim 1, characterized in that, The said Step 3 is to obtain the state matrix representing the system stability by using Equation (11): (11) In formula (11), is the state matrix of the system.

3. A method for evaluating the interaction stability between SVC and power system according to claim 2, characterized in that, The said Step 4 includes: Derive the system state matrix of the system dynamic harmonic domain model according to Equation (11), and obtain the dominant eigenvalues of the state matrix to determine the system stability using the Lyapunov criterion according to the distribution on the complex plane If the real part is negative, it means that the power system with static var compensator is small-signal stable; If has a positive real part, it indicates that the power system with static var compensator is small-signal unstable; If has a real part of 0, it means that the power system with static var compensator is critically stable.

4. A method for evaluating the interaction stability between SVC and power system according to claim 1, characterized in that, In step 1.2, the exact conduction angle is solved according to the following process : S1.2.1, when the firing angle of the thyristor-controlled reactor is , assuming that the initial value of the conduction angle of the thyristor switching function is , then the Toeplitz matrix formed by the switching function is derived; S1.2.2, according to the Toeplitz matrix obtained from the current conduction angle, combined with the dynamic harmonic domain equations under the steady state of the three-phase system derived from Equation (12), calculate the harmonic components of each order of the terminal voltage of the three-phase thyristor-controlled reactor TCR; (12) In formula (12), represents a zero matrix; S1.2.2, obtaining the time-domain function of the branch terminal voltage of the thyristor-controlled reactor by using Equation (3) , according to the principle that the integral of the terminal voltage of the thyristor-controlled reactor within the conduction time is zero, combining Equation (3) with the time-domain function to perform numerical integration, and obtaining the conduction angle of the thyristor-controlled reactor ; S1.2.3, Substitute the conduction angle into step S1.2.2 for iteration until the conduction angle meets the convergence criterion to obtain the accurate conduction angle .

5. A method for evaluating the interaction stability between SVC and power system according to claim 1, characterized in that The calculation process of the control part of the static var compensator in the said Step 2.2 is as follows: Step 2.2.1: Determine the per-unit value of the bus voltage effective value using Equation (13) based on the relationship between the fundamental frequency component of the bus voltage and the bus voltage effective value in the dynamic harmonic domain model : (13) In Equation (13), and are respectively two fundamental frequency voltage vectors of the bus voltage , and V base is the effective value of the voltage reference; Step 2.2.2: Use a second-order low-pass filter to filter out the harmonic components in V rms and determine the effective value V rmsf of the bus voltage after filtering using Equation (14): (14) In formula (14), denotes the differential of, denotes the differential of, where T1 and T2 are the time constants of the second-order low-pass filter; Step 2.2.3: Under the constant AC voltage control mode, the control part of the static var compensator adopts PI control, so as to use Equation (15) to determine the calculation formula of PI control: (15) In Equation (15), denotes the differential of, is the output susceptance, k pv and k iv are the proportional and integral coefficients of PI control, respectively.

6. A method for evaluating the interaction stability between SVC and power grid according to claim 5, characterized in that: Based on the SVC and power grid interaction stability evaluation method, it is applied to optimize the PI control parameters: When the system operates stably in the fixed AC voltage control mode, taking the current proportionality coefficient k pv and integral coefficient k iv of PI control as the reference, increase k pv while keeping k iv unchanged, plot the motion trajectory of the dominant eigenvalue of the system state matrix . Then, increase k iv while keeping k pv unchanged, plot the motion trajectory of the dominant eigenvalue of the system state matrix . Thus, according to the motion trajectories of the dominant eigenvalues in the two cases, use the Lyapunov criterion to determine the stable regions of the PI control parameters k pv and k iv , thereby realizing the optimization of the PI control parameters.

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